Dynamical Modeling and Simulation of Multi-body Systems by Using Udwadia-Kalaba Theory

人工智能是一门新兴的具有挑战力的学科。

自人工智能诞生以来,发展迅速,产生了许多分支。

诸如强化学习、模拟环境、智能硬件、机器学习等。

但是,在当前人工智能技术迅猛发展,为人们的生活带来许多便利。

下面是搜索整理的人工智能英文参考文献的分享，供大家借鉴参考。

人工智能英文参考文献一：[1]Lars Egevad,Peter Str?m,Kimmo Kartasalo,Henrik Olsson,Hemamali Samaratunga,Brett Delahunt,Martin Eklund. The utility of artificial intelligence in the assessment of prostate pathology[J]. Histopathology,2020,76(6).[2]Rudy van Belkom. The Impact of Artificial Intelligence on the Activities ofa Futurist[J]. World Futures Review,2020,12(2).[3]Reza Hafezi. How Artificial Intelligence Can Improve Understanding in Challenging Chaotic Environments[J]. World Futures Review,2020,12(2).[4]Alejandro Díaz-Domínguez. How Futures Studies and Foresight Could Address Ethical Dilemmas of Machine Learning and Artificial Intelligence[J]. World Futures Review,2020,12(2).[5]Russell T. Warne,Jared Z. Burton. Beliefs About Human Intelligence in a Sample of Teachers and Nonteachers[J]. Journal for the Education of the Gifted,2020,43(2).[6]Russell Belk,Mariam Humayun,Ahir Gopaldas. Artificial Life[J]. Journal of Macromarketing,2020,40(2).[7]Walter Kehl,Mike Jackson,Alessandro Fergnani. Natural Language Processing and Futures Studies[J]. World Futures Review,2020,12(2).[8]Anne Boysen. Mine the Gap: Augmenting Foresight Methodologies with Data Analytics[J]. World Futures Review,2020,12(2).[9]Marco Bevolo,Filiberto Amati. The Potential Role of AI in Anticipating Futures from a Design Process Perspective: From the Reflexive Description of “Design” to a Discussion of Influences by the Inclusion of AI in the Futures Research Process[J]. World Futures Review,2020,12(2).[10]Lan Xu,Paul Tu,Qian Tang,Dan Seli?teanu. Contract Design for Cloud Logistics (CL) Based on Blockchain Technology (BT)[J]. Complexity,2020,2020.[11]L. Grant,X. Xue,Z. Vajihi,A. Azuelos,S. Rosenthal,D. Hopkins,R. Aroutiunian,B. Unger,A. Guttman,M. Afilalo. LO32: Artificial intelligence to predict disposition to improve flow in the emergency department[J]. CJEM,2020,22(S1).[12]A. Kirubarajan,A. Taher,S. Khan,S. Masood. P071: Artificial intelligence in emergency medicine: A scoping review[J]. CJEM,2020,22(S1).[13]L. Grant,P. Joo,B. Eng,A. Carrington,M. Nemnom,V. Thiruganasambandamoorthy. LO22: Risk-stratification of emergency department syncope by artificial intelligence using machine learning: human, statistics or machine[J]. CJEM,2020,22(S1).[14]Riva Giuseppe,Riva Eleonora. OS for Ind Robots: Manufacturing Robots Get Smarter Thanks to Artificial Intelligence.[J]. Cyberpsychology, behavior and social networking,2020,23(5).[15]Markus M. Obmann,Aurelio Cosentino,Joshy Cyriac,Verena Hofmann,Bram Stieltjes,Daniel T. Boll,Benjamin M. Yeh,Matthias R. Benz. Quantitative enhancement thresholds and machine learning algorithms for the evaluation of renal lesions using single-phase split-filter dual-energy CT[J]. Abdominal Radiology,2020,45(1).[16]Haytham H. Elmousalami,Mahmoud Elaskary. Drilling stuck pipe classification and mitigation in the Gulf of Suez oil fields using artificial intelligence[J]. Journal of Petroleum Exploration and Production Technology,2020,10(10).[17]Rüdiger Schulz-Wendtland,Karin Bock. Bildgebung in der Mammadiagnostik –Ein Ausblick <trans-title xml:lang="en">Imaging in breast diagnostics—an outlook [J]. Der Gyn?kologe,2020,53(6).</trans-title>[18]Nowakowski Piotr,Szwarc Krzysztof,Boryczka Urszula. Combining an artificial intelligence algorithm and a novel vehicle for sustainable e-waste collection[J]. Science of the Total Environment,2020,730.[19]Wang Huaizhi,Liu Yangyang,Zhou Bin,Li Canbing,Cao Guangzhong,Voropai Nikolai,Barakhtenko Evgeny. Taxonomy research of artificial intelligence for deterministic solar power forecasting[J]. Energy Conversion and Management,2020,214.[20]Kagemoto Hiroshi. Forecasting a water-surface wave train with artificial intelligence- A case study[J]. Ocean Engineering,2020,207.[21]Tomonori Aoki,Atsuo Yamada,Kazuharu Aoyama,Hiroaki Saito,Gota Fujisawa,Nariaki Odawara,Ryo Kondo,Akiyoshi Tsuboi,Rei Ishibashi,Ayako Nakada,Ryota Niikura,Mitsuhiro Fujishiro,Shiro Oka,Soichiro Ishihara,Tomoki Matsuda,Masato Nakahori,Shinji Tanaka,Kazuhiko Koike,Tomohiro Tada. Clinical usefulness of a deep learning‐based system as the first screening on small‐bowel capsule endoscopy reading[J]. Digestive Endoscopy,2020,32(4).[22]Masashi Fujii,Hajime Isomoto. Next generation of endoscopy: Harmony with artificial intelligence and robotic‐assisted devices[J]. Digestive Endoscopy,2020,32(4).[23]Roberto Verganti,Luca Vendraminelli,Marco Iansiti. Innovation and Design in the Age of Artificial Intelligence[J]. Journal of Product Innovation Management,2020,37(3).[24]Yuval Elbaz,David Furman,Maytal Caspary Toroker. Modeling Diffusion in Functional Materials: From Density Functional Theory to Artificial Intelligence[J]. Advanced Functional Materials,2020,30(18).[25]Dinesh Visva Gunasekeran,Tien Yin Wong. Artificial Intelligence in Ophthalmology in 2020: A Technology on the Cusp for Translation and Implementation[J]. Asia-Pacific Journal of Ophthalmology,2020,9(2).[26]Fu-Neng Jiang,Li-Jun Dai,Yong-Ding Wu,Sheng-Bang Yang,Yu-Xiang Liang,Xin Zhang,Cui-Yun Zou,Ren-Qiang He,Xiao-Ming Xu,Wei-De Zhong. The study of multiple diagnosis models of human prostate cancer based on Taylor database by artificial neural networks[J]. Journal of the Chinese Medical Association,2020,83(5).[27]Matheus Calil Faleiros,Marcello Henrique Nogueira-Barbosa,Vitor Faeda Dalto,JoséRaniery Ferreira Júnior,Ariane Priscilla Magalh?es Tenório,Rodrigo Luppino-Assad,Paulo Louzada-Junior,Rangaraj Mandayam Rangayyan,Paulo Mazzoncini de Azevedo-Marques. Machine learning techniques for computer-aided classification of active inflammatory sacroiliitis in magnetic resonance imaging[J]. Advances in Rheumatology,2020,60(1078).[28]Balamurugan Balakreshnan,Grant Richards,Gaurav Nanda,Huachao Mao,Ragu Athinarayanan,Joseph Zaccaria. PPE Compliance Detection using Artificial Intelligence in Learning Factories[J]. Procedia Manufacturing,2020,45.[29]M. Stévenin,V. Avisse,N. Ducarme,A. de Broca. Qui est responsable si un robot autonome vient à entra?ner un dommage ?[J]. Ethique et Santé,2020.[30]Fatemeh Barzegari Banadkooki,Mohammad Ehteram,Fatemeh Panahi,Saad Sh. Sammen,Faridah Binti Othman,Ahmed EL-Shafie. Estimation of Total Dissolved Solids (TDS) using New Hybrid Machine Learning Models[J]. Journal of Hydrology,2020.[31]Adam J. Schwartz,Henry D. Clarke,Mark J. Spangehl,Joshua S. Bingham,DavidA. Etzioni,Matthew R. Neville. Can a Convolutional Neural Network Classify Knee Osteoarthritis on Plain Radiographs as Accurately as Fellowship-Trained Knee Arthroplasty Surgeons?[J]. The Journal of Arthroplasty,2020.[32]Ivana Nizetic Kosovic,Toni Mastelic,Damir Ivankovic. Using Artificial Intelligence on environmental data from Internet of Things for estimating solar radiation: Comprehensive analysis[J]. Journal of Cleaner Production,2020.[33]Lauren Fried,Andrea Tan,Shirin Bajaj,Tracey N. Liebman,David Polsky,Jennifer A. Stein. Technological advances for the detection of melanoma: Part I. Advances in diagnostic techniques[J]. Journal of the American Academy of Dermatology,2020.[34]Mohammed Amoon,Torki Altameem,Ayman Altameem. Internet of things Sensor Assisted Security and Quality Analysis for Health Care Data Sets Using Artificial Intelligent Based Heuristic Health Management System[J]. Measurement,2020.[35]E. Lotan,C. Tschider,D.K. Sodickson,A. Caplan,M. Bruno,B. Zhang,Yvonne W. Lui. Medical Imaging and Privacy in the Era of Artificial Intelligence: Myth, Fallacy, and the Future[J]. Journal of the American College of Radiology,2020.[36]Fabien Lareyre,Cédric Adam,Marion Carrier,Juliette Raffort. Artificial Intelligence in Vascular Surgery: moving from Big Data to Smart Data[J]. Annals of Vascular Surgery,2020.[37]Ilesanmi Daniyan,Khumbulani Mpofu,Moses Oyesola,Boitumelo Ramatsetse,Adefemi Adeodu. Artificial intelligence for predictive maintenance in the railcar learning factories[J]. Procedia Manufacturing,2020,45.[38]Janet L. McCauley,Anthony E. Swartz. Reframing Telehealth[J]. Obstetrics and Gynecology Clinics of North America,2020.[39]Jean-Emmanuel Bibault,Lei Xing. Screening for chronic obstructive pulmonary disease with artificial intelligence[J]. The Lancet Digital Health,2020,2(5).[40]Andrea Laghi. Cautions about radiologic diagnosis of COVID-19 infection driven by artificial intelligence[J]. The Lancet Digital Health,2020,2(5).人工智能英文参考文献二：[41]K. Orhan,I. S. Bayrakdar,M. Ezhov,A. Kravtsov,T. ?zyürek. Evaluation of artificial intelligence for detecting periapical pathosis on cone‐beam computed tomography scans[J]. International Endodontic Journal,2020,53(5).[42]Avila A M,Mezi? I. Data-driven analysis and forecasting of highway traffic dynamics.[J]. Nature communications,2020,11(1).[43]Neri Emanuele,Miele Vittorio,Coppola Francesca,Grassi Roberto. Use of CT andartificial intelligence in suspected or COVID-19 positive patients: statement of the Italian Society of Medical and Interventional Radiology.[J]. La Radiologia medica,2020.[44]Tau Noam,Stundzia Audrius,Yasufuku Kazuhiro,Hussey Douglas,Metser Ur. Convolutional Neural Networks in Predicting Nodal and Distant Metastatic Potential of Newly Diagnosed Non-Small Cell Lung Cancer on FDG PET Images.[J]. AJR. American journal of roentgenology,2020.[45]Coppola Francesca,Faggioni Lorenzo,Regge Daniele,Giovagnoni Andrea,Golfieri Rita,Bibbolino Corrado,Miele Vittorio,Neri Emanuele,Grassi Roberto. Artificial intelligence: radiologists' expectations and opinions gleaned from a nationwide online survey.[J]. La Radiologia medica,2020.[46]?. ? ? ? ? [J]. ,2020,25(4).[47]Savage Rock H,van Assen Marly,Martin Simon S,Sahbaee Pooyan,Griffith Lewis P,Giovagnoli Dante,Sperl Jonathan I,Hopfgartner Christian,K?rgel Rainer,Schoepf U Joseph. Utilizing Artificial Intelligence to Determine Bone Mineral Density Via Chest Computed Tomography.[J]. Journal of thoracic imaging,2020,35 Suppl 1.[48]Brzezicki Maksymilian A,Bridger Nicholas E,Kobeti? Matthew D,Ostrowski Maciej,Grabowski Waldemar,Gill Simran S,Neumann Sandra. Artificial intelligence outperforms human students in conducting neurosurgical audits.[J]. Clinical neurology and neurosurgery,2020,192.[49]Lockhart Mark E,Smith Andrew D. Fatty Liver Disease: Artificial Intelligence Takes on the Challenge.[J]. Radiology,2020,295(2).[50]Wood Edward H,Korot Edward,Storey Philip P,Muscat Stephanie,Williams George A,Drenser Kimberly A. The retina revolution: signaling pathway therapies, genetic therapies, mitochondrial therapies, artificial intelligence.[J]. Current opinion in ophthalmology,2020,31(3).[51]Ho Dean,Quake Stephen R,McCabe Edward R B,Chng Wee Joo,Chow Edward K,Ding Xianting,Gelb Bruce D,Ginsburg Geoffrey S,Hassenstab Jason,Ho Chih-Ming,Mobley William C,Nolan Garry P,Rosen Steven T,Tan Patrick,Yen Yun,Zarrinpar Ali. Enabling Technologies for Personalized and Precision Medicine.[J]. Trends in biotechnology,2020,38(5).[52]Fischer Andreas M,Varga-Szemes Akos,van Assen Marly,Griffith L Parkwood,Sahbaee Pooyan,Sperl Jonathan I,Nance John W,Schoepf U Joseph. Comparison of Artificial Intelligence-Based Fully Automatic Chest CT Emphysema Quantification to Pulmonary Function Testing.[J]. AJR. American journal ofroentgenology,2020,214(5).[53]Moore William,Ko Jane,Gozansky Elliott. Artificial Intelligence Pertaining to Cardiothoracic Imaging and Patient Care: Beyond Image Interpretation.[J]. Journal of thoracic imaging,2020,35(3).[54]Hwang Eui Jin,Park Chang Min. Clinical Implementation of Deep Learning in Thoracic Radiology: Potential Applications and Challenges.[J]. Korean journal of radiology,2020,21(5).[55]Mateen Bilal A,David Anna L,Denaxas Spiros. Electronic Health Records to Predict Gestational Diabetes Risk.[J]. Trends in pharmacological sciences,2020,41(5).[56]Yao Xiang,Mao Ling,Lv Shunli,Ren Zhenghong,Li Wentao,Ren Ke. CT radiomics features as a diagnostic tool for classifying basal ganglia infarction onset time.[J]. Journal of the neurological sciences,2020,412.[57]van Assen Marly,Banerjee Imon,De Cecco Carlo N. Beyond the Artificial Intelligence Hype: What Lies Behind the Algorithms and What We Can Achieve.[J]. Journal of thoracic imaging,2020,35 Suppl 1.[58]Guzik Tomasz J,Fuster Valentin. Leaders in Cardiovascular Research: Valentin Fuster.[J]. Cardiovascular research,2020,116(6).[59]Fischer Andreas M,Eid Marwen,De Cecco Carlo N,Gulsun Mehmet A,van Assen Marly,Nance John W,Sahbaee Pooyan,De Santis Domenico,Bauer Maximilian J,Jacobs Brian E,Varga-Szemes Akos,Kabakus Ismail M,Sharma Puneet,Jackson Logan J,Schoepf U Joseph. Accuracy of an Artificial Intelligence Deep Learning Algorithm Implementing a Recurrent Neural Network With Long Short-term Memory for the Automated Detection of Calcified Plaques From Coronary Computed Tomography Angiography.[J]. Journal of thoracic imaging,2020,35 Suppl 1.[60]Ghosh Adarsh,Kandasamy Devasenathipathy. Interpretable Artificial Intelligence: Why and When.[J]. AJR. American journal of roentgenology,2020,214(5).[61]M.Rosario González-Rodríguez,M.Carmen Díaz-Fernández,Carmen Pacheco Gómez. Facial-expression recognition: An emergent approach to the measurement of tourist satisfaction through emotions[J]. Telematics and Informatics,2020,51.[62]Ru-Xi Ding,Iván Palomares,Xueqing Wang,Guo-Rui Yang,Bingsheng Liu,Yucheng Dong,Enrique Herrera-Viedma,Francisco Herrera. Large-Scale decision-making: Characterization, taxonomy, challenges and future directions from an Artificial Intelligence and applications perspective[J]. Information Fusion,2020,59.[63]Abdulrhman H. Al-Jebrni,Brendan Chwyl,Xiao Yu Wang,Alexander Wong,Bechara J. Saab. AI-enabled remote and objective quantification of stress at scale[J]. Biomedical Signal Processing and Control,2020,59.[64]Gillian Thomas,Elizabeth Eisenhauer,Robert G. Bristow,Cai Grau,Coen Hurkmans,Piet Ost,Matthias Guckenberger,Eric Deutsch,Denis Lacombe,Damien C. Weber. The European Organisation for Research and Treatment of Cancer, State of Science in radiation oncology and priorities for clinical trials meeting report[J]. European Journal of Cancer,2020,131.[65]Muhammad Asif. Are QM models aligned with Industry 4.0? A perspective on current practices[J]. Journal of Cleaner Production,2020,258.[66]Siva Teja Kakileti,Himanshu J. Madhu,Geetha Manjunath,Leonard Wee,Andre Dekker,Sudhakar Sampangi. Personalized risk prediction for breast cancer pre-screening using artificial intelligence and thermal radiomics[J]. Artificial Intelligence In Medicine,2020,105.[67]. Evaluation of Payer Budget Impact Associated with the Use of Artificial Intelligence in Vitro Diagnostic, Kidneyintelx, to Modify DKD Progression:[J]. American Journal of Kidney Diseases,2020,75(5).[68]Rohit Nishant,Mike Kennedy,Jacqueline Corbett. Artificial intelligence for sustainability: Challenges, opportunities, and a research agenda[J]. International Journal of Information Management,2020,53.[69]Hoang Nguyen,Xuan-Nam Bui. Soft computing models for predicting blast-induced air over-pressure: A novel artificial intelligence approach[J]. Applied Soft Computing Journal,2020,92.[70]Benjamin S. Hopkins,Aditya Mazmudar,Conor Driscoll,Mark Svet,Jack Goergen,Max Kelsten,Nathan A. Shlobin,Kartik Kesavabhotla,Zachary A Smith,Nader S Dahdaleh. Using artificial intelligence (AI) to predict postoperative surgical site infection: A retrospective cohort of 4046 posterior spinal fusions[J]. Clinical Neurology and Neurosurgery,2020,192.[71]Mei Yang,Runze Zhou,Xiangjun Qiu,Xiangfei Feng,Jian Sun,Qunshan Wang,Qiufen Lu,Pengpai Zhang,Bo Liu,Wei Li,Mu Chen,Yan Zhao,Binfeng Mo,Xin Zhou,Xi Zhang,Yingxue Hua,Jin Guo,Fangfang Bi,Yajun Cao,Feng Ling,Shengming Shi,Yi-Gang Li. Artificial intelligence-assisted analysis on the association between exposure to ambient fine particulate matter and incidence of arrhythmias in outpatients of Shanghai community hospitals[J]. Environment International,2020,139.[72]Fatemehalsadat Madaeni,Rachid Lhissou,Karem Chokmani,Sebastien Raymond,Yves Gauthier. Ice jam formation, breakup and prediction methods based on hydroclimatic data using artificial intelligence: A review[J]. Cold Regions Science and Technology,2020,174.[73]Steve Chukwuebuka Arum,David Grace,Paul Daniel Mitchell. A review of wireless communication using high-altitude platforms for extended coverage and capacity[J]. Computer Communications,2020,157.[74]Yong-Hong Kuo,Nicholas B. Chan,Janny M.Y. Leung,Helen Meng,Anthony Man-Cho So,Kelvin K.F. Tsoi,Colin A. Graham. An Integrated Approach of Machine Learning and Systems Thinking for Waiting Time Prediction in an Emergency Department[J]. International Journal of Medical Informatics,2020,139.[75]Matteo Terzi,Gian Antonio Susto,Pratik Chaudhari. Directional adversarial training for cost sensitive deep learning classification applications[J]. Engineering Applications of Artificial Intelligence,2020,91.[76]Arman Kilic. Artificial Intelligence and Machine Learning in Cardiovascular Health Care[J]. The Annals of Thoracic Surgery,2020,109(5).[77]Hossein Azarmdel,Ahmad Jahanbakhshi,Seyed Saeid Mohtasebi,Alfredo Rosado Mu?oz. Evaluation of image processing technique as an expert system in mulberry fruit grading based on ripeness level using artificial neural networks (ANNs) and support vector machine (SVM)[J]. Postharvest Biology and Technology,2020,166.[78]Wafaa Wardah,Abdollah Dehzangi,Ghazaleh Taherzadeh,Mahmood A. Rashid,M.G.M. Khan,Tatsuhiko Tsunoda,Alok Sharma. Predicting protein-peptide binding sites with a deep convolutional neural network[J]. Journal of Theoretical Biology,2020,496.[79]Francisco F.X. Vasconcelos,Róger M. Sarmento,Pedro P. Rebou?as Filho,Victor Hugo C. de Albuquerque. Artificial intelligence techniques empowered edge-cloud architecture for brain CT image analysis[J]. Engineering Applications of Artificial Intelligence,2020,91.[80]Masaaki Konishi. Bioethanol production estimated from volatile compositions in hydrolysates of lignocellulosic biomass by deep learning[J]. Journal of Bioscience and Bioengineering,2020,129(6).人工智能英文参考文献三：[81]J. Kwon,K. Kim. Artificial Intelligence for Early Prediction of Pulmonary Hypertension Using Electrocardiography[J]. Journal of Heart and Lung Transplantation,2020,39(4).[82]C. Maathuis,W. Pieters,J. van den Berg. Decision support model for effects estimation and proportionality assessment for targeting in cyber operations[J]. Defence Technology,2020.[83]Samer Ellahham. Artificial Intelligence in Diabetes Care[J]. The American Journal of Medicine,2020.[84]Yi-Ting Hsieh,Lee-Ming Chuang,Yi-Der Jiang,Tien-Jyun Chang,Chung-May Yang,Chang-Hao Yang,Li-Wei Chan,Tzu-Yun Kao,Ta-Ching Chen,Hsuan-Chieh Lin,Chin-Han Tsai,Mingke Chen. Application of deep learning image assessment software VeriSee? for diabetic retinopathy screening[J]. Journal of the Formosan Medical Association,2020.[85]Emre ARTUN,Burak KULGA. Selection of candidate wells for re-fracturing in tight gas sand reservoirs using fuzzy inference[J]. Petroleum Exploration and Development Online,2020,47(2).[86]Alberto Arenal,Cristina Armu?a,Claudio Feijoo,Sergio Ramos,Zimu Xu,Ana Moreno. Innovation ecosystems theory revisited: The case of artificial intelligence in China[J]. Telecommunications Policy,2020.[87]T. Som,M. Dwivedi,C. Dubey,A. Sharma. Parametric Studies on Artificial Intelligence Techniques for Battery SOC Management and Optimization of Renewable Power[J]. Procedia Computer Science,2020,167.[88]Bushra Kidwai,Nadesh RK. Design and Development of Diagnostic Chabot for supporting Primary Health Care Systems[J]. Procedia Computer Science,2020,167.[89]Asl? Bozda?,Ye?im Dokuz,?znur Begüm G?k?ek. Spatial prediction of PM 10 concentration using machine learning algorithms in Ankara, Turkey[J]. Environmental Pollution,2020.[90]K.P. Smith,J.E. Kirby. Image analysis and artificial intelligence in infectious disease diagnostics[J]. Clinical Microbiology and Infection,2020.[91]Alklih Mohamad YOUSEF,Ghahfarokhi Payam KAVOUSI,Marwan ALNUAIMI,Yara ALATRACH. Predictive data analytics application for enhanced oil recovery in a mature field in the Middle East[J]. Petroleum Exploration and Development Online,2020,47(2).[92]Omer F. Ahmad,Danail Stoyanov,Laurence B. Lovat. Barriers and pitfalls for artificial intelligence in gastroenterology: Ethical and regulatory issues[J]. Techniques and Innovations in Gastrointestinal Endoscopy,2020,22(2).[93]Sanne A. Hoogenboom,Ulas Bagci,Michael B. Wallace. Artificial intelligence in gastroenterology. The current state of play and the potential. How will it affect our practice and when?[J]. Techniques and Innovations in Gastrointestinal Endoscopy,2020,22(2).[94]Douglas K. Rex. Can we do resect and discard with artificial intelligence-assisted colon polyp “optical biopsy?”[J]. Techniques and Innovations in Gastrointestinal Endoscopy,2020,22(2).[95]Neal Shahidi,Michael J. Bourke. Can artificial intelligence accurately diagnose endoscopically curable gastrointestinal cancers?[J]. Techniques and Innovations in Gastrointestinal Endoscopy,2020,22(2).[96]Michael Byrne. Artificial intelligence in gastroenterology[J]. Techniques and Innovations in Gastrointestinal Endoscopy,2020,22(2).[97]Piet C. de Groen. Using artificial intelligence to improve adequacy of inspection in gastrointestinal endoscopy[J]. Techniques and Innovations in Gastrointestinal Endoscopy,2020,22(2).[98]Robin Zachariah,Andrew Ninh,William Karnes. Artificial intelligence for colon polyp detection: Why should we embrace this?[J]. Techniques and Innovations in Gastrointestinal Endoscopy,2020,22(2).[99]Alexandra T. Greenhill,Bethany R. Edmunds. A primer of artificial intelligence in medicine[J]. Techniques and Innovations in Gastrointestinal Endoscopy,2020,22(2).[100]Tomohiro Tada,Toshiaki Hirasawa,Toshiyuki Yoshio. The role for artificial intelligence in evaluation of upper GI cancer[J]. Techniques and Innovations in Gastrointestinal Endoscopy,2020,22(2).[101]Yahui Jiang,Meng Yang,Shuhao Wang,Xiangchun Li,Yan Sun. Emerging role of deep learning‐based artificial intelligence in tumor pathology[J]. Cancer Communications,2020,40(4).[102]Kristopher D. Knott,Andreas Seraphim,Joao B. Augusto,Hui Xue,Liza Chacko,Nay Aung,Steffen E. Petersen,Jackie A. Cooper,Charlotte Manisty,Anish N. Bhuva,Tushar Kotecha,Christos V. Bourantas,Rhodri H. Davies,Louise A.E. Brown,Sven Plein,Marianna Fontana,Peter Kellman,James C. Moon. The Prognostic Significance of Quantitative Myocardial Perfusion: An Artificial Intelligence–Based Approach Using Perfusion Mapping[J]. Circulation,2020,141(16).[103]Muhammad Asad,Ahmed Moustafa,Takayuki Ito. FedOpt: Towards Communication Efficiency and Privacy Preservation in Federated Learning[J]. Applied Sciences,2020,10(8).[104]Wu Wenzhi,Zhang Yan,Wang Pu,Zhang Li,Wang Guixiang,Lei Guanghui,Xiao Qiang,Cao Xiaochen,Bian Yueran,Xie Simiao,Huang Fei,Luo Na,Zhang Jingyuan,Luo Mingyan. Psychological stress of medical staffs during outbreak of COVID-19 and adjustment strategy.[J]. Journal of medical virology,2020.[105]. Eyenuk Fulfills Contract for Artificial Intelligence Grading of Retinal Images[J]. Telecomworldwire,2020.[106]Kim Tae Woo,Duhachek Adam. Artificial Intelligence and Persuasion: A Construal-Level Account.[J]. Psychological science,2020,31(4).[107]McCall Becky. COVID-19 and artificial intelligence: protecting health-care workers and curbing the spread.[J]. The Lancet. Digital health,2020,2(4).[108]Alca?iz Mariano,Chicchi Giglioli Irene A,Sirera Marian,Minissi Eleonora,Abad Luis. [Autism spectrum disorder biomarkers based on biosignals, virtual reality and artificial intelligence].[J]. Medicina,2020,80 Suppl 2.[109]Cong Lei,Feng Wanbing,Yao Zhigang,Zhou Xiaoming,Xiao Wei. Deep Learning Model as a New Trend in Computer-aided Diagnosis of Tumor Pathology for Lung Cancer.[J]. Journal of Cancer,2020,11(12).[110]Wang Fengdan,Gu Xiao,Chen Shi,Liu Yongliang,Shen Qing,Pan Hui,Shi Lei,Jin Zhengyu. Artificial intelligence system can achieve comparable results to experts for bone age assessment of Chinese children with abnormal growth and development.[J]. PeerJ,2020,8.[111]Hu Wenmo,Yang Huayu,Xu Haifeng,Mao Yilei. Radiomics based on artificial intelligence in liver diseases: where we are?[J]. Gastroenterology report,2020,8(2).[112]Batayneh Wafa,Abdulhay Enas,Alothman Mohammad. Prediction of the performance of artificial neural networks in mapping sEMG to finger joint angles via signal pre-investigation techniques.[J]. Heliyon,2020,6(4).[113]Aydin Emrah,Türkmen ?nan Utku,Namli G?zde,?ztürk ?i?dem,Esen Ay?e B,Eray Y Nur,Ero?lu Egemen,Akova Fatih. A novel and simple machine learning algorithm for preoperative diagnosis of acute appendicitis in children.[J]. Pediatric surgery international,2020.[114]Ellahham Samer. Artificial Intelligence in Diabetes Care.[J]. The Americanjournal of medicine,2020.[115]David J. Winkel,Thomas J. Weikert,Hanns-Christian Breit,Guillaume Chabin,Eli Gibson,Tobias J. Heye,Dorin Comaniciu,Daniel T. Boll. Validation of a fully automated liver segmentation algorithm using multi-scale deep reinforcement learning and comparison versus manual segmentation[J]. European Journal of Radiology,2020,126.[116]Binjie Fu,Guoshu Wang,Mingyue Wu,Wangjia Li,Yineng Zheng,Zhigang Chu,Fajin Lv. Influence of CT effective dose and convolution kernel on the detection of pulmonary nodules in different artificial intelligence software systems: A phantom study[J]. European Journal of Radiology,2020,126.[117]Georgios N. Kouziokas. A new W-SVM kernel combining PSO-neural network transformed vector and Bayesian optimized SVM in GDP forecasting[J]. Engineering Applications of Artificial Intelligence,2020,92.[118]Qingsong Ruan,Zilin Wang,Yaping Zhou,Dayong Lv. A new investor sentiment indicator ( ISI ) based on artificial intelligence: A powerful return predictor in China[J]. Economic Modelling,2020,88.[119]Mohamed Abdel-Basset,Weiping Ding,Laila Abdel-Fatah. The fusion of Internet of Intelligent Things (IoIT) in remote diagnosis of obstructive Sleep Apnea: A survey and a new model[J]. Information Fusion,2020,61.[120]Federico Caobelli. Artificial intelligence in medical imaging: Game over for radiologists?[J]. European Journal of Radiology,2020,126.以上就是关于人工智能参考文献的分享，希望对你有所帮助。

1/4波片quarter-wave plateCG矢量耦合系数Clebsch-Gordan vector coupling coefficient; 简称“CG[矢耦]系数”。

X射线摄谱仪X-ray spectrographX射线衍射X-ray diffractionX射线衍射仪X-ray diffractometer[玻耳兹曼]H定理[Boltzmann] H-theorem[玻耳兹曼]H函数[Boltzmann] H-function[彻]体力body force[冲]击波shock wave[冲]击波前shock front[狄拉克]δ函数[Dirac] δ-function[第二类]拉格朗日方程Lagrange equation[电]极化强度[electric] polarization[反射]镜mirror[光]谱线spectral line[光]谱仪spectrometer[光]照度illuminance[光学]测角计[optical] goniometer[核]同质异能素[nuclear] isomer[化学]平衡常量[chemical] equilibrium constant[基]元电荷elementary charge[激光]散斑speckle[吉布斯]相律[Gibbs] phase rule[可]变形体deformable body[克劳修斯-]克拉珀龙方程[Clausius-] Clapeyron equation[量子]态[quantum] state[麦克斯韦-]玻耳兹曼分布[Maxwell-]Boltzmann distribution[麦克斯韦-]玻耳兹曼统计法[Maxwell-]Boltzmann statistics[普适]气体常量[universal] gas constant[气]泡室bubble chamber[热]对流[heat] convection[热力学]过程[thermodynamic] process[热力学]力[thermodynamic] force[热力学]流[thermodynamic] flux[热力学]循环[thermodynamic] cycle[事件]间隔interval of events[微观粒子]全同性原理identity principle [of microparticles][物]态参量state parameter, state property[相]互作用interaction[相]互作用绘景interaction picture[相]互作用能interaction energy[旋光]糖量计saccharimeter[指]北极north pole, N pole[指]南极south pole, S pole[主]光轴[principal] optical axis[转动]瞬心instantaneous centre [of rotation][转动]瞬轴instantaneous axis [of rotation]t 分布student's t distributiont 检验student's t testＫ俘获K-captureＳ矩阵S-matrixＷＫＢ近似WKB approximationＸ射线X-rayΓ空间Γ-spaceα粒子α-particleα射线α-rayα衰变α-decayβ射线β-rayβ衰变β-decayγ矩阵γ-matrixγ射线γ-rayγ衰变γ-decayλ相变λ-transitionμ空间μ-spaceχ 分布chi square distributionχ 检验chi square test阿贝不变量Abbe invariant阿贝成象原理Abbe principle of image formation阿贝折射计Abbe refractometer阿贝正弦条件Abbe sine condition阿伏伽德罗常量Avogadro constant阿伏伽德罗定律Avogadro law阿基米德原理Archimedes principle阿特伍德机Atwood machine艾里斑Airy disk爱因斯坦-斯莫卢霍夫斯基理论Einstein-Smoluchowski theory 爱因斯坦场方程Einstein field equation爱因斯坦等效原理Einstein equivalence principle爱因斯坦关系Einstein relation爱因斯坦求和约定Einstein summation convention爱因斯坦同步Einstein synchronization爱因斯坦系数Einstein coefficient安[培]匝数ampere-turns安培[分子电流]假说Ampere hypothesis安培定律Ampere law安培环路定理Ampere circuital theorem安培计ammeter安培力Ampere force安培天平Ampere balance昂萨格倒易关系Onsager reciprocal relation凹面光栅concave grating凹面镜concave mirror凹透镜concave lens奥温电桥Owen bridge巴比涅补偿器Babinet compensator巴耳末系Balmer series白光white light摆pendulum板极plate伴线satellite line半波片halfwave plate半波损失half-wave loss半波天线half-wave antenna半导体semiconductor半导体激光器semiconductor laser半衰期half life period半透[明]膜semi-transparent film半影penumbra半周期带half-period zone傍轴近似paraxial approximation傍轴区paraxial region傍轴条件paraxial condition薄膜干涉film interference薄膜光学film optics薄透镜thin lens保守力conservative force保守系conservative system饱和saturation饱和磁化强度saturation magnetization本底background本体瞬心迹polhode本影umbra本征函数eigenfunction本征频率eigenfrequency本征矢[量] eigenvector本征振荡eigen oscillation本征振动eigenvibration本征值eigenvalue本征值方程eigenvalue equation比长仪comparator比荷specific charge; 又称“荷质比(charge-mass ratio)”。

Adaptive control of dynamic mobile robots withnonholonomic constraintsFarzad Pourboghrat *,Mattias P.KarlssonDepartment of Electrical and Computer Engineering,Southern Illinois University,Carbondale,IL 62901-6603,USAReceived 16November 1999;accepted 22August 2000AbstractThis paper presents adaptive control rules,at the dynamics level,for the nonholonomic mobile robots with unknown dynamic parameters.Adaptive controls are derived for mobile robots,using backstepping technique,for tracking of a reference trajectory and stabilization to a fixed posture.For the tracking problem,the controller guarantees the asymptotic convergence of the tracking error to zero.For stabili-zation,the problem is converted to an equivalent tracking problem,using a time varying error feedback,before the tracking control is applied.The designed controller ensures the asymptotic zeroing of the sta-bilization error.The proposed control laws include a velocity/acceleration limiter that prevents the robot Õs wheels from slipping.Ó2002Elsevier Science Ltd.All rights reserved.Keywords:Mobile robot;Nonholonomic constraint;Dynamics level motion control;Stabilization and tracking;Adaptive control;Backstepping technique;Asymptotic stability1.IntroductionMotion control of mobile robots has found considerable attention over the past few years.Most of these reports have focused on the steering or trajectory generation problem at the ki-nematics level i.e.,considering the system velocities as control inputs and ignoring the mechanical system dynamics [1–3].Very few reports have been published on control design in the presence of uncertainties in the dynamic model [4].Some preliminary results on control of nonholonomic systems with uncertainties are given in Refs.[4–6].Two of the most important control problems concerning mobile robots are tracking of a refer-ence trajectory and stabilization to a fixed posture.The tracking problem has received solutions *Corresponding author.Tel.:+1-618-453-7026.E-mail address:pour@ (F.Pourboghrat).0045-7906/02/$-see front matter Ó2002Elsevier Science Ltd.All rights reserved.PII:S0045-7906(00)00053-7242 F.Pourboghrat,M.P.Karlsson/Computers and Electrical Engineering28(2002)241–253including classical nonlinear control techniques[1,2,7].The basic idea is to have a reference car that generates a trajectory for the mobile robot to follow.In Refs.[1,2],nonlinear velocity control inputs were defined that made the tracking error go to zero as long as the reference car was moving.In Ref.[7],they used input–output linearization to make a mobile platform follow a desired trajec-tory.The problem of stabilization about afixed posture has been shown to be rather complicated. This is due to violating the BrockettÕs condition[8],which states that for nonholonomic systems a single equilibrium solution cannot be asymptotically stabilized using continuous static state feedback[9,10].The BrockettÕs condition essentially states that for nonholonomic systems an equilibrium solution can be asymptotically stabilized only by either a time varying,a discontin-uous,or a dynamic state feedback.In addressing the above problem,in Ref.[10]a smooth feedback control was presented for the kinematics control problem resulting in a globally marginally stable closed loop system.They also designed a smooth feedback control for a dynamical state-space model resulting in a Lagrange stable closed loop system,as defined in their paper.A two dimensional Lyapunov function was utilized in Ref.[3]to prescribe a set of desired trajectories to navigate a mobile robot to a specified configuration.The desired trajectory was then tracked using sliding mode control,resulting in discontinuous control signals.The mobile robot was shown to be exponentially stable for a class of quadratic Lyapunov functions.In Ref.[9],they formulated a reduced order state equation for a class of nonholonomic systems.Several other researchers have later used this reduced order state equation in their studies.In Ref.[4],the problem of controlling nonholonomic mechanical sys-tems with uncertainties,at the dynamics level,was ing the reduced state equation in Ref.[9],they proposed an adaptive controller for a number of important nonholonomic control problems,including stabilization of general systems to an equilibrium manifold and stabilization of differentiallyflat and Caplygin systems to an equilibrium point.In Ref.[2],they gave several examples on how the stabilization problem can be solved for a mobile robot at the kinematics level.Their solutions included time-varying control,piecewise continuous control,and time-varying piecewise continuous control.They also showed how a solution to the tracking problem could be extended to work even for the stabilization problem.Here,we present adaptive control schemes for the tracking problem and for the problem of stabilization to afixed posture when the dynamic model of the mobile robot contains unknown parameters.Our work is based on,and can be seen as an extension of,the work presented in Refs. [1,2].Using backstepping technique we derive adaptive control laws that work even when the model of the dynamical system contains uncertainties in the form of unknown constants.The assumption for the uncertainty in robotÕs parameters,particularly the mass,and hence the inertia, can be justified in real applications such as in automotive manufacturing industry and warehouses, where the robots are to move a variety of parts with different shapes and masses.In these cases,the robotÕs mass and inertia may vary up to10%or20%,justifying an adaptive control approach.2.Dynamic model of mobile robotHere,we consider a three-wheeled mobile robot moving on a horizontal plane(Fig.1).The mobile robot features two differentially driven rear wheels and a castor front wheel.The radius ofthe wheels is denoted r and the length of the rear wheel axis is 2l .Inputs to the system are two torques T 1and T 2,provided by two motors attached to the rear wheels.The dynamic model for the above wheeled-mobile robot is given by Refs.[10,11].€x ¼k m sin /þb 1u 1cos /€y ¼Àk cos /þb 1u 1sin /€/¼b 2u 28><>:ð1Þ_x sin /À_y cos /¼0ð2Þwhere b 1¼1=ðrm Þ,b 2¼l =ðrI Þ,and that m and I denote the mass and the moment of inertia of the mobile robot,respectively.Also,u 1¼T 1þT 2and u 2¼T 1ÀT 2are the control inputs,and k is the Lagrange multiplier,given by k ¼Àm _/_x cos /þ_y sin /ðÞ.Here,it is assumed that b 1and b 2are unknown constants with known signs.The assumption that the signs of b 1and b 2are known is practical since b 1and b 2represent combinations of the robot Õs mass,moment of inertia,wheel radius,and distance between the rear wheels.Eq.(2)is the nonholonomic constraint,coming from the assumption that the wheels do not slip.The triplet vector function q t ðÞ¼x t ðÞ;y t ðÞ;/t ðÞ½ T denotes the trajectory (position and orientation)of the robot with respect to a fixed workspace frame.That is,at any given time,q ¼½x ;y ;/ T describes the robot Õs configuration (posture)at that time.We assume that,at any time,the robot Õs posture,q ¼½x ;y ;/ T ,as well as its derivative,_q¼½_x ;_y ;_/ T ,are available for feedback.3.Tracking problem definitionThe tracking problem consists of making the trajectory q of the mobile robot follow a reference trajectory q r .The reference trajectory q r t ðÞ¼x r t ðÞ;y r t ðÞ;/r t ðÞ½ T is generated by a reference ve-hicle/robot whose equations are_xr ¼v r cos /r _y r¼v r sin /_/r ¼x r8<:ð3ÞThe subscript ‘‘r’’stands for reference,and v r and x r are the reference translational (linear)velocity and the reference rotational (angular)velocity,respectively.We assume that v r and x r ,as well as their derivatives are available and that they all are bounded.Assumption A 1.For the tracking problem it is assumed that the reference velocities v r and x r do not both go to zero simultaneously.That is,it is assumed that at any time either lim t !1v r t ðÞ90and/or lim t !1x r t ðÞ90.The tracking problem,under the Assumption A 1,is to find a feedback control law u 1u 2 ¼u q ;_q ;q r ;v r ;x r ;_v r ;_x r ðÞsuch that lim t !1~q t ðÞ¼0,where ~q t ðÞ¼q r t ðÞÀq t ðÞis defined as the trajectory tracking error.As in Ref.[1],we define the equivalent trajectory tracking error ase ¼T ~qð4Þwhere e ¼½e 1;e 2;e 3 T ,and T ¼cos /sin /0Àsin /cos /00010@1A .Note that since T matrix is nonsingular,e is nonzero as long as ~q¼0.Assuming that the angles /r and /are given in the range ½Àp ;p ,we have the equivalent trajectory tracking error e ¼0only if q ¼q r .The purpose of the tracking controller is to force the equivalent trajectory tracking error e to 0.In the sequel we refer to e as the trajectory tracking error.Using the nonholonomic constraint (2),the derivative of the trajectory tracking error given in Eq.(4)can be written as,[1],_e1¼e 2x Àv þv r cos e 3_e 2¼Àe 1x þv r sin e 3_e3¼x r Àx 8<:ð5Þwhere v and x are the translational and rotational velocities of the mobile robot,respectively,and are expressed asv ¼_xcos /þ_y sin /x ¼_/ð6Þ4.Tracking controller designHere,the goal is to design a controller to force the tracking error e ¼½e 1;e 2;e 3 T to ing backstepping technique,since the actual control variables u 1and u 2do not appear in Eq.(5),we consider variables v and x as virtual controls.Let v d and x d denote the desired virtual controls for the mobile robot.That is,with v d and x d the trajectory tracking error e converges tozero asymptotically.Also let us define ~vand ~x as virtual control errors.Then,v and x can be written asv ¼v d þ~vx ¼x d þ~x ð7Þ244 F.Pourboghrat,M.P.Karlsson /Computers and Electrical Engineering 28(2002)241–253Let us choose the virtual controls v d and x d ,asv d v r ;x r ;e 1;e 3ðÞ¼v r cos e 3þk 1v r ;x r ðÞe 1x d v r ;x r ;e 2;e 3ðÞ¼x r þk 2v r e 2þk 3v r ;x r ðÞsin e 3ð8Þwhere k 2is a positive constant and k 1ðÁÞand k 3ðÁÞare bounded continuous functions with bounded first derivatives,strictly positive on R ÂR -ð0;0Þ.Observe that our approach from here on is general for any v d and x d (with well defined first derivatives),i.e.any differentiable control law that makes the kinematics model of the mobile robot track a desired trajectory can be used instead of Eq.(8).Eq.(8)is similar to the control law proposed by Ref.[1],but with the advantage,as we are going to prove later,that it can be used to track any reference trajectory as long as As-sumption A 1holds.Now,consider the following adaptive control scheme:u 1¼^b 1ðÀc 1~v þe 1þ_v d Þu 2¼^b 2 Àc 2~x þ1k 2sin e 3þ_x d _^b 1¼Àc 1sign b 1ðÞ~v ðÀc 1~v þe 1þ_v d Þ_^b 2¼Àc 2sign b 2ðÞ~x Àc 2~x þ1k 2sin e 3þ_x d ð9Þwhere c 1,c 2,c 1,and c 2are positive constants and ^b 1is an estimate of b 1¼1=b 1and ^b 2is an estimate of b 2¼1=b 2.Result 1.If Assumption A 1holds ,then the adaptive control scheme (9)makes the origin e ¼0uniformly asymptotically stable.Proof .Consider the following Lyapunov function candidateV 1¼12e 21Àþe 22Áþ1k 21ðÀcos e 3Þð10Þwhere k 2is a positive constant.Clearly V 1is positive definite and V 1¼0only if e ¼0.Taking the time derivative of V 1,we obtain_V 1¼e 1ðÀv þv r cos e 3Þþe 2v r sin e 3þ1k 2sin e 3x r ðÀx Þð11ÞFurthermore,using Eqs.(7)and (8),we have_V 1¼Àk 1e 21Àk 3k 2sin 2e 3À~v e 1À~x 1k 2sin e 3ð12ÞIn view of Eqs.(1),(2)and (6),we find the time derivatives of ~vand ~x ,as _~v¼_v À_v d ¼€x cos /À_x sin /_/þ€y sin /þ_y cos /_/À_v d ¼b 1u 1À_v d _~x ¼_x À_x d ¼€/À_x d ¼b 2u 2À_x d ð13ÞF.Pourboghrat,M.P.Karlsson /Computers and Electrical Engineering 28(2002)241–253245Consider the Lyapunov function candidateV2¼V1þ12ð~v2þ~x2Þþb1j j2c1~b21þb2j j2c2~b22ð14Þwhere~b1¼b1À^b1¼1=b1À^b1and~b2¼b2À^b2¼1=b2À^b2.Considering Eq.(9)we get:_V 2¼Àk1e21Àk3k2sin2e3Àc1~v2Àc2~x260ð15ÞSince V2is bounded from below and_V2is negative semi-definite,V2converges to afinite limit. Also,V2,as well as,e1,e2,e3,~v,~x,^b1,and^b2are all bounded.Furthermore,using Eqs.(5),(7)–(9)and(13),the second derivative of V2can be written as€V 2¼À2k1e1e2ðx rþk2v r e2þk3sin e3þ~xÞþ2k1e1ðk1e1þ~vÞÀ_k1e21þ2k3k2cos e3sin e3ðk2v r e2þk3sin e3þ~xÞÀ_k3k2sin2e3À2c1~vðb1^b1ðÀc1~vþe1þ_v dÞÀ_v dÞÀ2c2~x b2^b2Àc2~xþ1k2sin e3þ_x dÀ_x dð16Þwhich from the properties of k1,k2,and k3,the assumption that v r and x r and their derivatives are bounded,and from the above results,can be shown to be bounded,i.e.,_V2is uniformly contin-uous.Since V2ðtÞis differentiable and converges to some constant value and that€V2is bounded,by BarbalatÕs lemma,_V2tðÞ!0as t!1.This in turn implies that e1,e3,~v,and~x converge to zero [12,13].To show that e2also goes to zero,note that,using the above results,thefirst error equation can be written as_e1¼e2x rÀk1e1ð17ÞThe second derivative of e1is€e1¼_x r e2þx rðÀe1xþv r sin e3ÞÀk1e2x rðÀk1e1ÞÀ_k1e1ð18Þwhich can be shown to be bounded by once again using the properties of k1,the assumptions on v r and x r,and Eqs.(7)and(8).Since e1is differentiable and converges to zero and€e1is bounded,by BarbalatÕs lemma,_e1,and hence,e2x r tend to zero.Proceeding in the same manner,the third error equation can be written as_e3¼Àk2v r e2Àk3sin e3ð19Þand its second derivative can be shown to be bounded.Since e3is differentiable and converges to zero and€e3is bounded,again by BarbalatÕs lemma,_e3!0as t!1.Hence,k2v r e2and thus v r e2 tend to zero as t!1.Clearly,both v r e2and x r e2converge to zero.However,since v r and x r do not both tend to zero(by Assumption A1),e2must converge to zero.That is,e1,e2,e3,~v,and~x must all converge to zero.hIn Section3,we demonstrated that the system is stable if k2is a positive constant,and that k1ðÁÞand k3ðÁÞare bounded continuous functions with boundedfirst derivatives and are strictly positive on RÂR-ð0;0Þ.To get a better understanding on how the control gains affect the response of the system,we write the equations for the closed loop system when~v and~x are equal to zero as[1] 246 F.Pourboghrat,M.P.Karlsson/Computers and Electrical Engineering28(2002)241–253_e¼Àk 1e 1þx r þk 2v r e 2þk 3sin e 3ðÞe 2Àx r þk 2v r e 2þk 3sin e 3ðÞe 1þv r sin e 3Àk 2v r e 2Àk 3sin e 30@1A ð20ÞBy linearizing the differential equation (20)around e ¼0,we get_e¼Ae ð21Þwhere A ¼Àk 1x r 0Àx r 0v r 0Àk 2v r Àk 30@1A ð22ÞTo simplify the analysis,we assume that v r and x r are constants.The system Õs closed loop poles are now equal to the roots of the following characteristic polynomial equation:s ðþ2nx 0Þs 2Àþ2nx 0s þx 20Áð23Þwhere n and x 0are positive real numbers.The corresponding control gains arek 1¼2nx 0k 2¼x 20Àx 2r v 2r k 3¼2nx 0ð24ÞWith a fixed pole placement strategy (n and x 0are constant),the control gain k 2increaseswithout bound when v r tends to zero.One way to avoid this is by letting the closed loop polesdepend on the values of v r and x r .As in Ref.[2],we choose x 0¼x 2r þbv 2r ÀÁð1=2Þwith b >0.The control gains then becomek 1¼2n x 2r Àþbv 2rÁ1=2k 2¼b k 3¼2n x 2r Àþbv 2r Á1=2ð25Þand the resulting control is now defined for any values of v r and x r .In the above,it is shown that the proposed algorithm works for any desired velocities,ðv d ;x d Þ.However,in practice,if the tracking errors initially are large or if the reference trajectory does not have a continuous curvature (e.g.,if the reference trajectory is a straight line connected to a circle segment),either or both of the virtual reference velocities in Eq.(8)might become too large for a real robot to attain in practice.Hence,the translational/rotational acceleration might become too large causing the robot to slip [1].In order to prevent the mobile robot from slipping,in a real application,a simple velocity/acceleration limiter may be implemented [1],as shown in Fig.2.This limits the virtual reference velocities ðv d ;x d Þby constants ðv max ;x max Þand the virtual referenceaccelerations ða ;a Þby constants ða max ;a max Þ,where a ¼_vd and a ¼_x d are the virtual reference accelerations.In practice,these parameters must be determined experimentally as the largest values with which the mobile robot never slips.F.Pourboghrat,M.P.Karlsson /Computers and Electrical Engineering 28(2002)241–253247An important advantage of adding the limiter is that it lowers the control gains indirectly only when the tracking errors are large,i.e.,when too high a gain could cause the robot to slip,while for small tracking errors it does not affect the performance at all.Thus,by using the limiter one can have higher control gains for small tracking errors to allow for better tracking,while letting the limiter to‘‘scale down’’the gains,indirectly,for large tracking errors,to prevent the robot from slipping.5.Simulation results for tracking control problemHere,the results of computer simulation,using MATLAB/SIMULINK,are presented for a mobile robot with the proposed tracking control and with the velocity/acceleration limiter.The computer simulations for the above controller without the limiter,although not shown here,produce similar results,but with somewhat different transient characteristics.All simulations have the common parameters of c1¼c2¼100,c1¼c2¼10and b¼250.Also selected are,the damping factor n¼1,v max¼1:5m/s,x max¼3rad/s,a max¼5m/s2and a max¼25rad/s2.Moreover,the robotÕs dy-namic parameters are chosen as b1¼b2¼0:5,which are assumed to be unknown to the con-troller,but with known signs.Simulation results for the case where the reference trajectory is a straight line are shown in Figs. 3and4for t2½0;10 .The reference trajectory is given by x rðtÞ¼0:5t,y rðtÞ¼0:5t and/rðtÞ¼p=4, defining a straight line,starting from q rð0Þ¼½x rð0Þ;y rð0Þ;/rð0Þ T¼½0;0;p=4 T.The mobile robot, however,is initially at qð0Þ¼½xð0Þ;yð0Þ;/ð0Þ T¼½1;0;0 T,where/¼0indicates that the robot is heading toward positive direction of x.As it can be seen from thesefigures,first the robot backs up and then heads toward the virtual reference robot moving on the straight line.Figs.5and6show the simulation results for tracking a circular trajectory.The reference trajectory is a point moving counter clockwise on a circle of radius1,starting at q rð0Þ¼½x rð0Þ;y rð0Þ;/rð0Þ T¼½1;0;p=2 T.The reference velocity is kept constant at v rðtÞ¼0:5m/s.The initial conditions for the mobile robot,however,is taken as qð0Þ¼½xð0Þ;yð0Þ;/ð0Þ T¼½0;0;0 T.Again,as it is seen from thesefigures,the robot immediately heads toward the reference robot,which is moving on the circle.It then reaches it quickly and continues to track it.6.Stabilization problem definitionThe stabilization problem,given an arbitrary desired posture q d ,is to find a feedback control law,u 1u 2¼u q Àq d ;_q ;t ðÞ,such that lim t !1q t ðÞÀq d ðÞ¼0,for any arbitrary initial robot posture q ð0Þ.Without loss of generality,we may take q d ¼½0;0;0 T.6.1.Stabilization controller designRecall that there is no continuous static state feedback that can asymptotically stabilize a nonholonomic system about a fixed posture [8–10].The approach to the problem taken here is the dynamic extension of that in Ref.[2]where a kinematics model of the mobile robot is used.In-stead of designing a new controller for the stabilization problem the same controller as for the tracking problem is used.The idea is to let the reference vehicle move along a path that passes through the point ðx d ;y d Þwith heading angle /d .The stabilization to a fixed posture problem isnow equivalent to,and can be treated as,a tracking problem(convergence of the tracking errors to zero)with the additional requirement that the reference vehicle should itself be asymptotically stabilized about the desired posture.As in Ref.[2],we let the reference vehicle move along the x-axis,i.e.y rðtÞ¼0and/rðtÞ¼0,for all values on t.The design method is the same as derived for the tracking case.However,in this casev r¼_x r¼Àk4x rþgðe;tÞ;ð26Þwithgðe;tÞ¼k e k sin tð27Þwhere k4>0.Different time-varying functions gðe;tÞhave also been suggested in the literature,see Refs.[2,11]and the references therein.Since,from the Section5,the tracking errors e1,e2,and e3are bounded,the time-varying function gðe;tÞis bounded.Therefore v r and the state x r also remain bounded.By taking the time derivative of Eq.(26),it can be shown in the same way that_v r is bounded.Since v r and_v r are bounded,the assumptions made in Section3concerning the reference velocity are fulfilled.If v r is not equal to zero,then e must converge to zero.When e tends to zero,gðe;tÞalso tends to zero. Therefore,the robotÕs position x must track x r,which converges to zero and hence lead the mobile robot to the desired posture.6.2.Simulation results for stabilization control problemHere,the simulation results for the stabilization problem are shown in Figs.7and8.The control parameters and system parameters are the same as for the simulations shown for the tracking problem and k4¼1.The mobile robot is initially at qð0Þ¼½xð0Þ;yð0Þ;/ð0Þ T¼½0;1;0 T.As it is seen from thefigures,the stabilization about thefinal posture at the origin is achieved quite satisfactorily.Note,in this case,that the robot actually turns around and backs up into the final posture.7.ConclusionsTwo important control problems concerning mobile robots with unknown dynamic parameters have been considered,namely,tracking of a reference trajectory and stabilization to afixed posture.An adaptive control law has been proposed for the tracking problem and has been ex-tended for the stabilization problem.A simple velocity/acceleration limiter was added to the controller,for practical applications,to avoid any slippage of the robotÕs wheels,and to improve the tracking performance.Several simulation results have been included to demonstrate the performance of the proposed adaptive control law.References[1]Kanayama Y,Kimura Y,Miyazaki F,Noguchi T.A stable tracking control method for an autonomous mobilerobot.vol.1.Proceedings of IEEE International Conference on Robotics and Automation,Cincinnati,Ohio,1990, p.384–9.[2]Canudas de Wit C,Khennouf H,Samson C,Sordalen OJ.Nonlinear control design for mobile robots.In:ZhengYF,editor.Recent trends in Mobile robots,World Scientific,1993.p.121–56.[3]Guldner J,Utkin VI.Stabilization of nonholonomic mobile robot using Lyapunov functions for navigation andsliding mode control.Control-Theory Adv Technol1994;10(4):635–47.[4]Colbaugh R,Barany E,Glass K.Adaptive Control of Nonholonomic Mechanical Systems.Proceedings of35thConference on Decision and Control,Kobe,Japan,1996.p.1428–34.[5]Fierro R,Lewis FL.Control of nonholonomic mobile robot:backstepping kinematics into dynamics.J Robot Sys1997;14(3)149-163.[6]Jiang ZP,Pomet bining backstepping and time-varying techniques for a new set of adaptive controllers.Proceedings of33rd IEEE Conf on Decision and Control,Lake Buena Vista,FL,1994.p.2207–12.[7]Sarkar N,Yun X,Kumar V.Control of mechanical systems with rolling constraints:application to dynamiccontrol of mobile robots.Int J Robot Res1994;13(1):55–69.[8]Brockett RW.Asymptotic stability and feedback stabilization.In:Brockett RW,Millman RS,Sussmann HJ,editors.Differential Geometric Control Theory,Boston,MA:Birkhauser;1983.p.181–91.[9]Bloch AM,Reyhanoglu MR,McClamroch NH.Control and stabilization of nonholonomic dynamic systems.IEEE Trans Automat Contr1992;37(11):1746–56.[10]Campion G,d’Andrea-Novel B,Bastin G.Controllability and state feedback stabilization of nonholonomicmechanical systems.Canudas de Wit C,editor.Advanced Robot Control,Berlin:Springer;1991.p.106–24. [11]Kolmanovsky I,McClamroch NH.Developments in nonholonomic control problems.IEEE Contr Sys Magaz1995;15(6):20–36.[12]Krstic M,Kanellakopoulos I,Kokotovic P.Nonlinear and Adaptive Control Design,New York:Wiley;1995.[13]Karlsson MP.Control of nonholonomic systems with applications to mobile robots.Master Thesis,SouthernIllinois University,Carbondale,IL62901,USA,1997.Farzad Pourboghrat received his Ph.D.degree in Electrical Engineering from the University of Iowa in1984. He is now with the Department of Electrical and Computer Engineering at Southern Illinois University at Carbondale(SIU-C)where he is an Associate Professor.His research interests are in adaptive and slidingcontrol with applications to DSP embedded systems,mechatronics,flexible structures andMEMS.Mattias Karlsson received the B.S.E.E.degree from the University of Bor a s,Sweden and the M.S.E.E.degree from Southern Illinois University,Carbondale,IL,in1995and1997,respectively.He has been employed at Orian Technology since1997.He is currently an on-site consultant at Caterpillar Inc.Õs Technical Center, Mossville,IL.His current interests include control algorithm development for mechanical and electrical systems and software development for embedded systems.F.Pourboghrat,M.P.Karlsson/Computers and Electrical Engineering28(2002)241–253253。

㊀第４９卷第４期煤炭科学技术Ｖｏｌ ４９㊀Ｎｏ ４㊀㊀２０２１年４月ＣｏａｌＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ㊀Ａｐｒ．２０２１㊀移动扫码阅读邓志刚．动静载作用下煤岩多场耦合冲击危险性动态评价技术［Ｊ］．煤炭科学技术，２０２１，４９（４）：１２１－１３２ ｄｏｉ：１０ １３１９９／ｊ ｃｎｋｉ ｃｓｔ ２０２１ ０４ ０１５ＤＥＮＧＺｈｉｇａｎｇ．Ｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｍｅｔｈｏｄｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｏｎｓｉｄｅｒｉｎｇｄｙｎａｍｉｃａｎｄｓｔａｔｉｃｌｏａｄ［Ｊ］．ＣｏａｌＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ，２０２１，４９（４）：１２１－１３２ ｄｏｉ：１０ １３１９９／ｊ ｃｎｋｉ ｃｓｔ ２０２１ ０４ ０１５动静载作用下煤岩多场耦合冲击危险性动态评价技术邓㊀志㊀刚１，２（１．煤炭科学技术研究院有限公司安全分院，北京㊀１０００１３；２．煤炭资源高效开采与洁净利用国家重点实验室，北京㊀１０００１３）摘㊀要：深部开采冲击地压灾害孕灾过程中既有静态基础量又有动态变化量，剧增的原岩应力与覆岩断裂㊁井下爆破等引起的动载扰动是诱发冲击地压灾害的源头，因此实现冲击危险性快速㊁高精度评价必须综合考虑动静载作用㊂笔者开展了典型煤岩霍普金森压杆试验及数值模拟，分析了动载对煤岩体破坏作用以及对应力场的影响，针对应力变化可以直接引起介质中震动波波速变化，且波速变化前的幅值与变化幅度均受应力场影响这一特性，掌握了震动场与应力场的耦合关系，建立了多场耦合冲击危险性动态评价技术：以原岩应力场表示煤岩孕灾过程的静态基础量，以采动应力场和震动场表示煤岩孕灾过程的动态变化量，以波速异常指数㊁波速梯度指数㊁应力异常指数㊁应力梯度指数为评价指标可实现煤岩冲击危险性动态评价㊂研究结果表明：动载作用下能量以震动波形式传递，造成应力场的重新分布，应力呈现分区传递特点，并且在能量达到某一阈值后引起煤岩损伤破坏，但无论动载直接作用在岩石上还是煤体上，岩石是能量传递路径，煤层是能量耗散㊁释放主体，破坏主要发生在煤体中㊂多场耦合冲击危险性评价技术在某工作面经现场应用，在工作面逐渐揭露断层过程中冲击危险性由强冲击危险性降低到中等冲击危险性，现场监测数据表明评价结果与现场实际相符㊂关键词：动静载荷；冲击危险性；震动场；多场耦合；动态评价中图分类号：ＴＤ３２４㊀㊀㊀文献标志码：Ａ㊀㊀㊀文章编号：０２５３－２３３６（２０２１）０４－０１２１－１２Ｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｍｅｔｈｏｄｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｏｎｓｉｄｅｒｉｎｇｄｙｎａｍｉｃａｎｄｓｔａｔｉｃｌｏａｄＤＥＮＧＺｈｉｇａｎｇ１，２（１．ＭｉｎｅＳａｆｅｔｙＴｅｃｈｎｏｌｏｇｙＢｒａｎｃｈ，ＣｈｉｎａＣｏａｌＲｅｓｅａｒｃｈＩｎｓｔｉｔｕｔｅ，Ｂｅｉｊｉｎｇ㊀１０００１３，Ｃｈｉｎａ；２．ＳｔａｔｅＫｅｙＬａｂｏｒａｔｏｒｙｏｆＣｏａｌＭｉｎｉｎｇａｎｄＣｌｅａｎＵｔｉｌｉｚａｔｉｏｎ，Ｂｅｉｊｉｎｇ㊀１０００１３，Ｃｈｉｎａ）收稿日期：２０２０－１２－０２；责任编辑：朱恩光基金项目：国家科技重大专项资助项目（２０１６ＺＸ０５０４５００３－００６－００２）；国家自然科学基金面上资助项目（５１６７４１４３）作者简介：邓志刚（１９８１ ），男，吉林长春人，研究员，博士，中国煤炭科工集团三级首席科学家㊂Ｔｅｌ：０１０－８４２６１５８１，Ｅ－ｍａｉｌ：ｄｅｎｇｚｈｉｇａｎｇ２００４＠１６３．ｃｏｍＡｂｓｔｒａｃｔ：Ｓｔａｔｉｃｂａｓｉｃｑｕａｎｔｉｔｙａｎｄｄｙｎａｍｉｃｖａｒｉａｔｉｏｎｑｕａｎｔｉｔｙｅｘｉｓｔｉｎｔｈｅｐｒｏｃｅｓｓｏｆｒｏｃｋｂｕｒｓｔｉｎｄｅｅｐｍｉｎｉｎｇ．Ｄｙｎａｍｉｃｌｏａｄｄｉｓｔｕｒｂａｎｃｅａｎｄｔｈｅｉｎｃｒｅａｓｉｎｇｏｆｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄａｒｅｔｈｅｓｏｕｒｃｅｏｆｒｏｃｋｂｕｒｓｔ．Ｔｈｅｒｅｆｏｒｅ，ｔｈｅｄｙｎａｍｉｃａｎｄｓｔａｔｉｃｌｏａｄｍｕｓｔｂｅｃｏｎｓｉｄｅｒｅｄｃｏｍｐｒｅｈｅｎｓｉｖｅｌｙｉｎｔｈｅｆａｓｔａｎｄｈｉｇｈ－ｐｒｅｃｉｓｉｏｎｅｖａｌｕａｔｉｏｎｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄ．Ｈｏｐｋｉｎｓｏｎｐｒｅｓｓｕｒｅｂａｒｅｘｐｅｒｉｍｅｎｔｓａｎｄｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓｗｅｒｅｃａｒｒｉｅｄｏｕｔｔｏａｎａｌｙｚｅｔｈｅｉｎｆｌｕｅｎｃｅｓｏｆｄｙｎａｍｉｃｌｏａｄｏｎｔｈｅｄａｍａｇｅａｎｄｓｔｒｅｓｓｆｉｅｌｄｏｆｔｈｅｃｏａｌｒｏｃｋ．Ｉｎｖｉｅｗｏｆｔｈｅｆａｃｔｔｈａｔｔｈｅｃｈａｎｇｅｏｆｓｔｒｅｓｓｃｏｕｌｄｄｉ⁃ｒｅｃｔｌｙｃａｕｓｅｔｈｅｃｈａｎｇｅｏｆｖｉｂｒａｔｉｏｎｗａｖｅｖｅｌｏｃｉｔｙａｎｄｔｈｅａｍｐｌｉｔｕｄｅｂｅｆｏｒｅａｎｄａｆｔｅｒｔｈｅｃｈａｎｇｅｏｆｗａｖｅｖｅｌｏｃｉｔｙｗｅｒｅａｆｆｅｃｔｅｄｂｙｔｈｅｓｔｒｅｓｓｆｉｅｌｄ，ｔｈｅｃｏｕｐｌｉｎｇｒｅｌａｔｉｏｎｓｈｉｐｂｅｔｗｅｅｎｖｉｂｒａｔｉｏｎｆｉｅｌｄａｎｄｓｔｒｅｓｓｆｉｅｌｄｗａｓｍａｓｔｅｒｅｄａｎｄｔｈｅｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｍｅｔｈｏｄｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄｗａｓｅｓｔａｂｌｉｓｈｅｄ．Ｉｎｔｈｅｐｒｏｃｅｓｓｏｆｃａｔａｓｔｒｏｐｈｅ，ｔｈｅｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄｒｅｐｒｅｓｅｎｔｓｔｈｅｓｔａｔｉｃｆｏｕｎｄａｔｉｏｎｑｕａｎｔｉｔｙ，ａｎｄｔｈｅｍｉｎｉｎｇｓｔｒｅｓｓｆｉｅｌｄａｎｄｔｈｅｖｉｂｒａｔｉｏｎｆｉｅｌｄｒｅｐｒｅｓｅｎｔｔｈｅｄｙｎａｍｉｃｃｈａｎｇｅｑｕａｎｔｉｔｙ．Ｔｈｅｗａｖｅｖｅｌｏｃｉｔｙａｎｏｍａｌｙｉｎｄｅｘ，ｗａｖｅｖｅｌｏｃｉｔｙｇｒａｄｉｅｎｔｉｎ⁃ｄｅｘ，ｓｔｒｅｓｓａｎｏｍａｌｙｉｎｄｅｘａｎｄｓｔｒｅｓｓｇｒａｄｉｅｎｔｉｎｄｅｘａｒｅｕｓｅｄａｓｅｖａｌｕａｔｉｏｎｉｎｄｅｘｅｓｔｏｒｅａｌｉｚｅｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄ．Ｔｈｅｒｅ⁃ｓｕｌｔｓｓｈｏｗｔｈａｔｔｈｅｅｎｅｒｇｙｉｓｔｒａｎｓｍｉｔｔｅｄｉｎｔｈｅｆｏｒｍｏｆｖｉｂｒａｔｉｏｎｗａｖｅｕｎｄｅｒｄｙｎａｍｉｃｌｏａｄ，ｒｅｓｕｌｔｉｎｇｉｎｔｈｅｒｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｓｔｒｅｓｓｆｉｅｌｄ．Ｔｈｅｓｔｒｅｓｓｐｒｅｓｅｎｔｓｔｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｚｏｎａｌｔｒａｎｓｍｉｓｓｉｏｎ，ａｎｄｃａｕｓｅｓｔｈｅｄａｍａｇｅｏｆｃｏａｌａｎｄｒｏｃｋｗｈｅｎｔｈｅｅｎｅｒｇｙｒｅａｃｈｅｓａｃｅｒｔａｉｎｔｈｒｅｓｈｏｌｄ．Ｈｏｗｅｖｅｒ，ｎｏｍａｔｔｅｒｔｈｅｄｙｎａｍｉｃｌｏａｄｄｉｒｅｃｔｌｙａｃｔｓｏｎｔｈｅｒｏｃｋｏｒｔｈｅｃｏａｌ，ｔｈｅｒｏｃｋｉｓｔｈｅｅｎｅｒｇｙｔｒａｎｓｆｅｒｐａｔｈ，ｔｈｅｃｏａｌｓｅａｍｉｓｔｈｅｍａｉｎｂｏｄｙｏｆｅｎｅｒｇｙｄｉｓｓｉｐａｔｉｏｎａｎｄｒｅｌｅａｓｅ，ａｎｄｔｈｅｆａｉｌｕｒｅｍａｉｎｌｙｏｃｃｕｒｓｉｎｔｈｅｃｏａｌ．Ｔｈｅｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｍｅｔｈｏｄｏｆｒｏｃｋｂｕｒｓｔ１２１２０２１年第４期煤炭科学技术第４９卷ｈａｚａｒｄｗａｓａｐｐｌｉｅｄｏｎａｃｅｒｔａｉｎｗｏｒｋｉｎｇｆａｃｅ．Ｔｈｅｒｏｃｋｂｕｒｓｔｈａｚａｒｄｗａｓｒｅｄｕｃｅｄｆｒｏｍｓｔｒｏｎｇｔｏｍｅｄｉｕｍｉｎｔｈｅｐｒｏｃｅｓｓｏｆｇｒａｄｕａｌｌｙｅｘｐｏｓｉｎｇｆａｕｌｔｓ．Ｔｈｅｆｉｅｌｄｍｏｎｉｔｏｒｉｎｇｄａｔａｓｈｏｗｅｄｔｈａｔｔｈｅｅｖａｌｕａｔｉｏｎｒｅｓｕｌｔｓｗｅｒｅｃｏｎｓｉｓｔｅｎｔｗｉｔｈｔｈｅａｃｔｕａｌｓｉｔｕａｔｉｏｎ．Ｋｅｙｗｏｒｄｓ：ｄｙｎａｍｉｃａｎｄｓｔａｔｉｃｌｏａｄｓ；ｒｏｃｋｂｕｒｓｔｈａｚａｒｄ；ｖｉｂｒａｔｉｏｎｆｉｅｌｄ；ｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇ；ｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎ０㊀引㊀㊀言我国多数矿井进入深部开采阶段，冲击地压灾害频度㊁强度显著增加［１］，冲击地压防治工作任重道远㊂２０１８年８月１日，国家煤矿安全监察局印发的‘防治煤矿冲击地压细则“开始实施，规定： 开采具有冲击倾向性的煤层必须进行冲击危险性评价 ， 开采冲击地压煤层必须进行采区㊁采掘工作面冲击危险性评价 ， 当评估煤层有冲击倾向性时，应当进行冲击危险性评价 ，并且以冲击危险性评价结果作为冲击地压监测㊁卸压等工作开展的依据㊂目前冲击危险性评价方法较多㊂一类是以冲击地压主要诱因为切入点的冲击危险性静态评价技术，如窦林名等［２］提出的综合指数法，综合考虑了岩体结构㊁力学特性㊁地质因素等条件㊂姜福兴等［３］采用模糊数学的方法，用垂直应力与煤体单轴抗压强度的比值㊁弹性能量指数２个指标评价煤体的冲击危险性，且根据应力叠加原理建立了冲击危险性评价模型，后又在此基础上提出了冲击地压分类评价技术手段㊂张科学等［６］综合考虑开采深度㊁冲击倾向性㊁煤层顶底板性质㊁地质构造㊁开采技术提出了基于层次分析法的煤层冲击危险性模糊综合评价模型㊂张宏伟等［７］应用地质动力区划方法对煤矿冲击危险进行评价㊂邓志刚［１０］基于三维地应力场反演技术开展了相关研究，综合考虑构造应力㊁采动影响等因素，实现了对采区宏观区域的冲击危险评价㊂欧阳振华等［１１］考虑瓦斯作用，将煤层气属性㊁抽采效果分析作为一类地质因素㊁开采技术条件，提出一种含瓦斯煤冲击危险性改进型综合指数评价方法㊂但是由于冲击地压致灾机理不清，灾害孕育㊁发展㊁发生的过程中影响因素繁杂，以及复杂多变的采掘及地质条件，致使静态评价方法主要是宏观上为煤层开采前的防冲工作提供一定参考，缺少对于采掘过程中因局部区域地质及开采条件变化㊁卸压措施等因素引起的冲击危险性动态变化的量化能力，因此，另一类基于现场监测数据的冲击危险性动态评价技术是当前研究工作的重点，如刘少虹等［１２］基于地音与电磁波ＣＴ探测数据提出的冲击危险性层次化评价方法；李宏艳等［１４］基于微震监测数据建立的考虑响应能量和无响应时间的冲击危险性动态评价技术㊂姜福兴等［１５］应用矿压观测法观测冲击地压工作面支架压力㊁立柱压缩量，判断工作面顶板来压规律，结合巷道的变形及其围岩应力分布进行观测，评价及预测冲击危险性㊂何学秋等［１７］采用电磁辐射法评价冲击危险性，主要参数为电磁辐射强度和脉冲数㊂曹民远等［１９］采用数值模拟和理论计算的方法分析了采掘工作面应力扰动叠加的影响，提出了近直立煤层动态权重评价法的计算体系㊂但是冲击地压的孕灾过程中既有静态基础量，又有动态变化量，因此目前仅依靠单一理论或方法快速㊁高精度的进行冲击危险性评价难度较大㊂我国煤矿进入深部开采后，剧增的原岩应力场成为冲击地压灾害发生的必要条件㊂覆岩断裂㊁井下爆破等带来的强动载扰动易成为诱发冲击灾变的充分条件，但目前冲击危险性评价的研究工作中少有兼顾动静载综合作用的理论或方法㊂为此，笔者以震动场㊁采动应力场表示孕灾过程中动态变化量，以原岩应力场表示孕灾过程中静态基础量㊂提出了波速异常指数㊁波速梯度指数㊁应力异常指数㊁应力梯度指数４个冲击危险性评价指标，并在此基础上建立了多场耦合冲击危险性动态评价技术以实现井下高精度冲击危险性动态评价㊂１㊀煤岩动载破坏试验分析１．１㊀典型煤岩动载破坏霍普金森压杆试验分离式霍普金森压杆（ＳＨＰＢ）试验系统（图１）由压杆系统㊁测量系统和数据采集处理系统３个部分组成㊂图１㊀ＳＨＰＢ试验装置Ｆｉｇ．１㊀ＳＨＰＢｅｘｐｅｒｉｍｅｎｔａｌｄｅｖｉｃｅ当动载试块受到不同气压后获得不同初速度撞击入射杆，在杆内产生入射脉冲εｉ，试件在该应力作用下产生高速变形，同时产生反射脉冲εｒ和透射脉冲εｔ㊂如图２所示㊂选取强冲击倾向性煤样试件４２２１邓志刚等：动静载作用下煤岩多场耦合冲击危险性动态评价技术２０２１年第４期个，中砂岩试件４个，尺寸均为ø５０ｍｍˑ１００ｍｍ㊂本次试验煤岩样取样点分别为某典型冲击地压矿井３－１煤回风大巷ＨＦ６导点处顶板和３１１１０２工作面煤层㊂煤岩物理力学参数见表１㊂分别采用气压０．２㊁０．４㊁０．６㊁０．８ＭＰａ发射子弹，撞击入射杆，记录其入射㊁反射和透射波曲线㊂图２㊀ＳＨＰＢ试验原理Ｆｉｇ．２㊀ＰｒｉｎｃｉｐｌｅｏｆＳＨＰＢｅｘｐｅｒｉｍｅｎｔａｌ㊀㊀煤样㊁岩样入射波㊁反射波和透射波曲线如图３㊁图４所示，仅出示驱动应力为０．２㊁０．４㊁０．８ＭＰａ时的结果㊂对比分析可知，随着撞击杆驱动应力增加，入射波波速幅值㊁入射波波速变化率均有所增加，反射波和透射波波峰和波谷增高，透射波持续时间缩短，这也和冲击地压发生的突然㊁猛烈性质一致㊂１．２㊀典型煤岩动载破坏数值模拟采取有限元方法对煤岩霍普金森压杆试验进行模拟，进一步分析动载作用下煤岩体损伤破坏机理㊂数值模型如图５所示㊂模拟试件分为煤样㊁岩样㊁煤－岩组合样，岩－煤组合样，其中煤－岩组合样是指震动波入射端在煤上，岩－煤组合样是指震动波入射端在岩石上㊂煤样㊁岩样尺寸为ø５０ｍｍˑ１００ｍｍ，煤岩组合样中煤㊁岩样尺寸均为ø５０ｍｍˑ５０ｍｍ㊂入射杆㊁透射杆材料参数按钢材设定［２０］，密度为７７９４ｋｇ／ｍ３，弹性模量为２１１ＧＰａ，泊松比为０．２８５㊂表１㊀煤岩物理力学参数Ｔａｂｌｅ１㊀Ｐｈｙｓｉｃａｌａｎｄｍｅｃｈａｎｉｃａｌｐａｒａｍｅｔｅｒｓｏｆｃｏａｌａｎｄｒｏｃｋ试样密度／（ｋｇ㊃ｍ－３）单轴抗压强度／ＭＰａ弹性模量／ＧＰａ泊松比抗拉强度／ＭＰａ内摩擦角／（ʎ）黏聚力／ＭＰａ煤样１３２５．４０３８．７６２３．４７４０．２８２２．４９３１８．５２１３．８９４岩样２１１１．９８４０．４３４７．３９５０．２２２２．８３９３５．６０１５．５２５图３㊀煤样不同气压下的波形Ｆｉｇ．３㊀Ｗａｖｅｆｏｒｍｓｏｆｃｏａｌｕｎｄｅｒｄｉｆｆｅｒｅｎｔａｉｒｐｒｅｓｓｕｒｅ图４㊀岩样不同气压下的波形Ｆｉｇ．４㊀Ｗａｖｅｆｏｒｍｓｏｆｒｏｃｋｕｎｄｅｒｄｉｆｆｅｒｅｎｔａｉｒｐｒｅｓｓｕｒｅ３２１２０２１年第４期煤炭科学技术第４９卷图５㊀霍普金森试验数值模型Ｆｉｇ．５㊀ＳＨＰＢｅｘｐｅｒｉｍｅｎｔｎｕｍｅｒｉｃａｌｍｏｄｅｌ煤岩物理力学参数见表２㊂加载在入射杆端部的震动波信号为ＳＨＰＢ试验中不同气压驱动子弹记录的入射杆应变波信号㊂不同震动波作用下煤岩体应力㊁损伤分布如图６ 图９所示，限于篇幅煤样㊁岩样仅出示驱动应力为０．２㊁０．４㊁０．８ＭＰａ时的结果，煤岩组合样仅出示驱动应力为０．２ＭＰａ和０．８ＭＰａ时的结果㊂分析可知，震动波作用引起煤岩应力重新分布，应力传递呈现分区传递特点，即存在应力传递优势面㊂在震动波波速峰值㊁波速变化率较低时，震动波对煤岩介质表２㊀数值模拟参数Ｔａｂｌｅ２㊀Ｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｐａｒａｍｅｔｅｒｓ试样弹性模量／ＧＰａ泊松比密度／（ｋｇ㊃ｍ－３）屈服强度／ＭＰａ单轴抗压强度／ＭＰａ内摩擦角／（ʎ）黏聚力／ＭＰａ煤样３．４７４０．３２１３２０１７．２５２４．６０１８．５２１３．８９０岩样７．６８３０．２３２５１９４４．９７５０．２７４３．１０１０．６５６图６㊀煤样应力与损伤分布情况Ｆｉｇ．６㊀Ｓｔｒｅｓｓａｎｄｄａｍａｇｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｃｏａｌｓｐｅｃｉｍｅｎ没有破坏作用，即震动波对煤岩介质的破坏与损伤存在阈值㊂煤岩体发生破坏的位置同时是单元受拉损伤㊁受压损伤极值位置，因此震动波作用下煤岩体破坏模式为拉压复合破坏㊂无论震动波直接作用在岩石上还是煤上，煤岩组合试件的破坏主要发生在煤体上，说明岩石是能量传播的路径，煤体是能量耗４２１邓志刚等：动静载作用下煤岩多场耦合冲击危险性动态评价技术２０２１年第４期图７㊀岩样应力与损伤分布情况Ｆｉｇ．７㊀Ｓｔｒｅｓｓａｎｄｄａｍａｇｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｒｏｃｋｓｐｅｃｉｍｅｎ图８㊀煤－岩样应力与损伤分布情况Ｆｉｇ．８㊀Ｓｔｒｅｓｓａｎｄｄａｍａｇｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｃｏａｌ－ｒｏｃｋｓｐｅｃｉｍｅｎ５２１２０２１年第４期煤炭科学技术第４９卷图９㊀岩－煤样应力与损伤分布情况Ｆｉｇ．９㊀Ｓｔｒｅｓｓａｎｄｄａｍａｇｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｒｏｃｋ－ｃｏａｌｓｐｅｃｉｍｅｎ散㊁释放的主体，这也符合冲击地压主要发生在煤层中的事实㊂１．３㊀震动场与煤岩冲击危险性的关联依据采煤工作面和掘进工作面煤岩体破坏失稳主要形式，结合ＳＨＰＢ试验和数值模拟研究结果，煤岩体震动场与冲击危险性的关系总结如下：①震动波是能量传递的载体，震动波所具有的能量超过一定阈值时可引起煤岩破坏，易诱发冲击地压灾害㊂②震动波传递引起应力分布变化，应力传递沿优势面进行㊂随着震动波能量增加，优势面周围易出现煤岩损伤破坏，引起煤岩冲击灾变㊂③当震源位于岩层时，能量传递速度较快，在煤岩界面发生衰减，煤体在震动波作用下发生破坏；当震源位于煤层时，煤体对震动波传递速度相对较慢，能量多耗散在煤层中，主要诱发煤体破坏，对岩层造成的破坏较小㊂２㊀煤岩动㊁静载冲击危险性评价指标考虑动静载作用煤岩冲击危险性评价指标包括应力场相关指标和震动场相关指标，其中静载作用主要表现为应力场的变化，动载作用主要引起震动场的变化㊂２．１㊀应力场冲击危险性评价指标基于煤矿冲击地压应力控制理论［２１］，煤岩体冲击破坏是应力作用的结果，一是取决于应力绝对值大小，二是应力梯度变化㊂因此，建立应力异常指数和应力梯度指数㊂应力异常指数表征一定区域内不同位置应力差异的指标，计算公式为γσ＝σｒ－σｍｉｎσｍａｘ－σｍｉｎˑ１０（１）式中：γσ为应力异常指数；σｒ为监测区域某点应力，ＭＰａ；σｍａｘ㊁σｍｉｎ分别为监测区域内实时应力最大值和最小值，ＭＰａ㊂应力梯度指数是表征一定区域内不同位置应力变化速度差异的指标，计算公式为ｇσ＝ｇσｒ－ｇσｍｉｎｇσｍａｘ－ｇσｍｉｎˑ１０（２）式中：ｇσ为应力梯度异常指数；ｇσｒ为监测区域内某一点的应力场梯度；ｇσｍａｘ㊁ｇσｍｉｎ分别为监测区域内应力最大㊁最小梯度㊂２．２㊀震动场冲击危险性评价指标综上，震动场波速绝对值㊁变化速率对煤岩破坏有显著影响㊂因此，提出表征震动波波速的波速异常指数和表征震动波波速变化速率的波速梯度指数，作为２个基于震动场的冲击危险性动态评价指数㊂波速异常指数表征一定区域内不同位置震动波波速的差异，计算公式为γθ＝θｒ－θｍｉｎθｍａｘ－θｍｉｎˑ１０（３）式中：γθ为波速异常指数；θｒ为监测区域某点震动波６２１邓志刚等：动静载作用下煤岩多场耦合冲击危险性动态评价技术２０２１年第４期波速，ｍ／ｓ；θｍａｘ㊁θｍｉｎ分别为监测区域内震动波波速最大值和最小值，ｍ／ｓ㊂波速梯度指数ｇθ是通过震动场波速变化速率表征煤岩体发生冲击地压的危险程度，计算公式为ｇθ＝ｇθｒ－ｇθｍｉｎｇθｍａｘ－ｇθｍｉｎˑ１０（４）式中：ｇθ为波速梯度异常指数；ｇθｒ为监测区域内某一点的震动波波速梯度；ｇθｍａｘ㊁ｇθｍｉｎ为监测区域内震动波波速最大㊁最小梯度㊂３㊀煤岩多场耦合冲击危险性动态评价技术结合笔者以往研究［２２］和上述研究成果可知，一方面煤岩应力场改变可以直接引起介质中震动波波速变化，且波速变化前的幅值与变化幅度均与应力场大小相关；另一方面，震动场传递会造成煤岩应力场的重新分布㊂因此，考虑动㊁静载作用开展煤岩冲击危险性动态评价关键在于分析震动场－应力场的耦合作用㊂煤炭开采之前，煤岩体处于重力和构造应力组成的原岩应力场之中；开采过程中，煤岩体形成采动应力场；原岩应力场和采动应力场相互作用，煤岩体损伤变形，震动产生，以弹性波的形式向外传播形成震动场㊂冲击地压是原岩应力场㊁采动应力场和震动场综合作用的结果，煤岩体中多场耦合关系如图１０所示㊂图１０㊀煤岩体中多场耦合关系Ｆｉｇ．１０㊀Ｆｉｅｌｄｉｎｃｏａｌｒｏｃｋｍａｓｓａｎｄｉｔｓｃｏｕｐｌｉｎｇｒｅｌａｔｉｏｎｓｈｉｐ为了准确描述煤岩体中各种场的关系，从冲击危险性评价角度建立统一数学模型Ｒ（ｔｉ，ｓ；ｍｊ）＝０㊀㊀（ｉ，ｊ＝１，２，３， ）（５）式中：ｔｉ为场的变量，一般情况下有多个，既可以是标量也可以是矢量；ｓ为场的源或者汇，通常只有一个；ｍｊ为煤岩体的物理性质变量，如弹性模量㊁泊松比㊁剪切模量㊁波速等多个变量㊂基于该函数煤岩体中的３种场的冲击危险性评价具体表达式如下：１）原岩应力场为Ｙ（ｈ，ｃ，ｆ；ρ，μ）＝０（６）式中：ｈ为采深；ｃ为地应力；ｆ为体积力；ρ为煤岩体密度；μ为泊松比㊂２）震动场为Ｓ（ｘ，ｙ，ｚ，ｔ，Ｅ，ｆ；ρ，μ）＝０（７）式中：ｘ㊁ｙ㊁ｚ为震源的位置坐标；ｔ为发震时间；Ｅ为震源能量㊂３）采动应力场为Ｆ（ｕ，ｆ；ρ，μ）＝０（８）式中：ｕ为位移㊂３．１㊀原岩应力场与采动应力场（ＲＭ）耦合冲击危险性评价模型㊀㊀原岩应力场冲击危险性评价指标见表３㊂原岩应力场冲击危险性指数定义为Ｒ＝（Ｒ１＋Ｒ２＋Ｒ３＋Ｒ４）／４（９）其中，Ｒ１㊁Ｒ２㊁Ｒ３㊁Ｒ４为不同评价指标得分㊂原岩应力冲击危险性反映煤岩体自身发生冲击地压的固有属性，其数值大小反映了煤岩体采动后，发生自发型冲击地压的可能性和危险性㊂原岩应力场冲击危险性指数取值与冲击危险等级关系见表４㊂表３㊀原岩应力场冲击危险性评价指标Ｔａｂｌｅ３㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｅｖａｌｕａｔｉｏｎｉｎｄｅｘｓｏｆｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄ变量影响因素阈值分值Ｒ１开采深度ｈｈɤ４００ｍ１４００ｍ＜ｈɤ６００ｍ２６００ｍ＜ｈɤ８００ｍ３ｈ＞８００ｍ４Ｒ２向落差大于３ｍ的断层推进的工作面或巷道，工作面或掘进工作面至断层的距离ＬｄＬｄȡ１００ｍ１５０ｍɤＬｄ＜１００ｍ２２０ｍɤＬｄ＜５０ｍ３Ｌｄ＜２０ｍ４Ｒ３向背斜或向斜推进的工作面或巷道，工作面或掘进工作面与之距离ＬｚＬｚȡ５０ｍ１２０ｍɤＬｚ＜５０ｍ２１０ｍɤＬｚ＜２０ｍ３Ｌｚ＜１０ｍ４Ｒ４同一水平煤层冲击地压发生次数ｎｎ＝０１ｎ＝１２２ɤｎ＜３３ｎȡ３４㊀㊀采动应力冲击危险指标包括：应力异常指数和应力梯度指数㊂二者取值与冲击危险等级之间的关系见表５㊁表６㊂７２１２０２１年第４期煤炭科学技术第４９卷表４㊀原岩应力场冲击危险性等级划分标准Ｔａｂｌｅ４㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄ阈值冲击危险性评价指数冲击危险等级Ｒɤ１１无１＜Ｒ＜２２弱２ɤＲ＜３３中等Ｒȡ３４强表５㊀应力异常指数冲击危险性等级划分标准Ｔａｂｌｅ５㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｓｔｒｅｓｓａｎｏｍａｌｙｉｎｄｅｘ阈值冲击危险性评价指数冲击危险等级γσɤ１１无１＜γσ＜３２弱３ɤγσ＜５３中等γσȡ５４强表６㊀应力梯度指数冲击危险性等级划分标准Ｔａｂｌｅ６㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｓｔｒｅｓｓｇｒａｄｉｅｎｔｉｎｄｅｘ阈值冲击危险性评价指数冲击危险等级ｇθɤ１１无１＜ｇθ＜３２弱３ɤｇθ＜５３中等ｇθȡ５４强㊀㊀基于原岩应力场与采动应力场耦合的冲击危险性评价模型为ＤＲＭ＝ａ１Ｒ＋ｂ１γσ＋ｃ１ｇσ（１０）㊀㊀其中：ＤＲＭ是原岩应力场与采动应力场耦合的冲击危险性评价指数；ａ１，ｂ１，ｃ１分别为原岩应力场和采动应力场耦合冲击危险性评价权重系数，不同矿井取值不同㊂原岩应力场与采动应力场耦合的冲击危险性指数取值与冲击危险等级之间的关系见表７㊂表７㊀原岩应力场与采动应力场耦合冲击危险性等级划分标准Ｔａｂｌｅ７㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｃｏｕｐｌｉｎｇｏｆｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄａｎｄｍｉｎｉｎｇｓｔｒｅｓｓｆｉｅｌｄ阈值冲击危险性评价指数冲击危险等级ＤＲＭɤ１１无１＜ＤＲＭ＜３２弱３ɤＤＲＭ＜５３中等ＤＲＭȡ５４强３．２㊀原岩应力场与震动场（ＲＳ）耦合冲击危险性评价模型㊀㊀震动场冲击危险性指标包括：波速异常指数和波速梯度指数㊂二者取值与冲击危险等级之间的关系见表８㊁表９㊂原岩应力场与震动场耦合的冲击危险性评价模型为ＤＲＳ＝ａ２Ｒ＋ｂ２γθ＋ｃ２ｇθ（１１）㊀㊀其中：ＤＲＳ为原岩应力场和震动场耦合的冲击危险性评价指数；ａ２，ｂ２，ｃ２为原岩应力场和震动场耦合冲击危险性评价权重系数，不同矿井取值不同㊂原岩应力场与震动场耦合的冲击危险性指数取值与冲击危险等级之间的关系见表１０㊂表８㊀波速异常指数冲击危险性等级划分标准Ｔａｂｌｅ８㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｗａｖｅｖｅｌｏｃｉｔｙａｎｏｍａｌｙｉｎｄｅｘ阈值冲击危险性评价指数冲击危险等级γθɤ１１无１＜γθ＜３２弱３ɤγθ＜５３中等γθȡ５４强表９㊀波速梯度指数冲击危险性等级划分标准Ｔａｂｌｅ９㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｗａｖｅｖｅｌｏｃｉｔｙｇｒａｄｉｅｎｔｉｎｄｅｘ阈值冲击危险性评价指数冲击危险等级ｇθɤ１１无１＜ｇθ＜３２弱３ɤｇθ＜５３中等ｇθȡ５４强表１０㊀原岩应力场与震动场耦合冲击危险性等级划分标准Ｔａｂｌｅ１０㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｃｏｕｐｌｉｎｇｏｆｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄａｎｄｖｉｂｒａｔｉｏｎｆｉｅｌｄ阈值冲击危险性评价指数冲击危险等级ＤＲＳɤ１１无１＜ＤＲＳ＜３２弱３ɤＤＲＳ＜５３中等ＤＲＳȡ５４强３．３㊀采动应力场与震动场（ＭＳ）耦合冲击危险性评价模型㊀㊀采动应力场与震动场耦合冲击危险性评价模型为ＤＭＳ＝ａ３γσ＋ｂ３ｇσ＋ｃ３γθ＋ｄ３ｇθ（１２）㊀㊀其中：ＤＭＳ为采动应力场与震动场耦合冲击危险性评价指数；ａ３，ｂ３，ｃ３，ｄ３分别为应力异常指数，应力梯度指数，波速异常指数，波速梯度指数的权重系数，不同矿井取值不同㊂采动应力场与震动场耦合的冲击危险性指数取值与冲击危险等级之间的关系见表１１㊂３．４㊀多场耦合（ＲＭＳ）冲击危险性动态评价模型冲击地压发生的本质是煤岩体具有的冲击能量８２１邓志刚等：动静载作用下煤岩多场耦合冲击危险性动态评价技术２０２１年第４期超过围岩吸收能量的极限㊂应力场可以表现煤岩体表１１㊀采动应力场与震动场耦合冲击危险性等级划分标准Ｔａｂｌｅ１１㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｃｏｕｐｌｉｎｇｏｆｍｉｎｉｎｇｓｔｒｅｓｓｆｉｅｌｄａｎｄｖｉｂｒａｔｉｏｎｆｉｅｌｄ阈值冲击危险性评价指数冲击危险等级ＤＭＳɤ１１无１＜ＤＭＳ＜３２弱３ɤＤＭＳ＜５３中等ＤＭＳȡ５４强未受扰动的地应力场和受采动影响而形成的采动应力场，是煤岩体承受应力的状态量㊂震动场主要表现煤岩体无法承受外部高应力差作用发生损伤破坏，在此过程中以震动形式释放出能量的时空域，可以表现煤岩体积蓄能量的过程㊂冲击地压的不仅发生在高应力区，也发生在煤岩体由低应力区向高应力区转化的过程中，采用煤岩体多场耦合的方法可以充分全面评价监测区域的冲击危险性㊂基于上述对ＲＭ耦合㊁ＲＳ耦合和ＭＳ耦合的冲击危险性评价模型，构建煤岩体多场耦合（ＲＭＳ）冲击危险性动态评价模型㊂冲击危险性指数算法如下Ｄ＝ＤＲＭ＋ＤＲＳ＋ＤＭＳ（１３）多场耦合冲击危险性评价指数Ｄ与冲击危险性等级的对应关系见表１２㊂表１２㊀多场耦合（ＲＭＳ）冲击危险性等级划分标准Ｔａｂｌｅ１２㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇ阈值冲击危险性评价指数冲击危险等级Ｄɤ５１无５＜Ｄ＜１０２弱１０ɤＤ＜１５３中等Ｄȡ１５４强４㊀工程应用选取典型冲击地压矿井３１１２０２工作面为现场，开展相关应用㊂４．１㊀工作面概况３１１２０２工作面是该矿井１２盘区第２个回采工作面，是首个沿空回采工作面，位于１２盘区北部，为３１１２０１接续工作面，东部以１２盘区辅运大巷为界，西部至１２盘区西部边界，南部为实体煤，北部为正在回采的３１１２０１工作面，保护煤柱宽度６ｍ㊂该工作面采用走向长壁综合机械化一次采全高采煤法，采高５．２５ｍ，工作面倾斜长度２９９ｍ，走向长度３１４０ｍ，全部垮落法管理顶板，两回采巷道采用液压支架进行超前支护㊂工作面布置如图１１所示㊂图１１㊀３１１２０２工作面布置Ｆｉｇ．１１㊀ＬａｙｏｕｔｏｆＮｏ．３１１２０２ｍｉｎｉｎｇｆａｃｅ经鉴定，３－１煤及其顶底板均具有弱冲击倾向性，３－１煤层冲击危险等级为中等冲击危险㊂３１１２０２工作面所在地层构造形态总体为一向北西倾斜的单斜构造，倾向３００ʎ ３２０ʎ㊁倾角１ʎ ３ʎ，地层产状沿走向及倾向均有一定变化，沿走向发育有宽缓的波状起伏㊂３１１２０２工作面受ＤＦ１９㊁ＤＦ１８㊁Ｆ２２㊁Ｆ２４断层影响较大，其中ＤＦ１９断层影响最为显著，该断层走向长度约１２００ｍ，落差６．５ １０．０ｍ，预计影响３１１２０２工作面走向长度５６０ｍ，对生产过程中的冲击地压灾害影响最大㊂３１１２０２工作面主要断层情况见表１３，３１１２０２工作面煤层顶底板结构特征见表１４㊂表１３㊀３１１２０２工作面断层特征Ｔａｂｌｅ１３㊀ＦａｕｌｔｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆＮｏ．３１１２０２ｍｉｎｉｎｇｆａｃｅ断层走向／（ʎ）倾向／（ʎ）倾角／（ʎ）性质落差／ｍＤＦ１８３１２４２７０正断层０ ５．０ＤＦ１９２９６２６４９正断层６．５ １０．０Ｆ２２２８５１５３０正断层１．１Ｆ２４３５７９０４６正断层０．３表１４㊀３１１２０２工作面煤层顶底板结构特征Ｔａｂｌｅ１４㊀ＳｔｒｕｃｔｕｒａｌｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｃｏａｌｓｅａｍｒｏｏｆａｎｄｆｌｏｏｒｉｎＮｏ．３１１２０２ｍｉｎｉｎｇｆａｃｅ顶底板岩性厚度／ｍ平均厚度／ｍ基本顶细粒砂岩９．２５ １９．７０１５．８４直接顶砂质泥岩２．２８ １２．８５８．５０直接底砂质泥岩４．６９ １２．９９７．６８基本底细粒砂岩５．２１ ２１．４５１４．８２４．２㊀多场耦合冲击危险性动态评价原岩应力场包括重力场和构造应力场，通过地应力测试及三维反演可得到㊂采动应力场通过应力在线监测系统监测得到㊂在３１１２０２回风巷生产帮安设应力在线监测系统，距离开切眼６０ｍ生产帮侧９２１２０２１年第４期煤炭科学技术第４９卷安设第１组应力测点，之后每隔４０ｍ安设一组，共布置１０组，主要监测工作面超前３００ｍ范围内回风巷一侧煤体采动应力分布情况；每组垂直于煤壁施工２个ø４４ｍｍ应力钻孔，孔深分别为１１ｍ和１６ｍ，钻孔间距１ｍ㊂当测点与工作面距离小于３０ｍ时开始回撤，随着工作面回采，测点依次前移，直至回采结束㊂测点布置方案如图１２所示㊂收集了３１１２０２工作面２０１９年５月至１１月的回风巷采动应力监测数据，并进行了分析和应用㊂图１２㊀应力在线监测测点布置Ｆｉｇ．１２㊀Ｌａｙｏｕｔｏｆｍｅａｓｕｒｉｎｇｐｏｉｎｔｓｆｏｒｏｎｌｉｎｅｓｔｒｅｓｓｍｏｎｉｔｏｒｉｎｇ工作面震动场数据由ＡＲＡＭＩＳＭ／Ｅ微震监测系统监测得到㊂３１１２０２工作面测站布置情况如图１３所示㊂井下布置４台微震拾震器（编号Ｓ９至Ｓ１２）和６个移动式监测探头（编号Ｔ１９至Ｔ２４），地面布置１台编号为Ａ２矿震测站组成联合监测网，对工作面进行全面监测㊂图１３㊀３１１２０２回采工作面微震监测系统测站布置Ｆｉｇ．１３㊀ＡｒｒａｎｇｅｍｅｎｔｏｆｔｈｅｓｔａｔｉｏｎｏｆｍｉｃｒｏｓｅｉｓｍｉｃｍｏｎｉｔｏｒｉｎｇｓｙｓｔｅｍｉｎＮｏ．３１１２０２ｍｉｎｉｎｇｆａｃｅ选取３１１２０２工作面回采至距离ＤＦ１９断层１０ｍ时，开始揭露ＤＦ１９断层时以及揭露ＤＦ１９断层２９５ｍ时，３个时间节点３１１２０２工作面超前１５０ｍ范围内的冲击危险性评价情况㊂回采至距离ＤＦ１９断层１０ｍ时，计算原岩应力场冲击危险性指数Ｒ，３－１煤层平均采深６２０ｍ，Ｒ１＝３；工作面距离断层１０ｍ，Ｒ２＝４；工作面前方无背斜或向斜，Ｒ３＝１；该区域未发生过冲击地压，Ｒ４＝１㊂根据式（９）计算得到Ｒ＝２．３㊂按照式（１）㊁式（２）计算得到γσ＝２．３，ｇσ＝３．３㊂３１１２０２工作面最大主应力与水平应力比约为１，取ａ１＝ｂ１＝ｃ１＝０．５，根据式（１０）计算得到ＤＲＭ＝４．０㊂同理计算出，揭露断层时ＤＲＭ＝５．０；揭露断层２９５ｍ时ＤＲＭ＝４．０㊂回采至距离ＤＦ１９断层１０ｍ时，Ｒ＝２．３；根据式（３）㊁（４）计算得到γθ＝３．４，ｇθ＝５．０；工作面最大主应力与水平应力比约为１，取ａ２＝ｂ２＝ｃ２＝０．５，根据式（１１）计算得到ＤＲＳ＝５．４㊂同理计算出，揭露断层时ＤＲＳ＝６．５；揭露断层２９５ｍ时ＤＲＳ＝４．５㊂回采至距离ＤＦ１９断层１０ｍ时，根据式（１）㊁式（２）计算得到γσ＝２．３，ｇσ＝３．３；根据式（３）㊁式（４）计算得到γθ＝３．４，ｇθ＝５．０㊂３１１２０２工作面最大主应力与水平应力比约为１，取ａ３＝ｂ３＝ｃ３＝ｄ３＝０．５，根据式（１２）计算得到ＤＭＳ＝７．０㊂同理计算出，揭露断层时ＤＭＳ＝９．２；揭露断层２９５ｍ时ＤＭＳ＝６．２㊂根据式（１３）计算得到，回采至距离ＤＦ１９断层１０ｍ时Ｄ＝１６．４，具有强冲击危险性；揭露断层时Ｄ＝２０．７，具有强冲击危险性；揭露断层２９５ｍ时Ｄ＝１４．７，具有中等冲击危险性㊂４．３㊀评价结果验证与对比依据３１１２０２工作面回采期间超前工作面３００ｍ范围内微震监测数据㊁钻孔应力监测数据平均值验证评价结果㊂在距离ＤＦ１９断层１０ｍ附近，当天微震释放总能量约为１９３００Ｊ，单次最大能量为７０００Ｊ，微震事件２６次；揭露断层时，当天微震释放总能量约为２２３００Ｊ，单次最大能量约为９０００Ｊ，微震事件１７次；揭露断层２９６ｍ附近，当天微震释放总能量约为７７００Ｊ，单次最大能量约为６０００Ｊ，微震事件６次㊂从微震事件能量㊁频次中可以看出冲击危险性降低㊂在距离断层１０ｍ附近㊁揭露断层附近以及揭露断层２９６ｍ附近选取３个煤层钻孔应力测点，３个测点应力监测数据如图１４所示㊂工作面推进过程中煤层应力数值增加，强冲击危险区域应力始终高于中等冲击危险区域㊂微震和煤层钻孔应力监测数据验证了冲击危险性动态评价结果的合理性㊂图１４㊀煤层钻孔应力监测数据平均值Ｆｉｇ．１４㊀Ａｖｅｒａｇｅｖａｌｕｅｓｏｆｓｔｒｅｓｓｍｏｎｉｔｏｒｉｎｇｄａｔａｓｉｎｃｏａｌｓｅａｍ０３１。

ADV ANCES IN ATMOSPHERIC SCIENCES,VOL.35,NOVEMBER2018,1372–1380•Original Paper•Predictable and Unpredictable Components of the Summer EastAsia–Pacific Teleconnection PatternXiaozhen LIN1,2,Chaofan LI∗3,Riyu LU1,2,and Adam A.SCAIFE4,51State Key Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing100029,China2University of Chinese Academy of Sciences,Beijing100029,China3Center for Monsoon System Research,Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing100029,China4Met Office Hadley Centre,FitzRoy Road,Exeter EX13PB,UK5College of Engineering,Mathematics and Physical Sciences,University of Exeter,Exeter,Devon EX44QF UK(Received17December2017;revised21April2018;accepted06June2018)ABSTRACTThe East Asia–Pacific(EAP)teleconnection pattern is the dominant mode of circulation variability during boreal sum-mer over the western North Pacific and East Asia,extending from the tropics to high latitudes.However,much of this pattern is absent in multi-model ensemble mean forecasts,characterized by very weak circulation anomalies in the mid and high latitudes.This study focuses on the absence of the EAP pattern in the extratropics,using state-of-the-art coupled sea-sonal forecast systems.The results indicate that the extratropical circulation is much less predictable,and lies in the large spread among different ensemble members,implying a large contribution from atmospheric internal variability.However, the tropical–mid-latitude teleconnections are also relatively weaker in models than observations,which also contributes to the failure of prediction of the extratropical circulation.Further results indicate that the extratropical EAP pattern varies closely with the anomalous surface temperatures in eastern Russia,which also show low predictability.This unpredictable circulation–surface temperature connection associated with the EAP pattern can also modulate the East Asian rainband.Key words:EAP pattern,circulation,seasonal forecast,surface temperature,eastern RussiaCitation:Lin,X.Z.,C.F.Li,R.Y.Lu,and A.A.Scaife,2018:Predictable and unpredictable components of the summer East Asia–Pacific teleconnection pattern.Adv.Atmos.Sci.,35(11),1372–1380,https:///10.1007/s00376-018-7305-5.1.IntroductionThe East Asia–Pacific(EAP)teleconnection pattern (Huang and Sun,1992),which is also referred to as the Pacific–Japan pattern(Nitta,1987),dominates the interan-nual variability of summer climate over the western North Pacific and East Asia(WNP-EA).It features anomalous zon-ally elongated centers that appear alternately between the equator and high latitudes in the meridional direction over the WNP-EA(Kosaka and Nakamura,2006;Lu and Lin, 2009).The circulation anomalies associated with the EAP pattern exhibit a meridional wave-like distribution with alter-nate cyclonic and anticyclonic anomalies(e.g.,Kosaka and Nakamura,2006,Fig.4;Lu and Lin,2009,Fig.2).The EAP pattern links closely with variation of the circulation not only over the subtropical WNP,manifesting as a change in the WNP subtropical high(Lu and Dong,2001;Lu,2004), but also over the midlatitude WNP-EA.This teleconnection ∗Corresponding author:Chaofan LIEmail:lichaofan@ pattern modifies water vapor transport and significantly influ-ences summer rainfall over East Asia.Anomalous convection around the Philippine Sea is gen-erally recognized as one of the wave sources for the EAP pat-tern,which propagates northward in the lower troposphere (Kawamura et al.,1996;Lu,2001;Kosaka and Nakamura, 2006).Nevertheless,the wave activity excited by the anoma-lous convection around the Philippine Sea appears mainly in the low-latitude regions to the south of35◦N(Kosaka and Nakamura,2006).In view of the remarkable circulation anomalies over midlatitude regions of the WNP-EA associ-ated with the EAP teleconnection pattern,it suggests that the underlying physical mechanisms may be related to Rossby wave propagation into the midlatitude regions(e.g.,Scaife et al.,2017),but the mechanisms behind the EAP pattern are not fully understood.As for the prediction of the EAP teleconnection pattern, forecast models generally capture the component associated with the tropical air–sea interactions(Kosaka et al.,2012, 2013;Li et al.,2012,2014a).These good forecasts man-ifest mainly over the subtropical WNP as variation of the©Institute of Atmospheric Physics/Chinese Academy of Sciences,and Science Press and Springer-Verlag GmbH Germany,part of Springer Nature2018NOVEMBER2018LIN ET AL.1373WNP subtropical high(Wang et al.,2009;Li et al.,2012). In the lower troposphere,high prediction skill shown by cur-rent coupled forecast systems is found over the WNP south of Japan for the zonal wind(Li et al.,2012).However,the pre-diction skill decreases rapidly northward to the midlatitude regions,particularly north of35◦N.In particular,the lower-tropospheric circulation related to the WNP subtropical high shows significant correlation with an anomalous cyclone or anticyclone over the midlatitude regions in observations,but no notable anomalies in the ensemble mean model output, as illustrated in Li et al.(2012).This implies either that this high-latitude component is simply unpredictable or that cur-rent coupled models may not capture the observed midlati-tude components of the EAP pattern.It further suggests that different(unpredictable)mechanisms are responsible for the midlatitude circulation associated with the EAP pattern,in addition to the tropical forcing.It is crucial to gain a better understanding of the underlying mechanism for the variation of the midlatitude circulation associated with the EAP tele-connection pattern,since this midlatitude circulation signifi-cantly affects the summer climate over East Asia.The summer of1998is special for several aspects.First, the EAP teleconnection pattern is clear in this summer(Fig. 1a).Second,associated with this EAP pattern,there is a strong anticyclonic anomaly over the WNP,which is typi-cal for the El Ni˜n o decaying summer and leads tofloods in East Asia(e.g.,Wang et al.,2000;Xie et al.,2016;Li et al., 2017).Finally,and most importantly,associated with strong tropical signals,the climate anomalies of this summer,at least in the tropics and subtropics,show high prediction skill(Li et al.,2012;MacLachlan et al.,2015).Therefore,this summer provides a good opportunity for us to investigate tropical–extratropical interaction.For this purpose,in this study we analyze the outputs of state-of-the-art coupled seasonal fore-cast systems,and compare the model results with observa-tions.The organization of this paper is as follows:Section2 introduces the data used.Section3analyzes the prediction of the EAP teleconnection pattern in1998and the related responses of summer prediction for surface temperature and precipitation.Section4provides a summary and discussion.2.Observed datasets and retrospective fore-castsWe use the monthly mean National Centers for Envi-ronmental Prediction–National Centers for Atmospheric Re-search reanalysis data(Kalnay et al.,1996)from1979to 2015in summer(June–July–August).We also use precipi-tation data from the Global Precipitation Climatology Project dataset(Adler et al.,2003),from1979to2015.Here,we only focus on the interannual variation and exclude the decadal or long-term component by removing a nine-year running aver-age.Two sets of retrospective forecast(hindcast)data are examined in this study.Thefirst is from the Ensembles-Based Predictions of Climate Change and their Impacts(EN-SEMBLES)seasonal forecast project(Van Der Linden and Mitchell,2009),which was an EU-funded integrated predic-tion project based onfive coupled atmosphere–ocean–land global models.It comprises hindcasts for the46-year period of1960–2005.For each year,seasonal forecasts were initial-ized on1May and run for seven months with nine members for each model.Therefore,there are45members for each year.We also use output from the Met Office Global Sea-sonal forecast system5(GloSea5)(MacLachlan et al.,2015). Hindcasts from GloSea5increase the ensemble size in our study;plus,GloSea5exhibits good prediction skill for East Asian precipitation and the WNP subtropical high(MacLach-lan et al.,2015;Li et al.,2016).The model used in this forecast system is the Hadley Center Global Environmental Model version3,with a horizontal resolution of0.83◦×0.56◦for the atmosphere and0.25◦for the ocean and sea-ice model. The retrospective forecasts in GloSea5were performed for each summer from1992to2011,with24members each year.The two hindcasts show similarity in the simulation of the EAP teleconnection pattern.The temporal correlation coeffi-cient for the EAP index[defined by Huang(2004)]between the ENSEMBLES(GloSea5)system and observations during 1960–2005(1992–2011)is0.57(0.50).Therefore,we com-bine all the ensemble members for1998in these two forecast systems together to investigate the predictability,with suffi-cient ensemble members(69)and using the overlapping hind-cast period(1992–2005)as climatology,and the anomalies are calculated by removing the climatology of the ensemble mean.3.Results3.1.Prediction of the EAP teleconnection pattern in1998Figure1shows the850-hPa horizontal wind anomalies in observations and model predictions in1998.In observations, the wind anomalies over the WNP-EA present a clear merid-ional teleconnection pattern with three centers along East Asia(Fig.1a).There are two anomalous anticyclones over the Philippine Sea and Northeast Asia,and one anomalous cyclone over East Asia.The multi-model ensemble(MME) mean result,by contrast,shows horizontal wind anomalies in the midlatitude regions that are small compared with the anti-cyclonic anomalies over the subtropical WNP(Fig.1b).The MME mean result only predicts the anticyclonic anomalies over the subtropical WNP.The extratropical part of the EAP teleconnection pattern is not well predicted in the ensemble mean,despite the strong tropical forcing in the year of1998. There are two possible causes of this difference:the extra-tropical EAP nodes could simply be unpredictable,or there could be model errors preventing its simulation in response to tropical forcing.To assess this further we examine the model integration members to determine if they can simulate the ex-tratropical part of the EAP pattern via internal unpredictable variability in the model.1374PREDICTION OF SUMMER EAST ASIA-PACIFIC PATTERN VOLUME35 Fig.1.850-hPa horizontal wind anomalies in the(a)observation and(b)MME mean posite850-hPa horizontal wind anomalies for(c)negative integration members and(d)positive integration membersin1998(units:m s−1).The“A”and“C”represent anticyclonic and cyclonic circulation anomalies,respec-tively.The green box indicates the domain of the midlatitude component of the EAP teleconnection pattern(40◦–50◦N,90◦–150◦E).According to the distinct difference of850-hPa horizon-tal wind anomalies between observations and the MME mean prediction,the zonal wind anomalies over(40◦–50◦N,110◦–150◦E)is defined as the midlatitude zonal wind index.To avoid the influence of the anticyclonic anomalies over the subtropical WNP,only the north part of cyclonic anomalies is adopted to define the index,for further investigation of the teleconnection between midlatitude zonal wind and the tropical part of the EAP pattern.A positive(negative)zonal wind index represents westerly(easterly)wind anomalies in the midlatitudes.In total,11/69(14/69)integration mem-bers have zonal wind indexes that are smaller(larger)than a standard deviation of−0.8(0.8).Figures1c and d show the composite spatial distribution of850-hPa horizontal wind anomalies for these negative and positive integration mem-bers.The wind anomalies for negative integration members (Fig.1c)show a tripolar pattern of anomalous centers,re-sembling well the observed wind anomalies(Fig.1a).It indi-cates that the negative index integration members can capture the EAP pattern over the WNP-EA.In contrast,the anticy-clonic anomaly over the subtropical WNP in positive integra-tion members(Fig.1d)extends northward to the midlatitudes,associated with a cyclonic anomalous center to the north of 50◦N,which is opposite to that in negative index integrations and observations in the midlatitude regions.The opposite anomalous circulation patterns between negative and positive integration members therefore lead to the weak circulation anomalies in midlatitude regions for MME mean prediction (Fig.1b),suggesting that large spread exists among model in-tegration members and that the extratropical part of the EAP pattern is reproduced but may not be predictable.A scatterplot of zonal wind indexes from the69integra-tion members in1998is shown in Fig.2(y-axis).It can be seen that zonal wind indexes are quite dispersed,with about half of the indexes being negative and the other half posi-tive.The zonal wind index in the MME mean prediction is small(0.003m s−1),while the zonal wind index in observa-tions is−1.40m s−1.The spread of the ensemble members does include the observed value.In comparison,the subtrop-ical component of the EAP pattern in1998,represented by the WNP monsoon index(WNPMI)following Wang and Fan(1999)[the850-hPa zonal wind anomalies between (5◦–15◦N,100◦–130◦E)and(20◦–30◦N,110◦–140◦E)],is well predicted by the ensemble members,as shown in Fig.2NOVEMBER 2018LIN ET AL.1375Fig.2.Scatterplot for the anomalies of the midlatitude zonal wind index (y -axis,as shown by the green box in Fig.1)and WNPMI (x -axis)from 69integrations in 1998.Black and grey dots represent the indexes in the MME mean and observations,respectively.Units:m s −1.(x -axis).Almost all members are negative,indicating that the models are able to simulate and predict the anomalous anti-cyclonic circulation over the subtropical WNP in 1998.The WNPMI is negative both in the observations and MME mean prediction,and the intensity of circulation anomalies in the MME mean prediction (−5.10m s −1)is close to that in ob-servations (−5.87m s −1).This is in accordance with the high prediction skill of the anticyclonic circulation anomaly in the subtropical WNP (Kosaka et al.,2012;Li et al.,2012),which to a large extent contributes to the prediction skill of the EAP index shown previously.However,the correlation coe fficient of these ensemble members between the zonal wind index and WNPMI is quite low (0.12),implying a largely indepen-dent variation of these two components of the EAP pattern in model predictions in 1998,regardless of strong tropical forc-ing.Further evidence of a lack of predictability in the mid-latitude component of the EAP pattern can be found from hindcast years besides 1998.The correlation coe fficient be-tween the predicted and observed zonal wind indices is only 0.21(0.23)for all hindcast years of ENSEMBLES (GloSea5).Similarly,the interannual variance of the ensemble mean pre-diction in ENSEMBLES (GloSea5)is 0.01(0.03)m 2s −2,which is much lower than that in observations (0.56m 2s −2for 1960–2005and 0.43m 2s −2for 1992–2011),while in all ensemble members,concatenated after subtracting the clima-tology of individual models from 1992to 2005,it is 0.42m 2s −2,which is similar to that in observation.These results confirm that little prediction skill exists in the midlatitude circulations of the EAP pattern,even though the pattern is realistically simulated by the model.However,there is also some evidence for model error in the teleconnection betweenthe midlatitude zonal wind and the WNP subtropical high:the correlation coe fficient between the zonal wind index and the WNPMI in all ensemble members from all hindcast years (1992to 2005)is 0.07,which is lower than that in observa-tions (0.52for 1979–2015),but still exceeds the 95%confi-dence level according to the Student’s t -test because of the large sample size.This implies that while the models can reproduce an EAP pattern through internal variability,they are not able to reproduce well the tropical–mid-latitude tele-connection,and an improvement in prediction skill may be expected if a better teleconnection to the variation in mid-latitude circulation associated with the EAP pattern can be reproduced.Similar situations exist in the five individual models of ENSEMBLES,and all models show significant inter-member variability (uncertainty of the prediction)for the midaltitude circulation related to the variations in the WNP subtropical high (Li et al.,2012,Fig.11).In addition,none of these models shows good prediction skill of the zonal wind index;correlations range between −0.11and 0.21.Di fferences in model performance might lie in the di fferent parameteriza-tions or residual internal variability among di fferent models and are not discussed further in this study.3.2.Response of surface temperature in eastern Russia Consistent with the atmospheric circulation,the surface temperature anomalies also show a meridional wave-like pat-tern with negative anomalies along the mei-yu rainband and positive anomalies over eastern Russia and the subtropical WNP (Fig.3a).The positive surface temperature anomalies averaged over the land area of eastern Russia (50◦–70◦N,120◦–160◦E)reach 1.16◦C.For the MME prediction,the anomalies are quite weak and even have the opposite sign in the midlatitude regions.The averaged temperature anomaly in eastern Russia is only −0.33◦C,suggesting a poor predic-tion of the observed temperature variation.Furthermore,the surface temperature anomalies over the midlatitude WNP-EA also demonstrate large contrast among di fferent groups of ensemble members,as shown in Fig. 3.For negative index cases (Fig.3c),the surface temperature anomalies show a relatively similar meridional wave-like pat-tern to observations (Fig 3a).In contrast,for positive integra-tion members (Fig.3d),the surface temperature anomalies to the north of 30◦N are opposite to those for negative in-tegration members and observations,with negative anoma-lies in eastern Russia and positive anomalies along 40◦N of the WNP-EA.The surface temperature anomalies around the Philippine Sea are positive for both integration groups,cor-responding to a good capability of models in predicting trop-ical temperatures.In general,the integration members that reproduce easterly (westerly)anomalies over the midlatitude regions,tend to predict the EAP teleconnection pattern well (badly),and predict positive (negative)surface temperature anomalies in eastern Russia and negative (positive)anoma-lies along the mei-yu rge spread in surface tem-perature among the integrations is found over the midlatitude regions.1376PREDICTION OF SUMMER EAST ASIA-PACIFIC PATTERN VOLUME35 Fig.3.As Fig.1but for surface temperature anomalies(units:◦C).The green box indicates the domain ofeastern Russia(50◦–70◦N,120◦–160◦E).An intimate relationship between the midlatitude circula-tion and surface temperature is further revealed via a scatter-plot of surface temperature in eastern Russia and zonal windindex among all model integrations(Fig.4a).Here,the sur-face temperature in eastern Russia is defined by the tempera-ture anomalies averaged over the land area in the region(50◦–70◦N,120◦–160◦E).This temperature index and the zonalwind index exhibit a negative relationship,with a correla-tion coefficient of−0.54,which exceeds the99%confidencelevel according to the Student’s t-test.A positive(negative)surface temperature anomaly in eastern Russia correspondsto an easterly(westerly)anomaly in the midlatitude WNP.Furthermore,the850-hPa wind anomalies regressed onto thetemperature index(Fig.4b)mainly appear over the midlati-tude regions north of30◦N,with an anomalous anticyclone ineastern Russia and a relatively weaker cyclonic anomaly overthe WNP-EA.The wind anomalies in the tropics are weak,suggesting that the surface temperatures in eastern Russia areroughly independent of the tropical anomalies in the modelintegrations.The relationship between the midlatitude zonal windanomalies and surface temperature anomalies in eastern Rus-sia not only exists among models integrations,but also inobservations,as shown in Fig.5.The correlation coefficientbetween the temperature index and zonal wind index for ob-servations during1979–2015(Fig.5a)is−0.60,also exceed-ing the99%confidence level according to the Student’s t-test.This is close to that in the model integrations,suggesting a re-alistic relationship in the model.Moreover,the850-hPa windanomalies related to the surface temperature in eastern Rus-sia(Fig.5b)resemble well those for models integrations inthe extratropical regions(Fig.4b).In the tropical/subtropicalWNP,on the other hand,there is an anticyclonic anomaly inobservations,which is absent in model integrations.This dif-ference between the observations and integrations is consis-tent with the idea that the extratropical part of the EAP is rel-atively independent of the tropical part in model predictionsat least.Given the close relationship between surface temper-ature in eastern Russia and midlatitude circulation,the limita-tion of prediction for the extratropical component of the EAPpotentially leads to the poor prediction of surface temperaturein eastern Russia,and the surface temperature in this regionin turn may enhance the spread of midlatitude zonal windsthrough modulating the meridional gradient of temperatures.3.3.Influence on the prediction of East Asian summerrainfallInterannual variation of East Asian summer rainfall issignificantly affected by the circulation anomalies associatedwith the EAP teleconnection pattern,particularly the subtrop-ical components(Lu and Dong,2001;Zhou and Yu,2005;Yang et al.,2010;Kosaka et al.,2012;Li et al.,2012).ThisNOVEMBER 2018LIN ET AL.1377Fig.4.(a)Scatterplot for the anomalies of temperature index (y -axis)and zonal wind index (x -axis)from 69integrations.The temperature index is defined by surface temperature anomalies averaged over the land area in the region (50◦–70◦N,120◦–160◦E),as shown by the green box in Fig.3.The value in the top-right corner of the diagram is the correlation coe fficient be-tween them.(b)850-hPa horizontal wind anomalies regressed onto the temperature index.Shading indicates regions exceed-ing the 95%significance level.Units:m s −1.section further explores the contribution from midlatitude cir-culation anomalies described in the preceding section to the East Asian summer rainfall.Figure 6shows the distribution of precipitation anomalies in 1998.Corresponding to the atmospheric circulation (Fig.1),the precipitation also demonstrates a meridional wave-like pattern in observations (Fig.6a),with positive anomalies along the East Asian mei-yu rainband and negative anoma-lies around the South China Sea,Philippine Sea and south of eastern Russia.The negative anomalies around the South China Sea and Philippine Sea result in an intensified WNP subtropical high (Fig.1a),which would further transfer more water vapor to East Asia and induce more rainfall along the East Asian mei-yu rainband.In addition,because of exces-sive water vapor transported by the midlatitude easterly wind (Fig.1a),more rainfall also appears around Northeast China,which resulted in serious flooding in the SonghuajiangandFig.5.As in Fig.4but for the observations from 1979to 2015.Nenjiang basin in that year (Li et al.,2014b).As the models generally predict the WNP subtropical high (Figs.1and 2),they predict well the associated rainfall in the subtropical WNP-EA regions,for both the MME mean and the ensemble members (Figs.6b–d).However,the MME mean result produces quite weak precipitation anomalies in the midlatitude WNP-EA,including the negative anomalies around the south of eastern Russia and positive anomalies around Northeast China (Fig.6b).Furthermore,although the models generally reproduce the positive rainfall anomalies along the East Asian mei-yu rainband,the large rainfall over the upper reaches of the Yangtze River basin,Korean Penin-sula and the Sea of Japan are also quite weak.The inability of the MME predictions in predicting the above precipitation anomalies connects closely to the lack of skill for the extra-tropical part of the EAP (Figs.6c and d).The precipitation anomalies in the negative integrations resemble well those in observations,especially in the midlatitude regions.The positive rainfall anomalies around the upper reaches of the Yangtze River basin,Korean Peninsula and the Sea of Japan are also successfully predicted in these integrations (Fig.6c).In contrast,in the positive integrations with westerly anoma-lies in the midlatitude regions,these positive precipitation anomalies together with the midlatitude anomalies do not ap-1378PREDICTION OF SUMMER EAST ASIA-PACIFIC PATTERN VOLUME35 Fig.6.As in Fig.3but for the precipitation anomalies(units:mm d−1).pear(Fig.6d),but show an opposite response to the observa-tions and the negative integrations.The difference between different categories of integra-tions demonstrate the impact from the midlatitude circulation (Fig.7).Corresponding to an easterly(westerly)anomaly, less(more)rainfall appears around the south of eastern Rus-sia and more(less)rainfall appears along the East Asian mei-yu rainband.These intimate relationships are detected not just in model integrations from1998,but also in all ensem-ble members concatenated after subtracting the climatology of individual models from all overlapping hindcast years and observations for all years from1979to2015.While the pre-cipitation anomalies in1998are largely modulated by the WNP subtropical high with strong tropical forcing,these sig-nificant relationships further suggest that larger differences in precipitation among integrations could still be anticipated along the East Asian mei-yu rainband,in other years with weak tropical forcing.In summary,the lack of skill in pre-dicting the midlatitude components of the EAP teleconnec-tion pattern suggests a considerable limitation in the seasonal prediction of East Asian summer rainfall,albeit with some potential improvement if modeled tropical teleconnections could be improved.4.ConclusionThis study focuses on the variation of midlatitude circu-lation associated with the EAP teleconnection pattern,based on seasonal forecasts from state-of-the-art coupled forecast systems.In association with strong tropical forcing,the EAP teleconnection pattern in1998,which is typically organized over the WNP-EA in observations,is not well predicted and instead shows quite weak anomalies in the extratropics.The predictions among different model integrations are further in-vestigated to reveal the decoupled tropical–extratropical pre-dictable patterns in models.A close relationship is detected between the variation of surface temperatures in eastern Russia and midlatitude circu-lation associated with the EAP pattern,not just among differ-ent model integrations,but also among all years in observa-tions.The integrations that predict positive(negative)surface temperature anomalies in eastern Russia tend to reproduce easterly(westerly)anomalies over the midlatitude regions. Similarly,anomalous easterly(westerly)winds tend to ap-pear over the midlatitude WNP/EA in the summer when the surface temperature is warm(cold)in eastern Russia.This coupled relationship increases the uncertainty and difficulty of the prediction of the extratropical component of the EAP pattern and the surface temperature in eastern Russia.Despite this,the midlatitude circulation anomalies asso-ciated with the EAP pattern do significantly modulate East Asian summer rainfall.The integrations predicted with east-erly(westerly)anomalies in the midlatitude WNP-EA tend to predict more(less)rainfall along the East Asian mei-yu rainband.As a result,the lack of skill for northern parts of the EAP suggest an important limit to seasonal prediction of。

基于多目标优化NSGA2改进算法的结构动力学模型确认赖文星;邓忠民;张鑫杰【摘要】传统结构动力学模型确认方法通常采用单目标优化,存在精度不足和稳定性差等缺点,难以满足实际工程需求.基于此,提出一种采用神经网络作为代理模型,建立以马氏距离和鲁棒性为不确定性量化指标的多目标优化模型,并将NSGA2多目标进化算法用于求解.针对NSGA2存在无法有效识别伪非支配解、计算效率低和解集质量较差等设计缺陷,提出一种基于支配强度的NSGA2改进算法INSGA2-DS.INSGA2-DS将支配强度引入非支配排序,采用新型拥挤距离公式和自适应精英保留策略,以提高收敛效率和解集质量.GARTEUR飞机算例的仿真结果表明,INSGA2-DS求解复杂工程问题时具有更好的收敛性和分布性,而考虑鲁棒性的结构动力学模型确认方法可以获得同时满足多种目标要求的Parcto解集,提高了模型确认的精度和稳定性.【期刊名称】《计算力学学报》【年(卷),期】2018(035)006【总页数】6页(P669-674)【关键词】NSGA2;模型确认;结构动力学;鲁棒性;多目标优化【作者】赖文星;邓忠民;张鑫杰【作者单位】北京航空航天大学宇航学院,北京100191;北京航空航天大学宇航学院,北京100191;北京航空航天大学宇航学院,北京100191【正文语种】中文【中图分类】TH212;O3131 引言多目标进化算法从20世纪90年代开始迅速发展，Deb等［1］提出第二代带精英保留策略的快速非支配排序算法NSGA2。

NSGA2采用快速非支配排序方法，基于拥挤距离的分布性方法和精英保留策略，凭借简单及高效等优点，广泛应用于科学计算和工程设计等领域。

Kollat等［2］将Epsilon支配概念引入 NSGA2，提出Epsilon-NSGA2算法；Zhang等［3］提出了基于分解的多目标进化算法MOEA／D，MOEA／D将多个目标分为若干组，再并行优化求解；Elhossini等［4］提出粒子群算法和进化算法的混合算法；Deb等［5］提出一种基于参考点的NSGA2算法，以提高高维优化能力；Shim等［6］将非支配排序与目标分解结合，以提高算法优化性能；Qiu等［7］提出用于多目标优化的自适应交叉差分演化算子。

第25卷第6期高压物理学报V o l.25,N o.6 2011年12月C H I N E S EJ O U R N A L O F H I G H P R E S S U R E P H Y S I C S D e c.,2011文章编号:1000-5773(2011)06-0508-06三维多物质弹塑性流体动力学E u l e r方法的并行算法研究及程序测试*马天宝1,费广磊1,张文耀2(1.北京理工大学爆炸科学与技术国家重点实验室,北京100081;2.北京理工大学计算机学院智能信息技术北京市重点实验室,北京100081)摘要:并行计算是解决爆炸与冲击问题大规模数值模拟最有效的手段之一㊂针对E u l e r方法并行程序设计的复杂性,阐述了三维多物质弹塑性流体动力学程序MM I C-3D并行设计的总体策略,基于消息传递接口(M P I)设计出相应的P MM I C-3D并行程序,并提出了一套实用的程序测试方案㊂结合聚能射流形成过程的数值模拟算例,在八节点的集群上测试了加速比㊁并行效率及可扩放性,分析了影响并行性能的因素㊂关键词:爆炸与冲击;E u l e r方法;并行计算;消息传递接口;程序测试中图分类号:O347;O358文献标识码:A1引言近年来,随着大规模科学与工程计算的需求,许多计算问题已经超出单机所能承受的能力范围,并行计算对于大规模科学与工程计算越来越重要[1]㊂目前,并行计算机的基本存储方式主要有共享存储与分布式存储两种㊂M P I(M e s s a g eP a s s i n g I n t e r f a c e) 消息传递接口是消息传递函数库的标准规范,是目前广泛使用的并行编程工具[2],M P I基于分布式存储,但同样适应于共享存储,具有移植性好㊁功能强大㊁效率高等多种优点㊂MM I C-3D(M u l t i-M a t e r i a l i nC e l l f o r3D)[3]是基于E u l e r型有限差分方法的用于爆炸与冲击问题仿真计算的三维多物质弹塑性流体动力学程序,能处理3种及3种以上物质混合格的界面计算问题,解决了三维E u l e r方法中多物质计算的难题,实现了对空中爆炸㊁密实介质中爆炸及聚能射流形成等典型的爆炸与冲击问题的数值模拟㊂在单机32位操作系统下,受限于计算机内存和计算速度,原有MM I C-3D 串行程序最多只能计算200万网格的问题,远远达不到工程和科研的需求,迫切需要将原有的串行程序改造为并行程序,以扩大计算规模,加快求解速度㊂并行程序设计不但包含了串行程序设计,而且还包含了更多富有挑战性的问题[4],由于并行程序需要通信㊁同步等操作,使得并行程序设计远比串行程序设计复杂得多㊂L a g r a n g e方法,无论采用显式或隐式差分格式,最后都会归结为代数或矩阵运算,对于这类运算都有现成的并行算法可用㊂采用E u l e r 方法,由于需要处理物质在网格间的输运问题,隐含在输运算法中的数据相关性及子区域间的关联性不易发现㊂本文针对E u l e r方法并行设计的复杂性,阐述了处理E u l e r输运算法中处理数据相关性的一种方法,以及挖掘子区域间关联性的过程㊂程序测试是程序开发的一个重要环节,考虑到并行程序的测试复杂性,将测试分为两个阶段,提出了一些实用的测试策略,缩短了整个程序的开发周期,并在八节点集群上测试了程序的并行性能㊂*收稿日期:2010-08-20;修回日期:2010-11-26基金项目:国家重点基础研究发展计划(2010C B832706);爆炸科学与技术国家重点实验室自主课题(Z D K T10-03b);国家自然科学基金(10972041)作者简介:马天宝(1981 ),男,博士,副教授,主要从事计算爆炸力学研究.E-m a i l:m a d a b a l@b i t.e d u.c n2 MM I C -3D 数学模型及数值方法介绍MM I C -3D 串行程序采用不考虑外力㊁外源和热传导,非守恒形式的E u l e r 流体弹塑性动力学偏微分方程组[5]㊂数值计算采用算子分裂格式,将上述非守恒形式的方程组分为L a g r a n g e 步和E u l e r 步进行计算,并在计算中按空间x ㊁y ㊁z 3个方向进行分裂㊂MM I C -3D 采用模糊界面方法,该方法是指在一个混合网格中,不区分物质界面;根据模糊方法计算体积比,把体积比作为模糊权重系数;对网格进行分类,不同类网格之间视为物质界面;对介质进行模糊排序,决定输运优先权和模糊输运表;根据模糊权重计算输运量;按模糊输运表进行输运;在建模和计算中应用模糊方法,故称为 模糊界面方法[6]㊂3 P MM I C -3D 并行算法实现的关键性问题P MM I C -3D (P a r a l l e l i z a t i o n f o rM u l t i -M a t e r i a l i nC e l l -3D )采用域分解并行策略,域分解是指把计算域分成若干子区域,一个处理器处理一个或多个子区域㊂采用域分解并行策略,P MM I C -3D 的并行算法设计主要应考虑如下问题:(1)如果原有串行算法有数据相关性,如何解除相关性;(2)采用计算域分区的并行方式,各子区域间关联性如何,即需要多少额外的网格储存临近子区域的信息㊂3.1 数据相关性分析MM I C -3D 程序采用欧拉型有限差分算法,分L a g r a n ge 步和E u l e r 输运步分别进行计算,使得当前计算网格最多受到周围26个网格的影响,这是能采用计算域分区方式对MM I C -3D 并行的有利条件,同时必须分析计算程序所有语句间的依赖关系,称之为相关分析(D e p e n d e n c y A n a l y s i s )㊂对于采用域分解策略的三维多物质流体弹塑性并行程序来说,在1个时间步内,在同1个空间三重循环下若满足:当前网格物理量的更新依赖于周围网格相关变量更新后的值,则该算法会存在数据相关性㊂用表达式表示为a ᶄi ,j ,k =f (a i ,j ,k ,a ᶄi ʃ1,jʃ1,k ʃ1)(1)其中a 的更新直接或间接依赖于周边网格a 更新后的值㊂采用E u l e r 方法的数值模拟,数据相关性一般出现在E u l e r 输运步上㊂模糊界面方法采用方向分裂 输运,3个方向的输运在1个空间三重循环下进行,当前网格的物理量的更新依赖于周边相关物理量更新后的值,更新后网格物理量影响周围网格相关量的更新,因此存在数据依赖性,且这种依赖关系影响到整个计算域㊂如何解除数据相关性,且保持原有的计算精度,要与具体算法结合起来㊂为消除P MM I C -3D 中E u l e r 输运步的数据相关性,当前网格输运采用相邻网格更新前的值,同时为了消除因此而带来过量输运的问题,将原有在1个空间三重循环下完成的3个方向的输运改为在3个空间三重循环下完成,即每个空间三重循环只进行1个方向的输运,3个方向的输运顺序随时间步交替变换㊂为考核因解除数据相关性而带来的精度影响,采用H a r i v e 和F l e t c h e [7-8]设计的测试精度的方法㊂该方法定义了L 1误差,其公式如下E =ði ,j ,k A (i ,j ,k )ΩF (i ,j ,k )t =T-F (i ,j ,k)e (2)式中:A(i ,j ,k )Ω为网格的体积,F (i ,j ,k )t =T为数值计算的网格介质体积分数,F (i ,j ,k )e为准确的网格介质体积分数㊂数值算例计算参数见表1,其结果为计算到400步的结果㊂由表1可以看出,并行算法的精度和原有串行算法的精度基本一致,说明所采用的解除数据相关性的策略是可行的㊂表1 计算参数和结果T a b l e 1 C a l c u l a t i o n p a r a m e t e r s a n d r e s u l t sC e l l n u m b e r S p a t i a l s t e pT i m e s t e p F l u i dv e l o c i t yEP a r a l l e l a l go r i t h m S e r i a l a l go r i t h m 50ˑ50ˑ500.10.1u x =0.5;u y =0.50.1640.162905 第6期 马天宝等:三维多物质弹塑性流体动力学E u l e r 方法的并行算法研究及程序测试3.2 子区域边界网格(层)数量的确定 子区域边界网格是用来储存临近子区域相关变量的额外网格㊂采用E u l e r 数值方法,子区域间的关联性,即子区域边界网格的数量取决于两个因素:(1)因算法本身所固有的因素,当前网格物理量依赖于周边网格物理量的更新;(2)当前网格物理量的更新需要周边网格的物理量㊂考虑到通信所占用的开销,子区域边界网格(层)的数量应该考虑以上两个因素所增加的网格(层)数的最小值㊂以一维E u l e r 输运步为例,说明子区域边界网格数量的确定过程㊂如图1(a )所示,其中u 为当前k 网格的速度值㊂k 网格的更新(输运)影响k +1网格的物理量,也就是说k +1网格的物理量依赖于k 网格和k +1网格物理量的更新(输运),即k 网格为k +1网格的依赖网格,k +1网格为k 网格的影响网格㊂因此若想保证图1(a )左端1网格更新正确,需要在计算域左侧增加1层网格,并参与计算更新(输运),如图1(a )的灰色虚网格㊂由于在实际的更新运算中,往往需要周边网格物理量的信息,因此考虑如下的差分格式u n +1k =(1-2r )u n k +r (u n k +1+u n k -1)(3)则k 网格更新需要k ㊁k +1㊁k -1网格的物理量㊂综合以上两种因素,对于一维E u l e r 输运步的运算来说,需要在计算域增加3层子区域边界网格,左边增加2层,右边增加1层,如图1(b)所示,其中左边灰色虚网格参与运算,两端的虚网格不参与运算更新㊂(a )E x t r a c e l l a d d e d c o n s i d e r i n g t h e f i r s t f a c t o r (b )E x t r a c e l l s a d d e d c o n s i d e r i n g tw o f a c t o r s 图1 一维E u l e r 输运步子区域边界虚网格确定过程F i g.1 T h e p r o c e s s o f e x t r a c e l l s a d d e d i nE u l e rm o d e l 4 P MM I C -3D 并行程序测试G.J .M ye r s 在他的名著‘软件的测试技巧“一书中给出测试的定义: 程序测试是为了发现错误而执行程序的过程 [9]㊂基于M P I 并行程序的测试与调试的主要困难在于:除了串行程序的所有问题之外,并行程序还会有一些其它的问题存在㊂具体体现在:(1)并行算法设计的复杂性,对于一个串行程序很容易实现的问题,并行实现起来可能就困难重重,潜在的算法逻辑错误不易发现;(2)多进程之间协同作业(任务的映射与分发),导致并行程序比串行程序难于驾驭;(3)基于M P I 的并行程序增加了通信㊁进程同步等操作,增加了程序潜在的风险,一些不当的操作可能会导致程序异常中断或死锁㊂考虑到基于M P I 并行程序的测试与调试的困难,把对P MM I C -3D 并行程序的测试分为2个阶段:阶段1,不依赖于实际的物理模型㊁测试分区对计算结果的影响;阶段2,设计合理的物理模型,测试计算结果是否符合物理规律㊂阶段1是阶段2的基础,只有在阶段1测试正确的基础上才能进行阶段2的测试㊂(a )2D g e o m e t r i cm o d e l (b )3D m o d e l 图2 聚能装药二维几何模型及三维模型图F i g .2 2D g e o m e t r i cm o d e l a n d 3D m o d e l o f s h a p e d c h a r ge 聚能射流算例的计算几何模型如图2所示,其中图2(a )为二维尺寸结构图,图2(b )为三维模型图㊂药柱直径为60mm ,高为90mm ㊂依据网格步长设计了4个算例,见表2㊂聚能射流的数值模拟涉及到的材料包括炸药㊁金属药型罩及空气3种介质㊂炸药采用B 炸药,金属罩采用45钢㊂爆轰产物采用J W L 状态方程;空气采用理想气体状态方程;对于金属材料,考虑其在高温㊁高压㊁高应变率下表现的动态行为,采用M i e -G r ün e i s e n 状态方程描述㊂起爆方式采用点起爆,并采用简单的燃烧模型模拟爆轰波在炸药中的传播过程㊂015 高 压 物 理 学 报 第25卷表2 射流算例模型T a b l e 2 M o d e l o f s h a p e d c h a r g e je t M o d e lC h a r g em a s s /(g )S p a t i a l s t e p/(m mˑm mˑm m )C e l ln u m b e r M o d e lC h a r g em a s s /(g )S p a t i a l s t e p/(m mˑm mˑm m )C e l ln u m b e rE x a m p l e 13401.00ˑ1.00ˑ1.0080ˑ80ˑ180E x a m p l e 33420.04ˑ0.04ˑ0.04227ˑ227ˑ480E x a m pl e 23440.06ˑ0.06ˑ0.06151ˑ151ˑ300E x a m pl e 43420.03ˑ0.03ˑ0.03301ˑ301ˑ600对于射流算例,阶段1的测试采用射流头部速度作为监测变量,监测精度为10-11m /s,算例1的分区方式为:3ˑ1ˑ1,1ˑ3ˑ1,1ˑ1ˑ3;算例2的分区方式为:1ˑ4ˑ1,1ˑ1ˑ4;算例3的分区方式为:2ˑ2ˑ2,1ˑ2ˑ4;算例4的分区方式为:2ˑ2ˑ8,2ˑ2ˑ6㊂测试表明,不同分区方式下的计算结果保持一致,表明P MM I C -3D 并行程序在网格数较多的情况下,分区方式不影响计算结果(算例4网格数为5436万)㊂图3展示了4种算例的三维射流图,从图3中可以看出,算例2㊁算例3及算例4的射流形状明显优于算例1,算例3和算例4射流形状差别不大㊂图4为4种算例的射流头部速度随时间的变化曲线,从图4中可以看出,随着网格数的增多,射流最大头部速度略有增加,算例2㊁算例3及算例4比较接近,三者最大头部速度分别为4.4㊁4.5和4.7k m /s ,比实验结果略小,而算例1最大头部速度仅为4.0k m /s㊂图3 32.51μs 时4种算例的三维数值模拟图F i g .3 T h r e e -d i m e n s i o n a l s i m u l a t i o n g r a p h s a t 32.51μs o f f o u r e x a m pl e s 图4 4种算例的射流头部速度随时间变化曲线F i g .4 T h e j e t t i p v e l o c i t y c h a n ge sw i t h t i m e 5 P MM I C -3D 并行性能测试并行程序除了满足分区方式不影响计算结果的最基本要求外,加速比㊁并行效率及可扩放性也是衡量并行程序质量的主要性能指标㊂P MM I C -3D 程序并行性能测试在自主定制的八节点集群上进行,每个节点包含两颗I n t e l 四核E 5620C P U ,主节点24G 内存,其余节点12G 内存㊂5.1 加速比及并行效率测试并行系统的加速比(S p e e d u p)是指对于一个给定的应用,并行程序的执行速度相对于串行程序的执行速度加快了多少倍,也称为 绝对加速 (A b s o l u t eS p e e d u p );对于给定问题,同一程序在单C P U 的运行时间除以在多个C P U 运行的时间,称为 相对加速 (R e l a t i v eS p e e d u p)㊂加速比除以处理机个数,称为并行效率㊂加速比及并行效率测试采用第4节中的射流测试算例中的算例2㊁算例3作为测试算例,二者的网格数分别为684万和2473万㊂射流测试中的算例2㊁算例3的加速比及并行效率如图5所示㊂从图5中可以看出:加速比随着进程数的增加而增加,用64进程时算例2和算例3的加速比可达到16倍和20倍;并行效率随着进程数的增多而降低,用64进程时算例2和算例3的并行效率只有25%和30%,这是由于进程数增多,通信开销所占的比重也会增加;一样的进程数下,加速比及并行效率随着网格数的增多而增大㊂115 第6期 马天宝等:三维多物质弹塑性流体动力学E u l e r 方法的并行算法研究及程序测试图5 加速比及并行效率F i g .5 T h e s p e e d u p a n de f f i c i e n c y ve r s u s t h en u m b e r of p r o c e s s o r s 5.2可扩放性测试图6 可扩放性折线F i g .6 S c a l a b i l i t y可扩放性是指在确定的应用背景下,计算机系统(或算法或编程等)的性能随处理器的增加而按比例提高的能力㊂可扩放性是和并行算法以及并行计算机体系结构放在一起讨论的,某个算法在某个机器上的可扩放性反映了该算法是否能有效利用不断增加的C P U 的能力㊂采用射流算例作为测试算例,其结果如图6所示,计算域为10c mˑ10c mˑ20c m ㊂对于不同的进程数,每个进程分配的网格数固定为100万㊂测试的进程数如图6横轴所示,纵轴为计算1000个时间步的总时间㊂理想的可扩放性折线应该是一条平行于横轴的直线㊂由图6可知:随着进程数的增多,平均每个进程处理固定网格数的时间逐渐增加,64进程下处理时间是单进程下处理时间的2.8倍㊂5.3 影响并行性能的因素图7 通信时间在总时间的百分比F i g .7 T h e p e r c e n t a ge of c o mm u n i c a t i o n t i m e t o t h e t o t a l t i m e影响并行性能的因素主要包括通信所占用的开销以及负载不均衡所造成的同步等待时间等㊂图7为射流测试算例3在不同进程数下通信时间占总时间的百分比曲线㊂从图7中可以看出,通信时间在计算总时间的百分比随着进程数的增多而快速增大,64进程时达到48%㊂这是由于:(1)P MM I C -3D 中每一个子模块中都有诸如密度㊁质量㊁速度㊁能量及动量等变量更新,而这些变量的变化会影响下一个子模块的计算,因此需要数据通信;(2)每个节点采用千兆网络及千兆交换机连接,实测数据通信速度为35~45M ,网络通信延迟及带宽也影响通信㊂通信开销比重过大是影响并行性能的最重要因素㊂6 结 论(1)E u l e r 数值方法由于需要处理物质在网格间的输运问题,隐含在输运算法中的数据相关性及子区域间的关联性不易发现,因此并行算法设计中潜在的逻辑性错误不易发觉㊂215 高 压 物 理 学 报 第25卷(2)由于P MM I C -3D 中通信过多及自主定制的集群通信延迟及带宽的限制,通信开销比重过大,影响了P MM I C -3D 的并行性能㊂优化程序结构㊁减少通信量是改善P MM I C -3D 并行性能的重要手段㊂(3)从射流算例的模拟结果看,随着网格数的增多计算精度越来越高,数值模拟三维图片的分辨率越来越高,表明所采用的并行算法是合理的;P MM I C -3D 并行程序增大了计算规模,加快了计算速度,达到了并行程序设计的目的㊂R e f e r e n c e s:[1] D o n g a r r a J ,F o s t e r I ,F o xG ,e t a l .S o u r c e b o o k o f P a r a l l e l C o m p u t i n g [M ].T r a n s l a t e d b y MoZY ,C h e n J ,C a oXL .B e i j i n g :P u b l i s h i n g H o u s e o fE l e c t r o n i c s I n d u s t r y ,2005.(i nC h i n e s e )D o n ga r r a J ,F o s t e r I ,F o xG ,等.并行计算综论[M ].莫则尧,陈 军,曹小林,译.北京:电子工业出版社,2005.[2] M a l a r d J .M P I :A M e s s a g e -P a s s i n g I n t e r f a c eS t a n d a r d [R ].U K :T h eU n i v e r s i t y o fE d i nb u r g h ,1994.[3] X u eM Y ,N i n g JG.R e s e a rc ho n 3DE u l e r i a nN u m e r i c a l S i m u l a t i o n f o rE x p l o s i o n [J ].A c t aA r m a m e n t a r i i ,2006,27(6A ):129-132.(i nC h i n e s e)薛妙轶,宁建国.三维爆炸问题的E u l e r 数值方法研究[J ].兵工学报,2006,27(6A ):129-132.[4] C h e nGL ,A nH ,C h e nL .T h eA r c h i t e c t u r e o f P a r a l l e l C o m p u t e [M ].B e i j i n g :H i gh e rE d u c a t i o nP r e s s ,2004.(i nC h i n e s e )陈国良,安 虹,陈 崚,等.并行算法实践[M ].北京:高等教育出版社,2004.[5] M aTB ,W a n g C ,N i n g JG.M u l t i -M a t e r i a l E u l e r i a nF o r m u l a t i o n s a n dH y d r o c o d e f o r t h e S i m u l a t i o n o f E x p l o s i o n s [J ].C M E S :C o m p u t e rM o d e l i n g i nE n g i n e e r i n g &Sc i e n c e s ,2008,33(2):155-178.[6] N i n g JG ,C h e nL W.F u z z y I n t e r f a c eT r e a t m e n t i nE u l e r i a n M e t h od [J ].S c iC h i n aSe rE-E n g M a t e rS c i ,2004,47(5):550-568.[7] H a r v i eDJE ,F l e c t c h e rD F .A N e w V o l u m eo fF l u i dA d v e c t i o nA l g o r i t h m :T h eS t r e a m S c h e m e [J ].JC o m p u t P h y s ,2000,162:1-32.[8] H a r v i eDJE ,F l e c t c h e rDF .A N e w V o l u m e o fF l u i dA d v e c t i o nA l g o r i t h m :T h eD if i n e dD o n a t i ng R e g i o nS ch e m e [J ].I n t JN u m e rM e t hF l ,2001,35:151-172.[9] S hi JM.S o f t w a r eE n g i n e e r i n g -P r i n c i p l e ,M e t h o d a n dA p p l y [M ].B e ij i n g :H i gh e rE d u c a t i o nP r e s s ,2002.(i nC h i n e s e )史济民.软件工程 原理㊁方法与应用[M ].北京:高等教育出版社,2002.S t u d y o nP a r a l l e lA l g o r i t h mo fE u l e r i a n M e t h o d f o rT h r e e -D i m e n s i o n a l M u l t i -M a t e r i a l P l a s t i c -E l a s t i cH yd r o k i ne t i c s MA T i a n -B a o 1,F E IG u a n g -L e i 1,Z H A N G W e n -Y a o 2(1.S t a t eK e y L a b o r a t o r y o f E x p l o s i o nS c i e n c e a n dT e c h n o l o g y ,B e i j i n g I n s t i t u t e o f T e c h n o l o g y ,B e i j i n g 100081,C h i n a ;2.B e i j i n g L a b o r a t o r y o f I n t e l l i g e n t I n f o r m a t i o nT e c h n o l o g y ,S c h o o l o f Co m p u t e rS c i e n c e a n dT e c h n o l o g y ,B e i j i n g I n s t i t u t e o f T e c h n o l o g y ,B e i j i n g 100081,C h i n a )A b s t r a c t :P a r a l l e l c o m p u t i n g o f 3De x p l o s i o na n d s h o c k p r o c e s s e s o n t h e p a r a l l e l c o m pu t e r i s e f f e c t i v e m e a n s f o r t h e l a r g e -s c a l en u m e r i c a l s t u d y o f e x p l o s i o na n d s h o c k p r o c e s s .C o n s i d e r i n g t h e c o m p l e x i t y o f t h e p a r a l l e l p r o g r a mm i n g ,t h e o v e r a l l s t r a t e g y f o r p a r a l l e l p r o g r a mm i n g o f 3D m u t i l -m a t e r i a l h y d r o -e l a s t o p l a s t i ch y d r o c o d eMM I C -3Dw a s d i s c u s s e d ,a n d t h e P MM I C -3D p a r a l l e l h y d r o c o d ew a s d e s i gn e d b a s e do nM P I (M e s s a g e P a s s i n g I n t e r f a c e ).I n a d d i t i o n ,a p r a c t i c a l p l a n o f p r o g r a mt e s t i n g w a s p r e s e n -t e d .T h e s p e e d u p ,e f f i c i e n c y a n ds c a l a b i l i t y o f t h eP MM I C -3D p a r a l l e lh yd r o c o d ewe r e t e s t e do nt h e c l u s t e r c o n s i s t i n g of 8n o d e s b a s e d o n t h e n u m e r i c a l e x a m p l e o f s h a p e d c h a rg e j e t ,a n d th e e f f e c t o f t h e b o t t l e n e c k s o f P MM I C -3D p a r a l l e l h yd r o c o d ew a s d i s c u s se d .K e y wo r d s :e x p l o s i o na n d s h o c k ;p a r a l l e l c o m p u t i n g ;M e s s a g eP a s s i n g I n t e r f a c e (M P I );p r o g r a mt e s t 315 第6期 马天宝等:三维多物质弹塑性流体动力学E u l e r 方法的并行算法研究及程序测试。

Reliability Engineering and System Safety 91(2006)992–1007Multi-objective optimization using genetic algorithms:A tutorialAbdullah Konak a,Ã,David W.Coit b ,Alice E.Smith caInformation Sciences and Technology,Penn State Berks,USA bDepartment of Industrial and Systems Engineering,Rutgers University cDepartment of Industrial and Systems Engineering,Auburn UniversityAvailable online 9January 2006AbstractMulti-objective formulations are realistic models for many complex engineering optimization problems.In many real-life problems,objectives under consideration conflict with each other,and optimizing a particular solution with respect to a single objective can result in unacceptable results with respect to the other objectives.A reasonable solution to a multi-objective problem is to investigate a set of solutions,each of which satisfies the objectives at an acceptable level without being dominated by any other solution.In this paper,an overview and tutorial is presented describing genetic algorithms (GA)developed specifically for problems with multiple objectives.They differ primarily from traditional GA by using specialized fitness functions and introducing methods to promote solution diversity.r 2005Elsevier Ltd.All rights reserved.1.IntroductionThe objective of this paper is present an overview and tutorial of multiple-objective optimization methods using genetic algorithms (GA).For multiple-objective problems,the objectives are generally conflicting,preventing simulta-neous optimization of each objective.Many,or even most,real engineering problems actually do have multiple-objectives,i.e.,minimize cost,maximize performance,maximize reliability,etc.These are difficult but realistic problems.GA are a popular meta-heuristic that is particularly well-suited for this class of problems.Tradi-tional GA are customized to accommodate multi-objective problems by using specialized fitness functions and introducing methods to promote solution diversity.There are two general approaches to multiple-objective optimization.One is to combine the individual objective functions into a single composite function or move all but one objective to the constraint set.In the former case,determination of a single objective is possible with methods such as utility theory,weighted sum method,etc.,but theproblem lies in the proper selection of the weights or utility functions to characterize the decision-maker’s preferences.In practice,it can be very difficult to precisely and accurately select these weights,even for someone familiar with the problem pounding this drawback is that scaling amongst objectives is needed and small perturbations in the weights can sometimes lead to quite different solutions.In the latter case,the problem is that to move objectives to the constraint set,a constraining value must be established for each of these former objectives.This can be rather arbitrary.In both cases,an optimization method would return a single solution rather than a set of solutions that can be examined for trade-offs.For this reason,decision-makers often prefer a set of good solutions considering the multiple objectives.The second general approach is to determine an entire Pareto optimal solution set or a representative subset.A Pareto optimal set is a set of solutions that are nondominated with respect to each other.While moving from one Pareto solution to another,there is always a certain amount of sacrifice in one objective(s)to achieve a certain amount of gain in the other(s).Pareto optimal solution sets are often preferred to single solutions because they can be practical when considering real-life problems/locate/ress0951-8320/$-see front matter r 2005Elsevier Ltd.All rights reserved.doi:10.1016/j.ress.2005.11.018ÃCorresponding author.E-mail address:konak@ (A.Konak).since thefinal solution of the decision-maker is always a trade-off.Pareto optimal sets can be of varied sizes,but the size of the Pareto set usually increases with the increase in the number of objectives.2.Multi-objective optimization formulationConsider a decision-maker who wishes to optimize K objectives such that the objectives are non-commensurable and the decision-maker has no clear preference of the objectives relative to each other.Without loss of generality, all objectives are of the minimization type—a minimization type objective can be converted to a maximization type by multiplying negative one.A minimization multi-objective decision problem with K objectives is defined as follows: Given an n-dimensional decision variable vector x¼{x1,y,x n}in the solution space X,find a vector x* that minimizes a given set of K objective functions z(x*)¼{z1(x*),y,z K(x*)}.The solution space X is gen-erally restricted by a series of constraints,such as g j(x*)¼b j for j¼1,y,m,and bounds on the decision variables.In many real-life problems,objectives under considera-tion conflict with each other.Hence,optimizing x with respect to a single objective often results in unacceptable results with respect to the other objectives.Therefore,a perfect multi-objective solution that simultaneously opti-mizes each objective function is almost impossible.A reasonable solution to a multi-objective problem is to investigate a set of solutions,each of which satisfies the objectives at an acceptable level without being dominated by any other solution.If all objective functions are for minimization,a feasible solution x is said to dominate another feasible solution y (x1y),if and only if,z i(x)p z i(y)for i¼1,y,K and z j(x)o z j(y)for least one objective function j.A solution is said to be Pareto optimal if it is not dominated by any other solution in the solution space.A Pareto optimal solution cannot be improved with respect to any objective without worsening at least one other objective.The set of all feasible non-dominated solutions in X is referred to as the Pareto optimal set,and for a given Pareto optimal set,the corresponding objective function values in the objective space are called the Pareto front.For many problems,the number of Pareto optimal solutions is enormous(perhaps infinite).The ultimate goal of a multi-objective optimization algorithm is to identify solutions in the Pareto optimal set.However,identifying the entire Pareto optimal set, for many multi-objective problems,is practically impos-sible due to its size.In addition,for many problems, especially for combinatorial optimization problems,proof of solution optimality is computationally infeasible.There-fore,a practical approach to multi-objective optimization is to investigate a set of solutions(the best-known Pareto set)that represent the Pareto optimal set as well as possible.With these concerns in mind,a multi-objective optimization approach should achieve the following three conflicting goals[1]:1.The best-known Pareto front should be as close aspossible to the true Pareto front.Ideally,the best-known Pareto set should be a subset of the Pareto optimal set.2.Solutions in the best-known Pareto set should beuniformly distributed and diverse over of the Pareto front in order to provide the decision-maker a true picture of trade-offs.3.The best-known Pareto front should capture the wholespectrum of the Pareto front.This requires investigating solutions at the extreme ends of the objective function space.For a given computational time limit,thefirst goal is best served by focusing(intensifying)the search on a particular region of the Pareto front.On the contrary,the second goal demands the search effort to be uniformly distributed over the Pareto front.The third goal aims at extending the Pareto front at both ends,exploring new extreme solutions.This paper presents common approaches used in multi-objective GA to attain these three conflicting goals while solving a multi-objective optimization problem.3.Genetic algorithmsThe concept of GA was developed by Holland and his colleagues in the1960s and1970s[2].GA are inspired by the evolutionist theory explaining the origin of species.In nature,weak and unfit species within their environment are faced with extinction by natural selection.The strong ones have greater opportunity to pass their genes to future generations via reproduction.In the long run,species carrying the correct combination in their genes become dominant in their population.Sometimes,during the slow process of evolution,random changes may occur in genes. If these changes provide additional advantages in the challenge for survival,new species evolve from the old ones.Unsuccessful changes are eliminated by natural selection.In GA terminology,a solution vector x A X is called an individual or a chromosome.Chromosomes are made of discrete units called genes.Each gene controls one or more features of the chromosome.In the original implementa-tion of GA by Holland,genes are assumed to be binary digits.In later implementations,more varied gene types have been introduced.Normally,a chromosome corre-sponds to a unique solution x in the solution space.This requires a mapping mechanism between the solution space and the chromosomes.This mapping is called an encoding. In fact,GA work on the encoding of a problem,not on the problem itself.GA operate with a collection of chromosomes,called a population.The population is normally randomly initia-lized.As the search evolves,the population includesfitterA.Konak et al./Reliability Engineering and System Safety91(2006)992–1007993andfitter solutions,and eventually it converges,meaning that it is dominated by a single solution.Holland also presented a proof of convergence(the schema theorem)to the global optimum where chromosomes are binary vectors.GA use two operators to generate new solutions from existing ones:crossover and mutation.The crossover operator is the most important operator of GA.In crossover,generally two chromosomes,called parents,are combined together to form new chromosomes,called offspring.The parents are selected among existing chromo-somes in the population with preference towardsfitness so that offspring is expected to inherit good genes which make the parentsfitter.By iteratively applying the crossover operator,genes of good chromosomes are expected to appear more frequently in the population,eventually leading to convergence to an overall good solution.The mutation operator introduces random changes into characteristics of chromosomes.Mutation is generally applied at the gene level.In typical GA implementations, the mutation rate(probability of changing the properties of a gene)is very small and depends on the length of the chromosome.Therefore,the new chromosome produced by mutation will not be very different from the original one.Mutation plays a critical role in GA.As discussed earlier,crossover leads the population to converge by making the chromosomes in the population alike.Muta-tion reintroduces genetic diversity back into the population and assists the search escape from local optima. Reproduction involves selection of chromosomes for the next generation.In the most general case,thefitness of an individual determines the probability of its survival for the next generation.There are different selection procedures in GA depending on how thefitness values are used. Proportional selection,ranking,and tournament selection are the most popular selection procedures.The procedure of a generic GA[3]is given as follows:Step1:Set t¼1.Randomly generate N solutions to form thefirst population,P1.Evaluate thefitness of solutions in P1.Step2:Crossover:Generate an offspring population Q t as follows:2.1.Choose two solutions x and y from P t based onthefitness values.ing a crossover operator,generate offspringand add them to Q t.Step3:Mutation:Mutate each solution x A Q t with a predefined mutation rate.Step4:Fitness assignment:Evaluate and assign afitness value to each solution x A Q t based on its objective function value and infeasibility.Step5:Selection:Select N solutions from Q t based on theirfitness and copy them to P t+1.Step6:If the stopping criterion is satisfied,terminate the search and return to the current population,else,set t¼t+1go to Step2.4.Multi-objective GABeing a population-based approach,GA are well suited to solve multi-objective optimization problems.A generic single-objective GA can be modified tofind a set of multiple non-dominated solutions in a single run.The ability of GA to simultaneously search different regions of a solution space makes it possible tofind a diverse set of solutions for difficult problems with non-convex,discon-tinuous,and multi-modal solutions spaces.The crossover operator of GA may exploit structures of good solutions with respect to different objectives to create new non-dominated solutions in unexplored parts of the Pareto front.In addition,most multi-objective GA do not require the user to prioritize,scale,or weigh objectives.Therefore, GA have been the most popular heuristic approach to multi-objective design and optimization problems.Jones et al.[4]reported that90%of the approaches to multi-objective optimization aimed to approximate the true Pareto front for the underlying problem.A majority of these used a meta-heuristic technique,and70%of all meta-heuristics approaches were based on evolutionary ap-proaches.Thefirst multi-objective GA,called vector evaluated GA (or VEGA),was proposed by Schaffer[5].Afterwards, several multi-objective evolutionary algorithms were devel-oped including Multi-objective Genetic Algorithm (MOGA)[6],Niched Pareto Genetic Algorithm(NPGA) [7],Weight-based Genetic Algorithm(WBGA)[8],Ran-dom Weighted Genetic Algorithm(RWGA)[9],Nondomi-nated Sorting Genetic Algorithm(NSGA)[10],Strength Pareto Evolutionary Algorithm(SPEA)[11],improved SPEA(SPEA2)[12],Pareto-Archived Evolution Strategy (PAES)[13],Pareto Envelope-based Selection Algorithm (PESA)[14],Region-based Selection in Evolutionary Multiobjective Optimization(PESA-II)[15],Fast Non-dominated Sorting Genetic Algorithm(NSGA-II)[16], Multi-objective Evolutionary Algorithm(MEA)[17], Micro-GA[18],Rank-Density Based Genetic Algorithm (RDGA)[19],and Dynamic Multi-objective Evolutionary Algorithm(DMOEA)[20].Note that although there are many variations of multi-objective GA in the literature, these cited GA are well-known and credible algorithms that have been used in many applications and their performances were tested in several comparative studies. Several survey papers[1,11,21–27]have been published on evolutionary multi-objective optimization.Coello lists more than2000references in his website[28].Generally, multi-objective GA differ based on theirfitness assign-ment procedure,elitisim,or diversification approaches.In Table1,highlights of the well-known multi-objective with their advantages and disadvantages are given.Most survey papers on multi-objective evolutionary approaches intro-duce and compare different algorithms.This paper takes a different course and focuses on important issues while designing a multi-objective GA and describes common techniques used in multi-objective GA to attain the threeA.Konak et al./Reliability Engineering and System Safety91(2006)992–1007 994goals in multi-objective optimization.This approach is also taken in the survey paper by Zitzler et al.[1].However,the discussion in this paper is aimed at introducing the components of multi-objective GA to researchers and practitioners without a background on the multi-objective GA.It is also import to note that although several of the state-of-the-art algorithms exist as cited above,many researchers that applied multi-objective GA to their problems have preferred to design their own customized algorithms by adapting strategies from various multi-objective GA.This observation is another motivation for introducing the components of multi-objective GA rather than focusing on several algorithms.However,the pseudo-code for some of the well-known multi-objective GA are also provided in order to demonstrate how these proce-dures are incorporated within a multi-objective GA.Table1A list of well-known multi-objective GAAlgorithm Fitness assignment Diversity mechanism Elitism ExternalpopulationAdvantages DisadvantagesVEGA[5]Each subpopulation isevaluated with respectto a differentobjective No No No First MOGAStraightforwardimplementationTend converge to theextreme of each objectiveMOGA[6]Pareto ranking Fitness sharing byniching No No Simple extension of singleobjective GAUsually slowconvergenceProblems related to nichesize parameterWBGA[8]Weighted average ofnormalized objectives Niching No No Simple extension of singleobjective GADifficulties in nonconvexobjective function space Predefined weightsNPGA[7]Nofitnessassignment,tournament selection Niche count as tie-breaker in tournamentselectionNo No Very simple selectionprocess with tournamentselectionProblems related to nichesize parameterExtra parameter fortournament selectionRWGA[9]Weighted average ofnormalized objectives Randomly assignedweightsYes Yes Efficient and easyimplementDifficulties in nonconvexobjective function spacePESA[14]Nofitness assignment Cell-based density Pure elitist Yes Easy to implement Performance depends oncell sizesComputationally efficientPrior information neededabout objective spacePAES[29]Pareto dominance isused to replace aparent if offspringdominates Cell-based density astie breaker betweenoffspring and parentYes Yes Random mutation hill-climbing strategyNot a population basedapproachEasy to implement Performance depends oncell sizesComputationally efficientNSGA[10]Ranking based onnon-dominationsorting Fitness sharing bynichingNo No Fast convergence Problems related to nichesize parameterNSGA-II[30]Ranking based onnon-dominationsorting Crowding distance Yes No Single parameter(N)Crowding distance worksin objective space onlyWell testedEfficientSPEA[11]Raking based on theexternal archive ofnon-dominatedsolutions Clustering to truncateexternal populationYes Yes Well tested Complex clusteringalgorithmNo parameter forclusteringSPEA-2[12]Strength ofdominators Density based on thek-th nearest neighborYes Yes Improved SPEA Computationallyexpensivefitness anddensity calculationMake sure extreme pointsare preservedRDGA[19]The problem reducedto bi-objectiveproblem with solutionrank and density asobjectives Forbidden region cell-based densityYes Yes Dynamic cell update More difficult toimplement than othersRobust with respect to thenumber of objectivesDMOEA[20]Cell-based ranking Adaptive cell-baseddensity Yes(implicitly)No Includes efficienttechniques to update celldensitiesMore difficult toimplement than othersAdaptive approaches toset GA parametersA.Konak et al./Reliability Engineering and System Safety91(2006)992–10079955.Design issues and components of multi-objective GA 5.1.Fitness functions5.1.1.Weighted sum approachesThe classical approach to solve a multi-objective optimization problem is to assign a weight w i to each normalized objective function z 0i ðx Þso that the problem is converted to a single objective problem with a scalar objective function as follows:min z ¼w 1z 01ðx Þþw 2z 02ðx ÞþÁÁÁþw k z 0k ðx Þ,(1)where z 0i ðx Þis the normalized objective function z i (x )and P w i ¼1.This approach is called the priori approach since the user is expected to provide the weights.Solving a problem with the objective function (1)for a given weight vector w ¼{w 1,w 2,y ,w k }yields a single solution,and if multiple solutions are desired,the problem must be solved multiple times with different weight combinations.The main difficulty with this approach is selecting a weight vector for each run.To automate this process;Hajela and Lin [8]proposed the WBGA for multi-objective optimization (WBGA-MO)in the WBGA-MO,each solution x i in the population uses a different weight vector w i ¼{w 1,w 2,y ,w k }in the calculation of the summed objective function (1).The weight vector w i is embedded within the chromosome of solution x i .Therefore,multiple solutions can be simulta-neously searched in a single run.In addition,weight vectors can be adjusted to promote diversity of the population.Other researchers [9,31]have proposed a MOGA based on a weighted sum of multiple objective functions where a normalized weight vector w i is randomly generated for each solution x i during the selection phase at each generation.This approach aims to stipulate multiple search directions in a single run without using additional parameters.The general procedure of the RWGA using random weights is given as follows [31]:Procedure RWGA:E ¼external archive to store non-dominated solutions found during the search so far;n E ¼number of elitist solutions immigrating from E to P in each generation.Step 1:Generate a random population.Step 2:Assign a fitness value to each solution x A P t by performing the following steps:Step 2.1:Generate a random number u k in [0,1]for each objective k ,k ¼1,y ,K.Step 2.2:Calculate the random weight of each objective k as w k ¼ð1=u k ÞP K i ¼1u i .Step 2.3:Calculate the fitness of the solution as f ðx Þ¼P K k ¼1w k z k ðx Þ.Step 3:Calculate the selection probability of each solutionx A P t as follows:p ðx Þ¼ðf ðx ÞÀf min ÞÀ1P y 2P t ðf ðy ÞÀf minÞwhere f min ¼min f f ðx Þj x 2P t g .Step 4:Select parents using the selection probabilities calculated in Step 3.Apply crossover on the selected parent pairs to create N offspring.Mutate offspring with a predefined mutation rate.Copy all offspring to P t +1.Update E if necessary.Step 5:Randomly remove n E solutions from P t +1and add the same number of solutions from E to P t +1.Step 6:If the stopping condition is not satisfied,set t ¼t þ1and go to Step 2.Otherwise,return to E .The main advantage of the weighted sum approach is a straightforward implementation.Since a single objective is used in fitness assignment,a single objective GA can be used with minimum modifications.In addition,this approach is computationally efficient.The main disadvan-tage of this approach is that not all Pareto-optimal solutions can be investigated when the true Pareto front is non-convex.Therefore,multi-objective GA based on the weighed sum approach have difficulty in finding solutions uniformly distributed over a non-convex trade-off surface [1].5.1.2.Altering objective functionsAs mentioned earlier,VEGA [5]is the first GA used to approximate the Pareto-optimal set by a set of non-dominated solutions.In VEGA,population P t is randomly divided into K equal sized sub-populations;P 1,P 2,y ,P K .Then,each solution in subpopulation P i is assigned a fitness value based on objective function z i .Solutions are selected from these subpopulations using proportional selection for crossover and mutation.Crossover and mutation are performed on the new population in the same way as for a single objective GA.Procedure VEGA:N S ¼subpopulation size (N S ¼N =K )Step 1:Start with a random initial population P 0.Set t ¼0.Step 2:If the stopping criterion is satisfied,return P t .Step 3:Randomly sort population P t .Step 4:For each objective k ,k ¼1,y K ,perform the following steps:Step 4.1:For i ¼1þðk 21ÞN S ;...;kN S ,assign fit-ness value f ðx i Þ¼z k ðx i Þto the i th solution in the sorted population.Step 4.2:Based on the fitness values assigned in Step 4.1,select N S solutions between the (1+(k À1)N S )th and (kN S )th solutions of the sorted population to create subpopulation P k .Step 5:Combine all subpopulations P 1,y ,P k and apply crossover and mutation on the combined population to create P t +1of size N .Set t ¼t þ1,go to Step 2.A similar approach to VEGA is to use only a single objective function which is randomly determined each time in the selection phase [32].The main advantage of the alternating objectives approach is easy to implement andA.Konak et al./Reliability Engineering and System Safety 91(2006)992–1007996computationally as efficient as a single-objective GA.In fact,this approach is a straightforward extension of a single objective GA to solve multi-objective problems.The major drawback of objective switching is that the popula-tion tends to converge to solutions which are superior in one objective,but poor at others.5.1.3.Pareto-ranking approachesPareto-ranking approaches explicitly utilize the concept of Pareto dominance in evaluatingfitness or assigning selection probability to solutions.The population is ranked according to a dominance rule,and then each solution is assigned afitness value based on its rank in the population, not its actual objective function value.Note that herein all objectives are assumed to be minimized.Therefore,a lower rank corresponds to a better solution in the following discussions.Thefirst Pareto ranking technique was proposed by Goldberg[3]as follows:Step1:Set i¼1and TP¼P.Step2:Identify non-dominated solutions in TP and assigned them set to F i.Step3:Set TP¼TPF i.If TP¼+go to Step4,else set i¼iþ1and go to Step2.Step4:For every solution x A P at generation t,assign rank r1ðx;tÞ¼i if x A F i.In the procedure above,F1,F2,y are called non-dominated fronts,and F1is the Pareto front of population P.NSGA[10]also classifies the population into non-dominated fronts using an algorithm similar to that given above.Then a dummyfitness value is assigned to each front using afitness sharing function such that the worst fitness value assigned to F i is better than the bestfitness value assigned to F i+1.NSGA-II[16],a more efficient algorithm,named the fast non-dominated-sort algorithm, was developed to form non-dominated fronts.Fonseca and Fleming[6]used a slightly different rank assignment approach than the ranking based on non-dominated-fronts as follows:r2ðx;tÞ¼1þnqðx;tÞ;(2) where nq(x,t)is the number of solutions dominating solution x at generation t.This ranking method penalizes solutions located in the regions of the objective function space which are dominated(covered)by densely populated sections of the Pareto front.For example,in Fig.1b solution i is dominated by solutions c,d and e.Therefore,it is assigned a rank of4although it is in the same front with solutions f,g and h which are dominated by only a single solution.SPEA[11]uses a ranking procedure to assign better fitness values to non-dominated solutions at underrepre-sented regions of the objective space.In SPEA,an external list E of afixed size stores non-dominated solutions that have been investigated thus far during the search.For each solution y A E,a strength value is defined assðy;tÞ¼npðy;tÞN Pþ1,where npðy;tÞis the number solutions that y dominates in P.The rank r(y,t)of a solution y A E is assigned as r3ðy;tÞ¼sðy;tÞand the rank of a solution x A P is calculated asr3ðx;tÞ¼1þXy2E;y1xsðy;tÞ.Fig.1c illustrates an example of the SPEA ranking method.In the former two methods,all non-dominated solutions are assigned a rank of1.This method,however, favors solution a(in thefigure)over the other non-dominated solutions since it covers the least number of solutions in the objective function space.Therefore,a wide, uniformly distributed set of non-dominated solutions is encouraged.Accumulated ranking density strategy[19]also aims to penalize redundancy in the population due to overrepre-sentation.This ranking method is given asr4ðx;tÞ¼1þXy2P;y1xrðy;tÞ.To calculate the rank of a solution x,the rank of the solutions dominating this solution must be calculatedfirst. Fig.1d shows an example of this ranking method(based on r2).Using ranking method r4,solutions i,l and n are ranked higher than their counterparts at the same non-dominated front since the portion of the trade-off surface covering them is crowded by three nearby solutions c,d and e. Although some of the ranking approaches described in this section can be used directly to assignfitness values to individual solutions,they are usually combined with variousfitness sharing techniques to achieve the second goal in multi-objective optimization,finding a diverse and uniform Pareto front.5.2.Diversity:fitness assignment,fitness sharing,and nichingMaintaining a diverse population is an important consideration in multi-objective GA to obtain solutions uniformly distributed over the Pareto front.Without taking preventive measures,the population tends to form relatively few clusters in multi-objective GA.This phenom-enon is called genetic drift,and several approaches have been devised to prevent genetic drift as follows.5.2.1.Fitness sharingFitness sharing encourages the search in unexplored sections of a Pareto front by artificially reducingfitness of solutions in densely populated areas.To achieve this goal, densely populated areas are identified and a penaltyA.Konak et al./Reliability Engineering and System Safety91(2006)992–1007997。

Experimental investigation and numerical simulation for weakening the thermal fluctuations in aT-junctionK.Gao a ,P.Wang b ,T.Lu a ,⇑,T.Song caCollege of Mechanical and Electrical Engineering,Beijing University of Chemical Technology,Beijing 100029,China bSchool of Energy and Power Engineering,Dalian University of Technology,Dalian 116024,China cChina Nuclear Power Technology Research Institute Co.,Ltd,Shenzhen 518124,Chinaa r t i c l e i n f o Article history:Received 25August 2014Received in revised form 17November 2014Accepted 4January 2015Available online 17January 2015Keywords:Experimental investigation Numerical simulation Tee junctionThermal fluctuationa b s t r a c tIn this work,the mixing processes of hot and cold fluids with and without a distributor are predicted by experiments and numerical simulations using large-eddy simulation (LES)on FLUENT platform.Temperatures at different positions of the internal wall and mixing conditions caused by T-junctions at different times are obtained,then the simulated normalized mean and root-mean square (RMS)temperature,velocity vector and temperature contour for the two structures,namely with and without a distributor,are compared.The results show that,compared with the a T-junction without a distributor,the mixing region of hot and cold water in the T-junction with distributor moves to the middle of the pipe,and the inclusion of the distributor reduces the temperature fluctuations of internal wall noticeably and makes the mixing of hot and cold water more efficient.Ó2015Elsevier Ltd.All rights reserved.1.IntroductionTee junction is a familiar structure that is universally used in pipeline systems of power plants,nuclear power plants and chemi-cal plants,it is often applied to mix hot and cold fluid of main and branch pipes.The fluctuations of fluid temperature are transported to the solid walls by heat convection and conduction.This can cause cyclical thermal stresses and subsequent thermal fatigue cracking of the piping (Lee et al.,2009).So far,leakage accidents took place in several light water and sodium cooled reactors due to thermal fati-gue.In 1998,a crack was discovered at a mixing tee in which cold water from a branch pipe flowed into the main pipe in the residual heat removal (RHR)system in a reactor in Civaux,France.Metallur-gical studies concluded that the crack was caused by a high degree of cycle thermal fatigue (Eric Blondet,2002).In 1990,sodium leak-age happened in the French reactor Superphenix (Ricard and Sperandio,1996).It has been established that mixing hot and cold sodium can induce temperature fluctuations and result in thermal fatigue (IAEA,2002).Therefore,it is significant to study how to weaken thermal fatigue of the piping wall to ensure the integrity and safety of the piping system in a nuclear power plant.In the analysis of thermal fatigue,temperature fluctuation is a very important evaluation parameter.A reliable lifetime assess-ment of these components is difficult because usually only thenominal temperature differences between the hot and cold fluids are known,whereas the instantaneous temperatures and heat fluxes at the surface are unknown (Paffumi et al.,2013).Kamaya and Nakamura (2011)used the transient temperature obtained by simulation to assess the distribution of thermal stress and fati-gue when cold fluid flowed into the main pipe from a branch pipe.Numerical simulation of flow in the tee has been carried out Simoneau et al.(2010)to get temperature and its fluctuation curves,and the numerical results were in good agreement with the experimental data.Through the analysis on thermal fatigue stress,it draw the conclusion that the enhanced heat transfer coef-ficient and the temperature difference between hot and cold fluids were primary factors of thermal fatigue failure of tees.Many numerical simulations and experiments have been carried out to evaluate the flow and heat transfer in a mixing tee junction (Metzner and Wilke,2005;Hu and Kazimi,2006;Hosseini et al.,2008;Durve et al.,2010;Frank et al.,2010;Jayaraju et al.,2010;Galpin and Simoneau,2011;Aulery et al.,2012;Cao et al.,2012).Turbulent models such as Reynolds-averaged Navier–Stokes (RANS),Unsteady Reynolds averaged Navier Stokes (URANS),Scale-Adaptive Simulation (SAS),Reynolds stress model (RSM),detached eddy simulations (DES),and LES have all been used in industrial applications.As one of the choices of turbulent model for predicting the mixing flow in tee junctions,the RSM can bemused to describe the momentum conservation of the mixing (Durve et al.,2010;Frank et al.,2010).Turbulent mixing phenomena in a T-junction have been numerically investigated using the k $x/10.1016/j.anucene.2015.01.0010306-4549/Ó2015Elsevier Ltd.All rights reserved.Corresponding author.based baseline Reynolds stress model(BSL RSM)(Frank et al.,2010) for two different cases.Durve et al.(2010)applied the RSM to pre-dict the velocityfield of three non-isothermal parallel jetsflowing in an experiment setup used to simulate theflow occurring at the core outlet region of a fast breeder reactor(FBR),with a Reynolds number of1.5Â104.Theflow in tube of different Reynolds numbers (Re)andflow velocity ratio were studied experimentally with three-dimensional scanning using particle image velocimetry(3D-SPIV) (Brücker,1997).Large-eddy simulation(LES)is an alternative turbulence model with different subgridscale models often employed to predict velocity and temperaturefluctuations.Indeed many numerical studies have shown the capability of LES to model thermalfluctu-ations in turbulent mixing.LES was performed(Lee et al.,2009)to analyze temperaturefluctuation in the tee junction and the simu-lated results were in good agreement with the experimental data. Thermal striping phenomena in the tee junction had been numer-ically investigated using LES(Hu and Kazimi,2006)for two differ-ent mixing cases,and the simulated normalized mean and root-mean square(RMS)was consistent with experimental results. LES in a mixing tee were carried out(Galpin and Simoneau, 2011)in order to evaluate the sensitivity of numerical results to the subgrid scale model by comparing the experimental results, and to investigate the possibility of reducing thefluid computa-tional domain at the inlet.Another simulation that mixing of a hot and a coldfluid stream in a vertical tee junction with an upstream elbow main pipe was carried out with LES(Lu et al., 2013).And the numerical results show that the normalized RMS temperature and velocity decrease with the increases of the elbow curvature ratio and dimensionless distance.In the meantime,many scholars have studied how to weaken the thermalfluctuation.Experiments and simulation were con-ducted(Wu et al.,2003)on a tee junction geometry with a sleeve tube in it.Theflow is divided into three types of jets by theflow velocity ratio in main and branch pipes.Through the analysis of flowfield and velocityfield of various jets types,it indicate that the addition of sleeve tube relieve the thermal shock caused by the coldfluid injection rge-eddy simulation have been used(Lu et al.,2010)to evaluate the thermal striping phe-nomena in tee junctions with periodic porous media,the temper-ature and velocityfield inside the tubes are obtained.The research revealed that the addition of a porous reduces the tem-perature and velocityfluctuations in the mixing tube.As mentioned above,experiments and numerical simulations for both tee junction geometry with a sleeve tube in it(Wu et al., 2003)and for a mixing tee with periodic porous media in it(Lu et al.,2010)have been carried out.The results of previous researches provide a good reference value for this work that anal-yses the role of distributor in weakening the thermalfluctuation of internal piping wall,and this structure has not been studied to date,to the best of our knowledge.In this work,mixing processes have been studied by the experiment and numerically predicted with LES.Then the simulated normalized mean and root-mean square(RMS)temperature,velocity vector and temperature con-tour of the two tees are compared.2.Experiment systemThe Experimentflowchart is presented in Fig.1.The experimen-tal system consists of four main components,a cold water supply line,a hot water supply line,a test section,and a data acquisition unit.The experiment device is shown in Fig.2.Experimentfluid was adjusted to the desired temperature by the heater and chiller, and then was pumped to the test section.After mixing thefluid is returned to the heater for recycling,some of the excessfluid is dis-charged through the overflow pipe.During the mixing of thefluids, the temperature of the mixingfluid is collected and recorded by the thermocouple probe installed on the tube wall.The experiment requires two different structures of the test sec-tion,Fig.3is the T-junction section without the branch liquid dis-tributor and Fig.4is that with the branch liquid distributor.The addition of this structure has two main functions:(1)changing the mixing position of hot and coldfluids:moving the mixing zone to the middle of the tube,and away from the main pipe wall;(2) increasing the intensity of mixing process:adding the fence near the outlet of distributor enhanced the mixed disturbance and the exacerbatedfluid mixing of the inner tube.For the convenience of observing and adjusting the mixing process,the test section is a round pipe made of plexiglass,and other pipes are made of steel. Fig.5is the physical model of the branch liquid distributor.The test conditions in the present experiment are shown in Table1.We collected the instantaneous temperature data of every measurement points by the data collector.The distribution of sam-pling points are shown in Fig.6,there are total eight thermocou-ples in the circumferential direction at each plane.In the T-junction section without the branch liquid distributor,the number of the collected plane is6(x/d m=1,2,3,4,6,8).That is to say there are48thermocouples in the structure without distributor.And in the T-junction section with the branch liquid distributor,the num-ber of the collected plane is5(x/d m=2,3,4,6,8),which means there are40thermocouples in the structure that with the distrib-utor.In both structures,the distance between measuring point the thermocouple probe and the inner wall is30mm.Since the collect-ing frequency of the collector is limited,we use1Hz as the collect-ing frequency after theflowfield is stable,and the total number of collection is800s.Table1shows the specific parameters of the test conditions.NomenclatureT time(s)Pr Prandtl numberLs mixing length of subgrid grid(m)T temperature(K)G acceleration of gravity(m/s2)K von Karman numberCs Smagorinsky numberS ij subgrid strain rate tensorM R momentum ratio of main pipe and branch pipe TÃnormalized mean temperaturesTÃrms normalized RMS temperaturesR d diameter ratioR v velocity ratiox,y,z axial coordinate(m)Greek symbolsqfluid density(kg/m3)b coefficient of thermal expansionl viscosity(Pa s)ltturbulent viscosity(Pa s)k thermal conductivity(w/(m k))C P heat capacity(J/(kg°C))K.Gao et al./Annals of Nuclear Energy78(2015)180–187181182K.Gao et al./Annals of Nuclear Energy78(2015)180–1871\4\11-thermometers 2\5\10-pressure gauge 3\9-flow meter 6-c ooler 7-heater8-overflow 12-test sec tion 13-thermoc ouple data c ollec torFig.1.Experimentflow chart.Fig.5.Physical model of the branch liquid distributor(a)the whole graph(b)theprofile map.Fig.2.Experiment device of thermalfluctuation.Fig.3.Schematic diagram of the T-junction section without the branch liquid distributor.Fig.4.Schematic diagram of the T-junction section with the branch liquid distributor.3.Numerical simulationFig.7is the numerical model based on the experimental section of T junction.The size of the model,boundary conditions are con-sistent with the experiment.In which,hot water enters from the left of main pipe,and cold water enters from the branch pipe,finally the mixingfluidflow out of the right of the main pipe.Dur-ing the calculation,the steady results offlowfield and heat transfer are obtained by Reynolds stress model(RSM)firstly,and then set @q@tþ@q u i@x i¼0ð1Þ@q u i@tþ@q u i u j@x j¼À@ p@x iÀq0bðTÀT0Þgþ@@x jlþltÀÁ@ u i@x jþ@ u j@x i!ð2Þ@q T@tþ@q Tu j@x j¼@@x jkc p@T@x jÀq T00u00j!ð3ÞIn these equations,q,b,l,l t,k and c p represent the density,ther-mal expansion coefficient,molecular viscosity,turbulent viscosity, thermal conductivity and specific heat capacity,respectively.The Smagorinsky–Lilly model is used for the turbulent viscosity,which is described as:lt¼q L2s j S jð4Þj S jTable1Experimental conditions.Main pipe Branch pipeFlow rate (m3/h)Temperature(K)Flow rate(m3/h)Temperature(K)Without distributor0.645304.650.270287.65With distributor0.645304.650.266287.65Fig.6.The distribution of sampling points on the planes.Physical model of T-junction(a)without the branch liquid distributor;(b)with the branch liquid distributor.K.Gao et al./Annals of Nuclear Energy78(2015)180–187183ij ¼12@ u i@x jþ@ u j@x ið7Þwhere k is the Von Karman constant of0.42;d is the distance to the closest wall;C s is the Smagorinsky constant of0.1;V is the volume of the computational cell.4.Results and discussionThe normalized mean and root-mean square temperature are used to describe the time-averaged temperature and temperature fluctuation intensity.The normalized temperature is defined as:ü1NX Ni¼1TÃið8ÞN is the total number of sample times.TÃi¼T iÀT cT hÀT cð9Þwhere T i is the transient temperature,T c is the coldfluid inlet tem-perature and T h is hotfluid inlet temperature.The root-mean square(RMS)of the normalized temperature is defined as:TÃrms¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1X Ni¼1TÃiÀTÃ2rð10Þ184K.Gao et al./Annals of Nuclear Energy78(2015)180–187parison of experimental and numerical resultsAs can be seen from the Fig.8,the numerical normalized mean temperature distributions at the plane x/d m=1and the plane x/ d m=2are in good qualitative agreement and in adequate quantita-tive agreement,and most of them are within the experimental deviation of±20%.Meanwhile,the lifting trends of the data are the same.In the direction of180°,the mean temperatures are both minimal.And with the angle decrease to0°,the temperatures are gradually increased.Quantitative differences between the experi-ment and numerical results are that the normalized mean temper-atures given by LES are larger than the experimental data.That is because we did not add insulation unit on tube wall in the exper-iment,leading the transfer of some heat into the air.And in the process of numerical simulation,we ignored the convective heat transfer between the wall and the air.As shown in Fig.9,although the numerical results and experi-mental results have a little difference at the plane x/dm=2around the location of225°and the plane x/dm=2around the location of 0°and315°,all of them are within the error range that can be accepted.Both the simulations and experimental results give a lar-ger mean temperature in the top half of the main pipe than in the bottom half.This verifies the validity of the LES model for predict-ing the mixing of hot and coldfluids in a tee junction.The normalized RMS temperature on the plane x/d m=1and plane x/d m=2are shown in Fig.10,respectively.Similar to the nor-malized mean temperature,the normalized RMS temperature lines agree very well with the experiment ones.Both of the maximum values appear at the bottom half of the pipe.This indicates that the maximum temperaturefluctuations of main pipe appear on the opposite of the branch pipe inlet in this condition.As shown in Fig.11,the numerical results and the experimental results have the same trend and the numerical data are agreed well with the experimental ones.By comparison with Figs.4and5,dif-ferent from the temperaturefluctuations distribution which with-out the branch liquid distributor,there are two peaks of high fluctuation located at the90°and270°directions along with the tube.This is because the direction is that of the outlet of branch liquid distributor,the coldfluidflowing out from the outlet of branch liquid distributor mixes very fast with the hotfluid,leading to dramatic changes of temperature.In summary,the LES simulation results obtained are generally in good qualitative and quantitative agreement with the experi-mental data for the case of T-junction with/without the branch liquid distributor.Based on this,we analyzed the numerical results further.And the results are reported in the section below.4.2.Numerical results with/without branch liquid distributorThe numerical data were sampled on the inner wall in the plane x/ d m=À1,À0.5,0,0.5,1,2,3,4,6and8.At the same time,the numer-ical data were sampled from points every5mm along the intersec-tional lines of planes of y/d m=0and sections of x/d m=À2,À1,0,1,2, 3,4,5and6,to get the points with the maximum normalized rootK.Gao et al./Annals of Nuclear Energy78(2015)180–187185mean square temperatures in the tee and on the top and bottom walls.Here,the temperature and velocityfields were determined with LES simulations for the case of tee junction with/without branch liquid distributor.The temperature contours and velocity vectors for the T-junction are shown in Figs.12and13,respectively.As can be seen in Fig.12,due to the large branch pipeflow velocity,hot and coldfluid mixing zone is mainly located in both upstream and downstream region of the intersections of the main pipe and the branch pipe.The vigorous mixing offluids in the tube leads to thermalfluctuation on the wall.But in the T-junction with the branch liquid distributor,the mixing region moves to the lower half and downstream region of the main pipe.This indicates that the distributor is advantageous to weaken thermalfluctuations on the wall.The same conclusion can be seen from Fig.13,the dis-tributor weaken thermalfluctuations on the wall of downstream region and the top of the main pipe.186K.Gao et al./Annals of Nuclear Energy78(2015)180–187Fig.14compares the normalized mean temperatures between two tees of different structures.As can be seen,wall temperature changes great in the direction of90°,135°,225°and270°in T-junc-tion with the distributor,because the directions are the distributor outlet directions.This indicates that the coldfluid mixes with hot fluid on the wall afterflows out of the distributor.At the same time,the temperature in the direction of180°also changes dra-matically.That is because the coldfluid moves down in the effects of gravity and buoyancy.As shown in Fig.15,for the tee with distributor,the maximum values of normalized RMS temperature are smaller than that of the tee without distributor in most directions.This indicates that the adding of the distributor can relieve thermalfluctuations on the wall to some extent.And for the T-junction with distributor,tem-perature tends to be stable after the plane of x/d m=6,which indi-cates that twofluids have made a full mixing,while for the initial tee,temperature is still in the dramatic change,and this shows that the improved structure can effectively reduce the mixing length.Fig.16shows the maximum normalized instantaneous temper-aturefluctuations in the tee and on the top and bottom walls in the plane y/d m=0.In the tee,the maximum normalized instantaneous temperaturefluctuations of the case without distributor vary from 0.45to0.8,which means that the hot and coldfluids alternate in this location.However,for the case with distributor,the tempera-turefluctuations in the tee as well as on the top and bottom walls are much smaller than those of the case without distributor.That also implies that the distributor can reduce the temperaturefluctu-ation effectively.The normalized instantaneous temperaturefluctuations cannot describe the relationship between power spectrum density(PSD) and frequency of the temperaturefluctuation.PSD against fre-quency is one of the most important parameter for thermal fatigue analysis,which can directly show how PSD is in a certain fre-quency.The PSDs of the points with maximum temperaturefluctu-ation for the cases with and without distributor against frequency were recorded by fast Fourier transform(FFT)and shown in Fig.17. The temperaturefluctuation of the case without distributor has the highest PSD,at the frequency of0.04Hz,whereas the distributor significantly reduces the PSD of the temperaturefluctuations with the frequency from0.01to0.1Hz.In addition,the PSD of temper-aturefluctuations decreases with the frequency increasing.5.ConclusionsAs thermal stratification can result in thermal fatigue in the pip-ing system of a nuclear power plant,safety and integrity evaluation of the piping system has become an important issue.In this work the temperaturefluctuation has been studied by the experiment and numerically predicted by LES for two types of vertical tee junc-tion:one with distributor in the branch pipe and another without. The numerical results of normalized mean and RMS temperatures for the two structures have been found to be in good qualitative and quantitative agreement with the experimental data,which val-idates the use of LES simulations to evaluate convective mixing in such geometries.At the same time,the simulated normalized mean and root-mean square(RMS)temperature,velocity vector and temperature contour of the two tees are compared.The numerical results show that thefluctuations of temperatures of the tee without the distrib-utor are larger than those of the tee with the distributor,which can be explained by the branch liquid distributor enhancing the mix-ing.Although both tees give the same momentum ratio between the main pipeflow and the branch pipeflow,mixing and convec-tive heat transfer are greatly enhanced by the presence of the branch liquid distributor.These all show that the structure is effec-tive for weakening the thermalfluctuation of tee piping wall when hot and coldfluids mix,and it can make the mixing more sufficient.AcknowledgementsThis work was supported by projects of the National Natural Science Foundation of China(No.51276009),Program for New Century Excellent Talents in University(No.NCET-13-0651),and the National Basic Research Program of China(No.2011CB706900). ReferencesAulery, F.,Toutant, A.,Monod,R.,Brillant,G.,Bataille, F.,2012.Numerical simulations of sodium mixing in a T-junction.Appl.Therm.Eng.37,38–43.Brücker,C.,1997.Study of the three-dimensionalflow in a T-junction using a dual-scanning method for three-dimensional scanning-particle-image velocimetry (3-D SPIV).Exp.Therm.Fluid Sci.14,35–44.Cao,Q.,Lu,D.,Lv,J.,2012.Numerical investigation on temperaturefluctuation of the parallel triple-jet.Nucl.Eng.Des.249,82–89.Durve,A.,Patwardhan,A.W.,Banarjee,I.,Padmakumar,G.,Vaidyanathan,G.,2010.Thermal striping in triple jetflow.Nucl.Eng.Des.240,3421–3434.Eric Blondet, C.F.,2002.High cycle thermal fatigue in french PWR.In:10th International Conference on Nuclear Engineering.Arlington,Virginia,USA,pp.429–436.Frank,T.,Lifante,C.,Prasser,H.M.,Menter,F.,2010.Simulation of turbulent and thermal mixing in T-junctions using URANS and scale-resolving turbulence models in ANSYS CFX.Nucl.Eng.Des.240,2313–2328.Galpin,J.,Simoneau,J.P.,rge Eddy Simulation of a thermal mixing tee in order to assess the thermal fatigue.Int.J.Heat Fluid Flow32,539–545. Hosseini,S.M.,Yuki,K.,Hashizume,H.,2008.Classification of turbulent jets in a T-junction area with a90-deg bend upstream.Int.J.Heat Mass Transfer51,2444–2454.Hu,L.-W.,Kazimi,M.S.,2006.LES benchmark study of high cycle temperature fluctuations caused by thermal striping in a mixing tee.Int.J.Heat Fluid Flow 27,54–64.IAEA,2002.Validation of Fast Reactor Thermomechanical and Thermohydraulic Codes,Vienna.Jayaraju,S.T.,Komen,E.M.J.,Baglietto,E.,2010.Suitability of wall-functions in Large Eddy Simulation for thermal fatigue in a T-junction.Nucl.Eng.Des.240,2544–2554.Kamaya,M.,Nakamura, A.,2011.Thermal stress analysis for fatigue damage evaluation at a mixing tee.Nucl.Eng.Des.241,2674–2687.Lee,J.I.,Hu,L.-W.,Saha,P.,Kazimi,M.S.,2009.Numerical analysis of thermal striping induced high cycle thermal fatigue in a mixing tee.Nucl.Eng.Des.239, 833–839.Lu,T.,Jiang,P.X.,Guo,Z.J.,Zhang,Y.W.,Li,H.,rge-eddy simulations(LES)of temperaturefluctuations in a mixing tee with/without a porous medium.Int.J.Heat Mass Transfer53,4458–4466.Lu,T.,Liu,S.M.,Attinger,D.,rge-eddy simulations of structure effects of an upstream elbow main pipe on hot and coldfluids mixing in a vertical tee junction.Ann.Nucl.Energy60,420–431.Metzner,K.J.,Wilke,U.,2005.European THERFAT project—thermal fatigue evaluation of piping system‘‘Tee’’-connections.Nucl.Eng.Des.235,473–484. Paffumi, E.,Radu,V.,Nilsson,K.F.,2013.Thermal fatigue striping damage assessment from simple screening criterion to spectrum loading approach.Int.J.Fatigue53,92–104.Ricard,J.B.,Sperandio,M.,1996.Fracture mechanics applied to superphenix reactor components.Int.J.Pressure Vessels Piping65,295–301.Simoneau,J.-P.,Champigny,J.,Gelineau,O.,2010.Applications of large eddy simulations in nuclearfield.Nucl.Eng.Des.240,429–439.Wu,H.L.,Peng,X.F.,Chen,T.K.,2003.Influence of sleeve tube on theflow and heat transfer behavior at a T-junction.Int.J.Heat Mass Transfer46,2637–2644.K.Gao et al./Annals of Nuclear Energy78(2015)180–187187。

A cohesive approach to thin-shell fracture and fragmentationFehmi Ciraka,*,Michael Ortiz b ,Anna Pandolfic a Center for Advanced Computing Research,California Institute of Technology,Pasadena,CA 91125,USAb Graduate Aeronautical Laboratories,California Institute of Technology,Pasadena,CA 91125,USAc Structural Engineering Department,Politecnico di Milano,20133Milano,ItalyReceived 15January 2004;received in revised form 9March 2004;accepted 20July 2004AbstractWe develop a finite-element method for the simulation of dynamic fracture and fragmentation of thin-shells.The shell is spatially discretized with subdivision shell elements and the fracture along the element edges is modeled with a cohesive law.In order to follow the propagation and branching of cracks,subdivision shell elements are pre-fractured ab initio and the crack opening is constrained prior to crack nucleation.This approach allows for shell fracture in an in-plane tearing mode,a shearing mode,or a bending of hinge mode.The good performance of the method is demon-strated through the simulation of petalling failure experiments in aluminum plates.Ó2005Elsevier B.V.All rights reserved.Keywords:Shells;Finite elements;Subdivision shape functions;Cohesive fracture;Petalling failure1.IntroductionThe experimental and analytical investigation of fracture and fragmentation of thin-plates and shells has elicited considerable interest in the past (see,e.g.,[13,14,27,32,33]).The analytic models proposed to date often introduce ad-hoc approximations regarding the likely failure modes and are restricted to a few regular geometries,loading conditions,and constitutive models.By contrast,numerical simulation of fracture and fragmentations of shells and plates has received comparatively less attention.A notable exception is fur-nished by the finite-element analysis of ‘‘surface-cracked’’plates and shells [12,15,24].In [25],Rice and Levy 0045-7825/$-see front matter Ó2005Elsevier B.V.All rights reserved.doi:10.1016/j.cma.2004.07.048*Corresponding author.Fax:+16266283994.E-mail address:cirak@ (F.Cirak).Comput.Methods Appl.Mech.Engrg.194(2005)2604–2618F.Cirak et al./Comput.Methods Appl.Mech.Engrg.194(2005)2604–26182605 introduced the concept of a line-spring with stretching and bending resistance for the analytical treatment of plates with a surface crack,and computed its compliance from fracture mechanics and energetic consid-erations.In thefinite-element context the line-spring is inserted at the location of the surface-crack in the plate or shell in order to compute quantities relevant for fracture mechanics[24].In the present work,fracture initiation and propagation is considered as a progressive failure phenom-enon in which the separation of the crackflanks is resisted by cohesive tractions.The relationship between the crack opening displacements and the tractions is given by a cohesive model.An appealing feature of the cohesive model is that it provides a complete theory of fracture without presuming a particular bulk mate-rial behavior or geometry of the specimen and the extent of the crack growth.In addition,cohesive models are able to overcome several shortcomings of classical fracture mechanics.For example,in fracture mechanics the conditions for crack growth are typically expressed in terms of parameters characterizing the amplitude of near-tipfields.This restricts the scope of the theory,e.g.,by requiring that the plastic or process zone be small relative to crack dimensions.For three-dimensional solids,cohesive laws may conveniently be encoded into cohesive elements in the form of double surfaces(e.g.,[4,17–23,30,35]and references therein).The opening of the cohesive elements is compatible with the deformation of the adjacent volume elements and is subject to a unilateral closure constraint.Cohesive elements may be inserted adaptively upon the attainment of a critical stress condition on the interelement boundary[4,22,23].The insertion of cohesive elements introduces new surfaces into the mesh,which undergoes complex topological transitions as a result.For three-dimensional solids these tran-sitions can be classified exhaustively[22,23],and appropriate actions may be taken in order to update the representation of the mesh in each case.Certain aspects of the mechanics of thin-shells greatly compound the integration of cohesive theories of fracture.Thus,within the framework of Kirchhoff–Love theory the strain energy density of thin-shells is expressed in terms of thefirst and second fundamental forms of the shell middle surface.Therefore,a con-formingfinite-element discretization requires smooth shape functions belonging to the Sobolev space H2. Cirak and co-workers[5,6]proposed a new type of discretization based on the concept of subdivision sur-faces which delivers smooth H2shape functions on unstructured meshes in a particularly natural and effi-cient way.In addition to several other advantages,an appealing feature of the subdivision elements is that the sole unknowns in thefinite-element solution are the nodal displacements.However,this comes at a cer-tain cost,namely,that the subdivision shape functions are non-local in the sense that the displacementfield within one element depends on the displacements of the nodes attached to the element and the immediately adjacent ring of nodes in the mesh.The natural extension of the cohesive element concept to shells consists of inserting cohesive elements at interelement edges,and constraining the opening of the cohesive elements to conform to the deformation of the middle surface of the shell and its normal.This approach allows for fracture in an in-plane or tearing mode,a shearing mode,or a bending of hinge mode.However,within a subdivision-element framework the essential difficulty resides in making the scheme adaptive,in the sense of inserting cohesive elements in an otherwise conforming mesh upon the attainment of some appropriate critical condition.The non-locality of the displacement interpolation renders the tracking of the topological transitions induced by the insertion of cohesive elements unmanageably complex.In order to sidestep this difficulty,we simply fragment ab ini-tio all the element edges by duplication of common nodes.In calculations,element conformity prior to frac-ture is enforced by the addition of a penalty term to the energy.Alternatively,in explicit dynamics calculations conformity is readily enforced by a displacement averaging technique.The organization of the paper is as follows.In Section2we introduce the used thin-shell theory;we de-scribe the kinematics,derive the weak form of the equilibrium equation,and introduce the spatial discret-ization with subdivision shape functions.The material models for bulk and cohesive surfaces are described in Section4.In Section5we conclude with selected application examples which demonstrate the feasibility and good performance of the method.2.Thin-shell with a crack through the thickness2.1.Kinematic descriptionWe begin with a brief review of the assumedfinite kinematics of the Kirchhoff–Love type shell model[5]. Subsequently,the extension of the kinematic description to the case of a fractured shell body is introduced. For alternative kinematic models for shells we refer to[2,3,28]and references therein.Consider a shell body of uniform reference thickness h occupying a reference configuration V,parame-trized with convective coordinates h1,h2,and h3uðh1;h2;h3Þ¼ xðh1;h2Þþh3 a3ðh1;h2ÞwithÀ h26h36h2:ð2:1ÞThe position of the shell middle surface is given by x and the unit normal to the middle surface also known as the shell director is defined bya3¼ a1 a2j a1Âa2j;ð2:2Þwith the covariant surface basis vectors1a a¼ x;a¼o x o h a:The mapping u maps the shell body into the deformed configuration Vuðh1;h2;h3Þ¼xðh1;h2Þþh3k a3ðh1;h2ÞwithÀ h26h36h2:ð2:3ÞThe thickness stretch parameter k¼h= h>0relates the deformed shell thickness h to the reference shell thickness h.We use a Kirchhoff–Love type kinematic assumption and assume that the deformed director a3is normal to the deformed shell middle surfacea3¼a1Âa2j a1Âa2j:ð2:4ÞWith the previous assumptions the deformation gradient F of the deformation mapping u uÀ1can be written asF¼o uo u¼o uo h ig i¼a a g aþk a3 g3þh3ðk a3Þ;ag a;ð2:5Þwhere g i¼o h i=o u are the contravariant basis vectors of the undeformed configuration.Next,we assume the existence of a crack in the shell body with the two opposite crackflanksCþC ½Àhþ=2;hþ=2 and CÀC½ÀhÀ=2;hÀ=2 lying on the plus and minus sides of the crack,denoted by+andÀ,respectively(see Fig.1).The two curves CþC and CÀCon the middle surface have in the parameterspace(h1,h2)the same parametric representationh1¼h1ðnÞ;h2¼h2ðnÞwith n2R:ð2:6ÞThe deformation is generally discontinuous across the crack and has a jumps u t¼uþÀuÀ:ð2:7Þ1In the derivations the index notation is used where the Greek indices range from1to2and the Latin indices from1to3.Further, a comma is used to denote partial differentiation and the summation convention is assumed to be in force.2606 F.Cirak et al./Comput.Methods Appl.Mech.Engrg.194(2005)2604–2618Using the previous kinematic assumptions (2.3),the jump in the deformation can be written ass u t ¼s x t þh 3s k a 3t :ð2:8ÞNote that the first term describes the discontinuity in the middle surface deformation and the second term the discontinuity in the shell normal.The discontinuities in the deformations can also be interpreted as the ‘‘opening displacement’’of the crack.For the subsequent derivations,we decompose the jump s u b into a normal and a shear component with respect to a local coordinate frame attached to the crack.To that purpose we first define an average unit normal n to the crack flanks C þC ½Àh þ=2;h þ=2 and C ÀC ½Àh À=2;h À=2n ¼12ðn þþn ÀÞj 1ðn þþn ÀÞj :ð2:9ÞThe crack surface normal vectors n ±are computed from the tangent vectors t ±and the shell directors a Æ3n Ƽt ÆÂa Æ3:ð2:10ÞThe tangent vectors are computed from the parametric location of the crack flanks (2.6)and the deforma-tion mappingt Ƽo u Æo h a o h ao n :ð2:11ÞThus,the jump in the deformations s u b ,here and henceforth denoted with d ,can be decomposed into the normal and tangential components d n and d s ,given respectively byd n ¼d Án ;d s ¼d Àd n n ¼ðI Àn n Þd ;d s ¼j d s j :ð2:12Þ2.2.Weak form of the equilibriumA standard semi-inverse approach is followed for deriving the shell equilibrium equations in weak form.The assumed reduced kinematic equations for the shell body (2.1)and (2.3)are introduced into the virtual work expression for the three-dimensional bodydP int ÀdP ext ¼0;ð2:13ÞF.Cirak et al./Comput.Methods Appl.Mech.Engrg.194(2005)2604–26182607with the internal and external virtual work dP int and dP ext,respectively.In combination with proper boundary conditions,which have been omitted here for brevity,the weak form gives the equilibrium con-figurations of the shell body.As previously mentioned,we consider fracture as a gradual separation phe-nomenon,resisted by cohesive tractions.Consequently,the internal virtual work expression contains the virtual work of the cohesive interface in addition to the virtual work of the bulk material dP int¼dP S;intþdP C;int;ð2:14ÞwithdP S;int¼ZX Z h=2À h=2P:d F l d h3d X;ð2:15aÞdP C;int¼ZC Z h=2À h=2TÁd d l d h3d C C;ð2:15bÞwhere P is thefirst Piola–Kirchhoffstress tensor,T is the related traction vector at the cohesive surface,and l accounts for the curvature of the shell in the computation of the volume[5].Note that for hyperelastic constitutive models,with internal energy density W for the bulk material and/for the cohesive interface, the tensor P and the vector T may be derived fromP¼o Wo F;T¼o/o d:ð2:16ÞSubstituting the shell kinematics(2.5)and(2.8)into internal virtual work expression(2.15)givesdP int¼Z Z h=2À h=2P:d a a g aþd a3 g3þh3kd a3;a g aÀÁl d h3d XþZC Z h=2À h=2TÁd s x tþh3kd s a3tÀÁl d h3d C C:ð2:17ÞIn(2.17)we disregard the spatial variation of the thickness stretch parameter k.Following[5],the thickness stretch k is computed from enforcing the thin-shell typical plane stress assumption on the constitutive level (see Section4).The stress resultant n i and the coupled force m a for the shell are defined asn i¼Z h=2À h=2PF TÁg i l d h3;m a¼Z h=2À h=2PF TÁg a h3l d h3ð2:18Þand substituting them into the internal work of the bulk material gives a more compact expressiondP S;int¼ZXn aÁd a aþn3Ád a3þm a kd a3;aÂÃd X:ð2:19ÞFor dynamic problems,the weak form of equilibrium is augmented by the virtual kinetic work dP kinþdP intÀdP ext¼0;ð2:20ÞwithdP kin¼ZX Z h=2À h=2q€uÁd u l d h3d X;ð2:21Þwhere q is the initial mass density of the bulk material and€u is the acceleration vector. 2608 F.Cirak et al./Comput.Methods Appl.Mech.Engrg.194(2005)2604–26183.Subdivision thin-shell elementsThe reference ( x)and deformed (x )shell middle surfaces are discretized with smooth subdivision shape functions,as introduced in [6].The interpolation within one element is accomplished with shape functions which have support on the element as well as on the one ring of neighboring elements (see Fig.2)x ¼XNP I ¼1N I x I ;x ¼X NP I ¼1N I x I :ð3:1ÞThe number of the control points NP involved in the interpolation of each element depends on the local connectivity of the mesh.For example,for regular patches where each of the three element vertices are inci-dent to six elements the interpolant derived from the Loop Õs subdivision scheme has NP =12control points[16,31].The overlapping local interpolations,each over one patch,combined lead to a global interpolation with square integrable curvatures.In presence of fracture,the smoothness and/or continuity of the interpolation has to be relaxed.In our implementation,we assume that cracks can only nucleate and propagate along element edges.Furthermore,once fracture nucleates,the element patches on the left and right side of the cracked edge interact only through cohesive tractions.The cohesive tractions are self-balanced internal forces derived from a cohesive fracture model (see Section 4.2).The topological changes necessary to the non-local subdivision functions and the underlying control mesh in order to describe the propagation of a single crack are rather compli-cated.Therefore,we chose to pre-fracture all the element patches,so that each patch possesses its own nodes and acts independently for the purpose of interpolation.Each element patch consists of a triangular element and all the nodes in the one neighborhood of that element (see Fig.2).The resulting interpolation of the shell middle surface is always smooth over one triangle and allows discontinuities along the edges depending on the positioning of the control nodes.Prior to crack nucleation,we propose two alternative approaches to enforce the coupling between the distinct elements.In the first approach the interaction of the elements is enforced by a stiffelastic cohesive interface model applied at all non-cracked edges.Once a crack nucleates,the interface model on that edge is replaced with a conventional cohesive model (see Sec-tion 4.2).In the second approach,all the vertices which have the same coordinates in the reference config-uration are initially algorithmically forced to have the same displacements.In the explicit dynamic case the related algorithmic procedures can easily be implemented with a pointer based data structure provided by,e.g.,C/C++.Once a crack nucleates along an edge,all the vertices in the domain of influence of that edge are allowed to move independently (see Fig.3).Furthermore,on all the edges connected to the two vertices of the cracked edge a cohesive interface is activated.The discretization of the cohesive internal virtual work (2.17)with the subdivision shape functions givesdP C ;int ¼Z C C Z h =2À h =2T Ád X N I x þI Àd X N I x ÀI h i ;n þh 3T Ák þd a 3X N I x þI Àk Àd a 3X N I x ÀI h io l d h 3d C C :ð3:2ÞF.Cirak et al./Comput.Methods Appl.Mech.Engrg.194(2005)2604–26182609Thus,the internal forces at the vertex I are given byf I Æint ¼o P int o x ÆI ¼ÆZ C Z h =2À h =2T N I l d h 3d C C ÆZ C Z h =2À h =2h 3k ÆT Áo a 3ðP N J x ÆJ Þo x ÆI l d h 3d C C :ð3:3ÞThe integral over the cohesive surface is numerically integrated with different rules along the edge C C and across the thickness À h 2; h 2ÂÃ.Along the edge we use three Gauss points and across the thickness more than three Simpson points.The integrals over the shell middle surface X are numerically integrated with seven Gauss points,which is exact for up to fifth order polynomials [36].The contribution of the shell to the inter-nal force vector is equivalent to the non-fractured shell (see [5]for details).4.Constitutive modelsIn the previous work on subdivision shells [5–7]compressible as well as incompressible hyperelastic material models have been used.In the present extension,we assume a viscoplastic behavior for the bulk and a cohesive model to account for the crack propagation.4.1.Finite deformation viscoplasticityThe inelastic behavior of the shell is described with a rate dependent finite deformation viscoplasticity model,based on a standard multiplicative decomposition of the deformation gradient into an elastic and inelastic part.We apply the fully implicit method proposed by Cuitin ˜o and Ortiz in [9],where,by using logarithmic and exponential mappings,the constitutive update algorithms used for small strain plasticity are extended to finite plasticity.The small strain plasticity model is a conventional J 2model with isotropic power-law hardening and power-law viscosity.The power-law hardening for the flow stress g has the formg ð p Þ¼r y 1þ p p 01=n ;ð4:1Þwhere r y is the initial yield stress, p and p0are the total and the reference plastic strains,respectively,and 1/n is the hardening exponent.The rate-dependent behavior is described in terms of the effective von Mises stress r effwith a power viscosity law and constant rate sensitivityr eff ¼g ð p Þ1þ_ pp 0 1=m ;ð4:2Þwhere _ p 0is the reference plastic strain rate and 1/m the strain rate sensitivity exponent.Effectively,the constitutive update algorithm gives the first Piola–Kirchhofftensor P for a given defor-mation gradient F and a set of history dependent variables.The equivalent Kirchhoffstress tensor s =PFT2610 F.Cirak et al./Comput.Methods Appl.Mech.Engrg.194(2005)2604–2618and its components in the deformed covariant basis s =s ij g i g j ,with g i =o u /o h i ,can be computed by applying proper transformations.The value of the thickness stretch parameter k is computed iteratively,e.g.,by means of a Newton–Raphson iteration,from the plane stress condition s 33=0(see,e.g.,[5,10]for details).4.2.Cohesive interface modelIn the computations subsequently presented we employ an irreversible cohesive model of the general form proposed in [19].In this model,the opening displacement d plays the role of a deformation measure while the tractions T is the conjugate stress measure.The free energy density per unit undeformed area is assumed to be of the form/¼/ðd ;q Þ;ð4:3Þwhere q is a suitable set of internal variables and d is a scalar effective opening displacement d ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib 2d 2s þd 2n q ð4:4Þdefined in terms of the normal d n and sliding d s opening displacements,as defined in (2.12).The parameter b effectively assigns different weights to the sliding and opening displacements.It can be shown,[19],that the relation between the opening displacement and cohesive traction is of the formT ¼T d ðb 2d S þd n n Þ;ð4:5Þwith the scalar effective tractionT ¼o /o dðd ;q Þ:ð4:6ÞEq.(4.5)identifies b as the ratio between the shear and the normal cohesive strength of the material.The parameter b can alternatively be regarded as the ratio of mode II to mode I fracture toughness of the bulk material [19].In the calculations we employ the monotonic envelope shown in Fig.4,and unloading is as-sumed to occur towards the origin.The parameters of the model are the maximum tensile stress r c and the mode I fracture energy density G c .The critical opening displacement is then given by d c =2G c /r c .As noted in the foregoing,we sidestep the need to track the topological transitions due to the insertion of cohesive elements by pre-fracturing all shell-element edges.In explicit dynamic calculations,conformity at the edges prior to crack nucleation can,e.g.,be enforced by a projection method consisting ofnodal F.Cirak et al./Comput.Methods Appl.Mech.Engrg.194(2005)2604–26182611momentum averaging.In the subsequently presented computations conformity is enforced by a penalty method.This effectively amounts to replacing the initial rigid portion of the cohesive law by a stifflinear response of the formT ¼k d ;ð4:7Þwhere k is a penalty parameter.In tension,this relation is replaced by the proper cohesive law when k d reaches r c .Under compression the penalty relation serves the purpose of enforcing the closure constraint.In particular,in bending dominated fracture,part of the shell thickness may be under compression,and hence uncracked,whereas the remainder of the thickness may be opening as a part-through crack.5.Applications5.1.Square plateIn order to gain insight into the sensitivity of the numerical solution on the choice of the penalty para-meter k (4.7)we consider a simply supported plate with a pre-fractured shell model.The plate is linear elas-tic and the penalty relation (4.7)is used in lieu of a cohesive law.This reduced model is similar in spirit to the interior penalty method for the bilaplacian equation introduced by Babuska et al.[1].It is known that this method has an inherent consistency error and therefore the convergence in the energy norm is not optimal.However,optimal convergence can be attained by means of a correction proposed by Hansbo et al.[11].The simply supported square plate has an edge length L =1and a thickness h =0.1and is subjected to uniform static pressure loading of p =0.1.We choose a Young Õs modulus E =69,000and a Poisson Õs ratio m =0.3.The plate is discretized into 1024elements and the deflected shapes are computed for k /E =500,1000,5000,10,000,and 50,000.Fig.5shows the normalized maximum out of plane displacement as func-tion of the penalty coefficient k .The displacements are normalized with the analytical series solution of6.425·10À5[29].It follows from this analysis that the non-fractured solution is ostensibly recovered for modestly large values of k .5.2.Petalling of aluminum platesThe present framework can be applied to a variety of thin plate and shell fracture and fragmentation problems,such as the perforation of thin-plates impacted by fast moving projectiles [8,13,14,26,27,34].2612 F.Cirak et al./Comput.Methods Appl.Mech.Engrg.194(2005)2604–2618As an example of application,we simulate the experiments of Landkof and Goldsmith[14]concerned with the petalling failure of circular aluminum plates with and without initial holes struck by hard-steel conical projectiles.In the experiments of Landkof and Goldsmith under consideration,the circular alumi-num(Al2024-0)target plates have a diameter of139.7mm and a thickness of1.27mm or3.175mm.For the plates with an initial hole at the center of the plate,the hole diameter is4.76mm,6.35mm,or9.53mm. The heat-treated steel projectile is cylindrical–conical in shape and has a diameter of d b=12.7mm,a length of L b=35.55mm,and a weight of m b=29.5g.The projectile has a striking velocity in the range of300–600m/s.The projectile velocity after passing through the target plate was measured and compared with the predictions of analytical models based on energetic considerations[14].In calculations we consider a solid plate and a perforated plate with a6.35mm diameter hole.The plate thickness is3.175mm in both cases. The striking velocity is v i=320m/s.The bulk material response of the aluminum plates is assumed to obey the J2-plasticity model described in Section4.1.The material parameters for the plasticity model are pro-vided in[14]and are collected in Table1.The material properties chosen for the cohesive model are col-lected in Table2.The weighting coefficient b has been chosen according to previous computations on aluminum specimens[21].Thefinite-element meshes used in calculations are shown in Fig.6.The time step of0.00045l s is chosen to be smaller than the critical time step for explicit integration.To contain the numerical effort,we decided not to model the contact between the plate and projectile.The effect of the projectile impact is simply simulated by applying a pressure history over the impact area corresponding to the force exerted by the conical tip of the projectile.The impact force has been computed from the decel-eration D v of the projectile,as measured in the experiments[14].We begin by estimating the time for the projectile to cross the plate as the ratio between the projectile length and initial bullet velocity,with the resultD t¼L bv b:ð5:1ÞA rough estimate of the impact force F is thus given by the deceleration times the bullet massF¼m b D vD t:ð5:2ÞThe average impact pressure corresponding to the force F is computed asp i ¼FA i¼4Fp db;ph¼FA i¼4FpðdbÀdhÞ;ð5:3Þwhere p i refers to the solid plate and p h to the plate with a hole.Based on an average velocity drop D v=40m/s,in simulations we set p i=159N/mm2and p h=213N/mm2.In order to account for the conical shape of the projectile nose,the pressure(see Fig.7)is applied on a progressively increasing circular area of radiusTable1J2-plasticity model with power-law hardening and rate dependency:material properties for the bulk behavior of Al2024-0[14] Mass density q=2719kgYoungÕs modulus E=69,000MPaPoissonÕs ratio m=0.33Yield stress r0=90MPaReference plastic strain e p0¼0:001Hardening exponent1/n=4Reference plastic strain rate_e p0¼0:00011/sRate sensitivity exponent1/m=0.01F.Cirak et al./Comput.Methods Appl.Mech.Engrg.194(2005)2604–26182613。

Eur.Phys.J.B73,433–437(2010) DOI:10.1140/epjb/e2010-00015-8 Regular Article T HE E UROPEANP HYSICAL J OURNAL BGenotype selection model with two time-correlated white noises X.-M.Zhang and B.-Q.Ai aLaboratory of Quantum Information Technology,ICMP and SPTE,South China Normal University,Guangzhou,P.R.China Received6April2009/Received infinal form4November2009Published online15January2010–c EDP Sciences,Societ`a Italiana di Fisica,Springer-Verlag2010Abstract.We study the steady state properties of a genotype selection model in the presence of two timecorrelated Gaussian white noises.Based on the corresponding Fokker-Planck equation the steady statesolution of the probability distribution has been investigated.Thefluctuation of both the mutation factorand the genetic factor can break the balance of the gene selection.Thefluctuation of the genetic factor canfacilitate the gene separation which allows us to select one gene-type haploid from a gene group while thefluctuation of the mutation factor impedes the gene separation.Remarkably,the correlation time betweenthe two noises can induce the system to change from two states to one.1IntroductionRecently,nonlinear stochastic systems with a noise term have been the subject of extensive investigations.The con-cept of a noise-induced transition has many applications in thefields of physics,chemistry and biology[1–5].Sci-entists have also pinned they hopes on nonlinear science to reveal the complexity and variety of biology.Over the past ten years more and more evidence has indicated that the noise plays an important part in nonlinear systems such as in phase transitions and stochastic sympathetic vibration caused by noises.Especially the stochastic sym-pathetic vibration caused by noise can reveal and explain some complex biology phenomena.In these systems the noise usually affects the dynamics through a system vari-able,i.e.,the noise is both multiplicative and additive. The focus of these investigations is to study the steady state properties of systems in whichfluctuations,gener-ally applied externally,are considered independent of the systems’characteristic dissipation.Since the two types of fluctuation have a common origin,they are correlated on the relevant timescale of the problem.Indeed,due to the finite transmission times of the signals or other key quanti-ties,the time delay is ubiquitous in many physical systems and the effects of noise on dynamical systems with time delays have recently gained considerable attention.These investigations have shown that the interplay between noise and time delay can fundamentally change the statistical properties of the system.Borromeo and coworkers have observed the nonequilibrium escape dynamics in a bistable a e-mail:aibq@ system under the influence of two Gaussian white noises, one obtained by recycling,the other with constant delay time,studied by means of numerical simulation,to exhibit stochastic synchronization.Under stationary conditions, an appreciable fraction of renewal trajectories gets locked to the noise-recycling delay time.The ensuing mechanism of resonant stochastic synchronization is reminiscent of stochastic resonance with the recycle delay time replacing the external drive period[6].The one-dimensional motion of a massless Brownian particle on a symmetric substrate can be rectified by reinjecting its driving noise through a realistic recycling procedure[7].The rectification of a massive Brownian particle moving on a periodic substrate can be achieved in the absence of spatial asymmetry,by having recourse to at least two periodic,zero-mean input noises[8].As a nonlinear equation,the genotype selection model possesses plenteous physical and biological significance.In this paper,we study the steady state properties of a geno-type selection model in the presence of two time-correlated Gaussian white noises.We place emphasis onfinding how the cross-correlation time affects the genotype selection model.It is found that both the mutation factor and the genetic factor can break the balance of gene selection.2The simple genotype selection modelWe select a haploid group as our object and suppose that each haploid may have gene A or gene B[9,10].The num-ber of gene A haploids,gene B haploids,and the total are N A(t),N B(t),and N(t)at time t,respectively.For434The European Physical Journal B N(t)=N A(t)+N B(t),we can make a transform as fol-lows:x(t)=N A(t)N(t),1−x(t)=N B(t)N(t),0≤x(t)≤1,(1)where x is the ratio of gene A number to total number.In this study,we only consider the fraction of gene A haploids,x.In timeΔt the change in the fraction of gene A contains two parts:mutation and heredity.So we obtain x(t+Δt)−x(t)=Δx1(t)+Δx2(t),(2)whereΔx1(t)is the change in the fraction of gene A caused by mutation andΔx1(t)is the change in the fraction of gene A caused by heredity.If gene A haploids and gene B haploids may have a mutation(A→B or B→A)during the process of heredity and the rates of A→B and B→A are m AΔt and m BΔt, respectively,we obtain the following equation,Δx1(t)=−m AΔtx(t)+m BΔt[1−x(t)].(3)On the other hand,on account of self-sow,the gene hap-loid has its rebirth rate,N A(t+Δt)=ωA N A(t),N B(t+Δt)=ωB N B(t),(4)whereωA=1+S t/2,ωB=1−S t/2,S t is the gene selection constant which will be infinitesimal(S t→0) for a very small time intervalΔt,andΔt is the time gap between border generations.From equations(1)and(4) we can getΔx2(t)=(1+S t/2)x(t)(1+S t/2)x(t)+(1−S t/2)[1−x(t)]−x(t),=S t x(t)[1−x(t)] 1−S t/2+S t x(t),≈S t x(t)[1−x(t)],as S t→0.(5) Considering equations(3)and(5)together we can get the differential equation for x(t)in the case ofΔt→0,dx(t)dt=β−γx(t)+μx(t)[1−x(t)],(6)whereβ=m B,γ=m A+m B,μ=limΔt→0S tΔt.In biologicalwords,βis the mutation factor andμis the genetic factor. In order to simplify the equation,we suppose m A+m B= 1.So the simplified gene selection dynamic equation is shown as follows[11]:dx(t)dt=β−x(t)+μx(t)[1−x(t)].(7)Now if some environmental external disturbance make the gene selection rate of the haploidfluctuate,it is likely to affect bothβandμin the form of mutation and genetic factors that are connected through a time-correlated pa-rameter.In other words the externalfluctuations affect the parameterμwhichfluctuates around a mean value,thus generating a genetic factor and at the same time environ-mentalfluctuations perturb the dynamics directly which gives rise to a mutation factor.So we havedx(t)dt=β−x(t)+μx(t)[1−x(t)]+x(t)[1−x(t)]ξ2(t)+ξ1(t),(8)whereξ1(t)andξ2(t)are Gaussian white noises with the following properties[12–16]:ξ1(t) = ξ2(t) =0,(9) ξ1(t)ξ1(t ) =2D1δ(t−t ),(10) ξ2(t)ξ2(t ) =2D2δ(t−t ),(11) ξi(t)ξj(t ) =λij√D1D2τijexp−|t−t |τij,(12)where i,j=1,2and i=j.It must be pointed out that two delta-correlated noises with exponentially decaying cross-correlation function have been extensively investi-gated[13–17].D1and D2are the strength of white noises ξ1(t)andξ2(t),respectively.In other words,D1and D2 are thefluctuation strength of the mutation and genetic factors,respectively.τis the cross-correlation time.t is the delay time,which exists due to the combination of di-verse propagation or transduction mechanisms.To avoid technical complications[6–8],we assume thatτij≡τ,of courseτ→0corresponds to taking the white noise limit ofξi(t).λdenotes the degree of correlation between the two white noisesξ1(t)andξ2(t).Here,without loss of gen-erality,λ11=λ22=1andλ12=λ21=λ.In particular, whenλ=0,the two noises are independent;λ=1,it indi-cates the two noises are identical,i.e.,ξ1(t)=ξ2(t);when λ=−1,the two noises are reverse,i.e.,ξ1(t)=−ξ2(t).3Steady state analysis of the modelWe now proceed with a probabilistic description corre-sponding to a Langevin equation(8)with the prescriptions (9,10,11,12)for the two correlated white noises.Follow-ing the methods in[7,19–22],the time evolution equation for the probability density is given by∂p(x(t),t)∂t=−∂∂xf(x(t))p(x(t),t)−∂∂xξ1(t)δ[x(t)−x(t)(1−x(t))]− x(t)ξ2(t)δ[x(t)−x(t)(1−x(t))] .(13)Here f(x(t))=β−x(t)+μx(t)[1−x(t)].The averages ··· in equation(13)can be calculated for Gaussian noises by the Novikov theorem[23,24].The resulting equation is theX.-M.Zhang and B.-Q.Ai:Genotype selection model with two time-correlated white noises435 Fokker-Planck description as given by[12,22,25]∂p(x(t),t)∂t =−∂∂xf(x(t))p(x(t),t)−D2∂∂xx(t)[1−x(t)]×∂∂xx(t)[1−x(t)]p(x(t),t)+λ√D1D21+τ(1−μ)2+4μβ∂∂xx(t)[1−x(t)]×∂∂xp(x(t),t)+λ√D1D21+τ(1−μ)2+4μβ×∂2∂x(t)2x(t)[1−x(t)]p(x(t),t)+D1∂2∂x(t)2p(x(t),t).(14)The Fokker-Planck equation(14)can be recast in a more simple form as∂p(x(t),t)∂t =−∂∂xf(x(t))−12∂∂xR(x(t),τ)−R(x(t),τ)∂∂xp(x(t),t),(15)where R(x(t),τ)is the effective diffusion constant R(x(t),τ)=D2[x(t)(1−x(t))]2+2λ√D1D21+τ(1−μ)2+4μβx(t)[1−x(t)]+D1.(16)The steady state solution of equation(14)whenτtends to infinity can be written asP st(x(t))=N0R(x(t),τ)−12exp xdyf(y)R(y,τ),(17)where N0is the normalized number.we carry out a numer-ical analysis for equation(17)and the results are presented in Figures1−5.In Figure1,we study the effects of the strength of the additive noise intensity(thefluctuation of the muta-tion factor)D1on the steady state probability distribu-tion(SPDF).As we can see,the curve is symmetric and the height of the peak decreases with increasing D1.For a small value of D1the curve shows a double peak and the distance between the two peaks becomes smaller.The left peak is near x=0while the right one is near x=1,which shows that the environmental selection yields a high prob-ability for one of the two(genes A and B).In this case it is easy to select one type of haploid from the group since the other haploid type number can be neglected with respect to the selected type number.This is different from the case in the presence of two white noises without time correla-tion.This is due to the transferability ofτ.As the value of D1increases,the curve shows a single peak(at x=0.5), which indicates that under this conditionenvironmental Fig.1.(Color online)P st(x)(steady probability density)as a function of x(the ratio of gene A number to the total)for different values of the mutation factor intensity D1=0.01,0.1 and2.0,respectively,at D2=0.5,τ=2.0,λ=0.1,β=0.5, andμ=0.0(units arerelative).Fig. 2.(Color online)Plot of P st(x)(probability density) against x(the ratio of gene A number to the total)for dif-ferent values of the genetic factor intensity D2.D2=0.5,1.5 and5.5,respectively,at D1=0.5,τ=2.0,λ=0.1,β=0.5, andμ=0.0(units are relative).selection gives the same chance to both the gene A hap-loid and the gene B haploid and it is not easy for us to select one haploid from the group.For a large value of D1, the single peak region vanishes and the height is weakly affected by D1,which indicates that the mutation factor plays a diffusing role in the process and draws the prob-ability distribution towards a uniform distribution.The feature is the same in the presence of two white noises without time correlation.On the other hand,from this curve we can deduce that the mutation factor can induce the phase transition from two peaks to one peak.There-fore,smallfluctuations of the mutation factor can help the gene separation.Figure2shows the effects of the strength of the mul-tiplicative noise intensity(thefluctuation of the genetic factor)D2on the SPDF.The curve is symmetric.For a small value of D2the curve shows a single peak(at436The European Physical JournalBFig. 3.(Color online)Plot of P st (x )(probability density)against x (the ratio of gene A number to the total)for dif-ferent values of the selection gene μ.μ=−1,−0.5,0,0.5and 1,respectively,at D 1=0.5,D 2=0.5,τ=2.0,β=0.5,and λ=0.1(units arerelative).Fig.st against x (the ratio of gene A number to the total)for dif-ferent values of the cross correlation time τ.τ=0.0,1.0,10.0,respectively,at D 1=5.0,D 2=1.5,β=0.5,μ=0.0,and λ=0.1(units are relative).x =0.5),which indicates that under this condition en-vironmental selection gives the same chance to both the gene A haploid and the gene B haploid and it is not easy for us to select one haploid from the group.The height of the single peak decreases with increasing D 2.As the value of D 2increases,the single peak vanishes and evolves into a double peak and the distance between the two peaks becomes larger with D 2.The height of the two peaks in-creases with D 2.The left peak is near x =0while the right one is near x =1,which shows that the environ-mental selection yields a high probability for one of the two (gene A and gene B).In this case it is easy to select one haploid type from the group since the other haploid type number can be neglected with respect to the selected type number.On the other hand,from this curve we can deduce that the genetic factor can induce the phasetran-Fig.5.Plot of x against τat D 1=5.0,D 2=1.5,β=0.5,μ=0.0,and λ=0.1.sition from one peak to double peaks.All of these features are similar to the case in the presence of two white noises without time correlation.Therefore,the fluctuation of the genetic factor can facilitate the gene separation.Figure 3shows the effects of the selection gene μon SPDF.When the genetic factor is zero (μ=0),the curve is symmetric and shows a single peak (at x =0.5).It is ev-ident that the gene A haploid and the gene B haploid have the same probability distribution,which indicates that un-der this condition environmental selection gives the same chance to both the gene A haploid and the gene B hap-loid and it is not easy for us to select one haploid from the group.If the selection rate gets a negative value the curve shows a single peak and the peak of the curve is biased to the left and the height of the peak decreases with μ.It is evident that the selection is unfair which is favourable to the gene B haploid.That is to say negative values of the genetic factor may help the separation of the gene B haploid.On the other hand,for a positive value of μthe curve shows a single peak biased to the right and the height of the peak increases with μ,which indicates that positive values of the genetic factor may help the sep-aration of the gene A haploid.All of these are the same as in the presence of two white noises without time corre-lation.Therefore,both negative and positive values of the genetic factor can facilitate the gene selection.Figure 4depicts the effects of the cross correlation time τof the two white noises on the SPDF.As we can see,the curve is symmetric and the height of the peak in-creases with increasing τ.For a small value of τthe curve shows a double peak and the distance between the two peaks becomes smaller with increasing τ.The left peak is near x =0while the right one is near x =1,which shows that the environmental selection yields a high probabil-ity for one of the two (genes A and B).In this case it is easy to select one haploid type from the group since the other haploid type number can be neglected with respect to the selected type number.As the value of τincreases,the curve gradually develops a single peak,which indicates that under this condition environmental selection gives the same chance to both the gene A haploid and the gene BX.-M.Zhang and B.-Q.Ai:Genotype selection model with two time-correlated white noises437haploid and it is not easy for us to select one haploid from the group.On the other hand,from this curve we can deduce that the cross correlation time can induce the phase transition from two peaks to one.Therefore,large correlation times act against the gene separation.Figure5shows the effects of different values ofτon the average value of x.As the curve shows,for a small value ofτthe average value of x increases rapidly while for a large value ofτthe average value of x increases slowly. 4ConclusionsWe have studied the steady state properties of a geno-type selection model in the presence of two time-correlated Gaussian white noises.The white noises–in both the mu-tation factor and the genetic factor–can break the single peak state to the double peak state,which indicates that the selection in this case dominates for one of the two (gene A and gene B).The mutation factor plays a diffus-ing role in the process,which causes the probability distri-bution to tend to a uniform distribution and the genetic factor can induce the phase transition from one peak to double peaks.Thefluctuations of both the mutation factor and the genetic factor can break the balance of the gene se-lection.Thefluctuation of the genetic factor can facilitate the gene selection while thefluctuation of the mutation factor acts against the gene rge correlation time will act against the gene separation.From the discus-sion above,wefind that the noise can change the nature of the selection from an equal probability selection to a dif-ferential probability one,which benefits us in selecting one haploid from a haploid group.The breaking of the sym-metry and the special gene selection are very important to producing gene order and biological evolution.This work was supported in part by National Natural Sci-ence Foundation of China with Grant No.30600122and GuangDong Provincial Natural Science Foundation with Grant No.06025073.References1. A.Fulinski,T.Telejko,Phys.Lett.A152,11(1991)2. B.Q.Ai,X.J.Wang,G.T.Liu,L.G.Liu,Phys.Rev.E67,022903(2003)3. B.Q.Ai,L.G.Liu,J.Phys.Chem.B112,9540(2008)4.J.M.Sancho,M.San Miguel,S.L.Katz,J.D.Gunton,Phys.Rev.A26,1958(1982)5. B.Q.Ai,L.G.Liu,Phys.Rev.E74,051114(2006)6.M.Borromeo,F.Marchesoni,Phys.Rev.E75,041106(2007)7.M.Borromeo,S.Giusepponi,F.Marchesoni,Phys.Rev.E74,031121(2006)8.M.Borromeo,F.Marchesoni,Chaos15,026110(2005)9. B.Q.Ai,X.J.Wang,L.G.Liu,M.Nakano,H.Matsuura,Commun.Theor.Phys.37,125(2002)10.W.David,J.R.Peck,Science279,1210(1998)11.G.Hu,Stochastic Forces and Nonlinear Sysistem(Shanghai Scientific,and Technological Education Publishing,Shanghai,1994)12.X.Luo,S.Zhu,Phys.Rev.E67,021104(2003)13.Y.Jia,J.R.Li,Phys.Rev.E53,5786(1996)14. D.C.Mei,G.Z.Xie,L.Cao,D.J.Wu,Phys.Rev.E59,3880(1999)15. D.C.Mei,C.Xie,L.Zhang,D.J.Wu,Phys.Rev.E68,051102(2003)16.P.K.Ghosh,B.C.Bag,D.S.Ray,J.Chem.Phys.127,044510(2007)17.G.Goswami,P.Majee,B.C.Bag,Int.J.Theor.Phys.47,1173(2008)18.P.Majee,B.C.Bag,J.Phys.A37,3352(2004)19.J.Masoliver,B.J.West,K.Lindenberg,Phys.Rev.A35,3086(1987)20.R.L.Stratonovich,Topics in the Theory of Random Noise(Gordon and Breach,New York,1963),Vol.121.K.Lindenberg,B.J.West,J.Stat.Phys.42,201(1986)22. D.J.Wu,L.Cao,S.Z.Ke,Phys.Rev.E50,2496(1994)23. E.A.Novikov,Zh.Eksp.Teor.Fiz.47,1919(1964)24. E.A.Novikov,Sov.Phys.JETP29,1290(1965)25.Y.Jia,J.R.Li,Phys.Rev.Lett.78,994(1997)。

[推荐][名词委审定]汉英力学名词(1993)[翻译与翻译辅助工具] [回复] [引用回复] [表格型] [跟帖] [转发到Blog] [关闭] [浏览930 次] 用户名: westbankBZ反应||Belousov-Zhabotinski reaction, BZ reactionFPU问题||Fermi-Pasta-Ulam problem, FPU problemKBM方法||KBM method, Krylov-Bogoliubov-Mitropolskii methodKS[动态]熵||Kolmogorov-Sinai entropy, KS entropyKdV 方程||KdV equationU形管||U-tubeWKB方法||WKB method, Wentzel-Kramers-Brillouin method[彻]体力||body force[单]元||element[第二类]拉格朗日方程||Lagrange equation [of the second kind][叠栅]云纹||moiréfringe; 物理学称“叠栅条纹”。

[叠栅]云纹法||moirémethod[抗]剪切角||angle of shear resistance[可]变形体||deformable body[钱]币状裂纹||penny-shape crack[映]象||image[圆]筒||cylinder[圆]柱壳||cylindrical shell[转]轴||shaft[转动]瞬心||instantaneous center [of rotation][转动]瞬轴||instantaneous axis [of rotation][状]态变量||state variable[状]态空间||state space[自]适应网格||[self-]adaptive meshＣ0连续问题||C0-continuous problemＣ1连续问题||C1-continuous problemＣＦＬ条件||Courant-Friedrichs-Lewy condition, CFL conditionＨＲＲ场||Hutchinson-Rice-Rosengren fieldＪ积分||J-integralＪ阻力曲线||J-resistance curveＫＡＭ定理||Kolgomorov-Arnol'd-Moser theorem, KAM theoremＫＡＭ环面||KAM torusｈ收敛||h-convergenceｐ收敛||p-convergenceπ定理||Buckingham theorem, pi theorem阿尔曼西应变||Almansis strain阿尔文波||Alfven wave阿基米德原理||Archimedes principle阿诺德舌[头]||Arnol'd tongue阿佩尔方程||Appel equation阿特伍德机||Atwood machine埃克曼边界层||Ekman boundary layer埃克曼流||Ekman flow埃克曼数||Ekman number埃克特数||Eckert number埃农吸引子||Henon attractor艾里应力函数||Airy stress function鞍点||saddle [point]鞍结分岔||saddle-node bifurcation安定[性]理论||shake-down theory安全寿命||safe life安全系数||safety factor安全裕度||safety margin暗条纹||dark fringe奥尔-索末菲方程||Orr-Sommerfeld equation奥辛流||Oseen flow奥伊洛特模型||Oldroyd model八面体剪应变||octohedral shear strain八面体剪应力||octohedral shear stress八面体剪应力理论||octohedral shear stress theory巴塞特力||Basset force白光散斑法||white-light speckle method摆||pendulum摆振||shimmy板||plate板块法||panel method板元||plate element半导体应变计||semiconductor strain gage半峰宽度||half-peak width半解析法||semi-analytical method半逆解法||semi-inverse method半频进动||half frequency precession半向同性张量||hemitropic tensor半隐格式||semi-implicit scheme薄壁杆||thin-walled bar薄壁梁||thin-walled beam薄壁筒||thin-walled cylinder薄膜比拟||membrane analogy薄翼理论||thin-airfoil theory保单调差分格式||monotonicity preserving difference scheme 保守力||conservative force保守系||conservative system爆发||blow up爆高||height of burst爆轰||detonation; 又称“爆震”。