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哈尔滨工业大学成人高等教育本科生毕业论文撰写规范毕业论文是学生在毕业前提交的一份具有一定科研价值和实用价值的学术论文。
它是本科学生开始从事工程设计、科学实验和科学研究的初步尝试，是学生在教师的指导下所取得成果的科学表述，是学生毕业及学位资格认定的重要依据。
毕业论文撰写是本科生培养过程的基本训练之一，其撰写应符合国家及各专业部门制定的有关标准，符合汉语语法规范。
指导教师应加强指导，严格把关。
1．论文结构及要求论文包括题目、中文摘要、外文摘要、目录、正文、致谢、参考文献和附录等几部分。
1.1 题目题目应恰当、准确地反映本课题的研究内容。
论文题目不应超过25字，不得使用标点符号，不设副标题。
1.2 摘要与关键词1.2.1 摘要摘要应扼要叙述本论文的主要内容、特点，文字要精炼，是一篇具有独立性和完整性的短文，应包括本论文的主要成果和结论性意见。
摘要中不宜使用公式、图表，不标注引用文献编号，避免将摘要写成目录式的内容介绍。
1.2.2 关键词关键词是供检索用的主题词条，应采用能覆盖论文主要内容的通用技术词条（参照相应的技术术语标准），一般列3～5个，按词条的外延层次从大到小排列，应在摘要中出现。
1.3 目录目录应独立成页，包括论文中全部章、节的标题及页码。
1.4 论文正文论文正文包括绪论、论文主体及结论等部分。
1.4.1 绪论绪论一般作为第1章。
绪论应说明选题的目的、背景和意义，国内外文献综述，以及论文所要研究的主要内容。
文管类论文的绪论是毕业论文的开头部分，一般包括说明论文写作的目的、意义，对所研究问题的认识以及提出问题。
绪论只是文章的开头，不必写章号。
1.4.2 论文主体论文主体是论文的主要部分，应该结构合理，层次清楚，重点突出，文字简练、通顺。
论文主体的内容要求参照《哈尔滨工业大学关于本科生毕业设计（论文）的若干规定》第六条。
论文主体各章后应有一节“本章小结”。
1.4.3 结论结论作为单独一章排列，但不加章号。
ieee fuzzy 短文-回复什么是IEEE Fuzzy？IEEE Fuzzy是一个国际知名的学术组织，专注于模糊逻辑和模糊系统领域的研究和发展。
IEEE Fuzzy的成立旨在促进学术界对模糊逻辑和模糊系统的理论研究和应用的探索，为相关领域的科学家和工程师提供一个交流和合作的平台，推动该领域的发展。
模糊逻辑是一种类似于布尔逻辑的形式，但相对于布尔逻辑的二元真值，模糊逻辑采用了连续的真值范围取值，从0到1之间。
这种取值范围引入了不确定性和模糊性的概念，可以更好地处理现实世界中模糊和不完全的信息。
在模糊逻辑的基础上发展起来的模糊系统是一种能够处理模糊数据和模糊问题的数学工具。
它通过建立模糊集合、模糊规则和模糊推理等方法，可以用来解决复杂的、不确定的和模糊的问题。
模糊系统的应用领域非常广泛，包括控制系统、决策支持系统、人工智能、模式识别等。
IEEE Fuzzy的成员包括了来自全球各地的研究人员、工程师和学生。
该组织通过举办国际会议、出版期刊和组织专题讨论等形式，促进学术界对模糊逻辑和模糊系统的研究，推动相关理论和技术的发展。
IEEE Fuzzy 的会议和期刊成为学术界交流的重要平台，吸引了众多学者的关注和参与。
IEEE Fuzzy组织的研究领域包括但不限于：模糊集合理论、模糊规则和推理、模糊控制、模糊决策、模糊优化、模糊图像处理、模糊模式识别等。
这些研究方向涉及到计算机科学、电子工程、控制理论、人工智能等多个学科领域。
在实际应用方面，IEEE Fuzzy的研究成果已经在许多领域产生了广泛的影响。
例如，在工业自动化中，模糊控制技术被用于优化控制系统的性能和健壮性；在金融领域，模糊决策支持系统可以帮助投资者做出模糊的金融决策；在医学图像处理中，模糊模式识别技术可以用来识别模糊的、不完整的医学图像等。
总之，IEEE Fuzzy作为一个国际知名的学术组织，为模糊逻辑和模糊系统领域的研究和应用提供了一个重要的平台。
SCI论文摘要中常用的表达方法要写好摘要，需要建立一个适合自己需要的句型库（选择的词汇来源于SCI高被引用论文）引言部分（1）回顾研究背景，常用词汇有review, summarize, present, outline, describe等（2）说明写作目的，常用词汇有purpose, attempt, aim等，另外还可以用动词不定式充当目的壮语老表达（3）介绍论文的重点内容或研究范围，常用词汇有study, present, include, focus, emphasize, emphasis, attention等方法部分（1）介绍研究或试验过程，常用词汇有test study, investigate, examine,experiment, discuss, consider, analyze, analysis等（2）说明研究或试验方法，常用词汇有measure, estimate, calculate等（3）介绍应用、用途，常用词汇有use, apply, application等结果部分（1）展示研究结果，常用词汇有show, result, present等（2）介绍结论，常用词汇有summary, introduce,conclude等讨论部分（1）陈述论文的论点和作者的观点，常用词汇有suggest, repot, present, expect, describe 等（2）说明论证，常用词汇有support, provide, indicate, identify, find, demonstrate, confirm, clarify等（3）推荐和建议，常用词汇有suggest,suggestion, recommend, recommendation, propose,necessity,necessary,expect等。
摘要引言部分案例词汇review•Author(s): ROBINSON, TE; BERRIDGE, KC•Title:THE NEURAL BASIS OF DRUG CRA VING - AN INCENTIVE-SENSITIZATION THEORY OF ADDICTION•Source: BRAIN RESEARCH REVIEWS, 18 (3): 247-291 SEP-DEC 1993 《脑研究评论》荷兰SCI被引用1774We review evidence for this view of addiction and discuss its implications for understanding the psychology and neurobiology of addiction.回顾研究背景SCI高被引摘要引言部分案例词汇summarizeAuthor(s): Barnett, RM; Carone, CD; 被引用1571Title: Particles and field .1. Review of particle physicsSource: PHYSICAL REVIEW D, 54 (1): 1-+ Part 1 JUL 1 1996:《物理学评论，D辑》美国引言部分回顾研究背景常用词汇summarizeAbstract: This biennial review summarizes much of Particle Physics. Using data from previous editions, plus 1900 new measurements from 700 papers, we list, evaluate, and average measuredproperties of gauge bosons, leptons, quarks, mesons, and baryons. We also summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review.SCI摘要引言部分案例attentionSCI摘要方法部分案例considerSCI高被引摘要引言部分案例词汇outline•Author(s): TIERNEY, L SCI引用728次•Title:MARKOV-CHAINS FOR EXPLORING POSTERIOR DISTRIBUTIONS 引言部分回顾研究背景，常用词汇outline•Source: ANNALS OF STATISTICS, 22 (4): 1701-1728 DEC 1994•《统计学纪事》美国•Abstract: Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm.In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues. On the theoretical side, results from the theory of general state space Markov chains can be used to obtain convergence rates, laws of large numbers and central limit theorems for estimates obtained from Markov chain methods. These theoretical results can be used to guide the construction of more efficient algorithms. For the practical use of Markov chain methods, standard simulation methodology provides several Variance reduction techniques and also gives guidance on the choice of sample size and allocation.SCI高被引摘要引言部分案例回顾研究背景presentAuthor(s): L YNCH, M; MILLIGAN, BG SC I被引用661Title: ANAL YSIS OF POPULATION GENETIC-STRUCTURE WITH RAPD MARKERS Source: MOLECULAR ECOLOGY, 3 (2): 91-99 APR 1994《分子生态学》英国Abstract: Recent advances in the application of the polymerase chain reaction make it possible to score individuals at a large number of loci. The RAPD (random amplified polymorphic DNA) method is one such technique that has attracted widespread interest.The analysis of population structure with RAPD data is hampered by the lack of complete genotypic information resulting from dominance, since this enhances the sampling variance associated with single loci as well as induces bias in parameter estimation. We present estimators for several population-genetic parameters (gene and genotype frequencies, within- and between-population heterozygosities, degree of inbreeding and population subdivision, and degree of individual relatedness) along with expressions for their sampling variances. Although completely unbiased estimators do not appear to be possible with RAPDs, several steps are suggested that will insure that the bias in parameter estimates is negligible. To achieve the same degree of statistical power, on the order of 2 to 10 times more individuals need to be sampled per locus when dominant markers are relied upon, as compared to codominant (RFLP, isozyme) markers. Moreover, to avoid bias in parameter estimation, the marker alleles for most of these loci should be in relatively low frequency. Due to the need for pruning loci with low-frequency null alleles, more loci also need to be sampled with RAPDs than with more conventional markers, and sole problems of bias cannot be completely eliminated.SCI高被引摘要引言部分案例词汇describe•Author(s): CLONINGER, CR; SVRAKIC, DM; PRZYBECK, TR•Title: A PSYCHOBIOLOGICAL MODEL OF TEMPERAMENT AND CHARACTER•Source: ARCHIVES OF GENERAL PSYCHIATRY, 50 (12): 975-990 DEC 1993《普通精神病学纪要》美国•引言部分回顾研究背景，常用词汇describe 被引用926•Abstract: In this study, we describe a psychobiological model of the structure and development of personality that accounts for dimensions of both temperament and character. Previous research has confirmed four dimensions of temperament: novelty seeking, harm avoidance, reward dependence, and persistence, which are independently heritable, manifest early in life, and involve preconceptual biases in perceptual memory and habit formation. For the first time, we describe three dimensions of character that mature in adulthood and influence personal and social effectiveness by insight learning about self-concepts.Self-concepts vary according to the extent to which a person identifies the self as (1) an autonomous individual, (2) an integral part of humanity, and (3) an integral part of the universe as a whole. Each aspect of self-concept corresponds to one of three character dimensions called self-directedness, cooperativeness, and self-transcendence, respectively. We also describe the conceptual background and development of a self-report measure of these dimensions, the Temperament and Character Inventory. Data on 300 individuals from the general population support the reliability and structure of these seven personality dimensions. We discuss the implications for studies of information processing, inheritance, development, diagnosis, and treatment.摘要引言部分案例•（2）说明写作目的，常用词汇有purpose, attempt, aimSCI高被引摘要引言部分案例attempt说明写作目的•Author(s): Donoho, DL; Johnstone, IM•Title: Adapting to unknown smoothness via wavelet shrinkage•Source: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 90 (432): 1200-1224 DEC 1995 《美国统计学会志》被引用429次•Abstract: We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: A threshold level is assigned to each dyadic resolution level by the principle of minimizing the Stein unbiased estimate of risk (Sure) for threshold estimates. The computational effort of the overall procedure is order N.log(N) as a function of the sample size N. SureShrink is smoothness adaptive: If the unknown function contains jumps, then the reconstruction (essentially) does also; if the unknown function has a smooth piece, then the reconstruction is (essentially) as smooth as the mother wavelet will allow. The procedure is in a sense optimally smoothness adaptive: It is near minimax simultaneously over a whole interval of the Besov scale; the size of this interval depends on the choice of mother wavelet. We know from a previous paper by the authors that traditional smoothing methods-kernels, splines, and orthogonal series estimates-even with optimal choices of the smoothing parameter, would be unable to perform in a near-minimax way over many spaces in the Besov scale.Examples of SureShrink are given. The advantages of the method are particularly evident when the underlying function has jump discontinuities on a smooth backgroundSCI高被引摘要引言部分案例To investigate说明写作目的•Author(s): OLTV AI, ZN; MILLIMAN, CL; KORSMEYER, SJ•Title: BCL-2 HETERODIMERIZES IN-VIVO WITH A CONSERVED HOMOLOG, BAX, THAT ACCELERATES PROGRAMMED CELL-DEATH•Source: CELL, 74 (4): 609-619 AUG 27 1993 被引用3233•Abstract: Bcl-2 protein is able to repress a number of apoptotic death programs. To investigate the mechanism of Bcl-2's effect, we examined whether Bcl-2 interacted with other proteins. We identified an associated 21 kd protein partner, Bax, that has extensive amino acid homology with Bcl-2, focused within highly conserved domains I and II. Bax is encoded by six exons and demonstrates a complex pattern of alternative RNA splicing that predicts a 21 kd membrane (alpha) and two forms of cytosolic protein (beta and gamma). Bax homodimerizes and forms heterodimers with Bcl-2 in vivo. Overexpressed Bax accelerates apoptotic death induced by cytokine deprivation in an IL-3-dependent cell line. Overexpressed Bax also counters the death repressor activity of Bcl-2. These data suggest a model in which the ratio of Bcl-2 to Bax determines survival or death following an apoptotic stimulus.SCI高被引摘要引言部分案例purposes说明写作目的•Author(s): ROGERS, FJ; IGLESIAS, CA•Title: RADIATIVE ATOMIC ROSSELAND MEAN OPACITY TABLES•Source: ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 79 (2): 507-568 APR 1992 《天体物理学杂志增刊》美国SCI被引用512•Abstract: For more than two decades the astrophysics community has depended on opacity tables produced at Los Alamos. In the present work we offer new radiative Rosseland mean opacity tables calculated with the OPAL code developed independently at LLNL. We give extensive results for the recent Anders-Grevesse mixture which allow accurate interpolation in temperature, density, hydrogen mass fraction, as well as metal mass fraction. The tables are organized differently from previous work. Instead of rows and columns of constant temperature and density, we use temperature and follow tracks of constant R, where R = density/(temperature)3. The range of R and temperature are such as to cover typical stellar conditions from the interior through the envelope and the hotter atmospheres. Cool atmospheres are not considered since photoabsorption by molecules is neglected. Only radiative processes are taken into account so that electron conduction is not included. For comparison purposes we present some opacity tables for the Ross-Aller and Cox-Tabor metal abundances. Although in many regions the OPAL opacities are similar to previous work, large differences are reported.For example, factors of 2-3 opacity enhancements are found in stellar envelop conditions.SCI高被引摘要引言部分案例aim说明写作目的•Author(s):EDV ARDSSON, B; ANDERSEN, J; GUSTAFSSON, B; LAMBERT, DL;NISSEN, PE; TOMKIN, J•Title:THE CHEMICAL EVOLUTION OF THE GALACTIC DISK .1. ANALYSISAND RESULTS•Source: ASTRONOMY AND ASTROPHYSICS, 275 (1): 101-152 AUG 1993 《天文学与天体物理学》被引用934•Abstract:With the aim to provide observational constraints on the evolution of the galactic disk, we have derived abundances of 0, Na, Mg, Al, Si, Ca, Ti, Fe, Ni, Y, Zr, Ba and Nd, as well as individual photometric ages, for 189 nearby field F and G disk dwarfs.The galactic orbital properties of all stars have been derived from accurate kinematic data, enabling estimates to be made of the distances from the galactic center of the stars‘ birthplaces. 结构式摘要•Our extensive high resolution, high S/N, spectroscopic observations of carefully selected northern and southern stars provide accurate equivalent widths of up to 86 unblended absorption lines per star between 5000 and 9000 angstrom. The abundance analysis was made with greatly improved theoretical LTE model atmospheres. Through the inclusion of a great number of iron-peak element absorption lines the model fluxes reproduce the observed UV and visual fluxes with good accuracy. A new theoretical calibration of T(eff) as a function of Stromgren b - y for solar-type dwarfs has been established. The new models and T(eff) scale are shown to yield good agreement between photometric and spectroscopic measurements of effective temperatures and surface gravities, but the photometrically derived very high overall metallicities for the most metal rich stars are not supported by the spectroscopic analysis of weak spectral lines.•Author(s): PAYNE, MC; TETER, MP; ALLAN, DC; ARIAS, TA; JOANNOPOULOS, JD•Title:ITERA TIVE MINIMIZATION TECHNIQUES FOR ABINITIO TOTAL-ENERGY CALCULATIONS - MOLECULAR-DYNAMICS AND CONJUGA TE GRADIENTS•Source: REVIEWS OF MODERN PHYSICS, 64 (4): 1045-1097 OCT 1992 《现代物理学评论》美国American Physical Society SCI被引用2654 •Abstract: This article describes recent technical developments that have made the total-energy pseudopotential the most powerful ab initio quantum-mechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in as many scientific disciplines as possible.SCI高被引摘要引言部分案例includes介绍论文的重点内容或研究范围•Author(s):MARCHESINI, G; WEBBER, BR; ABBIENDI, G; KNOWLES, IG;SEYMOUR, MH; STANCO, L•Title: HERWIG 5.1 - A MONTE-CARLO EVENT GENERA TOR FOR SIMULATING HADRON EMISSION REACTIONS WITH INTERFERING GLUONS SCI被引用955次•Source: COMPUTER PHYSICS COMMUNICATIONS, 67 (3): 465-508 JAN 1992:《计算机物理学通讯》荷兰Elsevier•Abstract: HERWIG is a general-purpose particle-physics event generator, which includes the simulation of hard lepton-lepton, lepton-hadron and hadron-hadron scattering and soft hadron-hadron collisions in one package. It uses the parton-shower approach for initial-state and final-state QCD radiation, including colour coherence effects and azimuthal correlations both within and between jets. This article includes a brief review of the physics underlying HERWIG, followed by a description of the program itself. This includes details of the input and control parameters used by the program, and the output data provided by it. Sample output from a typical simulation is given and annotated.SCI高被引摘要引言部分案例presents介绍论文的重点内容或研究范围•Author(s): IDSO, KE; IDSO, SB•Title: PLANT-RESPONSES TO ATMOSPHERIC CO2 ENRICHMENT IN THE FACE OF ENVIRONMENTAL CONSTRAINTS - A REVIEW OF THE PAST 10 YEARS RESEARCH•Source: AGRICULTURAL AND FOREST METEOROLOGY, 69 (3-4): 153-203 JUL 1994 《农业和林业气象学》荷兰Elsevier 被引用225•Abstract:This paper presents a detailed analysis of several hundred plant carbon exchange rate (CER) and dry weight (DW) responses to atmospheric CO2 enrichment determined over the past 10 years. It demonstrates that the percentage increase in plant growth produced by raising the air's CO2 content is generally not reduced by less than optimal levels of light, water or soil nutrients, nor by high temperatures, salinity or gaseous air pollution. More often than not, in fact, the data show the relative growth-enhancing effects of atmospheric CO2 enrichment to be greatest when resource limitations and environmental stresses are most severe.SCI高被引摘要引言部分案例介绍论文的重点内容或研究范围emphasizing •Author(s): BESAG, J; GREEN, P; HIGDON, D; MENGERSEN, K•Title: BAYESIAN COMPUTATION AND STOCHASTIC-SYSTEMS•Source: STATISTICAL SCIENCE, 10 (1): 3-41 FEB 1995《统计科学》美国•SCI被引用296次•Abstract: Markov chain Monte Carlo (MCMC) methods have been used extensively in statistical physics over the last 40 years, in spatial statistics for the past 20 and in Bayesian image analysis over the last decade. In the last five years, MCMC has been introduced into significance testing, general Bayesian inference and maximum likelihood estimation. This paper presents basic methodology of MCMC, emphasizing the Bayesian paradigm, conditional probability and the intimate relationship with Markov random fields in spatial statistics.Hastings algorithms are discussed, including Gibbs, Metropolis and some other variations. Pairwise difference priors are described and are used subsequently in three Bayesian applications, in each of which there is a pronounced spatial or temporal aspect to the modeling. The examples involve logistic regression in the presence of unobserved covariates and ordinal factors; the analysis of agricultural field experiments, with adjustment for fertility gradients; and processing oflow-resolution medical images obtained by a gamma camera. Additional methodological issues arise in each of these applications and in the Appendices. The paper lays particular emphasis on the calculation of posterior probabilities and concurs with others in its view that MCMC facilitates a fundamental breakthrough in applied Bayesian modeling.SCI高被引摘要引言部分案例介绍论文的重点内容或研究范围focuses •Author(s): HUNT, KJ; SBARBARO, D; ZBIKOWSKI, R; GAWTHROP, PJ•Title: NEURAL NETWORKS FOR CONTROL-SYSTEMS - A SURVEY•Source: AUTOMA TICA, 28 (6): 1083-1112 NOV 1992《自动学》荷兰Elsevier•SCI被引用427次•Abstract:This paper focuses on the promise of artificial neural networks in the realm of modelling, identification and control of nonlinear systems. The basic ideas and techniques of artificial neural networks are presented in language and notation familiar to control engineers. Applications of a variety of neural network architectures in control are surveyed. We explore the links between the fields of control science and neural networks in a unified presentation and identify key areas for future research.SCI高被引摘要引言部分案例介绍论文的重点内容或研究范围focus•Author(s): Stuiver, M; Reimer, PJ; Bard, E; Beck, JW;•Title: INTCAL98 radiocarbon age calibration, 24,000-0 cal BP•Source: RADIOCARBON, 40 (3): 1041-1083 1998《放射性碳》美国SCI被引用2131次•Abstract: The focus of this paper is the conversion of radiocarbon ages to calibrated (cal) ages for the interval 24,000-0 cal BP (Before Present, 0 cal BP = AD 1950), based upon a sample set of dendrochronologically dated tree rings, uranium-thorium dated corals, and varve-counted marine sediment. The C-14 age-cal age information, produced by many laboratories, is converted to Delta(14)C profiles and calibration curves, for the atmosphere as well as the oceans. We discuss offsets in measured C-14 ages and the errors therein, regional C-14 age differences, tree-coral C-14 age comparisons and the time dependence of marine reservoir ages, and evaluate decadal vs. single-year C-14 results. Changes in oceanic deepwater circulation, especially for the 16,000-11,000 cal sp interval, are reflected in the Delta(14)C values of INTCAL98.SCI高被引摘要引言部分案例介绍论文的重点内容或研究范围emphasis •Author(s): LEBRETON, JD; BURNHAM, KP; CLOBERT, J; ANDERSON, DR•Title: MODELING SURVIV AL AND TESTING BIOLOGICAL HYPOTHESES USING MARKED ANIMALS - A UNIFIED APPROACH WITH CASE-STUDIES •Source: ECOLOGICAL MONOGRAPHS, 62 (1): 67-118 MAR 1992•《生态学论丛》美国•Abstract: The understanding of the dynamics of animal populations and of related ecological and evolutionary issues frequently depends on a direct analysis of life history parameters. For instance, examination of trade-offs between reproduction and survival usually rely on individually marked animals, for which the exact time of death is most often unknown, because marked individuals cannot be followed closely through time.Thus, the quantitative analysis of survival studies and experiments must be based oncapture-recapture (or resighting) models which consider, besides the parameters of primary interest, recapture or resighting rates that are nuisance parameters. 结构式摘要•T his paper synthesizes, using a common framework, these recent developments together with new ones, with an emphasis on flexibility in modeling, model selection, and the analysis of multiple data sets. The effects on survival and capture rates of time, age, and categorical variables characterizing the individuals (e.g., sex) can be considered, as well as interactions between such effects. This "analysis of variance" philosophy emphasizes the structure of the survival and capture process rather than the technical characteristics of any particular model. The flexible array of models encompassed in this synthesis uses a common notation. As a result of the great level of flexibility and relevance achieved, the focus is changed from fitting a particular model to model building and model selection.SCI摘要方法部分案例•方法部分•（1）介绍研究或试验过程，常用词汇有test，study, investigate, examine,experiment, discuss, consider, analyze, analysis等•（2）说明研究或试验方法，常用词汇有measure, estimate, calculate等•（3）介绍应用、用途，常用词汇有use, apply, application等SCI高被引摘要方法部分案例discusses介绍研究或试验过程•Author(s): LIANG, KY; ZEGER, SL; QAQISH, B•Title: MULTIV ARIATE REGRESSION-ANAL YSES FOR CATEGORICAL-DATA •Source:JOURNAL OF THE ROY AL STA TISTICAL SOCIETY SERIES B-METHODOLOGICAL, 54 (1): 3-40 1992《皇家统计学会志，B辑：统计方法论》•SCI被引用298•Abstract: It is common to observe a vector of discrete and/or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes. The response vector can comprise repeated observations on one variable, as in longitudinal studies or genetic studies of families, or can include observations for different variables.This paper discusses a class of models for the marginal expectations of each response and for pairwise associations. The marginal models are contrasted with log-linear models.Two generalized estimating equation approaches are compared for parameter estimation.The first focuses on the regression parameters; the second simultaneously estimates the regression and association parameters. The robustness and efficiency of each is discussed.The methods are illustrated with analyses of two data sets from public health research SCI高被引摘要方法部分案例介绍研究或试验过程examines•Author(s): Huo, QS; Margolese, DI; Stucky, GD•Title: Surfactant control of phases in the synthesis of mesoporous silica-based materials •Source: CHEMISTRY OF MATERIALS, 8 (5): 1147-1160 MAY 1996•SCI被引用643次《材料的化学性质》美国•Abstract: The low-temperature formation of liquid-crystal-like arrays made up of molecular complexes formed between molecular inorganic species and amphiphilic organic molecules is a convenient approach for the synthesis of mesostructure materials.This paper examines how the molecular shapes of covalent organosilanes, quaternary ammonium surfactants, and mixed surfactants in various reaction conditions can be used to synthesize silica-based mesophase configurations, MCM-41 (2d hexagonal, p6m), MCM-48 (cubic Ia3d), MCM-50 (lamellar), SBA-1 (cubic Pm3n), SBA-2 (3d hexagonal P6(3)/mmc), and SBA-3(hexagonal p6m from acidic synthesis media). The structural function of surfactants in mesophase formation can to a first approximation be related to that of classical surfactants in water or other solvents with parallel roles for organic additives. The effective surfactant ion pair packing parameter, g = V/alpha(0)l, remains a useful molecular structure-directing index to characterize the geometry of the mesophase products, and phase transitions may be viewed as a variation of g in the liquid-crystal-Like solid phase. Solvent and cosolvent structure direction can be effectively used by varying polarity, hydrophobic/hydrophilic properties and functionalizing the surfactant molecule, for example with hydroxy group or variable charge. Surfactants and synthesis conditions can be chosen and controlled to obtain predicted silica-based mesophase products. A room-temperature synthesis of the bicontinuous cubic phase, MCM-48, is presented. A low-temperature (100 degrees C) and low-pH (7-10) treatment approach that can be used to give MCM-41 with high-quality, large pores (up to 60 Angstrom), and pore volumes as large as 1.6 cm(3)/g is described.Estimates 介绍研究或试验过程SCI高被引摘要方法部分案例•Author(s): KESSLER, RC; MCGONAGLE, KA; ZHAO, SY; NELSON, CB; HUGHES, M; ESHLEMAN, S; WITTCHEN, HU; KENDLER, KS•Title:LIFETIME AND 12-MONTH PREV ALENCE OF DSM-III-R PSYCHIATRIC-DISORDERS IN THE UNITED-STA TES - RESULTS FROM THE NATIONAL-COMORBIDITY-SURVEY•Source: ARCHIVES OF GENERAL PSYCHIATRY, 51 (1): 8-19 JAN 1994•《普通精神病学纪要》美国SCI被引用4350次•Abstract: Background: This study presents estimates of lifetime and 12-month prevalence of 14 DSM-III-R psychiatric disorders from the National Comorbidity Survey, the first survey to administer a structured psychiatric interview to a national probability sample in the United States.Methods: The DSM-III-R psychiatric disorders among persons aged 15 to 54 years in the noninstitutionalized civilian population of the United States were assessed with data collected by lay interviewers using a revised version of the Composite International Diagnostic Interview. Results: Nearly 50% of respondents reported at least one lifetime disorder, and close to 30% reported at least one 12-month disorder. The most common disorders were major depressive episode, alcohol dependence, social phobia, and simple phobia. More than half of all lifetime disorders occurred in the 14% of the population who had a history of three or more comorbid disorders. These highly comorbid people also included the vast majority of people with severe disorders.Less than 40% of those with a lifetime disorder had ever received professional treatment,and less than 20% of those with a recent disorder had been in treatment during the past 12 months. Consistent with previous risk factor research, it was found that women had elevated rates of affective disorders and anxiety disorders, that men had elevated rates of substance use disorders and antisocial personality disorder, and that most disorders declined with age and with higher socioeconomic status. Conclusions: The prevalence of psychiatric disorders is greater than previously thought to be the case. Furthermore, this morbidity is more highly concentrated than previously recognized in roughly one sixth of the population who have a history of three or more comorbid disorders. This suggests that the causes and consequences of high comorbidity should be the focus of research attention. The majority of people with psychiatric disorders fail to obtain professional treatment. Even among people with a lifetime history of three or more comorbid disorders, the proportion who ever obtain specialty sector mental health treatment is less than 50%.These results argue for the importance of more outreach and more research on barriers to professional help-seekingSCI高被引摘要方法部分案例说明研究或试验方法measure•Author(s): Schlegel, DJ; Finkbeiner, DP; Davis, M•Title:Maps of dust infrared emission for use in estimation of reddening and cosmic microwave background radiation foregrounds•Source: ASTROPHYSICAL JOURNAL, 500 (2): 525-553 Part 1 JUN 20 1998 SCI 被引用2972 次《天体物理学杂志》美国•The primary use of these maps is likely to be as a new estimator of Galactic extinction. To calibrate our maps, we assume a standard reddening law and use the colors of elliptical galaxies to measure the reddening per unit flux density of 100 mu m emission. We find consistent calibration using the B-R color distribution of a sample of the 106 brightest cluster ellipticals, as well as a sample of 384 ellipticals with B-V and Mg line strength measurements. For the latter sample, we use the correlation of intrinsic B-V versus Mg, index to tighten the power of the test greatly. We demonstrate that the new maps are twice as accurate as the older Burstein-Heiles reddening estimates in regions of low and moderate reddening. The maps are expected to be significantly more accurate in regions of high reddening. These dust maps will also be useful for estimating millimeter emission that contaminates cosmic microwave background radiation experiments and for estimating soft X-ray absorption. We describe how to access our maps readily for general use.SCI高被引摘要结果部分案例application介绍应用、用途•Author(s): MALLAT, S; ZHONG, S•Title: CHARACTERIZATION OF SIGNALS FROM MULTISCALE EDGES•Source: IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 14 (7): 710-732 JUL 1992•SCI被引用508次《IEEE模式分析与机器智能汇刊》美国•Abstract: A multiscale Canny edge detection is equivalent to finding the local maxima ofa wavelet transform. We study the properties of multiscale edges through the wavelet。
现代电子技术Modern Electronics TechniqueMar. 2024Vol. 47 No. 62024年3月15日第47卷第6期0 引 言语音情感识别（Speech Emotion Recognition, SER ）在人机交互和计算机辅助人际交流等应用中发挥着重要作用。
然而，由于自发情感表达的微妙性和模糊性，要使机器完全正确地解释出语音信号中所包含的情感是具有挑战性的。
尽管SER 已经得到了广泛的应用，但它的性能远远低于人类，识别过程仍然受到很多因素的困扰，因此，有必要进一步提高SER 系统的性能。
深度学习网络，例如卷积神经网络（CNN ）和递归神经网络（RNN ）等[1]，在SER 任务中表现出较高的效率，识别精度较传统方法也有了很大的提高。
注意力机制可以动态地聚焦于某些部分，目前已经被应用于神经网络中。
S. Mirsamadi 等将局部注意力机制引入语音神经网络，DOI ：10.16652/j.issn.1004‐373x.2024.06.021引用格式：何朝霞，朱嵘涛，罗辉.基于F‐DFCC 融合特征的语音情感识别方法[J].现代电子技术，2024，47（6）：131‐136.基于F⁃DFCC 融合特征的语音情感识别方法何朝霞1， 朱嵘涛1， 罗 辉2（1.长江大学 文理学院， 湖北 荆州 434023； 2.东北林业大学 计算机与控制工程学院， 黑龙江 哈尔滨 150040）摘 要： 结合神经网络、并行多特征向量和注意力机制，有助于提高语音情感识别的性能。
基于此，从前期已经提取的DFCC 参数入手，提取I‐DFCC 和Mid‐DFCC 特征参数，利用Fisher 比选取特征参数构成F‐DFCC ；再将F‐DFCC 特征参数与LPCC 、MFCC 特征参数进行对比并融合，输入到含双向LSTM 网络及注意力机制的ECAPA‐TDNN 模型中；最后，在CASIA 和RAVDESS 数据集上验证F‐DFCC 融合特征参数的有效性。
第28卷㊀第5期2023年10月㊀哈尔滨理工大学学报JOURNAL OF HARBIN UNIVERSITY OF SCIENCE AND TECHNOLOGY㊀Vol.28No.5Oct.2023㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀一种随机变论域Fuzzy 控制器在医疗头盔中的实现王㊀月1,㊀赵㊀辉1,㊀张㊀元2,㊀乌伦华1(1.哈尔滨理工大学理学院,哈尔滨150080;2.哈尔滨理工大学机械动力工程学院,哈尔滨150080)摘㊀要:目前的自适应模糊控制方法在实际问题中难以达到良好的效果㊂针对这一问题,提出一种随机变论域Fuzzy 控制器㊂首先,基于原有的伸缩因子设计一种简单㊁精准的随机伸缩因子,并通过仿真对比验证其性能;接着,以实际前后圈梁伸缩的长度与理想状态下前后圈梁伸缩的长度期望值的误差和误差的变化作为输入变量,引起旋钮转速变化的多少作为输出变量,设计随机变论域Fuzzy 控制器;最后,使用仿真实验对比响应曲线图分析得到,设计的模糊控制器性能明显提升,并且整个控制过程中超调小㊁稳定性高㊁响应时间有明显的缩短,实现了医疗头盔的治疗效果㊂关键词:随机变论域;伸缩因子;随机变论域Fuzzy 控制器;医疗头盔DOI :10.15938/j.jhust.2023.05.019中图分类号:TP273+.4文献标志码:A文章编号:1007-2683(2023)05-0150-09Implementation of a Random Variable UniversefuzzyController in Medical HelmetWANG Yue 1,㊀ZHAO Hui 1,㊀ZHANG Yuan 2,㊀WU Lunhua 1(1.College of Science,Harbin University of Science and Technology,Harbin 150080,China;2.School of Mechanical and Power Engineering,Harbin University of Science and Technology,Harbin 150080,China)Abstract :The current adaptive fuzzy control methods was difficult to achieve good results in practical problems.Aiming at thisproblem,a fuzzy controller with a random variation domain was proposed.Firstly,a simple and accurate random scaling factor was designed based on the original scaling factor,and its performance was verified by simulation comparison;Then,the error and error change of the expected value of the actual front and rear ring beam expansion and contraction and the length expectation of the front and rear ring beam expansion and contraction under ideal conditions are used as input variables,and the number of knob speed changes are used as the output variable,and the random variable domain Fuzzy controller was designed;Finally,the performance of the fuzzy controller of the design was significantly improved by comparing the response curve of the simulation experiment.And the entire control process is small,high stability,response time has been significantly shortened,to achieve the treatment effect of medical helmets.Keywords :random variable domain;telescopic factor;stochastic variable universe fuzzy controller;medical helmet㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀收稿日期:2022-04-02基金项目:四川省科技计划项目(2016JZ0014-1);黑龙江省自然科学基金(A201214).作者简介:王㊀月(1996 ),女,硕士研究生;张㊀元(1966 ),男,教授,博士研究生导师.通信作者:赵㊀辉(1963 ),男,教授,硕士研究生导师,E-mail:mathwindow@.0㊀引㊀言模糊控制是一种非线性控制,在工业制导㊁航天㊁机器人方面拥有着广泛的应用[1]㊂1974年英国马丹尼首先设计了模糊控制器,应用于锅炉和蒸汽机的控制,取得了成功㊂由此,模糊语言控制器㊁模糊控制论㊁模糊自动控制等概念,就从此开始诞生了㊂此后被很多国内外学者进行了更深入的研究㊂后续为了使控制器达到更高的精准度,1995年李洪兴教授首次提出变论域模糊控制器,其实质是插值器,并且根据维数的不同给出了相应的插值函数,克服了传统模糊控制器的不足之处[2]㊂例如,2000年,雷德明设计了一种新型模糊控制器 进化模糊控制器,其规则库由整数编码遗传算法在线调整,仿真结果验证了设计的合理性与有效性[3]㊂随后,李洪兴教授在变论域模糊控制器的基础上进一步提出了变论域自适应模糊控制器[4],文[5]和文[6]表明变论域自适应模糊控制器本质上是随着伸缩因子的加入使论域发生扩大或缩小的改变㊂文[7]研究了输入输出论域发生变化时对伸缩因子会有怎样的影响,其性能是否会有所改变㊂在对机械手的跟踪中通过伸缩因子的改变,及仿真实验结果验证了变论域自适应模糊控制器的有效性[8]㊂例如,2013年,谭兵文等分析了函数形式和模糊推理,两种选择变论域伸缩因子的方法,并对此进行改进,提出了使用误差分级的方法选择伸缩因子,最后进行仿真实验比较,得出使用误差分级选择伸缩因子性能更优㊁鲁棒性更好的结论[9]㊂随着伸缩因子的形式发生改变其论域也发生变化,这样能不断提高控制器的精度[10]㊂文[11]根据提出的一种混合型伸缩因子对三关节机械臂实现了精准的跟踪㊂文[12]实现了自吸泵在论域发生改变的情况下精度和性能的提升㊂医疗头盔是一种药物输送,治疗类似于阿尔茨海默症的仪器被广泛应用在医疗方面,从古代发展到现代,大量学者对进行更深的研究,并将其应用到生活各个领域[13]㊂瑞典曾推出一种治疗抑郁症的头戴式头盔,目前已经在英国发售,美国FDA也审核通过了治疗抑郁症的新型医疗头盔㊂在我国例如,2011年,张亚君等[14]研制出了分布式可控制医疗制冷头盔,解决了一些由于温度产生的影响头盔性能的因素;2017年,王彦杰等[16]研制的芳纶针织增强体头盔,表明耐热性,阻燃性能更好极大的体现了头盔的性能;2021年,郑韵等[16]在对畸形婴儿头颅重塑方面提出了矫形头盔,治疗康复了畸形婴儿并且疗效较明显,且畸形程度越轻头颅形态越容易得到矫正㊂本论文主要是根据模糊控制器的发展历程,及性能影响而产生的精度降低㊁鲁棒性不稳定㊁适用范围不广泛㊁时间超调等问题进行更深一步的研究㊂因此,本文根据实际情况等其他方面要求设计一种伸缩性能更好㊁更简单且稳定性更高的伸缩因子[17-20],并提出一种控制效果更显著的新型随机变论域Fuzzy控制器,将其应用到控制医疗头盔旋钮转速上,通过仿真实验分析验证本文设计的变论域模糊控制器的有效性与可靠性㊂1㊀随机变论域伸缩因子算法1.1㊀一种新型随机变论域伸缩因子的设计首先基于文[4]给出李洪兴提出的伸缩因子的概念㊂定义1㊀称函数α:Xң[0,1],x α(x)为论域X的伸缩因子,X=[-E,E],如果满足条件:1)对偶性:(∀xɪX)(α(x)=α(-x));2)保零性:α(0)=0;3)单调性:α在[0,E]上严格单调增;4)协调性:(∀xɪX)(|x|ɤα(x)E);∀xɪX,记X(x) α(x)X [-α(x)E,α(x)E] {α(x)xᶄ|xᶄɪX},称X(x)为X上的变论域㊂5)正规性:α(ʃE)=1㊂设0<τ<1,置α(x)=|x|E[]τ,则α(x)为满足定义1的伸缩因子,其中x为误差输入的精确值,E 为误差输入的最大值㊂以上李洪兴给出的伸缩因子需要进行复杂的运算,计算时间较长,对控制精度要求高㊂因此,应该选择一类精度高,且符合实际情况要求,较为简单的伸缩因子形式㊂下面根据文[13]提出一类改进的简单函数形式的伸缩因子㊂定义2㊀已知α(x)是一种变论域伸缩因子,输入论域为X,[-x e,x e]为随机变论域,E[-x e,x e]为随机变论域的期望,则称α∗(x)=α(x)+φ,为随机变论域伸缩因子㊂其中φ~N(0,σ2),E(α∗(x))=α(x)㊂需满足如下条件:1)对偶性:∀xɪX,E(α∗(-x))=E(α∗(x));2)避零性:当|x|=0时,α∗(0)ʂ0,E(α∗(0))ʂ0;3)单调性:E(α∗(x))在[0,x e]上严格单调递增,在[-x e,0]上严格单调递减;151第5期王㊀月等:一种随机变论域Fuzzy控制器在医疗头盔中的实现4)协调性:∀x ɪX ,|x |ɤα∗(x )x e ;5)正规性:E (α∗(ʃx e ))=1㊂具体形式如下:α∗(x )=1-11+kx 4+φ其中:x 为误差的精确值;k 为充分大的正数;φ~N (0,σ2)为随机变量㊂由于伸缩因子的变化引起论域的收缩或者扩张,假设初始论域为[-E ,E ]通过伸缩因子α∗(x )的 伸缩 论域变为[-α∗(x )E ,α∗(x )E ]㊂图1为论域随伸缩因子α∗(x )变化的图㊂图1㊀论域变化图Fig.1㊀Domain change map下面对上述所设计的伸缩因子满足定义2的5条性质进行稳定性分析㊂1.2㊀新型变论域伸缩因子稳定性分析对偶性:∀x ɪX ,有E α∗(-x ))=E (1-11+k (-x )4+φ()=E 1-11+kx4+φ()=E (α∗(x ));避零性:当|x |=0时,有α∗(0)=1-11+kx4+φʂ0,则E (α∗(0))ʂ0;调性:对∀x 1,x 2ɪ[0,x e ],当x 1<x 2时,α(x 1)=1-11+kx 41<1-11+kx 42=α(x 2),故有E (α∗(x 1))<E (α∗(x 2));协调性:当k 足够大时α∗(x )ң1,且|x |<1此时无论x 发生怎样的变化,都可以保证发生变化之后的论域是不会超过开始时论域的变化范围,因此协调性满足,故|x |ɤα∗(x )x e ;正规性:E (α∗(x e ))=E (1)=1㊂1.3㊀变论域伸缩因子的伸缩原理及仿真对比分析伸缩因子的伸缩原理为:误差x 减小ң11+kx 4增大则α(x )减小ң变论域伸缩因子的函数值减小ң故论域缩小㊂同理,误差x 增大ң11+kx 4减小则α(x )增大ң变论域伸缩因子的函数值增大ң故论域扩张㊂根据单调性可知当x 从x 1增大到x 2,有x 2>x 1,则1-11+kx 42>1-11+kx 41,论域扩张,由变论域伸缩因子的正规性知,当误差x 取得最大值x e 时,α(x e )=1,此时变化的论域最大即为[-x e ,x e ],不能再继续扩大㊂为了能更加清晰,直观的分析本文设计的随机变论域伸缩因子的性能,并与文[17]中传统伸缩因子做对比,在Matlab 软件中进行仿真,得到当x e =1,k 取104时随机变论域伸缩因子的对比函数图像和局部放大图像如图2㊁图3所示㊂图2㊀变论域伸缩因子对比函数图像Fig.2㊀Variable universe scaling factor contrastfunction image251哈㊀尔㊀滨㊀理㊀工㊀大㊀学㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第28卷㊀图3㊀变论域伸缩因子对比局部放大函数图像Fig.3㊀Variable universe scaling factor compare localmagnification function image㊀㊀由图2和图3可见,本文所设计的伸缩因子在0.81s时已经趋于稳定,与传统的伸缩因子相比缩短了时间㊂而且稳定性好,具有更强的调节能力㊂可以看出改进的伸缩因子可以自由的随误差e的变化而变化,有一定的自适应性㊂这也对下文模糊控制器的应用起着很重要的调节作用㊂2㊀随机变论域Fuzzy控制器在医疗头盔中的应用及仿真㊀㊀将传统的手动旋转旋钮控制旋钮转速升级为,用随机变论域Fuzzy控制器控制旋钮转速,将医疗头盔发挥到最大的性能,提高了头盔的使用性和工作效率㊂2.1㊀随机变论域Fuzzy控制器医疗头盔仪器的工作原理㊀㊀医疗头盔整个仪器的工作原理:根据电磁铁输入稳定的动力带动两侧旋钮与顶部旋钮转动,随机变论域Fuzzy控制器自动调节旋钮到最佳转速,之后旋钮带动两侧调节盘与顶部调节盘转动,调节盘再通过定位销带动前后圈梁伸缩,前后圈梁会根据头部大小自动调节到合适位置,当前后圈梁达到头部最佳位置后停止运动,实现在不同条件情况下头盔达到最佳头部的佩戴位置㊂图4㊁图5分别为医疗头盔仪器的结构主视图和整体的三维图㊂头盔能否精确的佩戴在人体头部上,取决于随机变论域Fuzzy控制器控制旋钮转速,调节前后圈梁的可伸缩长度的多少,基于在机械实验室实验人㊀㊀1.顶部旋钮2.顶部压盖3.定位销4.顶盖5.顶调节盘6.永磁铁7.电磁铁8.压片9.顶部内盖10.顶嵌盖11.顶部嵌条12.两侧连接梁13.弹簧一.图4㊀医疗头盔仪器的结构主视图Fig.4㊀Structure of the main view of the medicalhelmetinstrument图5㊀医疗头盔仪器的三维图Fig.5㊀Three-dimensional Diagram of medicalhelmet instrument员的多次试验结果,本文将选取前后圈梁可伸缩长度产生的误差e和误差的变化ec作为此随机变论Fuzzy控制器的输入,并经过一系列的量化计算后,得到模糊量E㊁EC㊂最后,再经过模糊推理㊁去模糊化得到精确的前后圈梁可伸缩长度f㊁随机变论域Fuzzy控制器的输出㊂2.2㊀随机变论域FUZZY控制器在医疗头盔仪器中的设计㊀㊀本文以双输入单输出系统为例进行设计,其工作原理为:随机变论域Fuzzy控制器通过输出的论域伸缩因子来调整自身论域的大小,然后再将圈梁伸缩长度的误差e和误差的变化ec进行模糊化处理,之后做模糊推理和解模糊化,最后计算旋钮转速的输出量㊂根据随机变论域Fuzzy控制器在医疗头盔仪器的工作原理得到其结构图如图6所示㊂351第5期王㊀月等:一种随机变论域Fuzzy控制器在医疗头盔中的实现图6㊀变论域Fuzzy控制器结构示意图Fig.6㊀Structure diagram of fuzzy controllerwith variable universe根据在机械实验室反复多次试验数据结果显示,圈梁可伸缩长度大概为0~188.7mm㊂以能否精准控制旋钮的转速作为评价指标,结合相关的实验数据及上述信息,可以设计随机变论域Fuzzy控制器步骤如下:2.2.1㊀输入㊁输出变量的模糊语言描述综合考虑到动态控制性能以及控制算法的可实现性两个主要方面,本文设计一个二维的模糊控制器,以实际前后圈梁伸缩的长度与理想状态下前后圈梁伸缩的长度期望值的误差E和误差的变化EC 作为随机变论域Fuzzy控制器的输入变量,引起旋钮转速变化的多少作为输出变量u㊂下面给出E和EC及u的论域范围㊂E和EC的论域为:{-6,-5,-4,-3,-2, -1,0,1,2,3,4,5,6},u的论域为:{-7-6,-5, -4,-3,-2,-1,0,1,2,3,4,5,6,7},误差E和控制量u的模糊集为:{NB,NM,NS,O,PS,PM,PB},分别对应{负大,负中,负小,零,正小,正中,正大},误差变化EC的模糊集为:{NB,NM,NS,NO,PO, PS,PM,PB},分别对应{负大,负中,负小,负零,正零,正小,正中,正大}㊂以上论域均采用区间变换的方法使其归属到无量纲的标准论域,均为[-6,6]㊂下面基于输入,输出语言变量论域的取值,选用三角型隶属度函数如下图7所示:2.2.2㊀建立模糊控制规则对医疗头盔旋钮转速情况可知,已知前后圈梁伸缩长度的误差大或较大时,此时应选择控制量为尽快消除误差变大为主的控制规则;已知前后圈梁伸缩长度的误差小或较小时,为防止系统有超调趋势,此时应选择的控制量以系统稳定性为主的控制规则㊂因此根据文[12]的模糊控制规则表进行适当的改进,可以设计出如表1所示56条模糊控制规则的随机变论域Fuzzy控制器规则表:图7㊀输入、输出隶属函数图Fig.7㊀Input and output membership function graph表1㊀模糊控制规则表Tab.1㊀Fuzzy control rule table㊀㊀EuEC㊀㊀NB NM NS O PS PM PB NB PB PB PM PM PM O O NM PB PB PM PM PM O O NS PB PB PM PS O NS NS NO PB PB PM O NS NM NM PO PB PB PS O NS NM NM PS PM PB O NM NM NM NM PM O O PS NB NB NB NB PB O O PS NB NB NB NB 2.2.3㊀模糊变量的赋值表和模糊控制查询表的确定㊀㊀根据上文确定出误差E㊁误差的变化EC㊁控制量u的论域与模糊集,下面根据数据的特征㊁实际旋转情况,给出论域内的元素对于模糊语言变量的隶属度,如表2,3,4所示模糊变量E㊁EC㊁u的隶属度㊂451哈㊀尔㊀滨㊀理㊀工㊀大㊀学㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第28卷㊀表2㊀模糊变量E的赋值表Tab.2㊀Apportionment table of fuzzy variable E㊀㊀eμE㊀㊀-6-5-4-3-2-10+1+2+3+4+5+6 NB0.90.80.50.2000000000NM0.10.9 1.00.90.100000000NS000.10.3 1.00.80000000O000000.20.90.200000PS00000000.8 1.00.30.100PM000000000.10.9 1.00.90.1PB0000000000.20.50.80.9表3㊀模糊变量EC的赋值表Tab.3㊀Apportionment table of fuzzy variable EC㊀㊀ecμEC㊀㊀-6-5-4-3-2-10+1+2+3+4+5+6 NB0.90.80.40.2000000000NM0.30.8 1.00.80.300000000NS000.20.6 1.00.90000000NO00000.6 1.00.6000000PO0000000.6 1.00.60000PS00000000.9 1.00.60.200PM000000000.30.8 1.00.80.3PB0000000000.20.40.80.9表4㊀模糊变量u的赋值表Tab.4㊀Apportionment table of fuzzy variable u㊀㊀Uμu㊀㊀-7-6-5-4-3-2-10+1+2+3+4+5+6+7 NB 1.00.90.40.100000000000 NM00.30.7 1.00.90.8000000000 NS0000.10.30.9 1.00.30000000 O0000000.6 1.00.6000000 PS00000000.3 1.00.90.30.1000 PM0000000000.80.9 1.00.70.30 PB000000000000.10.40.9 1.0㊀㊀下面模糊控制规则用if-then语句可以表示为: if E=NB and EC=NB then u=PB,由Mamdani推理法可得出第一条模糊控制条件语句,以及相对应确定的模糊关系R1,其形式可以概括如下:R1=NB EˑNB ECˑPB u,551第5期王㊀月等:一种随机变论域Fuzzy控制器在医疗头盔中的实现将上述56条模糊控制规则分别与确定的模糊关系R 1,R 2, ,R i 进行取合运算,可得总的模糊关系矩阵:R =R 1ᶱR 2ᶱ R i ,i =56因此当误差㊁误差的变化的模糊值为E 和EC 时,可以求出输出控制量u 1的模糊值为u 1=(E ˑEC ) R 1那么整个输出控制量进而也可以求得,用以下式表示所求得的模糊集合u ,即u =u 1+u 2+ +u 56最后结合最大隶属原则可以将求得的模糊输出量转化为精确量㊂根据以上的计算结果和语言变量论域的量化等级,可以给出模糊控制查询表,如表5所示㊂表5㊀模糊控制查询表Tab.5㊀Fuzzy control lookup table㊀㊀ECu E ㊀㊀-6-5-4-3-2-10+1+2+3+4+5+6-67676777442000-56666666442000-476767774420-37666666320-1-1-1-24445444100-1-1-1-14445441000-3-2-104445110-10-1-4-4-4+1222200-1-4-1-3-4-4-4+212120-3-4-4-3-3-4-4-4+30000-3-3-6-6-3-6-6-6-6+4000-2-4-4-7-7-6-6-7-6-7+5000-2-4-4-6-6-6-6-6-6-6+60-2-4-4-7-7-6-6-7-6-7㊀㊀由随机变论域Fuzzy 控制器采样时刻,得出控制变量E 和EC 模糊化的结果,则可根据上述建立的模糊控制查询表,很快地找到与之相对应的控制量u ,并且经过反模糊化计算,将其模糊量转化为精确量,最终的精确量作为随机变论域Fuzzy 控制器对医疗头盔旋钮施加具体㊁精准的转速,为实时控制的输出㊂2.3㊀Matlab 仿真及结果分析接下来对设计好的随机变论域Fuzzy 控制器做Matlab 仿真,伸缩因子选择上述所设计出的鲁棒性较强㊁伸缩性能较优的伸缩因子㊂选择以编写S 函数形式的方式进行仿真研究㊂首先,将模糊控制规则表输入到Matlab 软件中的Fuzzy 运行程序里,并根据输入与输出论域的变化,反复调节最终给出模糊推理系统特性曲图,如图8所示㊂图8㊀模糊推理系统特性曲图Fig.8㊀Characteristic surface of fuzzy inference system㊀㊀将预先设计好的S 函数运用到上文所设计好的模糊控制算法中,再加入变论域伸缩因子,保持其他参数不变,并在Simulink 模块下进行搭建仿真框图做仿真试验,如图9所示㊂651哈㊀尔㊀滨㊀理㊀工㊀大㊀学㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第28卷㊀图9㊀医疗头盔仪器变论域模糊控制器仿真框图Fig.9㊀Simulation block diagram of variable universefuzzy controller for medical helmet instrument由于考虑到医疗头盔仪器和常规的模糊控制器的作用效果方面等情况和系统的响应速度㊁控制精度之间存在的矛盾,选取上述已设计好的伸缩因子为该随机变论域Fuzzy 控制器的伸缩因子,并设α∗1(x )=α∗2(x )=β(y )=1-11+kx4+φ,将上述设计好的变论域伸缩因子应用在随机变论域Fuzzy 控制器上,并更新上述已编写好的模糊控制算法,再利用Simulink 仿真框图进行仿真模拟试验,则可以得到随机变论域Fuzzy 控制器在医疗头盔仪器的仿真响应曲线图,如图10所示㊂图10㊀变论域模糊控制器的响应曲线Fig.10㊀Response Curve of Fuzzy Controllerwith Variable Universe将文[21]中已有的传统型伸缩因子加入到随机变论域Fuzzy 控制器中,仿真结果如图11所示㊂图11㊀传统变论域模糊控制器的响应曲线Fig.11㊀Response curve of traditional variableuniverse fuzzy controller由图可见,将设计好的伸缩因子和目前已有传统型的伸缩因子分别应用到随机变论域Fuzzy 控制器上,仿真结果表明,新设计的伸缩因子超调㊁稳定性效果明显优于传统型伸缩因子㊂其运行环境为Windows10系统,进行操作㊂控制响应到平稳的时间从0.50s 缩短到0.38s,使得随机变论域Fuzzy 控制器,超调量小而且控制精度高,具有较强的自适应性,能在更短的时间内趋于稳定㊂结果表明新设计模糊控制器的控制效果明显优于传统的模糊控制器㊂3㊀结㊀论1)对新设计的一种随机变论域伸缩因子,验证其稳定性,并通过绘制仿真图对比分析,说明新设计伸缩因子的合理性㊂2)将新设计的伸缩因子应用到随机变论域Fuzzy 控制器上,并通过最后的对比响应曲线图说明,模糊控制器的精度得到了有效提高,并且在很大范围内解决了鲁棒性不稳定㊁适用范围不广泛㊁时间超调等问题㊂3)随着新设计的二维模糊控制器精度的提高,使得医疗头盔旋钮转速问题得到了改进,因此,不仅提高了在医学方面的工作效率也极大丰富了控制领域的适用范围㊂参考文献:[1]㊀ROBERT Babuska,HENK B Verbruggen.Fuzzy 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Supply and Demand Matching Model for Third Party Logistics Integrated PlatformChunhua JUComputer Science and Information EngineeringCollegeZhejiang Gongshang UniversityHangzhou, Chinajuchunhua@Bin SunComputer Science and Information EngineeringCollegeZhejiang Gongshang UniversityHangzhou, Chinasunbin0302@Abstract—In order to improve the supplier selection and matching supply with demand for third party logistics integrated platform, this paper proposes a three-layer evaluation index system for supply and demand matching considering factors of service areas and cooperation experiences, establishes a supply and demand matching model based on neural network. This model perfectly simulates the process of fuzzy integral diagnosis, with corresponding parameters of adaptive learning and training index systems of fuzzy neural network. Experiments show that this model can effectively evaluate comprehensive abilities of suppliers, with high level of accuracy and feasibility.Keywords- fuzzy neural network, third party logistics, integrated model, supply and demand matchingI.I NTRODUCTIONThird party logistics (3PL) integrated platform is a supplier integrating the whole supply chain. It supervises manufacturers and retailers as the sole connector between customers and suppliers providing logistics, services and information. It is vital important for 3PL integrated platform to match proper suppliers and customers for improving its competitiveness, even competitiveness of the whole supply chain.Nowadays, many researches on selection and matching in 3PL integrated platform are conducted. Gang W and Xiao ling G select logistic suppliers by analytical hierarchy process. Zhong W establishes evaluation model by judging matrixes. Zhi ying L adopts one-layer fuzzy integral diagnosis method and establishes evaluation model. Current methods have two problems: (1) these methods evaluate suppliers by comprehensive capability only. The results are used in the long run and different areas and demand in different logistic businesses are overlooked. (2) The role of qualitative indexes on selecting logistic suppliers is neglected. The weights of indexes lack accuracy and depend too much on subjective judges, with no scientific methods.This paper proposes a supply and demand matching model for third party logistics integrated platform based on neural network and establishes three-layer evaluation index system considering factors of service areas and cooperation experiences. Further, fuzzy neural network is adopted to learn and train different indexes and finally get evaluation indexes for matching supply and demand in one single logistic business, which provides scientific and appropriate principles for selecting suppliers.II.F UZZY NEURAL NETWORK MODEL OF SUPPLY AND DEMAND MATCHING FOR THIRD PARTY LOGISTICSINTEGRATED PLATFORMFuzzy neural network is a system combining fuzzy logic and fuzzy network, better than separate fuzzy system or fuzzy network. Fuzzy neural network can properly express fuzzy and qualitative knowledge, resembling human reasoning, and can deal with uncertainty and non-linear problems. It has many advantages, like concurrent calculation, distributive information storage, error toleration and adaptive learning.A.Fuzzy module of comprehensice capability index ofsuppliersThis module is to fuzzify the input of comprehensive capability index and calculate the fuzzy variable value of every input index. Fuzzy membership function adopts Gaussian function, with its definition:µ x eµ(1)Where µ denotes the center of membership function，σi denotes the width of membership function.Evaluation indexes of all the samples are divided into several classes with K-Mean clustering algorithm. The mean of x scores of all the samples under one certain class equals to µ value in the corresponding class. σ is computed as follows:σj=1n(x j`-μi)2nj=1Where n denotes sample size, x ` denotes index value of different samples in corresponding class.B.Experiment result analysisNeural network in fuzzy neural network this paper proposed adopts error back-propaganda, namely BP learning algorithm. In essence, BP algorithm computes output values in the direction of input to output, gets the errors of output values and sample values, then propagandizes errors in reverse and revises connection weights to reduce errors of output. Specific steps are as follows:2009 International Joint Conference on Artificial Intelligence•(1) Initializing ω and θ in a 0-1 scale at randomly, where ω is connection weight from neuron i to neuron j, θ is the threshold value of neuron j (hidden layer and output layer).•(2) Input the fuzzified training sample {x } and the corresponding expectation {y }, where p, l denote sample size and the number of input vectors respectively.•(3) Compute output O in different layers. As for input layer (the second layer in Figure 1), input equals to output, namely O x , where xdenotes the ith value of pth sample. As for hidden layer and output layer, O f（∑ω O θ ）, where O is the input of neuron i and meanwhile the output of neuron j. f(x) is a non-linear, differential and not decreasing function，generally, S-shaped function f x 1/ 1 e .•(4) Compute error signals in different layers. The error in output layer δ y O O 1 O , the error in hidden layer δ O 1O ∑δ ω•(5) Back-propaganda, revised weight: ω t 1 ω t αδ O , where α denotes learning rate.•(6) Compute errors: E∑∑ O y,when E is lower than the given error of fitting,network training is over, or else, turn to (3), andcontinue training.III.T HREE-LAYER E VALUATION I NDEX S YSTEM FOR L OGISTIC S UPPLY AND D EMAND M ATCHING Traditional methods adopt indexes limited to the factors of capabilities of suppliers, which can analyze and differentiate suppliers in capability, size and services to some extent. But not the supplier with the strongest capability adapts all the logistic businesses. Whether both parties match depends on the hard wares and soft wares of suppliers and whether the suppliers have advantages in given areas, and cooperation experiences (successful or awful) between customers and suppliers. This paper proposes a new index system contains the areas served by suppliers and cooperation experiences, in addition to the comprehensive abilities of suppliers. as Table 1 shows,TABLE I. T HREE-LAYER INDEX SYSTEM FOR SUPPLY AND DEMANDMATCHING OF LOGISTICSFirst Second ThirdComprehen-sive abilities of logistic suppliers operationalcapabilitytransportation xstorage xvalue-added service xinformatization xcustomization xtransportationservice xservicecapabilitywarehouse management xdata record ximport and export xpayment disbursement xCreditprice xstrength xlevel management xcorporate image xhuman resource xarea index and algorithm xcooperation experiences index xprehensive abilities of logistic suppliersComprehensive abilities of logistic supplies have threemain dimensions, operational capability (transportation anddelivery, storage, value-added service, informatization,customization), service capability (transportation service,warehouse management and operation, data record, importand export, payment disbursement), credit (price, strength,level management, corporate image, human resource).B.Area index and algorithmArea index refers to the coefficient of areas of thislogistic business and areas covered by suppliers, specificsteps as follow,Initialization: analyze historic business data of everysupplier (in near six months), get the main area network ofdaily business of suppliers, for example, Beijing toShanghai, separate and mark all the districts above the levelof county in this path and get the network of service areas,then put into array B[] (according to AdministrativeDivisions Statistics of the People's Republic of China issuedby Ministry of Civil Affairs of the People’s republic ofChina in 2005). Then, get the best path of this business (withalgorithm) and separate all the districts above the level ofcounty and put into array A. As Figure 1 shows, in thedashed line is service areas set of certain logistic supplier.Specific rules are as follow,•①if both the first and last element in string Abelongs to array B, then coverage coefficient is 1•②if one end of string A belongs to array B, thenjudge backwards till the other end (at j), return tocoverage coefficientc ,（0 c 1）•③if neither the first and last element belongs toarray B, then judge toward center and return tocoverage coefficientc 。
模糊神经网络简介
模糊神经网络(Fuzzy Neural Network)是一种集结模糊数学和神经网络学习规则的人工神经网络。
它能够学习和识别模糊的、不确定的和模糊的数据集，这样就可以应对实际问题中模糊的、不精确的和模糊的数据。
介绍
模糊神经网络的基本元素是神经元，它们连接组成了一个网络。
每个神经元都有一个输入和一个输出，输入可以是模糊或者非模糊的。
神经元的输出可以是逻辑值或者模糊值。
模糊值是由神经元的激活函数决定的。
激活函数通常是Sigmoid 函数、ReLU函数或者其他类型的函数。
与传统神经网络不同的是，模糊神经网络的权重和阈值可以是模糊的。
模糊神经网络的学习方法可以分为监督学习和非监督学习。
监督学习指的是在给定输入和输出对的情况下，计算权重和阈值。
常用的算法有误差反向传播算法和梯度下降算法。
非监督学习指的是在没有输入和输出对的情况下，根据相似性和差异性自动聚类。
模糊神经网络广泛应用于模糊控制，模糊模式识别，时间序列预测和多目标最优化等领域。
它在工业、农业、医疗和金融等领域中也有着广泛的应用。
例如，模糊神经网络可以应用于电力系统稳定性分析、车辆指挥控制、医疗诊断和金融分析等。
结论
总之，模糊神经网络是一种重要的人工神经网络，它具
有模糊性、可学习性和鲁棒性等特点。
它已经广泛应用于各种领域。
在未来，随着人工智能的发展，模糊神经网络也将发挥越来越重要的作用。
一维Hopfield神经网络模型的多稳态分析宿娟;何志蓉【摘要】本文讨论一维Hopfield神经网络模型的多稳态问题.当模型所含S型激活函数没有有界性限制时,本文首先讨论了模型平衡点的存在性,并进一步给出了模型取得一个,二个,或三个平衡点的参数条件以及每个平衡点的稳定性.然后本文研究了模型在参数所有取值情况下的平衡点个数及其稳定性.最后,通过两个实例及其数值模拟说明了结果的有效性.【期刊名称】《四川大学学报（自然科学版）》【年(卷),期】2016(053)002【总页数】5页(P260-264)【关键词】Hopfield神经网络;多稳态;激活函数;渐近稳定;平衡点【作者】宿娟;何志蓉【作者单位】成都师范学院数学系,成都610044;四川大学数学学院,成都610064【正文语种】中文【中图分类】O175由于Hopfield神经网络模型在优化,图像处理,规划等问题中有广泛应用[1-4],自提出以来就受到科学家们的关注.在模型的应用中,系统的动力学行为起到了至关重要的作用.稳定性作为重要的动力学行为之一,已有很多工作对其进行了讨论[4-15]. 在优化,平行计算及信号处理等领域中, 单稳态的神经网络对模型的设计和应用有重要作用.在早期的工作中,单稳态神经网络的讨论已取得较多的结果[5-9].多个平衡点的共存将极大的改变模型的动力学行为,甚至导致振动,极限环,混沌的发生[10,11].具有多个稳定平衡点或稳定周期轨的神经网络称为多稳态系统[12].在神经网络应用于联想记忆、模式识别时,系统存在多个平衡点是必备条件.在联想记忆、模式识别的应用中,多稳态的神经网络具有明显的优势.因此,无论在理论还是应用中多稳态神经网络的的研究都很有必要,而相关工作也受到越来越多的关注[12-15].激活函数对Hopfield神经网络模型的动力学性质有重大影响.常见的激活函数有如下三类: S型[11,12], 极限型[12,13]和线性阈值型 [14,15].文献[14,15]针对含线性阈值激活函数的二维模型分别讨论了非退化和退化平衡点的存在条件,并给出了多个平衡点存在的充要条件.文献[12]针对有界S型激活函数,通过构造自映射区域,利用Brouwer不动点定理获得了模型至少存在3n个平衡点的充分条件,其中n是系统的维数.激活函数的有界性是文献[12]中Brouwer不动点定理应用的关键性条件.针对模型中激活函数无界的情况,平衡点的存在性不能通过Brouwer不动点定理来获得.当激活函数没有有界性限制时,解决系统平衡点存在性的常用方法有压缩映射原理[5],同胚映射[6,7],或拓扑度理论[8].然而现有文献给出的充分条件对系统参数有较高的要求,也即是说将系统参数限定在一定的范围内,以此来保证系统平衡点的存在性.受文献[5～8,12,15]的启发,本文讨论一维Hopfield神经网络模型的多稳态问题,其中S型激活函数没有有界性的限制.首先,我们利用激活函数的性质获取平衡点的存在性,进一步利用几何方法讨论系统具有一至三个平衡点的条件及其稳定性结论,然后补充说明参数在其余情况下系统平衡点的个数及其稳定性.因此本文彻底解决了系统在参数所有取值时的平衡点问题.最后通过列举含有界和无界激活函数的模型, 利用数值模拟验证所得结论.本文讨论如下的一维Hopfield神经网络模型:其中u(t)表示神经元的状态变量;d,a,I是实数,这里d表示神经元恢复孤立静息状态的速率,a表示神经元自身的联络权,I表示外部输入;g(u)是R上的连续函数,称为神经元的激活函数.设满足-du0+ag(u0)+I=0,则称u0是系统(1)的平衡点.下面给出关于激活函数g(u)的三个假设:，H3 u<0时, g″(u)>0,u=0时, g″(u)=0,u>0时, g″(u)<0.满足假设条件H1-H3的激活函数既存在有界又存在无界的情况,例如arctan(ku),tanh(ku),k>0是有界的例子.而时时则为无界的例子.针对没有有界限性限制的激活函数,我们将通过函数性质的分析,获得系统在参数所有取值情况下的平衡点个数,再进一步分析所得平衡点的稳定性.为了以下证明的方便,取d,a为非零实数,而da=0的情况,我们将在注1中来说明. 引理3.1 若条件H2成立,则系统(1)存在平衡点.证明在条件H2下,无论g是否有界,等式成立.定义从式(2)和式(3)我们得出,当<0时,有而>0时,有事实上,从式(4)或式(5)以及F的连续性可以得出,存在u0满足F(u0)=0,即系统(1)的平衡点存在.证毕.无论激活函数有界或无界,引理3.1给出了系统(1)平衡点存在的条件.下面我们进一步就的取值范围,分<g′(0)和≥g′(0)三类情况讨论平衡点的个数和稳定性.为了证明的方便,首先我们在定理3.2中讨论<0和≥g′(0)的情况.定理3.2 若条件H1和H2成立,则(i) 当<0时,系统(1)存在唯一平衡点,且该平衡点在a<0时渐近稳定,a>0时不稳定; (ii) 当≥g′(0)时,系统(1)存在唯一平衡点.进一步若条件H3成立,g∈C3时,该平衡点在a<0时不稳定,a>0时渐近稳定.证明条件H2保证了平衡点的存在性, 下面我们将证明平衡点的唯一性和稳定性.(i) 当时,根据条件H1有,由此说明F(u)在R上严格单增.结合式(4),得到F(u)的零点唯一,即系统(1)的平衡点唯一,并记此平衡点为u0.我们将系统(1)的右端在点u0进行Taylor展开,得到o(u-u0)事实上a<0时,根据已知条件<0可以得出-d+ag′(u0)<0,结合式(6)得到平衡点u0渐近稳定.反之a>0时,平衡点u0不稳定.(i)得证.(ii) 当时,根据条件H1有,当且仅当=g′(0),u=0时,F′(u)=0.由此我们得到F(u)在R上严格单减,结合式(5), 得到F(u)的零点唯一,即系统(1)的平衡点唯一.为了证明方便,仍记此平衡点为u0.下面我们分两种情况讨论平衡点的稳定性.首先当=g′(0),u0=0且g∈C3时,根据条件H3我们可以得到g″(0)=0和g‴(0)<0,于是系统(1)的右端在点u0=0的Taylor 展式为‴(0)u3+o(u3)从式(7)得知,a<0时平衡点u0=0不稳定,而a>0时,平衡点u0=0渐近稳定.再对=g′(0),u0≠0或>g′(0)的情况讨论稳定性.我们仍将式(1)的右端在点u0进行Tayloy展开,所得结果与式(6)相同.根据已知条件=g′(0),u0≠0或,我们得到,结合式(6)得出平衡点u0在a<0时不稳定,a>0时渐近稳定.证毕.为了分析<g′(0)时系统平衡点的个数,下面我们约定定理中需要的两个符号.假设<g′(0),条件H1～H3成立,利用g′的取值范围和单调性,分别存在唯一的u1,u2满足通过F在点u1和u2取值的正负,我们在定理3.3中说明平衡点的个数,并在此基础上讨论平衡点的稳定性.定理3.3 设条件H1～H3成立,和u1,u2分别由式(3)和式(8)定义, 则(i) 当F(u1)>0或F(u2)<0时,系统(1)有唯一平衡点,且位于(u2,+∞)或(-∞,u1)内,该平衡点在a<0时不稳定,a>0时渐近稳定;(ii) 当F(u1)=0或F(u2)=0时,系统(1)有两个平衡点.若F(u1)=0,则点u1是平衡点且不稳定,而另一平衡点在(u2,+∞)内,且a<0时不稳定,a>0时渐近稳定; 若F(u2)=0,则点u2是平衡点且不稳定,而另一平衡点在(-∞,u1)内,且a<0时不稳定, a>0时渐近稳定;(iii) 在F(u1),F(u2)的其余取值情况下,系统(1)有三个平衡点,且分别在和(u2,+∞)内.当a<0时,(-∞,u1)和(u2,+∞)内的平衡点不稳定,而内的平衡点渐近稳定；当a>0时,(-∞,u1)和(u2,+∞)内的平衡点渐近稳定,而内的平衡点不稳定.证明当时,由H1～H3中g′(u)的性质和式(8)中u1,u2的定义有从上式容易得到F(u)的单调性和极值情况如表1所示.事实上从表1我们得到F(u1)<F(u2)(i) 若F(u1)>0,从式(9)容易得出F(u2)>0.结合式(5),表1和值F(u1), F(u2)的正负,我们得到F(u)的零点只能在(u2,+∞)内且唯一,即系统(1)的平衡点唯一且在(u2,+∞)内.将该平衡点记为u0,并且将系统(1)的右端在点u0进行Taylor展开,所得表达式与式(6)相同.由于u0∈(u2,+∞), 根据g′的单调性和式(8)中u2的定义有最后结合式(6)和式(10)得出平衡点u0在a<0时不稳定,a>0时渐近稳定.同理可证F(u2)<0时的结论.(i)得证.(ii) 当F(u1)=0时,由式(9)容易得到F(u2)>0.结合式(5),表1和值F(u1), F(u2)的正负可以得到F(u)只有两个零点,u1是其中之一,而另一零点在(u2,+∞)内, 仍记为u0. 将系统(1)的右端在点u1进行Taylor展开,从u1的定义和条件H3可以得出g″(u1)>0.因此无论a<0或a>0,从式(11)得到平衡点u1不稳定.平衡点u0的稳定性证明与上述(i)中的证明相同.同理可证F(u2)=0的结论. (ii)得证.(iii) 首先我们分析F(u1)和F(u2)满足的具体条件.将F(u1),F(u2)分别取作平面横坐标和纵坐标,在满足式(9)的区域内去掉(i),(ii)中F(u1)和F(u2)满足的条件,此时F(u1),F(u2)满足的条件即是F(u1)<0且F(u2)>0.结合式(5),表1,F(u1)<0且F(u2)>0得出F(u)只有3 个零点,且分别在(-∞,u1),(u1,u2)和(u2,+∞)内. F(u)的零点等同于系统(1)的平衡点.设上述三个区间内的平衡点分别为和.为了证明的方便, 统一用u0代表上述三个平衡点,并将系统(1)的右端在点u0进行Taylor展开,所得表达式与式(6)相同.根据g′(u)的单调性和所在区间容易得到,当a<0,u0 = 或u0 = 时, 有-d+ag′(u0)>0,结合式(6)知道平衡点和不稳定,而u0 = 时,有-d+ag′(u0)<0, 因此平衡点渐近稳定. 同理可得a>0时三个平衡点的稳定性. 证毕.注1 当da≠0时,定理3.2和定理3.3获得了参数所有取值和系统(1)的平衡点个数, 稳定性之间的关系.当da=0时, 若d≠0，a=0或d=a=0, 平衡点问题容易解决.当d=0,a≠0时, 若,则平衡点存在且唯一, 当a<0时该平衡点渐近稳定, a>0时不稳定;若∉,则平衡点不存在.从定理3.2, 3.3和注1得出,系统(1)中参数所有取值情况均已讨论,因此本文彻底解决了系统(1)的平衡点个数和稳定性问题.注2 若系统(1)存在唯一平衡点且渐近稳定,从其Taylor展式可以得到该平衡点是全局渐近稳定.因此定理3.2,定理3.3(i)和注1中的唯一平衡点若满足渐近稳定, 则一定是全局渐近稳定的.本节将通过两个实例来验证所得结论,其中例4.1和例4.2的激活函数分别是有界和无界的.例4.1 对系统(1), 取d=1.28,a=1,I=-0.64ln2+0.6,g(u)=tanh(2u).容易验证g(u)是满足条件H1～H3的有界函数.计算得<1.28<g′(0),根据定理3.3需进一步计算u1,u2.由g′(u)=1.28计算得出,因此有F(u1)=0,满足定理3.3(ii)的条件,因此我们得到系统存在两个平衡点,是其中之一且不稳定,而另一平衡点u0在内且渐近稳定.图1的数值模拟验证了所得结论.例4.2 令系统(1)中d=1,a=5,I=1.5,当时，，时,.容易验证g(u)是满足条件H1～H3的无界函数.计算得,根据定理3.3需进一步计算u1,u2.利用数学软件Maple14,数值求解方程由g′(u)=0.2得出u1=-1.9437，u2=3.1667,再将u1,u2代入F(u)计算得F(u1)=-0.8808<0, F(u2)=0.4466>0,满足定理3.3(iii)的条件, 因此系统存在三个平衡点,且分别在内.记上述三个区间内的平衡点分别为和，由定理3.3(iii)和a>0, 我们得出和渐近稳定,不稳定. 图2的数值模拟验证了所得结论.【相关文献】[1] Ghatee M, Niksirat M. 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