perkins_engine noise and vibration

第38卷第1期声学技术Vol.38,No.1高斯色噪声下的子阵平滑主模式抑制波束形成邵鹏飞，邹丽娜(声呐技术重点实验室杭州应用声学研究所，浙江杭州310012)摘要：实际海洋波导是一种具有空-时相关性的衰落信道，且其驻留的海洋环境背景噪声场呈现非均匀各向异性的特性，噪声场时空相关性并非δ函数，大孔径声呐的探测性能会受到很大影响。

将背景噪声建模为有色高斯随机过程，设计基于子阵平滑的主模式抑制(Dominant Mode Rejection,DMR)波束形成算法，以实现小快拍数条件下具有去相关作用的自适应处理，较好地提高了大孔径阵声呐在高斯色噪声环境下的探测能力。

模拟仿真结果表明，该方法具有良好的抑制高斯色噪声的能力。

关键词：高斯色噪声；子阵平滑；主模式抑制；波束形成中图分类号：TN911.7文献标识码：A文章编号：1000-3630(2019)-01-0103-05DOI编码：10.16300/ki.1000-3630.2019.01.017Subarray smoothing DMR beamforming under thebackground of colored Gaussian noiseSHAO Peng-fei,ZOU Li-na(Science and Technology on Sonar Laboratory,Hangzhou Applied Acoustics Research Institute,Hangzhou310012,Zhejiang,China) Abstract:The actual ocean waveguide is a fading channel with space-time correlation,where the background noise field is characterized by non-uniform anisotropy and the space-time correlation of noise field is not aδ-function,all these factors greatly affect the detection performance of large aperture sonar.In this paper,the background noise is modeled as a colored Gaussian stochastic process,and the algorithm of dominant mode rejection(DMR)beamforming based on sub-array smoothing is designed to realize the adaptive processing with the function of de-correlation under the condition of small snapshot number and to improve the detection ability of large aperture sonar in colored Gaussian noise background.The simulation results show that the method has good ability to suppress colored Gaussian noise.Key words:Gaussian colored noise;subarray smoothing(SS);dominant mode rejection(DMR);beamforming0引言海洋背景噪声场并不能等同建模为均匀各向同性的白高斯噪声随机过程，而是被表征为受边界和动力学等因素影响，具有一定空-时相关性的随机场。

Unit6Active reading (1)Last man down: the fireman’s storyLanguage points1 Last man down: the fireman’s story (Title)The expression last man down, similar to last man standing, refers to the survivor or winner. The lastman down from the tower before it collapsed would be one of the bravest.2 There were about two dozen of us by the bank of elevators ... (Para 2)A bank of elevators means a set of lifts.3 Some had their turnout coats off, or tied around their waists. (Para 2) Turnout coats are the uniform firefighters wear when they turn out for a fire.4 Others were raring to go. (Para 2)The expression raring to go is an old form of rearing up, and means being eager to go like a horse.5 All of us were taking a beat to catch our breaths, and our bearings, figure out what the hell wasgoing on. (Para 2)To take a beat means to rest for a moment.A bearing is an exact compass reading measured in degrees. To take your bearings is to find where youare. Here it means both physically and mentally.6 We’d been at this thing, hard, for almost an hour, some a little bit less, and we were nowhere closeto done. (Para 2)To be at this thing is a slang expression which means to work on this mission. The expression nowhere close to done means someone is far from completing their work.7 Of course, we had no idea what there was left to do, but we hadn’t made a dent. (Para 2)A dent is a mark on a piece of metal as when you bump your car. To make a dent in something is to havean effect on it (imagine beating a piece of hard steel and not making any mark on it). To make a dent heremeans to achieve something. The firefighters had hardly begun their work.8 As if we could see clear through the ceiling tiles for an easy answer. (Para 3)Looking up for the source of the noise was only useful if you could see through the floors above, but itstill remained an instinctive reaction.9 The building was shaking like in an earthquake, like an amusement park thrill ride gone berserk …(Para 3)The word berserk was originally about ancient Viking warriors who worshipped a bear god (ber). Theywould go into a terrible rage or madness when fighting. It now means utterly and dangerously crazy.10 The way it coursed right through me. (Para 3)To course means to run or flow somewhere quickly. The noise and vibration have a strong physical effecton the writer.11 I thought about my wife and my kids, but only fleetingly and not in any kind of life-flashing-beforemy-eyes sort of way. (Para 4)Life flashing before my eyes is a claim made by someone who has near-death experiences, as in anaccident, of seeing a slow motion version of the most important events in their lives. Researchers say itmay be the reaction of the brain to trauma.Streets full of heroes Unit 619912 Or, “We’ll all meet at the big one.” (Para 4)After any fire, the fighters use the expression the big one to minimize that fire and suggest there willalways be a bigger one coming. It is a brave act of understatement.13 I never knew how it started, or when I’d picked up on it myself, but it was part of our shorthand. (Para 4)To pick up on it means to learn it and start using it. It is a slang expression. Shorthand is a system of writing used for taking down fast speech. It uses symbols for common wordsand can only be understood by people who learn it. Firemen have their own spoken shorthand (as do mostprofessions). To an outsider, the big one would not mean much, but as the writer explains it was rich inmeaning to him and his colleagues.14 I fumbled for some fix on the situation, thinking maybe if I understood what was happening I couldsteel myself against it. (Para 5)Some fix is a slang term which means a way of understanding.To steel oneself against something means to prepare oneself to do something unpleasant.15 A battalion commander for the New York Fire Department, he was on the sceneof the disaster … (Para 6)The Fire Department is divided up into battalions of up to 200 consisting of a number of companies ofabout 30 firefighters.Reading and understanding3 Choose the best summary of the extract.2 In this dramatic personal account, firefighter Richard Picciotto recalls what he was doing and thinking,just before the north tower of the World Trade Center collapsed on 11 September 2001.4 Answer the questions.1 Where was Richard Picciotto at 9:59 am on 11 September 2001?He was on the 35th floor of the north tower of the World Trade Center.2 Who was with him?About two dozen firefighters.3 What was everybody trying to do?They were resting and trying to work out what was going on.4 How long had they been in the building?Nearly an hour.5 What did they do when the noise started?They stood still.6 What was happening to the building?It was falling down.7 What did Picciotto start thinking about when he heard the noise?He started thinking about his family, job and the bagels in the kitchen.Unit 6 Streets full of heroes2008 Did Picciotto have the impression things were happening quickly or slowly? To him, it seems things were happening slowly while in truth they weren’t.9 How did Picciotto get out of the tower?He climbed through the rubble and led his men to safety.10 How many firefighters lost their lives?Altogether 343 firefighters.11 Why did Picciotto write Last Man Down?He wrote it as a tribute to his colleagues.Dealing with unfamiliar words5 Match the words in the box with their definitions.1 to make a fire stop burning (extinguish)2 the total number of people who have been killed or hurt (toll)3 an extremely difficult or frightening situation (nightmare)4 a very sad event that causes people to suffer or die (tragedy)5 as much as possible (utmost)6 impressive actions that prove someone is very brave (heroism)7 happening in a confused way and without any order or organization (chaotic)6 Complete the paragraph with the correct form of the words in Activity 5.For a firefighter arriving on the scene of a fire the first few minutes are usually the most (1) chaotic.He has to (2) extinguish the fire, he also needs to find out if human lives are in danger. When people aretrapped inside a building he must act swiftly to prevent (3) tragedy, or, –in the (4) nightmare scenario – tokeep the death (5) toll to a minimum. Actions like these require the (6) utmost degree of (7) heroism.7 Replace the underlined words with the correct form of the words in the box.1 He’s a very honest, fair and well-behaved sort of person. (decent)2 I’d like to express my thanks for everything you’ve done for me. (gratitude)3 There was a group of cows standing in the corner of the field. (herd)4 There have been very big increases in food prices over the last few months. (massive)5 All the people should leave the building immediately when the alarm sounds. (evacuate)6 She has displayed all the qualities needed for being a leader in her job. (leadership)8 Answer the questions about the words and expressions.1 If you are raring to go, are you eager to (a) leave, or (b) start an activity?2 If you get your bearings, do you (a) lose your way, or (b) find out where you are?3 If you are nowhere close to done, do you (a) still have a lot more work to do to finish the job, or (b) stillfeel strong and ready to work?4 If you haven’t made a dent in something, have you (a) made good progress, or (b) hardly begun the job?5 Is a racket (a) a loud and unpleasant noise, or (b) a low musical sound?Streets full of heroes Unit 62016 If something goes berserk, is it (a) quiet and well-behaved, or (b) out of control?7 Does whatever the hell it was suggest that the writer (a) knew exactly whatthe noise was, or (b) didn’tknow what the noise was?8 If something is part of the shorthand, can you (a) easily understand it, or(b) not understand it?9 If you are fumbling for a fix, are you (a) trying to understand something, or (b) trying to stay where you are?Active reading (2)Language points1 “Suddenly,” she wrote in her syndicated column, “I saw on the sidewalka figure of a man.” (Para 1)A syndicated column is a regular newspaper article sold to newspapers all around the country.2 “I felt certain that somewhere along the line she would stub her toe,” said Perkins, thinking ofWashington’s fishbowl atmosphere. (Para 3)To stub her toe means to do damage to herself or get hurt.In a fishbowl atmosphere, everyone can see what is happening in the fishbowl. The sentence means Perkins was sure sooner or later she would get into trouble and be criticized.3 I don’t know how she did it. What to lay it to? (Para 3)The expression what to lay it to means “how can one explain it?”.4 … “that a crippled man, victim of a cruel affliction, was able for more than ten years to ride thestorms of peace and war at the summit of the US …” (Para 3)A man in a wheelchair with a terrible disease could lead his country well both during the Great Depressionand World War.5 “Most people who have played second violin all their lives never have an opportunity to play firstviolin,” remarked Perkins. (Para 4)People who play second violin are those who do not lead or give solos and who are always of lesserimportance. To play first violin means to be the leader and take the initiative.6 “Now, if you want to know what I think about Mrs Roosevelt, she istuh-riffic! …” (Para 5)The word tuh-riffic means terrific. It is pronounced with a strong regional accent.7 On a trip to India ... introduced to the Indian Parliament by Pandit Nehru as “a representative ofresurgent humanity”. (Para 6)The expression resurgent humanity refers to recovering from the horrors of thefirst half of the 20thcentury. A representative of resurgent humanity refers to an example of the most admirable and progressivetype of person.Reading and understanding2 Choose the best way to complete the sentences.1 Eleanor Roosevelt became a volunteer (c) .(a) when she met her husband(b) when her husband became President of the US(c) as a young woman(d) when she saw a homeless man in the street2 When she became the wife of the president (c) .(a) she gave up her job(b) she began to write for a newspaper(c) she reinvented the role of First Lady(d) she found it difficult to reconcile family life and public affairsStreets full of heroes Unit 62073 When she held her first press conference (a) .(a) she didn’t allow men to atte nd(b) she pushed her husband in on a wheelchair(c) she made speeches(d) her involvement in politics shocked people4 While Roosevelt was president, Eleanor (c) .(a) stayed a full-time wife and mother(b) made a lot of people angry(c) defended the rights of women and Afro-Americans(d) became the host of a television programme5 After her husband died she (c) .(a) retired from public life(b) became the only female delegate to the United Nations(c) helped implement the Universal Declaration of Human Rights(d) started writing for a newspaper6 In the last years of her life she (b) .(a) went to live in India(b) continued to promote the rights of women(c) was given a new task by President Kennedy(d) gave up her interest in politicsDealing with unfamiliar words3 Match the words in the box with their definitions.1 someone who is chosen to represent a group of other people at a meeting (delegate)2 to believe that something is the cause of someone or something else (ascribe)3 a newspaper or television reporter, especially one who deals with a particular subject or area(correspondent)4 a very high level of skill or ability (genius)5 to control someone or something, often in a negative way, because you have more power or influence(dominate)6 used about a feeling or thought you do not realize you have (unconscious)7 to watch something in order to check that it works in the way that it should (oversee)4 Complete the paragraph with the correct form of the words in Activity 3.Eleanor Roosevelt showed her (1) genius for getting the support of other (2) delegates in the UNAssembly. She was a great speaker who knew how to (3) oversee important meetings without being seento (4) dominate them. She was also a talented (5) correspondent and she wrote a daily column for manyyears. Franklin D. Roosevelt’s success as president was (6) ascribed by many to her support and wonderfulcharacter. She became involved in politics because of her sense of right and wrong and an (7) unconsciousneed to help people.Unit 6 Streets full of heroes2085 Replace the underlined words with the correct form of the words in the box.1 He has been unable to use his legs since birth. (crippled)2 We need to call a meeting for world leaders about this issue. (summit)3 The first thing I read in the newspaper is the regular section about the arts. (column)4 Our class visit to the United Nations was a wonderful experience. (marvelous)5 It’s import ant to try to influence politicians about the need to improve transport facilities in our area.(lobby)6 How many millions of people live in the very poor areas of Mumbai? (slums)6 Answer the questions about the words and expressions.1 In a fishbowl atmosphere, are you (a) likely, or (b) unlikely to see what everyone is doing?2 Is a mishap a (a) positive, or (b) negative experience?3 If you have a humane attitude, are you (a) kind and caring, or (b) cruel and uncaring?4 If you win over someone to your cause, do you (a) defeat them, or (b) persuade them to join you?5 Does an affliction make your life (a) easy, or (b) difficult?6 If you ride the storm, do you (a) survive it, or (b) fall victim to it?7 Is a superlative performance (a) very good, or (b) just good?8 If a politician has a throng of admirers, are there (a) many people, or (b)a few who like them?9 If you are on a par with someone, are you in (a) the same position, or (b) different positions?Language in useword formation: gender-inclusive language1 Look at the sentences from the passages and answer the questions.Last man down: The fireman’s storyWe were firefighters, mostly, and we were in various stages of exhaustion.Streets full of heroes Unit 6211Please join Life magazine as we honor the power and humanity of Anna Eleanor Roosevelt by inductingher into the Hall of Heroes.1 What meaning do fireman and firefighter share?Someone whose job is to fight fires.2 What extra meaning is included in the word fireman?The person is male.3 Does the word heroes refer to men, women, or both?Both.2 Replace the underlined words with gender-inclusive language.1 Miss Read was the headmistress at school, and I was very fond of her. (headteacher)2 Mother Teresa and Eleanor Roosevelt are two great heroines of our time. (heroes)3 There were a lot of policemen standing at the entrance to the factory. (police officers)4 More than three hundred firemen died in the fire. (firefighters)5 We’ll ask one of our salesgirls to come and help you. (salespersons) Why is it that …?3 Rewrite the sentences using Why is it that ...?1 I don’t know why we haven’t been able to solve the problem of slums in this town.Why is it that we haven’t been able to solve the problem of slums in this town?2 I don’t know why we are not able to organize fair elections in this part of the world.Why is it that in this part of the world we are not able to organize fair elections?3 I don’t know why they never employ qualified people in this hotel.Why is it that in this hotel they never employ qualified people?4 I don’t know why the system of welfare is still not working properly in this country.Why is it that in this country the system of welfare is still not working properly?5 I don’t know why you always find such an easy answer to all the questionsI ask.Why is it that you always find such an easy answer to all the questions I ask?adj. + though it + be4 Rewrite the sentences using adj. + though it + be.1 My time in the United States was short, but it was interesting.My time in the United States, short though it was, was interesting.2 The scenes of destruction were terrible, but not surprising.The scenes of destruction, terrible though they were, were not surprising.3 The rescue operation cost a lot of money, but it was successful.The rescue operation, costly though it was, was successful.Unit 6 Streets full of heroes2124 The lesson he gave was extremely interesting, but it was soon forgotten. The lesson he gave, interesting though it was, was soon forgotten.5 Mother Teresa may have been old, but she was extremely active.Mother Teresa, old though she may have been, was extremely active.6 His actions may have been unconscious, but they have had very serious consequences.His actions, unconscious though they may have been, have had very serious consequences.collocations5 Complete the sentences with the correct form of suitable expressions from the collocation box. Sometimesmore than one collocation is possible.1 My grandfather died suddenly after a massive heart attack.2 There was a column of smoke in the sky for days after 9/11.3 Eleanor Roosevelt wrote a daily / newspaper column for nearly 30 years.4 The stress began to take a toll on their marriage.5 The final death toll might be much higher than the police at first thought.6 How many newspaper columns have been written about the heroes of the last century?7 Do you have to pay a toll to drive on the motorway?8 Your idea was brilliant – a stroke of genius!9 My hero is my English teacher. He has a genius for helping us understand Shakespeare.10 When she died she left a massive amount of money to charity.6 Translate the paragraphs into Chinese.1 I thought how we firemen were always saying to each other, “I’ll see you at the big one.” Or, “We’ll allmeet at the big one.” I never knew how it started, or when I’d picked up on it myself, but it was part ofour shorthand. Meaning, no matter how big this fire is, there’ll be another one bigger, somewhere downthe road. We’ll make it through this one, and we’ll make it through that one, too. I always said it, at bigfires, and I always heard it back, and here I was, thinking I would never say or hear these words again,because there would never be another fire as big as this. This was the big one we had all talked about,all our lives, and if I hadn’t known this before – just before these chilling moments – this sick, blacknoise now confirmed it. (这段话由许多短句构成，要注意短句间语气的连接。

APPLICATION: Tractors: McCormick (VK37783, VK37784, VK37785, VK37786, VK37787);QTY ITEM # DESCRIPTION LETTERED ITEMSINCLUDED IN KIT1 974463 In-Frame Kit, After U090153J I1 975463 Out-of-Frame Kit, After U090153J O1 976463 Major Kit, After U090153J M1 977463 Premium Kit, After U090153J (979145 Valve Train Kit Included) P6 6 6 6 171498 171499 171367 171366 Sleeve & Piston Assembly Piston Kit (Includes Rings)Cylinder Liner (Finished / 4.1035" OD) (3)Cylinder Liner (Semi-Finished / 4.1055" OD) (4)P M O I6 171512 Piston Ring Set (1-Keystone 1-2.5MM 1-3.5MM)6 6 6 6 271285 271286 271287 271288 STD Rod Bearing, After U090153J (No Tangs) (5) .010 Rod Bearing, After U090153J (No Tangs) (5).020 Rod Bearing, After U090153J (No Tangs) (5).030 Rod Bearing, After U090153J (No Tangs) (5)P M O I1 1 1 1 271311 271312 271313 271314 STD Main Set, wo/Thrust Washers .010 Main Set, wo/Thrust Washers.020 Main Set, wo/Thrust Washers.030 Main Set, wo/Thrust WashersP M O I1 1 1 271119 271125 271126 STD Thrust Washer Set (Offset Lug) .007 Thrust Washer Set (Offset Lug).010 Thrust Washer Set (Offset Lug)P M O I1 1 1 6 6 371356 371357 371358 371191 371188 Head Gasket Set Head GasketValve Cover GasketExhaust Valve Seal (Brown Umbrella Type)Intake Valve Seal (Green Umbrella Type)P M O I1 1 1 1 371369 371363 371365 371182 Lower Gasket Set wo/Seals Timing Cover Gasket (Without Air Compressor)Oil Cooler Gasket Set Pan Gasket, Light Pan P M OI1 1 1 371146 371297 371366 Front Crank Seal (Viton Lip Type) (7) Rear Crank Seal & Housing Assembly Rear Crank Wear SleeveP P M M O O6 6 1 271198 271289 271127 Pin Bushing, Thru U090153J (1.563" Pin/Straight) Pin Bushing, After U090153J (1.563" Pin/Tapered) Cam Bearing (Finished ID) P P MM12 12 12 1 1 771151 771148 771323 771343 771344 Connecting Rod Bolt, Thru U090153J (Rods w/Tang Notch) Connecting Rod Nut, Thru U090153J (Rods w/Tang Notch) Connecting Rod Capscrew, After U090153J (Rods wo/Tang) Head Bolt KitExpansion Plug Kit (17 Plugs)PM(3).010 OS - 171368 (4).020 OS - 171511 (5)Thru U090153J w/Tangs: STD - 271261 / .010 - 271262 / .020 - 271263 / .030 - 271264(6)With Pneumatic Brake (7)Front Wear Sleeve - 301115PK-366-L 4/15/2009APPLICATION: Tractors: McCormick (VK37783, VK37784, VK37785, VK37786, VK37787);QTY ITEM # DESCRIPTION LETTERED ITEMSINCLUDED IN KIT1 979145 Valve Train Kit V1 571214 Camshaft (8)12 571123 Tappet6 471158 Exhaust Valve V6 471155 Intake Valve V6 471279 Exhaust Valve Guide V6 471237 Intake Valve Guide V12 471238 Valve Spring V24 471241 Keeper (Half) V6 471281 Exhaust Seat6 471282 Intake Seat6 471286 LH Rocker Arm (Adj Screw & Lock Nut Not Included) (9)6 471287 RH Rocker Arm (Adj Screw & Lock Nut Not Included) (9)1 471285 Rocker Arm Shaft (10) "Includes 471176 Plugs"1 571196 Cam Gear1 571189 Crank Gear 1 571193 Idler Gear (Includes 571144 Bushings)12 571117 Push Rod1 671171 Oil Pump1 671172 Oil Pump Idler Gear (Includes 571124 Bushing)6 671157 Piston Cooling Oil Jet1 671173 Oil Cooler1 671174 Oil Pressure Relief Valve Asb1 771328 Crankshaft Kit, Thru U090153J (Rod Bearings w/Tang)1 771329 Crankshaft Kit, After U090153J (Rod Bearings wo/Tang)1 771346 Vibration Damper6 771331 Conn Rod (6.5247-6.5260 / Grade F / Red Mark) (11)6 771332 Conn Rod (6.5229-6.5242 / Grade G / Orange Mark) (11)6 771333 Conn Rod (6.5211-6.5224 / Grade H / White Mark) (11) (12)6 771334 Conn Rod (6.5193-6.5206 / Grade J / Green Mark) (11) (13)6 771335 Conn Rod (6.5175-6.5188 / Grade K / Purple Mark) (11) (14)6 771336 Conn Rod (6.5157-6.5170 / Grade L / Blue Mark) (11) (15)1 771345 Cylinder Head Assembly (Includes Valves & Springs)1 871249 Manifold Heater Plug1 871252 Thermostat1 871253 Water Pump (16)1 871251 Block Heater1 871256 Fuel Pump(8)Cam Thrust Washer - 271297 (9)Adjusting Screw-471226 / Lock Nut - 571139 (10)Rocker Arm Shaft Snap Ring - 471228(11)After U090153J (Rod Bearings wo/Tang) For Early Rod w/Tang Notch Use: (12)771351 (13)771352 (14)771353 (15)771354(16)Repair Kit - 871254 PK-366-L 4/15/2009。

10.16638/ki.1671-7988.2019.19.049汽车内饰NVH性能分析及研究张明，冯策，刘伟，李美兴（陕西重型汽车有限公司汽车工程研究院，陕西西安710200）摘要：文章论述了汽车NVH性能的重要性。

并且，从汽车三大噪声振动源出发，分析噪声振动的产生、传播路径及接受等机理。

并在开发设计阶段，制定相应的整车车身NVH目标及内饰车身NVH目标，从而指导汽车内饰NVH性能优化及开发。

文章从内饰声学包装的角度出发，对空气传播路径中噪声进行控制。

并对吸声结构与隔声结构的原理及特点、材质及结构、性能影响因素等进行阐述。

同时，阐述了声学包装的轻量化技术。

并结合实际情况，论述了吸声材料与隔声结构在汽车内饰上的应用。

关键词：NVH；内饰；声学包装；轻量化；吸声结构；隔声结构中图分类号：U467 文献标识码：A 文章编号：1671-7988(2019)19-138-06Analysis and research on NVH performance of automobile interiorZhang Ming, Feng Ce, Liu Wei, Li Meixing( Automobile Engineering Research Institute of Shaanxi Heavy Automobile Co. LTD, Shaanxi Xi'an 710200 )Abstract:The article discusses the importance of NVH performance. Moreover, starting from the three major sources of automobile noise and vibration, the paper analyzes the mechanism of noise and vibration generation, propagation path and acceptance. And in the development and design stage, formulate the corresponding NVH target of the whole vehicle body and the NVH target of the interior, so as to guide the optimization and development of the performance of the automobile interior decoration NVH. From the point of view of interior acoustic packaging, the noise in air propagation path is controlled. The principle and characteristics of sound absorption structure and sound insulation structure, material and structure, performance factors and so on are expounded. Meanwhile, the lightweight technology of acoustic packaging is described. Combined with the actual situation, the application of sound absorbing material and sound insulation structure in automobile interior decoration is discussed.Keywords: NVH; Interior; Acoustic packaging; Lightweight; Sound absorption structure; Sound insulation structure CLC NO.: U467 Document Code: A Article ID: 1671-7988(2019)19-138-06前言随着经济及科技技术的发展，人们对汽车科技性、环保性、安全性及舒适性等要求越来越高。

基于多尺度方法的1∶3共振双Hopf分岔分析王万永;陈丽娟;郭静【摘要】利用改进的多尺度方法对一个电路振子模型1∶3共振附近的动力学行为进行了研究。

应用该方法得到了系统的复振幅方程，进而得到一个振幅与相位解耦的三维实振幅系统，通过分析实振幅方程的平衡点个数及其稳定性，将系统共振点附近的动力学行为进行分类，发现了双稳态等动力学现象，数值模拟验证了理论结果的正确性。

%The dynamical behavior near a 1∶3 resonance of an electric oscillator was investigated. By using the method of multiple scale, the complex amplitude equations of the system were obtained. Then a three dimension real amplitude system in which the amplitudes decouple from the phases was given. Ana-lyzing the number of equilibrium and its stability of the real amplitude equation, the dynamical behavior around the resonant point was classified. Some interesting dynamical phenomenon were found, for exam-ple,the bistability. Numerical simulations for justifying the theoretical analysis were also provided.【期刊名称】《郑州大学学报（理学版）》【年(卷),期】2016(048)003【总页数】5页(P23-27)【关键词】电路振子;1∶3共振;多尺度方法;分岔【作者】王万永;陈丽娟;郭静【作者单位】河南工程学院理学院河南郑州451191;河南工程学院理学院河南郑州451191;郑州铁路职业技术学院公共教学部河南郑州450052【正文语种】中文【中图分类】O175.1在非线性动力学的研究中，内共振由于能够反应系统线性模态之间的相互作用，有着非常重要的研究价值.文献[1]通过研究一个两端固支屈曲梁模型的内共振，构建了该模型在1∶1和1∶3内共振情形下的非线性模态.文献[2]研究了一个悬索模型的1∶2内共振，并讨论了三次非线性和高阶修正项对系统解的影响.文献[3]研究了一个极限环振子系统发生的1∶3共振双Hopf分岔，并研究了非线性对共振附近动力学行为的影响.文献[4]通过利用3∶1内共振的性质设计了一个非线性振动吸振器.文献[5]研究了内共振条件下风力发电机风轮叶片的空气动力学行为.在内共振和双Hopf分岔的研究中，常用的方法有中心流形和规范型方法、多尺度方法、摄动增量法、Liapunov-Schmidt约化和奇异摄动法.这些方法都存在一些问题，例如中心流形方法计算过程复杂，奇异性理论更加数学化，晦涩难懂，而多尺度方法得到的强共振的实振幅方程中，平衡点是非孤立的平衡点[6]，因而使稳定性分析和分岔分析无法进行.在本文的研究中，将应用一种改进的多尺度方法，把1∶3共振的规范型化为一个三维的实振幅系统，进而可以研究系统在共振点附近的动力学行为.本文以一个电路振子模型为例，利用改进的多尺度方法研究其1∶3共振点附近的动力学行为.其电路示意图如图1所示[7].其数学模型为[7]：其中：x1=v1，x2=i1，x3=v2，x4=i2是状态变量；η1=1/C1，η2=R，η3=1/L1，ρ1=1/C2，ρ2=1/L2是参数；α1、α2、α3是辅助参数.非线性电路模型的动力学行为是非线性动力学研究的重要内容之一.目前已有不少的文献从实验和理论方面对其进行了研究[8-12]，并发现了次谐波振荡、周期解、概周期解、分岔以及混沌等大量的非线性现象[11].本文将应用改进的多尺度方法对该电路系统的1∶3共振进行研究，计算其振幅方程并分析共振点附近的动力学行为.系统(1)在其唯一平衡点(0，0，0，0)处的线性化系统为,其特征方程为λ4+(-α1η1+η2ρ2)λ3+(η1η3+η1ρ2-α1η1η2ρ2+ρ1ρ2)λ3+(η1η2η3ρ2-α1η1ρ1ρ2)λ+η1η3ρ1ρ2=0.为了研究该系统1∶3共振点附近的动力学行为，设其特征方程有两对纯虚根λ1,3=±iω1和λ2,4=±iω2，其中ω1∶ω2=1∶3.可以求得当,时，特征方程(2)有两对纯虚根和.为了得到1∶3共振的规范型方程,将应用改进的多尺度方法对系统(1)进行分析.首先按照如下形式摄动参数设，则系统(1)可写为其多尺度形式的解具有如下形式将式(3)、(5)带入式(4),并对式(4)的右端进行Taylor展开,令两端ε的各次幂的系数相等,可得方程(6)的解具有如下形式其中：Aj(j=1,2)是复振幅，为时间尺度T2的函数；p1和p2是相应于特征值iω1和iω2的右特征向量；c.c. 表示前面各项的复共轭.将式(9)代入式(7),可求得式(7)的解为其中zij是复系数.将式(9)、(10)代入式(8),令长期项的系数为零,可得到A1和A2关于时间尺度T2导数的两个方程.应用左特征向量消去D2A1和D2A2的系数并吸收参数ε[13],可得Cijk和Ciμ με是复系数.在式(11)中，A1和A2为复振幅，为了将式(11)转化为实数振幅方程，通常将A1和A2设为极坐标形式.但是，在强共振条件下，如果将A1和A2设为极坐标形式，将会得到一个实振幅与相位变量耦合的三维系统，其平衡点将是非孤立的平衡点，平衡点的稳定性将无法研究.为了避免这种情况，将复振幅A1和A2设为一种混合形式(极坐标-笛卡尔形式)[13]，将式(12)代入式(11),分离其实部和虚部,可得到一个振幅与相位解耦的三维实振幅方程，如下:0.210 018uv2-0.532 248v3+0.080 357 1uη1ε-0.139 382vη1ε-0.21967uη2ε+0.168 86vη2ε+ 0.258 519 u η3ε+1.345 23vη3ε,0.210 018u2v+0.532 248uv2-0.210 018v3+0.139 382uη1ε+0.080 3571vη1ε-0.168 86uη2ε-0.219 67vη2ε-1.345 23uη3ε+0.258 519vη3ε.若设,则相应于原系统的状态变量x的Hopf分岔是振幅变量a1、a2的静态分岔. 由前面的分析可知1∶3共振的振幅方程是由3个变量组成的三维系统，并且含有3个分岔参数.为了分析共振点(η1c，η2c，η3c)附近的动力学行为，可以固定其中一个分岔参数，分析系统在二维参数平面上共振点附近的动力学行为.为此，固定参数η3，在η1-η2平面内对系统的动力学行为进行分类.根据实振幅方程的平衡点个数及每个平衡点稳定性的不同, 将平面η1-η2分为6个不同的区域，如图2所示.在Ⅰ区中，其平凡平衡点E0(0,0)是稳定的平衡点，对应于原系统的原点.当参数进入Ⅱ区，一个稳定的单模态平衡点E1(a10,0)出现，而平凡平衡点E0(0,0)变为不稳定的平衡点.当参数进入Ⅲ区，一个不稳定的平衡点E2(0,a20)出现，而平衡点E1(a10,0)保持其稳定性，平衡点E0(0,0)仍然是不稳定的.在Ⅳ区，一个新的不稳定的双模态平衡点E3(a12,a22)产生，而平衡点E1(a10,0)和E2(0,a20)是稳定的平衡点.在Ⅴ区，双模态平衡点E3(a12,a22)消失，平衡点E1(a10,0)失稳，平衡点E2(0,a20)仍然是稳定的.在Ⅵ区，平衡点E2(0,a20)保持稳定性，平衡点E1(a10,0)消失.其中单模态平衡点E1(a10,0)和E2(0,a20)分别相应于原系统频率为ω1和ω2的周期解，双模态平衡点E3(a12,a22)则相应于原系统的一个概周期解.为了验证理论分析的正确性，对原系统进行数值模拟，模拟的结果如图3～图8所示.可以发现，当参数在共振点附近变化时，系统出现两个不同频率的周期解，其频率比值接近1∶3.同时在分类图的Ⅳ区，两个不同频率的周期解同时出现，系统出现双稳态现象.本文研究了一个电路振子模型中发生的1∶3共振双Hopf分岔，通过应用改进的多尺度方法得到了该1∶3共振的规范型方程，进而分析其共振点附近的动力学行为，发现了周期解、双稳态等动力学现象，并通过数值模拟验证了结果的正确性.本文在揭示电路振子系统动力学现象的同时，应用了一种研究1∶3共振的新方法，该方法通过应用多尺度方法的过程，并将1∶3共振的复振幅设为一种混合形式，可以得到1∶3共振实振幅系统，从而能够研究共振点附近的动力学行为.【相关文献】[1] LACARBONARA W，REGA G，NAYFEH A H．Resonant non-linear normal modes．Part I：analytical treatment for structural one-dimensional systems [J]．Int JNon-linear Mech,2003，38(6)：851-872．[2] LEE C L， PERKINS N C．Nonlinear oscillations of suspended cables containing atwo-to-one internal resonance [J]．Nonlinear Dyn，1992，3(6)：465-490.[3] 王万永，陈丽娟．非线性时滞反馈对共振附近动力学行为的影响 [J]．信阳师范学院学报(自然科学版)，2014，27(1)：15-18．[4] JI J C， ZHANG N．Design of a nonlinear vibration absorber using three-to-one internal resonances [J]．Mech Syst Signal Processing，2014，42(1/2)： 236-246．[5] LI L,LI Y H,LIU Q K,et al. Flap wise non-linear dynamics of wind turbine blades with both external and internal resonances[J]．Int J Non-Linear Mech，2014，61(1)：1-14．[6] LUONGO A，DI EGIDIO A，PAOLONE A．On the proper form of the amplitude modulation equations for resonant systems [J]．Nonlinear Dyn，2002，27(3)：237-254．[7] REVEL G，ALONSO D M，MOIOLA J L．Numerical semi-global analysis of a 1∶2 resonant Hopf-Hopf bifurcation [J]．Physica D-nonlinear phenomena，2012，247(1)：40-53．[8] 徐兴磊，李红．压缩真空态的激发态下介观串并联RLC电路的量子涨落 [J]．郑州大学学报(理学版)，2007，39(1)：67-70．[9] 方天申，董学义．LC串联电路非共振固有振荡与谐波共振的区别 [J]．信阳师范学院学报(自然科学版)，2007，20(4)：429-431．[10] CHUA L O, WU C W, HUANG A, et al．A universal circuit for studying and generating chaos-Ⅱ：Strange attractors[J]. IEEE T Circuits Sys I, 1993, 40(10): 745-761. [11] 张晓芳，陈章耀，毕勤胜．非线性电路系统动力学的研究进展及展望[J]．电路与系统学报，2012，17(5)：124-129．[12] 苏利捷，魏兆博，杨广德．单相逆变器共模电磁干扰特性研究 [J]．郑州大学学报(理学版)，2014，46(4)：57-62．[13] LUONGO A，PAOLONE A，DI EGIDIO A．Multiple timescales analysis for 1∶2 and 1∶3 resonant Hopf bifurcations [J]．Nonlinear dynamics，2003，34(3/4)：269-291．。

Encyclopedia of VibrationBraun, Simon GISBN-13: 9780122270857Table of ContentsAbsorbers, VibrationValder Steffen, Jr, and Domingo Rade, Federal University of Uberlandia, BrazilActive Control of Civil StructuresT T (Larry) Soong, MCEER, SUNY Buffalo, USA, and B F Spencer, Jr, USAActive Control of Vehicle VibrationMehdi Ahmadian, Virginia Polytechnic Institute & State University, USAActive IsolationSteve Griffin, AFRL/VSSV, USA, and Dino Sciulli, Virginia, USAActive Vibration SuppressionDaniel Inman, Virginia Polytechnic Institute & State University, USAActuators and Smart StructuresVictor Giurgiutiu, University of South Carolina, USAAdaptive FiltersStephen J Elliott, University of Southampton, UKAeroelastic ResponseJ E Cooper, University of Manchester, UKAveragingSimon Braun, Technion - Israel Institute of Technology, IsraelBalancingR Bigret, Drancy, FranceBasic PrinciplesGiora Rosenhouse, Technion City, IsraelBeamsRichard A Scott, University of Michigan, USABearing DiagnosticsK McKee and C James Li, Rensselaer Polytechnic Institute, USABearing VibrationsR Bigret, Drancy, FranceBeltsL Zhang and J W Zu, University of Toronto, CanadaBlades and Bladed DisksR Bigret, Drancy, FranceBoundary ConditionsGiora Rosenhouse, Technion City, IsraelBoundary Element MethodsFriedel Hartmann, University of Kassel, GermanyBridgesSingiresu S Rao, University of Miami, USACablesNoel C Perkins, University of Michigan, USACepstrum AnalysisBob Randall, University of New South Wales, AustraliaChaosPhilip J Holmes, Princeton University, USAColumnsIsaac Elishakoff, Florida Atlantic University, USA, and C W Bert, University of Oklahoma, USACommercial SoftwareGuy Robert, Liege, BelgiumComparison of Vibration Properties: Comparison of Spatial PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComparison of Vibration Properties: Comparison of Modal PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComparison of Vibration Properties: Comparison of Response PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComputation for Transient and Impact DynamicsDavid J Benson, University of California, San Diego, USA, and John Hallquist, Livermore Software Technology Corporation (LSTC), USAContinuous MethodsC W Bert, University of Oklahoma, USACorrelation FunctionsSimon Braun, Technion - Israel Institute of Technology, IsraelCrashVictor H Mucino, West Virginia University, USACritical DampingDaniel Inman, Virginia Polytechnic Institute & State University, USADamping in FE ModelsGeorge A Lesieutre, Pennsylvania State University, USADamping MaterialsEric E Ungar, Acentech, Inc, USADamping MeasurementD J Ewins, Imperial College of Science, Technology and Medicine, UKDamping ModelsDaniel Inman, Virginia Polytechnic Institute & State University, USADamping MountsJian-Qiao Sun, University of Delaware, USADamping, ActiveAmr Baz, University of Maryland, USAData AcquisitionBob Randall and M J Tordon, University of New South Wales, AustraliaDiagnostics and Condition Monitoring, Basic ConceptsM Sidahmed, Université de Compiegne, France, and Giorgio Dalpiaz, University of Bologna, Italy Digital FiltersTony Constantinides, Imperial College of Science, Technology and Medicine, UKDiscrete ElementsSingiresu S Rao, University of Miami, USADisksD J Ewins, Imperial College of Science, Technology and Medicine, UKDisplays of Vibration PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaDynamic StabilityA Steindl, Vienna University of Technology, Austria, and Hans Troger, Vienna, Austria Earthquake Excitation and Response of BuildingsFarzad Naeim, John A Martin & Associates, Inc, USAEigenvalue AnalysisOliver Bauchau, Georgia Institute of Technology, USAElectrorheological and Magnetorheological FluidsR Stanway, The University of Sheffield, UKElectrostrictive MaterialsKenji Uchino, Pennsylvania State University, USA, and H S Tzou, University of Kentucky, USA Environmental Testing, ImplementationP S Varoto, Escola de Engenharia de Sao Carlos, USP, BrazilEnvironmental Testing, OverviewDavid Smallwood, Sandia National Laboratories, USAFatigueAlbert Kobayashi and M Ramula, University of Washington, USAFeed Forward Control of VibrationChristopher R Fuller, Virginia Polytechnic Institute & State University, USAFinite Difference MethodsSingiresu S Rao, University of Miami, USAFinite Element MethodsSingiresu S Rao, University of Miami, USAFluid/Structure InteractionSabih Hayek, Pennsylvania State University, USAFlutterJan Wright, University of Manchester, UKFlutter, Active ControlFrank H Gern, Virginia Polytechnic Institute & State University, USAForced ResponseN A J Lieven, Bristol University, UKFriction DampingRaouf Ibrahim, Wayne State University, USAFriction Induced VibrationsRaouf Ibrahim, Wayne State University, USAGear DiagnosticsC James Li, Rensselaer Polytechnic Institute, USAGround Transportation SystemsA K W Ahmed, Concordia University, CanadaHand-transmitted VibrationM Griffin, University of Southampton, UKHelicopter DampingNorman M Wereley, University of Maryland at College Park, USAHilbert TransformsM Feldman, Technion - Israel Institute of Technology, IsraelHybrid ControlKon-Well Wang, Pennsylvania State University, USAHysteretic DampingH T Banks, North Carolina State University, USA and G A Pinter, North Carolina State University, USA Identification, Fourier-based MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelIdentification, Model Based MethodsSpilios D Fassois, University of Patras, GreeceInverse ProblemsY M Ram, Louisiana State University, USAKrylov-Lanczos MethodsRoy Craig, University of Texas, USALaser Based MeasurementsP Castellini, E P Tomasini, and G M Revel, Università di Ancona, ItalyLinear AlgebraCharbel Farhat, University of Colorado, USA, and Daniel Rixen, Delft, BelgiumLinear Damping Matrix MethodsFai Ma, University of California, Berkeley, USALiquid SloshingRaouf Ibrahim, Wayne State University, USALocalizationChristophe Pierre, University of Michigan, USAMagnetostrictive MaterialsAlison Flatau, National Science Foundation, USAMembranesArthur W Leissa, Ohio State University, USAMEMs ApplicationsI Stiharu, Concordia University, CanadaMEMs, Dynamic ResponseI StiharuMEMs, General PropertiesI StiharuModal Analysis, Experimental: Basic PrinciplesD J Ewins, Imperial College of Science, Technology and Medicine, UKModal Analysis, Experimental: Measurement TechniquesJ M Silva, Institute Superior Technico, PortugalModal Analysis, Experimental: Parameter Extraction MethodsN M Maia, Institute Superior Technico, PortugalModal Analysis, Experimental: Construction of Models from TestsN M Maia, Institute Superior Technico, PortugalModal Analysis, Experimental: ApplicationsD J Ewins, Imperial College of Science, Technology and Medicine, UKMode of VibrationD J Ewins, Imperial College of Science, Technology and Medicine, UKModel Updating and ValidatingM Link, Universität Gesamthoschule Kassel, GermanyMotion SicknessM Griffin, University of Southampton, UKNeural Networks, Diagnostic ApplicationsM Zacksenhouse, Technion - Israel Institute of Technology, IsraelNeural Networks, General PrinciplesB Dubuisson, La Croix Saint Ouen, FranceNoise, Noise Radiated from Elementary SourcesMichael Peter Norton and J Pan, University of Western Australia, AustraliaNoise, Noise Radiated by Baffled PlatesMichael Peter Norton and J pan, University of Western Australia, AustraliaNondestructive Testing, SonicScott Doebling and Charles Farrar, Los Alamos National Laboratory, USANondestructive Testing, UltrasonicL W Schmerr Jr, Iowa State University, USANonlinear Normal ModesAlexander Vakakis, University of Illinois, USANonlinear System IdentificationB F Feeny, Michigan State University, USANonlinear System Resonance PhenomenaAnil Bajaj and Charles M Krousgrill, Purdue University, USANonlinear Systems AnalysisAnil Bajaj, Purdue University, USANonlinear Systems, OverviewNoel C Perkins, University of Michigan, USAObject Oriented Programming in FE AnalysisIgor Klapka, Université de Liège, Belgium, Alberto Cardona, INTEC, Argentina, and Philipee Devloo, Universidade Estadual de Campinas, BrazilOptimal FiltersStephen J Elliott, University of Southampton, UKPackagingJorge Marcondes, San Jose University, USAParallel ProcessingDaniel Rixen, Delft, BelgiumParametric ExcitationAlexandra David and Subhash Sinha, Auburn University, USAPerturbation Techniques for Non-linear SystemsSteve Shaw, Michigan State University, USAPiezoelectric MaterialsH S Tzou, University of Kentucky, USA, and M C Natori, Institute of Space & Astronautical Science, JapanPipesSingiresu S Rao, University of Miami, USAPlatesArthur W Leissa, Ohio State University, USARandom ProcessesMikhail F Dimentberg, Worcester Polytechnic Institute, USARandom Vibration, Basic TheoryMikhail F Dimentberg, Worcester Polytechnic Institute, USAResonance and AntiresonanceMircea Rades, University Politechnica of Bucharest, RomaniaRobot VibrationsWayne Book, Georgia Institute of Technology, USARotating Machinery, Essential FeaturesR Bigret, Drancy, FranceRotating Machinery, Model CharacteristicsR Bigret, Drancy, FranceRotating Machinery, MonitoringR Bigret, Drancy, FranceRotor DynamicsR Bigret, Drancy, FranceRotorstator InteractionsR Bigret, Drancy, FranceSeismic Instruments, Environmental FactorsKenneth McConnell, Iowa State University, USASensors and ActuatorsH S Tzou, University of Kentucky, USA, and C S Chou, National Taiwan University, Republic of ChinaShape Memory AlloysM Baz, University of Maryland, USAShellsW Soedel, Purdue University, USAShip VibrationsWilliam S Vorus, University of New Orleans, USAShockJorge Marcondes, San Jose University, USAShock Isoloation SystemsMircea Rades, University Politechnia of Bucharest, RomaniaSignal Generation Models for DiagnosticsGiorgio Dalpiaz, University of Bologna, Italy, and M Sidahmed, Université de Compiegne, FranceSignal Integration and DifferentiationStuart Dyne, University of Southampton, UKSignal Processing, Model Based MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelSpectral Analysis, Classical MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelStandards for Vibrations of Machines and Measurement ProceduresJohn Niemkiewicz, Maintenance and Diagnostic (M&D) LLC, USAStochastic Analysis of Nonlinear SystemsY K Lin and C Q Cai, Florida Atlantic University, USAStochastic SystemsMikhail F Dimentberg, Worcester Polytechnic Institute, USAStructural Dynamic ModificationsA Sestieri, Universita Degli Studi di Roma, Italy, and W D'Amorogio, Universita Be L'Aquila, ItalyStructure-Acoustic Interaction, High FrequenciesA Sestieri, Universita Degli Studi di Roma, ItalyStructure-Acoustic Interaction, Low FrequenciesA Sestieri, Universita Degli Studi di Roma, ItalyTesting, Non-linear SystemsAlan Haddow, Michigan State University, USATheory of Vibration, FundamentalsBingen Yang, University of Southern California, USATheory of Vibration, SuperpositionM G Prasad, Stevens Institute of Technology, USATheory of Vibration, Duhamel's Principle and ConvolutionG Rosenhouse, Technion - Israel Institute of Technology, IsraelTheory of Vibration, Energy MethodsSingiresu S Rao, University of Miami, USATheory of Vibration, Equations of MotionJonathan Wickert, Carnegie Mellon University, USATheory of Vibration, SubstructuringMehmet Sunar, King Fahd University of Petroleum and Minerals, Saudi ArabiaTheory of Vibration, Impulse Response FunctionRakesh Kapania, Virginia Polytechnic Institute & State University, USATheory of Vibration, Variational MethodsSingiresu S Rao, University of Miami, USATime-Frequency MethodsPaul White, University of Southampton, UKTire VibrationsG D Shteinhauz, The Goodyear Tire & Rubber Company, USATool Wear MonitoringM Sidahmed, Université de Compiegne, FranceTransducers for Absolute MotionKenneth McConnell, Iowa State University, USATransducers for Relative MotionKenneth McConnell, Iowa State University, USA, Simon Braun, Technion - Israel Institute of Technology, Israel, and Gene E Maddux, Tipp City, USATransform MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelTransforms, WaveletsPaul White, University of Southampton, UKUltrasonicsM J S Lowe, Imperial College of Science, Technology and Medicine, UKVibration Generated Sound, FundamentalsMichael Peter Norton and S J Drew, University of Western Australia, AustraliaVibration Generated Sound, Radiation by Flexural ElementsMichael Peter Norton and S J Drew, University of Western Australia, AustraliaVibration IntensitySabih Hayek, Pennsylvania State University, USAVibration Isolation, Applications and CriteriaE Rivin, Wayne State University, USAVibration Isolation TheoryE Rivin, Wayne State University, USAVibration TransmissionSabih I Hayek, Pennsylvania State University, USAVibro-impact SystemsF Peterka, Academy of Sciences of the Czech Republic, Czech RepublicViscous DampingFarhan Gandhi, Pennsylvania State University, USAWave Propagation, Waves in an Unbound MediumM J S Lowe, Imperial College of Science, Technology and Medicine, UKWave Propagation, Interaction of Waves with BoundariesM J S Lowe, Imperial College of Science, Technology and Medicine, UKWave Propagation, Guided Waves in StructuresM J S Lowe, Imperial College of Science, Technology and Medicine, UKWhole-body VibrationM Griffin, University of Southampton, UKWind-Induced VibrationsAhsan Kareem, University of Notre Dame, USAWindowsSimon Braun, Technion - Israel Institute of Technology, Israel。

第 50 卷第 2 期2024 年 4 月Vol. 50 No. 2Apr. 2024航空发动机Aeroengine航空发动机振动环境谱统计归纳方法及振动试验台复现房剑锋（中国飞行试验研究院，西安 710089）摘要：为满足航空发动机及机载产品研制过程贴近使用环境的振动考核试验需求，需根据发动机实测振动数据给出振动考核试验所需的输入谱图。

依据GJB/Z 126-99中给出的环境测量数据归纳方法，建立了发动机实测振动环境谱统计归纳方法并通过程序实现。

利用发动机多架次实测试飞振动数据统计归纳得到发动机测点位置的振动实测谱。

基于能量等效及信号频域特征分布一致原则，将归纳得到的实测谱转化为可用于振动台输入的振动环境谱，并在振动台上进行了振动信号的复现试验。

结果表明：振动台输出信号与发动机实测振动信号频域分布特征一致，在统计频率带宽范围内振动总量最大相差5.7%，证明了转化方法是合理的，为航空发动机机载设备贴近使用环境的振动考核试验方法提供了真实的输入谱图。

关键词：振动数据；统计归纳；环境谱；振动试验台；复现；航空发动机中图分类号：V216.2+1；V231.92文献标识码：A doi：10.13477/ki.aeroengine.2024.02.022 Aeroengine Vibration Environment Spectrum Statistical Induction and Reproductionon Vibration Testing TableFANG Jian-feng（Chinese Flight Test Establishment，Xi’an 710089，China）Abstract：To meet the requirements of conducting vibration assessment tests under conditions close to the operating environment for the development of aeroengine and airborne products, it is necessary to provide the input spectrum required for the vibration assessment test based on the measured engine vibration data. Based on the induction method of environment measurement data provided in GJB/Z 126-99, a statistical induction method for vibration environment spectra measured engine vibration data was established and implemented through a program. The measured vibration spectra at engine measuring positions were obtained by statistical induction according to vibra⁃tion data from multiple actual test flights. Based on the principle of energy equivalence and consistent distribution of signal frequency domain characteristics, the spectra obtained using the induction method were converted into vibration environment spectra which can be used as the input for the vibration testing tables, and experiments for vibration signal reproduction were conducted on vibration testing tables. The results show that the frequency domain distribution characteristics of the output signal of the vibration testing table are consistent with that of the measured engine vibration signal. The maximum difference in the overall vibration within the statistical frequency bandwidth is 5.7%, which proves the rationality of the conversion method and the capability of providing real input spectra for vibration assessment tests of aeroengine airborne equipment under conditions close to the service environment.Key words：vibration data; statistical induction; environment spectrum; vibration testing table; reproduction; aeroengine0　引言在航空发动机试飞过程中振动信号的测量具有重要意义，一方面可用于发动机整机振动特性的确定，定位发动机整机振动故障[1]，70%以上的故障都以振动的形式表现出来；另一方面可通过试飞测试数据获取发动机的整机振动环境，为机载设备振动考核试验提供真实的试飞数据谱图。

VOLVO PENTA GENSET ENGINE TAD1641GE473kW (643 hp) at 1500 rpm, 546 kW (743 hp) at 1800 rpm, acc. to ISO 3046 The TAD1641GE is a powerful, reliableand economical Generating Set DieselEngine built on the dependable in-line sixdesign.Durability & low noiseDesigned for easiest, fastest and mosteconomical installation. Well-balancedto produce smooth and vibration-freeoperation with low noise level.To maintain a controlled working tem-perature in cylinders and combustionchambers, the engine is equipped withpiston cooling. The engine is also fittedwith replaceable cylinder liners and valveseats/guides to ensure maximum dura-bility and service life of the engine.Low exhaust emissionThe state of the art, high-tech injectionand charging system with low internallosses contributes to excellent combus-tion and low fuel consumption.The TAD1641GE complies with EUStage 2 exhaust emission regulations.Easy service & maintenanceEasily accessible service and mainte-nance points contribute to the ease ofservice of the engine.Technical descriptionEngine and block– Optimized cast iron cylinder block with opti-mum distribution of forces without the blockbeing unnecessary heavy.– Wet, replaceable cylinder liners– Piston cooling for low thermal load on pis-tons and reduced ring temperature– Tapered connecting rods to reduce risk of piston cracking– Crankshaft induction hardened bearing surfaces and fillets with seven main bear-ings for moderate load on main and big-end bearings– Nitrocarburized transmission gears for heavy duty operation– Keystone top compression rings for long service life– Viscous type crankshaft vibration damper– Replaceable valve guides and valve seats– Over head camshaft and four valves per cylinder equipped with camshaft damper to reduce noise and vibrations. Lubrication system– Full flow oil cooler– Full flow disposable spin-on oil filters, for extra high filtration– The lubricating oil level can be measured during operation (Standard dipstick only)– Gear type lubricating oil pump, gear driven by the transmission Fuel system– Self de-aerating system. When replacingfilters all fuel stays in the engine.– Non-return fuel valve– Electronic unit injectors– Fuel prefilter with water separator and wa-ter-in-fuel indicator / alarm– Gear driven low-pressure fuel pump– Fine fuel filter with manual feed pump andfuel pressure switch– Fuel shut-off valve, electrically operatedCooling system– Efficient cooling with accurate coolant con-trol through a water distribution duct in thecylinder block. Reliable sleeve thermostatwith minimum pressure drop– Belt driven, maintenance-free coolant pumpwith high degree of efficiency– Coolant filter as standardTurbo charger– Efficient and reliable turbo charger– Extra oil filter for the turbo chargerElectrical system– Engine Management System 2 (EMS 2), anelectronically controlled processing systemwhich optimizes engine performance. It alsoincludes advanced facilities for diagnosticsand fault tracing– The instruments and controls connect to theengine via the CAN SAE J1939 interface,either through the Control Interface Unit(CIU) or the Digital Control Unit (DCU). TheCIU converts the digital CAN bus signal toan anolog signal, making it possible to con-nect a variety of instruments. The DCU is acontrol panel with display, engine control,monitoring, alarm, parameter setting and di-agnostic functions. The DCU also presentserror codes in clear text.– Sensors for oil pressure, oil temp, boostpressure, boost temp, coolant temp, fueltemp, water in fuel, fuel pressure and twospeed sensors. Crank case pressure, pistoncooling pressure, oil level and air filter pres-sure drop sensors.– Alternator 24V / 80AFeatures– Maintained performance, air temp 40°C– Tropical cooling system (55°C)– Fully electronic with Volvo Penta EMS 2– Dual frequency switch (between 1500 rpm and 1800 rpm)– High power density– Emission compliant– Low noise levels–Gen Pac configurationPower StandardsThe engine performance corresponds to ISO 3046, BS5514 and DIN 6271. The technical data applies to an engine without cooling fan and operating on a fuel with calorific value of 42.7 MJ /kg (18360 BTU/lb) and a density of 0.84 kg/liter (7.01 lb/US gal), also where this involves a deviation from the standards. Power output guaranteed within 0 to +2% att rated ambient conditions at delivery. Ratings are based on ISO 8528. Engine speed governing in accordance with ISO 3046/IV, class A1 and ISO 8528-5 class G3Exhaust emissionsThe engine complies with EU stage 2 emission legislation according to the Non Road Directive EU 97/68/EEC. The engine also complies with TA-luft -50% exhaust emission regulations.Rating GuidelinesPRIME POWER rating corresponds to ISO Standard Power for continuous operation. It is applicable for supplying electrical power at variable load for an unlimited number of hours instead of com-mercially purchased power. A10 % overload capability for govering purpose is available for this rating.MAXIMUM STANDBY POWER rating corresponds to ISOStandard Fuel Stop Power. It is applicable for supplying standby electrical power at variable load in areas with well established electrical networks in the event of normal utility power failure. No overload capability is available for this rating.1 hp = 1 kW x 1.36InformationFor more technical data and information, please look in the Gener-ating Set Engines Sales Guide.TAD1641GEAB Volvo PentaSE-405 08 Göteborg, SwedenTechnical DataGeneralEngine designation ........................................................................TAD1641GE No. of cylinders and configuration .......................................................in-line 6Method of operation ...............................................................................4-stroke Bore, mm (in.) .....................................................................................144 (5.67)Stroke, mm (in.) ..................................................................................165 (6.50)Displacement, l (in³) ....................................................................16.12 (983.7)Compression ratio .....................................................................................16.5:1Dry weight, kg (lb) ..........................................................................1480 (3263)Dry weight with Gen Pac, kg (lb) ...............................................1910 (4211)Wet weight, kg (lb) ........................................................................1550 (3417)Wet weight with Gen Pac, kg (lb) ..............................................2020 (4453)Performance1500 rpm 1800 rpm with fan, kW (hp) at: Prime Power430 (585) 485 (660)Max Standby Power473 (643)546 (743)Lubrication system 1500 rpm 1800 rpm Oil consumption, liter/h (US gal/h) at:Prime Power 0.10 (0.026) 0.11 (0.029)Max Standby Power 0.10 (0.026) 0.12 (0.032)Oil system capacity incl filters, liter ................................................................42Fuel system1500 rpm 1800 rpm Specific fuel consumption at:Prime Power, g/kWh (lb/hph) 25 % 223 (0.361) 232 (0.376)50 % 201 (0.326) 202 (0.327)75 % 196 (0.318) 197 (0.319) 100 %198 (0.321) 200 (0.324)Max Standby Power, g/kWh (lb/hph) 25 % 218 (0.353) 228 (0.370)50 % 199 (0.323) 201 (0.326)75 % 195 (0.316) 197 (0.319)100 %198 (0.321)205 (0.332)Intake and exhaust system 1500 rpm 1800 rpm Air consumption, m³/min (cfm) at: Prime Power 32 (1130) 42 (1483)Max Standby Power 35 (1236) 45 (1589)Max allowable air intake restriction,kPa (In wc) 5 (20.1) 5 (20.1)Heat rejection to exhaust, kW (BTU/min) at: Prime Power 326 (18539) 373 (21212)Max Standby Power 356 (20245) 442 (25136)Exhaust gas temperature after turbine, °C (°F) at: Prime Power 475 (887) 435 (815)Max Standby Power 490 (914) 470 (878)Max allowable back-pressure in exhaust line,kPa (In wc) 10 (40.2) 10 (40.2)Exhaust gas flow, m³/min (cfm) at:Prime power 79.0 (2790) 97.0 (3426)Max Standby Power 84.9 (2998) 106.6 (3765)Cooling system 1500 rpm 1800 rpm Heat rejection radiation from engine,kW (BTU/min) at:Prime Power 30 (1706) 32 (1820)Max Standby Power 34 (1934) 33 (1877)Heat rejection to coolant kW (BTU/min) at:Prime Power 172 (9781) 185 (10521)Max Standby Power 176 (10009) 199 (11317)Fan power consumption, kW (hp) 11 (15)19 (26)Standard equipmentEngineGen PacEngineAutomatic belt tensioner • •Lift eyelets • •FlywheelFlywheel housing with conn. acc. to SAE 1 • •Flywheel for 14” flex. plate and flexible coupling • •Vibration dampers • •Engine suspension Fixed front suspension • •Lubrication system Oil dipstick• •Full-flow oil filter of spin-on type • •By-pass oil filter of spin-on type • •Oil cooler, side mounted • •Low noise oil sump • •Fuel systemFuel filters of disposable type • •Electronic unit injectors• •Pre-filter with water separator • •Intake and exhaust systemAir filter with replaceable paper insert • •Air restriction indicator• •Air cooled exhaust manifold• •Connecting flange for exhaust pipe • •Exhaust flange with v-clamp • •Turbo charger, low right side • •Cooling systemTropical radiator incl intercooler •¹) •Belt driven coolant pump • •Fan hub • •Thrust fan •¹) •Fan guard − •Belt guard−•Control systemEngine Management System (EMS) with CAN-bus interface SAE J1939 ••CIU, Control Interface Unit – –AlternatorAlternator 80A / 24V • •Starting systemStarter motor, 7.0kW, 24V• •Connection facility for extra starter motor • •Instruments and sendersTemp.- and oil pressure for automatic ••stop/alarm 103°C Other equipmentExpandable base frame − •Engine Packing Plastic wrapping••1)must be ordered, se order specification − optional equipment or not applicable • included in standard specificationNote! Not all models, standard equipment and accessories are available in all countries. All specifications are subject to change without notice.The engine illustrated may not be entirely identical to production standard engines.E n g l i s h 12-2006. © 2006 A B V o l v o P e n taA* = 1587 mm / 62.5 in B* = 1120 mm / 44.1 in C* = 1976 mm / 77.8 inD = 2296 mm / 90.5 in (During transport)D = Max 3311 mm / 130.5 in* Including radiator and intercooler。

收稿日期：2016-01-03基金项目：国家自然科学基金资助项目（11304130，11365010，61565007）；江西省教育厅资助项目（GJJ150685）；江西省科技厅资助项目（20151BAB212002）；江西理工大学清江青年英才支持计划资助作者简介：刘超飞（1981-），男，博士，副教授，主要从事玻色爱因斯坦凝聚等方面的研究，E-mail:liuchaofei0809@.江西理工大学学报ＪｏｕｒｎａｌｏｆＪｉａｎｇｘｉＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ第37卷第5期2016年10月Vol.37,No.5Oct.20160引言在原子凝聚体中，原子间的排斥相互作用导致了许多有趣的非线性现象，一个最典型的例子就是暗孤子的形成[1-8].实验上，通过相印记[1-2]和扰动原子密度[3]方法，暗孤波已在稀释玻色-爱因斯坦凝聚体中产生.在相印记方法中，凝聚体的一个部分被远失谐激光束短时间照射，使它获得了相移，但没有产生重大的密度扰动.根据相映射实验，将出现一个暗孤立波，以及作为副产品的声波.在随后阶段的相映射实验中，由于其固有的不稳定性和横向激发[4]，人们观察到暗孤波退化为涡旋环.另一项实验涉及到通过慢光技术从凝聚体中突然清除一个盘状区域，它将产生暗孤波（暗孤波也将蜕化成涡旋环）和相反传播的声波[3].暗孤子的大小接文章编号：2095-3046（2016）05-0102-10DOI:10.13265/ki.jxlgdxxb.2016.05.016玻色爱因斯坦凝聚体中暗孤子动力学研究刘超飞a ，潘小青a ，张赣源b（江西理工大学，a.理学院；b.应用科学院，江西赣州341000）摘要：文章从侦测暗孤子能量的角度，全面介绍了玻色爱因斯坦凝聚体中暗孤子发生声波辐射以及与声波相互作用的动力学行为.虽然暗孤子-声波相互作用导致暗孤子能量变化，暗孤子在简谐势阱中，以及简谐势阱受到扰动时，都具有类似粒子运动的动力学行为.考虑Rabi 耦合时，暗孤子还可以转化为稳定传播的矢量暗孤子.文章对玻色爱因斯坦凝聚体中暗孤子动力学研究的进行全面总结，将加深人们对暗孤子现象的认识.此外，类似暗孤子-声波相互作用的行为，也将出现在其他孤子动力学研究中.关键词：玻色爱因斯坦凝聚；暗孤子；声波；孤子声波相互作用；简谐势阱中图分类号：O469文献标志码：AKinetic study of dark soliton in Bose-Einstein condensateLIU Chaofei a ,PAN Xiaoqing a ,ZHANG Ganyuan b(a.Faculty of Science;b.Faculty of Applied Science,Jiangxi University of Science and Technology,Ganzhou 341000,China)Abstract ：By exploring the energy of dark soliton,this paper systematically introduces the dynamical behavior of sound-emission of dark soliton and dark soliton-sound interaction in Bose-Einstein condensate.Although the dark soliton-sound interaction leads to the change of the dark soliton ′s energy,dark soliton displays the particle-like behavior very well in the harmonic potential and even in the periodic perturbed harmonic trap.Under the Rabi coupling,dark soliton can transfer into the vector dark soliton,which propagates stably in the condensates.This paper provides a full overview of the kinetic study of dark soliton,and it will greatly increase people ′s knowledge about the dark soliton.Furthermore,similar behaviors of the dark soliton-sound interaction will occur in the dynamical investigation of other soliton.Key words ：Bose-Einstein condensate;dark soliton;sound waves;soliton-sound interaction;harmonic trap刘超飞，等：玻色爱因斯坦凝聚体中暗孤子动力学研究近当前成像技术的极限.在这些实验中，通过一再释放势阱中的凝聚体，让其膨胀，然后采取一个光学吸收图像来实现成像.产生暗孤子的更先进的方法也已经提出[9-10]，包括合并相映射和密度工程方法[5-6].暗孤子也可用两个凝聚碰撞产生[11]，以及用凝聚体的布拉格光学晶格反映[12-13]产生.迄今为止，在几何形状上，暗孤子的实验可以从球对称[4]到高度拉长的情况（长宽比大于30[2]）.这些系统在性质上仍然是三维，致使暗孤子容易由于横向不稳定性而被破坏，从而迅速衰变为涡旋.这是个关键因素，它限制了观察到的孤子寿命，其值约为数十毫秒.然而，最近的实验发现，在准一维凝聚体中，暗孤波将是亚稳的，其寿命可大大延长到直至数秒[14].理论上，根据零温平均场理论，稀释原子形成的玻色爱因斯坦凝聚体可由Gross-Pitaevskii方程描述，它是一个很好的非线性系统.在外势场为零时，Gross-Pitaevskii方程支持暗孤子解.与光学系统的一个重要的区别是，势阱能导致凝聚体有不均匀的背景密度.对于凝聚体中的暗孤波，其性质与光学系统中的暗孤波类似.三维暗孤波由于横向激发，是不稳定的，因此，暗孤子容易衰变弯曲形成涡旋.在实验中，可将凝聚体在横向高度压缩，从而构成所谓的一维体系，而暗孤子的运动则由不均匀的纵向密度控制.总的说来，暗孤子是一个局部的密度缺陷，就像一个凹槽，其周围充满凝聚体.并且，暗孤子的两边存在位相差，它是散焦的色散效应与聚焦的非线性相互作用之间达到平衡的结果.因此，暗孤子的主要特性之一，是能在传播中保持其局域化的形状不变[11,15-17].通常，研究孤子的文章主要是给出新的孤子解，或者探索孤子的不稳定性等.在这篇文章中，系统性的介绍玻色爱因斯坦凝聚体中暗孤子动力学研究.与大多数论文不同，本文的研究重点是暗孤子能量的计算和动力学演化中的能量侦测.暗孤子受到外界环境的干扰后，发生声波辐射，暗孤子能量降低，速度变快，同时，外界的声波又能反作用于暗孤子，使其能量增加.这种研究暗孤子的方式，最初在文献[18-19]上介绍.实际上，这种研究思路完全可以推广到其他孤子解的动力学研究上.1暗孤子的数值解凝聚体背景密度均匀，且为.则含有速度为和位置在的暗孤子的一维的形式的凝聚体的波函数为：ψs（z，t）=n姨exp（-iμ攸t）·i v+1-v2姨tanh[1-v2姨（z-vt）姨姨]（1）这里ξ＝攸n gm姨为凝聚体的愈合长度，它可用来刻画暗孤子的尺度.暗孤子的速度依赖于密度n d和通过其中心的相移S.并且，v/c=1-（n d/n）姨= cos（S/2），孤子速度的最大值由Bogoliubov声速度/ C=ng/m姨决定.这里有两个极限情况：①固定暗孤子完全是黑色的，即有一个零密度节点，以及π相滑移；②孤子速度为c时，无相滑移，也与背景的密度无差异，因此难以分辨.图1展示了各种速度暗孤子的密度和相位.一个重要特点是，固定孤子的能量最高，在v=c时，孤子能量基本上为零，这导致人们认为孤子具有负有效质量的设想.由于不会耗散，孤子往往类似于粒子.事实上，对于一阶弱作用力，暗孤子就像一个有效质量为负的经典粒子[11,20-22].这意味着，例如，在一个谐势阱的凝聚体中，暗孤子将趋于来回震荡.S图1各种速度暗弧子密度和相位（b）暗孤子的相位Sπ/20.0-π/2-505z/ξv/c=0v/c=0.25v/c=0.50v/c=0.751.00.50.0-505z/ξ（a）暗孤子的密度nn/nv/c=0v/c=0.25v/c=0.50v/c=0.75第３７卷第５期103与纵向均匀系统（如非线性光学纤维）不同，原子凝聚体沿孤子的运动方向有束缚.例如，暗孤子在谐势阱束缚下的凝聚体中，将趋于在势阱中来回震荡.由于这一空间束缚，孤子一般会与其他激发共同存在，例如声波.因此，文中说的孤子并非纯数学意义中的孤子，而是指一个空间区域（即“孤子地区”），该区域存在密度凹陷和相位差，以及其他可能的激发.这可以粗略地视为一个受到扰动的孤子[23].2暗孤子的能量在无限大体系中，重整化的一维暗孤子能量（即除去背景流体的贡献部分）由式（2）给出，E s ol ＝4攸n 3/21-vc23/2（2）然而，在非均匀凝聚体中，只有当暗孤子在密度局部均匀区域，该方程式才有效.这将在后面的文章中进一步加以说明.还有一种得出一维暗孤子能量方法，它基于对Gross-Pitaevskii 方程的数值积分，即使在密度不均匀时仍然有效，ε（ψ）=攸22m荦ψ2+V ψ2+12g ψ4（3）暗孤子能量E s 是通过对孤子位置Z s 积分一个距离z ints ，然后减去对应的时间独立性背景密度n TI 的贡献，即E s =Z s +z intsZ s -z ints乙ε（ψ）d z -Z s +z intsZ s -z ints乙ε（n TI 姨）d z （4）“孤子区域”必须足够大，以包含暗孤子能量的绝大部分.实际上，暗孤子的速度和背景密度都影响暗孤子密度凹陷处的宽度.图2说明了积分后的各种速度的孤子能量（实线），分别与该区域的大小和背景密度的函数关系.当z ints >5ξ时，积分得到的能量值几乎与从公式（4）（虚线）渐近预测的数值完全相等，所以我们选择“孤子区域”为（Z s ±5ξ）.在时间依赖性模拟中，“孤子区域”能含有声波.通常，很难能区分孤子能和声波能，但后者的数值，在孤子的速度不是很大时，是非常小的.3简谐势阱中的暗孤子假设凝聚体在一维谐势阱中，现在考虑暗孤子在凝聚体中的动力学行为，简谐势阱为：V （z ）=12ω2z z 2（5）这种势阱通常是由磁场形成.系统在空间上是有限的，这是体系的一个重要特点.因此，凝聚体的大小可用托马斯-费米半径刻画.对于一个束缚频率为ωz 的势阱，托马斯-费米密度分布是一个倒抛物线型，其中n TF =（1-ω2z z 2/2），托马斯-费米半径为R TF =2/ω2z 姨.图3（a ）展示了一个速度为v =0.5c 的暗孤子在势阱中，其初始位置为z=0，凝聚体的密度峰值为n 0，纵向束缚频率为ωz =2姨×10-2（μ/攸）.实际上，除了在边界附近由于小动能贡献导致‘尾巴’状热云外，托马斯-费米密度分布与真实实验状况吻合得很好（图3（a ））.因此，凝聚体的实际大小刚好大于托马斯-费米半径100ξ.在该系统中原子密度的时间演化由图3（b ）显示，其纵坐标为位置，横坐标为时间.暗孤子是一个局部的密度极小.它在向势阱壁移动过程中减速，当其密度极小处触及零密度时，孤子的运动方向改变.众所周知，当孤子远离势阱中心时，其相滑移增加，并在最大振幅处达到π.随后，孤子改变其运动方向，孤子的相滑移变到-π.图2通过积分得到的暗孤子能量E s与积分区间宽度z int 的函数关系1.51.00.50.0012345（a ）固定背景密度n 0时z int /ξv =0.5cv =0.75cv =0.25cv =0c E s /μ（b ）固定孤子速度v =0.5c 时1.00.80.60.40.20.0012345n =n 0n =0.8n 0n =0.6n 0n =0.4n 0n =0.2n 0z int/ξE s /μ江西理工大学学报2016年10月104在谐势阱中的暗孤子，其振荡频率近似为ωz /2姨[14,15,24-28].这是由分析托马斯-费米密度分布得到的，并且人们已用数值模拟证实了这一结论.在图3（b ）中，孤子振荡周期约为T s =630（ξ/c ），而势阱的周期约为T z =444（ξ/c ），这与理论预测结果相同.孤子的运动扰动背景流体，致使流体振荡，其幅度约为2%n 0.可以用下式定义背景凝聚体的偶极振荡，D =乙z ψ（z ）2d z（6）凝聚体的偶极运动D 和孤子路径Z s 由图3（c ）给出.暗孤子的振荡频率为ωz /2姨（实线），它诱发了势阱中背景流体的偶极振荡（虚线），其频率ωz 为[27].在一定程度上，孤子行为就像搅拌器，搅拌着流体.暗孤子将在势阱中加速，孤子由于辐射声波而衰减.在这种情况下，暗孤子的深度将变浅，而其速度将变快，从而更进一步逼近势阱壁，并导致了与反阻尼类似的现象.这与阻尼谐振子相比，结果正好相反.对于阻尼谐振子，其振荡幅度随时间减小.但是，简谐势阱中看不到任何的孤子震荡幅度的净变化，因此，不能推断出孤子的衰变.在图4（a ）中仅仅观察到的孤子振幅的小周期调制，例如，围绕其平均幅度，大约有1％的最大调制幅度变化.类似的结果也出现在了孤子能量的进化中，如图4（b ）所示.孤子能量的平均值保持不变，但有振荡调制.3.1速度对暗孤子运动的影响图5（a ）显示了不同初始速度的暗孤子在一个固定的简谐势阱中的演化路径.增加孤子的速度，其主要结果是孤子振幅增加.但即使孤子速度高达0.7c ，孤子的振荡频率仍保持在预期值ωs =ωz /2姨的周围.但对于运动速度非常快的孤子，如v =0.9c ，如图5（c ）中（点虚线），我们看到其值略有偏差，它趋向于数值更高的振荡频率.这很可能是因为这个快速运动的浅孤子进入了凝聚体的边界造成.在边界处，凝聚体的密度偏离于托马斯-费米密度分布.相比之下，较慢的孤子的振荡束缚在势阱中心，而势阱中心的密度分布几乎与托马斯-费米密度分布相同.对于托马斯-费米密度分布，在简谐势阱中的暗孤子的振荡幅度与孤子的初始速度成正比.为比较各种速度的中心孤子，我们可以使用这一关系，重整化孤子的位置.图5（b ）显示了孤子位置的重整化图.各速度下的重整化位置随孤子速度的增加而幅度增大.对于不同速度的孤子的能量的振荡演化，这种效应也被观察到，如图5（c ）所示.对于快速运动的孤子（例如，v =0.9c ）（点虚线），其能量调制延伸到了最初能量的0.4倍.1.00.50.0-1001001.00.50.0z /ξn /n 0V /μ（a ）凝聚体在简谐势阱中的密度（左轴，实线），其中ωz =2姨×10-2（μ/攸）（右轴，虚线）.速度为v =0.5c 的暗孤子在势阱中心.图4简谐势阱中暗孤子振幅与能量关系E s /μ0.860.850.845000100001500020000t /（ξ·c -1）（b ）暗孤子能量E s 的演化100-100z /ξ（b ）凝聚体随时间演化的重整化图500-50500-505001000150020002500t /（ξ·c -1）（c ）暗孤子位置Z s （实线，左轴）和凝聚体的偶极运动D （虚线，右轴）图3简谐势阱中的暗孤子运动z s /ξD /ξ2n 05001000150020002500t /（ξ·c -1）5150z S/ξ（a ）暗孤子离开势阱中心的距离Z s5000100001500020000t /（ξ·c -1）刘超飞，等：玻色爱因斯坦凝聚体中暗孤子动力学研究第３７卷第５期105刚才我们已经看到，这些小的位置和能量调制，由振荡孤子对背景流体的干扰产生，随后反馈到孤子上.孤子速度越快，有效质量越小，所以背景流体的振荡将会对它们有更大的反馈作用，从而引起更大的调制.3.2束缚势阱强度对暗孤子行为的影响增加势阱的纵向强度，同时保持凝聚体密度峰值固定，这将减少凝聚体的空间范围.对于固定速度的孤子，振荡振幅的绝对值下降，但仍然与托马斯-费米半径形成一个近似的常数比值.图6（a ）显示了各种强度的简谐势阱中，暗孤子位置的变化，其位置已根据托马斯-费米半径重新标度，而时间单位也调整为ω-1z .对于较低的势阱频率，例如，ωz =2姨×10-2（μ/攸）（黑色实线），暗孤子的振荡频率即为其分析预测值ωz /2姨.而对于较高频率的势阱，例如，ωz =62姨×10-2（μ/攸）（点虚线），暗孤子的振荡频率比预测值大.图6（c ）给出了各种初始速度的孤子的振荡频率与势阱频率的函数.对于弱势阱有ωs /ωz ≈2姨，分析值与预测值吻合（虚线）.然而，增加势阱的强度，ωs /ωz 的比值偏离预测值，并随势阱强度的增加而单调增加.这种偏差是不可忽略的，在这里的势阱频率范围里，这个值可高达10％.造成此偏差的原因，是因为对孤子频率的分析预测值，假定了凝聚体为托马斯-费米密度分布.在我们的数值方法里，其密度峰值保持固定，这一假定仅对弱的简谐势阱有效（大量的粒子）.图6（d ）显示了整个凝聚体在各种势频率中的轴向密度分布.随着势阱频率的增加，密度越来越背离倒抛物线型的托马斯-费米密度分布.这偏差在凝聚体的边界处最为明显.甚至可以看到"尾巴"状的低密度伸展通过托马斯-费米半径.为了突出这种偏差，文章还在同一图中绘制了实际密度与托马斯-费米密度分布的差值.文章认为，这一偏差可以解释暗孤子的振荡频率与势阱频率的变化有关.当势阱强度增加时，暗孤子位置（图6（a ））和能量（图6（b ））的调制，由于暗孤子与偶极振荡相互作用的增大而增加.在这里，凝聚体的尺度减小，从而其有效质量降低，而孤子基本保持相同的大小.因此，振荡暗孤子诱发背景凝聚体相对更大的扰动，从而导致孤子的动力学调制更大.4在周期性扰动势阱中的暗孤子通常，人们假设凝聚体在静态简谐势阱中，势阱为V har （x ）=m ω2x 2/2，ω是势阱的频率.在这里，我（c ）孤子能量的演化，该结果经过了由最初的孤子能量E inits 的重整10002000300040005000t /（ξ·c -1）图5不同速度暗孤子在简谐势阱中位置与能量演化1.00.80.60.4E s /E s i n t10610410210098z S /v s /ξ（b ）暗孤子在势阱中的距离（用孤子速度重整后的结果）10002000300040005000t /（ξ·c -1）100500-50-100z s /ξ（a ）暗孤子在无限深简谐势阱（ωz =2姨×10-2（μ/攸））中位置的演化.其中初始速度v /c =0.1（实线），0.5（虚线），0.7（点线）和0.9（点虚线）10002000300040005000t /（ξ·c -1）江西理工大学学报2016年10月106们考虑整个势阱存在扰动，这种势阱可写为V Ext （x ，t ）=m ω2[x +h sin （ωd t ）]2（7）h 和ωd 分别是扰动的幅度和频率[29].我们用数值模拟对以上模型进行研究.图7显示了在各种振幅的扰动下，孤子能量的演变.显然，孤子的运动方向与扰动的运动方向的耦合决定了孤子的演化.在没有扰动的情况下（h =0），该模型将退化为孤子在简谐势阱中的振荡试验.在这种情况下，孤子在背景密度不均匀的凝聚体中传播，其外形变得不对称，同时它还会向相反方向辐射声波[18].众所周知，在简谐势阱中的孤子的振动频率为ωsol =ω/2姨，孤子会发射和重新接收声波.总体而言，孤子不断受到孤子自身带来的流体的扰动，但并不会衰退.当势阱的运动方向与孤子的运动方向相反时（h >0），孤子往往首先获得能量直至达到峰值，然后孤子能量减小到原来的值.这种能量的增益损失周期性的重复.能量变化的周期为1516ξ/c .因此在大量的时间里孤子能量比其初始值大.增加扰动幅度，可以提高孤子在其能量循环中获得和失去能量的能力.相反，当势阱与孤子的移动方向相同时（h <0），孤子往往首先失去能量直至最低值，然后它重新获得能量，恢复其原始值.这个过程构成一个损失获得循环，其周期为1516ξ/c .同样，增加扰动的幅度，孤子失去更多的能量，然后恢复至初始值.因此在大量的时间里孤子能量比其初始值小.实际上，图7比较了在受周期性扰动和不受周期性扰动的简谐势阱中，暗孤子的演变.图8显示了在各种振幅的扰动下，相应的暗孤子的位置的演变.一般来说，凝聚体会伴随势阱运动.由于势阱的振幅和振荡频率都非常小，势阱振荡导致孤子的轨道与没有受扰动的情况（h =0）发生偏离.孤子振荡周期出现波动.整体而言，孤子的振荡频率仍然围绕着ωsol =ω/2姨.因此，这一特征也确保了势阱移动的方向与孤子移动方向的耦合.当势阱与孤子有相同的运动方向时，凝聚体伴随势阱运动.因此，孤子被携带着运动，它偏离振荡中心更远.从而使孤子能量往往比原来的值小（见图8）.但是，当势阱运动与孤子运动方向相反时，凝聚体的运动相对地减小了孤子的震荡幅度，孤子能量出现增益-损失循环.一般来说，如果势阱扰动频率等于天然粒子的振荡频率，很可能引发共鸣.虽然很多研究显示孤子具有粒子状特性，但是，孤子毕竟不是正常的粒子，因此即便势阱振荡与孤子震荡能很好的匹配，也无法造成孤子的共振行为.图6暗孤子在不同频率简谐势阱中位置与能量演化0.90.80.70204060t /ω-1（b ）对应的孤子能量的进化E s /μ（d ）图（a ）和（b ）凝聚体的密度（左轴），以及其与托马斯-费米值的密度偏离（n -n TF ）1.00.750.500.250.000.5 1.0Z /R TFn /n 00.040.020.00-0.02n -n T F /n 00.500.250.00-0.25-0.50z s /R T F（a ）暗孤子位置与托马斯-费米半径R TF 的比值.其中势阱强度ωz =ω0=2姨×10-2（μ/攸）（实线），2ω0（虚线），4ω0（点线）和6ω0（点虚线）204060t /ω-1刘超飞，等：玻色爱因斯坦凝聚体中暗孤子动力学研究第３７卷第５期（c ）孤子振荡频率ωs 与势阱频率ωz 的函数关系，其中.虚线为分析值ωs =ωz /2姨0.800.750.700.10.2ωs /ωzωz /（c ·ξ-1）v /c =0.25v /c =0.50v /c =0.751075暗孤子动力学研究展望实验中，暗孤子的确能展示良好的粒子状特性.例如，暗孤子在简谐势阱中，通常会来回振荡[11,15].如果一个静态的暗孤子最初位置不在势阱中心，它将受到势阱的外力作用，使之加速向势阱中心运动.最近，Parker 和他的同事考虑了对简谐势阱做一些修正，充分展示了可能出现的暗孤子行为[18,19,30].将一个紧束缚的势阱嵌入一个弱束缚的简谐势阱中，这样就可控制声波的逃逸[18].将光晶格势阱加入简谐势阱中，就可用于干扰暗孤子[30].此外，还可以考虑了参数驱动以及阻尼机制[19].而参考文献[31]中，有限温度效应对暗孤子的影响受到了系统性的探讨.类似的，Bilas 和Pavloff 研究了准一维玻色爱因斯坦凝聚体中，随机势对运动暗孤子的影响[32]，还研究了暗孤子在传播途中遇到障碍的情况[33].除了上述单成分凝聚体中暗孤子的工作，随着对BECs 中孤子的深入研究，人们在多元凝聚体混合物中还发现了矢量孤子、如亮-暗矢量孤子[34-37]、亮-亮矢量孤子、暗-暗矢量孤子[38-40].和单分量凝聚体相比，玻色爱因斯坦凝聚体的二元混合物已经被显示具有迷人的宏观量子现象，如复杂的空间结构[41-43]、亚稳态[44-46]、对称破缺不稳定性[47-49].迄今为止，我们已经知道种间相互作用系数对凝聚体混合物的基态结构起决定作用.当不等式g 12≤g 1g 2姨满足时，两种凝聚体是易融合的；当g 12>g 1g 2姨时，由于很强的种间排斥相互作用，凝聚体为不可融合的.就考察孤子来说，多个分量这个自由度的引入给系统带来了丰富的非线性现象，比如：孤子链、孤子对、多模激发等.除此之外，一种新型的孤子，即共生孤子，在两分量87Rb 和85Rb 的凝聚体中被发现.此时，只要分量间原子吸引力足够强，便能够克服各自分量原子内的排斥力而起到一个有效吸引的作用，从而在两分量玻色―爱因斯坦凝聚中形成亮孤子.其实，早在1993年，Kivshar 等[50]通过求图8扰动中的暗孤子震荡（b ）图（a ）的放大图.长度单位为ξ=攸/m μ姨（a ）在各种扰动幅度下，孤子轨迹随时间的变化403020100-10-20-30-40200040006000X /qt /（ξ·c -1）403020100-10-20-30-40300600900h =3ξh =2ξh =1ξh =0h =-1ξh =-2ξh =-3ξt /（ξ·c -1）X /q1.281.241.201.151.121.083000600090001200015000t /（ξ·c -1）（a ）在各种扰动幅度下，孤子能量随时间的变化.孤子初始速度为0.3c 和初始位置为x =0E /μ 1.281.241.201.151.121.0850010001500t /（ξ·c -1）（b ）图（a ）的放大图.体系参数为ω=2姨/100（c /ξ），ωd =ω/2姨h =3ξh =2ξh =1ξh =0h =-1ξh =-2ξh =-3ξ图7孤子能量受扰动幅度的影响E /μ江西理工大学学报2016年10月108解两个耦合非线性薛定谔方程，显示了矢量暗孤子存在的可能性.近来，在耦合的一维非线性薛定谔方程的框架内，双组分凝聚体的矢量暗孤子得到了相应的研究[51].然而，这些研究基于稳定的媒质.无论是凝聚体的种类，还是凝聚体两成分的比率，都是固定的.最近，Rabi 耦合[52]被用于将凝聚体从某一成分向其他成分的凝聚体转化.这就暗示着暗孤子在动态凝聚体媒质中运行是可能的.对于理想情况，即凝聚体种间相互作用与种内相互作用强度相同时，我们可以看到由一种成分构成的暗孤子可以转化为另一成分的暗孤子[53]（如图9所示）.并且，暗孤子转变为动态的矢量暗孤子后，其运动轨迹不受Rabi 耦合强度的影响.而种间相互作用与种内相互作用强度不相同时，矢量暗孤子的运动轨迹受到Rabi 耦合的影响比较明显.但是，这一长时间模拟所说明的最主要的结论为：暗孤子可以在具有Rabi 耦合的凝聚体中存在.这一结果在特定凝聚体比率的矢量暗孤子的设计上，具有非常重要的意义.将来，还可以通过控制Rabi 耦合，如在特定时间终结Rabi 耦合，从而得到特定比率的凝聚体混合物，以及矢量暗孤子.当然，矢量暗孤子稳定存在的内在机制等还有待进一步的探索.相信该研究成果将给实验上认识凝聚体中暗孤子等激发行为提供理论支持.6结论文章根据详细的能量计算分析，对玻色爱因斯坦凝聚体中暗孤子动力学行为的数值研究进行了系统的介绍.从分析暗孤子的数值解、暗孤子的能量计算开始，重点探讨了暗孤子在简谐势阱中的动力学行为，以及简谐势阱出现扰动时的情况.玻色爱因斯坦凝聚体中的暗孤子具有类似粒子的运动行为，在非均匀密度的凝聚体中，暗孤子发生声波图9玻色爱因斯坦凝聚体二元混合物中的矢量暗孤子的震荡行为.Rabi 耦合强度为0.025，g 1=g 2=g 12=1（a ）凝聚体成分1的演化和暗孤子震荡行为100500-50-1006001200180024003000t /（ξ·c -1）X0.13750.27500.41250.55000.58750.82500.96251.100ψ12（b ）凝聚体成分2的演化与暗孤子的震荡行为6001200180024003000X0.13750.27500.41250.55000.58750.82500.96251.100ψ22100500-50-100（c ）两凝聚体的密度和6001200180024003000X0.13750.27500.41250.55000.58750.82500.96251.100ψ12+ψ22100500-50-100t /（ξ·c -1）t /（ξ·c -1）刘超飞，等：玻色爱因斯坦凝聚体中暗孤子动力学研究第３７卷第５期109。

Series 8, washing machine, front loader, 9 kg, 1600 rpmWAX32LH9GBOptional accessoriesWMZ2200 : Floor securing componentWMZ2381 : Extension for cold water inlet /AquastopThe Serie|8 ActiveOxygen washing machinewith Home Connect removes odors withoutwashing in the smartest way.AntiStain: reliably removes four common stains.4D Wash System: highly efficient water and detergentpenetration for spotless results.Home Connect: home appliances with smart connectivity foran easier everyday life.Refresh ActiveOxygen: refreshes clothes without washing in45 minutes.EcoSilence Drive™: quiet and energy-efficient drive, with a 10-year warranty.Technical DataEnergy Efficiency Class: CWeighted energy consumption in kWh per 100 washing cycles ofeco 40-60 programme: 65 kWhMaximum capacity in kg: 9.0 kgThe water consumption of the eco programme in liters per cycle:48 lDuration of eco 40-60 programme in hours and mins at ratedcapacity: 3:47 hSpin-drying efficiency class of eco 40-60 programme: AAirborne acoustical noise emission class: AAirborne acoustical noise emissions : 70 dB(A) re 1 pWBuilt-in / Free-standing: Free-standingHeight of removable worktop: -2 mmDimensions of the product: 848 x 598 x 590 mmNet weight: 83.1 kgConnection Rating: 2300 WFuse protection: 10 AVoltage: 220-240 VFrequency: 50 HzApproval certificates: CE, E17D UKCA marking, VDELength electrical supply cord: 210 cmDoor hinge: LeftWheels: NoPower consumption standby/network: Please check the usermanual for how to switch off the WiFi module.: 1.5 WTime auto-standby/network: 5.0 minEAN code: 4242005184279Installation typology: Freestanding'!2E20A F-b i e c h j!1/3Series 8, washing machine, front loader, 9kg, 1600 rpm WAX32LH9GBThe Serie|8 ActiveOxygen washing machine with Home Connect removes odors without washing in the smartest way.Performance-Energy Efficiency Class¹: C-Energy² / Water³: 65 kWh / 48 litres -Load capacity: 1 - 9 kg-Programme duration⁴: 3:47 h:min -Spin drying efficiency class: A -Spin speed**: 400 - 1600 rpm -Noise level: 70 dB (A) re 1 pW -Noise efficiency class: A -Drum volume: 70 litresProgrammes/functions-Touch control buttons: On/off, Ready in, stain selection,Intensive Plus, Rinse Plus, Remote Start, start/pause with reload function, Temperature selection, SpeedPerfect,Prewash, Spin speed reduction/Rinse Hold -Standard programmes: cottons, easy care, delicates, wool hand wash-Special programmes: Drum clean with reminder, Shirts,HygienicSteam Odor Removal, Drain / Spin, Mixed Load,SportsWear, Single Rinse, Super Quick 15/30-Sensor electronics with safeguard monitoring system thatadjusts load and distribution and programme settings to protect clothesKey features-4D Wash System: highly efficient water and detergent fabricpenetration for spotless results.-Home Connect: Remote Monitoring and Control, Energy Management-Reload function / pause function-EcoSilence drive with 10 year warranty-AntiVibration Design - for more stability and quietness-EcoBar Plus function: five possible levels of energy and waterconsumption Additional features-Large LED-Display for programme status indication,temperature selection, max. spin speed, remaining timeand 24 h end time delay, ActiveOxygen activation and consumption indication-Control dial with integrated On / Off mode -VarioDrum: gentle and efficient washing -Drum interior light-Drum clean with reminder function-Sound insulation by additional noise reduction material -Aqua Protection-Foam detection system -Overdosage indication-Detergent dispensing: From front -Divider for Liquid Detergent -Child lock-Acoustic signals: BuzzerTechnical Information-Slide-under installation-Large chrome, white door with 171° opening and 32cmporthole opening-Dimensions (H x W): 84.8 cm x 59.8 cm -Appliance depth: 59.0 cm-Appliance depth incl. door: 63.2 cm-Appliance depth with open door: 106.3 cm¹ Scale of Energy Efficiency Classes from A to G² Energy consumption in kWh per 100 cycles (in programme Eco 40-60)³ Weighted water consumption in litres per cycle (in programme Eco 40-60)⁴ Duration of Eco 40-60 programme ** Values are rounded.2/3Series 8, washing machine, front loader, 9kg, 1600 rpmWAX32LH9GB3/3。

Unit6Active reading (1)Last man down: the fireman’s storyLanguage points1 Last man down: the fireman’s story (Title)The expression last man down, similar to last man standing, refers to the survivor or winner. The lastman down from the tower before it collapsed would be one of the bravest.2 There were about two dozen of us by the bank of elevators ... (Para 2)A bank of elevators means a set of lifts.3 Some had their turnout coats off, or tied around their waists. (Para 2) Turnout coats are the uniform firefighters wear when they turn out for a fire.4 Others were raring to go. (Para 2)The expression raring to go is an old form of rearing up, and means being eager to go like a horse.5 All of us were taking a beat to catch our breaths, and our bearings, figure out what the hell wasgoing on. (Para 2)To take a beat means to rest for a moment.A bearing is an exact compass reading measured in degrees. To take your bearings is to find where youare. Here it means both physically and mentally.6 We’d been at this thing, hard, for almost an hour, some a little bit less, and we were nowhere closeto done. (Para 2)To be at this thing is a slang expression which means to work on this mission. The expression nowhere close to done means someone is far from completing their work.7 Of course, we had no idea what there was left to do, but we hadn’t made a dent. (Para 2)A dent is a mark on a piece of metal as when you bump your car. To make a dent in something is to havean effect on it (imagine beating a piece of hard steel and not making any mark on it). To make a dent heremeans to achieve something. The firefighters had hardly begun their work.8 As if we could see clear through the ceiling tiles for an easy answer. (Para 3)Looking up for the source of the noise was only useful if you could see through the floors above, but itstill remained an instinctive reaction.9 The building was shaking like in an earthquake, like an amusement park thrill ride gone berserk …(Para 3)The word berserk was originally about ancient Viking warriors who worshipped a bear god (ber). Theywould go into a terrible rage or madness when fighting. It now means utterly and dangerously crazy.10 The way it coursed right through me. (Para 3)To course means to run or flow somewhere quickly. The noise and vibration have a strong physical effecton the writer.11 I thought about my wife and my kids, but only fleetingly and not in any kind of life-flashing-beforemy-eyes sort of way. (Para 4)Life flashing before my eyes is a claim made by someone who has near-death experiences, as in anaccident, of seeing a slow motion version of the most important events in their lives. Researchers say itmay be the reaction of the brain to trauma.Streets full of heroes Unit 619912 Or, “We’ll all meet at the big one.” (Para 4)After any fire, the fighters use the expression the big one to minimize that fire and suggest there willalways be a bigger one coming. It is a brave act of understatement.13 I never knew how it started, or when I’d picked up on it myself, but it was part of our shorthand. (Para 4)To pick up on it means to learn it and start using it. It is a slang expression. Shorthand is a system of writing used for taking down fast speech. It uses symbols for common wordsand can only be understood by people who learn it. Firemen have their own spoken shorthand (as do mostprofessions). To an outsider, the big one would not mean much, but as the writer explains it was rich inmeaning to him and his colleagues.14 I fumbled for some fix on the situation, thinking maybe if I understood what was happening I couldsteel myself against it. (Para 5)Some fix is a slang term which means a way of understanding.To steel oneself against something means to prepare oneself to do something unpleasant.15 A battalion commander for the New York Fire Department, he was on the sceneof the disaster … (Para 6)The Fire Department is divided up into battalions of up to 200 consisting of a number of companies ofabout 30 firefighters.Reading and understanding3 Choose the best summary of the extract.2 In this dramatic personal account, firefighter Richard Picciotto recalls what he was doing and thinking,just before the north tower of the World Trade Center collapsed on 11 September 2001.4 Answer the questions.1 Where was Richard Picciotto at 9:59 am on 11 September 2001?He was on the 35th floor of the north tower of the World Trade Center.2 Who was with him?About two dozen firefighters.3 What was everybody trying to do?They were resting and trying to work out what was going on.4 How long had they been in the building?Nearly an hour.5 What did they do when the noise started?They stood still.6 What was happening to the building?It was falling down.7 What did Picciotto start thinking about when he heard the noise?He started thinking about his family, job and the bagels in the kitchen.Unit 6 Streets full of heroes2008 Did Picciotto have the impression things were happening quickly or slowly? To him, it seems things were happening slowly while in truth they weren’t.9 How did Picciotto get out of the tower?He climbed through the rubble and led his men to safety.10 How many firefighters lost their lives?Altogether 343 firefighters.11 Why did Picciotto write Last Man Down?He wrote it as a tribute to his colleagues.Dealing with unfamiliar words5 Match the words in the box with their definitions.1 to make a fire stop burning (extinguish)2 the total number of people who have been killed or hurt (toll)3 an extremely difficult or frightening situation (nightmare)4 a very sad event that causes people to suffer or die (tragedy)5 as much as possible (utmost)6 impressive actions that prove someone is very brave (heroism)7 happening in a confused way and without any order or organization (chaotic)6 Complete the paragraph with the correct form of the words in Activity 5.For a firefighter arriving on the scene of a fire the first few minutes are usually the most (1) chaotic.He has to (2) extinguish the fire, he also needs to find out if human lives are in danger. When people aretrapped inside a building he must act swiftly to prevent (3) tragedy, or, –in the (4) nightmare scenario – tokeep the death (5) toll to a minimum. Actions like these require the (6) utmost degree of (7) heroism.7 Replace the underlined words with the correct form of the words in the box.1 He’s a very honest, fair and well-behaved sort of person. (decent)2 I’d like to express my thanks for everything you’ve done for me. (gratitude)3 There was a group of cows standing in the corner of the field. (herd)4 There have been very big increases in food prices over the last few months. (massive)5 All the people should leave the building immediately when the alarm sounds. (evacuate)6 She has displayed all the qualities needed for being a leader in her job. (leadership)8 Answer the questions about the words and expressions.1 If you are raring to go, are you eager to (a) leave, or (b) start an activity?2 If you get your bearings, do you (a) lose your way, or (b) find out where you are?3 If you are nowhere close to done, do you (a) still have a lot more work to do to finish the job, or (b) stillfeel strong and ready to work?4 If you haven’t made a dent in something, have you (a) made good progress, or (b) hardly begun the job?5 Is a racket (a) a loud and unpleasant noise, or (b) a low musical sound?Streets full of heroes Unit 62016 If something goes berserk, is it (a) quiet and well-behaved, or (b) out of control?7 Does whatever the hell it was suggest that the writer (a) knew exactly whatthe noise was, or (b) didn’tknow what the noise was?8 If something is part of the shorthand, can you (a) easily understand it, or(b) not understand it?9 If you are fumbling for a fix, are you (a) trying to understand something, or (b) trying to stay where you are?Active reading (2)Language points1 “Suddenly,” she wrote in her syndicated column, “I saw on the sidewalka figure of a man.” (Para 1)A syndicated column is a regular newspaper article sold to newspapers all around the country.2 “I felt certain that somewhere along the line she would stub her toe,” said Perkins, thinking ofWashington’s fishbowl atmosphere. (Para 3)To stub her toe means to do damage to herself or get hurt.In a fishbowl atmosphere, everyone can see what is happening in the fishbowl. The sentence means Perkins was sure sooner or later she would get into trouble and be criticized.3 I don’t know how she did it. What to lay it to? (Para 3)The expression what to lay it to means “how can one explain it?”.4 … “that a crippled man, victim of a cruel affliction, was able for more than ten years to ride thestorms of peace and war at the summit of the US …” (Para 3)A man in a wheelchair with a terrible disease could lead his country well both during the Great Depressionand World War.5 “Most people who have played second violin all their lives never have an opportunity to play firstviolin,” remarked Perkins. (Para 4)People who play second violin are those who do not lead or give solos and who are always of lesserimportance. To play first violin means to be the leader and take the initiative.6 “Now, if you want to know what I think about Mrs Roosevelt, she istuh-riffic! …” (Para 5)The word tuh-riffic means terrific. It is pronounced with a strong regional accent.7 On a trip to India ... introduced to the Indian Parliament by Pandit Nehru as “a representative ofresurgent humanity”. (Para 6)The expression resurgent humanity refers to recovering from the horrors of thefirst half of the 20thcentury. A representative of resurgent humanity refers to an example of the most admirable and progressivetype of person.Reading and understanding2 Choose the best way to complete the sentences.1 Eleanor Roosevelt became a volunteer (c) .(a) when she met her husband(b) when her husband became President of the US(c) as a young woman(d) when she saw a homeless man in the street2 When she became the wife of the president (c) .(a) she gave up her job(b) she began to write for a newspaper(c) she reinvented the role of First Lady(d) she found it difficult to reconcile family life and public affairsStreets full of heroes Unit 62073 When she held her first press conference (a) .(a) she didn’t allow men to atte nd(b) she pushed her husband in on a wheelchair(c) she made speeches(d) her involvement in politics shocked people4 While Roosevelt was president, Eleanor (c) .(a) stayed a full-time wife and mother(b) made a lot of people angry(c) defended the rights of women and Afro-Americans(d) became the host of a television programme5 After her husband died she (c) .(a) retired from public life(b) became the only female delegate to the United Nations(c) helped implement the Universal Declaration of Human Rights(d) started writing for a newspaper6 In the last years of her life she (b) .(a) went to live in India(b) continued to promote the rights of women(c) was given a new task by President Kennedy(d) gave up her interest in politicsDealing with unfamiliar words3 Match the words in the box with their definitions.1 someone who is chosen to represent a group of other people at a meeting (delegate)2 to believe that something is the cause of someone or something else (ascribe)3 a newspaper or television reporter, especially one who deals with a particular subject or area(correspondent)4 a very high level of skill or ability (genius)5 to control someone or something, often in a negative way, because you have more power or influence(dominate)6 used about a feeling or thought you do not realize you have (unconscious)7 to watch something in order to check that it works in the way that it should (oversee)4 Complete the paragraph with the correct form of the words in Activity 3.Eleanor Roosevelt showed her (1) genius for getting the support of other (2) delegates in the UNAssembly. She was a great speaker who knew how to (3) oversee important meetings without being seento (4) dominate them. She was also a talented (5) correspondent and she wrote a daily column for manyyears. Franklin D. Roosevelt’s success as president was (6) ascribed by many to her support and wonderfulcharacter. She became involved in politics because of her sense of right and wrong and an (7) unconsciousneed to help people.Unit 6 Streets full of heroes2085 Replace the underlined words with the correct form of the words in the box.1 He has been unable to use his legs since birth. (crippled)2 We need to call a meeting for world leaders about this issue. (summit)3 The first thing I read in the newspaper is the regular section about the arts. (column)4 Our class visit to the United Nations was a wonderful experience. (marvelous)5 It’s import ant to try to influence politicians about the need to improve transport facilities in our area.(lobby)6 How many millions of people live in the very poor areas of Mumbai? (slums)6 Answer the questions about the words and expressions.1 In a fishbowl atmosphere, are you (a) likely, or (b) unlikely to see what everyone is doing?2 Is a mishap a (a) positive, or (b) negative experience?3 If you have a humane attitude, are you (a) kind and caring, or (b) cruel and uncaring?4 If you win over someone to your cause, do you (a) defeat them, or (b) persuade them to join you?5 Does an affliction make your life (a) easy, or (b) difficult?6 If you ride the storm, do you (a) survive it, or (b) fall victim to it?7 Is a superlative performance (a) very good, or (b) just good?8 If a politician has a throng of admirers, are there (a) many people, or (b)a few who like them?9 If you are on a par with someone, are you in (a) the same position, or (b) different positions?Language in useword formation: gender-inclusive language1 Look at the sentences from the passages and answer the questions.Last man down: The fireman’s storyWe were firefighters, mostly, and we were in various stages of exhaustion.Streets full of heroes Unit 6211Please join Life magazine as we honor the power and humanity of Anna Eleanor Roosevelt by inductingher into the Hall of Heroes.1 What meaning do fireman and firefighter share?Someone whose job is to fight fires.2 What extra meaning is included in the word fireman?The person is male.3 Does the word heroes refer to men, women, or both?Both.2 Replace the underlined words with gender-inclusive language.1 Miss Read was the headmistress at school, and I was very fond of her. (headteacher)2 Mother Teresa and Eleanor Roosevelt are two great heroines of our time. (heroes)3 There were a lot of policemen standing at the entrance to the factory. (police officers)4 More than three hundred firemen died in the fire. (firefighters)5 We’ll ask one of our salesgirls to come and help you. (salespersons) Why is it that …?3 Rewrite the sentences using Why is it that ...?1 I don’t know why we haven’t been able to solve the problem of slums in this town.Why is it that we haven’t been able to solve the problem of slums in this town?2 I don’t know why we are not able to organize fair elections in this part of the world.Why is it that in this part of the world we are not able to organize fair elections?3 I don’t know why they never employ qualified people in this hotel.Why is it that in this hotel they never employ qualified people?4 I don’t know why the system of welfare is still not working properly in this country.Why is it that in this country the system of welfare is still not working properly?5 I don’t know why you always find such an easy answer to all the questionsI ask.Why is it that you always find such an easy answer to all the questions I ask?adj. + though it + be4 Rewrite the sentences using adj. + though it + be.1 My time in the United States was short, but it was interesting.My time in the United States, short though it was, was interesting.2 The scenes of destruction were terrible, but not surprising.The scenes of destruction, terrible though they were, were not surprising.3 The rescue operation cost a lot of money, but it was successful.The rescue operation, costly though it was, was successful.Unit 6 Streets full of heroes2124 The lesson he gave was extremely interesting, but it was soon forgotten. The lesson he gave, interesting though it was, was soon forgotten.5 Mother Teresa may have been old, but she was extremely active.Mother Teresa, old though she may have been, was extremely active.6 His actions may have been unconscious, but they have had very serious consequences.His actions, unconscious though they may have been, have had very serious consequences.collocations5 Complete the sentences with the correct form of suitable expressions from the collocation box. Sometimesmore than one collocation is possible.1 My grandfather died suddenly after a massive heart attack.2 There was a column of smoke in the sky for days after 9/11.3 Eleanor Roosevelt wrote a daily / newspaper column for nearly 30 years.4 The stress began to take a toll on their marriage.5 The final death toll might be much higher than the police at first thought.6 How many newspaper columns have been written about the heroes of the last century?7 Do you have to pay a toll to drive on the motorway?8 Your idea was brilliant – a stroke of genius!9 My hero is my English teacher. He has a genius for helping us understand Shakespeare.10 When she died she left a massive amount of money to charity.6 Translate the paragraphs into Chinese.1 I thought how we firemen were always saying to each other, “I’ll see you at the big one.” Or, “We’ll allmeet at the big one.” I never knew how it started, or when I’d picked up on it myself, but it was part ofour shorthand. Meaning, no matter how big this fire is, there’ll be another one bigger, somewhere downthe road. We’ll make it through this one, and we’ll make it through that one, too. I always said it, at bigfires, and I always heard it back, and here I was, thinking I would never say or hear these words again,because there would never be another fire as big as this. This was the big one we had all talked about,all our lives, and if I hadn’t known this before – just before these chilling moments – this sick, blacknoise now confirmed it. (这段话由许多短句构成，要注意短句间语气的连接。

汽车空调出风口啸叫的辨识及机理探究沈沉;王洋;刘斌;陶泽平【摘要】通过近场测量法获得实车空调出风口啸叫的声压数据,并分析其频谱,又通过耦合气动-声学数值计算研究流场结构并探究啸叫机理.试验结果表明,啸叫的发生与空调出风口的风门位置和内外压差联系密切.当幅值-频域信号中2 kHz以上部分存在明显的频谱峰值时,啸叫明显.啸叫产生的机理在于拟序涡结构脱落引发的有规律的压力脉动,辐射后形成较为规则的声压脉动.为预测啸叫、改进设计、预防啸叫提供理论依据.【期刊名称】《汽车工程学报》【年(卷),期】2015(005)003【总页数】6页(P229-234)【关键词】NVH;噪声辨识;数值模拟;气动噪声;啸叫【作者】沈沉;王洋;刘斌;陶泽平【作者单位】泛亚汽车技术中心,上海201201;泛亚汽车技术中心,上海201201;泛亚汽车技术中心,上海201201;泛亚汽车技术中心,上海201201【正文语种】中文【中图分类】U463.85+1乘用车噪声、振动与声振粗糙度（Noise、Vibration、Harshness，NVH）性能直接影响到乘坐舒适性，空调出风口啸叫是一种常见的NVH问题，会引起乘客不适与疲劳[1]，越来越多的主机厂和供应商开始关心并设法解决该问题。

汽车空调出风口啸叫是一种主观感受，定义并辨识啸叫在出风口研发和认证过程中十分重要。

相关研究已经表明：车内舒适性与响度、尖锐度、粗糙度、波动度等因素相关[2]，而出风口啸叫对车内噪声的响度、尖锐度、粗糙度都有明显的影响，所以研究并改善出风口啸叫具有重要的工程意义。

目前对于出风口啸叫的评估主要采取台架试验和整车试验两种方式，而对啸叫产生的机理缺少有效的分析方法。

啸叫的成因较为复杂，其影响因素包括风机、风门、风道、叶片等。

运用计算流体动力学（Computational Fluid Dynamics，CFD）分析啸叫形成机理对识别影响因素、改进设计、预防啸叫具有指导意义。

u1080p resolution for sharp imagesu Easy to install with auto zoom/focus lens, wizardand pre-configured modesu Fully configurable quad streamingu IR version with 15 m (50 ft) viewing distanceu Regions of interest and E-PTZThe HD indoor dome cameras from Bosch areprofessional surveillance cameras that provide highquality HD images for demanding security andsurveillance network requirements. These domes aretrue day/night cameras offering excellent performanceday or night.There is a version with a built-in active infraredilluminator that provides high performance in extremelow-light environments.System overviewEasy to install stylish indoor domeIdeal for indoor use, the stylish design is suitable forinstallations where appearance and flexible coverageare important. The varifocal lens allows you to choosethe coverage area to best suit your application. Usingthe proprietary pan/tilt/rotation mechanism, installerscan select the exact field of view. Mounting optionsare numerous, including surface, wall, and suspended-ceiling mounting.The automatic zoom/focus lens wizard makes it easyfor an installer to accurately zoom and focus thecamera for both day and night operation. The wizard isactivated from the PC or from the on-board camerapush button making it easy to choose the workflowthat suits best.The AVF (Automatic Varifocal) feature means that thezoom can be changed without opening the camera.The automatic motorized zoom/focus adjustment with1:1 pixel mapping ensures the camera is alwaysaccurately focused.FunctionsIntelligent Dynamic Noise Reduction reducesbandwidth and storage requirementsThe camera uses Intelligent Dynamic Noise Reductionwhich actively analyzes the contents of a scene andreduces noise artifacts accordingly.The low-noise image and the efficient H.264compression technology provide clear images whilereducing bandwidth and storage by up to 50%compared to other H.264 cameras. This results inreduced-bandwidth streams that still retain a highimage quality and smooth motion. The cameraprovides the most usable image possible by cleverlyoptimizing the detail-to-bandwidth ratio.Area-based encodingArea-based encoding is another feature which reduces bandwidth. Compression parameters for up to eight user-definable regions can be set. This allows uninteresting regions to be highly compressed, leaving more bandwidth for important parts of the scene. Bitrate optimized profileThe average typical optimized bandwidth in kbits/s for various image rates is shown in the table:Multiple streamsThe innovative multi-streaming feature delivers various H.264 streams together with an M‑JPEG stream. These streams facilitate bandwidth-efficient viewing and recording as well as integration with third-party video management systems.Depending on the resolution and frame rate selected for the first stream, the second stream provides a copy of the first stream or a lower resolution stream.The third stream uses the I-frames of the first stream for recording; the fourth stream shows a JPEG image at a maximum of 10 Mbit/s.Regions of interest and E-PTZRegions of Interest (ROI) can be user defined. The remote E-PTZ (Electronic Pan, Tilt and Zoom) controls allow you to select specific areas of the parent image. These regions produce separate streams for remote viewing and recording. These streams, together with the main stream, allow the operator to separately monitor the most interesting part of a scene while still retaining situational awareness.Built-in microphone, two-way audio and audio alarm The camera has a built-in microphone to allow operators to listen in on the monitored area. Two-way audio allows the operator to communicate with visitors or intruders via an external audio line input and output. Audio detection can be used to generate an alarm if needed.If required by local laws, the microphone can be permanently blocked via a secure license key. Tamper and motion detectionA wide range of configuration options is available for alarms signaling camera tampering. A built-in algorithm for detecting movement in the video can also be used for alarm signaling.Storage managementRecording management can be controlled by the Bosch Video Recording Manager (VRM) or the camera can use iSCSI targets directly without any recording software.Edge recordingThe MicroSD card slot supports up to 2 TB of storage capacity. A microSD card can be used for local alarm recording. Pre-alarm recording in RAM reduces recording bandwidth on the network, or — if microSD card recording is used — extends the effective life of the storage medium.Cloud-based servicesThe camera supports time-based or alarm-based JPEG posting to four different accounts. These accounts can address FTP servers or cloud-based storage facilities (for example, Dropbox). Video clips or JPEG images can also be exported to these accounts.Alarms can be set up to trigger an e-mail or SMS notification so you are always aware of abnormal events.Easy installationPower for the camera can be supplied via a Power-over-Ethernet compliant network cable connection. With this configuration, only a single cable connection is required to view, power, and control the camera. Using PoE makes installation easier and more cost-effective, as cameras do not require a local power source.The camera can also be supplied with power from+12 VDC power supplies.For trouble-free network cabling, the camera supports Auto-MDIX which allows the use of straight or cross-over cables.True day/night switchingThe camera incorporates mechanical filter technology for vivid daytime color and exceptional night-time imaging while maintaining sharp focus under all lighting conditions.Hybrid modeAn analog video output enables the camera to operate in hybrid mode. This mode provides simultaneous high resolution HD video streaming and an analog video output via an SMB connector. The hybrid functionality offers an easy migration path from legacy CCTV to a modern IP-based system.Access securityPassword protection with three levels and 802.1x authentication is supported. To secure Web browser access, use HTTPS with a SSL certificate stored in the camera.Complete viewing softwareThere are many ways to access the camera’s features: using a web browser, with the Bosch Video Management System, with the free-of-chargeBosch Video Client or Video Security Client, with the video security mobile app, or via third-party software. Video security appThe Bosch video security mobile app has been developed to enable Anywhere access to HD surveillance images allowing you to view live images from any location. The app is designed to give you complete control of all your cameras, from panning and tilting to zoom and focus functions. It’s like taking your control room with you.This app, together with the separately available Bosch transcoder, will allow you to fully utilize our dynamic transcoding features so you can play back images even over low-bandwidth connections.System integrationThe camera conforms to the ONVIF Profile S, ONVIF Profile Q and ONVIF Profile G specifications. Compliance with these standards guarantees interoperability between network video products regardless of manufacturer.Third-party integrators can easily access the internal feature set of the camera for integration into large projects. Visit the Bosch Integration Partner Program (IPP) website () for more information.HD standardsComplies with the SMPTE 274M-2008 Standard in:–Resolution: 1920x1080–Scan: Progressive–Color representation: complies with ITU-R BT.709–Aspect ratio: 16:9–Frame rate: 25 and 30 frames/sComplies with the SMPTE 296M-2001 Standard in:–Resolution: 1280x720–Scan: Progressive–Color representation: complies with ITU-R BT.709–Aspect ratio: 16:9–Frame rate: 25 and 30 frames/sInstallation/configuration notesDimensions mm (inch)Parts included•Camera•Screw kit•Installation documentation Technical specificationsSensitivity – (3200K, reflectivity 89%, F1.3, 30IRE)Ordering informationFLEXIDOME IP indoor 5000 HDProfessional IP dome camera for indoor HD surveillance. Varifocal 3 to 10 mm f1.3 lens; IDNR; day/ night; H.264 quad-streaming; cloud services; motion/ tamper/audio detection; microphone; 1080pOrder number NIN-51022-V3FLEXIDOME IP indoor 5000 IRProfessional IP dome camera for indoor HD surveillance. Varifocal 3 to 10 mm f1.3 lens; IDNR; day/ night; H.264 quad-streaming; cloud services; motion/ tamper/audio detection; microphone; 1080p; infrared Order number NII-51022-V3FLEXIDOME IP indoor 5000 HDProfessional IP dome camera for indoor HD surveillance. Automatic Varifocal 3 to 10 mm f1.3 lens; DC iris; IDNR; day/night; H.264 quad-streaming; cloud services; motion/tamper/audio detection; microphone; 1080pOrder number NIN-50022-A3FLEXIDOME IP indoor 5000 IRProfessional IP dome camera for indoor HD surveillance. Automatic Varifocal 3 to 10 mm f1.3 lens; DC iris; IDNR; day/night; H.264 quad-streaming; cloud services; motion/tamper/audio detection; microphone; 1080p; infraredOrder number NII-50022-A3AccessoriesNDA-LWMT-DOME Dome Wall MountSturdy wall L-shaped bracket for dome cameras Order number NDA-LWMT-DOMENDA-ADTVEZ-DOME Dome Adapter BracketAdapter bracket (used together with appropriate wall or pipe mount, or surface mount box)Order number NDA-ADTVEZ-DOMEVEZ-A2-WW Wall MountWall mount (Ø145/149 mm) for dome cameras (use together with appropriate dome adapter bracket); whiteOrder number VEZ-A2-WWVEZ-A2-PW Pipe MountPendant pipe mount (Ø145/149 mm) for dome cameras (use together with appropriate dome adapter bracket); whiteOrder number VEZ-A2-PWLTC 9213/01 Pole Mount AdapterFlexible pole mount adapter for camera mounts (use together with the appropriate wall mount bracket). Max. 9 kg (20 lb); 3 to 15 inch diameter pole; stainless steel strapsOrder number LTC 9213/01NDA-FMT-DOME In-ceiling mountIn-ceiling flush mounting kit for dome cameras(Ø157 mm)Order number NDA-FMT-DOMENDA-ADT4S-MINDOME 4S Surface Mount BoxSurface mount box (Ø145 mm / Ø5.71 in) for dome cameras (use together with the appropriate dome adapter bracket).Order number NDA-ADT4S-MINDOMEMonitor/DVR Cable SMB 0.3M0.3 m (1 ft) analog cable, SMB (female) to BNC (female) to connect camera to coaxial cableOrder number NBN-MCSMB-03MMonitor/DVR Cable SMB 3.0M3 m (9 ft) analog cable, SMB (female) to BNC (male) to connect camera to monitor or DVROrder number NBN-MCSMB-30MNPD-5001-POE Midspan PoE InjectorPower-over-Ethernet midspan injector for use with PoE enabled cameras; 15.4 W, 1-portOrder number NPD-5001-POENPD-5004-POE Midspan PoE InjectorPower-over-Ethernet midspan injectors for use with PoE enabled cameras; 15.4 W, 4-portsOrder number NPD-5004-POERepresented by:North America:Europe, Middle East, Africa:Asia-Pacific:China:Latin America and Caribbean:Bosch Security Systems, Inc. 130 Perinton Parkway Fairport, New York, 14450, USA Phone: +1 800 289 0096 Fax: +1 585 223 9180***********************.com Bosch Security Systems B.V.P.O. Box 800025617 BA Eindhoven, The NetherlandsPhone: + 31 40 2577 284Fax: +31 40 2577 330******************************Robert Bosch (SEA) Pte Ltd, SecuritySystems11 Bishan Street 21Singapore 573943Phone: +65 6571 2808Fax: +65 6571 2699*****************************Bosch (Shanghai) Security Systems Ltd.203 Building, No. 333 Fuquan RoadNorth IBPChangning District, Shanghai200335 ChinaPhone +86 21 22181111Fax: +86 21 22182398Robert Bosch Ltda Security Systems DivisionVia Anhanguera, Km 98CEP 13065-900Campinas, Sao Paulo, BrazilPhone: +55 19 2103 2860Fax: +55 19 2103 2862*****************************© Bosch Security Systems 2016 | Data subject to change without notice 188****8507|en,V9,01.Jun2016。

AbstractCompressive sensing and sparse inversion methods have gained a significant amount of attention in recent years due to their capability to accurately reconstruct signals from measurements with significantly less data than previously possible. In this paper, a modified Gaussian frequency domain compressive sensing and sparse inversion method is proposed, which leverages the proven strengths of the traditional method to enhance its accuracy and performance. Simulation results demonstrate that the proposed method can achieve a higher signal-to- noise ratio and a better reconstruction quality than its traditional counterpart, while also reducing the computational complexity of the inversion procedure.IntroductionCompressive sensing (CS) is an emerging field that has garnered significant interest in recent years because it leverages the sparsity of signals to reduce the number of measurements required to accurately reconstruct the signal. This has many advantages over traditional signal processing methods, including faster data acquisition times, reduced power consumption, and lower data storage requirements. CS has been successfully applied to a wide range of fields, including medical imaging, wireless communications, and surveillance.One of the most commonly used methods in compressive sensing is the Gaussian frequency domain compressive sensing and sparse inversion (GFD-CS) method. In this method, compressive measurements are acquired by multiplying the original signal with a randomly generated sensing matrix. The measurements are then transformed into the frequency domain using the Fourier transform, and the sparse signal is reconstructed using a sparsity promoting algorithm.In recent years, researchers have made numerous improvementsto the GFD-CS method, with the goal of improving its reconstruction accuracy, reducing its computational complexity, and enhancing its robustness to noise. In this paper, we propose a modified GFD-CS method that combines several techniques to achieve these objectives.Proposed MethodThe proposed method builds upon the well-established GFD-CS method, with several key modifications. The first modification is the use of a hierarchical sparsity-promoting algorithm, which promotes sparsity at both the signal level and the transform level. This is achieved by applying the hierarchical thresholding technique to the coefficients corresponding to the higher frequency components of the transformed signal.The second modification is the use of a novel error feedback mechanism, which reduces the impact of measurement noise on the reconstructed signal. Specifically, the proposed method utilizes an iterative algorithm that updates the measurement error based on the difference between the reconstructed signal and the measured signal. This feedback mechanism effectively increases the signal-to-noise ratio of the reconstructed signal, improving its accuracy and robustness to noise.The third modification is the use of a low-rank approximation method, which reduces the computational complexity of the inversion algorithm while maintaining reconstruction accuracy. This is achieved by decomposing the sensing matrix into a product of two lower dimensional matrices, which can be subsequently inverted using a more efficient algorithm.Simulation ResultsTo evaluate the effectiveness of the proposed method, we conducted simulations using synthetic data sets. Three different signal types were considered: a sinusoidal signal, a pulse signal, and an image signal. The results of the simulations were compared to those obtained using the traditional GFD-CS method.The simulation results demonstrate that the proposed method outperforms the traditional GFD-CS method in terms of signal-to-noise ratio and reconstruction quality. Specifically, the proposed method achieves a higher signal-to-noise ratio and lower mean squared error for all three types of signals considered. Furthermore, the proposed method achieves these results with a reduced computational complexity compared to the traditional method.ConclusionThe results of our simulations demonstrate the effectiveness of the proposed method in enhancing the accuracy and performance of the GFD-CS method. The combination of sparsity promotion, error feedback, and low-rank approximation techniques significantly improves the signal-to-noise ratio and reconstruction quality, while reducing thecomputational complexity of the inversion procedure. Our proposed method has potential applications in a wide range of fields, including medical imaging, wireless communications, and surveillance.。

面向小直径薄壁管表面质量检测的散斑干涉图像滤波方法研究陈杰阳雷罗建东陈杰1988—/男/硕士/毕业于四川大学/从事无损检测研究与应用工作/中国核动力研究设计院(成都610213)阳雷1980—/男/硕士/毕业于西南交通大学/从事无损检测研究与应用工作/中国核动力研究设计院(成都610213)罗建东1986—/男/博士/毕业于中国核动力研究设计院/从事无损检测研究与应用工作/中国核动力研究设计院(成都610213)摘要利用散斑干涉测量技术对材料表面质量进行检测时，干涉图像存在大量高频散斑噪声，严重影响了表面质量检测的准确度及测量精度。

本文以小直径薄壁管表面为检测对象，提出了一种自适应窗口傅里叶变换滤波方法对散斑噪声进行滤波，首先利用小波变换获得最佳的窗口大小，然后利用窗口傅里叶脊对应的振幅动态修正频谱阈值，最后利用傅里叶脊对应的局部频率设置相应的通频带完成傅里叶逆变换获得滤波后的图像，并与等值线窗口法和二阶方向偏微分方程法进行对比分析。

研究结果表明，自适应窗口傅里叶变换滤波法滤波效果最好，表面质量检测准确度及测量精度高。

关键词小直径管；薄壁管；散斑干涉；图像滤波；自适应窗口中图分类号:TG178文献标识码:ADOI：10.19694/ki.issn2095-2457.2020.15.016 AbstractThe interference image contains a lot of high frequency speckle noise when using the digital speckle interferometry to measure the material surface quality,which seriously affects the accuracy of surface quality detection and measurement accuracy.In this paper,an adaptive window Fourier transform filtering method is proposed to filter the speckle noise on the surface of small-diameter thin-walled tube.Firstly,the optimal window size is obtained by wavelet transform,then the amplitude corresponding to the window Fourier ridge is used to dynamically modify the spectrum threshold,and finally the corresponding pass band is set by the local frequency corresponding to the Fourier ridge to complete the Fourier transform The filtered image is obtained by inverse transformation and compared with contoured window method and second-order directional partial differential equation method.The results show that the adaptive window Fourier transform filtering method has good filtering effect,high accuracy of surface quality detection and measurement.Key WordsSmall-diameter pipe;Thin-walled pipe;Speckle fringe pattern; Filtering;Adaptive parameters0引言在核反应堆关键部件的研制过程中，必须针对小直径薄壁管的表面质量进行全面的检测及评价。

2011年3月第37卷第3期北京航空航天大学学报Journal of Beijing University of Aeronautics and AstronauticsMarch　2011Vol.37　No.3　收稿日期:2010⁃01⁃20　基金项目:国家863高技术研究发展计划基金资助项目(2009AA12Z313)　作者简介:刘　杨(1983-),女,内蒙古集宁人,博士生,mickeybaby2003@.考虑互相关干扰的郧孕杂信号捕获门限设定方法刘　杨 秦红磊 金　天(北京航空航天大学电子信息工程学院,北京100191) 摘 要:传统GPS 卫星信号捕获门限设定方法在互相关干扰情况下存在较大虚警概率,所以无法捕获弱信号.针对该问题进行分析,在此基础上提出一种针对多颗能量不同卫星同时存在情况下的信号检测模型和概率模型.信号检测模型在相关积分非相干累加基础上引入双门限多次检测,由于在考虑噪声的同时也考虑了互相关干扰对弱信号捕获的影响,其概率模型为非中心χ2分布.在原有的恒虚警门限检测方法基础上,提出考虑强信号互相关干扰对微弱信号检测影响情况下的门限计算方法作为新的门限上限,而将原有的门限计算方法作为门限的下限.在此基础上提出强、弱卫星信号共存时的检测思路,即先用门限上限检测强信号并进行互相关干扰消除处理,再用门限下限判断是否有弱信号存在.采用仿真数据和实际数据针对考虑互相关干扰的门限上限进行实验,并和原有门限方法进行比较,证明在强、弱信号共存情况下原有门限无法检测出卫星信号,而新的门限设定方法可以正常工作,并具有较高的检测概率和较低的虚警概率.关　键　词:微弱信号捕获;远近效应;恒虚警准则;门限设定中图分类号:TN 967.1文献标识码:A 文章编号:1001⁃5965(2011)03⁃0268⁃06Threshold setting method for GPS signal acquisitionunder cross⁃correlation effectLiu Yang　Qin Honglei　Jin Tian(School of Electronics and Information Engineering,Beijing University of Aeronautics and Astronautics,Beijing 100191,China)Abstract :Traditional global positioning system(GPS)signal acquisition threshold method suffers fromlarge false alarm ratio in the condition of cross correlation interference,and thus influences weak signal acqui⁃sition.This problem was analyzed and signal acquisition detector was improved under the situation of more than one satellites existing with different signal power.Double threshold multiple detection algorithm was intro⁃duced based on the coherent correlation and non⁃coherent accumulation.The statistical model is non⁃central chi⁃square distributed due to cross correlation influence.A threshold calculation method was put up in the weak signal detection based on the original fixed false alarm criterion,and this threshold was considered to be the upper threshold.The original threshold was considered to be the lower threshold.An algorithm was put up considering both strong and weak signal coexistence,strong signals were acquired first and then cross correla⁃tion interference was eliminated,weak signals were acquired after that.Simulated and real data have been used to test the upper threshold,results were compared with the original method.It is proved that originalmethod can’t detect satellite signals while new threshold works efficiently with high detection possibility and low false alarm ratio.Key words :weak signal acquisition;near⁃far problem;constant false alarm rate;threshold setting 近年以来,卫星导航定位系统得到越来越广泛的应用.目前在一般环境下卫星导航接收机能够达到满足需求的定位精度.然而,当接收机载体处于丛林、峡谷、都市、室内、浅水以及隧道等环境中时,卫星信号会受到不同程度的衰减,从而使通常的接收机无法完成信号的接收.为了打破这种应用上的瓶颈,要求卫星导航接收机具有强的微弱信号处理能力.高灵敏卫星导航接收机的研制始于本世纪初,其核心思想是通过信号处理实现对微弱卫星导航信号的捕获跟踪,从而实现复杂环境下的导航定位功能,增强接收机的可用性.微弱卫星导航信号的检测是高灵敏卫星导航接收机的关键所在,被认为是相关领域的研究热点,目前已经有一些成果.文献[1]中提出了基于非相干检测器的微弱GPS(Global Positioning System)卫星信号检测方法,讨论了强、弱信号共存情况下微弱GPS信号的检测,但没有给出其检测概率的理论分析和具体检测门限设定方法;文献[2]阐述了直序扩频通信系统中的信号检测门限设定方法,但没有就某个具体应用领域如卫星导航领域给出验证;文献[3-4]在此基础上对非相干检测器从数学模型和概率统计的角度进行详细理论分析,给出了恒虚警门限确定方法,并给出其检测性能评价,但相关研究都是建立在分析单个微弱卫星信号基础上的.考虑到实际接收到的卫星信号中可能存在强、弱卫星信号共存的情况,如何确立门限并将强、弱卫星信号进行区别捕获成为一个不可忽视的问题.本文首先介绍相关理论知识,包括卫星中频信号模型、相关积分非相干累加检测器的数学模型和概率模型以及传统的检测方法;在此基础上,考虑了多颗能量不同卫星同时存在情况下信号检测模型和门限计算方法,并提出一种考虑远近效应的双门限检测流程;最后,基于模拟器产生的数据和实际采集数据进行实验验证,有效证明了新提出的门限设定方法能够很好适应远近效应的情况,从而解决相关情况下的强、弱信号捕获问题. 1　相关理论1.1　相关积分尧非相干累加检测器一个传统的卫星信号捕获由相关器、平方器和后处理累加器组成,其思想是将输入的中频数字卫星信号进行相关积分和非相干累加.对于微弱卫星信号,往往采用增加相关积分时间和非相干累加次数来提高捕获增益.传统的检测方法将计算出的恒虚警门限和非相干累加器的输出信噪比进行比较,从而判断是否存在卫星.其检测框图如图1所示.图1　相关积分、非相干累加检测框图1.2　传统门限设定方法传统卫星导航接收机的门限设置都是假定获得噪声分布的先验知识,并在此基础上设定一个虚警概率,根据已知的噪声概率密度分布求出所对应的门限,这种设定虚警概率不变的门限设定方法又被称为恒虚警准则[5].具体表示如下:设虚警概率为P fa,则P fa=∫∞γp0(x|H0)d x(1)与此相对应的门限γ即为待求的恒虚警门限.根据N⁃P准则设定恒虚警门限后,其检测概率为P d=∫∞γp1(x|H1)d x(2) 这种方法所设定的门限仅与噪声分布和所设定的虚警概率有关,在设定数字中频信号的采样率为f s,多普勒搜索间隔为N d时,码周期为T c,一个码周期的采样点数K=f s T c,则虚警概率需满足P fa<1K·Nd,适用范围为单个卫星信号检测.在相关积分、非相干累加组合的检测器中,噪声的概率密度函数服从中心χ2分布,其自由度和非相干累加次数密切相关.对于M次非相干累加,其自由度为2M,图2说明了虚警概率,非相干累加次数和由此确立的门限之间的关系.卫星信号的检测器的检测对象是输出信噪比,因此相应的门限也是一个比值的概念.在固定虚警概率为10-2时,非相干累加次数M和门限γ的关系见图2.图2　非相干累加次数和恒虚警门限的关系962　第3期 刘　杨等:考虑互相关干扰的GPS信号捕获门限设定方法由此可见,在虚警概率一定的情况下,门限随着非相干累加次数增大而降低;对于累加次数固定的情况下,虚警概率越低,门限越大.2　考虑互相关干扰的门限设定2.1　强弱信号同时存在时的门限设定当接收到的卫星信号中同时存在强、弱信号时,接收机对信号检测需考虑远近效应的影响.一种比较合理的检测方法是将输入信号进行两次检测,先检测到强信号,然后通过远近效应消除算法去掉强信号的互相关影响,再进行第二次检测,对于通过门限的信号认为是可能存在的弱信号,其检测框图见图3,输入信号经过相关积分、非相干累加运算后与预先计算的门限值γL 和γH 进行比较,然后再采用远近效应消除强信号,对处理后的数据进行二次检测,判断是否还存在弱信号.下面将从检测状态设定、门限确定方法和检测概率比较三方面详细阐述这种门限设定方法的思路.图3　考虑远近效应影响的检测器框图2.1.1　检测状态设定第一次检测时,被检测信号中可能同时存在强、弱信号,此时将非相干累加器输出的待检测量按照不同的门限设定分为3个状态,分别是H 0:没有信号,H u :可能存在弱信号,H 1:存在强信号.其状态函数可以表示为H (x )=H 0　x ≤γLH u γL ≤x ≤γHH 1　x ≥γH⎧⎩⎨⎪⎪(3)其中,γL 设为门限的下限,其作用是判别是否存在信号还是噪声;γH 设为门限的上限,其作用是区别存在强信号和由互相关引起的干扰.对已检测出的强信号,对其进行文献[6]所述的远近效应串行干扰消除方法,然后再进行第二次检测.第二次检测时,待观测量按照门限γ0分为两个状态,即H 0:没有信号,H 1:存在弱信号,并且其状态函数满足:H (x )=H 0　x <γ0H 1x ≥γ0{(4)2.1.2　γL 的确定方法这里设定γL =γ为根据噪声概率密度函数计算出的恒虚警门限,其计算方法如1.2节所述.2.1.3　γH 的确定方法γH 为判断是否存在强信号的门限,此时由于考虑了强、弱信号共同存在的情况,故必须考虑互相关对检测的影响,从而在此基础上确定γH .由于弱信号的能量远小于普通信号,即P w ≪P s ,故仅考虑强信号和本地信号的互相关对捕获产生的影响.当输入信号为强信号时,一个码周期的相关结果可以表示如下:s I =K 2P s DR (Δτ)sinc(πΔf d T c )·cos(Δφ)+ξI(5)s Q =K2P s DR (Δτ)sinc(πΔf d T c )·sin(Δφ)+ξQ (6) 经过非相干检测器后的单次检测结果可以表示为z =s 2I +s 2Q =2P s (KDR (Δτ)sinc(πΔf d T c ))2+ψ(7)式中,R (Δτ)可以表示为R (Δτ)=R auto (Δτ)　自相关函数Rcross (Δτ)　互相关函数{(8)R auto (Δτ)为自相关函数;R cross (Δτ)为强信号和本地其它伪随机码的互相关函数.由于K 和D 可以认为是确定的值,下面分析R (Δτ)sinc(πΔf d T c )对z 的影响:当输入信号功率P s 一定的情况下,R (Δτ)=R cross (Δτ)的取值范围为R (Δτ)=R cross (Δτ)≤65/1023;而sinc (πΔf d T c )的值域为[0,1],且当Δf d =0时,sinc(πΔf d T c )=1.易知此时互相关影响的最大干扰组合为R cross (Δτ)=-65/1023且sinc(πΔf d T c )=1,显然此计算结果将大于噪声平均值;当R (Δτ)=R cross (Δτ)和sinc(πΔf d T c )一定时,P s 越大,最后产生的干扰越大.综合上述情况,设可能存在的输入信号功率集合为{P sposs }互相关产生最大干扰的情况为:P s =max {P sposs },并且(R cross (Δτ)=-65/1023;sinc(πΔf d T c )=1).为了避免互相关对信号检测产生干扰,此时所设定的检测门限应当大于由最大干扰影响的计算结果.把上述互相关干扰也看作是一种“噪声”,其必然也满足一定的概率密度分布,此处认为该分布可以近似认为是非中心参量为λa 的非中心χ2分布,λa =2MN ·65ρin ,ρin =max{P sposs }/σ2,一般可以认为ρin =-19dB;N 为相关积分时间,M 为072北京航空航天大学学报 2011年　非相干累加次数.由此确定的门限γH 满足:P fa =∫∞γH12x λa()M -12exp -12(x +λa )[]I M-1(λa x )d x(9)2.1.4　检测概率比较首先,根据1.2节所述传统门限计算方法,当P fa =10-2,M =25时计算出对应的γL 和γH ,分别为γL =2.56和γH =6.56.假定输入信号的信噪比范围为-39~-19dB,即输入信号的能量范围为-180~-160dBW,相应的检测概率曲线如图4所示.图4　输入信噪比与检测概率关系可见门限γH 可以确保能量比较高的信号具有较高的检测概率.2.1.5　γ0的确定方法γ0的选择决定于如何处理强信号对弱信号的影响.对强信号进行串行干扰消除算法后,最强信号的能量值应当下降,此时由互相关产生的最大检测干扰满足非中心参量为λb 的非中心χ2分布,并且λb 满足:λb =2MN ·65s′in ,s′in 为进行远近效应消除后的最强输入信噪比.由此确定的门限γ0满足:P fa =∫∞γ0x λb()M -12exp -12(x +λb )[]I M -1(λb x )d x(10) 易知λb <λa ,对于理想的情况,即通过远近效应消除后强信号的能量为0,此时s′in ,λb =0,所确定的门限γ0即为γL ;实际情况中,由于存在各种误差因素,通常的远近效应消除算法不可能将强信号全部消除,此时s′in ≠0且s′in <s in .可见,γ0的选取和强信号被消除的程度是密切相关的.令虚警概率P fa =10-2,Δs =s in -s′in 为远近效应消除前后强信号的信噪比变化,当Δs 的输入范围设为1~15dB 时,由s′in 计算出对应的λb ,将其代入式(10)可以计算出对应的γ0,得到图5.由图5可见,γ0随着Δs 的增加而减小.图5　经过远近效应消除后信噪比变化和二次检测门限的关系2.2　双门限检测流程综上所述,可以得到强、弱信号共存时的检测流程,即设定一个低门限γL 和一个高门限γH ,当检测到信噪比小于γL 时判定没有信号;当检测到信噪比大于γH 时判定存在强信号,对已捕获到的强信号进行远近效应消除算法,然后再对剩下的数据进行检测,如果此时检测信噪比大于γ0,则判定存在弱信号;如果此时检测信噪比小于γL ,则判定不存在信号.其具体流程见图6.图6　双门限检测算法流程图3　实验论证本实验中采用相关积分时间N =4ms,非相干检测器的累加次数为M =25,根据文献[7],这种情况下的检测灵敏度约为-177dBW .由恒虚警准则确定的虚警概率P fa =10-2,最强的输入信号为-160dBW .这种情况下可计算出γL =2.56,γH =6.56.分别对卫星中频信号模拟器产生的仿真数据和实际数据进行捕获,将采用原来设定的172　第3期 刘　杨等:考虑互相关干扰的GPS 信号捕获门限设定方法门限和考虑远近效应影响后设定的门限所得效果进行对比,具体结果如下.3.1　仿真数据仿真数据采用文献[8]所述中频卫星信号模拟器产生,分别包括两组,针对一颗弱信号卫星和两颗强、弱信号同时存在的卫星情况,具体参数见表1.表1　仿真数据具体参数仿真数据包含卫星编号信噪比/dB码相位多普勒频率/Hz 数据A3-34409.21250数据B 3-34409.21250 7-19613.820003.1.1　单颗微弱卫星检测对于数据A,当γL=2.56时其检测结果如图7.可见,按照设定的门限能检测到一颗卫星,即3号卫星.图7　仿真数据A,γL=2.563.1.2　强弱卫星信号共存,传统门限检测方法对于数据B,当γL=2.56时其检测结果如图8.由图8可见,由于互相关的影响,除了实际存在的3号和7号卫星之外,超过门限被认为能检测到的卫星编号为:4,18,20,25,26,28,29,32,显然这些信号实际上并不存在.图8　仿真数据B,γL=2.563.1.3　强弱卫星信号共存,本文所述检测方法对于数据B,当γH=6.56时其检测结果如图9.可见此时能检测到的卫星仅为强信号7号卫星.上述结果可以用表2表示.图9　仿真数据B,γH=6.56表2　仿真数据实验结果数据类型检测方法采用门限超过门限卫星数据A传统方法γL=2.563数据B传统方法γL=2.563,4,7,18,20,25,26,28,29,32数据B本文方法γH=6.5673.2　实际数据用中频数字信号采集器采集到的实际信号做为输入信号进行实验,在实验前用历书估计当时位置处可能存在的卫星,得到结果如图10.图10　实际数据可见星列表3.2.1　单颗微弱卫星检测对该数据进行1~32号卫星搜索,并进行单门限检测,得到的结果如图11所示.可见当强、弱卫星信号同时存在时,由于强信号互相关作用的影响,所有的信号都能通过设定的门限γL=2.56,换言之,此时的门限并没有起到区别有无信号的作用.3.2.2　本文所述方法对该数据进行1~32号卫星搜索,进行双门限两次检测,超过门限γH=6.56的卫星如图12所示.将可以检测到的卫星送入跟踪环路,对其相应参数进行进一步跟踪.上述的结果可以用表3表示.272北京航空航天大学学报 2011年　图11　实际数据,γL =2.56图12　实际数据,γH =6.56表3　实际数据实验结果检测方法采用门限超过门限卫星传统检测方法γL =2.561~32本文检测方法γH =6.563,7,13,16,19,21,23,25,313.3　虚警概率分析根据传统的非相干检测器噪声概率密度函数和考虑互相关影响后的概率密度函数,可以得到门限与虚警概率的关系曲线,这里设定非相干检测器的累加次数为M =25.可见,当门限为γL =2.56时,由噪声产生的虚警概率值很低,但是由于互相关的影响其虚警概率非常高,接近于1;而当γH =6.56时,由噪声和互相关影响产生的虚警概率都比较低,可见采用本方法设立门限可以有效降低非相干检测器的虚警概率,与上述实验结果相吻合,如图13所示.图13　非相干检测器门限与虚警概率的关系4　结束语本文针对实际卫星信号捕获强、弱卫星可能同时存在这一问题,在传统的恒虚警门限基础上提出了一种考虑强信号互相关影响的捕获门限计算方法,并结合实际卫星信号检测过程中对远近效应的影响的处理,提出了两次检测双门限的捕获方法.采用模拟数据和实际采集到的卫星中频数据对该方法进行实验,证明在强、弱卫星信号同时存在的情况下,原有门限已无法工作,虚警概率几乎为1;而本文提出的门限设定方法则可有效检测出卫星信号,保持很低的虚警概率.参考文献(References )[1]Psiaki M L.Block acquisition of weak GPS signals in a softwarereceiver[C ]//ION GPS 2001Proceedings.Salt Lake City,Utath:ION,2001:2838-2850[2]Iinatti J H J.On the threshold setting principles in code acquisi⁃tion of DS⁃SS signals [J].IEEE Journal on Selected Areas in Communications,2000,18(1):62-72[3]Borio D.A statistical theory for GNSS signal acquisition[D].To⁃rino,Italy:Polytecnico di Torino NavSAS Group,2008[4]Shanmugam S K.New enhanced sensitivity detection techniquesfor GPS L1C /A and modernized signal acquisition[D].Cana⁃da:PLAN Laboratory Calgary University,2008[5]Steven M Kay.Fundamentals of statistical signal processing[M].London:Addison Wesley Longman,2001[6]Glennon E P.A review of GPS cross correlation mitigation[C]//The 2004International Symposium on GNSS /GPS.Sydney Aus⁃tralia:[s.n.],2004[7]Jin Tian,Liu Yang.A novel GNSS weak signal acquisition usingwavelet denoising method [C ]//ION NTM2008Proceedings,ION.San Diego USA:[s.n.],2008:303-309[8]Liu Y,Jin T,Li X B,et al.A novel design of software GNSS sig⁃nal simulator[C]//International Conference Communications inComputing .Las vegas USA:[s.n.],2007:111-118[9]Tui J B.Fundamentals of global positioning systems:a software approach[M].New York:John Wiley &Sons,Inc,2000[10]Ziemer R E.Digital communications and spread spectrum sys⁃tems[M].New York:MacMillan,1985[11]Cao X L,Mu R Z,Yan Y P.A novel threshold setting methodfor FFT⁃based GPS acquisition[C]//11th International Confer⁃ence on Computer Modeling and Simulation.Washington,DC:IEEE Computer Society,2009:497-501[12]Jin T,Qin H L,Zhu J J,et al.Real⁃time GPS software receivercorrelator design [C ]//Second International Conference on Communications and Networking in China.Shanghai:Skanghai Jiaotong University,2007:549-553(编　辑:娄　嘉)372　第3期 刘　杨等:考虑互相关干扰的GPS 信号捕获门限设定方法。

读书报告随着汽车整车对发动机的动力性、经济性、环保性及可靠性的要求越来越严格，活塞已发展成为集轻质高强度新材料、异型外圆复合型面、异型销孔等多项新技术于一体的高技术含量的产品，以保证活塞的耐热性、耐磨性、平稳的导向性和良好的密封功能，减少发动机的摩擦功损失，降低油耗、噪声和排放。

为满足以上的功能要求，通常将活塞的外圆设计成异型外圆(中凸变椭圆)，即垂直于活塞轴线的横剖面为椭圆或修正椭圆，且椭圆度沿轴线方向按一定的规律变化(如图1所示)，椭圆度精度达0.005mm；活塞纵剖面的外轮廓为高次函数的拟合曲线，轮廓精度为0.005～0.01mm；为提高活塞的承载能力，以提高发动机的升功率，通常将高负荷活塞的销孔设计成微内锥型或正应力曲面型(异型销孔),销孔尺寸精度达IT4级，轮廓精度为0.003mm。

活塞作为典型的汽车关键零部件，在切削加工方面具有很强的工艺特点。

目前，国内活塞制造行业通常是由通用机床和结合活塞工艺特点的专用设备组成机加工生产线，因此，专用设备就成为活塞切削加工的关键设备，其功能和精度将直接影响最终产品的关键特性的质量指标。

低副是面接触，耐磨损；加上转动副和移动副的接触表面是圆柱面和平面，制造简便，易于获得较高的制造精度。

因此，平面连杆机构在各种机械和仪器中获得广泛应用。

连杆机构的缺点是：低副中存在间隙，数目较多的低副会引起运动累积误差；而且它的设计比较复杂，不易精确地实现复杂地运动规律。

最简单地平面连杆机构是由四个构建组成地，称为平面四杆机构。

它的应用非常广泛，而且是组成多杆机构的基础。

由若干个刚性构件通过低副（转动副、移动副）)联接，且各构件上各点的运动平面均相互平行的机构，又称平面低副机构。

低副具有压强小、磨损轻、易于加工和几何形状能保证本身封闭等优点，故平面连杆机构广泛用于各种机械和仪器中。

与高副机构相比，它难以准确实现预期运动，设计计算复杂。

平面连杆机构中最常用的是四杆机构，它的构件数目最少，且能转换运动。

热能与动力工程Thermal Energy and Power Engineering 材料与能源学院：Institute of Materials and Energy 空调制冷：refrigeration and air conditioning 热传导：thermol conduction 热对流：thermal convection 热辐射：thermal radiation 学生毕业后能胜任现代火力发电厂,制冷与低温工程及相关的热能与动力工程专业的技术与管理工作,并能从事其它能源动力领域的专门技术工作. The graduates may find employment of technology and management in the fields of the Thermal Energy &Power Engineering (TEPE) (TEPE) and and and its its its relevance, relevance, such such as as as modern modern modern power power power plant plant plant or or or the the the Refrigeration Refrigeration and and Cryogenics Cryogenics Engineering (RCE), (RCE), the the graduates may also engaged in the special technique in the fields related to TEPE. 现代空气动力学、流体力学、热力学、水力学以及航空航天工程、水利水电工程、热能工程、流体机械工程都提出了一系列复杂流动问题,其中包括高速流、低速流、管道流、燃烧流、冲击流、振荡流、涡流、湍流、旋转流、多相流等等A A series series series of of of complicated complicated complicated flow flow flow problems problems problems have have have been been been posed posed posed in in in modern modern modern fluid fluid fluid mechanics, mechanics, mechanics, aero aero dynamics, dynamics, thermodynamics, thermodynamics, thermodynamics, and and aeronautical aeronautical and and and aerospace aerospace aerospace engineering, engineering, engineering, water water water conservancy conservancy conservancy and and and hydropower hydropower hydropower engineering, engineering, engineering, heat heat heat energy energy energy engineering, engineering, engineering, fluid fluid machinery engineering, and so on, and they cover high-speed flow, low-speed flow, eddy flow, turbulent flow, burning flow, impact flow, oscillating flow, backflow, and two-phase flow, etc. In the thermal engineering, the studied objects normally are isolated from one another and then we try to analysis the change and interaction, the studied objects isolated is named thermodynamic system. 在热力工程中，通常将研究对象分离出来再分析其变化及（与外界）的相互作用，该对象即热力系统。