高精度、高效率硬支承平衡机测量系统若干关键技术研究
|
摘要
论文基于对硬支承平衡机测量技术发展现状的分析，从完善平衡机振动系统的动力学分析、高效不平衡测量的数据处理方法以及平衡机振动信号模拟生成这三个方面展开研究。
平衡机的测量方程通常从振动微分方程得到，但若将基座振动的影响考虑在内，振动系统微分方程将十分复杂。本文将多体模型方法引入到不平衡振动系统分析中，与微分方程方法相比，同样具有高精度下具有较小的计算量，同时能够详细得到各部分的状态量。
现有各种不平衡振动信号处理方法的不平衡提取精度非常依赖于样本数据的长度，影响平衡效率尤其是低速动平衡的效率，针对这一问题本文提出了基于残差MUSIC谱分析的不平衡信号处理方法。MUSIC谱内含对信号组成成分和结构特征的建模和预测，具有很高的频率分辨率。通过遍历匹配信号的幅值和相位求取残差的MUSIC谱极小值的方法，利用较少的数据样本即可以得到满足精度要求的不平衡信号的幅值和相位。采用该方法对现场采样振动信号进行了提取，并与相关滤波法的提取结果进行了对比，结果表明该方法具有较高提取的精度和良好的重复性。
探索了采用AR预测模型对采样振动信号进行预测和延拓，增加有效数据样本的方法。将其应用到基于残差MUSIC谱分析法提取不平衡信号的方法中，可以进一步缩短对信号长度的要求。数据仿真验证了该处理方法的有效性。同时也对现场平衡机信号进行了提取，能够在有限长度内准确提取出不平衡信号的幅值和相位。
针对一直以来无法独立评估平衡机测量系统性能、无法有效评价各种不平衡振动信号处理方法的问题，探索了对不平衡振动信号进行数字模拟建立不平衡振动信号库的可能性。在分析干扰源并对其进行频域分析和功率谱分析的基础上，建立了用于估计平衡机振动信号功率谱的AR模型，给出了阶数选取的依据并进行了实验对比。采用改进的协方差法求解了该功率谱模型的参数。由Ziggurat方法生成的高斯白噪声信号通过该AR功率谱模型完成对传感器输出信号的数字仿真。实验对比了仿真信号与实际振动传感器输出信号的功率谱，结果表明仿真信号与传感器信号具有很强的相似性。
研制了高精度通用硬支承动平衡机测量系统。系统采用嵌入式结构，基于linux系统的人机交互编程，用户界面友好，系统稳定性强，具有较好的扩展能力。系统的最小可达剩余不平衡量为0.1μm，一次不平衡降低率为95%，满足高精度机床主轴等旋转机械的动平衡试验要求。
Considering the high efficacy and general feature, hard-bearingbalancing machine has advantages over soft-bearing one in unbalancingmeasurement. These advantages are from its vibration responseequivalent to static force when ignoring the rotor’s inertia. In the presentresearch, vibration response is analyzed by the establishment of dynamicdifferential equation. To obtain distinct physical-mathematical equation,these analyses do not involve the influence of the base. In the thesis, themulti-body dynamic model, comprising the mass and rigidity of the base,is introduced to comprehensively analyze vibration response ofunbalancing machine. Besides lower computational complexity, thismethod can get more vibration information of unbalancing machine andprovide theoretical evidences for designing the base of the balancingmachine。
The extraction efficacy and precision of unbalancing signal is limitedby the length of the sampling data. MUSIC spectrum based on residualerror, which can predict the element and structure of the unknown signal,is presented to improve this problem. The amplitude and phase of theunbalancing signal can be determined after matching signal retrieval. Theexperiment results validate this proposed method could improve theextraction precision of unbalancing signal from the limited lengthsampling signal.
To further improve extraction precision of unbalancing signal fromshorter data, AR model is adopted to predict and extend the shorter signal,with the result of expanding useful information of the specimen. Then the above MUSIC spectrum is used to separate unbalancing signal from thepredicted signal. The final experiment results show the effectiveness ofthis method in terms of shorter sampling data.
There are various processing methods to extract unbalancing signal,but lacking of a criterion to evaluate their effectiveness. Especially, thereis short evaluation method of performance of the measurement system ofbalancing machine. A new method is proposed to simulate the vibrationsignal of the balancing machine. Based on analyzing the disturbancesources, the AR power model of vibration signal is built, and the principleof AR order is proposed. Then the improved covariance method isapplied to estimate the parameters of power model. Vibration signal canbe obtained after the built Gauss white noise goes through this AR powermodel. Experiments results show the effectiveness of this simulatedvibration signal.
Finally, a hard-bearing balancing prototype machine is realized. Thisdesigned unbalancing machine has excellent properties, includinguser-friendly interface, robust stability, great extensibility and highmeasurement precision with0.1μm minimum achievable residual and95%unbalance reduction ratio.
平衡机的测量方程通常从振动微分方程得到，但若将基座振动的影响考虑在内，振动系统微分方程将十分复杂。本文将多体模型方法引入到不平衡振动系统分析中，与微分方程方法相比，同样具有高精度下具有较小的计算量，同时能够详细得到各部分的状态量。
现有各种不平衡振动信号处理方法的不平衡提取精度非常依赖于样本数据的长度，影响平衡效率尤其是低速动平衡的效率，针对这一问题本文提出了基于残差MUSIC谱分析的不平衡信号处理方法。MUSIC谱内含对信号组成成分和结构特征的建模和预测，具有很高的频率分辨率。通过遍历匹配信号的幅值和相位求取残差的MUSIC谱极小值的方法，利用较少的数据样本即可以得到满足精度要求的不平衡信号的幅值和相位。采用该方法对现场采样振动信号进行了提取，并与相关滤波法的提取结果进行了对比，结果表明该方法具有较高提取的精度和良好的重复性。
探索了采用AR预测模型对采样振动信号进行预测和延拓，增加有效数据样本的方法。将其应用到基于残差MUSIC谱分析法提取不平衡信号的方法中，可以进一步缩短对信号长度的要求。数据仿真验证了该处理方法的有效性。同时也对现场平衡机信号进行了提取，能够在有限长度内准确提取出不平衡信号的幅值和相位。
针对一直以来无法独立评估平衡机测量系统性能、无法有效评价各种不平衡振动信号处理方法的问题，探索了对不平衡振动信号进行数字模拟建立不平衡振动信号库的可能性。在分析干扰源并对其进行频域分析和功率谱分析的基础上，建立了用于估计平衡机振动信号功率谱的AR模型，给出了阶数选取的依据并进行了实验对比。采用改进的协方差法求解了该功率谱模型的参数。由Ziggurat方法生成的高斯白噪声信号通过该AR功率谱模型完成对传感器输出信号的数字仿真。实验对比了仿真信号与实际振动传感器输出信号的功率谱，结果表明仿真信号与传感器信号具有很强的相似性。
研制了高精度通用硬支承动平衡机测量系统。系统采用嵌入式结构，基于linux系统的人机交互编程，用户界面友好，系统稳定性强，具有较好的扩展能力。系统的最小可达剩余不平衡量为0.1μm，一次不平衡降低率为95%，满足高精度机床主轴等旋转机械的动平衡试验要求。
Considering the high efficacy and general feature, hard-bearingbalancing machine has advantages over soft-bearing one in unbalancingmeasurement. These advantages are from its vibration responseequivalent to static force when ignoring the rotor’s inertia. In the presentresearch, vibration response is analyzed by the establishment of dynamicdifferential equation. To obtain distinct physical-mathematical equation,these analyses do not involve the influence of the base. In the thesis, themulti-body dynamic model, comprising the mass and rigidity of the base,is introduced to comprehensively analyze vibration response ofunbalancing machine. Besides lower computational complexity, thismethod can get more vibration information of unbalancing machine andprovide theoretical evidences for designing the base of the balancingmachine。
The extraction efficacy and precision of unbalancing signal is limitedby the length of the sampling data. MUSIC spectrum based on residualerror, which can predict the element and structure of the unknown signal,is presented to improve this problem. The amplitude and phase of theunbalancing signal can be determined after matching signal retrieval. Theexperiment results validate this proposed method could improve theextraction precision of unbalancing signal from the limited lengthsampling signal.
To further improve extraction precision of unbalancing signal fromshorter data, AR model is adopted to predict and extend the shorter signal,with the result of expanding useful information of the specimen. Then the above MUSIC spectrum is used to separate unbalancing signal from thepredicted signal. The final experiment results show the effectiveness ofthis method in terms of shorter sampling data.
There are various processing methods to extract unbalancing signal,but lacking of a criterion to evaluate their effectiveness. Especially, thereis short evaluation method of performance of the measurement system ofbalancing machine. A new method is proposed to simulate the vibrationsignal of the balancing machine. Based on analyzing the disturbancesources, the AR power model of vibration signal is built, and the principleof AR order is proposed. Then the improved covariance method isapplied to estimate the parameters of power model. Vibration signal canbe obtained after the built Gauss white noise goes through this AR powermodel. Experiments results show the effectiveness of this simulatedvibration signal.
Finally, a hard-bearing balancing prototype machine is realized. Thisdesigned unbalancing machine has excellent properties, includinguser-friendly interface, robust stability, great extensibility and highmeasurement precision with0.1μm minimum achievable residual and95%unbalance reduction ratio.
引文
[1].王汉英,张.,徐锡林,转子平衡技术与平衡机[M].北京:机械工业出版社:1988.
[2].周仁睦,转子动平衡-原理、方法和标准[M].北京:化学工业出版社:1992.
[3].西季柯夫(吴介卿译),转子的动平衡法[M].北京:机械工业出版社:1954.
[4].三轮修三,下.朱.,旋转机械的平衡[M].北京:机械工业出版社:1992.
[5].胡红波,刘志勇,王存堂螺旋桨液压静平衡计算机检测系统研发[A], In中国机械工程学会流体传动与控制分会第六届全国流体传动与控制学术会议[C],中国甘肃兰州,2010; pp59-60-61.
[6].钱立保,蒋义海,螺旋桨修理中的静平衡检验方法研究[J].装备制造技术,2012,(03),pp8-9+28.
[7].龙旭平,螺旋桨静不平衡问题的探讨[J].湖南交通科技,2000,(01),pp55-57.
[8].罗江洪,谢伟,多叶螺旋桨整桨静平衡方法研究[J].中国舰船研究,2007,(03),pp52-55.
[9].张兴奎,张风仪,对螺旋桨静平衡及静平衡试验的思考[J].中国修船,1998,(06),pp10-14.
[10].王存堂,胡红波,刘志勇,船用螺旋桨静平衡计算机检测原理与实验研究[J].船舶工程,2011,(02),pp41-43+52.
[11].侯悦民,季林红,金德闻,小卫星动平衡灵敏度分析[J].中国空间科学技术,2003,(03),pp29-36.
[12].侯悦民,季林红,张晓燕,动平衡对小卫星姿态的影响及配重优化[J].航天制造技术,2002,(03),pp21-26.
[13].Lombard, J.-P.,Jean, P.,Lubrina, P. Calibrated non linear dissipative model of fan bladeddisk[A], In ASME Turbo Expo2010: Power for Land, Sea, and Air, GT2010, June14,2010-June18,2010[C], Glasgow, United kingdom,2010; pp705-713.
[14].Van der Wijk, V.,Demeulenaere, B.,Gosselin, C., etc., Comparative Analysis for Low-Massand Low-Inertia Dynamic Balancing of Mechanisms[J]. Journal of Mechanisms and Robotics,2012,4(3).
[15].van der Wijk, V.,Herder, J. L.,Demeulenaere, B., Comparison of various dynamic balancingprinciples regarding additional mass and additional inertia[J]. Journal of Mechanisms andRobotics,2009,1(4),pp1-9.
[16].叶能安,硬支承平衡机的误差分析[J].试验机与材料试验,1986,(01),pp1-6+13+55.
[17].盛德恩,软支承与硬支承动平衡机的测量特点[J].微电机,1995,(02),pp43-46.
[18].盛德恩,刘克华,硬支承平衡机原理误差的消除及新型平衡机的构想[J].制造技术与机床,2004,(07),pp43-46.
[19].曹继光.硬支承平衡机误差分析与提高精度的新方法[D].1988.
[20].De Smidt, H. A. Automatic balancing of bladed-disk/shaft system via passive autobalancerdevices[A], In1801Alexander Bell Drive, Suite500, Reston, VA20191-4344, United States,2010; pp372-386.
[21].Gosiewski, Z., AUTOMATIC BALANCING OF FLEXIBLE ROTORS, PART II:SYNTHESIS OF SYSTEM[J]. Journal of Sound and Vibration,1987,114(1),pp103-119.
[22].Desmidt, H. A.,Jung, D., Automatic balancing of twin co-planar rotors[J]. Journal ofVibration and Acoustics, Transactions of the ASME,2012,134(1).
[23].Kim, J. J.,Agrawal, B. N., Automatic mass balancing of air-bearing-based three-axisrotational spacecraft simulator[J]. Journal of Guidance, Control, and Dynamics,2009,32(3),pp1005-1017.
[24].Lee, C.-W.,Joh, Y.-D.,Kim, Y.-D., Automatic modal balancing of flexible rotors duringoperation. Computer controlled balancing head[J]. Proceedings of the Institution of MechanicalEngineers. Part C. Mechanical engineering science,1990,204(1),pp19-28.
[25].Rodrigues, D. J.,Champneys, A. R.,Friswell, M. I., etc., Automatic two-plane balancing forrigid rotors[J]. International Journal of Non-Linear Mechanics,2008,43(6),pp527-541.
[26].Intelligent low-speed balancing machine for large-scale rotors[R].00266817;1996;
[27].Zhao, D.,Cai, P.,Qi, W. Research on unbalance signal extraction under the constraints of lowoperation speed and limited acquisition time[A], In4th International Conference of Asian Societyfor Precision Engineering and Nanotechnology, ASPEN2011, November16,2011-November18,2011[C], Hong Kong, China,2012; pp618-623.
[28].朱伟清,动力涡轮转子低速动平衡的特点[J].汽轮机技术,2001,(02),pp126-128.
[29].Tan, S. G.,Wang, X. X. Low speed balancing of flexible rotors considering influences ofrunning speeds[A], In Proceedings of the1996International Gas Turbine and AeroengineCongress& Exhibition, June10,1996-June13,1996[C], Burmingham, UK,1996; pp5pp-5pp.
[30].陈争.混沌背景中的小信号检测研究[D].硕士,湘潭大学2008.
[31].董永贵,向莉,多路振动信号的伪同步采样及其在转子动平衡中的应用[J].仪表技术与传感器,2004,(8),p3.
[32].李星辰.正弦弱信号的自适应检测方法的研究[D].硕士,重庆大学2009.
[33].刘健,潘双夏,杨克己, etc.,动平衡机用数字跟踪滤波器实现方法研究[J].仪器仪表学报,2005,(04),pp433-436.
[34].吕元通.窄带跟踪滤波技术的应用研究及硬件电路实现[D].2007.
[35].陶利民,李岳,温熙森,基于开关电容技术的信号跟踪滤波方法及其在转子动平衡中的应用[J].中国机械工程,2007,(04),pp427-430.
[36].陶利民,肖定邦,温熙森,用于动平衡测试的MDAC窄带跟踪滤波器[J].国防科技大学学报,2006,28(2),p5.
[37].Kinney, C. E.,De Callafon, R. A. Adaptive periodic noise cancelation for cooling fans withvarying rotational speed[A], In21st Biennial Conference on Mechanical Vibration and Noise,presented at-2007ASME International Design Engineering Technical Conferences andComputers and Information in Engineering Conference, IDETC/CIE2007, September4,2007-September7,2007[C], Las Vegas, NV, United states,2008; pp269-277.
[38].Delvecchio, S.,D'Elia, G.,Mucchi, E., etc., Advanced signal processing tools for the vibratorysurveillance of assembly faults in diesel engine cold tests[J]. Journal of Vibration and Acoustics,Transactions of the ASME,2010,132(2),pp0210081-02100810.
[39].Podgorski, A.,Charazka, P. An algorithm for estimation of the amplitude and phase of avibration signal used for determination of rotating mass unbalance[A], In IMTC'06-IEEEInstrumentation and Measurement Technology Conference, April24,2006-April27,2006[C],Sorrento, Italy,2006; pp1425-1429.
[40].Lou, S.,Jiang, X.,Scott, P. J., Algorithms for morphological profile filters and theircomparison[J]. Precision Engineering-Journal of the International Societies for PrecisionEngineering and Nanotechnology, Jul,2012,36(3),pp414-423.
[41].Liu, Z.,Wen, J.,He, T. Application of adaptive filtering based on harmonic wavelet in thedynamic unbalance of electro-spindle[A], In International Conference on Measuring Technologyand Mechatronics Automation, ICMTMA2010, March13,2010-March14,2010[C], Changsha,China,2010; pp597-600.
[42].Benitez-Read, E. E. APPLICATION OF ADAPTIVE FILTERING TO BALANCING OFROTATING MACHINES[A], In Conference Proceedings-28th Midwest Symposium on Circuitsand Systems.[C], Louisville, KY, USA,1985; pp776-779.
[43].Wang, X.,Zhang, B.,Zhang, D., etc., Application of artificial neural networks in rotorbalancing[J]. Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society ofElectrical Engineering,1998,18(4),pp262-266.
[44].Chang, X.,Zhang, X.,Zhang, Q. A method of phase estimation for sinusoid signal based oncorrelation algorithm[A], In International Conference on Space Information Technology2009,November26,2009-November27,2009[C], Beijing, China,2010; p China Academy of SpaceTechnology; The Second Acad. China Aerosp. Sci. Ind. Corp.; Huazhong University of Scienceand Technology.
[45].Bailin, H.,Lianming, S. Instrumentation model and data processing of tire dynamic balanceusing multi-sensors[A], In3rd International Conference on Innovative Computing Informationand Control, ICICIC'08, June18,2008-June20,2008[C], Dalian, Liaoning, China,2008.
[46].Zheng, J.,Li, M.,Chen, Q., etc. Extraction of unbalance signals from miniature-rotor dynamicbalancing machine[A], In Proceedings of the second International Symposium on InstrumentationScience and Technology, August18,2002-August22,2002[C], Jinan, China,2002; pp3/507-3/511.
[47].Qin, P.,Cai, P., Extracting dynamic balancing signal based on improved empirical modedecomposition[J]. Yi Qi Yi Biao Xue Bao/Chinese Journal of Scientific Instrument,2007,28(1),pp103-107.
[48].杨浩,李星辰,罗建,自适应正弦数字滤波在微弱信号提取中的研究[J].压电与声光,2010,32(4).
[49].王培一.用开关电容滤波器(SCF)实现跟踪滤波的研究[D].1988.
[50].王晓雷,鲁墨武,庞耀宗, etc.,相敏检波法在硬支承动平衡检测中的应用[J].沈阳航空工业学院学报,2008,(03),pp41-43.
[51].杨健,周保堂,微速差双转子系统振动信号分离法研究[J].中国机械工程,2002,13(8),p4.
[52].鲁顺昌,开关电容带通滤波器设计原理[J].西华大学学报(自然科学版),2006,(05),pp51-53+106-107.
[53].杨克己,基于谐波小波的自适应滤波在高精度动平衡检测系统中的应用[J].仪器仪表学报,2005,26(8),p3.
[54].郑建彬,田春仿,基于离散小波变换的动平衡机不平衡量提取算法研究[J].测控技术,2002,(08),pp21-23+26.
[55].郑建彬,基于DFT的动平衡机不平衡量提取算法[J].武汉理工大学学报(交通科学与工程版),2002,(03),pp318-320.
[56].吴少波,陆秋海,积分型数字跟踪滤波法及其在转子动平衡中的应用[J].工程力学,2003,20(1),p4.
[57].杨克己,武二永,高精度动平衡测量中自适应滤波技术的应用研究[J].仪器仪表学报,2005,(01),pp32-35+58.
[58].王翠珍,唐金元,对称RC双T网络在选频放大电路中的应用[J].科技信息,2010,(31).
[59].郑建彬,凌玲,朱丹,动平衡机数字带通滤波器设计[J].武汉汽车工业大学学报,1998,(03),pp44-47.
[60].秦鹏,蔡萍,改进经验模态分解在动平衡信号提取中的应用[J].仪器仪表学报,2007,(01),pp103-107.
[61].Zhou, C.-G.,Haber, F.,Jaggard, D. L., Resolution threshold of MUSIC with unknownspatially colored noise[J]. IEEE Transactions on Signal Processing,1993,41(1),pp511-516.
[62].Cai, T.,Duan, S.-X.,Liu, B.-Y., etc., Real-valued MUSIC algorithm for power harmonics andinterharmonics estimation[J]. International Journal of Circuit Theory and Applications,2011,39(10),pp1023-1035.
[63].Liu, Z.,Liao, G. Detection of the number of signal sources utilizing MUSIC spectrumuniformity[A], In2011IEEE International Conference on Signal Processing, Communications andComputing, ICSPCC2011, September14,2011-September16,2011[C], Xi'an, China,2011; pIEEE Xi'an Section; IEEE Hong Kong Section; Northwestern Polytechnical University; XidianUniversity; Xi'an Jiaotong University.
[64].朱晓农,国产平衡机的现状与发展预测[J].试验技术与试验机,1997,(Z2),pp10-20.
[65].Jiang, X.,Jiang, Y.,Wang, Y., etc., Non-Markovian decay of a three-level Λ-type atom in aphotonic-band-gap reservoir[J]. Physical Review A,2006,73(3),p033802.
[66].池哲儒,黄风雷,产生任意幅值分布随机信号的方法[J].试验机与材料试验,1987,(06),pp7-13.
[67].杨志东,丛大成,韩俊伟, etc.,基于扩展型准牛顿优化算法的单轴正弦扫频振动控制[J].振动与冲击,2008,(03),pp99-103+112+182-183.
[68].杨志东.液压振动台振动环境模拟的控制技术研究[D].博士,哈尔滨工业大学2009.
[69].Yang, Z.,Huang, Q.,Han, J., etc., Adaptive inverse control of random vibration based on thefiltered-X LMS algorithm[J]. Earthquake Engineering and Engineering Vibration,2010,9(1),pp141-146.
[70].孙宁,李瑰贤,随机振动信号的一种简单模拟计算方法[J].振动与冲击,2000,(02),pp52-53+65+96.
[71].孙宁,李瑰贤,一种能实现变刚度特性的新型抗振冲机构设计[J].机械设计,2000,(07),pp16-19+48.
[72].施毅坚,具有特定功率谱形式的随机信号数字模拟[J].南京航空航天大学学报,1991,(04),pp135-139.
[73].罗海坤,吴嗣亮,王永庆,基于改进ziggurat算法的高斯白噪声发生器[J].系统工程与电子技术,2011,(04),pp879-883.
[74].何志华,一种高效率的随机信号发生器[J].计算机仿真,2010,(10),pp321-325.
[75].樊昊.数字随机信号发生的研究[D].硕士,南京理工大学2006.
[76].Qin, P.,Cai, P.,Hu, Q., etc. A novel vibration structure for dynamic balancingmeasurement[A], In Third International Symposium on Precision Mechanical Measurements,August2,2006-August6,2006[C], Xinjiang, China,2006; pp Int. Committee on Measurementsand Instrumentation, ICMI; National Natural Science Foundation of China, China; ChineseSociety for Measurement, China.
[77].Zhao, D.,Cai, P. Permanent calibration in high frequency ratio (0.3) dynamic unbalancemeasurement[A], In2012International Workshop on Information and Electronics Engineering,IWIEE2012, March10,2012-March11,2012[C], Harbin, China,2012; pp4278-4281.
[78].Qin, P.,Cai, P.,Hu, Q., etc., Virtual vibration system for dynamic balancing measurement byinstantaneous motion center[J]. Jixie Gongcheng Xuebao/Chinese Journal of MechanicalEngineering,2006,42(10),pp209-214.
[79].Zhao, D.,Qin, P.,Cai, P., Research on a novel vibration system for dynamic balancingmeasurement based on flexure hinge mechanism[J]. Key Engineering Materials,2008,381-382pp121-124.
[80].叶能安,余.,动平衡原理与动平衡机[M].武汉:华中工学院出版社:1985.
[81].Kang, Y.,Tseng, M.-H.,Wang, S.-M., etc., An accuracy improvement for balancingcrankshafts[J]. Mechanism and Machine Theory,2003,38(12),pp1449-1467.
[82].Zhou, S.,Shi, J., Active balancing and vibration control of rotating machinery: A survey[J].Shock and Vibration Digest,2001,33(5),pp361-371.
[83].Yu, Y.-Q.,Lin, J. Active balancing of a flexible linkage with redundant drives[A], In ASME2002International Design Engineering Technical Conferences and Computers and Information inEngineering Conference, IDETC/CIE2002, September29,2002-October2,2002[C], Montreal,QC, Canada,2002; pp165-170.
[84].Arias-Montiel, M.,Silva-Navarro, G. Active unbalance control in an asymmetrical rotorsystem using a suspension with linear actuators[A], In Active and Passive Smart Structures andIntegrated Systems2010, March8,2010-March11,2010[C], San Diego, CA, United states,2010;pp The Society of Photo-Optical Instrumentation Engineers (SPIE); American Society ofMechanical Engineers.
[85].Chaesil, K.,Yoon Gyo, J.,Soo Yong, C., etc. Vibration control simulation for a multi-bodyhigh speed flexible rotor model using a phase adjusting method[A], In ICCAS-SICE,2009[C],18-21Aug.2009,2009; pp2286-2290.
[86].Wang, Y.-Y.,Yu, Z.-P.,Jin, X.-X., Validation of multi-body dynamic model for full vehicle[J].Jisuan Lixue Xuebao/Chinese Journal of Computational Mechanics,2011,28(1),pp59-62.
[87].Theodossiades, S.,Teodorescu, M.,Rahnejat, H., From multi-body to many-body dynamics[J].Proceedings of the Institution of Mechanical Engineers, Part C: Journal of MechanicalEngineering Science,2009,223(12),pp2835-2847.
[88].Zhang, G.,Lu, N.,Che, R. Dynamic analysis on rigid-flexible coupled multi-body system witha few flexible components[A], In2011International Conference on Quality, Reliability, Risk,Maintenance, and Safety Engineering, ICQR2MSE2011, June17,2011-June19,2011[C], Xi'an,China,2011; pp1010-1015.
[89].Shao, K.,Liu, C.,Bi, F., etc. Vibrating simulation of diesel engine based on multi-bodydynamics[A], In2011International Conference on Civil Engineering and Transportation, ICCET2011, October14,2011-October16,2011[C], Jinan, China,2011; pp706-711.
[90].Jerkovsky, W. System theory aspects of multi-body dynamics[A], In Decision and Controlincluding the17th Symposium on Adaptive Processes,1978IEEE Conference on[C], Jan.1978,1978; pp348-359.
[91].Li, H.,Fu, S.,Xiang, C., Multi-body dynamics simulation of a tracked vehicle power train inconsideration of multi-source excitations[J]. International Journal of Computational IntelligenceSystems,2011,4(3),pp314-320.
[92].Zhou, S.,Xie, Y.,Xie, J., etc., Dynamic response analysis of heavy-load depressed center flatbased on multi-body dynamics simulation[J]. Jixie Gongcheng Xuebao/Journal of MechanicalEngineering,2011,47(18),pp110-114.
[93].Li, J. Z.,Tan, S. H. N.,Cheong, C. H., etc. Multi body solid dynamic model and its applicationin human kinematic analysis[A], In5th IASTED International Conference on Biomechanics,BioMech2007, August20,2007-August22,2007[C], Honolulu, HI, United states,2007; pp48-51.
[94].Gao, F.,Yap, F. F.,Yan, Y. Modeling of hard disk drives for vibration analysis using aflexible multi-body dynamics formulation[A], In Asia-Pacific Magnetic Recording Conference,2004. APMRC2004[C],16-19Aug.2004,2004; pp38-39.
[95].Hale-Heighway, B.,Murray, C.,Douglas, S., etc., Multi-body dynamic modelling ofcommercial vehicles[J]. Computing&Control Engineering Journal,2002,13(1),pp11-15.
[96].Song, F.-z.,Shao, H.-y.,Song, B. Control of Rotor Unbalance Vibration with MagneticDynamic Absorber[A], In Control and Automation,2007. ICCA2007. IEEE InternationalConference on[C], May302007-June12007,2007; pp329-331.
[97].Sun, L.,Hang, B., Dynamic balance instrumentation of automobile tire[J]. ICIC ExpressLetters,2009,3(4),pp1287-1292.
[98].Arakelian, V.,Dahan, M., Dynamic balancing of mechanisms[J]. Mechanics ResearchCommunications,2000,27(1),pp1-6.
[99].Chen, M.,Ma, J.-S.,Gao, Y., Application of finite segment method to multi-body dynamicanalysis of automatic arms[J]. Zhendong yu Chongji/Journal of Vibration and Shock,2008,27(7),pp158-160.
[100]. Jonghoon, P.,Wan-Kyun, C.,Youngil, Y. Geometric numerical integration algorithms forarticulated multi-body systems[A], In Intelligent Robots and Systems,2004.(IROS2004).Proceedings.2004IEEE/RSJ International Conference on[C],28Sept.-2Oct.2004,2004; pp3803-3808vol.4.
[101]. Kim, C.,Jung, Y. G.,Cho, S. Y., etc. Vibration control simulation for a multi-body highspeed flexible rotor model using a phase adjusting method[A], In ICROS-SICE International JointConference2009, ICCAS-SICE2009, August18,2009-August21,2009[C], Fukuoka, Japan,2009; pp2286-2290.
[102].芮筱亭，贠来峰，陆毓琪，何斌，王国平,多体系统传递矩阵法及其应用[M].北京:科学出版社:2008.
[103]. Su, W.,Ni, J.,Liu, G., etc. The effect of channel mismatch on the spatial spectrum andresolution ability of MUSIC algorithm[A], In Radar,1996. Proceedings., CIE InternationalConference of[C],8-10Oct1996,1996; pp96-99.
[104]. Zhiguo, L.,Guisheng, L. Detection of the number of signal sources utilizing MUSICspectrum uniformity[A], In Signal Processing, Communications and Computing (ICSPCC),2011IEEE International Conference on[C],14-16Sept.2011,2011; pp1-4.
[105]. Jinlin, N. Bearing (frequency) estimation via MUSIC spectrum estimator withouteigendecomposition[A], In Circuits and Systems,1992. ISCAS '92. Proceedings.,1992IEEEInternational Symposium on[C],10-13May1992,1992; pp1463-1466vol.3.
[106]. Chen, J.-f.,Ma, H. An accurate real-time algorithm for spectrum peaks search in2DMUSIC[A], In Multimedia Technology (ICMT),2011International Conference on[C],26-28July2011,2011; pp3385-3388.
[107].王燕,吴昕,变频调速系统应用中共模干扰问题及其分析模型[J].电力电子技术,2007,(12),pp51-53+78.
[108].赵磊.伺服及变频驱动环境下测试系统抗干扰理论和方法研究[D].硕士,天津理工大学2009.
[109].孟进,马伟明,张磊, etc., PWM变频驱动系统传导干扰的高频模型[J].中国电机工程学报,2008,(15),pp141-146.
[110]. Xinwei, C.,Shengcai, J.,Shishan, Q., etc. An improved correlation method of phasedifference detection between two signals in polarimetric radar signal processing system[A], InMicrowave Conference,2009. APMC2009. Asia Pacific[C],7-10Dec.2009,2009; pp469-472.
[111]. Pop, S.,Pitica, D.,Ciascai, I. A Correlation Method for Improving Temperature SensorsMeasurements[A], In Electronics Technology,30th International Spring Seminar on[C],9-13May2007,2007; pp342-345.
[112]. Miao, B.,Zane, R.,Maksimovic, D. A modified cross-correlation method for systemidentification of power converters with digital control[A], In Power Electronics SpecialistsConference,2004. PESC04.2004IEEE35th Annual[C],20-25June2004,2004; pp3728-3733Vol.5.
[113]. Tseng, B. D. A modified discrete fourier transform with a doubled frequencyresolution[A], In34th Asilomar Conference, October29,2000-November1,2000[C], PacificGrove, CA, United states,2000; pp190-191.
[114]. Samant, A.,Shearman, S., High-resolution frequency analysis with a small data record[J].Spectrum, IEEE,1999,36(9),pp82-86.
[115]. Pal, S.,Beheshti, S. A New Look at Frequency Resolution in Power Spectral DensityEstimation[A], In Computational Intelligence in Image and Signal Processing,2007. CIISP2007.IEEE Symposium on[C],1-5April2007,2007; pp88-94.
[116]. Gu, H., Frequency resolution and estimation of AR spectral analysis[J]. IEEETransactions on Signal Processing,1993,41(1),pp432-436.
[117]. Angrisani, L.,Baccigalupi, A.,D'Arco, M., Evaluating phase noise power spectrum withvariable frequency resolution[J]. IEEE Transactions on Instrumentation and Measurement,2004,53(3),pp685-691.
[118]. Wax, M., ORDER SELECTION FOR AR MODELS BY PREDICTIVELEAST-SQUARES[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing,1988,36(4),pp581-588.
[119]. Tanii, H.,Kuramoto, K.,Nakajima, H., etc. A fuzzy logic approach to predict humanbody weight based on AR model[A], In2011IEEE International Conference on Fuzzy Systems,FUZZ2011, June27,2011-June30,2011[C], Taipei, Taiwan,2011; pp1022-1025.
[120]. Li, X. Modeling and predicting total electron content by semi-parametric autoregressive(AR) model[A], In2011International Conference on Advanced Materials and EngineeringMaterials, ICAMEM2011, November22,2011-November24,2011[C], Shenyang, Liaoning,China,2012; pp705-709.
[121]. Khorshidi, S.,Karimi, M.,Towhidi, M., etc. Optimal autoregressive (AR) model orderselection in the sense of predictive error[A], In201018th Iranian Conference on ElectricalEngineering, ICEE2010, May11,2010-May13,2010[C], Isfahan, Iran,2010; pp140-144.
[122]. Khorshidi, S.,Karimi, M.,Nematollahi, A. R., New autoregressive (AR) order selectioncriteria based on the prediction error estimation[J]. Signal Processing,2011,91(10),pp2359-2370.
[123]. Grabowski, D. Application of time-frequency representations to classification ofvibration signals of electric motors[A], In Sixth International Conference on VibrationMeasurements by Laser Techniques: Advances and Applications, June22,2004-June25,2004[C], Ancona, Italy,2004; pp143-152.
[124]. Hong, Y. X.,Jing, X.,Feng, C. Z. Precision spectrum analysis of the grinding wheelunbalanced signal[A], In2010International Conference on Computer, Mechatronics, Control andElectronic Engineering, CMCE2010, August24,2010-August26,2010[C], Changchun, China,2010; pp249-252.
[125]. Zerubia, J.,Alengrin, G., Estimation of ARMA(p, q) parameters[J]. Signal Processing,1991,22(1),pp53-60.
[126]. Ortigueira, M. D., A three step algorithm for ARMA modeling[J]. Signal Processing,1988,15(1),pp23-30.
[127]. Kowalski, A.,Szynal, D., An optimal prediction in general ARMA models[J]. Journal ofMultivariate Analysis,1990,34(1),pp14-36.
[128]. Kizilkaya, A.,Kayran, A. H., ARMA model parameter estimation based on theequivalent MA approach[J]. Digital Signal Processing,2006,16(6),pp670-681.
[129]. Yuan, J.-T.,Lee, H.-H. Autoregressive spectral estimation based on asymmetrictwo-sided prediction[A], In20079th International Symposium on Signal Processing and itsApplications, ISSPA2007, Febrary12,2007-Febrary15,2007[C], Sharjah, United arab emirates,2007.
[130]. Reddy, N. S.,Swamy, M. N. S., HIGH-RESOLUTION FORMANT EXTRACTIONFROM LINEAR-PREDICTION PHASE SPECTRA[J]. IEEE Transactions on Acoustics, Speech,and Signal Processing,1984, ASSP-32(6),pp1136-1144.
[131]. Schoen, M. P.,Chinvorarat, S.,Kaur, B. S. K., etc. Predictive intelligent filter design insignal processing using AR and ARMA models[A], In2004ASME International MechanicalEngineering Congress and Exposition, IMECE, November13,2004-November19,2004[C],Anaheim, CA, United states,2004; pp457-462.
[132]. Gallego, A.,Carrion, M. C.,Ruiz, D. P., etc., Relationship between AR-modellingbispectral estimation and the theory of linear prediction[J]. Signal Processing,1994,37(3),pp381-388.
[133].叶建华.多点激励随机振动试验控制技术及实现的研究[D].2004.
[134].刘小勇.振动系统的实时信号处理与控制[D].2003.
[135].关广丰,丛大成,韩俊伟, etc.,随机振动功率谱复现迭代算法的研究[J].地震工程与工程振动,2006,26(6),p6.
[136]. J.S. Bendat, A. G. P.,相关分析和谱分析的工程应用[M].北京:国防工业出版社:1983; p187.
[137]. Poulimenos, A. G.,Fassois, S. D., Parametric time-domain methods for non-stationaryrandom vibration modelling and analysis—A critical survey and comparison[J]. MechanicalSystems and Signal Processing,2006,20(4),pp763-816.
[138]. Modak, S. V.,Rawal, C.,Kundra, T. K., Harmonics elimination algorithm for operationalmodal analysis using random decrement technique[J]. Mechanical Systems and Signal Processing,2010,24(4),pp922-944.
[139]. Braun, S., Random data: Analysis and measurement procedures: J. S. Bendat and A. G.Piersol,2nd edition,566pages, John Wiley, New York,1986[J]. Mechanical Systems and SignalProcessing,1987,1(1),p135.
[140]. Shen, H.,Zhang, P.,Wang, K., Improved linear congruential random numbergenerators[J]. Qinghua Daxue Xuebao/Journal of Tsinghua University,2009,49(2),pp191-193.
[141]. Ahn, B. Study on a high-speed Gaussian random number generator[A], In Proceedingsof the1996IEEE Asia Pacific Conference on Circuits and Systems, November18,1996-November21,1996[C], Seoul, South Korea,1996; pp30-32.
[2].周仁睦,转子动平衡-原理、方法和标准[M].北京:化学工业出版社:1992.
[3].西季柯夫(吴介卿译),转子的动平衡法[M].北京:机械工业出版社:1954.
[4].三轮修三,下.朱.,旋转机械的平衡[M].北京:机械工业出版社:1992.
[5].胡红波,刘志勇,王存堂螺旋桨液压静平衡计算机检测系统研发[A], In中国机械工程学会流体传动与控制分会第六届全国流体传动与控制学术会议[C],中国甘肃兰州,2010; pp59-60-61.
[6].钱立保,蒋义海,螺旋桨修理中的静平衡检验方法研究[J].装备制造技术,2012,(03),pp8-9+28.
[7].龙旭平,螺旋桨静不平衡问题的探讨[J].湖南交通科技,2000,(01),pp55-57.
[8].罗江洪,谢伟,多叶螺旋桨整桨静平衡方法研究[J].中国舰船研究,2007,(03),pp52-55.
[9].张兴奎,张风仪,对螺旋桨静平衡及静平衡试验的思考[J].中国修船,1998,(06),pp10-14.
[10].王存堂,胡红波,刘志勇,船用螺旋桨静平衡计算机检测原理与实验研究[J].船舶工程,2011,(02),pp41-43+52.
[11].侯悦民,季林红,金德闻,小卫星动平衡灵敏度分析[J].中国空间科学技术,2003,(03),pp29-36.
[12].侯悦民,季林红,张晓燕,动平衡对小卫星姿态的影响及配重优化[J].航天制造技术,2002,(03),pp21-26.
[13].Lombard, J.-P.,Jean, P.,Lubrina, P. Calibrated non linear dissipative model of fan bladeddisk[A], In ASME Turbo Expo2010: Power for Land, Sea, and Air, GT2010, June14,2010-June18,2010[C], Glasgow, United kingdom,2010; pp705-713.
[14].Van der Wijk, V.,Demeulenaere, B.,Gosselin, C., etc., Comparative Analysis for Low-Massand Low-Inertia Dynamic Balancing of Mechanisms[J]. Journal of Mechanisms and Robotics,2012,4(3).
[15].van der Wijk, V.,Herder, J. L.,Demeulenaere, B., Comparison of various dynamic balancingprinciples regarding additional mass and additional inertia[J]. Journal of Mechanisms andRobotics,2009,1(4),pp1-9.
[16].叶能安,硬支承平衡机的误差分析[J].试验机与材料试验,1986,(01),pp1-6+13+55.
[17].盛德恩,软支承与硬支承动平衡机的测量特点[J].微电机,1995,(02),pp43-46.
[18].盛德恩,刘克华,硬支承平衡机原理误差的消除及新型平衡机的构想[J].制造技术与机床,2004,(07),pp43-46.
[19].曹继光.硬支承平衡机误差分析与提高精度的新方法[D].1988.
[20].De Smidt, H. A. Automatic balancing of bladed-disk/shaft system via passive autobalancerdevices[A], In1801Alexander Bell Drive, Suite500, Reston, VA20191-4344, United States,2010; pp372-386.
[21].Gosiewski, Z., AUTOMATIC BALANCING OF FLEXIBLE ROTORS, PART II:SYNTHESIS OF SYSTEM[J]. Journal of Sound and Vibration,1987,114(1),pp103-119.
[22].Desmidt, H. A.,Jung, D., Automatic balancing of twin co-planar rotors[J]. Journal ofVibration and Acoustics, Transactions of the ASME,2012,134(1).
[23].Kim, J. J.,Agrawal, B. N., Automatic mass balancing of air-bearing-based three-axisrotational spacecraft simulator[J]. Journal of Guidance, Control, and Dynamics,2009,32(3),pp1005-1017.
[24].Lee, C.-W.,Joh, Y.-D.,Kim, Y.-D., Automatic modal balancing of flexible rotors duringoperation. Computer controlled balancing head[J]. Proceedings of the Institution of MechanicalEngineers. Part C. Mechanical engineering science,1990,204(1),pp19-28.
[25].Rodrigues, D. J.,Champneys, A. R.,Friswell, M. I., etc., Automatic two-plane balancing forrigid rotors[J]. International Journal of Non-Linear Mechanics,2008,43(6),pp527-541.
[26].Intelligent low-speed balancing machine for large-scale rotors[R].00266817;1996;
[27].Zhao, D.,Cai, P.,Qi, W. Research on unbalance signal extraction under the constraints of lowoperation speed and limited acquisition time[A], In4th International Conference of Asian Societyfor Precision Engineering and Nanotechnology, ASPEN2011, November16,2011-November18,2011[C], Hong Kong, China,2012; pp618-623.
[28].朱伟清,动力涡轮转子低速动平衡的特点[J].汽轮机技术,2001,(02),pp126-128.
[29].Tan, S. G.,Wang, X. X. Low speed balancing of flexible rotors considering influences ofrunning speeds[A], In Proceedings of the1996International Gas Turbine and AeroengineCongress& Exhibition, June10,1996-June13,1996[C], Burmingham, UK,1996; pp5pp-5pp.
[30].陈争.混沌背景中的小信号检测研究[D].硕士,湘潭大学2008.
[31].董永贵,向莉,多路振动信号的伪同步采样及其在转子动平衡中的应用[J].仪表技术与传感器,2004,(8),p3.
[32].李星辰.正弦弱信号的自适应检测方法的研究[D].硕士,重庆大学2009.
[33].刘健,潘双夏,杨克己, etc.,动平衡机用数字跟踪滤波器实现方法研究[J].仪器仪表学报,2005,(04),pp433-436.
[34].吕元通.窄带跟踪滤波技术的应用研究及硬件电路实现[D].2007.
[35].陶利民,李岳,温熙森,基于开关电容技术的信号跟踪滤波方法及其在转子动平衡中的应用[J].中国机械工程,2007,(04),pp427-430.
[36].陶利民,肖定邦,温熙森,用于动平衡测试的MDAC窄带跟踪滤波器[J].国防科技大学学报,2006,28(2),p5.
[37].Kinney, C. E.,De Callafon, R. A. Adaptive periodic noise cancelation for cooling fans withvarying rotational speed[A], In21st Biennial Conference on Mechanical Vibration and Noise,presented at-2007ASME International Design Engineering Technical Conferences andComputers and Information in Engineering Conference, IDETC/CIE2007, September4,2007-September7,2007[C], Las Vegas, NV, United states,2008; pp269-277.
[38].Delvecchio, S.,D'Elia, G.,Mucchi, E., etc., Advanced signal processing tools for the vibratorysurveillance of assembly faults in diesel engine cold tests[J]. Journal of Vibration and Acoustics,Transactions of the ASME,2010,132(2),pp0210081-02100810.
[39].Podgorski, A.,Charazka, P. An algorithm for estimation of the amplitude and phase of avibration signal used for determination of rotating mass unbalance[A], In IMTC'06-IEEEInstrumentation and Measurement Technology Conference, April24,2006-April27,2006[C],Sorrento, Italy,2006; pp1425-1429.
[40].Lou, S.,Jiang, X.,Scott, P. J., Algorithms for morphological profile filters and theircomparison[J]. Precision Engineering-Journal of the International Societies for PrecisionEngineering and Nanotechnology, Jul,2012,36(3),pp414-423.
[41].Liu, Z.,Wen, J.,He, T. Application of adaptive filtering based on harmonic wavelet in thedynamic unbalance of electro-spindle[A], In International Conference on Measuring Technologyand Mechatronics Automation, ICMTMA2010, March13,2010-March14,2010[C], Changsha,China,2010; pp597-600.
[42].Benitez-Read, E. E. APPLICATION OF ADAPTIVE FILTERING TO BALANCING OFROTATING MACHINES[A], In Conference Proceedings-28th Midwest Symposium on Circuitsand Systems.[C], Louisville, KY, USA,1985; pp776-779.
[43].Wang, X.,Zhang, B.,Zhang, D., etc., Application of artificial neural networks in rotorbalancing[J]. Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society ofElectrical Engineering,1998,18(4),pp262-266.
[44].Chang, X.,Zhang, X.,Zhang, Q. A method of phase estimation for sinusoid signal based oncorrelation algorithm[A], In International Conference on Space Information Technology2009,November26,2009-November27,2009[C], Beijing, China,2010; p China Academy of SpaceTechnology; The Second Acad. China Aerosp. Sci. Ind. Corp.; Huazhong University of Scienceand Technology.
[45].Bailin, H.,Lianming, S. Instrumentation model and data processing of tire dynamic balanceusing multi-sensors[A], In3rd International Conference on Innovative Computing Informationand Control, ICICIC'08, June18,2008-June20,2008[C], Dalian, Liaoning, China,2008.
[46].Zheng, J.,Li, M.,Chen, Q., etc. Extraction of unbalance signals from miniature-rotor dynamicbalancing machine[A], In Proceedings of the second International Symposium on InstrumentationScience and Technology, August18,2002-August22,2002[C], Jinan, China,2002; pp3/507-3/511.
[47].Qin, P.,Cai, P., Extracting dynamic balancing signal based on improved empirical modedecomposition[J]. Yi Qi Yi Biao Xue Bao/Chinese Journal of Scientific Instrument,2007,28(1),pp103-107.
[48].杨浩,李星辰,罗建,自适应正弦数字滤波在微弱信号提取中的研究[J].压电与声光,2010,32(4).
[49].王培一.用开关电容滤波器(SCF)实现跟踪滤波的研究[D].1988.
[50].王晓雷,鲁墨武,庞耀宗, etc.,相敏检波法在硬支承动平衡检测中的应用[J].沈阳航空工业学院学报,2008,(03),pp41-43.
[51].杨健,周保堂,微速差双转子系统振动信号分离法研究[J].中国机械工程,2002,13(8),p4.
[52].鲁顺昌,开关电容带通滤波器设计原理[J].西华大学学报(自然科学版),2006,(05),pp51-53+106-107.
[53].杨克己,基于谐波小波的自适应滤波在高精度动平衡检测系统中的应用[J].仪器仪表学报,2005,26(8),p3.
[54].郑建彬,田春仿,基于离散小波变换的动平衡机不平衡量提取算法研究[J].测控技术,2002,(08),pp21-23+26.
[55].郑建彬,基于DFT的动平衡机不平衡量提取算法[J].武汉理工大学学报(交通科学与工程版),2002,(03),pp318-320.
[56].吴少波,陆秋海,积分型数字跟踪滤波法及其在转子动平衡中的应用[J].工程力学,2003,20(1),p4.
[57].杨克己,武二永,高精度动平衡测量中自适应滤波技术的应用研究[J].仪器仪表学报,2005,(01),pp32-35+58.
[58].王翠珍,唐金元,对称RC双T网络在选频放大电路中的应用[J].科技信息,2010,(31).
[59].郑建彬,凌玲,朱丹,动平衡机数字带通滤波器设计[J].武汉汽车工业大学学报,1998,(03),pp44-47.
[60].秦鹏,蔡萍,改进经验模态分解在动平衡信号提取中的应用[J].仪器仪表学报,2007,(01),pp103-107.
[61].Zhou, C.-G.,Haber, F.,Jaggard, D. L., Resolution threshold of MUSIC with unknownspatially colored noise[J]. IEEE Transactions on Signal Processing,1993,41(1),pp511-516.
[62].Cai, T.,Duan, S.-X.,Liu, B.-Y., etc., Real-valued MUSIC algorithm for power harmonics andinterharmonics estimation[J]. International Journal of Circuit Theory and Applications,2011,39(10),pp1023-1035.
[63].Liu, Z.,Liao, G. Detection of the number of signal sources utilizing MUSIC spectrumuniformity[A], In2011IEEE International Conference on Signal Processing, Communications andComputing, ICSPCC2011, September14,2011-September16,2011[C], Xi'an, China,2011; pIEEE Xi'an Section; IEEE Hong Kong Section; Northwestern Polytechnical University; XidianUniversity; Xi'an Jiaotong University.
[64].朱晓农,国产平衡机的现状与发展预测[J].试验技术与试验机,1997,(Z2),pp10-20.
[65].Jiang, X.,Jiang, Y.,Wang, Y., etc., Non-Markovian decay of a three-level Λ-type atom in aphotonic-band-gap reservoir[J]. Physical Review A,2006,73(3),p033802.
[66].池哲儒,黄风雷,产生任意幅值分布随机信号的方法[J].试验机与材料试验,1987,(06),pp7-13.
[67].杨志东,丛大成,韩俊伟, etc.,基于扩展型准牛顿优化算法的单轴正弦扫频振动控制[J].振动与冲击,2008,(03),pp99-103+112+182-183.
[68].杨志东.液压振动台振动环境模拟的控制技术研究[D].博士,哈尔滨工业大学2009.
[69].Yang, Z.,Huang, Q.,Han, J., etc., Adaptive inverse control of random vibration based on thefiltered-X LMS algorithm[J]. Earthquake Engineering and Engineering Vibration,2010,9(1),pp141-146.
[70].孙宁,李瑰贤,随机振动信号的一种简单模拟计算方法[J].振动与冲击,2000,(02),pp52-53+65+96.
[71].孙宁,李瑰贤,一种能实现变刚度特性的新型抗振冲机构设计[J].机械设计,2000,(07),pp16-19+48.
[72].施毅坚,具有特定功率谱形式的随机信号数字模拟[J].南京航空航天大学学报,1991,(04),pp135-139.
[73].罗海坤,吴嗣亮,王永庆,基于改进ziggurat算法的高斯白噪声发生器[J].系统工程与电子技术,2011,(04),pp879-883.
[74].何志华,一种高效率的随机信号发生器[J].计算机仿真,2010,(10),pp321-325.
[75].樊昊.数字随机信号发生的研究[D].硕士,南京理工大学2006.
[76].Qin, P.,Cai, P.,Hu, Q., etc. A novel vibration structure for dynamic balancingmeasurement[A], In Third International Symposium on Precision Mechanical Measurements,August2,2006-August6,2006[C], Xinjiang, China,2006; pp Int. Committee on Measurementsand Instrumentation, ICMI; National Natural Science Foundation of China, China; ChineseSociety for Measurement, China.
[77].Zhao, D.,Cai, P. Permanent calibration in high frequency ratio (0.3) dynamic unbalancemeasurement[A], In2012International Workshop on Information and Electronics Engineering,IWIEE2012, March10,2012-March11,2012[C], Harbin, China,2012; pp4278-4281.
[78].Qin, P.,Cai, P.,Hu, Q., etc., Virtual vibration system for dynamic balancing measurement byinstantaneous motion center[J]. Jixie Gongcheng Xuebao/Chinese Journal of MechanicalEngineering,2006,42(10),pp209-214.
[79].Zhao, D.,Qin, P.,Cai, P., Research on a novel vibration system for dynamic balancingmeasurement based on flexure hinge mechanism[J]. Key Engineering Materials,2008,381-382pp121-124.
[80].叶能安,余.,动平衡原理与动平衡机[M].武汉:华中工学院出版社:1985.
[81].Kang, Y.,Tseng, M.-H.,Wang, S.-M., etc., An accuracy improvement for balancingcrankshafts[J]. Mechanism and Machine Theory,2003,38(12),pp1449-1467.
[82].Zhou, S.,Shi, J., Active balancing and vibration control of rotating machinery: A survey[J].Shock and Vibration Digest,2001,33(5),pp361-371.
[83].Yu, Y.-Q.,Lin, J. Active balancing of a flexible linkage with redundant drives[A], In ASME2002International Design Engineering Technical Conferences and Computers and Information inEngineering Conference, IDETC/CIE2002, September29,2002-October2,2002[C], Montreal,QC, Canada,2002; pp165-170.
[84].Arias-Montiel, M.,Silva-Navarro, G. Active unbalance control in an asymmetrical rotorsystem using a suspension with linear actuators[A], In Active and Passive Smart Structures andIntegrated Systems2010, March8,2010-March11,2010[C], San Diego, CA, United states,2010;pp The Society of Photo-Optical Instrumentation Engineers (SPIE); American Society ofMechanical Engineers.
[85].Chaesil, K.,Yoon Gyo, J.,Soo Yong, C., etc. Vibration control simulation for a multi-bodyhigh speed flexible rotor model using a phase adjusting method[A], In ICCAS-SICE,2009[C],18-21Aug.2009,2009; pp2286-2290.
[86].Wang, Y.-Y.,Yu, Z.-P.,Jin, X.-X., Validation of multi-body dynamic model for full vehicle[J].Jisuan Lixue Xuebao/Chinese Journal of Computational Mechanics,2011,28(1),pp59-62.
[87].Theodossiades, S.,Teodorescu, M.,Rahnejat, H., From multi-body to many-body dynamics[J].Proceedings of the Institution of Mechanical Engineers, Part C: Journal of MechanicalEngineering Science,2009,223(12),pp2835-2847.
[88].Zhang, G.,Lu, N.,Che, R. Dynamic analysis on rigid-flexible coupled multi-body system witha few flexible components[A], In2011International Conference on Quality, Reliability, Risk,Maintenance, and Safety Engineering, ICQR2MSE2011, June17,2011-June19,2011[C], Xi'an,China,2011; pp1010-1015.
[89].Shao, K.,Liu, C.,Bi, F., etc. Vibrating simulation of diesel engine based on multi-bodydynamics[A], In2011International Conference on Civil Engineering and Transportation, ICCET2011, October14,2011-October16,2011[C], Jinan, China,2011; pp706-711.
[90].Jerkovsky, W. System theory aspects of multi-body dynamics[A], In Decision and Controlincluding the17th Symposium on Adaptive Processes,1978IEEE Conference on[C], Jan.1978,1978; pp348-359.
[91].Li, H.,Fu, S.,Xiang, C., Multi-body dynamics simulation of a tracked vehicle power train inconsideration of multi-source excitations[J]. International Journal of Computational IntelligenceSystems,2011,4(3),pp314-320.
[92].Zhou, S.,Xie, Y.,Xie, J., etc., Dynamic response analysis of heavy-load depressed center flatbased on multi-body dynamics simulation[J]. Jixie Gongcheng Xuebao/Journal of MechanicalEngineering,2011,47(18),pp110-114.
[93].Li, J. Z.,Tan, S. H. N.,Cheong, C. H., etc. Multi body solid dynamic model and its applicationin human kinematic analysis[A], In5th IASTED International Conference on Biomechanics,BioMech2007, August20,2007-August22,2007[C], Honolulu, HI, United states,2007; pp48-51.
[94].Gao, F.,Yap, F. F.,Yan, Y. Modeling of hard disk drives for vibration analysis using aflexible multi-body dynamics formulation[A], In Asia-Pacific Magnetic Recording Conference,2004. APMRC2004[C],16-19Aug.2004,2004; pp38-39.
[95].Hale-Heighway, B.,Murray, C.,Douglas, S., etc., Multi-body dynamic modelling ofcommercial vehicles[J]. Computing&Control Engineering Journal,2002,13(1),pp11-15.
[96].Song, F.-z.,Shao, H.-y.,Song, B. Control of Rotor Unbalance Vibration with MagneticDynamic Absorber[A], In Control and Automation,2007. ICCA2007. IEEE InternationalConference on[C], May302007-June12007,2007; pp329-331.
[97].Sun, L.,Hang, B., Dynamic balance instrumentation of automobile tire[J]. ICIC ExpressLetters,2009,3(4),pp1287-1292.
[98].Arakelian, V.,Dahan, M., Dynamic balancing of mechanisms[J]. Mechanics ResearchCommunications,2000,27(1),pp1-6.
[99].Chen, M.,Ma, J.-S.,Gao, Y., Application of finite segment method to multi-body dynamicanalysis of automatic arms[J]. Zhendong yu Chongji/Journal of Vibration and Shock,2008,27(7),pp158-160.
[100]. Jonghoon, P.,Wan-Kyun, C.,Youngil, Y. Geometric numerical integration algorithms forarticulated multi-body systems[A], In Intelligent Robots and Systems,2004.(IROS2004).Proceedings.2004IEEE/RSJ International Conference on[C],28Sept.-2Oct.2004,2004; pp3803-3808vol.4.
[101]. Kim, C.,Jung, Y. G.,Cho, S. Y., etc. Vibration control simulation for a multi-body highspeed flexible rotor model using a phase adjusting method[A], In ICROS-SICE International JointConference2009, ICCAS-SICE2009, August18,2009-August21,2009[C], Fukuoka, Japan,2009; pp2286-2290.
[102].芮筱亭，贠来峰，陆毓琪，何斌，王国平,多体系统传递矩阵法及其应用[M].北京:科学出版社:2008.
[103]. Su, W.,Ni, J.,Liu, G., etc. The effect of channel mismatch on the spatial spectrum andresolution ability of MUSIC algorithm[A], In Radar,1996. Proceedings., CIE InternationalConference of[C],8-10Oct1996,1996; pp96-99.
[104]. Zhiguo, L.,Guisheng, L. Detection of the number of signal sources utilizing MUSICspectrum uniformity[A], In Signal Processing, Communications and Computing (ICSPCC),2011IEEE International Conference on[C],14-16Sept.2011,2011; pp1-4.
[105]. Jinlin, N. Bearing (frequency) estimation via MUSIC spectrum estimator withouteigendecomposition[A], In Circuits and Systems,1992. ISCAS '92. Proceedings.,1992IEEEInternational Symposium on[C],10-13May1992,1992; pp1463-1466vol.3.
[106]. Chen, J.-f.,Ma, H. An accurate real-time algorithm for spectrum peaks search in2DMUSIC[A], In Multimedia Technology (ICMT),2011International Conference on[C],26-28July2011,2011; pp3385-3388.
[107].王燕,吴昕,变频调速系统应用中共模干扰问题及其分析模型[J].电力电子技术,2007,(12),pp51-53+78.
[108].赵磊.伺服及变频驱动环境下测试系统抗干扰理论和方法研究[D].硕士,天津理工大学2009.
[109].孟进,马伟明,张磊, etc., PWM变频驱动系统传导干扰的高频模型[J].中国电机工程学报,2008,(15),pp141-146.
[110]. Xinwei, C.,Shengcai, J.,Shishan, Q., etc. An improved correlation method of phasedifference detection between two signals in polarimetric radar signal processing system[A], InMicrowave Conference,2009. APMC2009. Asia Pacific[C],7-10Dec.2009,2009; pp469-472.
[111]. Pop, S.,Pitica, D.,Ciascai, I. A Correlation Method for Improving Temperature SensorsMeasurements[A], In Electronics Technology,30th International Spring Seminar on[C],9-13May2007,2007; pp342-345.
[112]. Miao, B.,Zane, R.,Maksimovic, D. A modified cross-correlation method for systemidentification of power converters with digital control[A], In Power Electronics SpecialistsConference,2004. PESC04.2004IEEE35th Annual[C],20-25June2004,2004; pp3728-3733Vol.5.
[113]. Tseng, B. D. A modified discrete fourier transform with a doubled frequencyresolution[A], In34th Asilomar Conference, October29,2000-November1,2000[C], PacificGrove, CA, United states,2000; pp190-191.
[114]. Samant, A.,Shearman, S., High-resolution frequency analysis with a small data record[J].Spectrum, IEEE,1999,36(9),pp82-86.
[115]. Pal, S.,Beheshti, S. A New Look at Frequency Resolution in Power Spectral DensityEstimation[A], In Computational Intelligence in Image and Signal Processing,2007. CIISP2007.IEEE Symposium on[C],1-5April2007,2007; pp88-94.
[116]. Gu, H., Frequency resolution and estimation of AR spectral analysis[J]. IEEETransactions on Signal Processing,1993,41(1),pp432-436.
[117]. Angrisani, L.,Baccigalupi, A.,D'Arco, M., Evaluating phase noise power spectrum withvariable frequency resolution[J]. IEEE Transactions on Instrumentation and Measurement,2004,53(3),pp685-691.
[118]. Wax, M., ORDER SELECTION FOR AR MODELS BY PREDICTIVELEAST-SQUARES[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing,1988,36(4),pp581-588.
[119]. Tanii, H.,Kuramoto, K.,Nakajima, H., etc. A fuzzy logic approach to predict humanbody weight based on AR model[A], In2011IEEE International Conference on Fuzzy Systems,FUZZ2011, June27,2011-June30,2011[C], Taipei, Taiwan,2011; pp1022-1025.
[120]. Li, X. Modeling and predicting total electron content by semi-parametric autoregressive(AR) model[A], In2011International Conference on Advanced Materials and EngineeringMaterials, ICAMEM2011, November22,2011-November24,2011[C], Shenyang, Liaoning,China,2012; pp705-709.
[121]. Khorshidi, S.,Karimi, M.,Towhidi, M., etc. Optimal autoregressive (AR) model orderselection in the sense of predictive error[A], In201018th Iranian Conference on ElectricalEngineering, ICEE2010, May11,2010-May13,2010[C], Isfahan, Iran,2010; pp140-144.
[122]. Khorshidi, S.,Karimi, M.,Nematollahi, A. R., New autoregressive (AR) order selectioncriteria based on the prediction error estimation[J]. Signal Processing,2011,91(10),pp2359-2370.
[123]. Grabowski, D. Application of time-frequency representations to classification ofvibration signals of electric motors[A], In Sixth International Conference on VibrationMeasurements by Laser Techniques: Advances and Applications, June22,2004-June25,2004[C], Ancona, Italy,2004; pp143-152.
[124]. Hong, Y. X.,Jing, X.,Feng, C. Z. Precision spectrum analysis of the grinding wheelunbalanced signal[A], In2010International Conference on Computer, Mechatronics, Control andElectronic Engineering, CMCE2010, August24,2010-August26,2010[C], Changchun, China,2010; pp249-252.
[125]. Zerubia, J.,Alengrin, G., Estimation of ARMA(p, q) parameters[J]. Signal Processing,1991,22(1),pp53-60.
[126]. Ortigueira, M. D., A three step algorithm for ARMA modeling[J]. Signal Processing,1988,15(1),pp23-30.
[127]. Kowalski, A.,Szynal, D., An optimal prediction in general ARMA models[J]. Journal ofMultivariate Analysis,1990,34(1),pp14-36.
[128]. Kizilkaya, A.,Kayran, A. H., ARMA model parameter estimation based on theequivalent MA approach[J]. Digital Signal Processing,2006,16(6),pp670-681.
[129]. Yuan, J.-T.,Lee, H.-H. Autoregressive spectral estimation based on asymmetrictwo-sided prediction[A], In20079th International Symposium on Signal Processing and itsApplications, ISSPA2007, Febrary12,2007-Febrary15,2007[C], Sharjah, United arab emirates,2007.
[130]. Reddy, N. S.,Swamy, M. N. S., HIGH-RESOLUTION FORMANT EXTRACTIONFROM LINEAR-PREDICTION PHASE SPECTRA[J]. IEEE Transactions on Acoustics, Speech,and Signal Processing,1984, ASSP-32(6),pp1136-1144.
[131]. Schoen, M. P.,Chinvorarat, S.,Kaur, B. S. K., etc. Predictive intelligent filter design insignal processing using AR and ARMA models[A], In2004ASME International MechanicalEngineering Congress and Exposition, IMECE, November13,2004-November19,2004[C],Anaheim, CA, United states,2004; pp457-462.
[132]. Gallego, A.,Carrion, M. C.,Ruiz, D. P., etc., Relationship between AR-modellingbispectral estimation and the theory of linear prediction[J]. Signal Processing,1994,37(3),pp381-388.
[133].叶建华.多点激励随机振动试验控制技术及实现的研究[D].2004.
[134].刘小勇.振动系统的实时信号处理与控制[D].2003.
[135].关广丰,丛大成,韩俊伟, etc.,随机振动功率谱复现迭代算法的研究[J].地震工程与工程振动,2006,26(6),p6.
[136]. J.S. Bendat, A. G. P.,相关分析和谱分析的工程应用[M].北京:国防工业出版社:1983; p187.
[137]. Poulimenos, A. G.,Fassois, S. D., Parametric time-domain methods for non-stationaryrandom vibration modelling and analysis—A critical survey and comparison[J]. MechanicalSystems and Signal Processing,2006,20(4),pp763-816.
[138]. Modak, S. V.,Rawal, C.,Kundra, T. K., Harmonics elimination algorithm for operationalmodal analysis using random decrement technique[J]. Mechanical Systems and Signal Processing,2010,24(4),pp922-944.
[139]. Braun, S., Random data: Analysis and measurement procedures: J. S. Bendat and A. G.Piersol,2nd edition,566pages, John Wiley, New York,1986[J]. Mechanical Systems and SignalProcessing,1987,1(1),p135.
[140]. Shen, H.,Zhang, P.,Wang, K., Improved linear congruential random numbergenerators[J]. Qinghua Daxue Xuebao/Journal of Tsinghua University,2009,49(2),pp191-193.
[141]. Ahn, B. Study on a high-speed Gaussian random number generator[A], In Proceedingsof the1996IEEE Asia Pacific Conference on Circuits and Systems, November18,1996-November21,1996[C], Seoul, South Korea,1996; pp30-32.