车辆的结构—声耦合振动分析及其控制研究
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摘要
车辆乘坐室的振动和噪声问题已成为制约其快速发展的一个重要方面。目前,车辆中振动和噪声信号的特征提取方法以及振动响应的评估手段都还很不成熟,因此深入的研究车辆中振动和噪声信号的特征提取方法以及振动响应的评估手段对车辆中振动和噪声的控制具有重要的理论意义和工程价值。
本文针对车辆工程中NVH的研究内容,对车辆振动和噪声信号的特征提取与结构振动响应的统计估计方法进行了深入的研究,本文研究的主要内容归纳如下:
(1)提出了一种适用于强噪声背景下振动信号特征提取的方法。针对目前应用于车辆中信号的特征提取方法,根据车辆中振动和噪声信号的特点,对它们进行对比研究,提出了一种名为时序多相关-经验模式分解的方法,该方法对强噪声背景下,车辆中非线性、非平稳信号的特征提取具有较好的效果,对信号中混叠的噪声类型和强度没有特别的限制,具有很强的适应性;该方法通过对信号的多相关处理后再做经验模式分解,然后对分解得到的本征模态函数做相关性选择,增加的计算量很小。
(2)提出了一种分析随机质量板振动响应的方法并对其振动响应进行了统计分析。为了分析随机质量板的振动响应,以Lagrange动力学方程和Rayleigh-Ritz能量法为基础,给出了一种计算随机质量板振动响应的分析方法,对其振动响应进行了统计分析,并应用Monte Carlo数值仿真方法进行了验证。
(3)基于本征正交分解方法,提出了相关激励作用时,结构响应的统计估计方法。给出了相关激励作用下,结构响应统计估计的相对偏差的计算表达式,以及相关激励作用下,结构响应统计估计时载荷参数的确定方法。研究表明:响应统计分析与输入激励的相关性及特征频率的相关性直接相关联,随着结构振动频率的增加,响应的相对偏差逐渐减小,考虑激励的相关性及特征频率的相关性得到的相对偏差表达式与试验结果能够更好的吻合。
(4)给出了SEA在复杂耦合系统中的响应统计估计方法及其载荷参数的确定方法。研究结构表明:当有载荷作用在子系统上时,载荷参数与子系统上的输入能量和整个系统的输入能量的比值以及子系统上的载荷参数有关;不相关输入是相关输入时的一种特殊情况,它们可以用统一的表达式来表示。复杂系统响应统计估计的试验表明,考虑相关激励的影响,能够使得计算得到的平均能量与试验值更好的吻合,并且随着频率的增加,相关激励的影响逐渐减弱,并且随着传递路径的增加,子系统响应的相对偏差逐渐增大。
综上所述,本文较系统地研究了车辆NVH中涉及到的两个方面的内容:车辆振动和噪声信号的特征提取以及振动响应的统计估计方法。研究结果对于提高车辆NVH性能,指导车辆NVH设计以及后期修改等方面具有重要的理论意义和工程应用价值。
The vibration and noise problems of passenger compartment in vehicles having been an important restriction for its rapid development. At present, the processing methods of vibration and noise signal and the assessment tools of vibration response in vehicles are still immature. Therefore, the systematical studies on the feature extraction method of vibration and noise signal and the method of the statistical estimation method of vibration response in vehicles has not only important theoretical significance, but also practical value.
For the research of noise, vibration and harshness (NVH) in vehicle, a further study into the feature extraction method of vibration and noise signal and the statistical estimation method of structural vibration response have been made in this paper. The main contents of this paper are summarized as follows:
(1) A novel method for suppressing the strong background noises in the feature extraction of vibration signal is proposed. According to the characteristics of vehicle vibration and noise signal, after comparing some presently applied feature extraction methods, it proposed a new method: multi-correlation of time series and empirical mode decomposition. Which can eliminate the effect of zero-average noise in sampling series, get over the difficulties of frequency identification in the subsequence analysis that caused by strong background noise, protrude the feature components of original signal, is of preferable for nonlinear, non-stationary vibration signals. This method has no special restrictions for the type and strength of noise, and a strong adaptability. After the processing of multi-correlation of time series, it provides a wonderful former data for spectrum analysis; then from using empirical mode decomposition, it can sufficiently put up the needed feature signal, and plus little increase in computational time.
(2) A method which can analyses the vibration response of the variable mass plate is presented. Based on the Lagrange’s dynamics equation and Rayleigh-Ritz energy method, the response analysis method is described and the statistical character is pointed out. It demonstrated the proposed method using Monte Carlo number simulation.
(3) Based on the proper orthogonal decomposition (POD), the statistical estimation method of vibration response, when the correlative excitations acting on the structure, is proposed,and the relative deviation calculation expression and calculation method of load parameters in response statistical estimate is given. The results indicate that the statistical analysis of response is directly connected with the relativity of the input excitation and the correlation of nature frequency, the relative deviation decreases gradually with the increment of vibration frequency, the calculation expression of relative deviation which considered the excitation relativity and correlation of nature frequency can in concordance with the result of experimentation better.
(4) The statistical estimation method of response and the calculation method of load parameters in the complex coupling system which using statistical energy analysis (SEA), The results show that: the load parameters is connected with the ratio of the input energy of the subsystem and the input energy of the whole system, and with the load parameters of the subsystem; the irrelevant excitation is a special case of correlative excitation, they can be expressed in a unified expression. The experiments of complex system response statistical estimation have shown that: considering the correlative excitations, the calculation results of the average energy are better consistent with the result of experiment. With the increment of vibration frequency, the influence of correlative excitation gradually weakened, when the number of transmission paths increased, the relative deviation of subsystem response gradually increased.
In conclusion, the two areas, the feature extraction method of vibration and noise signal and the statistical estimation method of vibration response of NVH in vehicle, are systematically studied in this paper. The results has an important theoretical significance and engineering applications for improving vehicle NVH performance, guiding vehicles NVH designs, as well as the later revisions of the structure.
本文针对车辆工程中NVH的研究内容,对车辆振动和噪声信号的特征提取与结构振动响应的统计估计方法进行了深入的研究,本文研究的主要内容归纳如下:
(1)提出了一种适用于强噪声背景下振动信号特征提取的方法。针对目前应用于车辆中信号的特征提取方法,根据车辆中振动和噪声信号的特点,对它们进行对比研究,提出了一种名为时序多相关-经验模式分解的方法,该方法对强噪声背景下,车辆中非线性、非平稳信号的特征提取具有较好的效果,对信号中混叠的噪声类型和强度没有特别的限制,具有很强的适应性;该方法通过对信号的多相关处理后再做经验模式分解,然后对分解得到的本征模态函数做相关性选择,增加的计算量很小。
(2)提出了一种分析随机质量板振动响应的方法并对其振动响应进行了统计分析。为了分析随机质量板的振动响应,以Lagrange动力学方程和Rayleigh-Ritz能量法为基础,给出了一种计算随机质量板振动响应的分析方法,对其振动响应进行了统计分析,并应用Monte Carlo数值仿真方法进行了验证。
(3)基于本征正交分解方法,提出了相关激励作用时,结构响应的统计估计方法。给出了相关激励作用下,结构响应统计估计的相对偏差的计算表达式,以及相关激励作用下,结构响应统计估计时载荷参数的确定方法。研究表明:响应统计分析与输入激励的相关性及特征频率的相关性直接相关联,随着结构振动频率的增加,响应的相对偏差逐渐减小,考虑激励的相关性及特征频率的相关性得到的相对偏差表达式与试验结果能够更好的吻合。
(4)给出了SEA在复杂耦合系统中的响应统计估计方法及其载荷参数的确定方法。研究结构表明:当有载荷作用在子系统上时,载荷参数与子系统上的输入能量和整个系统的输入能量的比值以及子系统上的载荷参数有关;不相关输入是相关输入时的一种特殊情况,它们可以用统一的表达式来表示。复杂系统响应统计估计的试验表明,考虑相关激励的影响,能够使得计算得到的平均能量与试验值更好的吻合,并且随着频率的增加,相关激励的影响逐渐减弱,并且随着传递路径的增加,子系统响应的相对偏差逐渐增大。
综上所述,本文较系统地研究了车辆NVH中涉及到的两个方面的内容:车辆振动和噪声信号的特征提取以及振动响应的统计估计方法。研究结果对于提高车辆NVH性能,指导车辆NVH设计以及后期修改等方面具有重要的理论意义和工程应用价值。
The vibration and noise problems of passenger compartment in vehicles having been an important restriction for its rapid development. At present, the processing methods of vibration and noise signal and the assessment tools of vibration response in vehicles are still immature. Therefore, the systematical studies on the feature extraction method of vibration and noise signal and the method of the statistical estimation method of vibration response in vehicles has not only important theoretical significance, but also practical value.
For the research of noise, vibration and harshness (NVH) in vehicle, a further study into the feature extraction method of vibration and noise signal and the statistical estimation method of structural vibration response have been made in this paper. The main contents of this paper are summarized as follows:
(1) A novel method for suppressing the strong background noises in the feature extraction of vibration signal is proposed. According to the characteristics of vehicle vibration and noise signal, after comparing some presently applied feature extraction methods, it proposed a new method: multi-correlation of time series and empirical mode decomposition. Which can eliminate the effect of zero-average noise in sampling series, get over the difficulties of frequency identification in the subsequence analysis that caused by strong background noise, protrude the feature components of original signal, is of preferable for nonlinear, non-stationary vibration signals. This method has no special restrictions for the type and strength of noise, and a strong adaptability. After the processing of multi-correlation of time series, it provides a wonderful former data for spectrum analysis; then from using empirical mode decomposition, it can sufficiently put up the needed feature signal, and plus little increase in computational time.
(2) A method which can analyses the vibration response of the variable mass plate is presented. Based on the Lagrange’s dynamics equation and Rayleigh-Ritz energy method, the response analysis method is described and the statistical character is pointed out. It demonstrated the proposed method using Monte Carlo number simulation.
(3) Based on the proper orthogonal decomposition (POD), the statistical estimation method of vibration response, when the correlative excitations acting on the structure, is proposed,and the relative deviation calculation expression and calculation method of load parameters in response statistical estimate is given. The results indicate that the statistical analysis of response is directly connected with the relativity of the input excitation and the correlation of nature frequency, the relative deviation decreases gradually with the increment of vibration frequency, the calculation expression of relative deviation which considered the excitation relativity and correlation of nature frequency can in concordance with the result of experimentation better.
(4) The statistical estimation method of response and the calculation method of load parameters in the complex coupling system which using statistical energy analysis (SEA), The results show that: the load parameters is connected with the ratio of the input energy of the subsystem and the input energy of the whole system, and with the load parameters of the subsystem; the irrelevant excitation is a special case of correlative excitation, they can be expressed in a unified expression. The experiments of complex system response statistical estimation have shown that: considering the correlative excitations, the calculation results of the average energy are better consistent with the result of experiment. With the increment of vibration frequency, the influence of correlative excitation gradually weakened, when the number of transmission paths increased, the relative deviation of subsystem response gradually increased.
In conclusion, the two areas, the feature extraction method of vibration and noise signal and the statistical estimation method of vibration response of NVH in vehicle, are systematically studied in this paper. The results has an important theoretical significance and engineering applications for improving vehicle NVH performance, guiding vehicles NVH designs, as well as the later revisions of the structure.
引文
[1] Dinsmore M L, Saha P, Carey A B, et al. Automotive Noise and Vibration Control Practices in the New Millennium. SAE Paper, 2003-01-1589. 2003.
[2] Dovstam K, Goransson P, Semeniuk B. Mode-Based Prediction of Vibrations in Complex Automotive Structures, a Review of Shortcomings. SAE Paper, 2005-01-2343. 2005.
[3]庞剑;谌刚;何华.汽车噪声与振动:理论与应用.北京:北京理工大学出版社, 2006.
[4]林逸,马天飞,姚为民,等.汽车NVH特性研究综述.汽车工程. 2002, 24(3): 177-181.
[5]姚德源,王其政.统计能量分析原理及其应用.北京:北京理工大学, 1995.
[6] Lyon R H, Dejong R G. Theory and Application of Statistical Energy Analysis, 2nd Ed. Boston: Butterworth-Heinemann, 1995.
[7] Mohammed A D. A study of uncertainty in applications of statistical energy analysis, [dissertation], Southampton: University of Southampton, 1990.
[8] Fahy F J, Mohammed A D. A study of uncertainty in applications of sea to coupled beam and plate systems, part I: Computational experiments. Journal of Sound and Vibration. 1992, 158(1): 45-67.
[9]张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社, 1998.
[10]于德介,程军圣,杨宇.机械故障诊断的Hilbert-Huang变换方法.北京:科学出版社, 2006.
[11]李舜酩,廖庆斌.工程信号处理的研究与发展.江苏省博士后学术大会论文集. 2005, 12: 284-290.
[12]张贤达.时间序列分析——高阶统计量方法.北京:清华大学出版社, 1996.
[13] Swami A, Giannakis G B, Zhou G. Bibliography on higher-order statistics. Signal Processing. 1997, 60(1): 65-126.
[14] Mccormick A C, Nandi A K. Bispectral and trispectral features for machine condition diagnosis. IEE Proceedings of the Vision and Image Signal Process. 1999, 146(5): 229–234.
[15] Fackrell J W, White P R, Hammond J K, et al. The interpretation of the bispectra of vibration signals--: I. Theory. Mechanical Systems and Signal Processing. 1995, 9(3): 257-266.
[16] Fackrell J W, White P R, Hammond J K, et al. The interpretation of the bispectra of vibration signals--: II. Experimental results and applications. Mechanical Systems and Signal Processing. 1995, 9(3): 267-274.
[17]杨江天,陈家骥,曾子平.双谱分析及其在机械诊断中的应用.中国机械工程. 2000, 11(4): 424-426.
[18] Simonovski I G, Boltezar M I, Gradisek J A, et al. Bispectral analysis of the cutting process. Mechanical Systems and Signal Processing. 2002, 16(6): 1093-1104.
[19] Radkowski S, Smalko Z, Pietak A, et al. Use of bispectral analysis in condition monitoring of machinery. Granada, Spain, Proceedings of 3rd European Workshop on Structural Health Monitoring, 2006.
[20] Rypdal K, Oynes F. Bispectral analysis: A tool for diagnosing nonlinear coherence in turbulence. Physics Letters A. 1993, 184(1): 114-118.
[21]舒红宇,熊木权.车辆减振器噪声诊断的双谱分析法.重庆大学学报(自然科学版). 2005, 28(3): 1-3.
[22] Hillis A J, Neild S A, Drinkwater B W, et al. Global crack detection using bispectral analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2006, 462(2069): 1515–1530.
[23] Murray A, Penman J. Extracting useful higher order features for condition monitoring using artificial neural networks. IEEE Transactions on Signal Processing. 1997, 45(11): 2821–2828.
[24] Fitzpatrick J A, Rice H J. Equivalent time domain procedures for bispectral analysis. Journal of Sound and Vibration. 1990, 137(1): 131-134.
[25] Lutes L D, Chen D C. Trispectrum for the response of a non-linear oscillator. International Journal of Non-Linear Mechanics. 1991, 26(6): 893-909.
[26] Antoni J. The spectral kurtosis: a useful tool for characterising non-stationary signals. Mechanical Systems and Signal Processing. 2006, 20(2): 282-307.
[27] Antoni J, Randall R B. The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines. Mechanical Systems and Signal Processing. 2006, 20(2): 308-331.
[28]樊养余,孙进才,熊克,等.四阶累积量对角切片法提取舰船辐射噪声特征.声学学报. 2002, 27(5): 435-442.
[29]张严,王树勋,李生红.二次相位耦合的112维谱分析.电子学报. 1996, 24(4): 109-112.
[30]樊养余,陶宝祺,熊克,等.舰船噪声的112维谱特征提取.声学学报. 2002, 27(1): 71-76.
[31]李亚安,冯西安,樊养余,等.基于112维谱的舰船辐射噪声低频线谱成分提取.兵工学报. 2004, 25(238-341).
[32]杨龙兴,贾民平.旋转机械故障诊断的112维循环谱分析方法.东南大学学报(自然科学版). 2004, 34(6): 766-770.
[33]史广智,胡均川.基于小波包和112维谱的舰船辐射噪声频域特征提取及融合.声学技术. 2004, 23(1): 4-7.
[34]何正嘉,訾艳阳,孟庆丰,等.机械设备非平稳信号的故障诊断原理及应用.北京:高等教育出版社, 2001.
[35] Stromberg J. A modified Haar system and higher order spline systems on Rn as unconditional bases for Hardy spaces. California, Conference in harmonic analysis in honor of Antoni Zygmund, 1981.
[36] Mallat S G. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1989, 11(7): 674-693.
[37] Mallat S G. Multiresolution approximation and wavelet orthonormal bases of L2(R). Transactions of the American Mathematical Society. 1989, 315(1): 68-87.
[38] Daubechies I. Orthonormal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics. 1988, 41(7): 909-996.
[39] Daubechies I. The wavelet transform, Time-frequency localization and signal analysis. IEEE Transactions on Information Theory. 1990, 36(5): 961-1005.
[40] Daubechies I. Orthonormal bases of compactly supported wavelets II: variations on a theme. SIAM Journal on Mathematical Analysis. 1993, 24(2): 499-519.
[41] Newland D E. Harmonic Wavelet Analysis. Proceedings of Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 1993, 443(1917): 203-225.
[42] Newland D E. Harmonic and Musical Wavelets. Proceedings of Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 1994, 444(1922): 605-620.
[43]李舜酩,许庆余.微弱振动信号的谐波小波频域提取.西安交通大学学报. 2004,38(1): 51-55.
[44]李舜酩.谐波小波包方法及其对转子亚频轴心轨迹的提取.机械工程学报. 2004, 40(9): 133-137.
[45]李瑰贤,韩继光.改进谐波小波及其在振动信号时频分析中的应用.振动工程学报. 2001, 14(4): 388-391.
[46]宋友,李其汉.基于小波变换的转子动静件碰摩故障诊断研究.振动工程学报. 2002, 15(3): 319-322.
[47] Li L, Qu L, Liao X. Haar wavelet for machine fault diagnosis. Mechanical Systems and Signal Processing. 2007, 21(4): 1773-1786.
[48] Peng Z K, Chu F L. Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography. Mechanical Systems and Signal Processing. 2004, 18(2): 199-221.
[49]廖庆斌,李舜酩,覃小攀.车辆振动信号的特征提取方法比较.吉林大学学报(工学版). 2007, 37(4): 910-914.
[50] Dalpiaz G, Rivola A. Condition monitoring and diagnostics in automatic machines: comparison of vibration analysis techniques. Mechanical Systems and Signal Processing. 1997, 11(1): 53-73.
[51]杨世锡,胡劲松,吴昭同,等.旋转机械振动信号基于EMD的希尔伯特变换和小波变换时频分析比较.中国电机工程学报. 2003, 23(6): 102-107.
[52] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 1998, 454(1971): 903-995.
[53] Huang N E, Shen Z, Long S R. A new view of nonlinear water waves: The Hilbert spectrum. Annual Review of Fluid Mechanics. 1999, 31: 417-457.
[54] Huang N E, Wu M C, Long S R, et al. A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proceedings of Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 2003, 459(2037): 2317-2345.
[55] Peng Z K, Tse P W, Chu F L. A comparison study of improved Hilbert-Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing. Mechanical Systems and Signal Processing. 2005, 19(5): 974-988.
[56] Shen G, Tao L, Chen Z. Gearbox fault diagnosis based on empirical mode decomposition. Chinese Journal of Mechanical Engineering. 2004, 17(3): 454-456.
[57] Liu B, Riemenschneider S, Xu Y. Gearbox fault diagnosis using empirical modedecomposition and Hilbert spectrum. Mechanical Systems and Signal Processing. 2006, 20(3): 718-734.
[58] Yu D J, Cheng J S, Yang Y. Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings. Mechanical Systems and Signal Processing. 2005, 19(2): 259-270.
[59] Loutridis S J. Damage detection in gear systems using empirical mode decomposition. Engineering Structures. 2004, 26(12): 1833-1841.
[60] Chen H G, Yan Y J, Jiang J S. Vibration-based damage detection in composite wingbox structures by HHT. Mechanical Systems and Signal Processing. 2007, 21(1): 307-321.
[61] Xu Y L, Chen J. Structural damage detection using empirical mode decomposition: experimental investigation. Journal of Structure Engineering. 2004, 130(11): 1279-1288.
[62] Flandrin P, Rilling G, Goncalves P. Empirical mode decomposition as a filter bank. IEEE Signal Processing Letters. 2004, 11(2): 112-114.
[63] Li H, Deng X, Dai H. Structural damage detection using the combination method of EMD and wavelet analysis. Mechanical Systems and Signal Processing. 2007, 21(1): 298-306.
[64] Langley R S, Bardell N S. A review of current analysis capabilities applicable to the high frequency vibration prediction of aerospace structures. The Aeronautical Journal. 1998, 102(1015): 287-297.
[65] Lyon R H. Statistical energy analysis and structural fuzzy. The Journal of the Acoustical Society of America. 1995, 97(5): 2878-2881.
[66]叶武平.车内噪声预测及控制的统计能量分析法研究, [博士学位论文].上海:同济大学, 2001.
[67]韩增尧,曲广吉.统计能量分析的研究进展.航天器工程. 2000, 9(1): 15-22.
[68] Dejong R G. A study of vehicle interior noise using statistical energy analysis. SAE Paper: 850960. 1985.
[69]伍先俊,朱石坚.统计能量法及其在船舶声振预测中的应用综述.武汉理工大学学报(交通科学与工程版). 2004, 28(2): 212-215.
[70] Davy J L. The ensemble variance of random noise in a reverberation room. Journal of Sound and Vibration. 1986, 107(3): 361-373.
[71] Culla A, Sestieri A. Is it possible to treat confidentially SEA the wolf in sheep's clothing? Mechanical Systems and Signal Processing. 2006, 20(6): 1372-1399.
[72] Langley R S, Brown A W. The ensemble statistics of the energy of a random systemsubjected to harmonic excitation. Journal of Sound and Vibration. 2004, 275(3-5): 823-846.
[73] Langley R S, Brown A W. The ensemble statistics of the band-averaged energy of a random system. Journal of Sound and Vibration. 2004, 275(3-5): 847-857
[74] Cotoni V, Langley R S, Kidner M R. Numerical and experimental validation of variance prediction in the statistical energy analysis of built-up systems. Journal of Sound and Vibration. 2005, 288(3): 701-728.
[75] Langley R S, Cotoni V. Response variance prediction in the statistical energy analysis of built-up systems. The Journal of the Acoustical Society of America. 2004, 115(2): 706-718.
[76] Radcliffe C J, Huang X L. Putting statistics into the Statistical Energy Analysis of automotive vehicles. Journal of vibration and acoustics. 1997, 119(4): 629-634.
[77] Langhe K D, Sas P. Statistical analysis of the power injection method. The Journal of the Acoustical Society of America. 1996, 100(1): 294-303.
[78] Langley R S. A general derivation of the statistical energy analysis equations for coupled dynamic systems. Journal of Sound and Vibration. 1989, 135(3): 499-508.
[79]孙进才,王敏庆,盛美萍.统计能量分析(SEA)研究的新进展.自然科学进展. 1998, 8(2): 129-136.
[80] Huang X L, Radcliffe C J. Probability distribution of statistical energy analysis model responses due to parameter randomness. ASME Journal of Vibration and Acoustics. 1998, 20: 641-647.
[81]王其政.机构耦合动力学.北京:宇航出版社, 1999.
[82] Schroeder M R. Frequency-Correlation Functions of Frequency Responses in Rooms. The Journal of the Acoustical Society of America. 1962, 34(12): 1819-1823.
[83] Lyon R H. Statistical analysis of power injection and response in structures and rooms. The Journal of the Acoustical Society of America. 1969, 45(3): 545-565.
[84] Waterhouse R V. Estimation of monopole power radiated in a reverberation chamber. The Journal of the Acoustical Society of America. 1978, 64(5): 1443-1446.
[85] Davy J L. The relative variance of the transmission function of a reverberation room. Journal of Sound and Vibration. 1981, 77(4): 455-479.
[86] Davy J L. Improvements to formulae for the ensemble relative variance of random noise in a reverberation room. Journal of Sound and Vibration. 1987, 115(1): 145-161.
[87] Lyon R H. Variability in SEA. Columbus, The Ohio State University, Proceedings of India-USA Symposium on Emerging Trends in Vibration and Noise Engineering,2001.
[88] Mehta M L. Random Matrices, 3nd Edition. Singapore: Elsevier, 2006.
[89] Brody T A, Flores J, French J B, et al. Random-matrix physics: Spectrum and strength fluctuations. Reviews of Modern Physics. 1981, 53(3): 385-479.
[90] Weaver R L. Spectral statistics in elastodynamics. The Journal of the Acoustical Society of America. 1989, 85(3): 1005-1013.
[91] Davy J L. The distribution of modal frequencies in a reverberation room. Poughkeepsie, NY, Proceedings of the International Conference on Noise Control Engineering, 1990.
[92] Ellegaard C, Guhr T, Lindemann K, et al. spectral statistics of acoustic resonances in aluminum blocks. Physical Review Letters. 1995, 75(8): 1546-1549.
[93] Ellegaard C, Guhr T, Lindemann K, et al. Symmetry breaking and spectral statistics of acoustic resonances in quartz blocks. Physical Review Letters. 1996, 77(24): 4918-4921.
[94] Bertelsen P, Ellegaard C, Hugues E. Distribution of eigenfrequencies for vibrating plates. European Physical Journal B. 2000, 15(1): 87-96.
[95] Weaver R L. On the ensemble variance of reverberation room transmission functions, the effect of spectral rigidity. Journal of Sound and Vibration. 1989, 130(3): 487-491.
[96] Burkhardt J, Weaver R L. The effect of decay rate variability on statistical response predictions in acoustic systems. Journal of Sound and Vibration. 1996, 196(2): 147-164.
[97] Burkhardt J, Weaver R L. Spectral statistics in damped systems. Part I. Modal decay rate statistics. The Journal of the Acoustical Society of America. 1996, 100(1): 320-326.
[98] Burkhardt J, Weaver R L. Spectral statistics in damped systems. Part II. Spectral density fluctuations. The Journal of the Acoustical Society of America. 1996, 100(1): 327-334.
[99] Lobkis O I, Weaver R L, Rozhkov I. Power variances and decay curvature in a reverberant system. Journal of Sound and Vibration. 2000, 237(2): 281-302.
[100] Langley R S, Cotoni V. The ensemble statistics of the vibrational energy density of a random system subjected to single point harmonic excitation. The Journal of the Acoustical Society of America. 2005, 118(5): 3064-3076.
[101] Manning J E. Variance and Confidence Intervals for SEA Predictions. SAE Papers, 2005-01-2432. 2005.
[102] Langley R S, Brown A W. The ensemble statistics of the energy of a random systemsubjected to harmonic excitation. Journal of Sound and Vibration. 2004, 275(3-5): 823-846.
[103]张建,顾崇衔.相关输入时保守或非保守耦合系统的统计能量分析.振动工程学报. 1990, 3(1): 10-17.
[104]刘明治.相关激励下的统计能量分析法(SEA)研究.力学学报. 1994, 26(5): 559-569.
[105]廖庆斌,李舜酩.统计能量分析的响应统计估计及其研究进展.力学进展. 2007, 37(3): 337-345.
[106]陈进,姜鸣.高阶循环统计量理论在机械故障诊断中的应用.振动工程学报. 2001, 14(2): 121-134.
[107] Raghuveer M R. Time-domain approaches to quadratic phase coupling estimation. IEEE Transactions On Automatic Control. 1990, 35(1): 48-56.
[108] Wang C, James T G. Rotating machine fault detection based on HOS and artificial neural networks. Journal of Intelligent Manufacturing. 2002, 13(4): 283-293.
[109] Lee J E, Fassois S D. On the problem of stochastic experimental modal analysis based on multiple-excitation multiple-response data, part I: Dispersion analysis of continuous-time structural systems. Journal of Sound and Vibration. 1993, 161(1): 33-56.
[110]杨景义,王信义.试验模态分析.北京:北京理工大学出版社, 1990.
[111] Fassois S D, Lee J E. On the problem of stochastic experimental modal analysis based on multiple-excitation multiple-response data, part II: The modal analysis approach. Journal of Sound and Vibration. 1993, 161(1): 57-87.
[112] Lin J. Feature extraction of machine sound using wavelet and its application in fault diagnosis. NDT&E International. 2001, 34(1): 25-30.
[113]李舜酩,李允平,许庆余.小波分析在车辆振动信号检测中的应用.农业机械学报. 1998, 29(3): 108-112.
[114]姜洪开,何正嘉,段晨东.冗余第2代小波构造及机械信号特征提取.西安交通大学学报. 2004, 38(11): 1140-1142.
[115]贾民平,凌娟,许飞云,等.基于时序分析的经验模式分解法及其应用.机械工程学报. 2004, 40(9): 54-57.
[116] Peng Z K, Peter W T, Chu F L. An improved Hilbert-Huang transform and its application in vibration analysis. Journal of Sound and Vibration. 2005, 286(1-2): 187-205.
[117] Cohen L. Time-Frequency Analysis: Theory and application. Englewood Cliffs, NJ: Prentice Hall, 1995.
[118] Gabor D. Theory of Communication. Journal of Institute for Electrical Engineering. 1946, 93(3): 429-457.
[119] Boashash B. Estimating and interpreting the instantaneous frequency of a signal. I - Fundamentals. IEEE Transactions on Signal Processing. 1992, 80(4): 520-538
[120] Wang W J, McFadden P D. Application of orthogonal wavelets to early gear damage detection. Mechanical Systems and Signal Processing, 1995, 9(5): 497-507.
[121] (美)贝达物, (美)皮尔索.相关分析和谱分析的工程应用(凌福根译).北京:国防工业出版社, 1983.
[122]林循泓.振动模态参数识别及其应用.南京:东南大学出版社, 1990
[123] Nikias C L, Raghuveer M R. Higher order spectra analysis. N J: Prentice-Hall, 1993.
[124]胡广书.数字信号处理——理论、算法与实现.北京:清华大学出版社, 1997.
[125]傅志方.振动模态分析与参数辨识.上海:上海交通大学出版社, 1990.
[126]管迪华.模态分析技术.北京:清华大学出版社, 1996.
[127]金新灿,孙守光,邢鸿麟,等.环境随机激励下高速客车的工作模态分析.铁道学报. 2003, 25(5): 24-28.
[128]江世媛,姚熊亮,黄国权.简化的舱段船壳模型试验模态分析.哈尔滨工程大学学报. 2003, 24(5): 483-486.
[129] Ren W X, Peng X L, Lin Y Q. Experimental and analytical studies on dynamic characteristics of a large span cable-stayed bridge. Engineering Structures. 2005, 27(4): 535-548.
[130] Herrin D W, Wu T W, Seybert A F. The energy source simulation method. Journal of Sound and Vibration. 2004, 278(1-2): 135-153.
[131] Ewins D J. Modal Testing: Theory, Practive And Application. Hertfordshire: Research Studies Press, 1984.
[132]廖庆斌,李舜酩,朱丽娟.基于随机激励的某机匣模态实验与分析.航空动力学报. 2005, 20(6): 932-936.
[133] Alampalli S. Effects of testing, analysis, damage, and environment on modal parameters. Mechanical Systems and Signal Processing. 2000, 14(1): 63-74.
[134]《公路工程技术标准》. (JTJ001一1997). 1997.
[135] Kompella M S, Bernhard B J. Measurement of the statistical variation of structural-acoustic characteristics of automotive vehicles. SAE Paper, 931272. 1993.
[136] Legresley P A, Alonso J J. Airfoil design optimization using reduced order models based on proper orthogonal decomposition. AIAA Paper, 2000-2545, 2000.
[137]赵松原,黄明恪. POD降阶算法中对基模态表达的改进.南京航空航天大学学报. 2006, 38(2): 131-135.
[138] Carassale L. POD-based filters for the representation of random loads on structures. Probabilistic Engineering Mechanics. 2005, 20(3): 263-280.
[139] Holmes P, Lumley J L, Berkooz G. Turbulence, Coherent Structures, Symmetry and Dynamical Systems. Cambridge: Cambridge University Press, 1996.
[140] Glegg S A, Devenport W J. Proper orthogonal decomposition of turbulent flows for aeroacoustic and hydroacoustic applications. Journal of Sound and Vibration. 2001, 239(4): 767-784.
[141] Tubino F, Solari G. Double Proper Orthogonal Decomposition for Representing and Simulating Turbulence Fields. Journal of Engineering Mechanics. 2005, 131(12): 1302-1312.
[142] Lin Y K. Probabilistic Theory of Structural Dynamics. New York: McGraw-Hill, 1967.
[143]曹志远.板壳振动理论.北京:中国铁道出版社, 1989.
[144] Aglietti G S, Gabriel S B, Langley R S, et al. A modeling technique for active control design studies with application to spacecraft microvibrations. The Journal of the Acoustical Society of America. 1997, 102(4): 2158-2166.
[145] Norton M P. Fundamentals of Noise and Vibration Analysis for Engineers. Cambridge: Cambridge University Press, 1989.
[146] Adhikari S. Uncertainty Propagation in Linear Systems: An Exact Solution Using random Matrix Theory. Hawaii, 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 2007.
[147]陈塑寰.结构振动分析的矩阵摄动理论.重庆:重庆出版社, 1991.
[148] Bies D A, Hamid S. In situ determination of loss and coupling loss factors by the power injection method. Journal of Sound and Vibration. 1980, 70(2): 187-204.
[149] Sun J C, Wang C, Sun Z H. Modification of energy balance equation in statistical energy analysis. Chinese Journal of Acoustics. 1996, 15(1): 1-7.
[2] Dovstam K, Goransson P, Semeniuk B. Mode-Based Prediction of Vibrations in Complex Automotive Structures, a Review of Shortcomings. SAE Paper, 2005-01-2343. 2005.
[3]庞剑;谌刚;何华.汽车噪声与振动:理论与应用.北京:北京理工大学出版社, 2006.
[4]林逸,马天飞,姚为民,等.汽车NVH特性研究综述.汽车工程. 2002, 24(3): 177-181.
[5]姚德源,王其政.统计能量分析原理及其应用.北京:北京理工大学, 1995.
[6] Lyon R H, Dejong R G. Theory and Application of Statistical Energy Analysis, 2nd Ed. Boston: Butterworth-Heinemann, 1995.
[7] Mohammed A D. A study of uncertainty in applications of statistical energy analysis, [dissertation], Southampton: University of Southampton, 1990.
[8] Fahy F J, Mohammed A D. A study of uncertainty in applications of sea to coupled beam and plate systems, part I: Computational experiments. Journal of Sound and Vibration. 1992, 158(1): 45-67.
[9]张贤达,保铮.非平稳信号分析与处理.北京:国防工业出版社, 1998.
[10]于德介,程军圣,杨宇.机械故障诊断的Hilbert-Huang变换方法.北京:科学出版社, 2006.
[11]李舜酩,廖庆斌.工程信号处理的研究与发展.江苏省博士后学术大会论文集. 2005, 12: 284-290.
[12]张贤达.时间序列分析——高阶统计量方法.北京:清华大学出版社, 1996.
[13] Swami A, Giannakis G B, Zhou G. Bibliography on higher-order statistics. Signal Processing. 1997, 60(1): 65-126.
[14] Mccormick A C, Nandi A K. Bispectral and trispectral features for machine condition diagnosis. IEE Proceedings of the Vision and Image Signal Process. 1999, 146(5): 229–234.
[15] Fackrell J W, White P R, Hammond J K, et al. The interpretation of the bispectra of vibration signals--: I. Theory. Mechanical Systems and Signal Processing. 1995, 9(3): 257-266.
[16] Fackrell J W, White P R, Hammond J K, et al. The interpretation of the bispectra of vibration signals--: II. Experimental results and applications. Mechanical Systems and Signal Processing. 1995, 9(3): 267-274.
[17]杨江天,陈家骥,曾子平.双谱分析及其在机械诊断中的应用.中国机械工程. 2000, 11(4): 424-426.
[18] Simonovski I G, Boltezar M I, Gradisek J A, et al. Bispectral analysis of the cutting process. Mechanical Systems and Signal Processing. 2002, 16(6): 1093-1104.
[19] Radkowski S, Smalko Z, Pietak A, et al. Use of bispectral analysis in condition monitoring of machinery. Granada, Spain, Proceedings of 3rd European Workshop on Structural Health Monitoring, 2006.
[20] Rypdal K, Oynes F. Bispectral analysis: A tool for diagnosing nonlinear coherence in turbulence. Physics Letters A. 1993, 184(1): 114-118.
[21]舒红宇,熊木权.车辆减振器噪声诊断的双谱分析法.重庆大学学报(自然科学版). 2005, 28(3): 1-3.
[22] Hillis A J, Neild S A, Drinkwater B W, et al. Global crack detection using bispectral analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2006, 462(2069): 1515–1530.
[23] Murray A, Penman J. Extracting useful higher order features for condition monitoring using artificial neural networks. IEEE Transactions on Signal Processing. 1997, 45(11): 2821–2828.
[24] Fitzpatrick J A, Rice H J. Equivalent time domain procedures for bispectral analysis. Journal of Sound and Vibration. 1990, 137(1): 131-134.
[25] Lutes L D, Chen D C. Trispectrum for the response of a non-linear oscillator. International Journal of Non-Linear Mechanics. 1991, 26(6): 893-909.
[26] Antoni J. The spectral kurtosis: a useful tool for characterising non-stationary signals. Mechanical Systems and Signal Processing. 2006, 20(2): 282-307.
[27] Antoni J, Randall R B. The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines. Mechanical Systems and Signal Processing. 2006, 20(2): 308-331.
[28]樊养余,孙进才,熊克,等.四阶累积量对角切片法提取舰船辐射噪声特征.声学学报. 2002, 27(5): 435-442.
[29]张严,王树勋,李生红.二次相位耦合的112维谱分析.电子学报. 1996, 24(4): 109-112.
[30]樊养余,陶宝祺,熊克,等.舰船噪声的112维谱特征提取.声学学报. 2002, 27(1): 71-76.
[31]李亚安,冯西安,樊养余,等.基于112维谱的舰船辐射噪声低频线谱成分提取.兵工学报. 2004, 25(238-341).
[32]杨龙兴,贾民平.旋转机械故障诊断的112维循环谱分析方法.东南大学学报(自然科学版). 2004, 34(6): 766-770.
[33]史广智,胡均川.基于小波包和112维谱的舰船辐射噪声频域特征提取及融合.声学技术. 2004, 23(1): 4-7.
[34]何正嘉,訾艳阳,孟庆丰,等.机械设备非平稳信号的故障诊断原理及应用.北京:高等教育出版社, 2001.
[35] Stromberg J. A modified Haar system and higher order spline systems on Rn as unconditional bases for Hardy spaces. California, Conference in harmonic analysis in honor of Antoni Zygmund, 1981.
[36] Mallat S G. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1989, 11(7): 674-693.
[37] Mallat S G. Multiresolution approximation and wavelet orthonormal bases of L2(R). Transactions of the American Mathematical Society. 1989, 315(1): 68-87.
[38] Daubechies I. Orthonormal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics. 1988, 41(7): 909-996.
[39] Daubechies I. The wavelet transform, Time-frequency localization and signal analysis. IEEE Transactions on Information Theory. 1990, 36(5): 961-1005.
[40] Daubechies I. Orthonormal bases of compactly supported wavelets II: variations on a theme. SIAM Journal on Mathematical Analysis. 1993, 24(2): 499-519.
[41] Newland D E. Harmonic Wavelet Analysis. Proceedings of Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 1993, 443(1917): 203-225.
[42] Newland D E. Harmonic and Musical Wavelets. Proceedings of Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 1994, 444(1922): 605-620.
[43]李舜酩,许庆余.微弱振动信号的谐波小波频域提取.西安交通大学学报. 2004,38(1): 51-55.
[44]李舜酩.谐波小波包方法及其对转子亚频轴心轨迹的提取.机械工程学报. 2004, 40(9): 133-137.
[45]李瑰贤,韩继光.改进谐波小波及其在振动信号时频分析中的应用.振动工程学报. 2001, 14(4): 388-391.
[46]宋友,李其汉.基于小波变换的转子动静件碰摩故障诊断研究.振动工程学报. 2002, 15(3): 319-322.
[47] Li L, Qu L, Liao X. Haar wavelet for machine fault diagnosis. Mechanical Systems and Signal Processing. 2007, 21(4): 1773-1786.
[48] Peng Z K, Chu F L. Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography. Mechanical Systems and Signal Processing. 2004, 18(2): 199-221.
[49]廖庆斌,李舜酩,覃小攀.车辆振动信号的特征提取方法比较.吉林大学学报(工学版). 2007, 37(4): 910-914.
[50] Dalpiaz G, Rivola A. Condition monitoring and diagnostics in automatic machines: comparison of vibration analysis techniques. Mechanical Systems and Signal Processing. 1997, 11(1): 53-73.
[51]杨世锡,胡劲松,吴昭同,等.旋转机械振动信号基于EMD的希尔伯特变换和小波变换时频分析比较.中国电机工程学报. 2003, 23(6): 102-107.
[52] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 1998, 454(1971): 903-995.
[53] Huang N E, Shen Z, Long S R. A new view of nonlinear water waves: The Hilbert spectrum. Annual Review of Fluid Mechanics. 1999, 31: 417-457.
[54] Huang N E, Wu M C, Long S R, et al. A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proceedings of Royal Society of London Series A: Mathematical, Physical and Engineering Sciences. 2003, 459(2037): 2317-2345.
[55] Peng Z K, Tse P W, Chu F L. A comparison study of improved Hilbert-Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing. Mechanical Systems and Signal Processing. 2005, 19(5): 974-988.
[56] Shen G, Tao L, Chen Z. Gearbox fault diagnosis based on empirical mode decomposition. Chinese Journal of Mechanical Engineering. 2004, 17(3): 454-456.
[57] Liu B, Riemenschneider S, Xu Y. Gearbox fault diagnosis using empirical modedecomposition and Hilbert spectrum. Mechanical Systems and Signal Processing. 2006, 20(3): 718-734.
[58] Yu D J, Cheng J S, Yang Y. Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings. Mechanical Systems and Signal Processing. 2005, 19(2): 259-270.
[59] Loutridis S J. Damage detection in gear systems using empirical mode decomposition. Engineering Structures. 2004, 26(12): 1833-1841.
[60] Chen H G, Yan Y J, Jiang J S. Vibration-based damage detection in composite wingbox structures by HHT. Mechanical Systems and Signal Processing. 2007, 21(1): 307-321.
[61] Xu Y L, Chen J. Structural damage detection using empirical mode decomposition: experimental investigation. Journal of Structure Engineering. 2004, 130(11): 1279-1288.
[62] Flandrin P, Rilling G, Goncalves P. Empirical mode decomposition as a filter bank. IEEE Signal Processing Letters. 2004, 11(2): 112-114.
[63] Li H, Deng X, Dai H. Structural damage detection using the combination method of EMD and wavelet analysis. Mechanical Systems and Signal Processing. 2007, 21(1): 298-306.
[64] Langley R S, Bardell N S. A review of current analysis capabilities applicable to the high frequency vibration prediction of aerospace structures. The Aeronautical Journal. 1998, 102(1015): 287-297.
[65] Lyon R H. Statistical energy analysis and structural fuzzy. The Journal of the Acoustical Society of America. 1995, 97(5): 2878-2881.
[66]叶武平.车内噪声预测及控制的统计能量分析法研究, [博士学位论文].上海:同济大学, 2001.
[67]韩增尧,曲广吉.统计能量分析的研究进展.航天器工程. 2000, 9(1): 15-22.
[68] Dejong R G. A study of vehicle interior noise using statistical energy analysis. SAE Paper: 850960. 1985.
[69]伍先俊,朱石坚.统计能量法及其在船舶声振预测中的应用综述.武汉理工大学学报(交通科学与工程版). 2004, 28(2): 212-215.
[70] Davy J L. The ensemble variance of random noise in a reverberation room. Journal of Sound and Vibration. 1986, 107(3): 361-373.
[71] Culla A, Sestieri A. Is it possible to treat confidentially SEA the wolf in sheep's clothing? Mechanical Systems and Signal Processing. 2006, 20(6): 1372-1399.
[72] Langley R S, Brown A W. The ensemble statistics of the energy of a random systemsubjected to harmonic excitation. Journal of Sound and Vibration. 2004, 275(3-5): 823-846.
[73] Langley R S, Brown A W. The ensemble statistics of the band-averaged energy of a random system. Journal of Sound and Vibration. 2004, 275(3-5): 847-857
[74] Cotoni V, Langley R S, Kidner M R. Numerical and experimental validation of variance prediction in the statistical energy analysis of built-up systems. Journal of Sound and Vibration. 2005, 288(3): 701-728.
[75] Langley R S, Cotoni V. Response variance prediction in the statistical energy analysis of built-up systems. The Journal of the Acoustical Society of America. 2004, 115(2): 706-718.
[76] Radcliffe C J, Huang X L. Putting statistics into the Statistical Energy Analysis of automotive vehicles. Journal of vibration and acoustics. 1997, 119(4): 629-634.
[77] Langhe K D, Sas P. Statistical analysis of the power injection method. The Journal of the Acoustical Society of America. 1996, 100(1): 294-303.
[78] Langley R S. A general derivation of the statistical energy analysis equations for coupled dynamic systems. Journal of Sound and Vibration. 1989, 135(3): 499-508.
[79]孙进才,王敏庆,盛美萍.统计能量分析(SEA)研究的新进展.自然科学进展. 1998, 8(2): 129-136.
[80] Huang X L, Radcliffe C J. Probability distribution of statistical energy analysis model responses due to parameter randomness. ASME Journal of Vibration and Acoustics. 1998, 20: 641-647.
[81]王其政.机构耦合动力学.北京:宇航出版社, 1999.
[82] Schroeder M R. Frequency-Correlation Functions of Frequency Responses in Rooms. The Journal of the Acoustical Society of America. 1962, 34(12): 1819-1823.
[83] Lyon R H. Statistical analysis of power injection and response in structures and rooms. The Journal of the Acoustical Society of America. 1969, 45(3): 545-565.
[84] Waterhouse R V. Estimation of monopole power radiated in a reverberation chamber. The Journal of the Acoustical Society of America. 1978, 64(5): 1443-1446.
[85] Davy J L. The relative variance of the transmission function of a reverberation room. Journal of Sound and Vibration. 1981, 77(4): 455-479.
[86] Davy J L. Improvements to formulae for the ensemble relative variance of random noise in a reverberation room. Journal of Sound and Vibration. 1987, 115(1): 145-161.
[87] Lyon R H. Variability in SEA. Columbus, The Ohio State University, Proceedings of India-USA Symposium on Emerging Trends in Vibration and Noise Engineering,2001.
[88] Mehta M L. Random Matrices, 3nd Edition. Singapore: Elsevier, 2006.
[89] Brody T A, Flores J, French J B, et al. Random-matrix physics: Spectrum and strength fluctuations. Reviews of Modern Physics. 1981, 53(3): 385-479.
[90] Weaver R L. Spectral statistics in elastodynamics. The Journal of the Acoustical Society of America. 1989, 85(3): 1005-1013.
[91] Davy J L. The distribution of modal frequencies in a reverberation room. Poughkeepsie, NY, Proceedings of the International Conference on Noise Control Engineering, 1990.
[92] Ellegaard C, Guhr T, Lindemann K, et al. spectral statistics of acoustic resonances in aluminum blocks. Physical Review Letters. 1995, 75(8): 1546-1549.
[93] Ellegaard C, Guhr T, Lindemann K, et al. Symmetry breaking and spectral statistics of acoustic resonances in quartz blocks. Physical Review Letters. 1996, 77(24): 4918-4921.
[94] Bertelsen P, Ellegaard C, Hugues E. Distribution of eigenfrequencies for vibrating plates. European Physical Journal B. 2000, 15(1): 87-96.
[95] Weaver R L. On the ensemble variance of reverberation room transmission functions, the effect of spectral rigidity. Journal of Sound and Vibration. 1989, 130(3): 487-491.
[96] Burkhardt J, Weaver R L. The effect of decay rate variability on statistical response predictions in acoustic systems. Journal of Sound and Vibration. 1996, 196(2): 147-164.
[97] Burkhardt J, Weaver R L. Spectral statistics in damped systems. Part I. Modal decay rate statistics. The Journal of the Acoustical Society of America. 1996, 100(1): 320-326.
[98] Burkhardt J, Weaver R L. Spectral statistics in damped systems. Part II. Spectral density fluctuations. The Journal of the Acoustical Society of America. 1996, 100(1): 327-334.
[99] Lobkis O I, Weaver R L, Rozhkov I. Power variances and decay curvature in a reverberant system. Journal of Sound and Vibration. 2000, 237(2): 281-302.
[100] Langley R S, Cotoni V. The ensemble statistics of the vibrational energy density of a random system subjected to single point harmonic excitation. The Journal of the Acoustical Society of America. 2005, 118(5): 3064-3076.
[101] Manning J E. Variance and Confidence Intervals for SEA Predictions. SAE Papers, 2005-01-2432. 2005.
[102] Langley R S, Brown A W. The ensemble statistics of the energy of a random systemsubjected to harmonic excitation. Journal of Sound and Vibration. 2004, 275(3-5): 823-846.
[103]张建,顾崇衔.相关输入时保守或非保守耦合系统的统计能量分析.振动工程学报. 1990, 3(1): 10-17.
[104]刘明治.相关激励下的统计能量分析法(SEA)研究.力学学报. 1994, 26(5): 559-569.
[105]廖庆斌,李舜酩.统计能量分析的响应统计估计及其研究进展.力学进展. 2007, 37(3): 337-345.
[106]陈进,姜鸣.高阶循环统计量理论在机械故障诊断中的应用.振动工程学报. 2001, 14(2): 121-134.
[107] Raghuveer M R. Time-domain approaches to quadratic phase coupling estimation. IEEE Transactions On Automatic Control. 1990, 35(1): 48-56.
[108] Wang C, James T G. Rotating machine fault detection based on HOS and artificial neural networks. Journal of Intelligent Manufacturing. 2002, 13(4): 283-293.
[109] Lee J E, Fassois S D. On the problem of stochastic experimental modal analysis based on multiple-excitation multiple-response data, part I: Dispersion analysis of continuous-time structural systems. Journal of Sound and Vibration. 1993, 161(1): 33-56.
[110]杨景义,王信义.试验模态分析.北京:北京理工大学出版社, 1990.
[111] Fassois S D, Lee J E. On the problem of stochastic experimental modal analysis based on multiple-excitation multiple-response data, part II: The modal analysis approach. Journal of Sound and Vibration. 1993, 161(1): 57-87.
[112] Lin J. Feature extraction of machine sound using wavelet and its application in fault diagnosis. NDT&E International. 2001, 34(1): 25-30.
[113]李舜酩,李允平,许庆余.小波分析在车辆振动信号检测中的应用.农业机械学报. 1998, 29(3): 108-112.
[114]姜洪开,何正嘉,段晨东.冗余第2代小波构造及机械信号特征提取.西安交通大学学报. 2004, 38(11): 1140-1142.
[115]贾民平,凌娟,许飞云,等.基于时序分析的经验模式分解法及其应用.机械工程学报. 2004, 40(9): 54-57.
[116] Peng Z K, Peter W T, Chu F L. An improved Hilbert-Huang transform and its application in vibration analysis. Journal of Sound and Vibration. 2005, 286(1-2): 187-205.
[117] Cohen L. Time-Frequency Analysis: Theory and application. Englewood Cliffs, NJ: Prentice Hall, 1995.
[118] Gabor D. Theory of Communication. Journal of Institute for Electrical Engineering. 1946, 93(3): 429-457.
[119] Boashash B. Estimating and interpreting the instantaneous frequency of a signal. I - Fundamentals. IEEE Transactions on Signal Processing. 1992, 80(4): 520-538
[120] Wang W J, McFadden P D. Application of orthogonal wavelets to early gear damage detection. Mechanical Systems and Signal Processing, 1995, 9(5): 497-507.
[121] (美)贝达物, (美)皮尔索.相关分析和谱分析的工程应用(凌福根译).北京:国防工业出版社, 1983.
[122]林循泓.振动模态参数识别及其应用.南京:东南大学出版社, 1990
[123] Nikias C L, Raghuveer M R. Higher order spectra analysis. N J: Prentice-Hall, 1993.
[124]胡广书.数字信号处理——理论、算法与实现.北京:清华大学出版社, 1997.
[125]傅志方.振动模态分析与参数辨识.上海:上海交通大学出版社, 1990.
[126]管迪华.模态分析技术.北京:清华大学出版社, 1996.
[127]金新灿,孙守光,邢鸿麟,等.环境随机激励下高速客车的工作模态分析.铁道学报. 2003, 25(5): 24-28.
[128]江世媛,姚熊亮,黄国权.简化的舱段船壳模型试验模态分析.哈尔滨工程大学学报. 2003, 24(5): 483-486.
[129] Ren W X, Peng X L, Lin Y Q. Experimental and analytical studies on dynamic characteristics of a large span cable-stayed bridge. Engineering Structures. 2005, 27(4): 535-548.
[130] Herrin D W, Wu T W, Seybert A F. The energy source simulation method. Journal of Sound and Vibration. 2004, 278(1-2): 135-153.
[131] Ewins D J. Modal Testing: Theory, Practive And Application. Hertfordshire: Research Studies Press, 1984.
[132]廖庆斌,李舜酩,朱丽娟.基于随机激励的某机匣模态实验与分析.航空动力学报. 2005, 20(6): 932-936.
[133] Alampalli S. Effects of testing, analysis, damage, and environment on modal parameters. Mechanical Systems and Signal Processing. 2000, 14(1): 63-74.
[134]《公路工程技术标准》. (JTJ001一1997). 1997.
[135] Kompella M S, Bernhard B J. Measurement of the statistical variation of structural-acoustic characteristics of automotive vehicles. SAE Paper, 931272. 1993.
[136] Legresley P A, Alonso J J. Airfoil design optimization using reduced order models based on proper orthogonal decomposition. AIAA Paper, 2000-2545, 2000.
[137]赵松原,黄明恪. POD降阶算法中对基模态表达的改进.南京航空航天大学学报. 2006, 38(2): 131-135.
[138] Carassale L. POD-based filters for the representation of random loads on structures. Probabilistic Engineering Mechanics. 2005, 20(3): 263-280.
[139] Holmes P, Lumley J L, Berkooz G. Turbulence, Coherent Structures, Symmetry and Dynamical Systems. Cambridge: Cambridge University Press, 1996.
[140] Glegg S A, Devenport W J. Proper orthogonal decomposition of turbulent flows for aeroacoustic and hydroacoustic applications. Journal of Sound and Vibration. 2001, 239(4): 767-784.
[141] Tubino F, Solari G. Double Proper Orthogonal Decomposition for Representing and Simulating Turbulence Fields. Journal of Engineering Mechanics. 2005, 131(12): 1302-1312.
[142] Lin Y K. Probabilistic Theory of Structural Dynamics. New York: McGraw-Hill, 1967.
[143]曹志远.板壳振动理论.北京:中国铁道出版社, 1989.
[144] Aglietti G S, Gabriel S B, Langley R S, et al. A modeling technique for active control design studies with application to spacecraft microvibrations. The Journal of the Acoustical Society of America. 1997, 102(4): 2158-2166.
[145] Norton M P. Fundamentals of Noise and Vibration Analysis for Engineers. Cambridge: Cambridge University Press, 1989.
[146] Adhikari S. Uncertainty Propagation in Linear Systems: An Exact Solution Using random Matrix Theory. Hawaii, 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 2007.
[147]陈塑寰.结构振动分析的矩阵摄动理论.重庆:重庆出版社, 1991.
[148] Bies D A, Hamid S. In situ determination of loss and coupling loss factors by the power injection method. Journal of Sound and Vibration. 1980, 70(2): 187-204.
[149] Sun J C, Wang C, Sun Z H. Modification of energy balance equation in statistical energy analysis. Chinese Journal of Acoustics. 1996, 15(1): 1-7.