爆震特征提取及累积量检测算法研究
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摘要
爆震检测是汽车电子控制系统中的重要环节,准确的爆震检测和实时控制可以改善发动机的动力性和经济性,但是振动信号的低信噪比使得轻微爆震识别比较困难。本文对爆震信号处理方法和轻微爆震识别进行了系统的研究。在研究功率谱密度估计爆震特征频率和小波变换爆震分析基础上,进一步研究应用高阶累积量进行爆震信号处理的方法,提出了基于三阶累积量的振动信号降噪及爆震特征提取算法,以及基于峰度的爆震强度计算及分级方法,为进一步提升爆震探测识别技术奠定理论技术基础。
     功率谱密度反映了信号的功率随频率的变化情况,据此提出了利用参数化功率谱估计算法准确估计爆震特征频率,并以此为依据设计数字带通滤波器。实验分析表明在爆震较强时,滤波方法是一种效果良好且简单易行的爆震检测方法,但是当爆震较弱或背景噪声较强时,滤波方法仍然残留了大量的噪声,不利于准确检测轻微爆震和进行临界爆震分析。
     爆震一般持续时间较短,而小波变换良好的时频局部化分析特征,使其适合用于爆震信号处理,因此通过分量分析,研究利用离散小波变换提取爆震特征的有效方法,并采用两种爆震强度评价指标分析比较了小波变换方法和滤波方法的性能。研究表明,如果从信号的峰值幅值来评价爆震,对于弱爆震检测,二者的性能基本相同,但是在中轻度爆震检测方面,小波变换方法优于滤波方法。
     为了提高轻微爆震检测的精度,本文提出了一种基于三阶累积量的振动信号降噪方法。该方法利用了三阶累积量抑制对称噪声的性质,结合检测函数和合理的阈值,能有效地消除振动噪声,并提取爆震特征。模拟实验分析和实测振动信号分析均表明,与其它方法相比,该方法明显地提升了信噪比,更适用于轻微爆震识别。针对爆震实时控制的需要,进一步研究了振动信号的四阶累积量特征,分析信号的峰度与爆震强度的相关性,并提出了基于峰度的爆震强度检测算法,定量地计算爆震强度。结果表明,该信号处理算法计算量小,简便快捷,在此基础上进一步研究了爆震强度分级方法,将更加有效提高爆震控制效率。
Knock control is one of important parts for automobile electronic control system. Serious engine knock decreases power performance of the vehicle, increases pollution or damages mechanical parts. However, when the engine works with light knock, engine power and fuel economy will be improved. Therefore, it is important to detect knock and provide feedback information to control system, so that the engine can work with light knock. In this process, the accurate light knock identify is a necessary pre-condition.
     The mostly used methods for knock detection use accelerometers to measure cylinder vibration, since the accelerometer is costless and the measure system is easy to maintain. But the vibration signal is induced by engine knock indirectly, and the drawback is that the low signal-to-noise ratio of the vibration signal makes the light knock detection difficult. Therefore, this paper researched knock signal processing methods, proposed some new knock feature extraction, knock intensity determine and light knock detection methods. The simulated experiement and real vibration signals processing results verified the validity of these methods.
     Vibration signals were obtained with an accelerometer mounted on the engine cylinder head. Knock was induced through changing ignition advance angle. A lot of signals with different working conditions were recorded for analyzed.
     Fourier spectrum of the vibration signal was analyzed, the results indicated that knock lead to larger amplitude in a special band, which includes the knock characteristic frequency. But this is only a rough evaluation for engine knock with influence of noise, it cann’t be used to detect knock intensity accurately. In order to find out exact knock frequency, a method using power spectrum estimation was proposed in this paper. AR model was used to describe typical knock process, and model parameters were estimated with Burg and covariance algorithms. The experiment result showed that knock characteristic frequency can be estimated, but the results were different for different vibration signals, it illustrated that knock frequency was affected by the engine working condition. For the engine used in the experiment system, variations in the fundamental knock frequency can be as much as±600Hz.
     Through power spectrum estimation results of many signals with different engine working conditions, a band range of knock frequency was obtained. The band-pass filter was used to extract knock information. According to power spectrum estimation results, the center frequency and the cut-off frequency were decided. Because the IIR filter involves few memory units and it has high efficiency, so an IIR filter was chosen. In order to avoide distortion of knock component, Butterworth filter was applied, since the amplitude response within the appointed band is flat.The advantage of the filtering method is that parameters of the programmable filter can be adjusted conveniently when used for different engines. The results of real signals processing indicate that the performance of filtering method is good when knock is strong, however, when knock is light or noise is strong, the performance decrease, so filtering method is not sufficient to detect light knock accurately.
     Wavelet transform is an effective tool to detect abnormal signals because of its multi-resolution. Wavelet transform is suitable to identify knock, since knock always cause amplitude increasing abruptly. Application of wavelet transform in knock feature extraction was researched in this paper. When applied the mother wavelet function, because the duration of knock is short, wavelet functions with compact supports is beneficial to knock detection. Discrete wavelet transform was applied to analyze signals with different knock intensity. The experiment result indicated that the knock feature included in the detail component d 2 was obvious for strong knock, while the knock feature included in the detail component d 3 was obvious for light knock. Actually, the probability of engine working with strong knock is low, it means more to identify light knock, so the detail component d 3 should be used for further research.
     In order to compare filtering method and wavelet transform method, two kinds of knock intensity criteria were chosen. Calculated the peak and root mean square of the signal processed with filtering method and wavelet transform method. The experiment results indicate that the peak and root mean square have correlation when used for knock evaluation. When knock is light, the performance of them is the same. But if knock is strong, the root mean square of knock signal is more sensitive than the peak, because both of amplitude and lasting time increase with strong engine knock.
     Compared with two methods, if the criterion of root mean square was applied, two methods performed alike. But when the criterion of peak was applied, wavelet transform method is better than filtering method for moderate knock. However, the experiment result indicated that wavelet transform method didn’t act better than filtering method for light knock detection.
     In order to identify light knock accurately, knock signal processing method with higher order cumulants was proposed in this paper. The skewness of the vibration noise was analyzed, and the result showed that the skewnee was close to be zero, so the probability distribution near to be symmetrical. Because third-order cumulants are effective to remove noise with symmetrical distribution, a vibration signal denoising method with third-order cumulants was proposed. Based on the detection function proposed, the method can enhance the impact of the knock signal components by setting a reasonable threshold and suppress vibration noise.
     In order to select the appropriate threshold, analyzed the relationship between sets of knock signal and non-knock signal’s detection function value and the threshold. If the threshold is too small, more noise will be kept down; if the threshold value increases, although the noise is removed much more, some of useful sample data also be discarded because of the smaller amplitude, which corresponds the end part of the knock process. Balance these two factors, this paper choose a suitable threshold, which retain more than 90% of the knock-component, while more than 90% of the noise will be removed.
     Applied third-order cumulants based method to extract knock feature from real vibration signals, and compared it with filtering method, advantages of the proposed method were explained with two important aspects. Firstly, third-order cumulants based method can remove much more background noise, improve signal-to-noise ratio, so the character of the entire knock process was observed clearly. Secondly, the estimated knock energy in time domain was closed to the actual value. When the signal-to-noise ratio is low, the improvement is more obvious. The real vibration signals processing results also confirmed that knock feature extracted using third-order cumulants based method is better, which is also helpful to improve the performance of light knock detection.
     A knock detection method with less computation was proposed in this paper, so as to fulfill the real time knock control. Fourth-order cumulants of the vibration signals were analyzed, and the results indicate that probability distribution of the vibration signal is not Gaussian, but the super-Gaussian. With the determined engine operating condition, kurtosis of the vibration signal has special correlation with knock intensity. As the kurtosis contains the information of current knock intensity, this paper proposes a knock intensity determination method using kurtosis. Because kurtosis is the special diagonal slice of fourth-order cumulants, computation involved in the approach is simple. The experiment confirmed the method was effective, and it can provide numerical values for variety of knock intensity.
     After the knock intensity was calculated numerically, a method was proposed to classify a variety of knock conditions. With a determined engine rotation speed, six groups of vibration signals were collected when ignition advance angle was increased with the step of 2 o CA, and each group contains at least 100 cycles. The first group of signals corresponds to knock-free status; while the final group of signals corresponds to serious knock. Calculated knock intensity for each group of signals using the proposed method in this paper, and analyzed how the numerical values were affected by ignition advance angle. According to the experiment result, a series of thresholds were set up, in order to divide knock conditions into four grades: non-knock, light knock, moderate knock and severe knock. The ignition advance angle adjusting strategy can vary with different kinds of knock grades; so the method is helpful to improve the efficiency of the knock control system.
引文
[1]李继军,陈宝书,武得钰等,汽油机爆震自动控制系统研究[J],系统工程理论与实践,2000,6:115-117。
    [2]申荣卫,汽车电子技术[M],北京,机械工业出版社,2003.2。
    [3] Mallard E. Chatelier HL, Experimental and theoretical research on the combustion of gaseous melanges explosives, Annals Des Mines [J], 1883, Ser.4, 8: 274-381.
    [4] Ricardo H R, The High Speed Internal Combustion Engine[M], Blockne&Sons Ltd, London, Glsagow, 1923.
    [5] Theodore Male, Photographs at 500,000 Frames per Second of Combustion and Detonation in Reciprocating Engine[C], 3th Symposium on Combustion and Flame and Explosion Phenomena, 1949, vol.3,issue 1, pp.721-726.
    [6] Cearcy D. Miller, H. Lowell Olsen, Walter O. Logan, Jr., and Gordon E. Osterstrom, Analysis of Spark Ignition Engine Knock as Seen in Photographs Taken at 200,000 Frames Per Second[R], NACA Report No.857,1946.
    [7] Curry S, A Three Dimensional Study of Flame Propagation in a Spark Ignition Engine[C], SAE paper, 1963.
    [8] Yasuo Takagi, Teruyuki Itoh, and Tamatsu Iijima, An Analytical Study on Knocking Heat Release and Its Control in a Spark Ignition Engine[J], SAE Trans., Document Number: 880196, February 1988, pp.338-347.
    [9] Kwang Min Chun, Seonghoon Kim, and Tacksoo Kim, Flame Propagation and Knock Detection Using An Optical Fiber Technique in a Spark-Ignition Engine [C], SAE paper, No.931906, 1993.
    [10] Nernst W, Physikalisen-Chemische Belra-Chtungen Uber den Verbrennung -processen in der Gasmotoren Zeitschift Deutscher Ingenier [J]. Vol.49, No.35, 1905.
    [11] Guenther Von Elbe, Lewis B, Hydrocarbon Reactions and Knock in Internal Combustion Engine [J], Lnd.Eng. Chem. 1937, vol.29, No.5, pp.551-554.
    [12] K. Oppenheim, The Knock Syndrome--Its Cures and Its Victims [C], SAEfuels and lubricants meeting, Baltimore, No.841339, 1984.
    [13]高青,金英爱,孙志军,孙济美,内燃机爆震燃烧探测及其临界爆震判析[J],燃烧科学与技术, 2002, 8(4):381-383。
    [14]高青,金英爱,玄哲浩,李明,方瑛,发动机临界爆震控制特性研究[J],汽车工程,2003.10,25(6):547-551。
    [15] Olivier Boubal, Knock Detection in Automobile Engines[J], IEEE instrumentation & measurement magazine, Sept. 2000, 3(3):24-28.
    [16] Jean-Hugh Thomas, Bernard Dubuisson and Marie-Agnes Dillies-Peltier, Engine Knock Detection from Vibration Signals using Pattern Recognition[J], Meccanica,1997, 32:431-439.
    [17] M.M. Ettefagh, M.H. Sadeghi, V. Pirouzpanah, H. Arjmandi Tash, Knock detection in spark ignition engines by vibration analysis of cylinder block: A parametric modeling approach [J], Mechanical Systems and Signal Processing, 2008, 22:1495-1514.
    [18] Michael Brunt, Chris Pond, and John Biundo, Gasoline Engine Knock Analysis Using Cylinder Pressure Data [J], SAE Trans., No.980896, 1998, 106(3):1399-1412.
    [19] M. Syrimis and D. N. Assanis, Knocking Cylinder Pressure Data Characteristics in a Spark-Ignition Engine[J], Gas Turbines Power, April 2003, 125(2):494-499.
    [20] K.Sawamoto, Y.Kawamura, T.Kita, and K.Matsushita, Individual cylinder knock control by detecting cylinder pressure [J]. SAE Trans., 1987, 96(3):602-605.
    [21]锐意泰克汽车电子有限公司,爆震专项文档[R],2006。
    [22] Tassos H.Valtadoros, Engine knock Characteristics at the Audible Level[C]. SAE International Congress & Exposition, Detroit, No. 910567, February 1991.
    [23] Olivier Boubal and Jacques Oksman, Knock acoustic signal estimation using parametric inversion [J], IEEE transactions on instrumentation and measurement, Aug. 2000, 49(4): 890-895.
    [24] Remboski DJ Jr, Plee SL.Martin J K. An optical sensor for spark ignition engine combustion analysis and control [C]. SAE international congressand exposition,Detroit, No.890159, Mar 1989.
    [25]高青,金英爱,孙志军,孙济美,方瑛,点燃式发动机爆震测量及其强度分析[J],燃烧科学与技术,2003.8,9(4): 335-338。
    [26] Nobuyuki Kawahara, Eiji Tomita, and Mithun Kanti Roy, Visualization of Auto-Ignited Kernel and Propagation of Pressure Wave during Knocking Combustion in a Hydrogen Spark-Ignition Engine [J], International Journal of Hydrogen Energy, June 2009, 34(7):3156-3163.
    [27] G. Konig, D. Bradley, A. K. C. Lau, C. G. W. Sheppard, and R. R. Maly, Role of Exothermic Centers on Knock Initiation and Knock Damage [C], SAE international fuels and lubricants, Tulsa, No.902136,October 1990.
    [28] Michikata Kono, Seiichi Shiga, Seiichiro Kumagai, Kazuo Iinuma ,Thermodynamic and experimental determinations of knock intensity by using a spark-ignited rapid compression machine[J], Combustion and Flame, December 1983, Volume 54, Issues 1, pp.33-47.
    [29] Nobuyuki Kawahara, Eiji Tomita, and Yoshitomo Sakata, Auto-ignited kernels during knocking combustion in a spark-ignition engine[J], Proceedings of the Combustion Institute, 2007, vol.31, pp.2999–3006.
    [30] Mohamad Abu-Qudais. Exhaust Gas Temperature for Knock Detection and Controll in Spark Ignition Engine [J]. Energy Convers, Mgmt, 1996, Vol. 37, No.9, pp.1383-1392.
    [31]许沧粟,邢建国,基于火花塞离子电流信号的发动机爆震检测研究[J],内燃机工程,2002, 23(02):12-14。
    [32] Eric Ollivier, Jerome Bellettre, Mohand Tazerout, and Gilles C. Roy, Detection of knock occurrence in a gas SI engine from a heat transfer analysis [J], Energy Conversion and Management, 2006, vol. 47, pp.879–893.
    [33] Loubar K, Bellettre J, and Tazerout M. Unsteady heat transfer enhancement around an engine cylinder in order to detect knock [J]. Journal of Heat Transfer, 2005,127(3):278–286.
    [34] Kwang Min Chun, Sun Ki Min, Ki Won Park,Flame propagation measurement using ionization probes during fast acceleration [C],SAE paper, No.2000 -05-0157,June 2000.
    [35] Norihiko Nakamura,Eishi Ohno,Masanobu Kanamaru, and Tomoyuki Funayama, Detection of Higher Frequency Vibration to Improve Knock Controllability [J], SAE Trans., 1987, 96(3):607-614.
    [36] K. M. Chun, and K. W. Kim, Measurement and Analysis of Knock in a SI Engine Using the Cylinder Pressure and Block Vibration Signals[J], SAE, No.940146, 1994, pp.286–293.
    [37]彭生辉,内燃机爆震与爆震传感器的性能研究[D],合肥工业大学,2005。
    [38] Masayoshi Kaneyasu, Nobuo Kurihara, Kozo Katogi, and Hiroatsu Tokuda, Engine Knock Detection Using Multi-Spectrum Method [C], SAE paper, No.920702, 1992.
    [39] Jonghwa Lee, Sunghwan Hwang, Jinsoo Lim, and Yong-Seok Cho, A New Knock-Detection Method Using Cylinder Pressure, Block Vibration and Sound Pressure Signals From a SI Engine [C], SAE paper, No.981436, 1998.
    [40]王宇鹏,爆震反馈控制汽油机点火ECU技术研究[D],河北工业大学,2007.11。
    [41]韩宇石,电控汽油机爆震信号分析与检测[D],北京工业大学,2005.5。
    [42]张红光,汽油机爆震检测的研究[D],北京工业大学,1995。
    [43]姜卓,卓斌,现代汽油机电控系统的爆震检测与控制[J],车用发动机,2000,127(3):36-39。
    [44]吴平友,黄河,程庆,汽油发动机爆震分析与控制[J],传动技术, 2003,36(3):36-39。
    [45]钟祥麟,于秀敏,高磊,梁晶晶,汽油机爆震控制系统设计与判别技术[J],农业机械学报,2008,39(9):20-23。
    [46]于秀敏,高莹等,汽油机爆震信号测量与应用分析[J],内燃机学报,2000,13(4):399-403。
    [47] K.M.Chun, and J. B. Heywood, Characterization of Knock in a Spark- Ignition Engine [J], SAE, No. 890156, 1989, pp.1-14.
    [48] Gang Wu, A real time statistical method for engine knock detection [J], SAE Technical Paper, No.2007-01-1507, 2007, pp.245-252.
    [49] Gao Xiaofeng, Richard Stone, Chris Hudson, and Ian Bradbury, The Detection and Quantification of Knock in Spark Ignition Engines [C], SAE paper, No.932759, 1993.
    [50] C. Hudson, X. Gao, R. Stone, Knock measurement for fuel evaluation inspark ignition engines [J] ,FUEL,2001,Vol.80, pp.395-407.
    [51] S. Vulli, J.F.Dunne, R.Potenza, D.Richardson, P.King, Time-frequency analysis of single-point engine-block vibration measurements for multiple excitation-event identification [J], Journal of Sound and Vibration, 2009, Vol.321, pp.1129–1143.
    [52]杨建国,张建峰,刘晓峰,基于时频分析的汽油机爆震特征的提取[J],内燃机工程,2003,24(3):33-37。
    [53]王彦岩,杨建国,宋宝玉,基于DWT的汽油机爆震信号分析[J],北京航空航天大学学报, 2009, 35(10):1166-1169。
    [54] F. A. Shirazi and M. J. Mahjoob, Application of Discrete Wavelet Transform (DWT) in Combustion Failure Detection of IC Engines [C], Proceedings of the 5th International Symposium on image and Signal Processing and Analysis,2007, pp.482-486.
    [55] Jian-Da Wu, Jien-Chen Chen, Continuous wavelet transform technique for fault signal diagnosis of internal combustion engines [J], NDT&E Internationa, 2006, l(39):304–311.
    [56] Sung Tae Park, Jinguo Yang, Engine knock Detection based on wavelet transform [C], Proceedings of Russian-Korean International Symposium on Science and Technology (KORUS 04), IEEE MECHANICS, 2004, Volume 3, pp.80-83.
    [57] Jonathan M. Borg ,George Saikalis ,Shigeru Thomas Oho, Ka C. Cheok, Knock Signal Analysis Using the Discrete Wavelet Transform [C], SAE paper, No.2006-01-0226, 2006.
    [58] F. Molinaro, F. Casta, A. Denjean, Knocking Recognition in Engine Vibration Signal Using the Wavelet Transform[C], Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-scale Analysis, Victoria, 1992, pp.353-356.
    [59] Zhong Zhang, Eiji Tomita, Knocking detection using wavelet instantaneous correlation method [J], Society of Automotive Engineers of Japan (JSAE), 2002, Review 23, pp.443–449.
    [60] Zhong Zhang, Eiji Tomota, A New Diagnostic Method of Knocking in a Spark-Ignition Engine Using the Wavelet Transform [J], SAE, No.2000-01-1801, 2000, pp.1-8.
    [61] J. Fiolka, A Fast Method for Knock Detection using Wavelet Transform[C], Proceedings of International Conference on Mixed Design of Integrated Circuits and System (MIXDES), POLAND, 2006, pp.621-626.
    [62] G.B.Giannakis, M.K. Tsatsanis, A unifying maximum-likelihood view of cumulants and polyspectral measures for non-Gaussian signal classification and estimation [J], IEEE Trans.Information Theory, 1992, 38:386-406.
    [63]王树勋,高阶统计量在系统理论中的应用[J],自动化学报,1994,20(6):710-717。
    [64] B.M.Sadler, G.B. Giannakis, and L.S.Lii, Estimation and detection in non-Gaussian noise using higher-order cumulants[J], IEEE Trans. Signal Processing, 1994, 42(10):2729-2741.
    [65] T.Lobos, Z.leonowicz , J.Szymanda, P.Ruczewski, Application of higher-order spectra for signal processing in electrical power engineering [J], Computation and Mathematics in Electrical and Electronic Engineering, 1998,vol.17, No.5, pp.602-611.
    [66]张桂才,史铁林,杨叔子,基于高阶统计量的机械故障特征提取方法研究[J],华中理工大学学报,1999, 27(3):6-8。
    [67]尚万峰,关惠玲,李志军,基于高阶统计量自适应滤波的故障特征的提取[J],信号处理,2005, 21(5): 544-547。
    [68] Lai Wuxing, Peter W T, Zhang Guicai, and Shi Tielin. Classification of Gear Faults Using Cumulants and the Radial Basis Function Network [J]. Mechanical Systems and Signal Processing, 2004, 18(2):381-389.
    [69] Huang Jinying, Bi Shihua, Pan Hongxia, Yang Xiwang, The Research of Higher-order Cumulant Spectrum for Vibration Signals of Gearbox [C], IEEE International Conference on Information Acquisition, 2006, Weihai, pp.1395-1399.
    [70]邵忍平,黄欣娜,刘宏昱,胡军辉,高阶累积量分析理论及其在机械传动系统损伤检测中的应用[J],西北工业大学学报, 2008,26(2):259-264。
    [71] Colonness S, Scarano G, Transient signal detection using higher order moments [J], IEEE Trans on Signal Processing, 1999,47 (2): 515—520.
    [72] Sattar, F. Salomonsson, G., On detection using filter banks and higher order statistics[J], IEEE Transactions on Aerospace and Electronic Systems, 2000, 36(4):1179-1189.
    [73]范虹,孟庆丰,张优云,冯武卫,基于滤波器组和高阶累积量的信号特征检测[J],振动与冲击,2007,26(2):29-32。
    [74]张付军,黄英,葛蕴珊,孙业保,共振型传感器用于爆震闭环控制系统的研究[J],北京理工大学学报,1999,19(6):705-709。
    [75] Dues S.M. Combustion Knock Sensing, Sensor Selection and Application [J], SAE paper,No.900488, 1990, pp.93-103.
    [76] Bahman Samon, Giorgio Richard, Engine Knock Analysis and Detection Using Time Frequency Analysis [J], SAE paper,No.960618.
    [77]张玲华,郑宝玉,随机信号处理[M],清华大学出版社,2003。
    [78] Poularikas A D, The handbook of formulas and tables for signal processing [M], Springer, IEEE Press, 1998.
    [79] Burg J P, Maximum entropy spectral analysis[C], 37th Ann. Int. Soc. Explar Geophysics meeting, Oklahoma, 1967.
    [80] Peled A, Liu B, Digital signal processing: Theory, Design and Implementation [M], John Wiley & Sons, 1976.
    [81] W.J.Staszewski, and G.R.Tomlinson, Application of the wavelet transform to fault detection in a spur gear [J], Mechanical Systems and Signal Processing, 1994, 8(3):289-307.
    [82] Jing Lin, Feature extraction of machine sound using wavelet and its application in fault diagnosis [J], NDT&E International, 2001, 34:25-30.
    [83] F. A. Shirazi and M. J. Mahjoob, Application of Discrete Wavelet Transform (DWT) in Combustion Failure Detection of IC Engines [C], Proceedings of 5th International Symposium on image and Signal Processing and Analysis, 2007, pp.482-486.
    [84]成礼智,王红霞,罗永,小波的理论与应用[M],科学出版社,2004。
    [85]杨福生,小波变换的工程分析与应用[M],科学出版社,1999。
    [86] Mallat S. A theory for multiresolution signal decomposition: the wavelet representation [J], IEEE Transaction on Pattern Analysis andmachine Intelligence, 1989, 11(7): 674-693.
    [87] Mallat S. Multiresolution approximations and wavelet orthonormal bases of L2(R) [J], Transactions of the American Mathematical Society, 1989, 315(1): 69-87.
    [88] Mallat S G, Multifrequency Channel Decompositions of Images and Wavelet Models [J], IEEE Transactions on Acoustics, Speech and Signal Processing, 1989, 37(12):2091-2110.
    [89]谭善文,秦树人,汤宝平,小波基时频特性及其在分析突变信号中的应用[J],重庆大学学报,2001,24(2):12-17。
    [90]汪新凡,小波基选择及其优化[J],株洲工学院学报,2003,17(5):33-35。
    [91] Rivola A , White P R. Detection of Rolling Element Bement Bearing Damage by Statistical Vibration Analysis[J]. Journal of Sound and Vibration, 1998, 216(5): 889-910.
    [92] M.J.Hinich and G.R.Wilson, Detection of non-gaussian signal in non-gaussian noise using bispectrum [J], IEEE transactions on Signal Processing, 1990, vol.38, No.7, pp.1126-1131.
    [93]蒋平,贾民平,许飞云,胡建中,机械故障诊断中微弱信号处理特征的提取[J],振动、测试与诊断,2005,25(1):48-50。
    [94]张贤达,时间序列分析-高阶统计量方法[M],清华大学出版社,1996。
    [95] C.L.Nikias and J.M.Mendel, Signal processing with higher-order spectra [J], IEEE Signal processing Magazine, 1993, 10(3):10-37.
    [96]邱天爽,张旭秀,李小兵,孙永梅,统计信号处理-非高斯信号处理及其应用[M],电子工业出版社,2004。
    [97]张贤达,现代信号处理[M],清华大学出版社,2002。
    [98]韩军,内燃机的非平稳信号分析方法及其噪声源小波识别技术的研究[D],博士学位论文,天津大学,2004。
    [99] Albert H. Nuttall, Some Windows with Very Good Sidelobe Behavior [J], IEEE Transactions on Acoustics, Speech, and Signal Processing, February 1981,Vol.29, No.1, pp.84-91.
    [100]朱利民,钟秉林,贾民平,振动信号短时分析方法及在机械故障诊断中的应用[J],振动工程学报,2000,13(3):400-405。
    [101] S. Ker, F. Bonnardot and L. Duval, Algorithm comparison for real timeknock detection [C], IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 07), 2007, pp.397-400.
    [102] Mendel J.M. Tutorial in Higher-Order Statistics (Spectra) in signal processing and system theory: Theoretical results and some applications [J], Pro.IEEE, 1991, 79(3):278-305.
    [103] Dan Lazarescu, Vasile Lazaresc, Mihaela Uagureanu, Knock Detection based on Power Spectrum Analysis[C], International Symposium on Signals, Circuits and Systems (ISSCS 2005), Iasi, 2005. Vol.2, pp.701-704.
    [104]武得钰,傅茂林,李建权等,火花点火发动机爆震强度评价指标的研究[J],内燃机学报,1997,15(1):62-70。

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