小波自适应控制系统及其在噪声主动控制中的应用研究
|
摘要
随着现代社会的发展，噪声控制问题日益引起了人们的高度重视和极大关注。无论在民用领域还是军事领域，噪声不但污染环境，损害健康，致使设备疲劳损伤，而且可能危及生命，噪声控制已经成为了一个迫切需要解决的世界性难题，世界各国都投入了大量的人力和物力对此展开了深入的研究。
就噪声主动控制系统而言，目前普遍使用的是自适应控制策略，而且已经取得了丰硕的成果。但自适应控制尚不完善，其中的许多算法存在着明显的不足和特定性。因此运用新的信息分析手段对控制算法进行研究是一个非常有潜力的、具有重要意义的工作。针对这一问题，本文选择了以控制算法和控制方法为切入点，从理论上和实验上进行了研究和探讨。
从总体上讲，本文的主要研究工作如下：
1.本文首先分析了几种常用的最小均方(Least Mean Square, LMS)算法，利用计算机仿真对每一种算法的性能进行比较，总结了影响LMS算法的重要因素，这些都为算法的改进工作提供了重要依据。
2. 本文把小波分析理论和LMS算法结合起来提出了两种结构形式的小波自适应算法，即：分解LMS算法（Decomposition LMS, D-LMS）和分解重构LMS算法（Decomposition and Reconstruction LMS, DR-LMS），对每一种算法进行了深入的理论分析。为了提高小波自适应算法的实时性，推导出了MALLAT算法的一种高效的实现方法。为了从仿真的角度考察小波自适应算法的性能，建立了系统辨识的仿真模型，获得了分别采用小波自适应算法和LMS算法的系统辨识结果。结果表明，与LMS算法相比，小波自适应算法的性能得到了很大的提高，使得控制系统的设计具备了强有力的工具。
3. 根据Filtered-X LMS算法的思想和随机自适应控制理论，建立了小波自适应控制系统。根据D-LMS算法和DR-LMS算法，本文设计了两种形式的小波自适应控制器，在解决小波自适应控制的系统辨识问题时，引入了并行在线系统辨识方法，把D-LMS算法和DR-LMS算法应用了到该辨识方法中，提高了系统辨识的精度。
4. 在以上研究的基础上，把小波自适应控制系统应用到基于智能结构思想的噪声主动控制中，完成了小波自适应控制系统的硬件和软件设计，建立了实验系统，并进行了大量的实时控制实验。实验结果表明，无论对
于频率简单的噪声信号还是频率成分复杂的噪声信号，小波自适应控制系统都能对其进行有效的抑制，从而从实验上证明了小波理论的引入改善了自适应算法的性能，提高了自适应控制系统的稳定性和适应性。
With the development of society, the topic of noise control has been received considerable attention. Either in civil or military domain, noise is polluting the environment, doing harm to our health. Even our lives are badly endangered, so the noise control is becoming important and urgent. The works in this domain have been widely investigated all over the world.
As far as the active noise control system, the adaptive control strategy is generally adopted, and that the results are comparatively satisfying. However, the adaptive control also is not perfect in many aspects, for instance, the deficiencies in many adaptive algorithms are extraordinarily distinct. Consequently it is promising and significant to improve the performance of adaptive algorithm by means of new methods. Aimed at this matter, the control algorithm and control way are investigated in this paper.
On the whole, the work in the paper is made up of the following part:
1. Firstly, the several LMS (Least Mean Square, LMS) algorithms are analyzed and their performance is compared by the simulation results, which offer gist for the improvement of algorithm.
2. Combining the Wavelets and LMS algorithm, the paper brings forward two classes of Wavelets Adaptive Algorithm (WAF) with different structure, viz., D-LMS algorithm and DR-LMS algorithm. Theoretically investigation on each algorithm is made in details. In order to achieve the real-time of WAF, the fast use of WALLAT algorithm is brought out in the paper. To study on the performance of WAF, the simulations of system identification with D-LMS algorithm and DR-LMS algorithm are made. The simulations indicate that the performance of WAF is greatly improved, which offer the powerful and efficient method for design of control system.
Based on Filtered-X LMS algorithm and random adaptive control, the Wavelet Adaptive Control System (WACS) is constructed in the paper. The wavelet adaptive controller is developed; the adaptive equation of the parameter matrix of each controller is presented in details. Because, in adaptive control, the precision and real-time of system identification can have direct effect on control quality, the method of system identification is
3. vital. In the paper, the parallel on-line system identification is applied in control system, which effectively solves the problem in system identification.
4. Finally, active noise control with the wavelet adaptive control system (WACS) is explored. Corresponding hardware and software of wavelet adaptive controller are developed. The real-time experiment with WACS shows that noise with simple or complex frequency components can be greatly and rapidly reduced, which indicates that introducing Wavelet to LMS algorithm has improved the performance of LMS and WACS.
就噪声主动控制系统而言，目前普遍使用的是自适应控制策略，而且已经取得了丰硕的成果。但自适应控制尚不完善，其中的许多算法存在着明显的不足和特定性。因此运用新的信息分析手段对控制算法进行研究是一个非常有潜力的、具有重要意义的工作。针对这一问题，本文选择了以控制算法和控制方法为切入点，从理论上和实验上进行了研究和探讨。
从总体上讲，本文的主要研究工作如下：
1.本文首先分析了几种常用的最小均方(Least Mean Square, LMS)算法，利用计算机仿真对每一种算法的性能进行比较，总结了影响LMS算法的重要因素，这些都为算法的改进工作提供了重要依据。
2. 本文把小波分析理论和LMS算法结合起来提出了两种结构形式的小波自适应算法，即：分解LMS算法（Decomposition LMS, D-LMS）和分解重构LMS算法（Decomposition and Reconstruction LMS, DR-LMS），对每一种算法进行了深入的理论分析。为了提高小波自适应算法的实时性，推导出了MALLAT算法的一种高效的实现方法。为了从仿真的角度考察小波自适应算法的性能，建立了系统辨识的仿真模型，获得了分别采用小波自适应算法和LMS算法的系统辨识结果。结果表明，与LMS算法相比，小波自适应算法的性能得到了很大的提高，使得控制系统的设计具备了强有力的工具。
3. 根据Filtered-X LMS算法的思想和随机自适应控制理论，建立了小波自适应控制系统。根据D-LMS算法和DR-LMS算法，本文设计了两种形式的小波自适应控制器，在解决小波自适应控制的系统辨识问题时，引入了并行在线系统辨识方法，把D-LMS算法和DR-LMS算法应用了到该辨识方法中，提高了系统辨识的精度。
4. 在以上研究的基础上，把小波自适应控制系统应用到基于智能结构思想的噪声主动控制中，完成了小波自适应控制系统的硬件和软件设计，建立了实验系统，并进行了大量的实时控制实验。实验结果表明，无论对
于频率简单的噪声信号还是频率成分复杂的噪声信号，小波自适应控制系统都能对其进行有效的抑制，从而从实验上证明了小波理论的引入改善了自适应算法的性能，提高了自适应控制系统的稳定性和适应性。
With the development of society, the topic of noise control has been received considerable attention. Either in civil or military domain, noise is polluting the environment, doing harm to our health. Even our lives are badly endangered, so the noise control is becoming important and urgent. The works in this domain have been widely investigated all over the world.
As far as the active noise control system, the adaptive control strategy is generally adopted, and that the results are comparatively satisfying. However, the adaptive control also is not perfect in many aspects, for instance, the deficiencies in many adaptive algorithms are extraordinarily distinct. Consequently it is promising and significant to improve the performance of adaptive algorithm by means of new methods. Aimed at this matter, the control algorithm and control way are investigated in this paper.
On the whole, the work in the paper is made up of the following part:
1. Firstly, the several LMS (Least Mean Square, LMS) algorithms are analyzed and their performance is compared by the simulation results, which offer gist for the improvement of algorithm.
2. Combining the Wavelets and LMS algorithm, the paper brings forward two classes of Wavelets Adaptive Algorithm (WAF) with different structure, viz., D-LMS algorithm and DR-LMS algorithm. Theoretically investigation on each algorithm is made in details. In order to achieve the real-time of WAF, the fast use of WALLAT algorithm is brought out in the paper. To study on the performance of WAF, the simulations of system identification with D-LMS algorithm and DR-LMS algorithm are made. The simulations indicate that the performance of WAF is greatly improved, which offer the powerful and efficient method for design of control system.
Based on Filtered-X LMS algorithm and random adaptive control, the Wavelet Adaptive Control System (WACS) is constructed in the paper. The wavelet adaptive controller is developed; the adaptive equation of the parameter matrix of each controller is presented in details. Because, in adaptive control, the precision and real-time of system identification can have direct effect on control quality, the method of system identification is
3. vital. In the paper, the parallel on-line system identification is applied in control system, which effectively solves the problem in system identification.
4. Finally, active noise control with the wavelet adaptive control system (WACS) is explored. Corresponding hardware and software of wavelet adaptive controller are developed. The real-time experiment with WACS shows that noise with simple or complex frequency components can be greatly and rapidly reduced, which indicates that introducing Wavelet to LMS algorithm has improved the performance of LMS and WACS.
引文
[1] 方丹群，王文奇，孙家麟，《噪声控制》，北京出版社，1986
[2] 陈克安，马远良，《自适应有源噪声控制—原理、算法及实现》，西北工业大学出版社，1993
[3] 黄尚廉，智能结构—工程学科萌生的一场革命，压电与生光，Vol.15，No.1，1993，pp.13-15
[4] 陶宝祺，《智能材料 结构》，国防工业出版社，1997
[5] C.A. Rogers, Intelligent material system-the dawn of a new materials age, J. Intelligent material system and structures, Vol. 4, 1993, pp.4-12
[6] Fuller C R Hansen C H, Silcox R J and Snyder S D, Active control of interior noise in model aircraft fuselages using piezoelectric actuators, AIAA Paper ,1990, pp.90-3392.
[7] Pan J. and Hansen C H, Active control of noise transmission through a panel into a cavity I: analytical study, J. Acoust. Soc. Am, 1991, 87, pp.1488-92.
[8] Pan J. and Hansen C H, Active control of noise transmission through a panel into a cavity II: experimental study, J. Acoust. Soc. Am, 1991,90, pp.1488-92.
[9] Pan J. and Hansen C H, Active control of noise transmission through a panel into a cavity III: effect of the actuators location, J. Acoust. Soc. Am, 1991,90, pp.1493-501.
[10] Fuller C R, Hansen C H and Snyder S D, Experiments on active control of sound radiation from a panel using a piezoceramic actuator, J. Acoust. Soc. Am, 1991,150, pp.179-90.
[11] E.F. Crawley and J.de Luis, Use of piezoelectric actuators as elements of intelligent structures AIAA J. 1987 25 1373-85.
[12] M.R Flemming, An experimental in investigation of the harmonic excitation of simply supported plates with surface bonded piezoceramic actuators, VPI&SU Master of Science thesis Department of Mechanical Engineering, March 1991.
[13] Clark R.L. and Fuller C.R, Control, of Sound Radiation with Adaptive Structures, J. Intelligent Materials Systems and Structures, Vol.2 No.3, 1991, pp.431-452.
[14] Widrow, A comparison of adaptive algorithm based on method of steepest descent and random search, IEEE Transaction ASSP 24, Sept. 1976
[15] D.G.Luenberger, Optimization by vector space methods, 1969
[16] A.P.Naglor, Linear operator theory in science and engineering, 1976
[17] C.F.N.Cowan, P.M.Grant , Adaptive Filters, Englewood Cliffs, NJ: Prentice Hall,1985
[18] M.L.Honig, D.G.Messerschimitt, Adaptive Filter: Structure,Algorithm and Application, Boston, Kluwer Academic Publisher,1986
[19] 陈尚勤，李晓峰，《快速自适应信息处理》，人民邮电出版社，1993
[20] Simon Haykin, 自适应滤波器原理(第三版), 电子工业出版社，1998
[21] P.Goupillaud, A.Grossmann and J.Morlet, Cycle-octave and related transforms in seismic signal analysis, Geoexploration, Vol. 23, 1984
[22] A.Grossmann and J.Morlet, Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM. J. Math. Anal.,Vol.15 No.4, 1984
[23] S. Mallat, Multiresolution approximation and wavelets, Tech. Rep., Dep. Comput. Inform. Sci., Univ. Pensylvania, PA, Sept 1987
[24] I.Daubechies, Orthogonal bases of compactly supported wavelets, Commun. Pure Appl. Math. ,Vol. XLI, 1988
[25] S.Mallat, A theory for multiresolution signal decomposition: The wavelet representation, IEEE trans. Patt. Anal. Machine Intell., Vol.11, No.7,1989. pp.674-93
[26] S.Mallat, Multifrequency channel decompositions of images and wavelet models, IEEE trans. Acoust. Speech Signal Processing, Vol.37 Dec. 1989
[27] 王群仙，李少远，李俊芳，小波分析及其在控制中的应用，控制与决策，Vol.15 No.4, 2000, pp.385-389
[28] 张建刚，张杰，提高辨识精度的多分辨分析方法，97' 中国控制会议论文集，庐山，1997， pp.559-62
[29] 徐长江，宋文忠，基于小波变换估计传递函数，自动化学报，Vol.23,No.6, 1997, pp.835-38
[30] J.H.Lee, Z Yu, Tuning of model predictive controllers for robust performance.
Computers and Chemical Engineering, Vol.18, No.1,1998 pp.15-37
[31] D.L Donobo. De-noising by soft thresholding, IEEE Trans.on Infor. Theory, Vol.41,No.3, 1995 613-26
[32] Q Zhang ,A Benveniste, Wavelet network, IEEE Trans. On NN Vol.3,No.4,1992, pp.1485-97
[33] 刘山，吴铁军， 一种基于小波逼近的稳定直接自适应控制算法，自动化学报，Vol.23, No.5,1997, pp.636-40
[34] B.Delyon, A Juditsky, A benveniste, Accuracy analysis for wavelet approximation, IEEE trans on NN, Vol. 6, No.2, 1995, pp.332-48
[35] B. Widrow S. D. Stearns, Adaptive Signal Processing, Prenice-Hall, Inc. 1985
[36] R.R Bitmead and B. D.O.Anderson, Performance of adaptive estimation algorithms in dependent random environments, IEEE Trans. Autom. Control, vAC25, 1980, pp 788-794.
[37] Nagumo, J.I.,A.Noda, A learning method for System Identification, IEEE Trans. Autom. Control, vol. AC-12, 1967, pp. 282-287
[38] Douglas,S.C.,and T.H.-Y.Meng, Normalized data nonlinearities for LMS Adaptation, IEEE Trans. Acoust. Speech Signal Process., vol. 42, pp. 1352-1365
[39] W.A.Gardner, Learning characteristics of stochastic gradient descent algorithm: a general study, analysis, and critique, Signal Processing, v6, April, 1984, pp.113-33.
[40] J.G. Proakis, Digital Communications, 3rd Ed., McGraw-Hill, New York, 1995
[41] S.Roy and J.J.Shynk, Analysis of the momentum LMS algorithm, IEEE Trans.on Acoust. Speech Signal Processing, vASSP-38, 1990, pp.2088-98,
[42] 崔锦泰(美)，小波分析导论，程正兴译，西安交通大学出版社，1995
[43] I.Daubechies, Ten lectures on wavelets, CBMSNSF Regional Conference Series in Application Mathematics, SIAM Press, Philadelphia Pennsylvania, Vol.61,1992.
[44] 刘贵忠，邸双亮，小波分析及其应用，西安电子科技大学出版社，1992
[45] S.Hosur and A.H.Tewfik, Wavelet transform domain LMS algorithm, IEEE Int. Conf. Acoust. Speech Signal Processing, April,1993,Vol.3 pp.508-10
[46] M. Doroslovacki and H. Fan, Wavelet-based adaptive filtering, IEEE Int. Conf. Acoust. Speech Signal Processing, April, 1993, Vol.3 pp.488-91
[47] J.C.Lee and C.K.Un, Performance of transform domain LMS adaptive digital filters, IEEE Trans. Acoust. Speech Signal Processing, Vol.ASSP-34, 1986, No.3, pp.499-510
[48] A.Gilloire and M. Vetterli, Adaptive filtering in subbands with critical sampling: Analysis experiments and application to acoustic echo cancellation, IEEE Trans. Signal Processing, Vol.40, No.8, 1992, pp.1862-75.
[49] D. F. Marshall, W.K.Jenkins and J.J.Murphy, The useof orthogonal transforms for improving performance of adaptive filters, IEEE Trans. Circuits Syst.,Vol.36, No.4,1989, pp.474-83
[50] S.Gazor and B.Farhang-Boroujeny, Quantization effects in transform domain normalized LMS algorithm, IEEE Trans. Circuit Syst. II: Aanlog Digital Signal Processing, Vol.39, No.1, 1992, pp.1-7
[51] P.L.Feintuch, N.J. Bershad and A.K.Lo, A frequency domain model for fitered LMS algorithm-Stability analysis design and elimination of the training mode, IEEE Trans. Acoust. Speech, and Signal Processing, Vol. ASSP-41,1993, pp.1518-31
[52] H.Ohmori, T.Murase and A.Sano, Design of universal direct adaptive control on frequency domain approach, Proc. the 30th IEEE Conf. Decision and Control, Brighton, UK, 1991,pp.2710-18
[53] R.Coifman, Y. Meyer and V.Wickerhauser, Wavelet analysis and signal processing, Wavelet Analysis and Their Applications, Jones and Bartllet Boston, 1992,pp.153-78
[54] Gaviphat Lekutai, Adaptive self-tuning neuro wavelet network controllers[Dissertation], Virginia Polytechnic Institute and State University, pp.71-79.
[55] G.Beylkin, R.Coifman and V.Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. On Pure and Applied Math., Vol.XLIV,1991, pp.141-83
[56] i. Daubechies, Orthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., Vol.41,1988, pp.909-96
[57] R.R. Coifman et. al., Signal processing and compression with wave packets , Preprint, Dept. of Math., Yale Univ.,1990
[58] J.M. Combes, A.Grossmann and Ph. Tchamitchian, Eds, Wavelets: Time-frequency methods and phase space, 2nd edition Springer-Verlag, New York, NY, 1989
[59] F.C.Chen, Back-propagation neual networks for nonlinear self-tuning adaptive
control ,IEEE Control Systems Magazine, Special Issue on Neural Networks for Control System, April, 1990, pp44-8
[60] Dorolovacki, M.I., and Fan., H., Wavelet-based linear system modeling and adaptive filtering, IEEE Trans. Signal Processing, Vol.44,1996, pp.1156-67
[61] [瑞典] K.J.奥斯特隆姆，B.威顿马克，李清泉等译，自适应控制，科学出版社，1992
[62] 李清泉 自适应控制系统理论设计与应用，科学出版社，1990
[63] 李树英，许茂增，随机系统的滤波与控制，国防工业出版社，1991
[64] 赵长安等，控制系统设计手册（上），国防工业出版社，1991
[65] S.M. Veres, Self-tuning control by model unfalsification (Part I), Int.J.Control. Vol.73,No.17,2000,1548-59
[66]Youping Zhang and Petros A. Ioannou, A new linear adaptive controller: Design, analysis and performance, IEEE Trans. On Auto. Control, Vol.45, No.5, 2000, pp.883-97
[67] B.维德罗，S.D.史蒂恩斯，王永德，龙宪惠 译，自适应信号处理，四川大学出版社，1991
[68] S.Kadambe and P.Srinivasan, Application of adaptive wavelets for speech coding, Proceedings of the IEEE-SP International Symposium of Timer-Frequency and Time-Scale Analysis, 1994, pp. 632-35
[69] S.A.Imhoff, D.Y.Roeum and M.R.Rosiek, New classes of frame wavelets for application, Wavelet Application 11, H.H.Szu, Ed., Proceedings SPIE- The International Society for Optical Engineering, V2491, 1995, pp.923-34
[70] Zhang Qinghua, Albet Benveniste, Wavelet networks, IEEE Trans.on NN, Vol.3 No.6,1992, pp.889-898
[71] Leontaritis I J, Billings S A. Model selection and validation methods for non-linear systems, International Journal of Control, Vol.45, No.1, 1987,pp.311-341
[72] Sen M.Kuo, Mingjie Wang, and Ke Chen, Active noise control system with parallel on-line error path modeling algorithm, Noise Control Engineering Journal, Vol.39, No.3, pp.119-27.
[73] Eriksson L J., Allie M. C., Use of random noise for on-line transducer modeling in an adaptive active attenuation system. J. Acoust. Soc. Am. Vol.85,No.2,1989 pp.797-802.
[74] J.I.Nagumo, A. Noda, A learning method for system identification, IEEE Trans. Automat. Contr. Vol.AC-12 June 1967 pp.282-287
[75] L.Eriksson and M.Allie, Use of Random Noise for On-line Transducer Modeling in an Adaptive Active Attenuation System, Journal of the Acoustical Society of America, Vol.85,No.2, Feb, 1989, pp.797-802.
[76] J.Tapia and Sen M. Kuo, New Adaptive On-line Modeling Techniques for Active Noise Control Systems, IEEE International Conference on Systems Engineering, Pittsburgh, Pennsylvania, August 1990, pp.280-3.
[77] Clark R.L.and Gibbs G.P, A novel approach to feedforward higher harmonic control. J.Acoust.Soc.Am,Vol.96, pp.926-36.
[78] Elliott S.J, I. M.Stothers, P.A. Nelson, A multiple error LMS algorithm and its application it the active control of sound and vibration, IEEE Tans. on ASSP , Vol.ASSP-35(10), 1987, pp.1423-34.
[79] N.Erdol and Basbug, Wavelet transform based adaptive filtering, in Signal Processing, VI:Theories and Applications, J. Vandewalle, R.Boite, M.Moonen, and A.Oosterlinck, Eds. Amsterdam, The Netherlands: Elsevier Science, 1992, pp.1117-20
[80] N.J.Bershad, Nonlinear quantization effects in the LMS and block LMS adaptive algorithms-A comparison, IEEE Trans. Acoust. Speech, Signal Processing, Vol.37, Oct. 1989, pp.1504-12
[81] G.Lekutai, and H. VanLandingham, Self-tuning control of nonlinear systems using neural network adaptive frame wavelets, IEEE Int. Conf. Man, and Cybernatics ,Orlando, FL, 1997
[82] B.A. Telfer, H.H. Szu, and G.J. Dobeck, Adaptive Wavelet classification of acoustic backscatter, Wavelet Applications, H.H.Szu, Ed., Proceedings of SPIE-The International Society for Optical Engineering, V2242, 1994, pp.661-68
[83] R.K.Young, Wavelet Theory and Its Application, Kluwer Academic Publishers, Boston, MA,1993
[84] Pan J. and Hansen C H，Active control of noise transmission through a panel into a cavity I: analytical study. J.Acoust.Soc.Am.Vol.87,1991, pp.1488-92.
[85] Pan J. and Hansen C H, Active control of noise transmission through a panel into a cavity II: experimental study. J.Acoust.Soc.Am.Vol.90,1991 pp.1488-92.
[86] Koshigoe S, Gillis J T and Falangas E T. A new approach for active control of sound transmission through an elastic plate backed by a rectangular cavity, J.Acoust.Soc.Am.Vol.94, 1993, pp.900-7.
[87] Fuller C R, Hansen C H and Snyder S D. Experiments on active control of sound
radiation from a panel using a piezoceramic actuator, J.Acoust.Soc.Am. Vol.150,1991, pp.179-90.
[88] M.R Flemming, An experimental in investigation of the harmonic excitation of simply supported plates with surface bonded piezoceramic actuators. VPI&SU Master of Science thesis Department of Mechanical Engineering, March 1991.
[89] Bor-Tsuen Wang and Chris R. Fuller and Emilios K. Dimitriadis, Active control of noise transmission through rectangular plates using multiple piezoelectric or point force actuators". J. Acoust. Soc. Am. Vol. 90, No. 5, 1991 , pp.2820-30.
[90] 黄尚廉，国家自然科学重点基金‘智能机械结构及系统基础’申请书,1996.
[91] 黄尚廉，国家科委九五重大基础研究建议书.
[92] Texas Instruments, TMS320c3x User's Guide, July,1997
[93] B.Balachandran, A.sampath, J.Park, Feedforward active interior noise control, Smart Structures and Materials, SPIE, Vol. 2443,1995, pp.670-81
[94] A. Sampath, B.Balachandran, Active Structural acoustic control of bandlimited disturbances, Smart Structures and Materials, SPIE, Vol. 2717,1996, pp.422-33
[95] S.Koshigoe and J.W. Murdock, A unified analysis of both active and passive damping for a plate with piezoelectric transducers, Journal of Acoustical Society of America, Vol. 93, No.1, 1993, pp.346-55
[96] 杜功焕，朱哲民，龚秀芬，声学基础(上)，上海科学技术出版社，1981，pp.197-198
[2] 陈克安，马远良，《自适应有源噪声控制—原理、算法及实现》，西北工业大学出版社，1993
[3] 黄尚廉，智能结构—工程学科萌生的一场革命，压电与生光，Vol.15，No.1，1993，pp.13-15
[4] 陶宝祺，《智能材料 结构》，国防工业出版社，1997
[5] C.A. Rogers, Intelligent material system-the dawn of a new materials age, J. Intelligent material system and structures, Vol. 4, 1993, pp.4-12
[6] Fuller C R Hansen C H, Silcox R J and Snyder S D, Active control of interior noise in model aircraft fuselages using piezoelectric actuators, AIAA Paper ,1990, pp.90-3392.
[7] Pan J. and Hansen C H, Active control of noise transmission through a panel into a cavity I: analytical study, J. Acoust. Soc. Am, 1991, 87, pp.1488-92.
[8] Pan J. and Hansen C H, Active control of noise transmission through a panel into a cavity II: experimental study, J. Acoust. Soc. Am, 1991,90, pp.1488-92.
[9] Pan J. and Hansen C H, Active control of noise transmission through a panel into a cavity III: effect of the actuators location, J. Acoust. Soc. Am, 1991,90, pp.1493-501.
[10] Fuller C R, Hansen C H and Snyder S D, Experiments on active control of sound radiation from a panel using a piezoceramic actuator, J. Acoust. Soc. Am, 1991,150, pp.179-90.
[11] E.F. Crawley and J.de Luis, Use of piezoelectric actuators as elements of intelligent structures AIAA J. 1987 25 1373-85.
[12] M.R Flemming, An experimental in investigation of the harmonic excitation of simply supported plates with surface bonded piezoceramic actuators, VPI&SU Master of Science thesis Department of Mechanical Engineering, March 1991.
[13] Clark R.L. and Fuller C.R, Control, of Sound Radiation with Adaptive Structures, J. Intelligent Materials Systems and Structures, Vol.2 No.3, 1991, pp.431-452.
[14] Widrow, A comparison of adaptive algorithm based on method of steepest descent and random search, IEEE Transaction ASSP 24, Sept. 1976
[15] D.G.Luenberger, Optimization by vector space methods, 1969
[16] A.P.Naglor, Linear operator theory in science and engineering, 1976
[17] C.F.N.Cowan, P.M.Grant , Adaptive Filters, Englewood Cliffs, NJ: Prentice Hall,1985
[18] M.L.Honig, D.G.Messerschimitt, Adaptive Filter: Structure,Algorithm and Application, Boston, Kluwer Academic Publisher,1986
[19] 陈尚勤，李晓峰，《快速自适应信息处理》，人民邮电出版社，1993
[20] Simon Haykin, 自适应滤波器原理(第三版), 电子工业出版社，1998
[21] P.Goupillaud, A.Grossmann and J.Morlet, Cycle-octave and related transforms in seismic signal analysis, Geoexploration, Vol. 23, 1984
[22] A.Grossmann and J.Morlet, Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM. J. Math. Anal.,Vol.15 No.4, 1984
[23] S. Mallat, Multiresolution approximation and wavelets, Tech. Rep., Dep. Comput. Inform. Sci., Univ. Pensylvania, PA, Sept 1987
[24] I.Daubechies, Orthogonal bases of compactly supported wavelets, Commun. Pure Appl. Math. ,Vol. XLI, 1988
[25] S.Mallat, A theory for multiresolution signal decomposition: The wavelet representation, IEEE trans. Patt. Anal. Machine Intell., Vol.11, No.7,1989. pp.674-93
[26] S.Mallat, Multifrequency channel decompositions of images and wavelet models, IEEE trans. Acoust. Speech Signal Processing, Vol.37 Dec. 1989
[27] 王群仙，李少远，李俊芳，小波分析及其在控制中的应用，控制与决策，Vol.15 No.4, 2000, pp.385-389
[28] 张建刚，张杰，提高辨识精度的多分辨分析方法，97' 中国控制会议论文集，庐山，1997， pp.559-62
[29] 徐长江，宋文忠，基于小波变换估计传递函数，自动化学报，Vol.23,No.6, 1997, pp.835-38
[30] J.H.Lee, Z Yu, Tuning of model predictive controllers for robust performance.
Computers and Chemical Engineering, Vol.18, No.1,1998 pp.15-37
[31] D.L Donobo. De-noising by soft thresholding, IEEE Trans.on Infor. Theory, Vol.41,No.3, 1995 613-26
[32] Q Zhang ,A Benveniste, Wavelet network, IEEE Trans. On NN Vol.3,No.4,1992, pp.1485-97
[33] 刘山，吴铁军， 一种基于小波逼近的稳定直接自适应控制算法，自动化学报，Vol.23, No.5,1997, pp.636-40
[34] B.Delyon, A Juditsky, A benveniste, Accuracy analysis for wavelet approximation, IEEE trans on NN, Vol. 6, No.2, 1995, pp.332-48
[35] B. Widrow S. D. Stearns, Adaptive Signal Processing, Prenice-Hall, Inc. 1985
[36] R.R Bitmead and B. D.O.Anderson, Performance of adaptive estimation algorithms in dependent random environments, IEEE Trans. Autom. Control, vAC25, 1980, pp 788-794.
[37] Nagumo, J.I.,A.Noda, A learning method for System Identification, IEEE Trans. Autom. Control, vol. AC-12, 1967, pp. 282-287
[38] Douglas,S.C.,and T.H.-Y.Meng, Normalized data nonlinearities for LMS Adaptation, IEEE Trans. Acoust. Speech Signal Process., vol. 42, pp. 1352-1365
[39] W.A.Gardner, Learning characteristics of stochastic gradient descent algorithm: a general study, analysis, and critique, Signal Processing, v6, April, 1984, pp.113-33.
[40] J.G. Proakis, Digital Communications, 3rd Ed., McGraw-Hill, New York, 1995
[41] S.Roy and J.J.Shynk, Analysis of the momentum LMS algorithm, IEEE Trans.on Acoust. Speech Signal Processing, vASSP-38, 1990, pp.2088-98,
[42] 崔锦泰(美)，小波分析导论，程正兴译，西安交通大学出版社，1995
[43] I.Daubechies, Ten lectures on wavelets, CBMSNSF Regional Conference Series in Application Mathematics, SIAM Press, Philadelphia Pennsylvania, Vol.61,1992.
[44] 刘贵忠，邸双亮，小波分析及其应用，西安电子科技大学出版社，1992
[45] S.Hosur and A.H.Tewfik, Wavelet transform domain LMS algorithm, IEEE Int. Conf. Acoust. Speech Signal Processing, April,1993,Vol.3 pp.508-10
[46] M. Doroslovacki and H. Fan, Wavelet-based adaptive filtering, IEEE Int. Conf. Acoust. Speech Signal Processing, April, 1993, Vol.3 pp.488-91
[47] J.C.Lee and C.K.Un, Performance of transform domain LMS adaptive digital filters, IEEE Trans. Acoust. Speech Signal Processing, Vol.ASSP-34, 1986, No.3, pp.499-510
[48] A.Gilloire and M. Vetterli, Adaptive filtering in subbands with critical sampling: Analysis experiments and application to acoustic echo cancellation, IEEE Trans. Signal Processing, Vol.40, No.8, 1992, pp.1862-75.
[49] D. F. Marshall, W.K.Jenkins and J.J.Murphy, The useof orthogonal transforms for improving performance of adaptive filters, IEEE Trans. Circuits Syst.,Vol.36, No.4,1989, pp.474-83
[50] S.Gazor and B.Farhang-Boroujeny, Quantization effects in transform domain normalized LMS algorithm, IEEE Trans. Circuit Syst. II: Aanlog Digital Signal Processing, Vol.39, No.1, 1992, pp.1-7
[51] P.L.Feintuch, N.J. Bershad and A.K.Lo, A frequency domain model for fitered LMS algorithm-Stability analysis design and elimination of the training mode, IEEE Trans. Acoust. Speech, and Signal Processing, Vol. ASSP-41,1993, pp.1518-31
[52] H.Ohmori, T.Murase and A.Sano, Design of universal direct adaptive control on frequency domain approach, Proc. the 30th IEEE Conf. Decision and Control, Brighton, UK, 1991,pp.2710-18
[53] R.Coifman, Y. Meyer and V.Wickerhauser, Wavelet analysis and signal processing, Wavelet Analysis and Their Applications, Jones and Bartllet Boston, 1992,pp.153-78
[54] Gaviphat Lekutai, Adaptive self-tuning neuro wavelet network controllers[Dissertation], Virginia Polytechnic Institute and State University, pp.71-79.
[55] G.Beylkin, R.Coifman and V.Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. On Pure and Applied Math., Vol.XLIV,1991, pp.141-83
[56] i. Daubechies, Orthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., Vol.41,1988, pp.909-96
[57] R.R. Coifman et. al., Signal processing and compression with wave packets , Preprint, Dept. of Math., Yale Univ.,1990
[58] J.M. Combes, A.Grossmann and Ph. Tchamitchian, Eds, Wavelets: Time-frequency methods and phase space, 2nd edition Springer-Verlag, New York, NY, 1989
[59] F.C.Chen, Back-propagation neual networks for nonlinear self-tuning adaptive
control ,IEEE Control Systems Magazine, Special Issue on Neural Networks for Control System, April, 1990, pp44-8
[60] Dorolovacki, M.I., and Fan., H., Wavelet-based linear system modeling and adaptive filtering, IEEE Trans. Signal Processing, Vol.44,1996, pp.1156-67
[61] [瑞典] K.J.奥斯特隆姆，B.威顿马克，李清泉等译，自适应控制，科学出版社，1992
[62] 李清泉 自适应控制系统理论设计与应用，科学出版社，1990
[63] 李树英，许茂增，随机系统的滤波与控制，国防工业出版社，1991
[64] 赵长安等，控制系统设计手册（上），国防工业出版社，1991
[65] S.M. Veres, Self-tuning control by model unfalsification (Part I), Int.J.Control. Vol.73,No.17,2000,1548-59
[66]Youping Zhang and Petros A. Ioannou, A new linear adaptive controller: Design, analysis and performance, IEEE Trans. On Auto. Control, Vol.45, No.5, 2000, pp.883-97
[67] B.维德罗，S.D.史蒂恩斯，王永德，龙宪惠 译，自适应信号处理，四川大学出版社，1991
[68] S.Kadambe and P.Srinivasan, Application of adaptive wavelets for speech coding, Proceedings of the IEEE-SP International Symposium of Timer-Frequency and Time-Scale Analysis, 1994, pp. 632-35
[69] S.A.Imhoff, D.Y.Roeum and M.R.Rosiek, New classes of frame wavelets for application, Wavelet Application 11, H.H.Szu, Ed., Proceedings SPIE- The International Society for Optical Engineering, V2491, 1995, pp.923-34
[70] Zhang Qinghua, Albet Benveniste, Wavelet networks, IEEE Trans.on NN, Vol.3 No.6,1992, pp.889-898
[71] Leontaritis I J, Billings S A. Model selection and validation methods for non-linear systems, International Journal of Control, Vol.45, No.1, 1987,pp.311-341
[72] Sen M.Kuo, Mingjie Wang, and Ke Chen, Active noise control system with parallel on-line error path modeling algorithm, Noise Control Engineering Journal, Vol.39, No.3, pp.119-27.
[73] Eriksson L J., Allie M. C., Use of random noise for on-line transducer modeling in an adaptive active attenuation system. J. Acoust. Soc. Am. Vol.85,No.2,1989 pp.797-802.
[74] J.I.Nagumo, A. Noda, A learning method for system identification, IEEE Trans. Automat. Contr. Vol.AC-12 June 1967 pp.282-287
[75] L.Eriksson and M.Allie, Use of Random Noise for On-line Transducer Modeling in an Adaptive Active Attenuation System, Journal of the Acoustical Society of America, Vol.85,No.2, Feb, 1989, pp.797-802.
[76] J.Tapia and Sen M. Kuo, New Adaptive On-line Modeling Techniques for Active Noise Control Systems, IEEE International Conference on Systems Engineering, Pittsburgh, Pennsylvania, August 1990, pp.280-3.
[77] Clark R.L.and Gibbs G.P, A novel approach to feedforward higher harmonic control. J.Acoust.Soc.Am,Vol.96, pp.926-36.
[78] Elliott S.J, I. M.Stothers, P.A. Nelson, A multiple error LMS algorithm and its application it the active control of sound and vibration, IEEE Tans. on ASSP , Vol.ASSP-35(10), 1987, pp.1423-34.
[79] N.Erdol and Basbug, Wavelet transform based adaptive filtering, in Signal Processing, VI:Theories and Applications, J. Vandewalle, R.Boite, M.Moonen, and A.Oosterlinck, Eds. Amsterdam, The Netherlands: Elsevier Science, 1992, pp.1117-20
[80] N.J.Bershad, Nonlinear quantization effects in the LMS and block LMS adaptive algorithms-A comparison, IEEE Trans. Acoust. Speech, Signal Processing, Vol.37, Oct. 1989, pp.1504-12
[81] G.Lekutai, and H. VanLandingham, Self-tuning control of nonlinear systems using neural network adaptive frame wavelets, IEEE Int. Conf. Man, and Cybernatics ,Orlando, FL, 1997
[82] B.A. Telfer, H.H. Szu, and G.J. Dobeck, Adaptive Wavelet classification of acoustic backscatter, Wavelet Applications, H.H.Szu, Ed., Proceedings of SPIE-The International Society for Optical Engineering, V2242, 1994, pp.661-68
[83] R.K.Young, Wavelet Theory and Its Application, Kluwer Academic Publishers, Boston, MA,1993
[84] Pan J. and Hansen C H，Active control of noise transmission through a panel into a cavity I: analytical study. J.Acoust.Soc.Am.Vol.87,1991, pp.1488-92.
[85] Pan J. and Hansen C H, Active control of noise transmission through a panel into a cavity II: experimental study. J.Acoust.Soc.Am.Vol.90,1991 pp.1488-92.
[86] Koshigoe S, Gillis J T and Falangas E T. A new approach for active control of sound transmission through an elastic plate backed by a rectangular cavity, J.Acoust.Soc.Am.Vol.94, 1993, pp.900-7.
[87] Fuller C R, Hansen C H and Snyder S D. Experiments on active control of sound
radiation from a panel using a piezoceramic actuator, J.Acoust.Soc.Am. Vol.150,1991, pp.179-90.
[88] M.R Flemming, An experimental in investigation of the harmonic excitation of simply supported plates with surface bonded piezoceramic actuators. VPI&SU Master of Science thesis Department of Mechanical Engineering, March 1991.
[89] Bor-Tsuen Wang and Chris R. Fuller and Emilios K. Dimitriadis, Active control of noise transmission through rectangular plates using multiple piezoelectric or point force actuators". J. Acoust. Soc. Am. Vol. 90, No. 5, 1991 , pp.2820-30.
[90] 黄尚廉，国家自然科学重点基金‘智能机械结构及系统基础’申请书,1996.
[91] 黄尚廉，国家科委九五重大基础研究建议书.
[92] Texas Instruments, TMS320c3x User's Guide, July,1997
[93] B.Balachandran, A.sampath, J.Park, Feedforward active interior noise control, Smart Structures and Materials, SPIE, Vol. 2443,1995, pp.670-81
[94] A. Sampath, B.Balachandran, Active Structural acoustic control of bandlimited disturbances, Smart Structures and Materials, SPIE, Vol. 2717,1996, pp.422-33
[95] S.Koshigoe and J.W. Murdock, A unified analysis of both active and passive damping for a plate with piezoelectric transducers, Journal of Acoustical Society of America, Vol. 93, No.1, 1993, pp.346-55
[96] 杜功焕，朱哲民，龚秀芬，声学基础(上)，上海科学技术出版社，1981，pp.197-198