基于数据滤波的两阶段辨识方法
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摘要
论文以国家自然科学基金项目(NO.60973043)为背景,研究有色噪声干扰下线性、非线性系统的两阶段辨识方法.作者在查阅了相关文献的基础上,简要回顾了系统辨识的历史,综述了相关参数估计方法,并对两阶段辨识方法进行了深入研究,取得的研究成果如下：
1.针对有色噪声干扰的输出误差类系统,提出OEAR模型和Box-Jenkins模型的两阶段辨识方法.算法的主要思想是：根据噪声模型的结构设计相应的线性滤波器,用该滤波器对输入输出数据进行滤波处理,将系统转化为白噪声干扰的输出误差模型,再利用辅助模型辨识思想以及最小二乘原理,将系统模型参数和噪声模型参数交替辨识.仿真例子证明了算法的有效性.
2.很多非线性系统都可以用Hammerstein模型来描述,将两阶段辨识思想推广到Hammer-stein非线性动态调节模型,利用多项式C(z)对非线性结构输入和输出进行滤波处理,将系统模型转换为非线性受控自回归模型,然后利用最小二乘原理将转换后的系统模型和噪声模型进行交互估计,推导出基于数据滤波的的两阶段辨识算法.仿真例子对提出算法进行了仿真并和递推广义算法、随机梯度算法进行了比较.
3.针对一般有色噪声干扰的Hammerstein非线性系统,即干扰噪声为自回归滑动平均模型(ARMA)的输入非线性系统,借助数据滤波的思想和最小二乘原理,将辨识步骤分为系统模型和噪声模型辨识两个阶段,提出Hammerstein-CARARMA模型的两阶段辨识算法.计算机仿真说明该算法能得到高精度的参数估计.
4.针对输入非线性输出误差类系统,结合辅助模型算法和数据滤波的优点,推导出Hammerstein-OEAR模型基于数据滤波的两阶段辨识算法.算法将系统模型的不可测变量用辅助模型的输出代替,未知噪声项用其估计值代替.通过仿真例子说明算法的有效性.
论文推导和研究输出误差类系统和Hammerstein非线性系统的几种辨识算法,算法的可行性和优缺点采用计算机仿真的方法来验证,提出的辨识算法的收敛性有待近一步证明.
Based on the National Nature Science Foundation of China (NO.60973043), this thesis studies the two-stage identification methods for linear and nonlinear systems with colored noises. After reading some relevant references, the author briefly reviews the history of system iden-tification and overviews the existed parameter estimation methods in the exordium, and then derives the two-stage identification methods for different system models in detail in the next chapters. The main results are as follows:
1. For the output error type systems with colored noises, the two-stage identification methods are developed. The main idea is to design a linear filter according to the structure of noise model, and to transform the system model into an output error model with white noise by filtering the inputs and outputs of the system by the corresponding filter designed, and then to interactively identify the transformed system model and noise model by using the auxiliary model identification idea and the least squares principle. The simulation results show that the proposed algorithms are effective.
2. Many nonlinear systems can be described by Hammerstein systems, the two-stage iden-tification idea is extended to the Hammerstein dynamic adjustment model. Using the polynomial C(z) to filter the nonlinear inputs and outputs, the system model is trans-formed into a Hammerstein controlled auto regressive model. Then using the least squares principle to interactively identify the transformed system model and the noise model, the two-stage identification method based on data filtering is developed. The simulation exam-ple tests the proposed algorithm and compares with the recursive generalized least squares identification method and the stochastic gradient identification method.
3. For the Hammerstein nonlinear systems disturbed by the general colored noise, i.e., the noise with a auto regressive moving average (ARMA) model, the two-stage identification method based on data filtering is proposed. Based on the data filtering and the least squares principle, that is, the identification process contains two steps, the system model and noise model identification. Simulation shows that proposed algorithm can give high accurate parameter estimates.
4. For nonlinear output error type systems, the two-stage identification method based on data filtering is derived, combined with the advantages of auxiliary model algorithms and data filtering. The unmeasurable outputs and the unknown noise terms in the information vector are replaced with the outputs of an auxiliary model and estimates residual, respectively. Simulation examples demonstrate the method works well.
In summary, this thesis proposes the two-stage identification algorithms for output error linear systems and Hammerstein nonlinear systems, the performances of the algorithms are illustrated by computer simulations. The convergence of the two-stage identification algorithms need further proof.
1.针对有色噪声干扰的输出误差类系统,提出OEAR模型和Box-Jenkins模型的两阶段辨识方法.算法的主要思想是：根据噪声模型的结构设计相应的线性滤波器,用该滤波器对输入输出数据进行滤波处理,将系统转化为白噪声干扰的输出误差模型,再利用辅助模型辨识思想以及最小二乘原理,将系统模型参数和噪声模型参数交替辨识.仿真例子证明了算法的有效性.
2.很多非线性系统都可以用Hammerstein模型来描述,将两阶段辨识思想推广到Hammer-stein非线性动态调节模型,利用多项式C(z)对非线性结构输入和输出进行滤波处理,将系统模型转换为非线性受控自回归模型,然后利用最小二乘原理将转换后的系统模型和噪声模型进行交互估计,推导出基于数据滤波的的两阶段辨识算法.仿真例子对提出算法进行了仿真并和递推广义算法、随机梯度算法进行了比较.
3.针对一般有色噪声干扰的Hammerstein非线性系统,即干扰噪声为自回归滑动平均模型(ARMA)的输入非线性系统,借助数据滤波的思想和最小二乘原理,将辨识步骤分为系统模型和噪声模型辨识两个阶段,提出Hammerstein-CARARMA模型的两阶段辨识算法.计算机仿真说明该算法能得到高精度的参数估计.
4.针对输入非线性输出误差类系统,结合辅助模型算法和数据滤波的优点,推导出Hammerstein-OEAR模型基于数据滤波的两阶段辨识算法.算法将系统模型的不可测变量用辅助模型的输出代替,未知噪声项用其估计值代替.通过仿真例子说明算法的有效性.
论文推导和研究输出误差类系统和Hammerstein非线性系统的几种辨识算法,算法的可行性和优缺点采用计算机仿真的方法来验证,提出的辨识算法的收敛性有待近一步证明.
Based on the National Nature Science Foundation of China (NO.60973043), this thesis studies the two-stage identification methods for linear and nonlinear systems with colored noises. After reading some relevant references, the author briefly reviews the history of system iden-tification and overviews the existed parameter estimation methods in the exordium, and then derives the two-stage identification methods for different system models in detail in the next chapters. The main results are as follows:
1. For the output error type systems with colored noises, the two-stage identification methods are developed. The main idea is to design a linear filter according to the structure of noise model, and to transform the system model into an output error model with white noise by filtering the inputs and outputs of the system by the corresponding filter designed, and then to interactively identify the transformed system model and noise model by using the auxiliary model identification idea and the least squares principle. The simulation results show that the proposed algorithms are effective.
2. Many nonlinear systems can be described by Hammerstein systems, the two-stage iden-tification idea is extended to the Hammerstein dynamic adjustment model. Using the polynomial C(z) to filter the nonlinear inputs and outputs, the system model is trans-formed into a Hammerstein controlled auto regressive model. Then using the least squares principle to interactively identify the transformed system model and the noise model, the two-stage identification method based on data filtering is developed. The simulation exam-ple tests the proposed algorithm and compares with the recursive generalized least squares identification method and the stochastic gradient identification method.
3. For the Hammerstein nonlinear systems disturbed by the general colored noise, i.e., the noise with a auto regressive moving average (ARMA) model, the two-stage identification method based on data filtering is proposed. Based on the data filtering and the least squares principle, that is, the identification process contains two steps, the system model and noise model identification. Simulation shows that proposed algorithm can give high accurate parameter estimates.
4. For nonlinear output error type systems, the two-stage identification method based on data filtering is derived, combined with the advantages of auxiliary model algorithms and data filtering. The unmeasurable outputs and the unknown noise terms in the information vector are replaced with the outputs of an auxiliary model and estimates residual, respectively. Simulation examples demonstrate the method works well.
In summary, this thesis proposes the two-stage identification algorithms for output error linear systems and Hammerstein nonlinear systems, the performances of the algorithms are illustrated by computer simulations. The convergence of the two-stage identification algorithms need further proof.
引文
1.丁锋.系统辨识理论与方法+Matlab仿真[M].北京：电力出版社,2011.
2. Ljung L. Convergence analysis of parametric identification methods [J]. IEEE Transactions on Automatic Control,1978,23(5):770-783.
3. Yun B, Shinozuka. Identification of nonlinear structural dynamic systems [J]. Mechanics Based Design of Structures and Machines,1980,8(2):187-203.
4.赵大明,施朝健,彭静.应用扩展卡尔曼滤波算法的船舶运动模型参数辨识[J].上海海事大学学报,2008,29(3)：5-9.
5.张军华,于江波,王静等.基于维纳滤波的50HZ工业干扰去噪方法研究及应用[J].油气地球物理,2009,7(4)：12-15.
6.查宇飞,毕笃彦.一种基于粒子滤波的自适应运动目标跟踪方法[J].电子与信息学报,2007,29(1)：92-95.
7. Wang D Q, Ding F. Input-output data filtering based recursive least squares identification for CARARMA systems [J]. Digital Signal Processing,2010,20(4):991-999.
8. Xie L, Yang H Z, Ding F. Filtering based recursive least squares identification for non-uniformly sampled systems [C]. Proceedings of the 22nd Chinese Control and Decision Conference, May 26-28,2010, Xuzhou, China.
9.彭丁聪.卡尔曼滤波的基本原理及应用[J].软件导刊,2009,8(11)：32-34.
10. Wan E A, Van D M. The unscented Kalman filter for nonlinear estimation [J]. Adaptive Systems for Signal Posium,2000,5(12):153-158.
11.张友民,戴冠中,张洪才.并行卡尔曼滤波及其心动阵列实现综述[J].控制理论与应用,1993,10(1)：3-12.
12.耿妍,张瑞金.自适应滤波算法综述[J].信息与电子工程,2008,6(4)：312-317.
13.王婷婷,郭胜权.粒子滤波算法的综述[J].仪表技术,2009,67(6)：64-68.
14.穆国艳,陈树中.图像去噪的一种新方法[J].计算机工程,2003,29(5)：134-135.
15.曲从善,许化龙,谭营.非线性贝叶斯滤波算法综述[J].电光与控制,2008,15(8)：64-70.
16.胡耀斌,陈艾华,张春良.小波分析与维纳滤波相结合的消噪方法研究[J].电力系统通信,2006,27(162)：42-44.
17. Sugeno M, Kang G. Structure identification of fuzzy model [J]. Fuzzy Sets and Systems,1988, 28(1):15-33.
18.肖建,白裔峰,于龙.模糊系统结构辨识综述[J].西南交通大学学报,2006,41(2)：135-146.
19. Hadjili M L, Wertz V. Takagi-Sugeno fuzzy modeling incorporating input variables selection [J]. IEEE Transactions on Fuzzy Systems,2002,10(6):728-742.
20.王辉,肖建.基于多分辨率的模糊系统的函数逼近性分析[J].西南交通大学学报,2004,39(1)：26-30.
21.徐丽娜.神经网络控制[M].北京：电子工业出版社,2003.
22. Krzyzak A. Nonparametric estimation and classification using radial basis function nets and em-pirical risk minimization [J]. IEEE Transactions on Neural Networks,1996,7(2):475-487.
23. Narendrak S, Parthasarathy K. Identification and control of dynamic system using neural networks [J]. IEEE Transactions on Neural Networks,1990,1(1):4-27.
24. Zhang Q H, Benveniste A. Wavelet network [J]. IEEE Transactions on NN,1992,3(6):889-898.
25. Daubechies I. Orthonomal bases of compactly supported wavelets [J]. Comm on Pure and Appl.Math,1988,41:909-996.
26. Pati Y C, Krishnaprasad P S. Analysis and synthesis of feedforword neural networks using discrete affine wavelet [J]. IEEE Transactions on Neural Networks,1993,4(1):73-75.
27. Baskshi B R, Stephanopoulous G. Wave-net:a multiresolution, hiererchical neural network with localized learning [J]. American Institute Chemical Engineer Journal,1993,39(1):57-81.
28. Szu H, Teifer B, Kadambe S. Neural network adaptive wavelets for signal representation and classification [J]. Optical Engineering,1992,36(9):1907-1916.
29.沈雪勤,丁宇新.小波变换与小波神经元的选择[J].河北工业大学学报,1996,25(2)：83-88.
30.焦李成,王岭.区间估计的FWNN及其区间学习算法[J].电子学报,1998,26(4)：41-45.
31. Holland J H. Adaption in natural and artifical systems [M]. Ann Arbor:University of Michigan press,1975.
32.赵应丁,刘金刚.基于遗传算法的指纹图像二值化算法研究[J].计算机工程,2006,32(7)：169-171.
33.王建峰,吴庆标.分层遗传算法实现图像边缘检测[J].计算机工程与应用,2006,42(14)：95-96+151.
34.承向军,贺振欢,杨肇夏.基于遗传算法的交通信号机器学习控制方法[J].系统工程理论与实践,2004,24(2)：1-5.
35. Sunil C. Design and implementation of a genetic based algorithm for data mining [C]. Proceedings of the 26th International Conference on Very Large Databases. San Francisco:Morgan Kaufmann Publishers,2000:33-42.
36.何振亚,李文化.用于信号逼近的自适应时延小波神经网络[J].电子科学学刊,1998,20(5)：604-610.
37. Ding F, Chen T. Combined parameter and output estimation of dual-rate systems using an aux-iliary model [J]. Automatica,2004,40(10):1739-1748.
38. Ding F, Chen T. Parameter estimation of dual-rate stochastic systems by using an output error method [J]. IEEE Transactions on Automatic Control,2005,50(9):1436-1441.
39.丁锋,谢新民.传递函数阵子子模型参数递推估计：辅助模型方法[J].控制与决策,1991,6(6)：447-452.
40. Ding F, Yang HZ, Liu F. Performance analysis of stochastic gradient algorithm under weak con-ditions, Science in China Series F-Information Sciences,2008,51(9):1269-1280.
41.谢新民,丁锋.自适应控制系统[M].北京：清华大学出版社,2002.
42.方崇智,萧德云.过程辨识[M].北京：清华大学出版社,1988.
43.岳娜,肖永松.非线性动态调节模型的滤波式递推辨识算法[J].科技通报,2010,26(5)：704-707.
44. Krzyzak A, Partyka M A. Global identification of nonlinear Hammerstein systerms by recursive kernel approach [J]. Nonlinear Analysis, Theory, Methods and Applications,2005,63(5-7):1263-1272.
45. Goethals I, Pelckmans K. Identification of MIMO Hammerstein models using least squares support vector machines [J]. Automatica,2005,41(7):1263-1272.
46.穆朝絮,梁瑞鑫,李训明.非线性系统的LSSVM联合逆控制器[J].计算机工程,2009,35(12)：181-183.
47. Ding F, Shi Y, Chen T. Gradient-based identification algorithm for Hammerstein ARMAX systems [J]. Automatica,2006,34(3):1479-1489.
48.张文广,周邵磊,戴邵武等.一种基于改进遗传算法的新型小波神经网研究[J].计算机工程,2006,32(16)：198-200.
49.徐小平,钱富才,王峰等.基于改进粒子群算法的Hammerstein模型辨识[J].计算机工程,2008,34(14)：200-202.
50. Ding F, Chen T. Hierarchical gradient-based identification of multivariable discrete-time systems [J]. Automatica,2005,41(2):315-325.
51.丁锋,杨家本.随机梯度算法的收敛性分析[J].清华大学学报(自然科学版),1999,39(1)：83-86.
2. Ljung L. Convergence analysis of parametric identification methods [J]. IEEE Transactions on Automatic Control,1978,23(5):770-783.
3. Yun B, Shinozuka. Identification of nonlinear structural dynamic systems [J]. Mechanics Based Design of Structures and Machines,1980,8(2):187-203.
4.赵大明,施朝健,彭静.应用扩展卡尔曼滤波算法的船舶运动模型参数辨识[J].上海海事大学学报,2008,29(3)：5-9.
5.张军华,于江波,王静等.基于维纳滤波的50HZ工业干扰去噪方法研究及应用[J].油气地球物理,2009,7(4)：12-15.
6.查宇飞,毕笃彦.一种基于粒子滤波的自适应运动目标跟踪方法[J].电子与信息学报,2007,29(1)：92-95.
7. Wang D Q, Ding F. Input-output data filtering based recursive least squares identification for CARARMA systems [J]. Digital Signal Processing,2010,20(4):991-999.
8. Xie L, Yang H Z, Ding F. Filtering based recursive least squares identification for non-uniformly sampled systems [C]. Proceedings of the 22nd Chinese Control and Decision Conference, May 26-28,2010, Xuzhou, China.
9.彭丁聪.卡尔曼滤波的基本原理及应用[J].软件导刊,2009,8(11)：32-34.
10. Wan E A, Van D M. The unscented Kalman filter for nonlinear estimation [J]. Adaptive Systems for Signal Posium,2000,5(12):153-158.
11.张友民,戴冠中,张洪才.并行卡尔曼滤波及其心动阵列实现综述[J].控制理论与应用,1993,10(1)：3-12.
12.耿妍,张瑞金.自适应滤波算法综述[J].信息与电子工程,2008,6(4)：312-317.
13.王婷婷,郭胜权.粒子滤波算法的综述[J].仪表技术,2009,67(6)：64-68.
14.穆国艳,陈树中.图像去噪的一种新方法[J].计算机工程,2003,29(5)：134-135.
15.曲从善,许化龙,谭营.非线性贝叶斯滤波算法综述[J].电光与控制,2008,15(8)：64-70.
16.胡耀斌,陈艾华,张春良.小波分析与维纳滤波相结合的消噪方法研究[J].电力系统通信,2006,27(162)：42-44.
17. Sugeno M, Kang G. Structure identification of fuzzy model [J]. Fuzzy Sets and Systems,1988, 28(1):15-33.
18.肖建,白裔峰,于龙.模糊系统结构辨识综述[J].西南交通大学学报,2006,41(2)：135-146.
19. Hadjili M L, Wertz V. Takagi-Sugeno fuzzy modeling incorporating input variables selection [J]. IEEE Transactions on Fuzzy Systems,2002,10(6):728-742.
20.王辉,肖建.基于多分辨率的模糊系统的函数逼近性分析[J].西南交通大学学报,2004,39(1)：26-30.
21.徐丽娜.神经网络控制[M].北京：电子工业出版社,2003.
22. Krzyzak A. Nonparametric estimation and classification using radial basis function nets and em-pirical risk minimization [J]. IEEE Transactions on Neural Networks,1996,7(2):475-487.
23. Narendrak S, Parthasarathy K. Identification and control of dynamic system using neural networks [J]. IEEE Transactions on Neural Networks,1990,1(1):4-27.
24. Zhang Q H, Benveniste A. Wavelet network [J]. IEEE Transactions on NN,1992,3(6):889-898.
25. Daubechies I. Orthonomal bases of compactly supported wavelets [J]. Comm on Pure and Appl.Math,1988,41:909-996.
26. Pati Y C, Krishnaprasad P S. Analysis and synthesis of feedforword neural networks using discrete affine wavelet [J]. IEEE Transactions on Neural Networks,1993,4(1):73-75.
27. Baskshi B R, Stephanopoulous G. Wave-net:a multiresolution, hiererchical neural network with localized learning [J]. American Institute Chemical Engineer Journal,1993,39(1):57-81.
28. Szu H, Teifer B, Kadambe S. Neural network adaptive wavelets for signal representation and classification [J]. Optical Engineering,1992,36(9):1907-1916.
29.沈雪勤,丁宇新.小波变换与小波神经元的选择[J].河北工业大学学报,1996,25(2)：83-88.
30.焦李成,王岭.区间估计的FWNN及其区间学习算法[J].电子学报,1998,26(4)：41-45.
31. Holland J H. Adaption in natural and artifical systems [M]. Ann Arbor:University of Michigan press,1975.
32.赵应丁,刘金刚.基于遗传算法的指纹图像二值化算法研究[J].计算机工程,2006,32(7)：169-171.
33.王建峰,吴庆标.分层遗传算法实现图像边缘检测[J].计算机工程与应用,2006,42(14)：95-96+151.
34.承向军,贺振欢,杨肇夏.基于遗传算法的交通信号机器学习控制方法[J].系统工程理论与实践,2004,24(2)：1-5.
35. Sunil C. Design and implementation of a genetic based algorithm for data mining [C]. Proceedings of the 26th International Conference on Very Large Databases. San Francisco:Morgan Kaufmann Publishers,2000:33-42.
36.何振亚,李文化.用于信号逼近的自适应时延小波神经网络[J].电子科学学刊,1998,20(5)：604-610.
37. Ding F, Chen T. Combined parameter and output estimation of dual-rate systems using an aux-iliary model [J]. Automatica,2004,40(10):1739-1748.
38. Ding F, Chen T. Parameter estimation of dual-rate stochastic systems by using an output error method [J]. IEEE Transactions on Automatic Control,2005,50(9):1436-1441.
39.丁锋,谢新民.传递函数阵子子模型参数递推估计：辅助模型方法[J].控制与决策,1991,6(6)：447-452.
40. Ding F, Yang HZ, Liu F. Performance analysis of stochastic gradient algorithm under weak con-ditions, Science in China Series F-Information Sciences,2008,51(9):1269-1280.
41.谢新民,丁锋.自适应控制系统[M].北京：清华大学出版社,2002.
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