Recursive Bayesian Algorithm with Covariance Resetting for Identification of Box–Jenkins Systems with Non-uniformly Sampled Input Data

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• 作者：Shaoxue Jing ; Tianhong Pan ; Zhengming Li
• 关键词：Non ; uniformly sampled data system ; Box–Jenkins system ; Recursive Bayesian algorithm ; Covariance resetting
• 刊名：Circuits, Systems, and Signal Processing
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：35
• 期：3
• 页码：919-932
• 全文大小：724 KB
• 参考文献：1.F. Chongzhi, X. Deyun, Process Identification (Tsinghua University Press, Beijing, 1988)
  2.J. Chen, R. Ding, Two identification methods for dual-rate sampled-data nonlinear output-error systems. Math. Probl. Eng. (2014). doi:10.​1155/​2014/​329437
  3.F. Ding, G. Liu, X.P. Liu, Parameter estimation with scarce measurements. Automatica 47(8), 1646–1655 (2011)CrossRef MathSciNet MATH
  4.J. Ding, J. Lin, Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits Syst. Signal Process. 33(5), 1439–1449 (2014)CrossRef
  5.R.D. Gudi, S.L. Shah, M.R. Gray, Adaptive multirate state and parameter estimation strategies with application to a bioreactor. AIChE J. 41(11), 2451–2464 (1995)CrossRef
  6.J.H. Lee, M. Morari, Robust inferential control of multi-rate sampled-data systems. Chem. Eng. Sci. 47(4), 865–885 (1992)CrossRef
  7.J. Li, F. Ding, Maximum likelihood stochastic gradient estimation for hammerstein systems with colored noise based on the key term separation technique. Comput. Math. Appl. 62(11), 4170–4177 (2011)CrossRef MathSciNet MATH
  8.J. Li, F. Ding, Filtering-based recursive least-squares identification algorithm for controlled autoregressive moving average systems using the maximum likelihood principle. J. Vib. Control (2014). doi:10.​1177/​1077546314523634​
  9.W. Li, S.L. Shah, D. Xiao, Kalman filters in non-uniformly sampled multirate systems: for FDI and beyond. Automatica 44(1), 199–208 (2008)CrossRef MathSciNet MATH
  10.Y. Liu, F. Ding, Y. Shi, An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica 50(3), 962–970 (2014)CrossRef MathSciNet MATH
  11.L. Ljung, T. Söderström, Theory and Practice of Recursive Identification (The MIT Press, London, 1985)
  12.V. Peterka, Bayesian approach to system identification. Trends Prog. Syst. Identif. 1, 239–304 (1981)
  13.C.H. Reinsch, A stable, rational qr algorithm for the computation of the eigenvalues of an hermitian, tridiagonal matrix. Math. Comput. 25(115), 591–597 (1971)CrossRef MathSciNet MATH
  14.Y. Shi, T. Chen, 2-norm-based iterative design of filterbank transceivers: a control perspective. J. Control Sci. Eng. 1–7, 2008 (2008)
  15.Y. Shi, F. Ding, T. Chen, 2-norm based recursive design of transmultiplexers with designable filter length. Circuits Syst. Signal Process. 25(4), 447–462 (2006)CrossRef MathSciNet MATH
  16.M.T. Tham, S.N. Mansoori, Covariance resetting in recursive least squares estimation. In International Conference on Control, 1988. CONTROL 88 (IET, 1988), pp. 128–133
  17.S. Wang, V. Dinavahi, J. Xiao, Multi-rate real-time model-based parameter estimation and state identification for induction motors. Electric Power Appl. IET 7(1), 77–86 (2013)CrossRef
  18.D.S. Watkins, Fundamentals of Matrix Computations, vol. 64 (Wiley, Hoboken, 2004)
  19.D. Xiao, Theory of System Identification with Applications (Tsinghua University Press, Beijing, 2014)
  20.L. Xie, H. Yang, F. Ding, Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering. Math. Comput. Model. 54(1), 315–324 (2011)CrossRef MathSciNet MATH
  21.W. Yan, C. Du, C.K. Pang, A general multirate approach for direct closed-loop identification to the Nyquist frequency and beyond. Automatica 53, 164–170 (2015)CrossRef MathSciNet
  22.H. Zhang, G. Feng, H. Yan, Q. Chen, Observer-based output feedback event-triggered control for consensus of multi-agent systems. IEEE Trans. Ind. Electron. 61(9), 4885–4894 (2014)CrossRef
  23.L. Zhang, H. Gao, O. Kaynak, Network-induced constraints in networked control systemsa survey. IEEE Trans. Ind. Inform. 9(1), 403–416 (2013)CrossRef
  24.L. Zhou, X. Li, F. Pan, Gradient-based iterative identification for wiener nonlinear systems with non-uniform sampling. Nonlinear Dyn. 76(1), 627–634 (2014)CrossRef MathSciNet
  
• 作者单位：Shaoxue Jing (1) (2)
  Tianhong Pan (1)
  Zhengming Li (1)
  
  1. School of Electrical Information and Engineering, Jiangsu University, Zhenjiang, 212013, Jiangsu, China
  2. Department of Electrical Engineering, Huaian College of Information and Technology, Huaian, 223003, China
  
• 刊物类别：Engineering
• 刊物主题：Electronic and Computer Engineering
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5878

文摘

To identify the Box–Jenkins systems with non-uniformly sampled input data, a recursive Bayesian algorithm with covariance resetting was proposed in this paper. Considering the prior probability density functions of parameters and the observed input–output data, the parameters were estimated by maximizing the posterior probability distribution function. During the estimation, the variance of the noise was taken as a weighting factor, and the proposed algorithm was formulated as a weighted least squares. As a result, the accuracy of the estimates increased. Meanwhile, a modified covariance resetting strategy was integrated into the algorithm to improve the convergence rate, and the convergence of the algorithm was also analyzed. A simulation example was applied to validate the proposed algorithm. Keywords Non-uniformly sampled data system Box–Jenkins system Recursive Bayesian algorithm Covariance resetting