Expectation maximization estimation algorithm for Hammerstein models with non-Gaussian noise and random time delay from dual-rate sampled-data

Abstract This paper considers the robust identification for dual-rate input nonlinear equation-error systems with outliers and random time delay. To suppress the negative influence caused by the outliers to the accuracy of identification, the distribution of the noise is represented by a t-distribution rather than a Gaussian distribution. A random time delay is considered in the dual-rate input nonlinear systems. By treating the unknown time delay as the latent variable, the expectation maximization algorithm is derived for identifying the systems. Two numerical simulation examples demonstrate that the proposed algorithm can generate accurate identification results when the measurements are contaminated by the outliers.

[1]  Feng Ding,et al.  The Gradient-Based Iterative Estimation Algorithms for Bilinear Systems with Autoregressive Noise , 2017, Circuits, Systems, and Signal Processing.

[2]  Xunyuan Yin,et al.  Distributed moving horizon state estimation of two-time-scale nonlinear systems , 2017, Autom..

[3]  E. Bai,et al.  Block Oriented Nonlinear System Identification , 2010 .

[4]  Frédéric Gouaisbaut,et al.  Delay-dependent stability analysis of linear systems with time-varying delay , 2007, 2007 46th IEEE Conference on Decision and Control.

[5]  Biao Huang,et al.  Robust identification of piecewise/switching autoregressive exogenous process , 2009 .

[6]  F. Ding,et al.  Least-squares-based iterative and gradient-based iterative estimation algorithms for bilinear systems , 2017 .

[7]  Feng Ding,et al.  Some new results of designing an IIR filter with colored noise for signal processing , 2018, Digit. Signal Process..

[8]  P. J. Huber.  Robust Estimation of a Location Parameter , 1964 .

[9]  Feng Ding,et al.  Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering , 2017, Digit. Signal Process..

[10]  Yong Wang,et al.  An innovative parameter estimation for fractional order systems with impulse noise. , 2017, ISA transactions.

[11]  Yaojie Lu,et al.  Robust multiple-model LPV approach to nonlinear process identification using mixture t distributions , 2014 .

[12]  Yanjun Liu,et al.  Recursive Least Squares Algorithm for Nonlinear Dual-rate Systems Using Missing-Output Estimation Model , 2017, Circuits Syst. Signal Process..

[13]  Ji Huang,et al.  I2-I∞ filtering for multirate nonlinear sampled-data systems using T-S fuzzy models , 2013, Digit. Signal Process..

[14]  Shen Yin,et al.  Robust Global Identification and Output Estimation for LPV Dual-Rate Systems Subjected to Random Output Time-Delays , 2017, IEEE Transactions on Industrial Informatics.

[15]  Faicel Chamroukhi,et al.  Robust mixture of experts modeling using the t distribution , 2016, Neural Networks.

[16]  Biao Huang,et al.  FIR model identification of multirate processes with random delays using EM algorithm , 2013 .

[17]  Feng Ding,et al.  Parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle , 2017, IET Signal Process..

[18]  Alireza Fatehi,et al.  Robust Estimation of ARX Models With Time Varying Time Delays Using Variational Bayesian Approach , 2018, IEEE Transactions on Cybernetics.

[19]  Sirish L. Shah,et al.  Subspace identification for FDI in systems with non-uniformly sampled multirate data , 2006, Autom..

[20]  Feng Ding,et al.  Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering , 2017, J. Frankl. Inst..

[21]  Feng Ding,et al.  Hierarchical Least Squares Identification for Hammerstein Nonlinear Controlled Autoregressive Systems , 2015, Circuits Syst. Signal Process..

[22]  Dongguang Li,et al.  Application of dual-rate modeling to CCR octane quality inferential control , 2001, IEEE Trans. Control. Syst. Technol..

[23]  Yaojie Lu,et al.  Robust Diagnosis of Operating Mode Based on Time-Varying Hidden Markov Models , 2016, IEEE Transactions on Industrial Electronics.

[24]  Feng Ding,et al.  Iterative identification algorithms for bilinear-in-parameter systems with autoregressive moving average noise , 2017, J. Frankl. Inst..

[25]  Feng Ding,et al.  A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems , 2015, Digit. Signal Process..

[26]  Jaafar AlMutawa.  Diagnostics subspace identification method of linear state-space model with observation outliers , 2017, IET Signal Process..

[27]  Hassan K. Khalil,et al.  Multirate Sampled-Data Output Feedback Control With Application to Smart Material Actuated Systems , 2009, IEEE Transactions on Automatic Control.

[28]  Lino Guzzella,et al.  Recursive parameter estimation of exhaust gas oxygen sensors with input-dependent time delay and linear parameters , 2015 .

[29]  Fei Liu,et al.  Parameter estimation for a dual-rate system with time delay. , 2014, ISA transactions.

[30]  Er-Wei Bai.  An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998, Autom..

[31]  Christopher M. Bishop,et al.  Robust Bayesian Mixture Modelling , 2005, ESANN.

[32]  Myong Kee Jeong,et al.  Robust Probabilistic Multivariate Calibration Model , 2008, Technometrics.

[33]  Furong Gao,et al.  Multirate dynamic inferential modeling for multivariable processes , 2004 .

[34]  Jixin Qian,et al.  A Two-Stage Method for Identification of Dual-Rate Systems with Fast Input and Very Slow Output , 2009 .

[35]  Badong Chen,et al.  Adaptive recursive algorithm with logarithmic transformation for nonlinear system identification in α-stable noise , 2015, Digit. Signal Process..

[36]  Alireza Fatehi,et al.  A Data-Driven Hybrid ARX and Markov Chain Modeling Approach to Process Identification With Time-Varying Time Delays , 2017, IEEE Transactions on Industrial Electronics.

[37]  F. Alsaadi,et al.  Recursive parameter identification of the dynamical models for bilinear state space systems , 2017 .

[38]  J. Tukey.  The Future of Data Analysis , 1962 .

[39]  Biao Huang,et al.  Robust identification of switched regression models , 2009 .

[40]  M. Chadli,et al.  Data reconciliation: A robust approach using a contaminated distribution , 2008 .

[41]  Huiping Li,et al.  Robust H∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays , 2012, Autom..

[42]  Feng Ding,et al.  Identification methods for time-delay systems based on the redundant rules , 2017, Signal Process..

[43]  Feng Ding,et al.  The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise , 2017, J. Frankl. Inst..

[44]  K. Worden,et al.  Robust nonlinear system identification: Bayesian mixture of experts using the t-distribution , 2017 .

[45]  Yuquan Chen,et al.  An innovative parameter estimation for fractional-order systems in the presence of outliers , 2017 .