Neuro-fuzzy based identification method for Hammerstein output error model with colored noise

The proposed method is suitable for the identification problem of the nonlinear part separated from that of linear part.The proposed method can effectively compensate the bias caused by colored noise because of considering the correlation of noise at different times.The proposed method has high identification accuracy and good robustness in the presence of the disturbance of colored noise. In this paper, a neuro-fuzzy based identification procedure for Hammerstein output error model with colored noise is presented. Separable signal is used to realize the decoupling of the identification of dynamic linear part from that of static nonlinear part, and then correlation analysis method is adopted to identify the parameters of the linear part. Next, a filter is embedded to form extended Hammerstein model to calculate the noise correlation function by the information of zeros and poles of the extended model. The correlation functions which consist of the noise correlation function are applied to compensate the bias caused by colored noise. As a result, the parameters of the nonlinear part can be identified through recursive least square method. Examples results illustrate that the proposed approach has high identification accuracy and good robustness to the disturbance of colored noise.

[1]  Shivaram Kamat,et al.  Modeling of pH process using wavenet based Hammerstein model , 2007 .

[2]  S. Sung.  System Identification Method for Hammerstein Processes , 2002 .

[3]  José Luis Figueroa,et al.  Identification of uncertain MIMO Wiener and Hammerstein models , 2011, Comput. Chem. Eng..

[4]  Ronald K. Pearson,et al.  Nonlinear model-based control using second-order Volterra models , 1995, Autom..

[5]  Feng Ding,et al.  Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems , 2012, Math. Comput. Model..

[6]  Feng Ding,et al.  Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique , 2011, Comput. Math. Appl..

[7]  Shuzhi Sam Ge,et al.  A noniterative neuro-fuzzy based identification method for Hammerstein processes , 2005 .

[8]  M. E. Ahmed,et al.  Estimation of difference equation parameters of SISO systems by correlation analysis , 1982 .

[9]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[10]  Feng Ding,et al.  Recursive Least Squares Parameter Estimation for a Class of Output Nonlinear Systems Based on the Model Decomposition , 2016, Circuits Syst. Signal Process..

[11]  Thomas F. Edgar,et al.  A Gramian Based Approach to Nonlinearity Quantification and Model Classification , 2001 .

[12]  Min-Sen Chiu,et al.  Correlation analysis based MIMO neuro-fuzzy Hammerstein model with noises , 2016 .

[13]  Er-Wei Bai,et al.  Convergence of the iterative Hammerstein system identification algorithm , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  Min-Sen Chiu,et al.  The identification of neuro-fuzzy based MIMO Hammerstein model with separable input signals , 2016, Neurocomputing.

[15]  Feng Ding,et al.  Recursive least squares algorithm and gradient algorithm for Hammerstein–Wiener systems using the data filtering , 2016 .

[16]  D. Rollins,et al.  Continuous-Time Hammerstein Nonlinear Modeling Applied to Distillation (R&D Note) , 2004 .

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

[18]  Feng Ding,et al.  Decomposition Based Newton Iterative Identification Method for a Hammerstein Nonlinear FIR System with ARMA Noise , 2014, Circuits Syst. Signal Process..

[19]  X. Jing.  Frequency domain analysis and identification of block-oriented nonlinear systems , 2011 .

[20]  J. Suykens,et al.  Subspace identification of Hammerstein systems using least squares support vector machines , 2005 .

[21]  Enrique Baeyens,et al.  Subspace-based Identification Algorithms for Hammerstein and Wiener Models , 2005, Eur. J. Control.

[22]  Feng Ding,et al.  Identification of Hammerstein nonlinear ARMAX systems , 2005, Autom..

[23]  G. M. Colver,et al.  A continuous-time nonlinear dynamic predictive modeling method for Hammerstein processes , 2003 .

[24]  E. Bai.  Frequency domain identification of Hammerstein models , 2002 .

[25]  A. Palazoglu,et al.  Nolinear model predictive control using Hammerstein models , 1997 .

[26]  Feng Ding,et al.  Auxiliary model-based least-squares identification methods for Hammerstein output-error systems , 2007, Syst. Control. Lett..

[27]  Jozef Vörös,et al.  Iterative algorithm for parameter identification of Hammerstein systems with two-segment nonlinearities , 1999, IEEE Trans. Autom. Control..

[28]  E. Bai.  An optimal two stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998 .

[29]  M. Dehghani,et al.  Hammerstein model identification of multivariable nonlinear systems in the presence of colored noises , 2011, The 2nd International Conference on Control, Instrumentation and Automation.

[30]  O. Naeem,et al.  Non-linear model approximation and reduction by new input-state Hammerstein block structure , 2011, Comput. Chem. Eng..

[31]  Feng Ding,et al.  Recursive Parameter Estimation Algorithms and Convergence for a Class of Nonlinear Systems with Colored Noise , 2016, Circuits Syst. Signal Process..

[32]  Long Chen,et al.  A New Hybrid Fault Diagnostic Method for Combining Dependency Matrix Diagnosis and Fuzzy Diagnosis Based on an Enhanced Inference Operator , 2016, Circuits Syst. Signal Process..

[33]  Chen Zonghai,et al.  New identification method of nonlinear systems based on Hammerstein models , 2007 .

[34]  Adam Krzyżak,et al.  Global identification of nonlinear Hammerstein systems by recursive kernel approach , 2005 .

[35]  Er-Wei Bai,et al.  Identification of linear systems with hard input nonlinearities of known structure , 2002, Autom..

[36]  Er-Wei Bai,et al.  Iterative identification of Hammerstein systems with piecewise-linear nonlinearities , 2006, 2006 American Control Conference.

[37]  Guanrong Chen,et al.  Dual-mode predictive control algorithm for constrained Hammerstein systems , 2008, Int. J. Control.

[38]  Robert E. Kearney,et al.  Subspace Identification of SISO Hammerstein Systems: Application to Stretch Reflex Identification , 2013, IEEE Transactions on Biomedical Engineering.

[39]  Yong Zhang,et al.  Bias compensation methods for stochastic systems with colored noise , 2011 .