Wiener models robust identification of multi-rate process with time-varying delay using expectation-maximization algorithm. (October 2022) - Wang, Zeyu; Zhang, Yang; Jin, Qibing; Liu, Qie; Kelly, Adrian L.
Abstract: Multi-rate systems exist widely in the field of computer process control. Research on the multi-rate issue of linear systems is relatively mature and is gradually turning to multi-rate issues of nonlinear systems. Concurrently, irregular process disturbances (impulse noise, outliers, non-zero mean noise) and varying transmission delay problems are often overlooked or considered alone, which is lacking generality. Thus, the main objective of this paper is to formulate and solve the identification problem of multi-rate nonlinear Wiener models with time-varying delay and irregular process disturbances simultaneously. The probability graph model of the Wiener process is constructed. Under the expectation–maximization (EM) framework, the Scale outlier model and Location outlier model (both based on Gaussian mixture distribution) are separately introduced to model the contaminated output data. The time-varying delay at each sampling instant is assumed as a uniform distribution. An auxiliary model is applied to acquire the unmeasured middle variable. Then, a robust EM identification algorithm is developed and its convergence is analyzed. The validity of the developed approach is illustrated through two numerical examples and a simulation of the continuous stirred tank reactor. Highlights: The parameter estimation of Wiener model under time-varying delay, multi-rate sampling and irregular interference (impulse noise, outliers) is studied for the first time. Under the expectation–maximization framework, the Scale outlier model is introduced to model the contaminated output data. The time-varying delay at each sampling instant is assume to obey the uniform distribution. The proposed method can estimate the model parameter and time varying delay simultaneously. For the presence of non-zero mean noise, the Location outlier model is introduced to model the contaminated output data. The proposed method can further estimate the bias of non-zero noise. The probability graph model of the Wiener process is constructed. The idea of an auxiliary model is applied to acquire the unmeasured middle variable. The identification convergence of the proposed algorithm is analyzed.