Identification Methods For The Nonlinear Error-in-Variables Systems

With a large amount of industrial data available,it is of considerable interest to develop data-based models.The challenge lies in the significant noises that appear in all data collected from industry.Generally,an estimation procedure that considers output error but ignores input error will introduce bias.The errors-in-variables(EIV)model is a model that accounts for measurement noises in all observations(both input and output).In most of traditional EIV identification methods,the input generation dynamics is not considered,this thesis studies on the EIV systems with the input generation process.The main contents lie in:(1)A dynamic model is applied to describe the input generation process,and then the Kalman smoother is used to estimate its state using all available measurements.In order to utilize all of the observed variables in the EIV process,an augmented EIV model is derived to describe both input generation process and the EIV process dynamics itself.The parameters in the EIV model are then estimated by applying expectation maximization(EM)algorithm.Simulated numerical example and an experiment performed on a hybrid tank system are used to demonstrate the improved identification performance of the proposed method.(2)An augmented model approach for identification of nonlinear EIV systems is proposed.An EIV model accounts for uncertainties in the observations of both inputs and outputs.As the direct identification of nonlinear functions is difficult,we propose to approximate the nonlinear EIV model using multiple autoregressive exogenous(ARX)models.To estimate the noise-free input signal,we use a collection of particle filters which run in parallel corresponding to each of the multiple ARX models.The parameters of local models are estimated by applying EM algorithm,under a maximum likelihood framework,using the input-output data of the nonlinear EIV system.Simulated numerical examples and an experiment study on a multi-tank system are used to illustrate the efficacy of the proposed approach.(3)A robust identification approach to nonlinear EIV systems contaminated with outliers is presented.In this work,the measurement noise is modelled using the tdistribution,instead of traditional Gaussian distribution,to mitigate the effect of the outliers.The heavier tails of t-distribution,through the adjustable degrees of freedom,help to account for noise and outliers concomitantly.Further,to avoid the intricacies related to the direct nonlinear identification,we propose to approximate the nonlinear EIV dynamics using multiple local ARX models and aggregating them using an exponential weighting strategy.The parameters of local models and weighting parameters are estimated using EM algorithm,under the framework of Maximum Likelihood Estimation.Validation studies with simulated numerical examples and an experiment on a multi-tank system demonstrate superiority of the proposed method.(4)A Variational Bayesian(VB)approach to robust identification of nonlinear EIV systems contaminated with outliers is proposed.As the real process data is always subject to outliers,we propose to model them using the t-distribution through the adjustable degrees of freedom.Further,based on the input-output data of the nonlinear EIV system,we propose to approximate the nonlinear EIV dynamics using multiple local ARX models and combine them using a softmax function based weighting approach.The parameter estimation problem is casted in the Bayesian framework,and posterior distributions of the model parameters are estimated using the VB approach,instead of point estimations.A numerical example of continuous fermenter as well as an experiment conducted on the multi-tank system demonstrates effectiveness of the proposed method.Finally,a conclusion is made for the EIV systems,the perspectives at this research field for the next step which have been discussed,and some issues will be studied in detail for the future work.