Identification Of Nonlinear Systems With Non-ideal Process Data

In modern industry,majority of the industrial processes are nonlinear which may exhibit complicated intrinsic mechanism and complex inborn nonlinear property.Therefore,modeling of these practical processes with the first principle modeling method like mass,momentum and heat balances costs a lot of manpower.Moreover,the accuracy of the first principle model of a certain industrial process may decrease greatly due to sometimes it is difficult to comprehensively understand the complicated intrinsic mechanism of the industrial process.Since the process data contains abundant information about the dynamics of the process,then the data-driven system identification offers a favorable alternative for industrial processes modeling.System identification provides an effective and easy-implementation modeling method and it recovers the nonlinear process model only from the informative process data set without knowing the complicated intrinsic mechanism a priori.Therefore,system identification has attracted more and more attentions from the researchers.But during the identification of practical industrial processes,the quality of the collected process data might be inevitably deteriorated by external interference or some other reasons.For example sensor malfunctions may cause missing observations,different ways of data acquisition will result in dual-rate sampled data,undetermined process disturbances can introduce outliers in data and so on.Obviously,the identification data set may become non-ideal by the above identification problems,which puts forward higher requirements for the identification algorithms.This thesis mainly considers the identification of nonlinear systems with non-ideal process data and the nonlinear model structures are selected as linear parameter varying(LPV)models and nonlinear state-space models,respectively.First,the identification of nonlinear system which is described by LPV model is investigated with poor data quality.The LPV model which owns linear model structure and time-varying model parameters is widely studied in nonlinear system identification due to its ability to accurately describe the practical nonlinear processes.Then,the identification of nonlinear state-space model with poor data quality is considered and more generalized identification algorithms are obtained.The main contents of this dissertation are arranged as:The identification of LPV time-delay system with slow-rate sampled output data and output contaminated with outliers is considered.The input data of the system is fast-rate sampled while the output data is slow-rate sampled,and the slow-rate sampled period is assumed to be integral times of the fast-rate sampled period.The time-varying output time-delay is treated as a random integer at each sampling moment which follows the uniform distribution with the boundary known as a priori.The robust identification framework is established based on the Laplace distribution and expectation-maximization(EM)algorithm,the unknown time-delay is considered as an hidden variable.The formulas to estimate the model parameters are provided in the identification framework and the unknown time-delay is also estimated through maximizing its posterior distribution function.Robust identification of the LPV model with Markov time-varying time delays is considered.With the basic idea of global system identification,the varying LPV model parameters are represented as linear combinations of the meromorphic functions of the scheduling variables.The correlations between any two consecutive time delays are considered and a first-order Markov chain model is utilized to model the correlation between the time delays as they do not simply change randomly in reality.A transition probability matrix and an initial probability distribution vector of the Markov process are used to govern the switching mechanism of the time delays.The iterative updating formulas of model parameter and each element in the Markov transition probability matrix and the Markov initial probability distribution are derived simultaneously in the identification process.The robust multiple model strategy for nonlinear state-space system identification with the system output data corrupted by random outliers is investigated.With the basic idea of local system identification,a set of local nonlinear state-space models are firstly identified at the pre-chosen working points.At each sampling instant,the global system output can be seen as weighted combination of the local outputs and the normalized weights of the local models are calculated by a smooth exponential function.The developed identification approach is derived based on the EM algorithm and Laplace distribution and the equations to update all the local model parameters are presented.The validity widths of all the sub models are iteratively estimated by maximizing a nonlinear cost function in the developed approach.The robust identification of nonlinear time-delay state-space model with contaminated measurements is considered.The uncertain time-delay between the output and state variables is treated as a latent process variable and it is considered to be uniformly distributed and the boundary of it is known as a priori.The identification problem is formulated with the EM algorithm.The auxiliary nonlinear state-space delay model is introduced to numerically calculate the posterior distributions of the hidden state variables with the particle filtering.The equations to estimate the parameters and delay are all derived in the developed approach.The robust identification approach for nonlinear systems in state-space form with measurements contaminated with outliers and part of the measurements missing at random is studied.The robust identification framework is built based on the EM algorithm and Student's t-distribution.The appropriate probability distributions for missing observations and the resulted uncertainties are both considered in the identification process.The particle filtering with missing outputs is introduced in detail and the posterior distributions of the hidden states are iteratively estimated with it.The formulas to iteratively estimate the model parameters are presented in the proposed approach and also,the degree of freedom of the Student's t-distribution is iteratively estimated through solving a nonlinear equation in the identification process.