Identification Of Switched Systems Based On Gaussian Mixture Model Clustering

The switched system has a wide range of applications in actual engineering systems,and has achieved substantial results in the fields of control,filtering,and fault diagnosis.However,for the identification of the switched system,since the switched rules of the switched system are unknown,the input and output data collected from the switched system come from different subsystems.In the identification process,it is usually necessary to identify the parameters of each subsystem,as well as the switched time of the switched system,the residence time of the subsystem and the number of subsystems.Therefore,the identification of switched systems is more difficult than that of non-switched single-model systems,in which also lies the significance and purpose of this paper.This paper takes the switched system as the research object,mainly aiming at identifying the switched signal,the number of subsystems,and the parameters of the switched system.A two-stage identification method is proposed to identify the switched system.In the mode detection stage,the switched signal is estimated by Gaussian mixture model clustering,the number of subsystems is estimated according to the model selection criterion,and methods like K-means++,Naive Bayes classifier and 0-1criterion are proposed to improve the Gaussian mixture model clustering,thus increasing the accuracy of mode detection and reducing the complexity of the algorithm.In the parameter identification stage,the parameters of each subsystem are estimated by the auxiliary model multi-innovation generalized extended least square algorithm.The main innovations of this paper are as follows:1.For the identification of the switched system,a two-stage identification method is proposed to identify the switched system,which is divided into a mode detection and parameter identification.In the mode detection stage,a Gaussian mixture model is first established to represent the distribution of sampled data,and then the posterior probability of the sampled data belonging to each subsystem is calculated,next the model parameters are updated iteratively through the maximum likelihood estimation algorithm to make the Gaussian mixture model maximize the fitting of the distribution of the sampled data.Finally,the switched signal is estimated according to the maximum posteriori probability criterion.In the parameter identification stage,according to the estimated value of the switched signal,the sampling data is rearranged,and the parameter vector of each subsystem is estimated by the auxiliary model multi-innovation generalized extended least square algorithm to obtain the parameter estimated value of each subsystem in the switched system.According to the martingale convergence theorem,the convergence analysis of the auxiliary model multi-innovation generalized extended least squares algorithm is carried out.2.For some defects of Gaussian mixture model clustering,the improved Gaussian mixture model clustering is proposed.In order to solve the problem that the Gaussian mixture model clustering is sensitive to the initial model parameters,K-means++algorithm is used to select a group of appropriate initial model parameters,so as to promote the mode detection accuracy in the process of switched system identification.On this basis,taking full advantage of the mutual independence of the sampled data in the switched system,the Gaussian mixture model clustering and Naive Bayes classifier are combined to improve the mode detection accuracy in the switched system identification process.In order to reduce the algorithm complexity in the process of Gaussian mixture model clustering,the 0-1 discretization of the posterior probability is carried out in each iteration,which effectively reduces the algorithm complexity and calculation time in the process of Gaussian mixture model clustering.3.As the number of subsystems is unknown in the identification process of the switched system,the identification of the number of subsystems based on the model selection criterion is proposed.In general,in the identification process of switched system,the number of subsystems,switched time,and residence time of the subsystems are often unknown,only input data and output data can be sampled.So the identification of the number of subsystems is often neglected in the existing identification of switched systems.According to the AIC criterion and the BIC criterion,the number of subsystems in the switched system is identified by the maximum likelihood function of the sampled data and by comparing the best of the sampled data fitted by the model.The simulation results show that the number of subsystems in the switched system can be accurately identified by the AIC criterion and the BIC criterion.4.For the problem of silicon content prediction in the industrial iron-making process,a silicon content prediction model based on the principle of the switched system is proposed.Due to the dynamic changes of silicon content caused by the changes in various factors during the ironmaking process,the switched system model is taken into consideration to describe the dynamic process during the modeling process.On this basis,the Gaussian mixture model clustering is proposed to estimate the switched signal of the switched system,the subsystem parameters and the number of subsystems,and finally predict the silicon content in the iron-making process through the switched system prediction model.