Research On Compressed Sensing Measurement Identification Method

Recently,space material experiments have put forward higher standards for temperature control of high temperature crystal furnace,with the development of space science and technology.In order to solve the problem of low control precision,poor adaptability and low stability of PID control algorithm,it is necessary to draw support from the system identification.Based on statistical method,most of the identification algorithms estimate the internal model of the system by analyzing the correlation between the input and output data.In this way,it requires a large amount of statistical data for calculation,and the larger the amount of data,the closer the estimated system model is to the real system.However,this is very difficult to achieve for many practical systems.This paper solves this problem from the perspective of signal measurement.In the present context,any system can be represented as a signal that translates the identification problem of the system into how it is measured.The proposed compressed sensing theory in recent years provides a new framework for measuring signals,which shifts the focus of signal measurement from the frequency domain to the information of the signal,thus breaking the requirements of the traditional sampling theorem and greatly reducing the requirement for the amount of data.This paper makes use of the theory of compressed sensing to measure the system model,and on this basis,proposes a compressed measurement identification algorithm,in order to obtain accurate,stable and reliable system model by using the least measured data.Firstly,this paper applies the compressed measurement identification algorithm to the identification of linear time-invariant systems,and proves that the measurement of linear time-invariant systems is feasible and accurate.Even in the case of large measurement noise,stable measurement results can be procured.However,it has been found in experiments that a large amount of measurement noise is introduced by means of uniform sampling,so that the measurement accuracy is greatly reduced.In order to solve this problem,this paper modifies the form of the measurement matrix,and uses the non-uniform sampling data to measure the system,thus achieving the super-resolution of the measurement.Subsequently,the algorithm is extended to the identification of linear parametric systems.From the point of measurement,the measurement of a time-invariant system is a measurement of a static signal,while the measurement of a time-varying or parametric system is for a dynamic signal.Therefore,this paper uses the method of measuring dynamic signals to realize the identification of linear parametric systems.Although a linear parametric system can represent a partial nonlinear system,its scope of application is narrow.Hence,this paper combines the Volterra series expansion method to broaden the application range of the compression measurement identification algorithm in nonlinear systems.In addition,in the identification method of nonlinear systems using polynomial expansion method,an inevitable problem is "Curse of Dimensionality",and the application of the compressed sensing theorem indicates a new way to solve this problem.