The Robust Identification Of Linear Parameters Varying Models Based On Asymmetric Laplace Distribution

With the rapid development of modern industry,the internal mechanism of industrial equipments becomes more and more complex,and presents strong time variability and nonlinearity.Therefore,the mechanism modeling methods based on the classical Newton's law of kinematics,the law of conservation of energy and momentum,and the analysis of system dynamics are greatly limited.However the pressing needs of the accurate models promotes the rapid development of the researches about system identification,because it does not need complete and thorough analysis to the internal mechanism of the modeling processes,with little prior knowledge,design of experiments,input and output data acquisition system by system identification algorithm can obtain accurate mathematical model,and compared with the mechanism model,the mathematical model is more suitable for the design of the controller and the condition monitoring and fault diagnosis.However,the system identification method strongly depends on the data quality.However,in the actual industry,due to the limitations of equipment design,complex and harsh working conditions and complex working environment,it is difficult to ensure that the sensor can completely and accurately collect the experimental data without noise pollution or nearly containing white noise.To solve such problems,it is more effective and low-cost to solve the problems of noise and outliers in the data in the system identification algorithm than to redesign the data acquisition process.On the basis of existing studies at home and abroad,the thesis studies the robust parameters identification algorithm for linear parameters-varying models.The specific contents are summarized as follows:(1)The parameter estimation algorithm of linear variable parameter model with robustness for outliers and asymmetrically distributed noise is investigated.Firstly,two typical linear variable parameter models are introduced,and the product form of regression vector and parameter vector suitable for parameter identification is arranged.At the same time,the asymmetric Laplace distribution is introduced,and the probability density function and a generation mode of the probability distribution are analyzed,compared with the Gaussian distribution and the symmetric Laplace distribution.(2)In the framework of the expected maximization algorithm,noise modeling based on asymmetric Laplace distribution is dealt with.The asymmetric Laplace distribution was decomposed into normal distribution and exponential distribution,and the mean value of the logarithmic likelihood function on the random variable subject to exponential distribution was solved.The problem was reduced to parameter identification based on normal distribution,and the algorithm derivation was completed.(3)Several numerical simulations and engineering examples of continuous stirred reactor demonstrate the robustness of the proposed algorithm to outliers and asymmetrically distributed noise.Compared with the existing algorithm based on Gaussian distribution and Laplace distribution,the proposed algorithm is more robust.(4)In the conclusion,the main contributions of this research and the existing problems are summarized,and the future research direction is proposed.