Research Of Expectation Maximization Algorithm Applying To Operational Modal Analysis

Modal analysis technology is an important method to solve the vibration problems in engineering, which is widely used in many areas nowadays. Modal analysis methods include experimental modal analysis(EMA) and operational modal analysis(OMA).Measuring the external excitation is necessary for applying EMA, while this step could be skipped in OMA and the modal parameters can be extracted from the system response.Therefore,the OMA methods are able to be applied in structure character analysis,on-line modal analysis,and real-time detection of large-scale and complicated equipment which play an important role in solving problems in engineering.This paper studies the expectation maximization algorithm (EM algorithm) and applies it to OMA. EM algorithm is an iterative method for finding maximum likelihood estimates (MLE) of parameters in statistical models. When EM algorithm is used in OMA, its computational accuracy could be varied according to the selected initial values.The effectiveness of EM algorithm applying to OMA is proved by the means of simulation and experiment in this paper and the main points of the research can be summarized as follows: (1)The purpose and significance of this project have been introduced and the development history,application areas,literature reviews of the modal parameters analysis methods have been stated systematically.(2)The basic theory and mathematical derivation of modal analysis methods have been discussed. Several common EMA methods and OMA methods have been researched.(3)The feasibility of EM algorithm applying to operational modal parameters regconition have been discussed.This algorithm has very good statistical characteristics itself.If the selected initial values are appropriate,the global maximum can be searched efficiently. The results calculated by SSI algorithm can be used to initialize the EM algorithm when the modal parameters are extracted through EM algorithm.Moreover,the situation of using random points as initial values have been discussed.Applying EM algorithm with the initial value using random points generated by a proper method, the results could be relative accurate.(4)Through the ANSYS finite element analysis of simulated model of cantilever beam and free beam, we extracted every order natural frequencies of cantilever beam, good free beam and damaged free beam. As compared with the theoretical values calculated by vibration theory of beam,the effectiveness of finite element model analysis has been proved.(5)The EMA and OMA experiments have been conducted on account of the cantilever beam and free beam. The collected signals have been used to analyze modal parameters by the methods of SSI,EM based on SSI results and EM based on random points.The experiment result proved the effectiveness of EM algorithm applying to operational modal analysis.Besides,this algorithm is able to avoid the indication of fake modal and hidden modal when using the SSI algorithm and more precise parameters and clearer stabilization diagrams could be acquired.