Linear system identification technique by time series analysis
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Identification of linear dynamical systems using the finite difference time-domain (FDTD) method is inaccurate and problematic. This thesis investigates the use of time series analysis techniques for estimating parameters of a continuous-time (CT) model of linear dynamic systems. This application of time series analysis for system identification is based on the autoregressive moving-average (ARMA) model and its important characteristics. This thesis concentrates on the procedure of using time series analysis for identification of linear dynamical systems. The procedure consists of two steps. In the first step, an ARMA model is estimated by minimizing the residual sum of squares (RSS) from discrete-time (DT) data. In the process of optimization, the initial guess of parameters needs to be calculated first and then the loop of searching for the direction to minimize RSS starts. When the parameters changing is not obvious or the generation is overabundance, the search stops. In the second step, the ARMA model is converted into an ordinary differential equation (ODE) by using the equivalence relationships between the auto-covariance of the ARMA model and the ODE. In order to test and evaluate the application of time series analysis for dynamical system identification, analysis and numerical simulations are performed by using Matlab and Simulink. The results show that the method based on time series analysis is better than the FDTD method when the sampling time and/or the covariance of input noise is so big that finite-difference modeling cannot well present the original continuous system. A typical value of that will invalidate finite-difference modeling is about, where is the system's lowest natural frequency. As for using time series analysis to estimating first order system, the estimation is less accurate when the time constant is larger. When the second order system is estimated by using time series analysis, the sampling interval and damping ratio are the two factors that influence the estimation accuracy. For under-damped system, the accuracy decreases but still over 90% when increases to be between and of the response vibration period. However, for critical and over-damped system, the accuracy drops sharply and less than 80% sometimes.
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