Model analysis of multi-input/multi-output systemby vector ARMAX time series modeling

Abstract

The main objective of this work is to develop a parametric approach of analyzing the multi-input/multi-output (MIMO) time series data for the purpose of the identification of the modal parameters of mechanical structures. For this purpose the sork has been done about the following topics: i)building of the time series models appropriate for the experimental modal analysis, ii) application of the parameter estimation method, and iii) determination of the adequate order of the time series model. In order to represent the relationships between the input and the output of a open-loop system, the vector autoregressive moving average model with exogenous variables (ARMAX) is used as a time series model. A condition that no output responses can become the causes of some one response is added to the vector ARMAX model, so that the number of parameters to be estimated is minimized. Moreover, the vector ARMAX model is represented into two regression forms acording to the approaches of modeling the MIMO time series data, i.e., to the multiinput/single output (MOSO) model and to the MIMO model so as to be employed to the linear estimation method. In many cases so far, the MIMO data were treated with the MISO model in a consecutive manner mainly because of computer capacities. By noting that some of the modal parameters must be of the global characteristics regardless of measurement locations in theory, anMIMO modeling approach is taken to analyze a set of multiple random excitation/multiple response meausrements. The MISO approach is also applied to the sasm edata and the results by the two methods are compared. For the estimation of the model parameters, nonlinear optimization techniques have been mainly used so far, which make the computational burden to be heavy. In dorder to lighten such a burden a linear estimation method is employed, which consists of the following procedures: Initially, the residual data are estimated from the measured input and output data, and the...