Parameter estimations of structural dynamic systems using sequential prediction error method

Abstract

The parameter estimations of linear multi-degree-of-freedom structural dynamic systems are carried out in time domain with the aid of the sequential prediction error method. Methods for estimating the structrual parameters and the modal parameters are presented. The equation of motion is transfromed into the state space equation of the ovservable canonical form, and then into the auto-regressive and moving average model with auxiliary stochastic inpur(ARMAX model) to process the measurment data contaminated by the system noise as well as the output noise. The parameters of the ARMAX model are extimated by using the sequential prediction error method. Then, the parameters of the equation of motion are recovered thereafter. For the purpose of improving the robustness and performance of the sequential prediction error algorithm, some techniques such as exponential data weightion, golval data weighting, and square root estimation for multi-regression have been presented. In order to verify the accuracy of the esimation method, analytical simulation studies are performed for a model with two degrees of freedom on the basis of simulated data under various conditions of input and output noises it is shown that the presented methods yield good estimates even under relative large noise conditions. The method is also applied to the identification of the modal parameters of a building model based on experimenatal data. The estimated modal parameters from different sets of experiments are found to be very consistent. The re-evaluated responses based on the estimated parameters also show good agreements with the measured time histories.