Determining models of structures from earthquake records

Abstract

The problem of determining linear models of structures from seismic response data is studied using ideas from the theory of system identification. The investigation employs a general formulation called the output-error approach, in which optimal estimates of the model parameters are obtained by minimizing a selected measure-of-fit between the responses of the structure and the model. The question of whether the parameters can be determined uniquely and reliably in this way is studied for a general class of linear structural models. Because earthquake records are normally available from only a small number of locations in a structure, and because of measurement noise, it is shown that it is necessary in practice to estimate parameters of the dominant modes in the records, rather than the stiffness and damping matrices. Two output-error techniques are investigated. Tests of the first, an optimal filter method, show that its advantages are offset by weaknesses which make it unsatisfactory for application to seismic response. A new technique, called the modal minimization method, is developed to overcome these difficulties. It is a reliable and efficient method to determine the optimal estimates of modal parameters for linear structural models. The modal minimization method is applied to two multi- story buildings that experienced the 1971 San Fernando earthquake. New information is obtained concerning the properties of the higher modes of the taller building and more reliable estimates of the properties of the fundamental modes of both structures are found. The time-varying character of the equivalent linear parameters is also studied for both buildings. It is shown for the two buildings examined that the optimal, time-invariant, linear models with a small number of modes can reproduce the strong-motion records much better than had been supposed from previous work using less systematic techniques.