Time-Domain Parameter Estimation Algorithm for Structures. I: Computational Aspects

A time-domain equation error estimator is proposed for the problem of estimating constitutive parameters of a complex linear structure. We have assumed that the geometry and topology of the model are known and have measured the history of applied loads, and the accelerations at certain locations. For the proposed parameter estimation algorithm, we first estimate the displacement and velocity at the locations where accelerations have been measured by standard integration/filtering techniques. We recast the equations of motion as a discrete multistep method in terms of the displacements at the unmeasured degrees of freedom, and establish our measure of error as the weighted sum of residual forces at adjacent time points. We estimate the unknown constitutive parameters by solving a constrained nonlinear optimization problem, and take the parameter estimate to be the average of estimates over several time windows. We advocate the use of the recursive quadratic programming method to solve the optimization problem. The proposed time-domain estimator can accommodate response sampled incompletely in time, state, and space and is amenable to identification of complex structural systems.