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

Abstract

The authors propose a time-domain equation error estimator for the problem of estimating the constitutive parameters of a complex linear structure. From a mathematical model with known geometry, topology, load history, and responses at certain locations, a parameter estimation problem evolves that, when solved, determines the unknown constitutive parameters of that model. First, the authors estimate the displacement and velocity at the locations where accelerations have been measured by standard integration/filtering techniques. Next, the equations of motion are recast and established as a discrete multistep method in regards to displacements at the unmeasured degrees of freedom and weighted sum of residual forces at adjacent time points. Finally, the unknown constitutive parameters are estimated by solving a constrained nonlinear optimization problem, assuming the parameter estimate to be an average of estimates over several time intervals. The recursive quadratic programming method is the preferred 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.