Damage parameters and input force estimation for simple frame structures subjected to unknown excitations

Abstract

The present paper aims at estimating the damage parameters of the structures subjected to an unknown excitation. Damage parameters are characterized as the damage location and the reduction in stiffness. Typically, the damage identification is formulated as a joint state parameter estimation problem. Current work reformulates the problem, to estimate the excitation force simultaneously. The joint estimation problems are considered as nonlinear identification problems. The current study adopts a nonlinear identification algorithm that integrates an unbiased minimum variance estimator and an optimization scheme. The framework makes use of linear formulations alone. Conventional and popular nonlinear filtering algorithms essentially involves linearization approximations, with the inclusion of unknown input terms in the state vector. In turn, the unbiased Minimum Variance Estimator (MVE) algorithm incorporates the excitation as an unknown input term in the state equation and eliminates the difficulties associated with linearization. The optimization scheme chooses an optimal solution set of values, for the damage parameters as tailored in the coupling procedure. Due care in choosing and partitioning the observed data between the two schemes is pivotal. The applicability of the method to the damage estimation problem is illustrated through two examples. The first problem is to find the damage parameters of a discrete spring mass model subjected to an unknown input. The technique estimates the unknown input and response state time histories as well, based on the recorded vibration data. The second problem solves the joint estimation of damage parameters, input excitation, and responses of a plane frame subjected to earthquake excitation. The vibration data is synthetically generated, from the forward problem and adding adequate white noise, to replicate actual field data. Numerical results suggest that the technique is successful in identifying damage locations and damage quantities accurately. Practical relevance is that the unknown inputs are treated as unknown, and estimated alongside.