Damage parameters and input force estimation for simple frame structures subjected to unknown excitations - Shereena, O.A.; Rao, B.N. (Journal of Structural Engineering, 2024)
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 damageidentification is formulated as a joint state parameter estimation problem. Current work reformulates the problem, toestimate the excitation force simultaneously. The joint estimation problems are considered as nonlinear identificationproblems. The current study adopts a nonlinear identification algorithm that integrates an unbiased minimumvariance estimator and an optimization scheme. The framework makes use of linear formulations alone. Conventionaland popular nonlinear filtering algorithms essentially involves linearization approximations, with the inclusion ofunknown input terms in the state vector. In turn, the unbiased Minimum Variance Estimator (MVE) algorithmincorporates the excitation as an unknown input term in the state equation and eliminates the difficulties associatedwith linearization. The optimization scheme chooses an optimal solution set of values, for the damage parameters astailored in the coupling procedure. Due care in choosing and partitioning the observed data between the two schemesis pivotal. The applicability of the method to the damage estimation problem is illustrated through two examples. Thefirst problem is to find the damage parameters of a discrete spring mass model subjected to an unknown input. Thetechnique estimates the unknown input and response state time histories as well, based on the recorded vibrationdata. The second problem solves the joint estimation of damage parameters, input excitation, and responses of a planeframe subjected to earthquake excitation. The vibration data is synthetically generated, from the forward problem andadding adequate white noise, to replicate actual field data. Numerical results suggest that the technique is successfulin identifying damage locations and damage quantities accurately. Practical relevance is that the unknown inputs aretreated as unknown, and estimated alongside.