Structural damage identification through unscented Kalman inversion with l 1-norm regularization

Abstract

Advances in modal analysis have motivated finite element model updating for damage identification based on vibration monitoring. However, the model updating problem is usually ill-posed owing to limited and noisy measurement data, and the predominant sensitivity-based optimization approaches may suffer from large linearization errors. To address these challenges, this article proposes using the unscented Kalman inversion with l 1 -norm regularization (UKI- l 1 ) to solve the damage identification problem in a derivative-free manner. UKI- l 1 implements an explicit transformation converting the l 1 -norm regularized least-squares problem into the l 2 -norm regularized problem, which can be readily solved by the UKI with measurement augmentation. The effectiveness of the proposed approach is evaluated through identifying damage of a continuous beam structure and a reinforced concrete frame structure. Numerical investigation confirms the robustness of UKI- l 1 to measurement noise, and experimental study demonstrates that the damage identification results obtained by UKI- l 1 match well with expectations.