Sparse Bayesian learning for damage identification using nonlinear models: Application to weld fractures of steel-frame buildings

Abstract

Sparse Bayesian learning (SBL) is a well-established technique for tackling supervised learning problems, while taking advantage of the prior knowledge that the expected solution is sparse. Based on the premise that initial damage of a structure appears only in a limited number of locations, SBL has been explored for identifying structural damage, showing promising results. Existing SBL methods for structural damage identification use measurements related to modal properties and are thus limited to linear models. In this paper, we present a methodology that allows for application of SBL in nonlinear models, using time history measurements. We develop a two-step optimization algorithm in which the most probable values of the structural model parameters and the hyperparameters are iteratively obtained. An equivalent, single-objective, minimization problem that results in the most probable model parameter values is also derived. We consider the example problem of identifying damage in the form of weld fractures in a 15-story moment-resisting steel-frame building, using a nonlinear finite-element model and simulated acceleration data. Fiber elements and a bilinear material model are used to account for the change in local stiffness when cracks at the welds are subjected to tension, and the model parameters characterize the loss of stiffness as the cracks open under tension. The damage identification results demonstrate the effectiveness and robustness of the proposed methodology in identifying the existence, location, and severity of damage for a variety of different damage scenarios and levels of model and measurement error.