Novel Sparse Bayesian Learning for Structural Health Monitoring Using Incomplete Modal Data

Abstract

For civil structures, structural damage due to excessive loading or environmental degradation usually occurs in localized areas. A new, sparse, Bayesian probabilistic approach for computing the probability of localized stiffness reductions induced by damage is presented that uses noisy, incomplete modal data from before and after possible damage. The methodology employs a hierarchical form of the prior for the stiffness parameters that promotes spatial sparsity in the inferred stiffness reductions. To obtain the most plausible model of sparse stiffness reductions together with its uncertainty within a specified class of models, the method employs an optimization scheme that iterates between the groups of modal parameters and hyperpameters. The approach also adopts a recent published strategy for Bayesian dynamic model updating based on modal data that has two important benefits: (1) no matching of model and experimental modes is needed, and (2) solving the eigenvalue problem of a structural model is not required. For validation, a three-dimensional braced-frame model with simulated data from the Phase II benchmark problem sponsored by the IASC-ASCE task group on structural health monitoring is analyzed using the proposed method. The results show that no threshold is required to issue a damage alarm for the proposed approach and the occurrence of false-positive and false-negative damage detection is clearly reduced in the presence of modeling error.