Efficient Laplace prior-based sparse Bayesian learning for structural damage identification and uncertainty quantification

Abstract

Assessing the damage state from the measurement data is central to structural health monitoring. Due to the ubiquitous existence of uncertainty factors in structural model and measurement, quantifying the uncertainty information becomes more and more recognized for reliable damage assessment. To this end, a novel Laplace prior-based sparse Bayesian learning approach is proposed in this paper for damage identification and uncertainty quantification. The key motivation behind is that damage distribution is always spatially sparse and to enforce the sparsity, the Laplace prior is reasonably used within the Bayesian framework. Compared to the automatic relevance determination (ARD) Gaussian prior in conventional sparse Bayesian learning, the Laplace prior involves much less hyperparameters and therefore, leads to more efficient computation and less demanding of dataset. Moreover, it is found that the Laplace prior can be obtained by further enforcing the Gamma prior on the ARD Gaussian hyperparameters and in this way, uncertainty is easily quantified for the proposed approach through an equivalent ARD Gaussian model, circumventing the non-differentiability of the Laplace prior. Numerical and experimental examples have been studied to demonstrate the effectiveness, accuracy and efficiency of the proposed approach in structural damage identification and uncertainty quantification.