A Bayesian hypothesis testing-based statistical decision philosophy for structural damage detection

Abstract

In this article, a new statistical decision philosophy is developed to tackle structural damage detection problems which are defined in the context of novelty detection. In line with this philosophy, structural damage detection is achieved by deriving the posterior probability of damage presence from the Bayesian testing of two competing hypotheses, with the null and alternative hypotheses representing the undamaged and damaged states of a structure of concern, respectively. To resolve the tricky problem of prior appropriateness in Bayesian hypothesis testing, a general prior specification criterion is devised based on the notion of risk management, including the risk of false positive indication (an undamaged structure is incorrectly identified as damaged) and the risk of false negative indication (a damaged structure is incorrectly identified as undamaged). To determine an optimal risk level, two principles, namely the principle of posterior probability difference minimization (PPDM) and the principle of posterior probability product maximization (PPPM), are defined. The PPDM principle is to minimize the difference between the ability of a novelty detector to avoid a false positive and its ability to avoid a false negative, and the PPPM principle is to maximize the product of the two capabilities. Both principles essentially act as a means of achieving an optimal trade-off between the false positive and false negative risks stipulated in pursuing damage detection. To demonstrate the effectiveness of the proposed statistical decision philosophy for structural damage detection, experimental data obtained from a 5-story steel frame model and a 38-story concrete building model have been investigated.