TY - JOUR
T1 - A Bayesian hypothesis testing-based statistical decision philosophy for structural damage detection
AU - Zhang, Qiu Hu
AU - Ni, Yi Qing
N1 - Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region (SAR), China (Grant No. PolyU 152014/18E) and a grant from The Hong Kong Polytechnic University (Grant No. 1-W14J). The authors also appreciate the funding support by the Innovation and Technology Commission of Hong Kong SAR Government to the Hong Kong Branch of National Engineering Research Center on Rail Transit Electrification and Automation (Grant No. K-BBY1).
Publisher Copyright:
© The Author(s) 2022.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Bayesian hypothesis testing
KW - Damage detection
KW - novelty detection
KW - risk management
KW - statistical decision philosophy
UR - http://www.scopus.com/inward/record.url?scp=85143240305&partnerID=8YFLogxK
U2 - 10.1177/14759217221133292
DO - 10.1177/14759217221133292
M3 - Journal article
AN - SCOPUS:85143240305
SN - 1475-9217
JO - Structural Health Monitoring
JF - Structural Health Monitoring
ER -