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An efficient method for continuously estimating posterior failure probabilities based on a single reliability analysis
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AI
DOI：10.1016/j.probengmech.2026.103895.png)
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Abstract
En 中文
When distribution parameters are uncertain, it is necessary to employ a continuous estimation method for posterior failure probabilities (PFPs) to efficiently track changes in structural reliability as new observations become available. This study proposes an efficient method for continuously estimating PFPs, thereby addressing the lack of efficient and robust methods. In the proposed method, the integrand of PFP can be equivalently expressed as an explicit updating factor operation related to the observations and the estimations of the conditional failure probabilities based on a single reliability analysis in an augmented space. Thus, repeated reliability analyses are prevented when new observations are gradually incorporated. An interpolation-based method is designed to estimate all necessary conditional failure probabilities. This method first leverages the sifting property of the Dirac delta function to derive the transformed expression of the conditional probability density for the random input vector. A normal density approximating the Dirac delta function is then adopted as the interpolation weight function to solve the integral. This enables sifting the same set of sample information in the augmented space to calculate all conditional failure probabilities. An adaptive Kriging model of the performance function is introduced to further enhance the efficiency of the reliability analysis. Examples demonstrate that compared with existing advanced methods, the proposed method notably improves the efficiency of continuous PFP estimation while maintaining high accuracy.
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