Details
| Original language | English |
|---|---|
| Article number | 111768 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 222 |
| Early online date | 6 Aug 2024 |
| Publication status | Published - 1 Jan 2025 |
Abstract
Bayesian updating plays an important role in reducing epistemic uncertainty and making more reliable predictions of the structural failure probability. In this context, it should be noted that the posterior failure probability conditional on the updated uncertain parameters becomes a random variable itself. Hence, characterizing the statistical properties of the posterior failure probability is important, yet challenging task for risk-based decision-making. In this study, an efficient framework is proposed to fully characterize the statistical properties of the posterior failure probability. The framework is based on the concept of Bayesian updating and keeps the effect of aleatory and epistemic uncertainty separated. To improve the efficiency of the proposed framework, a weighted sparse grid numerical integration is suggested to evaluate the first three raw moments of the corresponding posterior reliability index. This enables the reuse of evaluation results stemming from previous analyses. In addition, the proposed framework employs the shifted lognormal distribution to approximate the probability distribution of the posterior reliability index, from which the mean, quantile, and even the distribution of the posterior failure probability can be easily obtained in closed form. Four examples illustrate the efficiency and accuracy of the proposed method, and results generated with Markov Chain Monte Carlo combined with plain Monte Carlo simulation are employed as a reference.
Keywords
- Bayesian updating, Posterior failure probability, Shifted lognormal distribution, Sparse grid numerical integration
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Mechanical Systems and Signal Processing, Vol. 222, 111768, 01.01.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An efficient Bayesian updating framework for characterizing the posterior failure probability
AU - Li, Pei Pei
AU - Zhao, Yan Gang
AU - Dang, Chao
AU - Broggi, Matteo
AU - Valdebenito, Marcos A.
AU - Faes, Matthias G.R.
N1 - Publisher Copyright: © 2024 The Authors
PY - 2025/1/1
Y1 - 2025/1/1
N2 - Bayesian updating plays an important role in reducing epistemic uncertainty and making more reliable predictions of the structural failure probability. In this context, it should be noted that the posterior failure probability conditional on the updated uncertain parameters becomes a random variable itself. Hence, characterizing the statistical properties of the posterior failure probability is important, yet challenging task for risk-based decision-making. In this study, an efficient framework is proposed to fully characterize the statistical properties of the posterior failure probability. The framework is based on the concept of Bayesian updating and keeps the effect of aleatory and epistemic uncertainty separated. To improve the efficiency of the proposed framework, a weighted sparse grid numerical integration is suggested to evaluate the first three raw moments of the corresponding posterior reliability index. This enables the reuse of evaluation results stemming from previous analyses. In addition, the proposed framework employs the shifted lognormal distribution to approximate the probability distribution of the posterior reliability index, from which the mean, quantile, and even the distribution of the posterior failure probability can be easily obtained in closed form. Four examples illustrate the efficiency and accuracy of the proposed method, and results generated with Markov Chain Monte Carlo combined with plain Monte Carlo simulation are employed as a reference.
AB - Bayesian updating plays an important role in reducing epistemic uncertainty and making more reliable predictions of the structural failure probability. In this context, it should be noted that the posterior failure probability conditional on the updated uncertain parameters becomes a random variable itself. Hence, characterizing the statistical properties of the posterior failure probability is important, yet challenging task for risk-based decision-making. In this study, an efficient framework is proposed to fully characterize the statistical properties of the posterior failure probability. The framework is based on the concept of Bayesian updating and keeps the effect of aleatory and epistemic uncertainty separated. To improve the efficiency of the proposed framework, a weighted sparse grid numerical integration is suggested to evaluate the first three raw moments of the corresponding posterior reliability index. This enables the reuse of evaluation results stemming from previous analyses. In addition, the proposed framework employs the shifted lognormal distribution to approximate the probability distribution of the posterior reliability index, from which the mean, quantile, and even the distribution of the posterior failure probability can be easily obtained in closed form. Four examples illustrate the efficiency and accuracy of the proposed method, and results generated with Markov Chain Monte Carlo combined with plain Monte Carlo simulation are employed as a reference.
KW - Bayesian updating
KW - Posterior failure probability
KW - Shifted lognormal distribution
KW - Sparse grid numerical integration
UR - http://www.scopus.com/inward/record.url?scp=85200591107&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2024.111768
DO - 10.1016/j.ymssp.2024.111768
M3 - Article
AN - SCOPUS:85200591107
VL - 222
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 111768
ER -