Bayesian Updating of Time-Dependent Structural Reliability Using the Method of Moment
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 4
Abstract
Bayesian updating of the reliability of deteriorating engineering structures based on inspection data has been attracting a lot of attention recently because it can provide more accurate estimates of the structural reliability as the number of inspection data increases. However, in the process of updating the reliability of deteriorating structures, it is not a trivial work to obtain the posterior distribution of the random variable of interest due to its multidimensional parameter integral space and complex integral function. This paper presents a new effective method for obtaining the explicit posterior distribution for the random variable of interest and evaluating time-variant reliability combined with all updated random variables. In the proposed method, the Smolyak-type quadrature formula is first applied to obtain the first three posterior moments of the uncertain parameters, and the three-parameter lognormal distribution is used to approximate their posterior probability distributions. Then, the two-layer Smolyak-type sparse grid is adopted to estimate the first three posterior moments of the random variable of interest, and its explicit posterior distribution can also be approximated by the three-parameter lognormal distribution. Finally, the time-variant reliability analysis considering Bayesian updating is conducted using all updated random variables. Numerical examples demonstrate that the proposed method requires less computational cost, but the results provided are almost the same as those of the Markov chain Monte Carlo simulation.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request, including computer codes of the numerical examples.
Acknowledgments
This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 51820105014, 51738001, and U1934217), the China Scholarship Council (Grant No. 201806370214), and Science and Technology Research and Development Program Project of China Railway Group Limited (Major Special Project No. 2020-Special-02). All the sources of supports are gratefully acknowledged.
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ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 4 • December 2021
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© 2021 American Society of Civil Engineers.
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Received: Apr 7, 2021
Accepted: Jul 31, 2021
Published online: Sep 8, 2021
Published in print: Dec 1, 2021
Discussion open until: Feb 8, 2022
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