A collaborative Bayesian optimization method for estimation of failure probability bounds under mixed uncertainties
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Fangqi Hong, Pengfei Wei, Jingwen Song, Marcos Valdebenito, Matthias Faes, Michael Beer, A collaborative Bayesian optimization method for estimation of failure probability bounds under mixed uncertainties, 14th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP14), Dublin, Ireland, 2023.Download Item:
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Uncertainty quantification has been realized as of vital importance in structural reliability engineering to achieve credible results especially when the available information is scarce, incomplete, imprecise, etc., and it is also recognized that the aleatory and epistemic uncertainties need to be distinguished and separated and characterized through the whole analysis process. For addressing the above challenge, beyond the classical probability models, imprecise probability models, such as probability boxes, evidence theory, and fuzzy probabilities, as well as non-probabilistic models with interval/convex models as examples, have been developed for addressing alternative cases. However, given the mixed inputs characterized by the probability model, the imprecise probability, and the non-probabilistic model, the resultant failure probability is presented to be an interval variable, and it is then the key to estimating the bounds, especially the upper bound, of this interval. Following our development of Collaborative and Adaptive Bayesian Optimization for estimating the bounds of the expectation of the structural response, we propose a generalization of it for efficiently estimating the bounds of the failure probability by introducing several key improvements. The method starts by training a Gaussian Process Regression (GPR) model in the joint aleatory and epistemic spaces and then inferring the resultant stochastic process models in the marginal subspaces. With the above treatments, the double-loop formulation is then decoupled and two acquisition functions are introduced for specifying the optimal training points respectively in the two marginal spaces. Different from the original CABO algorithm, the above inference is realized based on an efficient numerical simulation of the GPR model, and thus applies to any output of interest. The above process is repeated until the stopping criteria are satisfied in both subspaces. Numerical results indicate that the CABO algorithm is efficient and shows good performance of global convergence.
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Author: Wei, Pengfei; Beer, Michael; Faes, Matthias; ICASP14; Valdebenito, Marcos; Song, Jingwen; Hong, Fangqi
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