Subset simulation for problems with strongly non-Gaussian, highly anisotropic, and degenerate distributions

Shields, Michael D.; Giovanis, Dimitris G.; Sundar, V. S.

doi:10.1016/j.compstruc.2020.106431

Cited by 19 publications

(16 citation statements)

References 27 publications

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“…To alleviate these issues, more advanced sampling methods, such as delayed rejection Markov chain Monte Carlo [27], Hamiltonian Monte Carlo [41], and affine invariant ensemble sampling [40], have been proposed. In addition, an approximate COV estimate to the intermediate failure probability in subset i is given by [2]:…”

Section: Subset Simulationmentioning

confidence: 99%

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Reliability Estimation of an Advanced Nuclear Fuel using Coupled Active Learning, Multifidelity Modeling, and Subset Simulation

Dhulipala¹,

Shields²,

Chakroborty³

et al. 2022

Preprint

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Tristructural isotropic (TRISO)-coated particle fuel is a robust nuclear fuel and determining its reliability is critical for the success of advanced nuclear technologies. However, TRISO failure probabilities are small and the associated computational models are expensive. We used coupled active learning, multifidelity modeling, and subset simulation to estimate the failure probabilities of TRISO fuels using several 1D and 2D models. With multifidelity modeling, we replaced expensive high-fidelity (HF) model evaluations with information fusion from two low-fidelity (LF) models. For the 1D TRISO models, we considered three multifidelity modeling strategies: only Kriging, Kriging LF prediction plus Kriging correction, and deep neural network (DNN) LF prediction plus Kriging correction. While the results across these multifidelity modeling strategies compared satisfactorily, strategies employing information fusion from two LF models consistently called the HF model least often. Next, for the 2D TRISO model, we considered two multifidelity modeling strategies: DNN LF prediction plus Kriging correction (data-driven) and 1D TRISO LF prediction plus Kriging correction (physics-based). The physics-based strategy, as expected, consistently required the fewest calls to the HF model. However, the data-driven strategy had a lower overall simulation time since the DNN predictions are instantaneous, and the 1D TRISO model requires a non-negligible simulation time.

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Section: Subset Simulationmentioning

confidence: 99%

“…This estimator does not consider correlation between Markov chains and therefore underestimates the COV. A revised estimator that accounts for these correlations has been derived in Shields et al [40].…”

Section: Subset Simulationmentioning

confidence: 99%

Reliability Estimation of an Advanced Nuclear Fuel using Coupled Active Learning, Multifidelity Modeling, and Subset Simulation

Dhulipala¹,

Shields²,

Chakroborty³

et al. 2022

Preprint

Self Cite

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“…Monte Carlo [43], and an affine invariant sampler [44] were used to improve the robustness of the the subset simulation framework for highly nonlinear limit state functions and/or high-dimensional inputs. There has also been interest in using machine learning models such as neural networks [45] and support vector regression [46] for replacing expensive HF model evaluations to compute the function F (X X X).…”

Section: Monte Carlo Variance Reduction With Subset Simulationmentioning

confidence: 99%

Active Learning with Multifidelity Modeling for Efficient Rare Event Simulation

Dhulipala¹,

Shields²,

Spencer³

et al. 2021

Preprint

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While multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model.We demonstrate our framework using several academic case studies and two finite element (FE) model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

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“…These include algorithms based on repeated generations of the candidate state until the first acceptance criterion is satisfied [32], the related delayed rejection method [33,34,31], methods that translate gradually samples from the prior to samples from the posterior distribution through a combination of importance sampling and MCMC [35] and methods to adaptively update the proposal density in each conditional level [36]. Recently, [29] Shields et al proposed to use the affine invariant ensemble sampler with stretch moves [37], to perform SuS for problems where distributions or conditional distributions are strongly non-Gaussian, highly dependent, and/or degenerate. This is the method employed herein.…”

Section: Subset Simulationmentioning

confidence: 99%

“…We also note that SuS is employed herein using the affine invariant ensemble sampler as described in [29]. All of the tools necessary for implementation of the proposed method, including multi-model inference and SuS are available in the open-source UQpy Python toolbox [30].…”

Section: Introductionmentioning

confidence: 99%

Imprecise Subset Simulation

Giovanis¹,

Shields²

2021

Preprint

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The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the widely used Subset simulation (SuS) with Bayesian/information theoretic multi-model inference. The process starts with data used to infer probability distributions for the model inputs. Often such data sets are small. Multi-model inference is used to assess uncertainty associated with the model-form and parameters of these random variables in the form of model probabilities and the associated joint parameter probability densities. A sampling procedure is used to construct a set of equally probable candidate probability distributions and an optimal importance sampling distribution is determined analytically from this set. Subset simulation is then performed using this optimal sampling density and the resulting conditional probabilities are re-weighted using importance sampling. The result of this process are empirical probability distributions of failure probabilities that provide direct estimates of the uncertainty in failure probability estimates that result from inference on small data sets. The method is demonstrated to be both computationally efficient -requiring only a single subset simulation and nominal cost of sample re-weighting -and to provide reasonable estimates of the uncertainty in failure probabilities.

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Subset simulation for problems with strongly non-Gaussian, highly anisotropic, and degenerate distributions

Cited by 19 publications

References 27 publications

Reliability Estimation of an Advanced Nuclear Fuel using Coupled Active Learning, Multifidelity Modeling, and Subset Simulation

Reliability Estimation of an Advanced Nuclear Fuel using Coupled Active Learning, Multifidelity Modeling, and Subset Simulation

Active Learning with Multifidelity Modeling for Efficient Rare Event Simulation

Imprecise Subset Simulation

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