We tackle the problem of quantifying failure probabilities for expensive deterministic computer experiments with stochastic inputs under a fixed budget. The computational cost of the computer simulation prohibits direct Monte Carlo (MC) and necessitates a surrogate model, which may facilitate either a "surrogate MC" estimator or a surrogate-informed importance sampling estimator. We embrace the former, finding importance sampling too variable when budgets are limited, and propose a novel design strategy to effectively train a surrogate for the purpose of failure probability estimation. Existing works exhaust the entire evaluation budget on active learning through sequential contour location (CL), attempting to balance exploration with exploitation of the failure contour throughout the design, but we find exhaustive CL to be suboptimal. Instead we propose a novel two-stage surrogate design. In Stage 1, we conduct sequential CL to locate the failure contour. In Stage 2, once surrogate learning has saturated, we use a solely exploitative strategy -- allocating the remaining evaluation budget to MC samples with the highest classification entropy to ensure they are classified correctly. We propose a stopping criterion to determine the transition between stages without any tuning. Our two-stage design outperforms alternatives, including exhaustive CL and surrogate-informed importance sampling, on a variety of benchmark exercises. With these tools, we are able to effectively estimate small failure probabilities with only hundreds of simulator evaluations, showcasing functionality with both shallow and deep Gaussian process surrogates, and deploying our method on a simulation of fluid flow around an airfoil.
Johns Hopkins University（约翰斯·霍普金斯大学）；Idaho National Laboratory（爱达荷国家实验室）
Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process more feasible, but merging information from multiple low-fidelity and high-fidelity models poses several challenges. This paper presents a robust multi-fidelity surrogate modeling strategy in which the multi-fidelity surrogate is assembled using an active learning strategy using an on-the-fly model adequacy assessment set within a subset simulation framework …
In reliability analysis, methods used to estimate failure probability are often limited by the costs associated with model evaluations. Many of these methods, such as multifidelity importance sampling (MFIS), rely upon a computationally efficient, surrogate model like a Gaussian process (GP) to quickly generate predictions. The quality of the GP fit, particularly in the vicinity of the failure region(s), is instrumental in supplying accurately predicted failures for such strategies. We introduce an entropy-based GP adaptive design that, when paired with MFIS, provides more accurate failure pro…
University of Amsterdam（阿姆斯特丹大学）；ITMO University（圣光机大学）
In-Stent Restenosis is a recurrence of coronary artery narrowing due to vascular injury caused by balloon dilation and stent placement. It may lead to the relapse of angina symptoms or to an acute coronary syndrome. An uncertainty quantification of a model for In-Stent Restenosis with four uncertain parameters (endothelium regeneration time, the threshold strain for smooth muscle cells bond breaking, blood flow velocity and the percentage of fenestration in the internal elastic lamina) is presented. Two quantities of interest were studied, namely the average cross-sectional area and the maximu…
A two-stage procedure for simultaneously detecting multiple thresholds and achieving model selection in the segmented accelerate failure time (AFT) model is developed in this paper. In the first stage, we formulate the threshold problem as a group model selection problem so that a concave 2-norm group selection method can be applied. In the second stage, the thresholds are finalized via a refining method. We establish the strong consistency of the threshold estimates and regression coefficient estimates under some mild technical conditions. The proposed procedure performs satisfactorily in our…
Blinded sample size review for McNemar's test based on primary and surrogate endpoints
Institute of Medical Biostatistics, Epidemiology and Informatics (IMBEI), University Medical Center Mainz（美因茨大学医学中心医学生物统计学、流行病学和信息中心）；University of Bremen, Competence Center for Clinical Trials Bremen（不来梅大学不来梅临床试验能力中心）；Department of Ophthalmology, University Medical Center of the Johannes Gutenberg-University Mainz（约翰内斯·古腾堡美因茨大学医学中心眼科）
Surrogate-assisted optimal sampling for risk prediction under measurement constraints
University of Seoul（首尔大学）；Department of Statistics and Data Science, University of Seoul（首尔大学统计与数据科学系）；Department of Statistics, University of Seoul（首尔大学统计系）
Failure probability estimation problem is an crucial task in engineering. In this work we consider this problem in the situation that the underlying computer models are extremely expensive, which often arises in the practice, and in this setting, reducing the calls of computer model is of essential importance. We formulate the problem of estimating the failure probability with expensive computer models as an sequential experimental design for the limit state (i.e., the failure boundary) and propose a series of efficient adaptive design criteria to solve the design of experiment (DOE). In parti…
Complex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. Multi-stage models provide a simple but very general mathematical framework for studying the failure of complex systems, or equivalently, the onset of disease. They include the Armitage Doll multi-stage cancer model as a particular case, and have potential to provide new insights into how failures and disease, arise and progress. A method described by E.T. Jaynes is developed to provi…
University College London（伦敦大学学院）；Aalto University（阿尔托大学）；Getulio Vargas Foundation（热图利奥·瓦加斯基金会）；University of Manchester（曼彻斯特大学）；University of Helsinki（赫尔辛基大学）
Embarrassingly parallel Markov Chain Monte Carlo (MCMC) exploits parallel computing to scale Bayesian inference to large datasets by using a two-step approach. First, MCMC is run in parallel on (sub)posteriors defined on data partitions. Then, a server combines local results. While efficient, this framework is very sensitive to the quality of subposterior sampling. Common sampling problems such as missing modes or misrepresentation of low-density regions are amplified -- instead of being corrected -- in the combination phase, leading to catastrophic failures. In this work, we propose a novel c…
ETH Zurich（苏黎世联邦理工学院）；Technical University Munich（慕尼黑工业大学）
Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the development of active-learning reliability methods. These methods approximate the limit-state function (LSF) using surrogate models trained with a sequentially enriched set of model evaluations. A recently proposed method called stochastic spectral embedding (SSE) aims to improve the local approximation accuracy of global, spectral surrogate modelling techniques…
Several methods have been proposed in the literature to solve reliability-based optimization problems, where failure probabilities are design constraints. However, few methods address the problem of life-cycle cost or risk optimization, where failure probabilities are part of the objective function. Moreover, few papers in the literature address time-variant reliability problems in life-cycle cost or risk optimization formulations; in particular, because most often computationally expensive Monte Carlo simulation is required. This paper proposes a numerical framework for solving general risk o…
