Stochastic simulation methods for structural reliability under mixed uncertainties

Uncertainty quantification (UQ) has been widely recognized as one of the most important, yet challenging task in both structural engineering and system engineering, and the current researches are mainly on the proper treatment of different types of uncertainties, resulting from either natural randomness or lack of information, in all related sub-problems of UQ such as uncertainty characterization, uncertainty propagation, sensitivity analysis, model updating, model validation, risk and reliability analysis, etc. It has been widely accepted that those uncertainties can be grouped as either aleatory uncertainty or epistemic uncertainty, depending on whether they are reducible or not. For dealing with the above challenge, many non-traditional uncertainty characterization models have been developed, and those models can be grouped as either imprecise probability models (e.g., probability-box model, evidence theory, second-order probability model and fuzzy probability model) or non-probabilistic models (e.g., interval/convex model and fuzzy set theory). This thesis concerns the efficient numerical propagation of the three kinds of uncertainty characterization models, and for simplicity, the precise probability model, the distribution probability-box model, and the interval model are taken as examples. The target is to develop efficient numerical algorithms for learning the functional behavior of the probabilistic responses (e.g., response moments and failure probability) with respect to the epistemic parameters of model inputs, which is especially useful for making reliable decisions even when the available information on model inputs is imperfect. To achieve the above target, my thesis presents three main developments for improving the Non-intrusive Imprecise Stochastic Simulation (NISS), which is a general methodology framework for propagating the imprecise probability models with only one stochastic simulation. The first development is on generalizing the NISS methods to the problems with inputs including both imprecise probability models and non-probability models. The algorithm is established by combining Bayes rule and kernel density estimation. The sensitivity indices of the epistemic parameters are produced as by-products. The NASA Langley UQ challenge is then successfully solved by using the generalized NISS method. The second development is to inject the classical line sampling to the NISS framework so as to substantially improve the efficiency of the algorithm for rare failure event analysis, and two strategies, based on different interpretations of line sampling, are developed. The first strategy is based on the hyperplane approximations, while the second-strategy is derived based on the one-dimensional integrals. Both strategies can be regarded as post-processing of the classical line sampling, while the results show that their resultant NISS estimators have different performance. The third development aims at further substantially improving the efficiency and suitability to highly nonlinear problems of line sampling, for complex structures and systems where one deterministic simulation may take hours. For doing this, the active learning strategy based on Gaussian process regression is embedded into the line sampling procedure for accurately estimating the interaction point for each sample line, with only a small number of deterministic simulations. The above three developments have largely improved the suitability and efficiency of the NISS methods, especially for real-world engineering applications. The efficiency and effectiveness of those developments are clearly interpreted with toy examples and sufficiently demonstrated by real-world test examples in system engineering, civil engineering, and mechanical engineering

Forward uncertainty quantification with special emphasis on a Bayesian active learning perspective

Uncertainty quantification (UQ) in its broadest sense aims at quantitatively studying all sources of uncertainty arising from both computational and real-world applications. Although many subtopics appear in the UQ field, there are typically two major types of UQ problems: forward and inverse uncertainty propagation. The present study focuses on the former, which involves assessing the effects of the input uncertainty in various forms on the output response of a computational model. In total, this thesis reports nine main developments in the context of forward uncertainty propagation, with special emphasis on a Bayesian active learning perspective. The first development is concerned with estimating the extreme value distribution and small first-passage probabilities of uncertain nonlinear structures under stochastic seismic excitations, where a moment-generating function-based mixture distribution approach (MGF-MD) is proposed. As the second development, a triple-engine parallel Bayesian global optimization (T-PBGO) method is presented for interval uncertainty propagation. The third contribution develops a parallel Bayesian quadrature optimization (PBQO) method for estimating the response expectation function, its variable importance and bounds when a computational model is subject to hybrid uncertainties in the form of random variables, parametric probability boxes (p-boxes) and interval models. In the fourth research, of interest is the failure probability function when the inputs of a performance function are characterized by parametric p-boxes. To do so, an active learning augmented probabilistic integration (ALAPI) method is proposed based on offering a partially Bayesian active learning perspective on failure probability estimation, as well as the use of high-dimensional model representation (HDMR) technique. Note that in this work we derive an upper-bound of the posterior variance of the failure probability, which bounds our epistemic uncertainty about the failure probability due to a kind of numerical uncertainty, i.e., discretization error. The fifth contribution further strengthens the previously developed active learning probabilistic integration (ALPI) method in two ways, i.e., enabling the use of parallel computing and enhancing the capability of assessing small failure probabilities. The resulting method is called parallel adaptive Bayesian quadrature (PABQ). The sixth research presents a principled Bayesian failure probability inference (BFPI) framework, where the posterior variance of the failure probability is derived (not in closed form). Besides, we also develop a parallel adaptive-Bayesian failure probability learning (PA-BFPI) method upon the BFPI framework. For the seventh development, we propose a partially Bayesian active learning line sampling (PBAL-LS) method for assessing extremely small failure probabilities, where a partially Bayesian active learning insight is offered for the classical LS method and an upper-bound for the posterior variance of the failure probability is deduced. Following the PBAL-LS method, the eighth contribution finally obtains the expression of the posterior variance of the failure probability in the LS framework, and a Bayesian active learning line sampling (BALLS) method is put forward. The ninth contribution provides another Bayesian active learning alternative, Bayesian active learning line sampling with log-normal process (BAL-LS-LP), to the traditional LS. In this method, the log-normal process prior, instead of a Gaussian process prior, is assumed for the beta function so as to account for the non-negativity constraint. Besides, the approximation error resulting from the root-finding procedure is also taken into consideration. In conclusion, this thesis presents a set of novel computational methods for forward UQ, especially from a Bayesian active learning perspective. The developed methods are expected to enrich our toolbox for forward UQ analysis, and the insights gained can stimulate further studies

Uncertainty management in multidisciplinary design of critical safety systems

Managing the uncertainty in multidisciplinary design of safety-critical systems requires not only the availability of a single approach or methodology to deal with uncertainty but a set of different strategies and scalable computational tools (that is, by making use of the computational power of a cluster and grid computing). The availability of multiple tools and approaches for dealing with uncertainties allows cross validation of the results and increases the confidence in the performed analysis. This paper presents a unified theory and an integrated and open general-purpose computational framework to deal with scarce data, and aleatory and epistemic uncertainties. It allows solving of the different tasks necessary to manage the uncertainty, such as uncertainty characterization, sensitivity analysis, uncertainty quantification, and robust design. The proposed computational framework is generally applicable to solve different problems in different fields and be numerically efficient and scalable, allowing for a significant reduction of the computational time required for uncertainty management and robust design. The applicability of the proposed approach is demonstrated by solving a multidisciplinary design of a critical system proposed by NASA Langley Research Center in the multidisciplinary uncertainty quantification challenge problem

E-MCTS: Deep Exploration in Model-Based Reinforcement Learning by Planning with Epistemic Uncertainty

One of the most well-studied and highly performing planning approaches used in Model-Based Reinforcement Learning (MBRL) is Monte-Carlo Tree Search (MCTS). Key challenges of MCTS-based MBRL methods remain dedicated deep exploration and reliability in the face of the unknown, and both challenges can be alleviated through principled epistemic uncertainty estimation in the predictions of MCTS. We present two main contributions: First, we develop methodology to propagate epistemic uncertainty in MCTS, enabling agents to estimate the epistemic uncertainty in their predictions. Second, we utilize the propagated uncertainty for a novel deep exploration algorithm by explicitly planning to explore. We incorporate our approach into variations of MCTS-based MBRL approaches with learned and provided dynamics models, and empirically show deep exploration through successful epistemic uncertainty estimation achieved by our approach. We compare to a non-planning-based deep-exploration baseline, and demonstrate that planning with epistemic MCTS significantly outperforms non-planning based exploration in the investigated deep exploration benchmark.Comment: Submitted to NeurIPS 2023, accepted to EWRL 202