Structural reliability analysis for stochastic systems

Structural reliability analysis for stochastic systems A Warren Distinguished Lecture with Bruno Sudret Risk, Safety and Uncertainty Quantification ETH Zurich, Switzerland ABSTRACT Stochastic simulators, whose outputs exhibit intrinsic variability even for fixed inputs, are increasingly used to model complex engineering systems, e.g., wind turbines or structures subjected to environmental loading in wind and earthquake engineering. Yet, structural reliability analysis in this setting remains largely underdeveloped, as classical methods fail to account for latent stochasticity and quickly become computationally prohibitive. In this talk, Sudret first revisits the formulation of reliability problems for stochastic simulators, highlighting the fundamental differences with deterministic settings and their implications for failure probability estimation. Sudret then introduces stochastic emulators, with a focus on stochastic polynomial chaos expansions (SPCE) [1], which provide an efficient surrogate framework by explicitly separating parametric uncertainty from intrinsic model stochasticity. Building on this representation, Sudret proposes an active learning strategy tailored to stochastic systems [2,3]. The method leverages ensembles of SPCE models, obtained via likelihood-based sampling of the coefficients, to quantify epistemic uncertainty and identify regions of the input space that are both close to the limit state and sensitive to stochastic variability. This enables a targeted enrichment of the training data and a significant reduction in computational cost. The proposed framework is demonstrated on analytical benchmarks and a realistic, data-driven wind turbine reliability problem, illustrating its potential for scalable reliability analysis of nondeterministic systems. SPEAKER Bruno Sudret has bee a professor of Risk, Safety and Uncertainty Quantification at ETH Zurich since 2012. His teaching and research interests are computational methods for uncertainty quantification, reliability and sensitivity analysis, Bayesian approaches for model calibration and reliability-based design optimization, among others. Sudret received a master’s of science from the Ecole Polytechnique (France) in 1993. He then obtained master’s degree and a PhD degrees in civil engineering from the Ecole Nationale des Ponts et Chaussées (France) in 1996 and 1999, respectively. Sudret has been working in probabilistic engineering mechanics and uncertainty quantification for engineering systems since 2000: first as a post- doctoral fellow at the University of Berkeley (California), then as a researcher at EDF R&D (the French world leader in nuclear power generation) where he was the head of a group specialized in probabilistic engineering mechanics (2001- 2008). From 2008 to 2011 he worked as the Director of Research and Strategy at Phimeca Engineering (France). Sudret is the author and co-author of more than 350 publications in journal and conference proceedings. He currently serves on the editorial board of Reliability Engineering and Systems Safety, Probabilistic Engineering Mechanics and Structural Safety. He promotes the dissemination of uncertainty quantification techniques through the development of the software UQLab (www.uqlab.com) and the community platform UQWorld (https://uqworld.org/). [1] X. Zhu and B. Sudret, Stochastic polynomial chaos expansions to emulate stochastic simulators, International Journal for Uncertainty Quantification, vol. 13, no. 2, pp. 31–52, 2023. [2] A. Pires, M. Moustapha, S. Marelli, and B. Sudret, Reliability analysis for nondeterministic limit-states using stochastic emulators, Structural Safety, vol. 117, no. 102621, pp. 1–14, 2025. [3] A. Pires, M. Moustapha, S. Marelli, and B. Sudret, AL-SPCE – Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning, 2026, https://arxiv.org/abs/2507.04553.