SIPTA Seminar by Michael Beer: Efficient reliability analysis with imprecise probabilities

ABSTRACT: An efficient analysis of our engineered systems and structures is a key requirement for their proper design and operation. This requirement, however, is challenging engineers to come up with innovative solutions that can cope with the increasing complexity of our systems and structures and with the uncertainties involved. Imprecise probabilities have shown useful conceptual features to facilitate a modelling at a reasonable level of detail and capturing the remaining epistemic uncertainty in a set-valued manner. This approach allows for an optimal balance between model detailedness and imprecision of results to still derive useful decisions. However, it is also associated with some extensive numerical cost when applied in a crude way. This seminar will provide selected solutions for efficient numerical analysis with imprecise probabilities, specifically for reliability analysis, to attack high-dimensional and nonlinear problems. After an introductory overview on conceptual pathways for solution one intrusive and three non-intrusive specific developments will be discussed. These solutions include operator norm theory to solve first passage problems by linear algebra, intervening variables to moderate nonlinearities for linearized approximate solutions, the exploitation of topological properties of the reliability problem associated with line sampling, and the utilization of high dimensional model representation of the failure probability for non-intrusive efficient sampling. Engineering examples are presented to demonstrate the capabilities of the approaches and concepts. This talk is part of a series of seminars on imprecise probabilities that are organized by SIPTA, the "Society for Imprecise Probabilities: Theories and Applications". We also organize conferences and schools, provide documentation and maintain a mailing list and blog. More information is available at http://sipta.org. Info on the SIPTA seminars in particular is available at http://sipta.org/events/sipta-seminars Contents 00:00 - Start 01:03 - Introduction 16:39 - Semi-intrusive approaches 31:50 - Non-intrusive optimization approaches 44:25 - Non-intrusive imprecise stochastic simulation (NISS) 54:53 - Resumé