Uncertainty Quantification & Separation in Engineering Models

Effective engineering system management roots in reliable predictions of the system’s behaviour. This behaviour can be modelled with computational tools. Often, such modelling approaches contain uncertainties about calibration parameters, model fit, boundary conditions etc. These uncertainties have to be accounted for to produce reliable predictions of system behaviour. This becomes all the more important if the quantity of interest is the reliability of such a system since rare events (failure) are particularly sensitive to such uncertainties. Given the various sources of uncertainties and the often vague information based on which these are quantified, it is often not sufficient to express reliability by means of a single number (THE probability of failure). Instead, the influence of the single uncertainties on system failure should be represented separately, which requires computationally efficient reliability computations. This project aims at an integral methodology for the adaptive estimation of conditional reliability and conditional reliability sensitivities under unsteady information. Moreover, the assimilation of data within the analysis serves to reduce parameter uncertainty and is performed by a recently introduced method for Bayesian updating with structural reliability methods. The developed methods are combined with dimension reduction and surrogate modelling techniques to attain a high level of computational efficiency at a reasonable accuracy trade-off.

Researchers

Funding

DFG SPP 1886

Collaboration

Willcox Research Group at the Oden Institute for Computational Engineering and Sciences, UT Austin

Institute for Geometric and Pracitical Mathematics, RWTH Aachen

Chair of Structural Analysis, TUM

Institute for Computational Mechanics, TUM

Publications

Max Ehre, Iason Papaioannou, Karen E. Willcox, Daniel Straub (2021), Conditional reliability analysis in high dimensions based on controlled mixture importance sampling, Computer Methods in Applied Mechanics and Engineering 381, 113826, https://doi.org/10.1016/j.cma.2021.113826
Felix Schneider, Iason Papaioannou, Max Ehre, Daniel Straub (2020), Polynomial chaos based rational approximation in linear structural dynamics with parameter uncertainties, Computers & Structures 233, 106223, https://doi.org/10.1016/j.compstruc.2020.106223.
Max Ehre, Iason Papaioannou, Daniel Straub (2020), Global sensitivity analysis in high dimensions with PLS-PCE, Reliability Engineering & System Safety 198, 106861, https://doi.org/10.1016/j.ress.2020.106861.
Max Ehre, Iason Papaioannou, Daniel Straub (2020), A framework for global reliability sensitivity analysis in the presence of multi-uncertainty, Reliability Engineering & System Safety 195, 106726, https://doi.org/10.1016/j.ress.2019.106726.
Iason Papaioannou, Marco Daub, Martin Drieschner, Fabian Duddeck, Max Ehre, Lukas Eichner, Martin Eigel, Marco Götz, Wolfgang Graf, Lars Grasedyck, Robert Gruhlke, Dietmar Hömberg, Michael Kaliske, Dieter Moser, Yuri Petryna, Daniel Straub (2019), Assessment and design of an engineering structure with polymorphic uncertainty quantification, Surveys for Applied Mathematics and Mechanics - GAMM Mitteilungen, 42, e201900009, https://doi.org/10.1002/gamm.201900009.
Dmytro Pivovarov, Kai Willner, Paul Steinmann, Stephan Brumme, Michael Müller, Tarin Srisupattarawanit, Georg‐Peter Ostermeyer, Carla Henning, Tim Ricken, Steffen Kastian, Stefanie Reese, Dieter Moser, Lars Grasedyck, Jonas Biehler, Martin Pfaller, Wolfgang Wall, Thomas Kohlsche, Otto von Estorff, Robert Gruhlke, Martin Eigel, Max Ehre, Iason Papaioannou, Daniel Straub, Sigrid Leyendecker (2019), Challenges of order reduction techniques for problems involving polymorphic uncertainty, Surveys for Applied Mathematics and Mechanics - GAMM Mitteilungen, 42, e201900011, https://doi.org/10.1002/gamm.201900011.
Iason Papaioannou, Max Ehre, Daniel Straub (2019), PLS-based adaptation for efficient PCE representation in high dimensions, Journal of Computational Physics 387, 186-204, https://doi.org/10.1016/j.jcp.2019.02.046.
Sebastian Geyer, Iason Papaioannou, Daniel Straub (2019). Cross entropy-based importance sampling using Gaussian densities revisited. Structural Safety, 76, 15-27
Max Ehre, Iason Papaioannou, Daniel Straub (2018). Efficient estimation of variance-based reliability sensitivities in the presence of multi-uncertainty. Proc. 19th working conference of the IFIP Working Group 7.5 on Reliability and Optimization of Structural Systems (IFIP 2018). Zürich, Switzerland.
Iason Papaioannou, Max Ehre, Daniel Straub (2018). Efficient PCE representation for reliability analysis in high dimensions. Proc. 19th working conference of the IFIP Working Group 7.5 on Reliability and Optimization of Structural Systems (IFIP 2018). Zürich, Switzerland.
Max Ehre, Iason Papaioannou, Daniel Straub (2018). Efficient Conditional Reliability Updating with Sequential Importance Sampling. Proceedings in Applied Mathematics and Mechanics. 89th GAMM Annual Meeting. Munich, Germany.
Sebastian Geyer, Iason Papaioannou, Daniel Straub (2017). On the efficiency of cross entropy-based importance sampling with Gaussian densities. 15th International Probabilistic Workshop & 10th Dresdner Probabilistik Workshop. Dresden, Germany