In an engineering context, structural design optimization is usually performed virtually, based on numerical models to approximate the sets of partial differential equations that describe the physical behavior of the structure. Also, to account for the notion that our observation of reality is inherently limited, a multitude of efficient and effective numerical and theoretical tools to incorporate uncertainty in these models have been introduced, aimed at enhancing the objectivity of the obtained results. Especially the field of probabilistic methods has gained significant traction over the last few decades. However, valid criticism exists with respect to such approach, as more often than not, only partial or uninformative data are available to estimate the parameters that feed into these numerical models. This is a direct result from either practical or strategical limitations in gathering the necessary data to accurately describe the variability in these parameters, their correlation, or a combination of both [1]. The rather recent field of imprecise probabilities aims at overcoming these limitations of classical UQ methods by allowing for the explicit definition of an additional layer of uncertainty to objectively describe the effects of data insufficiencies.
In this talk, I will focus on the application of imprecise probability theory in the context of representing dependent uncertainties. These dependencies might manifest themselves between several epistemically uncertain scalar quantities, but also as (imprecise) space- or time-correlations. The accurate definition and modelling of such dependencies is highly non-trivial since data with a high spatial and stochastic resolution are required. More specifically, I will discuss some recent developments in the definition and efficient propagation of high-dimensional dependent interval uncertainties [2] and the modelling of cross-dependent interval fields [3]. Furthermore, I will present a new framework for the highly efficient propagation of imprecise stochastic processes [4] that allows for a full separation between aleatory and epistemic uncertainty, breaking the double loop effectively [5,6]. Finally, I will show that this framework can also be used to perform highly efficient reliability-based design optimization [7], even including discrete design variables.
References
1. Faes, M., & Moens, D. (2020). Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty. Archives of Computational Methods in Engineering, 27(3), 633–671.
2. Faes, M., & Moens, D. (2019). Multivariate dependent interval finite element analysis via convex hull pair constructions and the Extended Transformation Method. Computer Methods in Applied Mechanics and Engineering, 347, 85–102.
3. Faes, M., & Moens, D. (2020). On auto‐ and cross‐interdependence in interval field finite element analysis. International Journal for Numerical Methods in Engineering, 121(9), 2033–2050.
4. Faes, M., & Moens, D. (2019). Imprecise random field analysis with parametrized kernel functions. Mechanical Systems and Signal Processing, 134, 106334.
5. Faes, M., Valdebenito, M. A., Moens, D., & Beer, M. (2020). Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities. Preprint Submitted to MSSP.
6. Faes, M., Valdebenito, M. A., Moens, D., & Beer, M. (2020). Bounding the first excursion probability of linear structures subjected to imprecise stochastic loading. Computers & Structures, 239, 106320.
7. Faes, M., & Valdebenito, M. A. (2020). Fully decoupled reliability-based design optimization of structural systems subject to uncertain loads. Computer Methods in Applied Mechanics and Engineering, 371, 113313.
Speaker bio
Matthias Faes (1991) is a post-doctoral fellow of the Research Foundation Flanders (FWO) working at the Department of Mechanical Engineering of KU Leuven. He graduated summa cum laude as Master of Science in Engineering Technology in 2013 and obtained his PhD in Engineering Technology from KU Leuven in 2017. Since then, he is since working on advanced methodologies for non-probabilistic uncertainty quantification, including stochastic fields and interval techniques. He is a Laureate of the 2017 PhD award of the Belgian National Committee for Applied and Theoretical Mechanics, winner of the 2017 ECCOMAS European PhD award for best PhD thesis in 2017 on computational methods in applied sciences and engineering and winner of the 2019 ISIPTA - IJAR Young Researcher Award for outstanding contributions to research on imprecise probabilities. Furthermore, he managed to attract already more than 3.5 million euros in project funding, most notably a Horizon 2020 Marie Curie Innovative Training Network and a Humboldt fellowship to spend a research period of 6 months at the University of Hannover, Germany. He is the author of 50+ peer-reviewed papers in international journals and conference proceedings and has a Google scholar H-index of 12 (520+ citations).
