Civil Engineering Departmental Seminar - Efficient robust reliability analysis: decision making under incomplete knowledge 

Efficient robust reliability analysis: decision making under incomplete knowledge 

Numerical tools to approximate the solution of (sets of) differential equations have become indispensable in the design of engineering components from the micro-scale to complete structures. Thanks to these tools, an engineer is now able to design, test and optimize designs long before a first prototype is built. However, despite the highly detailed numerical predictions that can be obtained, the results of these calculations often show a non-negligible discrepancy with the actual physical behavior of the structure. At the core of this discrepancy lies uncertainty in the description of the model physics, as well as the governing parameters.

Uncertainties are for instance commonly encountered in the context of structural dynamics, where for instance the effect natural phenomena such as earthquakes or wind loads on structures has to be considered. Indeed, due to the sheer complexity of the underlying physics, the corresponding dynamical loads that act on the system often cannot be described in a crisp way. Stochastic processes provide a rigorous framework to deal with the uncertainties and space/time correlations of uncertain loads by resorting to the well-documented framework of probability theory. However, in practice, the analyst is often confronted with limited, incomplete or conflicting sources of data (i.e., epistemic uncertainty) due to limitations in time, budget and/or measurement resolution. In this case, there might be simply not enough information to warrant the computational cost of performing extremely detailed reliability analyses with very small failure probabilities. This begs the question: where should we invest our resources – in making our reliability analyses more accurate or in making them more robust?

In this talk, I will present some philosophical, theoretical and very practical numerical calculation schemes that are aimed at contributing to answering this question. The presentation will draw from recent work we performed in the field of reliability sensitivity and imprecise reliability analysis, highlighting recent advances in surrogate modelling (functional dimensionality reduction, Bayesian active learning, polynomial chaos expansions), decoupling schemes (operator norm theory) and efficient sampling schemes (multi-domain line sampling, directional importance sampling).