Efficient Bayesian multilevel uncertainty quantification for enhanced reliability assessment and decision support

• Applicants: Dr.-Ing. Iason Papaioannou; Professor Dr. Daniel Straub
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 449529210

The management of engineering structures and systems requires adequate predictions of their performance throughout their intended service life. For most applications, effective numerical models for such predictions exist, but the parameters of these models are commonly uncertain or random. This is particularly relevant when the interest is in the reliability of these systems, because rare events are most affected by uncertainty and randomness. As uncertainty arises from different sources, it has been recognized that providing a reliability estimate as a single number might not be sufficient, in particular if the underlying models are based on vague information. In many instances, it can be desirable to separate the influence of different sources of uncertainty on the final prediction. A common example is the separation into aleatory (intrinsically random/irreducible) and epistemic (reducible) uncertainties. Previously, the applicants developed a Bayesian probabilistic framework for the multilevel treatment of different classes of uncertainties in reliability analysis. The framework enables the assessment of the impact of the different inputs on the reliability of the structure or system of interest. It also enables the incorporation of data to reduce uncertainties and update the system reliability in an effective way. Such a multilevel treatment of uncertainties does however lead to computational challenges, as it can require a large number of conditional reliability evaluations. In this project, we develop advanced computational methods that facilitate a more efficient reliability assessment of engineering structures under multi-uncertainty. To achieve this, we combine advanced sequential importance sampling techniques with adaptive proxy (surrogate) models. The methods will be integrated in an already existing approach for Bayesian analysis of rare events to facilitate efficient data assimilation. The framework and developed methods will be extended to other quantities of interest than the system reliability, such as the variance of the system response, which will enable application of multilevel uncertainty quantification (UQ) to the robust design of engineering structures. The ultimate objective is to establish a general multilevel UQ framework that enables effective engineering decision support. To facilitate this, we will also enhance the framework with a formal decision-theoretic approach to interpreting the analysis results.

• DFG Programme: Research Grants