Dealing with Uncertainty with Confidence

This presentation was held at the 2020 NAFEMS UK Conference "Inspiring Innovation through Engineering Simulation". The conference covered topics ranging from traditional FEA and CFD, to new and emerging areas including artificial intelligence, machine learning and EDA.

Resource Abstract

In modern engineering systems uncertainty quantification must be performed to assure an adequate level of safety and reliability. Sources of uncertainty can be the inherent variability of physical quantities or events, adoption of approximate models, missing or insufficient data, and lack of knowledge. Especially for cases affected by a lack of data, where imprecise information or expert judgement is utilised, and there is a poor understanding of all the relevant underlying process, strong initial assumptions may be needed to use classical probabilistic methods. However, these assumptions can deeply influence the final results and lead to severe risk misjudgement.

Assessing the effect of uncertainty and accounting for individual contribution on the quantity of interest requires not only the adoption of efficient simulation methods but also the capability to provide some level of confidence to the analysis.

The first problem is addressed with the use of advanced Monte Carlo methods aim at estimating rare failure probabilities more efficiently than direct Monte Carlo. The latter is provided by adopting imprecise probability and representing the uncertainties using interval or probabilistic boxes. However, the proper propagation of such representation of uncertainty further increases the computational cost of the analysis.

To solve this problem, we present methods to robustly propagate probability boxes through expensive black box models, with a reliability assessment of the propagation of the epistemic uncertainty. We obtain a distribution free probability box for the output of the model, or alternatively an interval for the failure probability.

Our algorithms are sampling based, and so can be easily parallelised, and make no assumptions about the functional form of the model. In the first of two proposed algorithms we describe an approach to construct a metamodel for the probability box of the system response directly.

Our proposed methods are flexible and efficient and they are implemented into a open source general purpose software for uncertainty quantification named OpenCossan.