ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Uncertainty and Sensitivity Analysis of Functional Risk Curves Based on Gaussian Processes

12 September 2017, 11:40 – 12:10


Submitted by
Bertrand Iooss
Bertrand Iooss (EDF R&D), Loïc Le Gratiet (EDF R&D)
In industrial practice, the estimation of a functional risk curve (FRC) is often required as a quantitative measure of a system safety. A FRC gives the probability of an undesirable event in function of the value of a critical parameter of a considered physical system. Our purpose considers the qualification issues of non-destructive examination processes, where the FRC corresponds to the probability of flaw detection curves. FRCs are used in many other engineering framework, e.g. in the seismic fragility assessment.

The estimation of the FRC sometimes relies on deterministic phenomenological computer models which simulate complex physical phenomena. Uncertain input parameters of this computer code are modeled as random variables. Standard uncertainty treatment techniques require many model evaluations and a major algorithmic difficulty arises when the computer code under study is too time expensive to be directly used. For cpu-time expensive models, one solution consists in replacing the numerical model by a mathematical approximation, called a response surface or a metamodel. In this communication, the Gaussian process regression is used and applied in the particular context of a FRC as a quantity of interest. We focus on the Gaussian process metamodel in order to build FRCs from numerical experiments, allowing to obtain confidence bands.

Associated to the estimation of the quantity of interest, the sensitivity analysis step is performed to determine those parameters that mostly influence on model response. We propose new global sensitivity indices attached to the whole FRC, while showing how to develop them with a Gaussian process model.

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