DUHAMEL, Université Grenoble Alpes, INRIA, IFPEN
Abstract: Nowadays, many model (e.g. a calculation code) inversion issues are present in the industry. These problems are defined by finding all sets of parameters such that a certain quantity of interest remains in a certain area, for example below a threshold. In the field of floating wind for instance, a pre-calibration step consists in estimating model parameters that fit with a given accuracy the measured data (e.g. accelerations).
An effective way to solve this problem is to use Gaussian process meta-modeling (Kriging) with a sequential experiment design and an inversion-adapted enrichment criterion, such as the famous Bichon (also known as Expected Feasibility Function) and deviation number (denoted U) criteria. It is also possible to use a more elaborate class of criteria: the SUR (Stepwise Uncertainty Reduction) criteria, which in addition to taking into account the evaluation points and the available model evaluations, quantify the uncertainty reduction which can be achieved by the addition of the new point.
We propose here a SUR version of the Bichon criterion, with both theoretical aspects (explicit formulation of the criterion) and numerical aspects (implementation issues and comparisons with other criteria on classical test functions).
The part on theoretical aspects therefore presents the proposed SUR strategy, defined from a measure of uncertainty related to the Bichon criterion (integral of the Bichon criterion on the design space), as well as an explicit formulation of the SUR Bichon criterion allowing an efficient implementation. The part on numerical aspects presents the first results concerning the performance associated with this new criterion, compared to other classic criteria, and on common test functions.
The future prospects for this work are adapting this criterion to more complex data like functional uncertain input variables. In this particular framework, the design of experiment will have to be adapted.