A Reduced Order Model Approach for Fuzzy Field Analysis

Abstract

Due to imprecision, scarcity, and spatial variation in input data, the response of systems with governing parameters that possess spatial dependencies is hard to characterize accurately. Under such a scenario, fuzzy fields become an efficient tool for solving problems that exhibit uncertainty with a spatial component. Nevertheless, the propagation of the uncertainty associated with input parameters characterized as fuzzy fields towards the output response of a model can be quite demanding from a numerical viewpoint. Therefore, this contribution proposes an efficient numerical strategy for forward uncertainty quantification under the presence of fuzzy fields. In order to decrease numerical costs associated with uncertainty propagation, full system analyses are replaced by a reduced order model. This reduced order model projects the equilibrium equations to a small-dimensional space, which is constructed using a single analysis of the system plus a sensitivity analysis. The associated basis is enriched to ensure the quality of the approximate response and numerical cost reduction. A case study of seepage analysis shows that with the presented strategy, it is possible to accurately estimate the fuzzy total flow, with reduced numerical efforts.