A reduced-order model approach for fuzzy fields analysis

Characterization of the response of systems with governing parameters that exhibit both uncertainties and spatial dependencies can become quite challenging. In these cases, the accuracy of conventional probabilistic methods to quantify the uncertainty may be strongly affected by the availability of data. In 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 point of view. Therefore, this paper proposes an efficient numerical strategy for forward uncertainty quantification under fuzzy fields. This strategy is geared towards the analysis of steady-state, linear systems. To reduce the numerical cost associated with uncertainty propagation, full system analyses are replaced by a reduced-order model. This reduced-order model projects the equilibrium equations into a small-dimensional space constructed from a single analysis of the system plus sensitivity analysis. The associated basis is enriched to ensure the quality of the approximate response and numerical cost reduction. Case studies of heat transfer and seepage analysis show that with the presented strategy, it is possible to accurately estimate the fuzzy responses with reduced numerical effort.