Solution-Space-Reduction-Based Evidence Theory Method for Stiffness Evaluation of Air Springs with Epistemic Uncertainty

Abstract

In the Dempster–Shafer evidence theory framework, extremum analysis, which should be repeatedly executed for uncertainty quantification (UQ), produces a heavy computational burden, particularly for a high-dimensional uncertain system with multiple joint focal elements. Although the polynomial surrogate can be used to reduce computational expenses, the size of the solution space hampers the efficiency of extremum analysis. To address this, a solution-space-reduction-based evidence theory method (SSR-ETM) is proposed in this paper. The SSR-ETM invests minimal additional time for potentially high-efficiency returns in dealing with epistemic uncertainty. In the SSR-ETM, monotonicity analysis of the polynomial surrogate over the range of evidence variables is first performed. Thereafter, the solution space can be narrowed to a smaller size to accelerate extremum analysis if the surrogate model is at least monotonic in one dimension. Four simple functions and an air spring system with epistemic uncertainty demonstrated the efficacy of the SSR-ETM, indicating an apparent superiority over the conventional method.