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

Yin, Shengwen; Jin, Keliang; Bai, Yu; Zhou, Wei; Wang, Zhonggang

doi:10.3390/math11051214

Open AccessArticle

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

by

Shengwen Yin

,

Keliang Jin

,

Yu Bai

,

Wei Zhou

^* and

Zhonggang Wang

Key Laboratory of Traffic Safety on Track, Ministry of Education, School of Traffic & Transportation Engineering, Central South University, Changsha 410075, China

^*

Author to whom correspondence should be addressed.

Mathematics 2023, 11(5), 1214; https://doi.org/10.3390/math11051214

Submission received: 13 January 2023 / Revised: 15 February 2023 / Accepted: 24 February 2023 / Published: 1 March 2023

(This article belongs to the Special Issue Uncertainty Analysis, Decision Making and Optimization)

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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.

Keywords: solution space reduction; Dempster–Shafer evidence theory; monotonicity analysis; air spring; epistemic uncertainty; uncertainty quantification

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MDPI and ACS Style

Yin, S.; Jin, K.; Bai, Y.; Zhou, W.; Wang, Z. Solution-Space-Reduction-Based Evidence Theory Method for Stiffness Evaluation of Air Springs with Epistemic Uncertainty. Mathematics 2023, 11, 1214. https://doi.org/10.3390/math11051214

AMA Style

Yin S, Jin K, Bai Y, Zhou W, Wang Z. Solution-Space-Reduction-Based Evidence Theory Method for Stiffness Evaluation of Air Springs with Epistemic Uncertainty. Mathematics. 2023; 11(5):1214. https://doi.org/10.3390/math11051214

Chicago/Turabian Style

Yin, Shengwen, Keliang Jin, Yu Bai, Wei Zhou, and Zhonggang Wang. 2023. "Solution-Space-Reduction-Based Evidence Theory Method for Stiffness Evaluation of Air Springs with Epistemic Uncertainty" Mathematics 11, no. 5: 1214. https://doi.org/10.3390/math11051214

APA Style

Yin, S., Jin, K., Bai, Y., Zhou, W., & Wang, Z. (2023). Solution-Space-Reduction-Based Evidence Theory Method for Stiffness Evaluation of Air Springs with Epistemic Uncertainty. Mathematics, 11(5), 1214. https://doi.org/10.3390/math11051214

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

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