An Efficient Interval Uncertainty Optimization Approach Based on Quasi-sparse Response Surface

TL;DR

This paper introduces a novel, efficient method for structure uncertainty optimization using Quasi-sparse response surface, significantly reducing computational effort by minimizing sampling points and eliminating the inner optimization loop.

Contribution

The paper proposes a QSRS-based approach that selects key basis functions with penalty methods and employs orthogonal Chebyshev polynomials to evaluate local uncertainty, streamlining the optimization process.

Findings

Requires only 25% of sampling points compared to recent methods

Eliminates the inner optimization process

Validated on mathematical and engineering problems

Abstract

The structure uncertainty optimization problem is usually treated as double-loop optimization process, which is computation-intensive. In this paper, an efficient interval uncertainty optimization approach based on Quasi-sparse response surface (QSRS) is proposed for structure uncertainty optimization. In which, 1) with l_1 norm and l_2 norm penalty method, a few appropriate basis functions are selected form a large number of basis functions to construct QSRS accurately and only a few sampling points is required, 2) as the orthogonal chebyshev polynomials is employed as QSRS basis functions, the local uncertainty can be evaluated by the combination of QSRS and interval arithmetic. Hence, the inner optimization process is eliminated. One mathematical problem and one engineering problem are used to validate the efficiency of the proposed approach. The results show that only 25% sampling points is needed than recently published approach.