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

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.

arXiv commentl_1 norm and l_2 norm penalty, Uncertainty optimization, Quasi-sparse response surface, Interval uncertainty

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