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Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).

In DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.

The computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.

This paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

Meta-model method has been widely used in structural reliability optimization design. The main limitation of this method is that it is difficult to quantify the error caused by the meta-model approximation, which leads to the inaccuracy of the optimization results of the reliability evaluation. Taking the local high efficiency of the proxy model, this paper aims to propose a local effective constrained response surface method (LEC-RSM) based on a meta-model.

The operating mechanisms of LEC-RSM is to calculate the index of the local relative importance based on numerical theory and capture the most effective area in the entire design space, as well as selecting important analysis domains for sample changes. To improve the efficiency of the algorithm, the constrained efficient set algorithm (ESA) is introduced, in which the sample point validity is identified based on the reliability information obtained in the previous cycle and then the boundary sampling points that violate the constraint conditions are ignored or eliminated.

The computational power of the proposed method is demonstrated by solving two mathematical problems and the actual engineering optimization problem of a car collision. LEC-RSM makes it easier to achieve the optimal performance, less feature evaluation and fewer algorithm iterations.

This paper proposes a new RSM technology based on proxy model to complete the reliability design. The originality of this paper is to increase the sampling points by identifying the local importance of the analysis domain and introduce the constrained ESA to improve the efficiency of the algorithm.