Reliability-based design optimization (RBDO) has been widely used to search for the optimal design under the presence of parameter uncertainty in the engineering application. Unlike traditional deterministic optimization, RBDO problem takes the uncertainty of design variables and probabilistic reliability constraints into consideration. In the context of RBDO, a large number of model evaluations are required in the reliability analysis to estimate the failure probability. However, the intensive computation of reliability analysis makes it infeasible to address complex and expensive problems. In order to relieve the computational burden, an efficient polynomial chaos-enhanced radial basis function (PCE-RBF) approach is proposed. In this approach, RBF combined with sparse PC method is constructed to enhance predictive accuracy of metamodel. To refine the metamodel, local variation with minimum distance sampling criterion is proposed to select the sample points sequentially. Then, the refined PCE-RBF metamodel with acceptable accuracy is used to perform gradient-based optimization for solving RBDO problem. The performance of the proposed method is validated by four benchmark examples and truss structure issue.

在工程应用中存在参数不确定性的情况下，基于可靠性的设计优化（RBDO）已广泛用于搜索最佳设计。与传统的确定性优化不同，RBDO问题考虑了设计变量的不确定性和概率可靠性约束。在RBDO的背景下，可靠性分析中需要进行大量模型评估，以估计故障概率。但是，对可靠性分析的密集计算使其无法解决复杂而昂贵的问题。为了减轻计算负担，提出了一种有效的多项式混沌增强径向基函数（PCE-RBF）方法。该方法构造了RBF与稀疏PC相结合的方法，以提高元模型的预测精度。为了完善元模型，提出了采用最小距离采样准则的局部变化来依次选择采样点。然后，使用精炼的具有可接受精度的PCE-RBF元模型进行基于梯度的优化，以解决RBDO问题。通过四个基准实例和桁架结构问题验证了该方法的性能。