基于逐步回归分析的随机响应面法

制约随机响应面法广泛应用的重要原因在于响应面展开式中的待定系数过多,计算效率不高.本文研究建立了改进的随机响应面法.首先,利用Nataf变换将给定边缘累积分布函数的相关随机变量转变为独立标准正态随机变量,进而将结构随机响应量描述为独立标准正态随机变量的混沌多项式展开式;然后,根据线性无关原则选取最优概率配点,并引入逐步回归分析剔除响应面展开项中的次要项,从而大幅减少展开式中的待定系数.算例分析表明,该方法具有较高的计算精度和效率.

Improved stochastic response surface method based on stepwise regression analysis

An improved stochastic response surface method was proposed based on the stepwise regression analysis.The correlated random variables given the marginal cumulative distribution function were transformed into the independent standard normal variables according to the Nataf transformation,while the stochastic response of complex structure was expressed as the polynomial chaos expansion of independent standard normal variables.The optimal probabilistic collocation points were selected based on the linear independent criterion and the insignificant expansion terms were eliminated efficiently by the stepwise regression analysis.The numerical results show that the proposed method can reduce the probabilistic collocation points and unknown coefficients of polynomial expansion significantly on the condition of ensuring calculation accuracy.