非线性偏最小二乘回归法在均匀设计响应面法中的应用

摘要

The response surface method (RSM) with uniform design is widely used for current structural reliability analysis of multi-dimensional variables. However, it has the limitation of fitting the regression models in the original quasi-linear least squares (LS) method. To deal with this limitation, a new approach梩he partial least squares (PLS) method based on the traditional method is proposed for improvement. However, the quasi-linear regression method restricts the form of the model, thus the improvement in accuracy is limited and the result is unstable. So, this paper presents a partial least squares regression model to substitute the quasi-linear model for the calculation of reliability, which not only handles the correlation between the variables but also avoids the pre-assumptions for the form of the regression model. The results of several examples show that the method proposed in this paper can be used effectively to analyze structural reliability, especially in multidimensional and non-linear cases, and higher accuracy can be obtained as shown by comparing the results with those from the least squares regression method.%针对目前多维变量可靠度分析中广泛应用的均匀设计响应面法(RSM),指出了使用最小二乘(LS)法拟合拟线性回归模型时存在的局限性,并提出采用拟线性偏最小二乘(PLS)法来回归响应面系数.由于拟线性回归法限制了模型的形式,精度提高有限,结果也很不稳定,因此又提出用基于样条变换的偏最小二乘回归模型代替拟线性回归模型并用于结构失效概率的计算,既能处理最小二乘法无法解决的变量间多重相关性的问题,又能避开拟线性回归中预先对模型形式的假定.通过算例验证了基于样条变换的偏最小二乘法的适用性和有效性,尤其对于多维变量非线性程度较高的可靠度分析,与普通最小二乘法拟合的响应面相比,其模型更加精确,失效概率精度更高.