摘要
针对目前多维变量可靠度问题中广泛应用的均匀设计响应面法,分析了采用最小二乘法拟合样本数据回归模型时存在的局限性,并在已有方法的基础上提出了一种改进的方法。该方法将均匀设计与偏最小二乘回归技术相结合来回归响应面模型,从而计算结构的失效概率,有效的解决了变量间多重相关性及小样本条件下建立回归模型的问题。通过算例验证了该方法的适用性,尤其对于高维变量的可靠度问题,与最小二乘拟合响应面相比,计算结果更加精确。
For the current structural reliability analysis of multidimensional variables, the response surface methods （RSM） with the uniform design are widely used. To deal with the limitation of fitting the models in the utilization of the original Least Squares （LS） regression, a new approach based on the traditional method has been proposed for improvement. The method combines Partial Least Squares （PLS） with a uniform design to fit the response surface under the condition of small samples data with strong correlation in order to calculate structural reliability. The results of several examples shows that the Partial Least Squares method proposed in this paper can be used, especially in the high dimensional problem, to analyze the structural reliability, and higher accuracy can be obtained by comparing it with the original Least Squares technique.
出处
《工程力学》
EI
CSCD
北大核心
2013年第2期272-277,共6页
Engineering Mechanics
基金
国家"十一五"科技支撑计划项目(2006BAK20B00)
关键词
响应面法
均匀设计
偏最小二乘
多重相关性
结构可靠度
response surface method
uniform design
partial least square
correlation
structural reliability
