基于响应面模型的起重机主梁的结构稳健优化设计

Robust Optimization Design of Crane Girder Structure based on the Response Surface Model

针对起重机主梁结构的稳健优化设计,研究了拉丁超立方体试验设计技术、近似模型技术、基于方差的稳健设计模型构建过程和利用灰色绝对关联度求解多目标优化问题的方法,选取决定起重机主梁截面的5个主要尺寸参数为输入变量,以主梁跨中最大应力和垂直静刚度为响应变量,构建二次多项式响应面模型。在响应面模型的基础上,利用方差作为稳健性评价指标,以最大应力与垂直静刚度的方差和截面面积为3个目标,构建起重机主梁的多目标稳健优化设计模型,并利用灰色绝对关联度进行优化求解。优化结果表明:考虑参数不确定性的稳健优化设计在一定程度上可以降低性能指标对设计参数的敏感性,同时基于近似模型的优化设计可以为复杂工程提供很大的方便,为工程实际中的稳健优化设计提供指导。

For robust optimization design of crane girder structure,the paper studied the Latin hypercube experimental design,the approximate model,the building process of robust design model based on variance and the use of grey absolute correlation degree method for solving multi-objective optimization problems.Selecting five main dimension parameters that decide cross section of crane girder to be input variables,and selecting the maximum stress in the girder cross and vertical static stiffness to be response variables when construct quadratic polynomial response surface model.Managing the uncertainty of the parameters by using sensitivity estimation on the basis of the response surface model,building a multi-objective robust design model of the crane girders with the variance of the maximum stress and the variance of the vertical static stiffness and the cross section’s area being three goals,and using the grey absolute correlation degree method.The optimization results show that robust optimal design of considering the uncertainty of the parameter can reduce the sensitivity of the performance index to the design parameters,and optimization design based on the approximate model can provide great convenience for complex engineering,and provide the guidance for the optimizing design of later real engineering.