薄壁结构吸能预测的多元非线性回归分析

Multiple Nonlinear Regression Analysis for Energy Absorbing Prediction of Thin-walled Structure

为了研究试验参数对薄壁金属结构吸能特性的影响规律,预测和分析这一类型的薄壁结构吸能特性,针对轴向冲击载荷作用下薄壁结构动态响应的非线性特性,以数值模拟为基础,建立了结构吸能特性参数与试验参数之间的多元二次非线性回归模型,编制了Gauss-Newton迭代算法程序对该非线性回归模型参数进行求解.以方形薄壁结构为例,得到了比吸能E_s,有效撞击力AE和有效撞击行程SE分别与试验参数之间的非线性拟合数学方程,最后使用该二次非线性回归模型对这一类型的方形薄壁结构在轴向冲击载荷作用下的吸能特性进行预测.结果表明:方形薄壁结构各项吸能特性参数的回归值与试验值的相对误差控制在±6.0%以内,比吸能E_s、有效撞击力AE和有效撞击行程SE的相对预测误差平均值分别为0.683%、4.604%和3.392%,说明该模型预测精度比较理想.

In order to discuss the influence rule of experimental parameters on energy-absorbing characteristic of thin-walled structure,predict and analyze energy-absorbing characteristic of the same type like thin-walled structure.Based on numerical simulation,the multiple quadratic nonlinear regression model between energy-absorbing characteristic parameters and experimental parameters was established,what＇s more,a Gauss-Newton iterative algorithm program was worked out to solve the parameters of the nonlinear regression model.Take the square thin-walled structure for example,the nonlinear fitting equations between energy-absorbing characteristic parameters like pecific energy absorption Es,effective impact force AE,effective impact journey SE and experimental parameters were obtained.Then,the energy-absorbing characteristics of thin-walled structure of the same type were predicted by the model.The results showed that the relative error of various energy-absorbing characteristic parameters between the regression value and the experimental value within±6.0%,the means of relative prediction errors of pecific energy absorption Es,effective impact force AE and effective impact journey SE were 0.683%、4.604%and 3.392%,which indicated that the prediction accuracy was relatively high.