基于响应面法的结构动力学模型修正

摘要

为了获得精确的结构动力学模型,提出了响应面和优化相结合的方法.利用参数化模型和优化拉丁方试验设计获取样本点构造多项式响应面模型,最小二乘法确定多项式系数并检验响应面的拟合精度.用响应面计算结果与实验结果的误差构造目标函数,自适应模拟退火算法来优化修正响应面参数,将修正后的参数值带入有限元模型得到修正模型.以欧洲航空科技组织的基准模型GARTEUR飞机模型为算例,对比修正前后模态频率,结果表明修正后的模型在测试频段和预测频段具有良好的复现和预测能力,进而验证了基于响应面法与优化方法相结合的结构动力学有限元模型修正的有效性.%In order to obtain an accurate structural dynamics model,a method combining the response surface and optimization was proposed.The sample points were acquired by using parametric models and optimal latin hypercube experimental design to construct the polynomial response surface model.The least squares method was used to determine the polynomial coefficients and then to test the fitting accuracy of response surface.The error between the results of the calculated response surface and the actual test was taken as the objective function.An adaptive simulated annealing algorithm was employed to optimize response surface parameters.The updated model was then obtained by substituting optimized parameters into the non-updated FEM.The GARTEUR benchmark model of the European Aviation Organization was taken as an example.The comparison of modal frequencies of non-updated and updated FEMs proves the reappearance and prediction ability of the updated FEM,and verifies the effectiveness of the model updating methodology suggested in the paper.