一种利用等效模型与遗传算法的动态有限元模型修正方法(英文)

Dynamic finite element model updating using meta-model and genetic algorithm

为了解决现有动态有限元模型修正方法计算效率不高或者可能获得局部最优解的问题,提出了一种利用等效模型和遗传算法的动态有限元模型修正新方法.首先,在设计参数的取值范围内,根据预设的多项式模型的阶次以及自变量的个数,利用试验设计方法获得拟合响应面模型所需要的最优样本点;通过有限元分析获得样本数据,并利用回归分析获得响应面模型,从而以响应面模型逼近结构特征与设计参数之间的函数关系.然后,在遗传算法的适应度评估环节,利用响应面模型替代有限元模型计算对应于一组设计参数的结构特征,并计算遗传个体的适应度,最终通过进化获得最优解,即为修正后的设计参数.以汽车车架模型为例,对其进行有限元分析与模态试验,并利用所提出的方法进行模型修正.修正后,模态频率误差的均方值小于2%.用修改后结构的动态特性的测试结果,对修正后有限元模型的预测能力进行检验,模态频率预测误差的均方值小于2%.

Current dynamic finite element model updating methods are not efficient or restricted to the problem of local optima. To circumvent these, a novel updating method which integrates the meta-model and the genetic algorithm is proposed. Experimental design technique is used to determine the best sampling points for the estimation of polynomial coefficients given the order and the number of independent variables. Finite element analyses are performed to generate the sampling data. Regression analysis is then used to estimate the response surface model to approximate the functional relationship between response features and design parameters on the entire design space. In the fitness evaluation of the genetic algorithm, the response surface model is used to substitute the finite element model to output features with given design parameters for the computation of fitness for the individual. Finally, the global optima that corresponds to the updated design parameter is acquired after several generations of evolution. In the application example, finite element analysis and modal testing are performed on a real chassis model. The finite element model is updated using the proposed method. After updating, root-mean-square error of modal frequencies is smaller than 2%. Furthermore, prediction ability of the updated model is validated using the testing results of the modified structure. The root-mean-square error of the prediction errors is smaller than 2%.