基于统计分析技术的有限元模型修正研究

采用统计学的方差分析和回归分析技术研究模型修正的有关问题,主要包括基于方差分析的参数筛选、基于回归分析的响应面拟合和利用响应面进行模型修正三个方面。目前工程上采用的基于灵敏度分析的参数挑选方法根据参数在某设计点处的灵敏度进行挑选,而基于方差分析的参数筛选是从全局的角度,在整个设计空间上挑选对特征量有显著影响的设计参数。基于响应面的修正方法,首先在参数的整个设计空间范围内利用回归分析技术,以显式的响应面模型逼近特征量与设计参数间复杂的隐式函数关系,然后在其基础上进行迭代修正。提出的方法不但可以应用于线性、低频等现有的模型修正方法适用的范围,而且易于推广到非线性、冲击等现有修正方法较少涉及的领域。此外,现有的方法由于每次迭代都需要调用有限元分析软件进行计算,在缺少软件接口的情况下,较难实现工程应用。这种方法只在准备样本数据时需要进行有限元分析,修正过程中无需调用,因而利于工程应用。GARTEUR飞机模型有限元模型的修正结果验证了方法的有效性

Finite Element Model Updating Using Statistics Analysis

A new finite element model updation method using statistics analysis is presented. Major issues discussed are:parameter selection using variance analysis, response surface fitting using regression analysis and model updating based on response surface. The parameter screening method using variance analysis selects the design variables considering the global inforamation while the traditional method considers local sensitivity which only gives the information at one design point. Response surface is a closeform multinomial which gives the relationship between concerned features and selected design variables. It is an approximation to FEM and is used as a substitution in the updating iterations. The presented statisticalbased updating method can be applied without the restriction of linear assumption. In addition, there is no data exchange between the updating program and the finite element analysis program in the updating iteraton. This makes the method beneficial to be applied in engineering .GARTEUR aircraft test structure is employed to verify the effectiveness of the method.