基于径向基神经网络的有限元模型修正研究

Finite Element Model Updating Using Radial Basis Function Neural Network

设计参数型有限元模型修正属于结构动力学反问题 ,其理论基础是将结构的特征量视为设计参数的函数 ,然后依据特征量对设计参数的一阶导数信息进行迭代求解。本文提出了一种基于径向基神经网络的有限元模型修正方法 ,把模型修正归结为正问题进行研究。首先将特征量视为自变量 ,设计参数视为因变量 ,以径向基神经网络逼近两者之间的非线性映射关系 ,然后利用神经网络的泛化特性直接求解设计参数的目标值。不但无需迭代求解 ,而且避开了反问题所面临的复杂的非线性优化计算。 GARTEUR飞机模型仿真研究的结果表明 ,修正后设计参数误差在 2 %以内 ,模态频率误差在 1 %以内。

Design parameter based on finite element model updating is part of an inverse problem of structure dynamics. Features of the structure are used as a function of design parameters. Parameters are updated based on the first derivative. This paper presents a new method which treats the model updating as a positive problem. Features and design parameters are regarded as independent variables. The trained radial basis functional neural network is utilized as a map function. The target value of the design parameter can be directly estimated due to the generalization character of the neural network. The method avoids solving the complicated optimization problem which is difficult in the previous methods. Finite element modelling of the GARTEUR aircraft model is updated using the neural network based on updating method. Errors of design parameters by the present method are less than 2% and errors of modal frequencies less than 1%.