基于逆响应面法的有限元模型修正

基于响应面法（RSM）的有限元模型修正是以若干设计参数（如密度、弹性模量等）为自变量，以若干特征参数（如固有频率、振型等）为因变量，通过回归分析方法来拟合特征参数关于修正参数的显式表达式。提出的逆响应面法（IRSM）则是以特征参数作为自变量，设计参数作为因变量。利用此法的有限元模型修正可直接根据特征参数的目标值得到设计参数的修正量，而不需要经过迭代计算，有效地提高计算速度和精度。介绍逆响应面法及其应用，讨论使用响应面法和逆响应面法进行有限元模型修正的优缺点和适用范围，分析适合于逆响应面法的逆响应面函数、实验设计方案和回归精度检验的方法。利用逆响应面法对一简支梁进行有限元模型修正的结果表明，逆响应面法能高效准确地修正设计参数，对于输出变量少于输入变量的情况更能显著减少有限元计算次数，适用于复杂的工程结构。

An Inverse Response Surface Method for Finite Element Model Updating

The response surface method （RSM） for finite element （FE） model updating is usually used to obtain the explicit relationship between the characteristic parameters （such as natural frequencies and modals） and the design parameters （such as density and Young＇ s modulus） by the regression analysis method. In this method, the design parameters are used as independent variables and the characteristic parameters as dependent variables. This paper proposed an inverse response surface method （IRSM）, which is constructed by using the characteristic parameters as independent variables and the design parameters as dependent variables. Compared with RSM, using IRSM for FE model updating with the characteristic parameters as the target values is able to obtain the updated values directly without iteration, so that the computation can be speeded up with the accuracy improved efficiently. This paper introduced the IRSM and its application, discussed its advantages and disadvantages, and analyzed the function of IRSM, the design of experiment and the evaluation of regression accuracy. A numerical example of a simply supported beam showed that the IRSM can update the FE model efficiently and precisely, and notably reduce the cost of FE calculation in the case that the number of output parameters is less than the number of input parameters. This method is suitable for complex engineering structures.