基于模态参数灵敏度的模型修正方法研究

Research on Methods of Finite Element Model Updating Based on Modal Parameter Sensitivity

首先介绍了以模态参数作为修正对象的两种最常用的设计参数型模型修正方法,一是通过构建修正对象的残差型目标函数来建立优化模型,并优化得到修正参数的稳定解,二是利用修正对象的一阶泰勒展开式建立灵敏度矩阵方程,通过解方程得到修正参数的修正量。然后阐述了这两种有代表性的设计参数型模型修正方法的建模技术,给出了求解模型的数学方法,同时归纳了其模型修正过程的一般步骤,并指出了模态参数的灵敏度矩阵的计算是这两种模型修正方法的重要联系,最后提供了模态参数灵敏度的基本算法,这为工程应用提供了良好的理论保障。

Two methods for structural model updating regarding modal parameters as updating object are introduced.One method results in constrained optimization problem by using modal residuals as objective function,which is solved using optimization technique.The other method has been formulated as sensitivity matrix equation in terms of Taylor’s series expansion.Updating value of updating parameters are obtained by solving the sensitivity matrix equation.The modeling techniques which are performed by the two kinds of representative methods for finite element model updating are clarified,including the algorithms for solving those mathematical models.Of these methods,the important relation is pointed out,that is they all require the calculation of sensitivity matrix.Consequently,it provides a good benefit for engineering application by summing up the general steps of model modification process and giving basic algorithm of modal parameter sensitivity.