利用试验数据的结构动力学数学模型修正统一方法

Analytical Models Updating Based on ParameterCorrection Using Dynamic Test Data

近２０年来提出了一系列利用试验数据的结构动力学数学模型修正方法，用统一的观点来考查和比较各种不同的模型修正方法显得十分重要．本文提出一种统一方法，将数学模型修正表述为推广的最小二乘或贝叶斯系统识别问题，可通过优化方法求解。其中残差定义为由数学模型计算的动态参量和相应测试量、或其组合量之差．选择不同的残差量，如特征值、特征向量、特征方程、正交性条件、系统输入（力）、输出（响应）、频率响应等，可导出各种设计参数型数学模型修正方法．最后对由统一方法导出的各种数学模型修正算法进行了分析、比较和讨论．用统一方法推导的各种方法不仅涵盖了现有的主要设计参数型模型修正方法，而且还演绎出一些新的算法．

A variety of analytical model updating based on design parameter correction using dynamic test data has been developed over the past two decades. It will be important and helpful to view all model updating procedures from a unified perspective in order to compare and contrast the numerical characteristics of the different procedures.A unified approach of analytical model updating is proposed which can be served as a general framework to most design parameter based model updating algorithms documented in the literatures. Analytical model updating can be expressed as Expanded Least Squares or Bayessian Parameter Estimation problem,and solved by optimization procedures. Residual in the objective function is defined as the difference of a dynamic quantity which can be calculated from the analytical model and that measured from dynamic testing. Design parameter based model updating procedures differ from the choices of the dynamic quantities,such as eigenvalues,eigenvectors,eigenequations,orthogonalities,force input,dynamic response,frequency response function,etc.An assessment is also presented to compare the different updating procedures in the unified framework.