针对频响函数灵敏度分析法进行模型修正时，由于一阶近似固有的局限性，很难直接迭代得到正确收敛结果的问题，提出了频响函数灵敏度拟合函数进行基于模型修正的结构损伤识别方法。首先,采用模态参与变异系数准则选取激励点位置、频率响应有效独立法结合距离系数-有效独立法选取测点位置;然后，综合考虑频响函数对修正参数变化的灵敏度和频响函数的相关性，选择一个合理的频率点;最后，拟合随参数变化的频响函数灵敏度函数曲线，引入新的中间设计参数，从而建立中间设计参数的频响函数灵敏度方程组，通过求解中间设计参数的改变量来求解修正参数的改变量。三自由度质量—弹簧和二维桁架系统的数值算例验证了所提出方法的可行性;数值算例表明，该方法具有较高的计算效率和识别精度，也对随机噪声具有鲁棒性，同时有效地避免了灵敏度方程组数值平衡导致的收敛问题。
Abstract
Here, to solve the problem of it being difficult to get the correct convergence results through direct iteration due to inherent limitations of the first-order approximation when the FRF sensitivity analysis method was used for model updating, a method of FRF sensitivity fitting function was proposed for structural damage identification model updating.Firstly, excitation points were selected according to the variation coefficient criterion of modal participation, and combining the frequency response effective independence method and the distance coefficient effective independence method, positions of measuring points were chosen.Then, a reasonable frequency point was selected by comprehensively considering sensitivities of FRF to changes of correction parameters and correlation of FRF.Finally, the sensitivity function of FRF with variation of parameters was fitted, and introducing new intermediate design parameters, the sensitivity equation of FRF with intermediate design parameters was established.Changes of correction parameters were solved through solving changes of intermediate design parameters.Numerical examples of a 3-DOF mass-spring system and a 2-D truss system verified the feasibility of the proposed method.Numerical examples showed that the proposed method has higher computational efficiency and identification accuracy; it is robust to random noise; the convergence problem caused by numerical balance of sensitivity equations is effectively avoided.
关键词
频响函数(FRF) /
灵敏度分析 /
拟合函数 /
模型修正 /
损伤识别
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Key words
frequency response function (FRF) /
sensitivity analysis /
fitting function /
model updating /
damage identification
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