Due to its sensitivity to structural state, the strain mode has more advantages than the displacement mode in online structural health monitoring and damage identification. Since the strain mode and displacement mode are merely the different expressions of the same physical state and they are similar in mathematical expression, the relationship between strain and displacement can be applied to the least square complex frequency-domain method (LSCF) to analyze structural stress and strain. In this study, the frequency domain identification method of structural dynamics parameters is established based on strain measurement data. First of all, a parameterized common denominator model with strain as its variable is established. On this basis, the nonlinear least square problem is linearized and the error of the weighted least square linear equation is obtained. Then, the equation is solved by using the algorithm based on the reduction of regular equations. In this way the amount of computation is reduced and parameter redundancy is avoided by imposing the restriction on the modal parameters. Afterwards, an experimental system of a free beam structure is designed and the structural dynamic strain is measured using Fiber Bragg Grating strain sensors. Finally, the frequency and damping ratio are identified by means of LSCF based on the measured strain data. The acceleration results of the identification agree well with those of the traditional identification method based on the measurement data of acceleration. Besides, the strain mode shapes obtained by this identification method are also consistent with the simulation results. Therefore, numerical simulation and the experiment show that the proposed method based on LSCF can accurately identify the strain modes of structures.%由于应变模态对结构状态的敏感性,其在结构在线健康监测和损伤识别方面比位移模态更具优势.利用应变和位移的关系,将最小二乘复频域方法应用到结构应力应变分析中,建立基于应变测量数据的结构动力学参数频域辨识方法.由于应变模态和位移模态是同一种物理状态的不同表达形式,两者在数学表达上有相似性.首先建立以应变为变量的参数化公分母模型,在此基础上将非线性最小二乘问题进行线性化,得到加权线性最小二乘的方程误差.然后采用基于缩减正则方程的算法进行求解,减少计算量,并通过对模型参数施加约束来避免参数冗余.然后,设计并搭建一个自由梁的实验结构系统,利用光纤布拉格光栅应变传感器测量结构动应变数据,根据最小二乘复频域方法,基于应变测量数据辨识得到频率和阻尼比,与传统的基于加速度测量数据的辨识结果相吻合.另外,辨识所得应变模态振型与仿真结果也具有一致性.因此,数值仿真和实验验证表明,文中提出的基于最小二乘复频域方法能够准确辨识结构应变模态.
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