使用随机子空间法解决受力加速度响应的模态参数识别问题

当外力为高斯白色噪声激励,并且已知线性动态系统的初始条件时,加速度动态响应的随机递减函数和自由衰减振动响应不相等,这是因为在白噪声激励下此随机递减函数中存在一个奇异点;而直接使用有外力嵌入的受力加速度响应会对参数识别精度产生影响。针对随机子空间方法应用于加速度数据的数学基础加以论证,并证明用加速度响应来进行模态参数识别时,将会出现一个识别偏差问题;该偏差问题是因为其加速度相关函数,还受到外力之相关函数的影响。对原始随机子空间方法进行改进,采用无加权模式对Toeplize矩阵进行奇异值分解。透过一个三自由度动态系统的加速度响应进行模态参数识别。结果表明,该方法不仅能有效地消除外力的影响,更能提高其识别精度。

Using stochastic subspace identification to solve a modal parameter identification problem from force-embedded acceleration responses

This study deals with a problem when identifying modal parameters of a linear dynamic system resulting from forced acceleration response. The problem is attributed to an input force imposed on its impulse acceleration response. Without knowledge of the input force, use of the acceleration response can pose a problem on the identification accuracy of the modal parameters. The paper is aimed at proposing a stochastic subspace identification method to solve the problem of the force-embedded acceleration data. The performance of the proposed method applied to the acceleration response was demonstrated via simulation of a 3DOF linear dynamic system excited by white Gaussian noises. Results show that the use of the method can well identify the modal parameters of the dynamic system from the acceleration responses.