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本文提出了利用卡尔曼滤波技术识别线性定常振动系统参数的方法。首先,将系统动力学方程转化为离散的可观标准型状态方程,为了应用卡尔曼滤波技术,再将一个单输入多输出系统的标准型参数识别问题转化为若干个单输入单输出系统的状态估计问题。接着,介绍了三组实用的滤波公式,以及选取滤波器所需的初始信息的方法。然后列出了由滤波得到的标准型参数求得振动系统复模态参数和固有模态参数所用的转换公式。最后对本文提出的公式进行了讨论,并给出了一个模型的模拟试验结果。
In this paper, a method of identifying parameters of linear steady-state vibration system by using Kalman filter technique is proposed. First, the system dynamics equations are transformed into discrete observable standard state equations. In order to apply Kalman filtering, the standard parameter identification of a single-input multi-output system is transformed into the state estimation of several single-input single-output systems problem. Then, three practical filter formulas are introduced, along with the method of selecting the initial information needed by the filter. Then, the conversion formulas used to obtain the complex modal parameters and the natural modal parameters of the vibration system are obtained by filtering the standard parameters. Finally, the formulas proposed in this paper are discussed, and the simulation results of a model are given.