物理坐标系下状态空间模型的盲辨识
Blind Identification of State-Space Models in Physical Coordinates
摘要：
盲辨识在结构健康监测和音频信号处理等研究领域中广泛用于在没有输入信息的情况下对系统进行建模。现有的盲辨识方法各有优缺点，本文在简要介绍现有方法的基础上，提出了一种新的物理坐标系下状态空间模型的盲辨识方法。该方法首先将采集到的状态空间模型的输入数据看作周期信号序列的一部分，然后通过用输入模型扩充状态空间模型，将有输入和输出的状态空间模型变换为无输入的模型（其是周期性信号模型），并且之后仅使用输出信息来识别状态空间模型直到相似性变换，最后通过使用唯一的相似变换导出物理坐标中的状态空间模型。利用上述思想，可以得到状态空间系统的物理参数和模态参数。数值算例和实际算例验证了所提方法的有效性。实验结果表明了该方法的有效性。
英文摘要：
Blind identification is popular for modeling a system without the input information, such as in the research areas of structural health monitoring and audio signal processing. Existing blind identification methods have both advantages and disadvantages, in this paper, we briefly outline current methods and propose a novel blind identification method for identifying state-space models in physical coordinates. The idea behind this proposed method is first to regard the collected input data of a state-space model as a part of a periodic signal sequence, and then transform the state-space model with input and output into a model without input by augmenting the state-space model with the input model (which is a periodic signal model), and afterwards use merely the output information to identify a state-space model up to a similarity transformation, and finally derive the state-space model in physical coordinates by using a unique similarity transformation. With the above idea, physical parameters and modal parameters of a state-space system can be obtained. Both numerical and practical examples were used to validate the proposed method. The result showed the effectiveness of the novel blind identification method.
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