基于小波分析的分数阶系统辨识信号降噪的变尺度阈值方法

在目前愈来愈被关注的分数阶控制研究中，系统辨识的分数阶理论与方法是一个重要方向，其中，辨识实验检测数据的降噪是必须关注的课题。基于小波分析理论与方法，首先对系统辨识中常用的以伪随机二进制序列(PRBS)激励的分数阶系统输出信号及其干扰噪声的特性进行分析讨论，在此基础上，为克服常规阈值降噪法的局限性，提出了针对多层小波分解系数进行非线性变尺度量化改造的算法，进而形成了一种分数阶系统辨识信号降噪的变尺度阈值方法。仿真实验表明，该方法能够将噪声干扰削减到满意的水平，对于不同的信噪比情形具有很好的适用性。该研究旨在为进一步的辨识算法设计提供参考，以提高辨识精度。

Variable metric threshold algorithm for identification signal denoise of fractional system based on wavelet analysis

The identification theory and method of fractional system is an important research direction which has drawn much research attention recently, and how to reduce the noise about the identification test data is one of the subjects which must be focused on. In this paper, on the basis of wavelet theory and method, the characteristics of noise and output signal of fractional system were analyzed firstly. In order to overcome the limitations of the conventional threshold denoise method, a nonlinear variable metric algorithm for the multi level wavelet decomposition coefficient was proposed, and then a denoising method for identification signal of fractional system was formed. The simulation experiments indicate that this method can reduce the noise to a satisfactory level, and it also has good adaptability for different Signal-to-Noise Ratio (SNR) cases. Our research purpose is to provide a reference for further identification algorithm design and to improve identification precision.