College of Mechanical Engineering, Donghua University, Shanghai 201620, China.
Sensors (Basel). 2019 Nov 18;19(22):5032. doi: 10.3390/s19225032.
To suppress noise in signals, a denoising method called AIC-SVD is proposed on the basis of the singular value decomposition (SVD) and the Akaike information criterion (AIC). First, the Hankel matrix is chosen as the trajectory matrix of the signals, and its optimal number of rows and columns is selected according to the maximum energy of the singular values. On the basis of the improved AIC, the valid order of the optimal matrix is determined for the vibration signals mixed with Gaussian white noise and colored noise. Subsequently, the denoised signals are reconstructed by inverse operation of SVD and the averaging method. To verify the effectiveness of AIC-SVD, it is compared with wavelet threshold denoising (WTD) and empirical mode decomposition with Savitzky-Golay filter (EMD-SG). Furthermore, a comprehensive indicator of denoising (CID) is introduced to describe the denoising performance. The results show that the denoising effect of AIC-SVD is significantly better than those of WTD and EMD-SG. On applying AIC-SVD to the micro-vibration signals of reaction wheels, the weak harmonic parameters can be successfully extracted during pre-processing. The proposed method is self-adaptable and robust while avoiding the occurrence of over-denoising.
为了抑制信号中的噪声，提出了一种基于奇异值分解（SVD）和 Akaike 信息准则（AIC）的去噪方法 AIC-SVD。首先，选择 Hankel 矩阵作为信号的轨迹矩阵，并根据奇异值的最大能量选择其最佳行数和列数。在改进的 AIC 的基础上，确定了最优矩阵的有效阶数，用于混合高斯白噪声和有色噪声的振动信号。然后，通过 SVD 的逆运算和平均法对去噪后的信号进行重构。为了验证 AIC-SVD 的有效性，将其与小波阈值去噪（WTD）和带 Savitzky-Golay 滤波器的经验模态分解（EMD-SG）进行了比较。此外，还引入了一个综合去噪指标（CID）来描述去噪性能。结果表明，AIC-SVD 的去噪效果明显优于 WTD 和 EMD-SG。将 AIC-SVD 应用于反作用轮的微振动信号，在预处理过程中可以成功提取微弱的谐波参数。该方法具有自适应和鲁棒性，同时避免了过度去噪的发生。
