Long Junbo, Wang Haibin, Zha Daifeng, Li Peng, Xie Huicheng, Mao Lili
College of Electronic and Engineering Jiujiang University, Jiujiang, China.
College of Information Science and Engineering Technology Jiujiang University, Jiujiang, China.
PLoS One. 2017 Apr 13;12(4):e0175202. doi: 10.1371/journal.pone.0175202. eCollection 2017.
Stockwell transform(ST) time-frequency representation(ST-TFR) is a time frequency analysis method which combines short time Fourier transform with wavelet transform, and ST time frequency filtering(ST-TFF) method which takes advantage of time-frequency localized spectra can separate the signals from Gaussian noise. The ST-TFR and ST-TFF methods are used to analyze the fault signals, which is reasonable and effective in general Gaussian noise cases. However, it is proved that the mechanical bearing fault signal belongs to Alpha(α) stable distribution process(1 < α < 2) in this paper, even the noise also is α stable distribution in some special cases. The performance of ST-TFR method will degrade under α stable distribution noise environment, following the ST-TFF method fail. Hence, a new fractional lower order ST time frequency representation(FLOST-TFR) method employing fractional lower order moment and ST and inverse FLOST(IFLOST) are proposed in this paper. A new FLOST time frequency filtering(FLOST-TFF) algorithm based on FLOST-TFR method and IFLOST is also proposed, whose simplified method is presented in this paper. The discrete implementation of FLOST-TFF algorithm is deduced, and relevant steps are summarized. Simulation results demonstrate that FLOST-TFR algorithm is obviously better than the existing ST-TFR algorithm under α stable distribution noise, which can work better under Gaussian noise environment, and is robust. The FLOST-TFF method can effectively filter out α stable distribution noise, and restore the original signal. The performance of FLOST-TFF algorithm is better than the ST-TFF method, employing which mixed MSEs are smaller when α and generalized signal noise ratio(GSNR) change. Finally, the FLOST-TFR and FLOST-TFF methods are applied to analyze the outer race fault signal and extract their fault features under α stable distribution noise, where excellent performances can be shown.
斯托克韦尔变换（ST）时频表示（ST-TFR）是一种将短时傅里叶变换与小波变换相结合的时频分析方法，而利用时频局部化频谱的ST时频滤波（ST-TFF）方法能够从高斯噪声中分离信号。ST-TFR和ST-TFF方法被用于分析故障信号，在一般高斯噪声情况下是合理且有效的。然而，本文证明机械轴承故障信号属于α稳定分布过程（1 < α < 2），甚至在某些特殊情况下噪声也是α稳定分布。在α稳定分布噪声环境下，ST-TFR方法的性能会下降，随之ST-TFF方法失效。因此，本文提出了一种采用分数低阶矩和ST的新的分数低阶ST时频表示（FLOST-TFR）方法以及逆FLOST（IFLOST）。还提出了一种基于FLOST-TFR方法和IFLOST的新的FLOST时频滤波（FLOST-TFF）算法，并给出了其简化方法。推导了FLOST-TFF算法的离散实现，并总结了相关步骤。仿真结果表明，在α稳定分布噪声下，FLOST-TFR算法明显优于现有的ST-TFR算法，在高斯噪声环境下也能更好地工作，且具有鲁棒性。FLOST-TFF方法能够有效滤除α稳定分布噪声并恢复原始信号。FLOST-TFF算法的性能优于ST-TFF方法，在α和广义信噪比（GSNR）变化时使用该算法混合均方误差更小。最后，将FLOST-TFR和FLOST-TFF方法应用于分析外圈故障信号并在α稳定分布噪声下提取其故障特征，能展现出优异的性能。
