增强Ramanujan模态分解方法及其在滚动轴承故障诊断中的应用

针对现有的滚动轴承故障诊断方法（例如：小波变换和集合经验模态分解）的周期识别能力并不稳定等问题，我们提出了具有良好的周期分量提取能力的自适应周期模态分解(Adaptive periodic mode decomposition, APMD)方法。然而该方法所采用的最大似然估计方法在强噪声背景下估计周期时常出现错误，这导致APMD在强背景噪声下的周期提取性能并不稳定。为此，我们定义了自适应频率加权能量算子(Adaptive frequency weighted energy operator，AFWEO)，并将其用于增强周期脉冲。然后，提出了一种新的周期估计策略以提高周期估计的准确性，并在此基础上提出了增强Ramanujan模态分解(Enhanced Ramanujan mode decomposition, ERMD)方法。滚动轴承仿真和实验信号分析结果表明，新的周期估计策略在强背景噪声下依然有效，同时也说明了ERMD具有优良的周期成分识别和提取能力，是一种有效的滚动轴承故障诊断方法。

Enhanced Ramanujan Mode Decomposition Method and Its Application to Rolling Bearing Fault Diagnosis

The period recognition ability of the existing rolling bearing fault diagnosis methods (such as wavelet transform and ensemble empirical mode decomposition) is not stable. We propose adaptive periodic mode decomposition (APMD) method with good capability of extracting periodic components. However, the maximum likelihood estimation method used in the APMD often fails to estimate the period under strong noise background, which results in the unstable performance of period extraction under strong noise background. Therefore, we define an adaptive frequency weighted energy operator (AFWEO) and use it to enhance period impulses. Then, we propose a new period estimation strategy to improve the accuracy of the period estimation. On this basis, we propose the enhanced Ramanujan mode decomposition (ERMD) method. Emulational and experimental signal analysis results of rolling bearings show that the new period estimation strategy is still effective under strong background noise, and ERMD is an effective method for rolling bearing fault diagnosis because of its excellent ability of identifying and extracting periodic components.