To solve the problem that the random distribution of noise in the time-frequency (TF) plane largely affects the readability of TF representations, a novel signal adaptive decomposition algorithm processed in TF domain, which provides adequate information about the time-varying instantaneous frequency, is presented in this paper. The theoretical basis of this algorithm is short-time Fourier transform (STFT). The research into the algorithm comprises two steps: the TF plane denoising takes sparse low-rank matrix estimation as a priority and then achieves signal decomposition based on reassignment vector (RV). A low-rank matrix approximation scheme, which exploits the sparse properties of the TF transformation coefficient and uses non-convex penalty, is put forward to obtain clean STFT. Then, a new approach called RV, which is different from the traditional mode decomposition methods such as Empirical Mode Decomposition (EMD), is used to estimate the characteristic curve corresponding to the TF ridges of the interested modes. Based on the classical reassignment method, RV has a solid theory foundation. Moreover, it can identify different signal components such as stationary signal, modulating signal and impulse characteristic. Combining the advantages of low-rank matrix approximation approach and those of RV defined in TF plane, a novel signal adaptive decomposition method is proposed in this paper to identify fault characteristics. To illustrate the effectiveness of the method, fault signals of rolling bearing under stationary condition and time-varying speed are respectively analyzed.

中文翻译：

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基于重新分配矢量的自适应模式分解新方法及其在滚动轴承故障诊断中的应用

为了解决噪声在时频（TF）平面中的随机分布会严重影响TF表示的可读性的问题，在TF域中处理的一种新型信号自适应分解算法，该算法可提供有关时变瞬时频率的足够信息，本文介绍。该算法的理论基础是短时傅立叶变换（STFT）。该算法的研究包括两个步骤：TF平面去噪以稀疏低秩矩阵估计为优先，然后基于重分配矢量（RV）实现信号分解。提出了一种利用TF变换系数的稀疏性质并采用非凸罚分的低秩矩阵逼近方案，以得到纯净的STFT。然后，一种叫做RV的新方法 与传统的模式分解方法（如经验模式分解（EMD））不同，该方法用于估计与感兴趣模式的TF峰相对应的特征曲线。RV基于经典的重新分配方法，具有坚实的理论基础。而且，它可以识别不同的信号分量，例如固定信号，调制信号和脉冲特性。结合低秩矩阵逼近方法和在TF平面中定义的RV的优点，提出了一种新的信号自适应分解方法来识别故障特征。为了说明该方法的有效性，分别分析了静止状态和时变速度下滚动轴承的故障信号。