信号共振稀疏分解方法是最近由Ivan W. Selesnick提出的一种新的非线性信号分解方法。该方法首先根据待分析信号选择合适的品质因子，通过品质因子可调小波获得相应的基函数库，然后利用形态学分量分析方法建立信号稀疏表示的目标函数，最后通过优化求解，将一个复杂信号分解成由振荡成份组成的高共振分量和由冲击成份组成的低共振分量及随机噪声。当机械设备发生故障时，其振动信号通常由瞬态冲击信号、谐振信号及噪声构成。本项目拟将信号共振稀疏分解思想引入机械故障诊断，研究用信号共振稀疏分解方法从各类机械故障信号中有效分离出冲击信号与谐振信号，在此基础上建立完整、系统的基于信号共振稀疏分解的机械故障诊断方法。由于信号冲击成份包含了设备与冲击相关的故障信息，而谐振信号则反映了设备的运行工况和与冲击无关的故障信息，因此，本项目研究成果能有效用于机械故障振动信号的特征提取与分析，提高机械故障诊断的准确性。

Resonance-based sparse signal decomposition method is a novel nonliner signal decompositon mehtod recently proposed by Ivan W.Selesnick. In this method, the suitable Q-factor is selected according to the analyzed signal,the base function dictionary is acquired by wavelet transform with tunable Q-factor, and the target function is built by morphological component analysis；then, the optimal result is got by the split augmented Lagrangian shrinkage algorithm. By using of the resonance-based sparse signal decomposition method,a complex signal can be decomposed into high resonance component with oscillating component and low resonance component with impluse component. When a damage occurs in a mechanical system, its vibration signal is always composed of transient impluse signal,oscllating signal and noise. This project intends to introduce the resonance-based sparse signal decomposition method into mechanical fault diagnosis, and use it to separate the impluse signal and oscillating signal from mechanical fault vibration signals.This project will build complete and systematic mechanical fault diagnosis mehods based on resnonace-based sparse signal decomposition. Since the impluse component contains the fault information of a equipment related to impluse, and the oscillating component can reflect the working condition of a equipment and contains the fault infromation non-related to impluse, therefore, the reserch results in this project can be used to extract fault characteristics and enhance the accuracy of mechanical fault diagnosis effectively.