中文摘要：

故障齿轮箱的振动信号通常耦合着稳态调制和冲击调制成分。信号稀疏表示的成功应用表明了它对特征提取的有效性，但主要集中在冲击成分的提取，而忽略了稳态调制成分，且设计的字典没有明确的物理意义，通用性较差。提出一种新的基于匹配追踪的齿轮箱耦合调制信号分离方法。设计的基于幅值调制谐波原子的稳态调制字典和基于单自由度冲击响应原子的冲击调制字典，融合了齿轮箱运行工况参数和结构特征，物理意义明确，通用性广。仿真和试验验证了该方法在强噪声背景下和混合调制成分完全耦合情况下的有效性。通过幅值系数恢复，可有效改进匹配追踪算法的过匹配问题。

英文摘要：

Vibration of faulty gearbox usually consists of smooth modulation and impulse modulation components. The successful application of signal sparse representation has demonstrated its effectiveness of feature extraction. However, it mainly concentrates in the impulse components but ignores the smooth modulation components, and the designed dictionary is lack of clear physical meaning, which brings poor universality. A novel method based on matching pursuit is proposed for coupling modulation signal separation of gearbox vibration. The designed smooth modulation dictionary based on the amplitude modulation atom fuses the operation and structure characteristics of gearbox, as well as the designed pulse modulation dictionary based on the impulse response function of single-degree-freedom system. So the dictionaries have clear physical meaning and wide universality. Simulation and experiment test validates the effectiveness of the proposed method, even if under the condition of strong noise and fully coupled modulation signals. The approach of amplitude recovery can significantly reduce the influence of over-matching.