双树复小波时频构造在齿轮系装配间隙检测的应用

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To optimize the time-frequency localizability of discrete wavelet transform in extracting nonstationary and periodic fault signatures of mechanical equipment, a time-frequency domain constructing scheme of dual tree complex wavelet transform （DTCWT） is investigated. Frequency responses with imposed phase shift condition and reduced energy leakage are designed for the prototype filters of scaling functions in the frequency domain. Subsequently, in the time domain the orthogonality and the energy leakage of the constructed DTCWT are further addressed. The regularity of the constructed DTCWT can be guaranteed even at zero vanishing moment. The reduced energy leakage effect of the constructing method is validated via numerical simulations. The constructed DTCWT is utilized to analyze the vibration signal of the gear train of a heavy-duty lathe and to successfully extract the weak periodic modulation signatures induced by the assembly clearance of the sliding gears. The extracting performance is superior to Daubechies orthonormal wavelet and DTCWT constructed purely in the time domain.为优化离散小波变换在机械设备非平稳周期性故障特征提取的时频局部化能力，研究了一种时频域的双树复小波构造方法。通过调整复尺度函数滤波器的频率响应函数，获得初始滤波器的冲击响应向量，然后从时域上利用迭代优化算法增强构造结果的正交性，来进一步抑制能量泄漏，从而可在零消失矩下保证构造结果的正则性。数值仿真表明，时频域构造方法具有低能量泄漏的特性，在重型车床主轴箱齿轮系的振动信号应用中，可有效地提取由滑移齿轮装配间隙引起的微弱周期性调制特征，提取效果明显优于经典Daubechies规范正交小波，以及纯粹时域构造的双树复小波。