非光滑变尺度凸峰频率识别法的优化及应用

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摘要基于非光滑变尺度SD(Smooth and Discontinuous)极限系统的非线性拓扑特性，优化了非光滑变尺度凸峰频率识别法，并将其应用到了轴承早期故障信号检测中。利用类同宿轨的周期性，推导了非光滑随机类次谐Melnikov函数，给出了均方意义下出现简单零点的充分必要条件，揭示了初始相位和噪声耦合因素对变尺度SD极限系统混沌阈值的影响。经数值模拟，发现微弱信号初始相位的存在会导致非光滑变尺度凸峰法识别频率时出现偏差或不可识别。当频率识别出现偏差时，利用数据的几何特性给出一个线性修正公式；当频率不可识别时，构造了检测方程组，使凸峰频率识别法依然有效。通过一个高速列车轮对轴承早期故障实例，运用优化非光滑变尺度凸峰频率识别法，确定了轮对轴承可能发生故障的位置。结果显示优化的非光滑变尺度凸峰频率识别法可更准确识别轮对轴承早期故障信号的频率，方法简单且精度较高。

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	李海萍1
	2
	田瑞兰1
	3
	薛强1
	3
	张杨昆1
	3
	张小龙1
	3

关键词 ： SD极限系统, 非光滑变尺度凸峰频率识别法, 随机类次谐Melnikov方法, 相位

Abstract：Based on the nonlinear topological characteristics of non-smooth variable scale Smooth and Discontinuous(SD) limit system, the non-smooth variable scale crest frequency identification method is optimized and applied to the early fault signal detection of bearing. Using the periodicity of homoclinic-like orbit, the non-smooth random subharmonic-like Melnikov function is derived, which leads to the necessary and sufficient conditions for the occurrence of simple zeros in the mean square sense. The effects of non-smooth and noise coupling factors on the chaotic threshold of non-smooth variable scale SD limit system are revealed. The numerical simulation results show that the initial phase of weak signal leads to the deviation or unrecognizability of non-smooth variable scale-convex-peak method. When there is a deviation in frequency identification, a linear correction formula is given by using the geometric characteristics of the data; When the frequency is unrecognizable, the detection equations are constructed to make the convex peak frequency identification method still effective. Through an example of early fault of wheel set bearing of high-speed train, the possible fault location of wheel set bearing is determined by using the optimized non-smooth variable scale convex peak frequency identification method. The results show that the non-smooth variable scale convex peak frequency identification method can accurately identify the frequency of early fault signal of wheel set bearing, and the method is simple and accurate.

Key words： SD limit systems non-smooth variable scale-convex-peak frequency identification method stochastic subharmonic-like Melnikov method phase

收稿日期: 2021-11-15 出版日期: 2023-03-28

引用本文:

李海萍1,2，田瑞兰1,3，薛强1,3，张杨昆1,3，张小龙1,3. 非光滑变尺度凸峰频率识别法的优化及应用[J]. 振动与冲击, 2023, 42(6): 143-151.
LI Haiping1,2，TIAN Ruilan1,3，XUE Qiang1,3，ZHANG Yangkun1,3，ZHANG Xiaolong1,3. Optimization and application of non-smooth variable scale-convex-peak frequency identification method. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(6): 143-151.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I6/143

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