非光滑变尺度凸峰频率识别法的优化及应用  

Optimization and application of non-smooth variable scale-convex-peak frequency identification method

作　　者：李海萍 田瑞兰[1,3] 薛强 张杨昆[1,3] 张小龙 LI Haiping;TIAN Ruilan;XUE Qiang;ZHANG Yangkun;ZHANG Xiaolong(Department of Engineering Mechanics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;School of Science,Hebei University of Science and Technology,Shijiazhuang 050018,China;State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学工程力学系,石家庄050043 [2]河北科技大学理学院,石家庄050018 [3]石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄050043

出　　处：《振动与冲击》2023年第6期143-151,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(11872253,12072203,12102274,11602151);河北省“三三三人才工程”基金(A202005007);百名优秀创新人才支持计划基金(SLRC2019037)。

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。Based on the nonlinear topological characteristics of a non-smooth variable scale smooth and discontinuous(SD)limit system,the non-smooth variable scale crest frequency identification method was optimized and applied to the early fault signal detection of bearings.Using the periodicity of homoclinic-like orbit,the non-smooth random subharmonic-like Melnikov function was derived,which led 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 the non-smooth variable scale SD limit system were revealed.The numerical simulation results show that the initial phase of weak signal leads to the deviation or unrecognizability of the non-smooth variable scale-convex-peak method.When there was a deviation in frequency identification,a linear correction formula was given by using the geometric characteristics of the data.When the frequency was unrecognizable,the detection equations were constructed to make the convex peak frequency identification method still effective.Through an example of the early fault of a wheel set bearing of a high-speed train,the possible fault location of the wheel set bearing was 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 the wheel set bearing,and the method is simple and accurate.

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 

分 类 号：TH133.3[机械工程—机械制造及自动化] TH165.3