基于复数微分算子的最优化分解方法及其应用
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摘要
针对机械故障振动信号的非线性与非平稳特征,提出一种基于复数微分算子的最优化分解(Optimization Decomposition Based on Complex Differential Operators,CDOOD)方法。该方法通过优化滤波器的参数将非线性信号分解,以得到的非线性信号分解余量能量最小为优化目标,在优化过程中运用复数微分算子约束得到多个内禀窄带分量(Intrinsic Narrow-Band Components,简称INBC)。将CDOOD方法应用于仿真信号和机械复合故障信号分析,并与自适应最稀疏时频分析(Adaptive Sparsest Time Frequency Analysis,简称ASTFA)方法和经验模态分解(Empirical Mode Decomposition,简称EMD)方法进行对比。结果表明,CDOOD能够有效抑制端点效应和模态混淆,并且在提高分量准确性和正交性等方面具有一定优势,同时可以有效应用于旋转机械复合故障的诊断。
For the nonlinear and non-stationary characteristics of mechanical fault vibration signals, an Optimal Decomposition based on Complex Differential Operators(CDOOD) is proposed. In this method, the original non-linear signal is decomposed into several intrinsic narrow-band components(INBCs) through optimizing the filter parameters with the minimum energy of the decomposition margin as the optimization objective. These INBCs are constrained by the complex differential operator in the optimization process. Then, the CDOOD method is applied to the analysis of simulation signals and the composite mechanical signals. This method is compared with the Adaptive Sparsest Time Frequency Analysis(ASTFA) and Empirical Mode Decomposition(EMD). The results show that the CDOOD method is superior to the other two methods in restraining end effects and mode mixing, and improving the orthogonality and accuracy of the components,and can be effectively applied to the diagnosis of composite failure of rotating machinery.
For the nonlinear and non-stationary characteristics of mechanical fault vibration signals, an Optimal Decomposition based on Complex Differential Operators(CDOOD) is proposed. In this method, the original non-linear signal is decomposed into several intrinsic narrow-band components(INBCs) through optimizing the filter parameters with the minimum energy of the decomposition margin as the optimization objective. These INBCs are constrained by the complex differential operator in the optimization process. Then, the CDOOD method is applied to the analysis of simulation signals and the composite mechanical signals. This method is compared with the Adaptive Sparsest Time Frequency Analysis(ASTFA) and Empirical Mode Decomposition(EMD). The results show that the CDOOD method is superior to the other two methods in restraining end effects and mode mixing, and improving the orthogonality and accuracy of the components,and can be effectively applied to the diagnosis of composite failure of rotating machinery.
引文
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[2]陈世平,王振忠,俞辉,等.改进小波包多阈值去噪法及其工程应用[J].中国机械工程,2017,28(20):2414-2419.
[3]HUANG N E,SHEN Z,LONG S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[C].Proc Royal Society London A,1998(454):903-995.
[4]LEI Y,LIN J,HE Z,et al.A review on empirical mode decomposition in fault diagnosis of rotating machinery[J].Mechanical Systems&Signal Processing,2013,35(1-2):108-126.
[5]王斐,房立清,吕岩.局部特征尺度分解和局部切空间排列在故障特征频率提取中的应用[J].中国机械工程,2017,28(5):565-569.
[6]赵海洋,韩辉,王金东,等.改进局部均值分解方法及其在往复压缩机轴承故障诊断中的应用[J].噪声与振动控制,2016,36(4):135-139.
[7]吴占涛,程军圣,杨宇.自适应特征尺度分解方法及其应用[J].中国机械工程,2015,26(23).
[8]HOU THOMAS Y,SHI ZUO QIANG.Adaptive data analysis via sparse time-frequency representation[J].Advances in Adaptive Data Analysis,2011,3(1-2):1-28.
[9]FREI MARK G.Intrinsic time-scale decomposition:timefrequency-energy analysis and real-time filtering of nonstationary signals[C].Proceedings Mathematical Physical&Engineering Sciences,2007,463(2078):321-342.
[10]PENG S,HWANG W L.Adaptive signal decomposition based on local narrow band signals[J].IEEETransactions on Signal Processing,2008,56(7):2669-2676,12.
[11]GUO B,PENG S,HU X,et al.Complex-valued differential operator-based method for multi-component signal separation[J].Signal Processing,2016,132:66-76,10.
[12]赵荣珍,赵孝礼,何敬举,等.相关流形距离在转子故障数据集分类中的应用方法[J].振动与冲击,2017,36(18):125-130.