针对数据驱动时频分析（DDTFA）方法的初始相位函数选取问题，提出一种可准确、快速且自适应优选初始相位函数的改进DDTFA方法。引入数学中函数求极值的思想，将信号的初始相位函数选取问题转换为初始解集的连续寻优问题，通过对DDTFA中的高斯牛顿迭代算法进行精简，以初始解集中的初始相位函数迭代一次斜率的变化量为导数获得初始解集的连续导数集，进而求得局部极大值，并以局部极大值对应信号分量的能量最强为准则优选信号的初始相位函数，进而完成信号分解。仿真分析与齿轮箱故障诊断实例表明，该方法可准确、快速且自适应地优选初始相位函数，并有效提取故障特征，且具有一定抗噪性。
Abstract
Aiming at initial phase function selection of the data-driven time-frequency analysis (DDTFA) method, an improved DDTFA method was proposed to optimize initial phase function accurately, quickly and adaptively.Introducing the idea of solving extreme values of a function in mathematics, a signal’s initial phase function selection problem was converted into a continuous optimization of an initial solution set.Through simplifying Gauss-Newton iterative algorithm in DDTFA, the slope variation of initial phase function in an initial solution set before and after first iteration was taken as the derivative to obtain the continuous derivative set of the initial solution set, and further get local extreme values.Then the energy of signal components corresponding to local extreme values being the maximum was taken as the criterion to optimally choose initial phase function of a signal, and further complete signal decomposition.Simulation analysis and actual examples of gearboxes’ fault diagnosis showed that the proposed method can correctly, rapidly and adaptively optimize initial phase function, and effectively extract fault features; it has a certain anti-noise ability.
关键词
故障诊断 /
数据驱动 /
时频分析 /
齿轮箱 /
初始相位函数
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Key words
fault diagnosis /
data-driven /
time-frequency analysis (DDTFA) method /
gearbox /
initial phase function
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参考文献
[1] KAN M S, TAN A C C, MATHEW J. A review on prognostic techniques for non-stationary and non-linear rotating systems[J]. Mechanical Systems & Signal Processing, 2015, 62-63:1-20.
[2] HUANG N E, SHEN Z, LONG S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proceedings Mathematical Physical & Engineering Sciences, 1998, 454(1971):903-995.
[3] WU Z H, HUANG N E.. Ensemble empirical mode decomposition:A noise-assisted data analysis method [J]. Advances in Adaptive Data Analysis, 2009, 1(01):1-41.
[4] Smith J S. The local mean decomposition and its application to EEG perception data[J]. Journal of the Royal Society Interface, 2005, 2(5):443-454.
[5] 雷亚国, 孔德同, 李乃鹏,等. 自适应总体平均经验模式分解及其在行星齿轮箱故障检测中的应用[J]. 机械工程学报, 2014, 50(3):64-70.
LEI Ya-guo,KONG De-tong,LI Nai-peng,etal.Adaptive Ensemble Emprictical Mode Decomposition and Its Application to Fault Detection of Planetary Gearboxes[J].Journal of Mechanical Engineering, 2014, 50(3):64-70.
[6] Liu W Y, Gao Q W, Ye G, et al. A novel wind turbine bearing fault diagnosis method based on Integral Extension LMD[J]. Measurement, 2015, 74:70-77.
[7] HOU T Y, SHI Z Q. Adaptive Data Analysis via Sparse Time-Frequency Representation.[J]. Advances in Adaptive Data Analysis, 2011, 03(01&02):1-28.
[8] HOU T Y, Shi Z Q. Data-driven time–frequency analysis[J]. Applied & Computational Harmonic Analysis, 2013, 35(2):284-308.
[9] HOU T Y, SHI Z Q, Tavallali P. Convergence of a data-driven time–frequency analysis method[J]. Applied & Computational Harmonic Analysis, 2014, 37(2):235-270.
[10] 李宝庆, 程军圣, 吴占涛,等. 基于GA的自适应最稀疏时频分析方法及应用[J]. 中国机械工程, 2016, 27(1):66-72.
LI Baoqing,CHENG Junsheng,WU Zhantao,etal. Adativeand Sparsest Tme-frequecy Analysis Method Based on Genetic Algorithm and Its Application [J].China Mechanical engineering，2016 27(1): 66-72.
[11] 程军圣, 李宝庆, 彭延峰,等. 基于自适应最稀疏时频分析的阶次方法及应用[J]. 振动工程学报, 2016, 29(3):542-548.
CHENG Jun-sheng,LI Bao-qing,PENG Yanfeng,etal. The order analysis method based on the adaptive and sparsest time-frequecy analysis method and its application[J]. Journal of Vibration Engineering，2016，29(3): 542-548.
[12] 彭延峰, 刘贞涛, 程军圣,等. 基于初值优化的自适应最稀疏时频分析方法[J]. 湖南大学学报(自科版), 2017, 44(8):50-56.
PENG Yan-feng,LIU Zhen-tao,CHENG Jun-sheng,etal. Adaptive and Sparsest Time-frequency Analysis Method Based on Initial Value Optimization[J].Journal of Hunan University(Natural Sciences),2017, 44(8):50-56.
[13] 欧龙辉, 彭晓燕, 杨宇,等. GS-ASTFA方法及其在滚动轴承寿命预测中的应用[J]. 振动与冲击, 2017, 36(11):14-19.
OU Long-hui,PENG Xiao-yan,YANG Yu, etal. GS -ASTFA Method and Its Application in life prediction of rolling bearings[J].Journal of Vibration and Shock, 2017, 36(11):14-19.
[14] 洪加威. 论黄金分割法的最优性[J]. 数学的实践与认识, 1973(2):36-43.
Hong Jia-wei.The optimality of golden section method[J].Mathematics In Practice and Theory，1973，2: 34-41.
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