有理Hermite插值的LMD方法在复合故障诊断中的应用研究
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摘要
针对复合故障信号的多分量耦合调制特征及局部均值分解方法存在的包络误差现象,提出了一种基于有理分段三次Hermite插值的LMD方法,该方法通过计算"最优参数区间"确定每个小区间的最优参数,选择"最优参数区间"中的任意参数调整插值样条的形状,使插值样条无限逼近于被插值目标,提高了包络曲线的拟合精度和准确度。采用仿真数据对比的形式,验证了有理Hermite插值LMD方法的逼近能力和高拟合精度。将该方法应用到齿轮和滚动轴承复合故障信号的诊断中,再次证明了该方法的高拟合精度,实现了对复合故障信号的准确诊断。
In view of the multi-component coupling modulation characteristics of complex fault signals and the envelope error phenomenon of the local average decomposition method,an LMD method based on rational sub-interval Hermite interpolation is proposed. Through calculating the optimal parameter interval,the optimal parameter between the cells and the parameter in the optimal parameter interval is selected to adjust the shape of the interpolation spline so that the interpolation spline is infinitely close to the target to be interpolated,thereby improving the fitting precision and accuracy of the envelope curve. The comparison of simulation data is used to verify the approximation ability and high fitting accuracy of the rational Hermite interpolation LMD method. The method is applied to the diagnosis of compound fault signals of gear and rolling bearing,and the high fitting accuracy of the method is proved again. The accurate diagnosis of compound fault signal is realized.
In view of the multi-component coupling modulation characteristics of complex fault signals and the envelope error phenomenon of the local average decomposition method,an LMD method based on rational sub-interval Hermite interpolation is proposed. Through calculating the optimal parameter interval,the optimal parameter between the cells and the parameter in the optimal parameter interval is selected to adjust the shape of the interpolation spline so that the interpolation spline is infinitely close to the target to be interpolated,thereby improving the fitting precision and accuracy of the envelope curve. The comparison of simulation data is used to verify the approximation ability and high fitting accuracy of the rational Hermite interpolation LMD method. The method is applied to the diagnosis of compound fault signals of gear and rolling bearing,and the high fitting accuracy of the method is proved again. The accurate diagnosis of compound fault signal is realized.
引文
[1]李蓉.齿轮箱复合故障诊断方法研究[D].长沙:湖南大学,2013:1-13.
[2]LEVECQUE N,MAHFOUD J,VIOLETTE D.Vibration reduction of a single cylinder reciprocating compressor based on multistagbalancing[J].Mechanism and Machine Theory,2011,46:1-9.
[3]唐贵基,庞彬.基于ITD和切片双谱的滚动轴承局部损伤故障诊断[J].轴承,2014(8):43-47.
[4]WANG Hongchao,CHEN Jin,DONG Guangming.Feature extraction of rolling bearing’s early weak fault based on EEMD and tunable Qfactor wavelet transform[J].Mechanical Systems and Signal Processing,2014,48(1/2):103-119.
[5]LIN M J,JENG Y.Application of the VLF-EM method with EEMD to the study of a mud volcano in southern Taiwan[J].Geomorphology,2010,119(1/2)97-110.
[6]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.
[7]罗毅,甄立敬.基于小波包与倒频谱分析的风电机组齿轮箱齿轮裂纹诊断方法[J].振动与冲击,2015,34(3):210-214.
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[9]何田,林意洲,郜普刚,等.局部均值分解在齿轮故障诊断中的应用研究[J].振动与冲击,2011,30(6):196-201.
[10]胡猛.基于局部均值分解的滚动轴承故障诊断方法研究[D].秦皇岛:燕山大学,2016:10-18.
[11]赵海洋,徐敏强,王金东.有理Hermite插值局部均值分解方法及其往复压缩机故障诊断应用[J].机械工程学报,2015,51(1):83-89.
[12]马文瑞,许璐.一种双参数的有理三次Hermite样条的逼近性及其应用[J].合肥学院学报(自然科学版),2013,23(1):20-24.
[13]谢进,檀结庆,李声锋.有理三次Hermite插值样条及其逼近性质[J].工程数学学报,2011,28(3):385-392.
[14]DUAN Q,DJIDJELI K,PRICE W G,et al.Rational cubic spline based on function values[J].Computer and Graphics,1998,22(4):479-486.
[15]DUAN Q,DJIDJELI K,PRICE W G,et al.Theapproximation properties of some rational cubic splines[J].International Journal of Computer Mathematics,1999,72(2):155-166.
[16]SARFRAZ M.Cubic spline curves with shape control[J].Computer and Graphics,1994,18(5):707-713.
[17]DUAN Q,LIU A K,CHENG F H.Constrained interpolation using rational cubic spline with linear denominators[J].Korean Journal of Computational and Applied Mathematics,1999,6(1):203-215.
[2]LEVECQUE N,MAHFOUD J,VIOLETTE D.Vibration reduction of a single cylinder reciprocating compressor based on multistagbalancing[J].Mechanism and Machine Theory,2011,46:1-9.
[3]唐贵基,庞彬.基于ITD和切片双谱的滚动轴承局部损伤故障诊断[J].轴承,2014(8):43-47.
[4]WANG Hongchao,CHEN Jin,DONG Guangming.Feature extraction of rolling bearing’s early weak fault based on EEMD and tunable Qfactor wavelet transform[J].Mechanical Systems and Signal Processing,2014,48(1/2):103-119.
[5]LIN M J,JENG Y.Application of the VLF-EM method with EEMD to the study of a mud volcano in southern Taiwan[J].Geomorphology,2010,119(1/2)97-110.
[6]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.
[7]罗毅,甄立敬.基于小波包与倒频谱分析的风电机组齿轮箱齿轮裂纹诊断方法[J].振动与冲击,2015,34(3):210-214.
[8]唐贵基,王晓龙.基于局部均值分解和切片双谱的滚动轴承故障诊断研究[J].振动与冲击,2013,32(24):83-88.
[9]何田,林意洲,郜普刚,等.局部均值分解在齿轮故障诊断中的应用研究[J].振动与冲击,2011,30(6):196-201.
[10]胡猛.基于局部均值分解的滚动轴承故障诊断方法研究[D].秦皇岛:燕山大学,2016:10-18.
[11]赵海洋,徐敏强,王金东.有理Hermite插值局部均值分解方法及其往复压缩机故障诊断应用[J].机械工程学报,2015,51(1):83-89.
[12]马文瑞,许璐.一种双参数的有理三次Hermite样条的逼近性及其应用[J].合肥学院学报(自然科学版),2013,23(1):20-24.
[13]谢进,檀结庆,李声锋.有理三次Hermite插值样条及其逼近性质[J].工程数学学报,2011,28(3):385-392.
[14]DUAN Q,DJIDJELI K,PRICE W G,et al.Rational cubic spline based on function values[J].Computer and Graphics,1998,22(4):479-486.
[15]DUAN Q,DJIDJELI K,PRICE W G,et al.Theapproximation properties of some rational cubic splines[J].International Journal of Computer Mathematics,1999,72(2):155-166.
[16]SARFRAZ M.Cubic spline curves with shape control[J].Computer and Graphics,1994,18(5):707-713.
[17]DUAN Q,LIU A K,CHENG F H.Constrained interpolation using rational cubic spline with linear denominators[J].Korean Journal of Computational and Applied Mathematics,1999,6(1):203-215.