板带轧机非线性扭转与垂直振动模型及其特性研究
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摘要
轧机作为现代钢铁工业中的核心设备之一，在钢铁生产中具有举足轻重的地位。轧机在轧制生产过程中产生的振动一直以来是困扰钢铁行业中产品质量提高的技术难题，严重制约着轧制产品质量的提升和生产效率的提高。为了得到有效抑制轧机振动的策略，确保轧机系统运行稳定性，提高轧制产品的质量，轧机振动问题的研究已成为学者关注的重点。
基于广义耗散Lagrange原理，考虑轧机中不同的非线性因素，分别建立了接轴刚度参激变化下的两自由度扭振动力学模型、含间隙多自由度扭振动力学模型、轧件对称滞后变形下辊系垂直振动模型、轧件不对称滞后变形下辊系垂直振动模型和液压缸弹性约束下辊系多分段非线性板带轧机垂直振动模型。这五种模型可为进一步研究轧机非线性振动特性提供理论基础。
采用多尺度法、增量谐波平衡法等非线性求解方法求得各个模型的近似解析解，分析轧机在参激、接轴间隙、轧件滞后变形和液压缸约束下的多分段等不同非线性因素影响下的振动特性，研究随着不同参数变化对轧机稳定性的影响规律。运用奇异性理论分析轧机振动系统的稳定性，并得到轧机非线性振动系统的失稳临界条件。
研究基于HHT的非平稳信号时频分析方法，提出边界特征尺度延拓方法，通过采用信号内部和边缘处变化趋势最为相似的子波来对端点处数据进行延拓，抑制HHT时频分析中的端点效应问题。以1780热连轧机传动系统扭振、机架辊系垂振振动测试数据为例，运用HHT方法对实际轧机传动系统扭振和轧机辊系垂直振动信号进行了特征提取，验证轧机中存在的参激、接轴间隙、轧件变形滞后和液压缸作用下表现出的多分段等不同非线性因素对轧机传动系统扭转振动和轧机辊系垂直振动特性的影响。
通过研究发现系统在不同非线性因素影响下会产生相应的非线性振动行为，给板带轧机的稳定轧制造成不利影响，当非线性程度达到一定程度时系统就会出现轧制失稳现象。通过稳定性分析发现轧制参数在一点范围内波动时轧制稳定性随之变化，利用振动系统失稳临界条件可以给出稳定轧制参数区域，给轧制生产中工艺参数设定提供指导。
As one of the key equipment in iron and steel industry, rolling mill plays a veryimportant role in the process of iron and steel producing. In the process of rolling,vibration is a serious technical problem which beset the iron and steel industry to improveproduct quality and restricts the rolling product quality promotion and the productionefficiency improved. In order to obtain the effectively control strategies of the rolling millvibration to ensure the operation stability of rolling mill systems, improve the quality ofrolled products, rolling mill vibration problem has become the focus of the researchers.
Based on the generalized dissipation Lagrange principle, respectively established thetwo degree of freedom and the multi degree of freedom torsion vibration mechanics modelunder the parameters excitation of rolling mill drive system, considering the deformationof rolled piece showed the hysteretic nonlinear characteristics in the process of loadingwith cyclical change, the establishment of mill roll system lag nonlinear vibration model,considering under the action of hydraulic cylinder, the system show more piecewiseconstraints nonlinear factors, establish the multiple piecewise nonlinear strip mill verticalvibration model. These five models provide basis of theory for studying on the rolling millnonlinear vibration characteristics in further.
Use the method of multiple scales, the incremental harmonic balance method, thenonlinear solution for each model the approximate analytical solution, analysis mill in andexcitation, answer axial clearance, work piece hysteretic deformation and hydrauliccylinder under the restriction of the many section and so on the different nonlinear factorsunder the influence of the vibration characteristic, research with different parameters onthe mill the factors influencing the stability of the law. By using Lyapunov stability theoryand singularity theory analysis mill vibration system stability, and get mill nonlinearvibration system instability critical condition.
Based on the research of HHT non-stationary signal time and frequency analysis, thepaper proposes boundary characteristic scale continuation method, through the use ofsignal internal and edge change trend the most similar wavelet to tip data continuation, restrain HHT time-frequency analysis of end effect. As the test data of1780hot rollingmill drive system torsion vibration and frame system vertical vibration an example, theuse of HHT method to actual mill drive system torsion vibration and mill roll systemvertical vibration signal feature extraction, verify the influence existing in the mill andexcitation, answer axial clearance, the work piece deformation hysteretic and hydrauliccylinder under the action of show more section and so on the different nonlinear factors onthe rolling mill drive system torsion vibration and mill roll system vertical vibrationcharacteristic.
Through the study found that system influenced by different nonlinear factors willproduce the corresponding nonlinear vibration behavior, to the stability of the rolling stripmill, threaten, when nonlinear degree to certain degree system will appear rollinginstability phenomenon. Through the stability analysis found that rolling parameters in arange of rolling stability when change, the use of vibration system instability criticalcondition can give stable rolling parameters area, to rolling production process parametersset provide guidance.
基于广义耗散Lagrange原理，考虑轧机中不同的非线性因素，分别建立了接轴刚度参激变化下的两自由度扭振动力学模型、含间隙多自由度扭振动力学模型、轧件对称滞后变形下辊系垂直振动模型、轧件不对称滞后变形下辊系垂直振动模型和液压缸弹性约束下辊系多分段非线性板带轧机垂直振动模型。这五种模型可为进一步研究轧机非线性振动特性提供理论基础。
采用多尺度法、增量谐波平衡法等非线性求解方法求得各个模型的近似解析解，分析轧机在参激、接轴间隙、轧件滞后变形和液压缸约束下的多分段等不同非线性因素影响下的振动特性，研究随着不同参数变化对轧机稳定性的影响规律。运用奇异性理论分析轧机振动系统的稳定性，并得到轧机非线性振动系统的失稳临界条件。
研究基于HHT的非平稳信号时频分析方法，提出边界特征尺度延拓方法，通过采用信号内部和边缘处变化趋势最为相似的子波来对端点处数据进行延拓，抑制HHT时频分析中的端点效应问题。以1780热连轧机传动系统扭振、机架辊系垂振振动测试数据为例，运用HHT方法对实际轧机传动系统扭振和轧机辊系垂直振动信号进行了特征提取，验证轧机中存在的参激、接轴间隙、轧件变形滞后和液压缸作用下表现出的多分段等不同非线性因素对轧机传动系统扭转振动和轧机辊系垂直振动特性的影响。
通过研究发现系统在不同非线性因素影响下会产生相应的非线性振动行为，给板带轧机的稳定轧制造成不利影响，当非线性程度达到一定程度时系统就会出现轧制失稳现象。通过稳定性分析发现轧制参数在一点范围内波动时轧制稳定性随之变化，利用振动系统失稳临界条件可以给出稳定轧制参数区域，给轧制生产中工艺参数设定提供指导。
As one of the key equipment in iron and steel industry, rolling mill plays a veryimportant role in the process of iron and steel producing. In the process of rolling,vibration is a serious technical problem which beset the iron and steel industry to improveproduct quality and restricts the rolling product quality promotion and the productionefficiency improved. In order to obtain the effectively control strategies of the rolling millvibration to ensure the operation stability of rolling mill systems, improve the quality ofrolled products, rolling mill vibration problem has become the focus of the researchers.
Based on the generalized dissipation Lagrange principle, respectively established thetwo degree of freedom and the multi degree of freedom torsion vibration mechanics modelunder the parameters excitation of rolling mill drive system, considering the deformationof rolled piece showed the hysteretic nonlinear characteristics in the process of loadingwith cyclical change, the establishment of mill roll system lag nonlinear vibration model,considering under the action of hydraulic cylinder, the system show more piecewiseconstraints nonlinear factors, establish the multiple piecewise nonlinear strip mill verticalvibration model. These five models provide basis of theory for studying on the rolling millnonlinear vibration characteristics in further.
Use the method of multiple scales, the incremental harmonic balance method, thenonlinear solution for each model the approximate analytical solution, analysis mill in andexcitation, answer axial clearance, work piece hysteretic deformation and hydrauliccylinder under the restriction of the many section and so on the different nonlinear factorsunder the influence of the vibration characteristic, research with different parameters onthe mill the factors influencing the stability of the law. By using Lyapunov stability theoryand singularity theory analysis mill vibration system stability, and get mill nonlinearvibration system instability critical condition.
Based on the research of HHT non-stationary signal time and frequency analysis, thepaper proposes boundary characteristic scale continuation method, through the use ofsignal internal and edge change trend the most similar wavelet to tip data continuation, restrain HHT time-frequency analysis of end effect. As the test data of1780hot rollingmill drive system torsion vibration and frame system vertical vibration an example, theuse of HHT method to actual mill drive system torsion vibration and mill roll systemvertical vibration signal feature extraction, verify the influence existing in the mill andexcitation, answer axial clearance, the work piece deformation hysteretic and hydrauliccylinder under the action of show more section and so on the different nonlinear factors onthe rolling mill drive system torsion vibration and mill roll system vertical vibrationcharacteristic.
Through the study found that system influenced by different nonlinear factors willproduce the corresponding nonlinear vibration behavior, to the stability of the rolling stripmill, threaten, when nonlinear degree to certain degree system will appear rollinginstability phenomenon. Through the stability analysis found that rolling parameters in arange of rolling stability when change, the use of vibration system instability criticalcondition can give stable rolling parameters area, to rolling production process parametersset provide guidance.
引文
[1] A. Bar, A. wi toniowski. Interdependence between the rolling speed and non-linear vibrations ofthe mill system [J]. Journal of Materials Processing Technolog,2004,155:2116-2121.
[2] Fujita K, Saito T. Unstable vibration of roller mills [J]. Journal of Sound and Vibration,2006,297(1):329-350.
[3] Younes. Mohammad, Shahtout M, Damir M. A parameters design approach to improve productquality and equipment performance in hot rolling [J]. Journal of Material Process Technology,2006,132(1):83-92.
[4] Wang Jingcheng, Chen Chunzhao. On the optimization of a rolling force model for a hot stripfinishing line [J]. ISA Transactions,2007,46(4):527-531.
[5]侯福祥,张杰,曹建国,等.带钢冷轧机振动问题的研究进展及评述[J].钢铁研究学报,2007,19(10):6-10。
[6] X. D. Shu, C. M. Li, J. Zhao. Theoretical and experimental study of varying rule of rollingmoment about cross-wedge rolling [J]. Journal of Materials Processing Technology,2007,187(12):752-756.
[7] Brusa. Eugenio, Lemma. Luca, Benasciutti. D. Vibration analysis of a Sendzimir cold rolling milland bearing fault detection [J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,2010,224(8):1645-1654.
[8] Brusa. Eugenio, Lemma. Luca. Numerical and experimental analysis of the dynamic effects incompact cluster mills for cold rolling [J]. Journal of Materials Processing Technology,2009,209(5):2436-2445.
[9] Bar. A, Bar. O. Types of mid-frequency vibrations appearing during the rolling mill operation [J].Journal of Materials Processing Technology,2005,162-163:461-464.
[10]时培明.轧机非线性扭振系统动力学行为研究[D].秦皇岛：燕山大学学位论文,2008.
[11]马维金.轧机自激振动诊断及结构动力学修改[D].太原：太原理工大学学位论文,2006.
[12] Farley. Tom. Rolling mill vibration and its impact on productivity and product quality [J]. LightMetal Age,2006,64(6):12-14.
[13] Paluh James H, Hills Gary R, Wojtkowski Thomas C. Design and selection of universal joints forrolling mills [J]. Iron and Steel Engineer,1997,74(12):42-48.
[14] Arif S. Malik, Ramana V. Grandhi A. Computational method to predict strip profile in rolling mills[J]. Journal of Materials Processing Technology,2008,206(12):263-274.
[15] I.S. Choi, J.A. Rossiter, P.J. Fleming. Looper and tension control in hot rolling mills: A survey [J].Journal of Process Control,2007,17(6):509-521.
[16] Zhang Ruicheng, Tong Chaonan. Torsional vibration control of the main drive system of a rollingmill based on an extended state observer and linear quadratic control [J]. Journal of Vibration andControl,2006,12(3):313-327.
[17] Kong T, Yang D C H. Modelling of tandem rolling mills including tensional stress propagation [J].Proceedings of the Institution of Mechanical Engineers Part E: Journal of Process MechanicalEngineering,1993,207(E2):143-150.
[18] Singh V P, Samir S Nandi. Torsional vibrations in branch system-A transfer matrix approach [J].Journal of the Institution of Engineers (India): Mechanical Engineering Division,2002,83(4):52-55.
[19] Wang Jingcheng, Chen Chunzhao. On the optimization of a rolling force model for a hot stripfinishing line [J]. ISA Transactions,2007,46(4):527-531.
[20] Anssi T. Karttunen, Raimo von Hertzen. Polymer cover induced self-excited vibrations of nippedrolls [J]. Journal of Sound and Vibration,2011,330(16):3959-3972.
[21]钟掘,唐华平.高速轧机若干振动问题-复杂机电系统耦合动力学研究[J].振动、测试与诊断,2002,22(1):1-8.
[22] S. F. Asokanthan, P. A. Meehan. Non-linear vibration of a torsional system driven by a Hooke’sjoint [J]. Journal of Sound and Vibration,2000,233(2):297-310.
[23] Belli, P. Bittanti, S. De Marco. On the origin of torsional vibrations in hot rolling mills and apossible remedy [J]. Journal of Dynamic Systems, Measurement and Control, Transactions of theASME,2004,126(4):811-823.
[24] Butler, David H E, Churches Michael A, et al. Compensation of a digitally controlled static powerconverter for the damping of rolling mill torsional vibration[J]. IEEE Transactions on IndustryApplications,1992,28(2):427-433.
[25] CAI GanWei, Zhong Jue. Global coupled equations for dynamic analysis of planishing mill [J].Transactions of Nonferrous Metals Society of China (English Edition),2003,13(1):14-19.
[26] Mohieddine Jelali. Performance assessment of control systems in rolling mills–application tostrip thickness and flatness control [J]. Journal of Process Control,2007,26(4):123-129.
[27] J.Q.Pan, J. Pan, R.S.Ming, T. Lin. Three-dimensional Response and Intensity of TorsionalVibration in a Stepped Shaft [J]. Journal of Sound and vibration,2000,236(1):115-128.
[28] S. I. Chang. Torsional Instabilities and Non-linear Oscillation of a System Incorporating AHooke's Joint [J]. Journal of Sound and vibration,2000,229(4):993-1002
[29] Zygmunt Drzymala, A. wi toniowski. Nonlinear vibration in cold rolling mill [J]. Mecanique&Industries,2003,68(4):151-158.
[30] Wladyslaw, Dobrucki. Directions in inverstigations into the dynamic phenomena of rolling mill [J].Jouanal of Materials Processing Technology,1996,61(4):323-327.
[31]赵弘.轧机扭振及抑制研究[D].北京：北京科技大学学位论文，2006:1-2.
[32] John Pittner, Marwan A. Control of a continuous tandem cold metal rolling process [J]. ControlEngineering Practice,2008,16(9):1379-1390.
[33] Shi Peiming, Jiang Jinshui, Liu Bin, et al. Torsional vibration measuring of spanless points ofrotating shaft [J]. Chinese Journal of Scientific Instrument,2007,28(s4):1-3.
[34]陈勇辉,史铁林,杨叔子.四辊冷带轧机非线性参激振动的研究[J].机械工程学报,2003,39(4):56-60.
[35] Liu Bin, Shi Peiming, Hou Dongxiao, et al. Rotational speed oscillation measuration of rollingmill torsional vibration [J]. Chinese Journal of Scientific Instrument,2007,28(s4):5-7.
[36] M.Salmni Tehrani, P.Hartley, H.Moslemi Naeini, et al. Localosed edge bucking in cold roolforming of symmetric channek section[J]. Thin-walled structure,2006,44(2):184-196.
[37] Tang Huaping, Ding Rui. Investigation for parametric vibration of rolling mill [J]. Transactions ofNonferrous Metals Society of China,2002,12(3):485-488.
[38] L. Hua, Z.J. Zuo, J. LAN et al. Research on following motion rule of guide roller in cold rollinggroove ball ring [J]. Journal of Materials Processing Technology,2007,187(12):743-746.
[39]林鹤,康祖立.初轧机轧制打滑引起的扭振响应[J].北京科技大学学报,1991,13(1):31-36.
[40]孙志辉,邹家祥,何汝迎,等.2030板带冷连轧机的振动分析[J].北京科技大学学报,1997,19(S1):61-64.
[41] W. Dobrucki, P.Sobkowiak. Laboratory investigation of the continuous seamless-tube rollingprocess (Mandrel mill process) using models [J]. Journal of Mechanical Working Technology,1980,19(3):285-294.
[42] W. Dobrucki, A. Bar. Changes in roll-gap shape in the case of vibrations in a four-high rolling millstand [J]. Journal of Mechanical Working Technology,1989,61(4):328-337.
[43] A. wi toniowski, A. Bar. Parameterical excitement vibration in tandem mills—mathematicalmodel and its analysis [J]. Journal of Materials Processing Technolog,2003,134:224-224.
[44]王章海,王德俊.轧制参数对轧机主传动系统自激振动的影响[J].东北大学学报,1998,19(4):45-48.
[45]王章海,王德俊.打滑状态下轧机主传动系统的动态特性[J].东北大学学报,1998,19(5):79-82.
[46]孟令启,徐如松,王建勋,等.中厚板轧机非线性参激的振动[J].重庆大学学报,2008,31(4):393-397.
[47]孟令启,王建勋,吴浩亮,等.中厚板立辊轧机主传动系统的非线性扭振[J].华南理工大学学报(自然科学版),2009,32(2):25-28+34.
[48]张瑞成，童朝南.基于LMI方法的轧机传动系统机电振动H∞控制[J].北京科技大学学报,2006,28(2):179-184.
[49]张瑞成，童朝南.基于自抗扰控制技术的轧机传动系统机电振动控制[J].北京科技大学学报,2006,28(6):978-984.
[50]闫晓强,刘丽娜,曹曦,等. CSP轧机万向接轴弯扭耦合振动[J].北京科技大学学报,2008,30(10):1158-1162.
[51]闫晓强.热连轧机机电液耦合振动控制[J].机械工程学报,2011,47(17):61-65.
[52] Yarita I, Furukawa K, Seino Y. An Analysis of Chattering in cold rolling of Ultrathin Gauge SteelStrip [J]. Transctions ISIJ,1978,19(1):1-10.
[53] L. Chefneux, J.P. Fischbach, J. Gouzou. Study and industrial control of chatter in cold rolling [J].Iron and Steel Engineer,1984,61(11):17-26.
[54] Tamiya T, Furui K, Lida H, et al. Analysis of chattering Phenomenon in cold Rolling[C]. In: ISIJed. Proceedings of the International Conference on Steel Rolling, Tokyo,1980,2:1191-1202.
[55] J. Tlusty, G Chandra, S. Critchley, et al. Chatter in cold rolling [J]. CIRP Annals-ManufacturingTechnology.1982,31(1):195-199.
[56] O. Pawelski, W. Rasp, K. Friedewald. Chattering in cold rolling-Theory of interaction of plasticand elastic deformation. Proceeding of4th International Steel Rolling Conference: The Scienceand Technology of Flat Rolling, Deauville, France,1987,2:E.11.1-E.11.5.
[57] Yukio Kimura, Yasuhiro Sodani, Nobuo Nishiura, et al. Analysis of Chatter in Tandem ColdRolling Mills[J]. ISIJ International,2003,43(1):77-84.
[58] Robert E. Jone, Quan Qi. Chatter Dynamics in Sheet Rolling [J]. International Journal ofMechanical Science,1994,36(7):617-630.
[59] G.L. Nessler, J.F. Cory. Cause and solution of fifth-octave backup roll chatter on4-h cold millsand temper-mills [J]. Iron and Steel Engineer,1989,66(12):33-37.
[60] R E Johnson, Q Qi. Chatter dynamics in sheet rolling [J]. Int. J. Mech. Sci,1994,36(7):617-630.
[61] I.S Yun, W.R.D. Wilson, K.F. Ehmann. Chatter in the strip rolling process, Part I: dynamic modelof rolling [J]. Trans. ASME: J. Manufact. Sci. Eng.1998,120(2):330-336.
[62] I.S Yun, W.R.D. Wilson, K.F. Ehmann. Chatter in the strip rolling process, Part II: dynamic rollingexperiments [J]. Trans. ASME: J. Manufact. Sci. Eng.1998,120(2):337-342.
[63] I.S Yun, W.R.D. Wilson, K.F. Ehmann. Chatter in the strip rolling process, Part III: chatter model[J]. Trans. ASME: J. Manufact. Sci. Eng,1998,120(2):343-348.
[64] I.S Yun, W.R.D. Wilson, K.F. Ehmann, et al. Review of chatter studies in cold rolling [J].International Journal of Machine Tools&Manufactrue,1998,38(1):1499-1530.
[65] I.S Yun, W.R.D. Wilson, K.F. Ehmann, et al. Chatter in rolling [J]. Transactions of the NAMRIXXIII of SME,1995:13-19.
[66] Pei-Hua Hu, Huyue Zhao, Kornel F. Ehmann. Third-octave-mode chatter in rolling. Part1: chattermodel [J]. Proceedings of the Institution of Mechanical Engineer, Part B: Journal of EngineeringManufacture,2006,220(8):1267-1277.
[67] Pei-hua Hu, Huyue Zhao, Ehmann.K.F. Third-octave-mode chatter in rolling. Part2: Stability of asingle-stand mill [J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal ofEngineering Manufacture,2006,220(8):1293-1303.
[68] Pei-Hua Hu, Kornel F. Ehmann. A dynamic model of the rolling process. Part I: homogeneousmodel [J]. International Journal of Machine Tools&Manufacture,2000,40(1):1-19.
[69] Pei-Hua Hu, Kornel F. Ehmann. Fifth octave mode chatter in rolling [J]. Proc. Instn. Mech. Engrs.2001,1:797-809.
[70]王长松,孙民生,袁希.宽带钢冷轧机颤振仿真与分析[J].北京科技大学学报,1994,16:57-60.
[71]王长松,陈志健,陈先霖.冷带轧机颤振现象的分析与仿真[J].北京科技大学学报,1991,13(1):15-19.
[72]邹家祥,徐乐江.冷连轧机系统振动控制[M].北京:冶金工业出版社,1998.
[73]刘力,岳海龙,邹家祥.高速冷轧机辊缝摩擦系数影响因素的研究[J].重型机械,2001,2:9-12.
[74]杨其俊,连家创.高速冷带轧机垂直自激振动稳定性分析的数值计算方法[J].振动与冲击,1996,15(3):16-22.
[75]杨其俊，连家创，段振勇.四辊冷轧机减振装置的研究[J].钢铁,1996,31(11):71-75.
[76]陈勇辉,刘世元,廖广兰.四辊冷带轧机三倍频颤振机理的研究[J].机械工程学报,2003,39(6):118-123.
[77]陈勇辉,史铁林,杨叔子.四辊冷带轧机非线性参激振动的研究[J].机械工程学报,2003,39(4):56-60.
[78]范小彬,臧勇,吴迪平,等. CSP轧机振动和振纹的试验研究[J].钢铁,2006,41(10):54-58.
[79]范小彬,臧勇.热连轧机横向-垂向耦合振动研究[J].机械设计与制造,2011,(4):93-95.
[80] Yildiz. Sansal K, Forbes. J. Fraser, Huang. Biao, et al. Dynamic modelling and simulation of a hotstrip finishing mill [J]. Applied Mathematical Modelling,2009,33(7):3208-3225.
[81] Du Xiaozhong, Yang Quan, Lu Cheng, et al. Optimization of Short Stroke Control Preset forAutomatic Width Control of Hot Rolling Mill [J]. Journal of Iron and Steel Research, International,2010,17(6):161-20.
[82]瞿志豪,柴绍宽,叶黔元.1420冷连轧机的动态特性及颤振分析[J].振动与冲击,2006,25(4):25-29
[83] Ma. Weijin, Wang. Junyuan, Li. Fenglan, et al. Experimental modal analysis of roller gap sensorstructure on hot rolling mill [J]. Advanced Materials Research,2010,97:4328-4331.
[84]申延智,刘宏民,熊杰,等.厚板轧机含间隙主传动系统混沌动力学分析[J].工程力学,2010,27(7):232-236.
[85]侯东晓,陈浩,刘彬,等.轧机辊系垂直非线性参激振动特性分析[J].振动与冲击,2009,28(11):1-5+199.
[86]刘浩然,侯东晓,时培明,等.轧机辊系滞后非线性垂直振动系统的振动特性[J].机械工程学报,2011,47(13):65-71.
[87]何正嘉,訾艳阳,张西宁.现代信号处理及工程应用[M].西安交通大学出版社，2007,10.
[88] P. Frank Pai. Time–frequency characterization of nonlinear normal modes and challenges innonlinearity identification of dynamical systems [J]. Mechanical Systems and Signal Processing,2011,25:2358–2374.
[89] Alan V. Oppenheim, Ronald W. Discrete-time signal processing [M]. Publishing House ofElectronics Industry,2011.
[90] Bruce A, Donoho D, GAO Hongye. Wavelet analysis. IEEE Spectrum, Oct.1996:33(10)26-35
[91] Jing Lin. Feature extraction of machine sound using wavelet and its application in fault diagnosis[J]. NDT&E International,2001,34:25-30.
[92] Fabrício Nogueira Correa, Breno Pinheiro Jacob, Webe Joao Mansur Formulation of an efficienthybrid time–frequency domain solution procedure for linear structural dynamic problems [J].Computers and Structures,2010,88:331–346.
[93]刘彬,戴桂平,林洪彬.一种改进的基于小波变换的包络提取算法研究[J].仪器仪表学报，2006,27(1):34-37.
[94]冯辅周,司爱威,饶国强,等.基于小波相关排列熵的轴承早期故障诊断技术[J].机械工程学报,2012,48(13):73-79.
[95] VONG C M，WONG P K，TAM L M，et al. Ignition pattern analysis for automotive engine troublediagnosis using wavelet packet transform and support vector machines [J]. Chinese Journal ofMechanical Engineering，2011，24(5)：870-878.
[96] Abdelhamid Daamouche, Latifa Hamami, Naif Alajlan, et al. A wavelet optimization approach forECG signals classification [J]. Biomedical Signal Processing and Control,2012,7(4):342–349.
[97]胡爱军. Hilbert-Huang变换在旋转机械振动信号分析中的应用研究[D].保定：华北电力大学学位论文,2008.
[98]程军胜.基于Hilbert-Huang变换的旋转机械故障诊断方法研究[D].长沙：湖南大学学位,2005.
[99]邓拥军,王伟,钱成春,等. EMD方法及Hilbert变换中边界问题的处理,科学通报[J].2001,46,(3):257-263.
[100]陆凡东,方向,郭涛,等. EMD与SLS法在爆破振动加速度信号时域积分中的应用[J].振动与冲击,2012,31(9):90-93,101.
[101]胡利萍,宋恩亮,李宝清,等.一种适用于流数据分析的快速EMD算法[J].振动与冲击.2012,31(8):116-120.
[102]刘胜,张兰勇,于大泳,等.改进的Hilbert-Huang变换及在电磁辐射测量中的应用研究[J].仪器仪表学报,2010,31(10):2174-2179.
[103]董红生,张爱华,邱天爽,等.基于Hilbert谱的心率变异信号时频分析方法[J].仪器仪表学报,2011,32(2):271-278.
[104]杨江天,周培钰.经验模态分解和Laplace小波在机车柴油机齿轮系故障诊断中的应用[J].机械工程学报，2011,47(7):109-115.
[105]卢志茂,金辉,张春祥,等.基于HHT和OSF的复杂环境语音端点检测[J].电子与信息学报,2012,34(1):213-217.
[106]Nikolaos Tsakalozos, Konstantinos Drakakis, Scott Rickard. A formal study of the nonlinearityand consistency of the Empirical Mode Decomposition [J]. Signal Processing,2012,92:1961-1969.
[107]M Manjula, A V R S Sarma. Comparison of Empirical Mode Decomposition and Wavelet BasedClassification of Power Quality Events [J]. Energy Procedia,2012,14:1156–1162.
[108]N. Roveri, A. Carcaterra. Damage detection in structures under traveling loads by Hilbert–Huangtransforms [J]. Mechanical Systems and Signal Processing,2012,28:128–144.
[109]Ramadan A. Esmaeel, Farid Taheri. Delamination detection in laminated composite beams usingthe empirical mode decomposition energy damage index [J]. Composite Structures,2012,94:1515–1523.
[110]Md. Ashfanoor Kabir, Celia Shahnaz. Denoising of ECG signals based on noise reductionalgorithms in EMD and wavelet domains [J]. Biomedical Signal Processing and Control,2012,7(5):481–489.
[111]Eduardo Pinheiro, Octavian Postolache, Pedro Girao. Empirical Mode Decomposition andPrincipal Component Analysis implementation in processing non-invasive cardiovascular signals[J]. Measurement,2012,45(2):175–181.
[112]Ken Z. Kuai, Christina W. Tsai. Identification of varying time scales in sediment transport usingthe Hilbert–Huang Transform method [J]. Journal of Hydrology,2011,420:245–254.
[113]Norden E Huang, Zheng Shen, Steven R Long, et al. The empirical mode decomposition and theHilbert spectrum for nonlinear and non-stationary time series analysis [J]. Proc. R. Soc. Lond. A,1998,454(1971):903–995.
[114]N. E. Huang, Z. Shen, S. R. Long. A new view of nonlinear water waves: the hilbert spectrum [J].Ann Rev Fluid Mech,1999,31:417–457.
[115]Norden E. Huang，Zhaohua Wu. A Review on Hilbert-Huang Transform: Method and itsApplications to Geophysical Studies [DB]. Reviews of Geophysics,46, RG2006/2008.
[116]Chuan Li, MingLiang A generalized synchrosqueezing transform for enhancing signaltime–frequency representation [J]. Signal Processing,2012,92:2264–2274.
[2] Fujita K, Saito T. Unstable vibration of roller mills [J]. Journal of Sound and Vibration,2006,297(1):329-350.
[3] Younes. Mohammad, Shahtout M, Damir M. A parameters design approach to improve productquality and equipment performance in hot rolling [J]. Journal of Material Process Technology,2006,132(1):83-92.
[4] Wang Jingcheng, Chen Chunzhao. On the optimization of a rolling force model for a hot stripfinishing line [J]. ISA Transactions,2007,46(4):527-531.
[5]侯福祥,张杰,曹建国,等.带钢冷轧机振动问题的研究进展及评述[J].钢铁研究学报,2007,19(10):6-10。
[6] X. D. Shu, C. M. Li, J. Zhao. Theoretical and experimental study of varying rule of rollingmoment about cross-wedge rolling [J]. Journal of Materials Processing Technology,2007,187(12):752-756.
[7] Brusa. Eugenio, Lemma. Luca, Benasciutti. D. Vibration analysis of a Sendzimir cold rolling milland bearing fault detection [J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,2010,224(8):1645-1654.
[8] Brusa. Eugenio, Lemma. Luca. Numerical and experimental analysis of the dynamic effects incompact cluster mills for cold rolling [J]. Journal of Materials Processing Technology,2009,209(5):2436-2445.
[9] Bar. A, Bar. O. Types of mid-frequency vibrations appearing during the rolling mill operation [J].Journal of Materials Processing Technology,2005,162-163:461-464.
[10]时培明.轧机非线性扭振系统动力学行为研究[D].秦皇岛：燕山大学学位论文,2008.
[11]马维金.轧机自激振动诊断及结构动力学修改[D].太原：太原理工大学学位论文,2006.
[12] Farley. Tom. Rolling mill vibration and its impact on productivity and product quality [J]. LightMetal Age,2006,64(6):12-14.
[13] Paluh James H, Hills Gary R, Wojtkowski Thomas C. Design and selection of universal joints forrolling mills [J]. Iron and Steel Engineer,1997,74(12):42-48.
[14] Arif S. Malik, Ramana V. Grandhi A. Computational method to predict strip profile in rolling mills[J]. Journal of Materials Processing Technology,2008,206(12):263-274.
[15] I.S. Choi, J.A. Rossiter, P.J. Fleming. Looper and tension control in hot rolling mills: A survey [J].Journal of Process Control,2007,17(6):509-521.
[16] Zhang Ruicheng, Tong Chaonan. Torsional vibration control of the main drive system of a rollingmill based on an extended state observer and linear quadratic control [J]. Journal of Vibration andControl,2006,12(3):313-327.
[17] Kong T, Yang D C H. Modelling of tandem rolling mills including tensional stress propagation [J].Proceedings of the Institution of Mechanical Engineers Part E: Journal of Process MechanicalEngineering,1993,207(E2):143-150.
[18] Singh V P, Samir S Nandi. Torsional vibrations in branch system-A transfer matrix approach [J].Journal of the Institution of Engineers (India): Mechanical Engineering Division,2002,83(4):52-55.
[19] Wang Jingcheng, Chen Chunzhao. On the optimization of a rolling force model for a hot stripfinishing line [J]. ISA Transactions,2007,46(4):527-531.
[20] Anssi T. Karttunen, Raimo von Hertzen. Polymer cover induced self-excited vibrations of nippedrolls [J]. Journal of Sound and Vibration,2011,330(16):3959-3972.
[21]钟掘,唐华平.高速轧机若干振动问题-复杂机电系统耦合动力学研究[J].振动、测试与诊断,2002,22(1):1-8.
[22] S. F. Asokanthan, P. A. Meehan. Non-linear vibration of a torsional system driven by a Hooke’sjoint [J]. Journal of Sound and Vibration,2000,233(2):297-310.
[23] Belli, P. Bittanti, S. De Marco. On the origin of torsional vibrations in hot rolling mills and apossible remedy [J]. Journal of Dynamic Systems, Measurement and Control, Transactions of theASME,2004,126(4):811-823.
[24] Butler, David H E, Churches Michael A, et al. Compensation of a digitally controlled static powerconverter for the damping of rolling mill torsional vibration[J]. IEEE Transactions on IndustryApplications,1992,28(2):427-433.
[25] CAI GanWei, Zhong Jue. Global coupled equations for dynamic analysis of planishing mill [J].Transactions of Nonferrous Metals Society of China (English Edition),2003,13(1):14-19.
[26] Mohieddine Jelali. Performance assessment of control systems in rolling mills–application tostrip thickness and flatness control [J]. Journal of Process Control,2007,26(4):123-129.
[27] J.Q.Pan, J. Pan, R.S.Ming, T. Lin. Three-dimensional Response and Intensity of TorsionalVibration in a Stepped Shaft [J]. Journal of Sound and vibration,2000,236(1):115-128.
[28] S. I. Chang. Torsional Instabilities and Non-linear Oscillation of a System Incorporating AHooke's Joint [J]. Journal of Sound and vibration,2000,229(4):993-1002
[29] Zygmunt Drzymala, A. wi toniowski. Nonlinear vibration in cold rolling mill [J]. Mecanique&Industries,2003,68(4):151-158.
[30] Wladyslaw, Dobrucki. Directions in inverstigations into the dynamic phenomena of rolling mill [J].Jouanal of Materials Processing Technology,1996,61(4):323-327.
[31]赵弘.轧机扭振及抑制研究[D].北京：北京科技大学学位论文，2006:1-2.
[32] John Pittner, Marwan A. Control of a continuous tandem cold metal rolling process [J]. ControlEngineering Practice,2008,16(9):1379-1390.
[33] Shi Peiming, Jiang Jinshui, Liu Bin, et al. Torsional vibration measuring of spanless points ofrotating shaft [J]. Chinese Journal of Scientific Instrument,2007,28(s4):1-3.
[34]陈勇辉,史铁林,杨叔子.四辊冷带轧机非线性参激振动的研究[J].机械工程学报,2003,39(4):56-60.
[35] Liu Bin, Shi Peiming, Hou Dongxiao, et al. Rotational speed oscillation measuration of rollingmill torsional vibration [J]. Chinese Journal of Scientific Instrument,2007,28(s4):5-7.
[36] M.Salmni Tehrani, P.Hartley, H.Moslemi Naeini, et al. Localosed edge bucking in cold roolforming of symmetric channek section[J]. Thin-walled structure,2006,44(2):184-196.
[37] Tang Huaping, Ding Rui. Investigation for parametric vibration of rolling mill [J]. Transactions ofNonferrous Metals Society of China,2002,12(3):485-488.
[38] L. Hua, Z.J. Zuo, J. LAN et al. Research on following motion rule of guide roller in cold rollinggroove ball ring [J]. Journal of Materials Processing Technology,2007,187(12):743-746.
[39]林鹤,康祖立.初轧机轧制打滑引起的扭振响应[J].北京科技大学学报,1991,13(1):31-36.
[40]孙志辉,邹家祥,何汝迎,等.2030板带冷连轧机的振动分析[J].北京科技大学学报,1997,19(S1):61-64.
[41] W. Dobrucki, P.Sobkowiak. Laboratory investigation of the continuous seamless-tube rollingprocess (Mandrel mill process) using models [J]. Journal of Mechanical Working Technology,1980,19(3):285-294.
[42] W. Dobrucki, A. Bar. Changes in roll-gap shape in the case of vibrations in a four-high rolling millstand [J]. Journal of Mechanical Working Technology,1989,61(4):328-337.
[43] A. wi toniowski, A. Bar. Parameterical excitement vibration in tandem mills—mathematicalmodel and its analysis [J]. Journal of Materials Processing Technolog,2003,134:224-224.
[44]王章海,王德俊.轧制参数对轧机主传动系统自激振动的影响[J].东北大学学报,1998,19(4):45-48.
[45]王章海,王德俊.打滑状态下轧机主传动系统的动态特性[J].东北大学学报,1998,19(5):79-82.
[46]孟令启,徐如松,王建勋,等.中厚板轧机非线性参激的振动[J].重庆大学学报,2008,31(4):393-397.
[47]孟令启,王建勋,吴浩亮,等.中厚板立辊轧机主传动系统的非线性扭振[J].华南理工大学学报(自然科学版),2009,32(2):25-28+34.
[48]张瑞成，童朝南.基于LMI方法的轧机传动系统机电振动H∞控制[J].北京科技大学学报,2006,28(2):179-184.
[49]张瑞成，童朝南.基于自抗扰控制技术的轧机传动系统机电振动控制[J].北京科技大学学报,2006,28(6):978-984.
[50]闫晓强,刘丽娜,曹曦,等. CSP轧机万向接轴弯扭耦合振动[J].北京科技大学学报,2008,30(10):1158-1162.
[51]闫晓强.热连轧机机电液耦合振动控制[J].机械工程学报,2011,47(17):61-65.
[52] Yarita I, Furukawa K, Seino Y. An Analysis of Chattering in cold rolling of Ultrathin Gauge SteelStrip [J]. Transctions ISIJ,1978,19(1):1-10.
[53] L. Chefneux, J.P. Fischbach, J. Gouzou. Study and industrial control of chatter in cold rolling [J].Iron and Steel Engineer,1984,61(11):17-26.
[54] Tamiya T, Furui K, Lida H, et al. Analysis of chattering Phenomenon in cold Rolling[C]. In: ISIJed. Proceedings of the International Conference on Steel Rolling, Tokyo,1980,2:1191-1202.
[55] J. Tlusty, G Chandra, S. Critchley, et al. Chatter in cold rolling [J]. CIRP Annals-ManufacturingTechnology.1982,31(1):195-199.
[56] O. Pawelski, W. Rasp, K. Friedewald. Chattering in cold rolling-Theory of interaction of plasticand elastic deformation. Proceeding of4th International Steel Rolling Conference: The Scienceand Technology of Flat Rolling, Deauville, France,1987,2:E.11.1-E.11.5.
[57] Yukio Kimura, Yasuhiro Sodani, Nobuo Nishiura, et al. Analysis of Chatter in Tandem ColdRolling Mills[J]. ISIJ International,2003,43(1):77-84.
[58] Robert E. Jone, Quan Qi. Chatter Dynamics in Sheet Rolling [J]. International Journal ofMechanical Science,1994,36(7):617-630.
[59] G.L. Nessler, J.F. Cory. Cause and solution of fifth-octave backup roll chatter on4-h cold millsand temper-mills [J]. Iron and Steel Engineer,1989,66(12):33-37.
[60] R E Johnson, Q Qi. Chatter dynamics in sheet rolling [J]. Int. J. Mech. Sci,1994,36(7):617-630.
[61] I.S Yun, W.R.D. Wilson, K.F. Ehmann. Chatter in the strip rolling process, Part I: dynamic modelof rolling [J]. Trans. ASME: J. Manufact. Sci. Eng.1998,120(2):330-336.
[62] I.S Yun, W.R.D. Wilson, K.F. Ehmann. Chatter in the strip rolling process, Part II: dynamic rollingexperiments [J]. Trans. ASME: J. Manufact. Sci. Eng.1998,120(2):337-342.
[63] I.S Yun, W.R.D. Wilson, K.F. Ehmann. Chatter in the strip rolling process, Part III: chatter model[J]. Trans. ASME: J. Manufact. Sci. Eng,1998,120(2):343-348.
[64] I.S Yun, W.R.D. Wilson, K.F. Ehmann, et al. Review of chatter studies in cold rolling [J].International Journal of Machine Tools&Manufactrue,1998,38(1):1499-1530.
[65] I.S Yun, W.R.D. Wilson, K.F. Ehmann, et al. Chatter in rolling [J]. Transactions of the NAMRIXXIII of SME,1995:13-19.
[66] Pei-Hua Hu, Huyue Zhao, Kornel F. Ehmann. Third-octave-mode chatter in rolling. Part1: chattermodel [J]. Proceedings of the Institution of Mechanical Engineer, Part B: Journal of EngineeringManufacture,2006,220(8):1267-1277.
[67] Pei-hua Hu, Huyue Zhao, Ehmann.K.F. Third-octave-mode chatter in rolling. Part2: Stability of asingle-stand mill [J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal ofEngineering Manufacture,2006,220(8):1293-1303.
[68] Pei-Hua Hu, Kornel F. Ehmann. A dynamic model of the rolling process. Part I: homogeneousmodel [J]. International Journal of Machine Tools&Manufacture,2000,40(1):1-19.
[69] Pei-Hua Hu, Kornel F. Ehmann. Fifth octave mode chatter in rolling [J]. Proc. Instn. Mech. Engrs.2001,1:797-809.
[70]王长松,孙民生,袁希.宽带钢冷轧机颤振仿真与分析[J].北京科技大学学报,1994,16:57-60.
[71]王长松,陈志健,陈先霖.冷带轧机颤振现象的分析与仿真[J].北京科技大学学报,1991,13(1):15-19.
[72]邹家祥,徐乐江.冷连轧机系统振动控制[M].北京:冶金工业出版社,1998.
[73]刘力,岳海龙,邹家祥.高速冷轧机辊缝摩擦系数影响因素的研究[J].重型机械,2001,2:9-12.
[74]杨其俊,连家创.高速冷带轧机垂直自激振动稳定性分析的数值计算方法[J].振动与冲击,1996,15(3):16-22.
[75]杨其俊，连家创，段振勇.四辊冷轧机减振装置的研究[J].钢铁,1996,31(11):71-75.
[76]陈勇辉,刘世元,廖广兰.四辊冷带轧机三倍频颤振机理的研究[J].机械工程学报,2003,39(6):118-123.
[77]陈勇辉,史铁林,杨叔子.四辊冷带轧机非线性参激振动的研究[J].机械工程学报,2003,39(4):56-60.
[78]范小彬,臧勇,吴迪平,等. CSP轧机振动和振纹的试验研究[J].钢铁,2006,41(10):54-58.
[79]范小彬,臧勇.热连轧机横向-垂向耦合振动研究[J].机械设计与制造,2011,(4):93-95.
[80] Yildiz. Sansal K, Forbes. J. Fraser, Huang. Biao, et al. Dynamic modelling and simulation of a hotstrip finishing mill [J]. Applied Mathematical Modelling,2009,33(7):3208-3225.
[81] Du Xiaozhong, Yang Quan, Lu Cheng, et al. Optimization of Short Stroke Control Preset forAutomatic Width Control of Hot Rolling Mill [J]. Journal of Iron and Steel Research, International,2010,17(6):161-20.
[82]瞿志豪,柴绍宽,叶黔元.1420冷连轧机的动态特性及颤振分析[J].振动与冲击,2006,25(4):25-29
[83] Ma. Weijin, Wang. Junyuan, Li. Fenglan, et al. Experimental modal analysis of roller gap sensorstructure on hot rolling mill [J]. Advanced Materials Research,2010,97:4328-4331.
[84]申延智,刘宏民,熊杰,等.厚板轧机含间隙主传动系统混沌动力学分析[J].工程力学,2010,27(7):232-236.
[85]侯东晓,陈浩,刘彬,等.轧机辊系垂直非线性参激振动特性分析[J].振动与冲击,2009,28(11):1-5+199.
[86]刘浩然,侯东晓,时培明,等.轧机辊系滞后非线性垂直振动系统的振动特性[J].机械工程学报,2011,47(13):65-71.
[87]何正嘉,訾艳阳,张西宁.现代信号处理及工程应用[M].西安交通大学出版社，2007,10.
[88] P. Frank Pai. Time–frequency characterization of nonlinear normal modes and challenges innonlinearity identification of dynamical systems [J]. Mechanical Systems and Signal Processing,2011,25:2358–2374.
[89] Alan V. Oppenheim, Ronald W. Discrete-time signal processing [M]. Publishing House ofElectronics Industry,2011.
[90] Bruce A, Donoho D, GAO Hongye. Wavelet analysis. IEEE Spectrum, Oct.1996:33(10)26-35
[91] Jing Lin. Feature extraction of machine sound using wavelet and its application in fault diagnosis[J]. NDT&E International,2001,34:25-30.
[92] Fabrício Nogueira Correa, Breno Pinheiro Jacob, Webe Joao Mansur Formulation of an efficienthybrid time–frequency domain solution procedure for linear structural dynamic problems [J].Computers and Structures,2010,88:331–346.
[93]刘彬,戴桂平,林洪彬.一种改进的基于小波变换的包络提取算法研究[J].仪器仪表学报，2006,27(1):34-37.
[94]冯辅周,司爱威,饶国强,等.基于小波相关排列熵的轴承早期故障诊断技术[J].机械工程学报,2012,48(13):73-79.
[95] VONG C M，WONG P K，TAM L M，et al. Ignition pattern analysis for automotive engine troublediagnosis using wavelet packet transform and support vector machines [J]. Chinese Journal ofMechanical Engineering，2011，24(5)：870-878.
[96] Abdelhamid Daamouche, Latifa Hamami, Naif Alajlan, et al. A wavelet optimization approach forECG signals classification [J]. Biomedical Signal Processing and Control,2012,7(4):342–349.
[97]胡爱军. Hilbert-Huang变换在旋转机械振动信号分析中的应用研究[D].保定：华北电力大学学位论文,2008.
[98]程军胜.基于Hilbert-Huang变换的旋转机械故障诊断方法研究[D].长沙：湖南大学学位,2005.
[99]邓拥军,王伟,钱成春,等. EMD方法及Hilbert变换中边界问题的处理,科学通报[J].2001,46,(3):257-263.
[100]陆凡东,方向,郭涛,等. EMD与SLS法在爆破振动加速度信号时域积分中的应用[J].振动与冲击,2012,31(9):90-93,101.
[101]胡利萍,宋恩亮,李宝清,等.一种适用于流数据分析的快速EMD算法[J].振动与冲击.2012,31(8):116-120.
[102]刘胜,张兰勇,于大泳,等.改进的Hilbert-Huang变换及在电磁辐射测量中的应用研究[J].仪器仪表学报,2010,31(10):2174-2179.
[103]董红生,张爱华,邱天爽,等.基于Hilbert谱的心率变异信号时频分析方法[J].仪器仪表学报,2011,32(2):271-278.
[104]杨江天,周培钰.经验模态分解和Laplace小波在机车柴油机齿轮系故障诊断中的应用[J].机械工程学报，2011,47(7):109-115.
[105]卢志茂,金辉,张春祥,等.基于HHT和OSF的复杂环境语音端点检测[J].电子与信息学报,2012,34(1):213-217.
[106]Nikolaos Tsakalozos, Konstantinos Drakakis, Scott Rickard. A formal study of the nonlinearityand consistency of the Empirical Mode Decomposition [J]. Signal Processing,2012,92:1961-1969.
[107]M Manjula, A V R S Sarma. Comparison of Empirical Mode Decomposition and Wavelet BasedClassification of Power Quality Events [J]. Energy Procedia,2012,14:1156–1162.
[108]N. Roveri, A. Carcaterra. Damage detection in structures under traveling loads by Hilbert–Huangtransforms [J]. Mechanical Systems and Signal Processing,2012,28:128–144.
[109]Ramadan A. Esmaeel, Farid Taheri. Delamination detection in laminated composite beams usingthe empirical mode decomposition energy damage index [J]. Composite Structures,2012,94:1515–1523.
[110]Md. Ashfanoor Kabir, Celia Shahnaz. Denoising of ECG signals based on noise reductionalgorithms in EMD and wavelet domains [J]. Biomedical Signal Processing and Control,2012,7(5):481–489.
[111]Eduardo Pinheiro, Octavian Postolache, Pedro Girao. Empirical Mode Decomposition andPrincipal Component Analysis implementation in processing non-invasive cardiovascular signals[J]. Measurement,2012,45(2):175–181.
[112]Ken Z. Kuai, Christina W. Tsai. Identification of varying time scales in sediment transport usingthe Hilbert–Huang Transform method [J]. Journal of Hydrology,2011,420:245–254.
[113]Norden E Huang, Zheng Shen, Steven R Long, et al. The empirical mode decomposition and theHilbert spectrum for nonlinear and non-stationary time series analysis [J]. Proc. R. Soc. Lond. A,1998,454(1971):903–995.
[114]N. E. Huang, Z. Shen, S. R. Long. A new view of nonlinear water waves: the hilbert spectrum [J].Ann Rev Fluid Mech,1999,31:417–457.
[115]Norden E. Huang，Zhaohua Wu. A Review on Hilbert-Huang Transform: Method and itsApplications to Geophysical Studies [DB]. Reviews of Geophysics,46, RG2006/2008.
[116]Chuan Li, MingLiang A generalized synchrosqueezing transform for enhancing signaltime–frequency representation [J]. Signal Processing,2012,92:2264–2274.