基于Lagrange插值的局部特征尺度分解方法及其应用  

The Method of Lagrange Interpolation Based Local Characteristic-scale Decomposition and Its Application

作　　者：吴占涛[1] 程军圣[1] 李宝庆[1] 郑近德[2] WU Zhantao CHENG Junsheng LI Baoqing ZHENG Jinde(State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China School of Mechanical Engineering, Anhui University of Technology, Ma＇anshan 243032, China)

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,湖南长沙410082 [2]安徽工业大学机械工程学院,安徽马鞍山243032

出　　处：《湖南大学学报（自然科学版）》2017年第4期63-70,共8页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(51375152);湖南省科技支撑计划资助项目(2014WK3005)~~

摘　　要：针对局部特征尺度分解(Local Characteristic-scale Decomposition,LCD)方法中均值曲线插值点的属性主要由相邻两同类极值点的属性决定,不能很好地体现数据的整体变化趋势,从而可能引起分解精度降低,提出了基于Lagrange插值的局部特征尺度分解(Lagrange Interpolation based Local Characteristic-scale Decomposition,LILCD)方法.该方法采用Lagrange插值取代LCD中的线性插值,且均值曲线的插值点是由相邻的3个同类极值点构成的Lagrange插值多项式计算产生.引入了对称系数的概念,并给出了最优对称系数评价准则.研究了LILCD方法的原理及最优对称系数评价准则,通过仿真信号将LILCD方法与LCD方法进行了对比,结果表明LILCD在提高分量精确性和正交性方面具有一定的优越性.将LILCD方法应用于转子不对中故障的诊断,结果表明了方法的有效性.A new non-stationary signal method——Lagrange Interpolation based Local Characteristic-scale Decomposition （LILCD） was proposed to improve the LCD method, in which the property of mean curve interpolation points was mainly decided by adjacent similar extremum points which cannot properly reflect the overall trends of signal, and the decomposition precision was lowered. To improve the LCD method, Lagrange interpolation was used in LILCD to replace the linear interpolation in LCD, and the mean curve interpolation points were computed with the Lagrange interpolation polynomial generated by three adjacent similar extremum points. Symmetric coefficient was introduced, and the optimal evaluation criteria of symmetric coefficient were given. The paper firstly studied the theory of LILCD, and then, simulation experiments were done to compare LILCD with LCD. The results have indicated that LILCD is more efficient in improving the veracity and orthogonality in components than LCD. Finally, the proposed method was applied to diagnose the rotor with misalignment fault, which indicates the effectiveness of LILCD.

关 键 词：局部特征尺度分解 LAGRANGE插值 故障诊断 不对中故障 时频分析 

分 类 号：TH165[机械工程—机械制造及自动化] TH911.7