1、使用五点三次平滑,命令窗口输入:a=G201for k=1:2 b(1)=(69*a(1)+4*(a(2)+a(4)-6*a(3)-a(5)/70; b(2)=(2*(a(1)+a(5)+27*a(2)+12*a(3)-8*a(4)/35; for j=3:N-2 b(j)=(-3*(a(j-2)+a(j+2)+12*(a(j-1)+a(j+1)+17*a(j)/35; end b(N-1)=(2*(a(N)+a(N-4)+27*a(N-1)+12*a(N-2)-8*a(N-3)/35; b(N)=(69*a(N)+4*(a(N-1)+a(N-3)-6*a(N-2)-a(N-4)/70; a=
2、b;endG201ph=a %G201ph为五点三次平滑法处理的数据subplot(2,1,2),plot(G201ph);%显示G201及G201ph及前面零均值化处理中做频域图的方法一样,做出G201及G201ph的频谱图G201p及G201php,得到图形如下:从时域图形上看,平滑处理使图形变得平滑,去除毛刺,从频域图形上看,高频部分明显变少变小,而低频部分基本无变化。因为故障的频率主要集中在低中频部分,这样处理后不仅对故障的分析无影响,而且去除部分噪音,减少干扰。1.4 滤波处理(原理公式见报告P13)%使用巴特沃斯滤波器进行滤波,命令窗口输入:wp=2400; %通带截至频率2400
3、hzws=2800; %阻带截至频率2800hzrp=2; %通带波动系数rs=60; %阻带波动系数N,wn =buttord(wp/(fs/2),ws/(fs/2),rp,rs,z);%建立巴特沃斯滤波器num,den=butter(N,wn);%建立数字滤波器H,W=freqz(num,den);%分析滤波器的幅频特性plot(W*fs/(2*pi),abs(H);grid;%巴特沃斯滤波器频率响应图得到巴特沃斯滤波器频率响应图:继续输入:G201lb=filtfilt(num,den,G201);% G201lb为G201滤波后的数据subplot(2,1,2),plot(G201lb
4、);%显示G201及G201lb及前面零均值化处理中做频域图的方法一样,做出G201及G201lb的频谱图G201p及G201lbp,得到图形如下:在时域内不能明显的看出处理前后的区别。但从频域图可以看出,2500Hz后的频率几乎不存在。因为低通滤波器的通带截至频率为2400hz,阻带截至频率为2800hz。可见滤波效果是很好的。以上介绍了一些数据预处理的方法,鉴于本文采集的原始信号数据较好,故只做零均值化这一项处理。3 时域特征值提取(原理公式见P15)G201m=sum(G201l)/20000; %G201m为均值,G201l为零均值化处理后结果,下同G201f=sum(G201l-G2
5、01m).2); %G201f为方差G201rms=sqrt(sum(G201l.2)/20000); %G201rms均方根值G201peak=(max(G201l)-min(G201l)/2; %G201peak为峰值G201c= G201peak/G201rms; %G201c为峰值因子G201k=sum(G201l.4)/(G201rms.4)*20000); %G201k为峭度系数G201s=(G201rms*20000)/sum(abs(G201l); %G201s为波形因子G201cl=G201peak/(sum(sqrt(abs(G201l)/20000).2; %G201cl
6、裕度因子G201i=(G201peak*20000)/sum(abs(G201l); %G201i脉冲因子由此得到G201的时域特征值根据前述方法一次得到G202G2010,Z201Z2010的时域特征值,建立表格状态样本时域特征值均值()方差均方根值RMS峰值peak峭度系数K峰值因子C裕度因子CL脉冲因子I波形因子S故障轴承G2016.85222340.800.34212.270113.32346.635718.225912.46491.8785G20222.34522605.740.36102.354914.21706.524218.821212.62771.9355G203-32.38
7、542902.360.38092.488613.53206.532618.932312.63601.9343G20415.32902630.680.36272.480313.87566.838819.028812.96441.8957G20515.89442510.690.35432.337913.26326.598518.574012.52711.8985G206-3.73632647.010.36382.393613.53826.579318.240812.42951.8892G207-2.06752379.660.34492.287112.38826.630517.562312.1190
8、1.8278G208-4.51022548.620.35702.451214.04576.866619.819513.28391.9346G2098.08802496.800.35332.337112.63046.614617.375712.08231.8266G20104.40802871.860.37892.316711.74176.113816.913411.38661.8625正常轴承Z2015.24191940.060.31151.58504.32035.08898.18286.73971.3244Z20227.71791805.180.30041.50304.46845.00278
9、.06126.63511.3263Z203-23.98241698.730.29141.37644.62554.72287.70336.31551.3372Z2042.58211677.680.28961.73994.88596.00739.68087.97701.3279Z2053.42741890.520.30751.52314.50354.95397.94036.55221.3226Z20628.42331688.290.29051.32473.92824.55947.21485.96471.3082Z20716.67021629.540.28541.46184.58805.12138.
10、23386.79211.3262Z208-17.69651605.220.28331.34904.43664.76187.67706.32011.3272Z20920.48481714.370.29281.45734.66104.97748.09836.64661.3354Z2010-4.03201790.060.29921.68775.19085.64129.37957.64671.3555列出时域参数的数字表后可以简单分析,故障轴承和正常轴承在方差,峰值,峭度系数,裕度因子,脉冲因子,波形因子差别较为明显,而在均值,均方根值,峰值因子差别不明显。4 频域特征值提取(原理公式见P18)4.1
11、频域参数for i=2:20000G201g(i)=(G201l(i)-G201l(i-1)/(1/10000); G201gg(i)=G201g(i)*G201l(i);G201msf=(sum(G201g).2)/(4*(pi2)*sum(G201l.2); %G201msf为均方频率G201fc=(sum(G201gg)/(2*pi*sum(G201l.2); %G201fc重心频率G201vf=G201msf-G201fc.2; %G201vf为频率方差由此得到G201l的频域参数。频域参数重心频率频率方差均方频率727.4390768683.09001297850.5751732.7
12、359755254.24021292156.1458783.7554830793.71491445066.2883772.6559858228.74341455225.8325708.5887743009.38451245107.3676807.0247876652.13131527941.0240776.6448825242.15171428419.3696752.5714842258.30101408621.9914839.0520952037.65141656045.8589774.6435842014.28501442086.89891947.72046177234.381699708
13、49.15392063.44766752047.589611009863.55702124.78896969666.443511484394.40282129.98197038297.661611575120.47852049.52726681185.600010881747.31072047.97916659325.170810853543.62932151.69967045509.332011675320.49502181.39907213367.433511971868.87642171.50927046245.891511761698.14522088.47246637350.7777
14、10999067.8211从上表可以看出,频域参数的特征值重复性和差异性都是比较良好的。4.2傅里叶变换(原理公式见P20)将G201l和Z201l(Z201l为Z201零均值化后数据)的fft变换后的G201lp及Z201lp做出,程序如下:G201lp=abs(fft(G201l,16384);G201lp=G201lp(1:8192,1);Z201lp=abs(fft(Z201l,16384);Z201lp=Z201lp(1:subplot(2,1,1),plot(G201lp); subplot(2,1,2),plot(Z201lp);如下图所示:能够区分两个状态且能代表自己频谱的区域
15、有:点(326,1)、区域(25603000)、点(3278,1)、区域(63106646)、区域(68507300)用标记。对故障轴承数据随机抽取G202fft、G206fft、G207fft、G209fft数据对比图形如下:从故障轴承抽样数据对比图形可以看出,各个特征值的性重复较好。对正常轴承数据随机抽取Z203fft、Z204fft、Z206fft、Z208fft数据对比图形如下: 图3-12正常轴承重复性FFT谱从正常轴承抽样数据对比图形可以看出,各个特征值的性重复较好。利用以下程序将G201G2010,Z201Z2010的傅里叶变换特征值及特征区域提取出来:G201ffttz=G20
16、1lp(326,1),sum(G201lp(2560:3000,1),G201lp(3278,1),sum(G201lp(6310:6646,1), sum(G201lp(6850:7300,1);%G201ffttz为G201l进行fft变换后提取的特征值建立表格:FFT频域特征值(326,1)(2560:3000,1)(3278,1)(6310:6646,1)(6850:7300,1)24.037016457.4591223.41115511.60235070.641936.131815337.1272216.35055283.45645046.534028.267118178.63982
17、13.62015642.920511.1246163.98695662.49845687.7720114.039916154.9008168.20395562.42985151.079936.935119195.7369179.82815528.26136344.334911.462918551.4539162.56425491.62415443.5653141.138515024.3193148.25905700.04945710.092437.458620519.3069148.70935955.78156390.374292.740220333.6468138.53706092.2449
18、5809.4190247.171610356.38888.211015539.769111057.7255179.159810083.433627.494314772.372010632.8833187.585210018.71816.226915396.491310692.6573212.92359502.587717.208415035.716910475.6605132.327710125.071418.669915691.313911033.8520210.835610029.603417.639215133.589610612.5788205.152910220.055918.711
19、914764.755710577.8874227.172010414.902020.944014186.354211097.2232173.456810161.368810.417015232.020110877.8867198.617310366.74376.862415144.132911205.66324.3功率谱处理(原理公式见P22)采用Welch平均周期法,采样频率为10000Hz,长度为16384点,分段时每段长度为4096,相邻两段重叠的点数为2048,因此分成了7段,窗函数为缺省。命令窗口输入以下程序:p,f=spectrum(G201l,4096,2048,fs);G201
20、gl=p(:,1);%采用Welch平均周期法,G201功率谱处理结果将G201gl和Z201gl显示出来,得到:点(82,1)、区域(660739)、点(820,1)、点(1473,1)、点(1616,1)、点(1639,1)点(1778,1)。对故障轴承数据随机抽取G202gl、G204gl、G206gl、G208gl数据对比图形如下:图3-14故障轴承重复性功率谱对正常轴承数据随机抽取Z203gl、Z204gl、Z209gl、Z2010gl数据对比图形如下:图3-15正常轴承重复性功率谱将G201G2010,Z201Z2010的傅里叶变换特征值及特征区域提取出来,建立表格:Welch平均
21、周期法功率谱特征值(82,1)(820,1)(1473,1)(1616,1)(1639,1)(1778,1)(660:739,1)0.36430.56650.21450.01790.04310.00878.86650.23510.50680.18650.02460.04410.012810.89370.26840.52910.12290.01150.03530.011012.02330.27000.34990.07680.01560.06600.008010.22350.42580.36920.13480.04520.00919.70170.22950.41230.11890.01260.08
22、690.014714.18950.15160.32130.02270.01630.04390.006511.97050.29760.28780.04740.01300.05170.00747.67650.21950.32900.10010.02170.03190.009415.1060.36300.28870.15710.02510.04680.011413.5650.65381.22961.31050.24273.87390.36680.01870.01171.43032.31200.31313.50240.47740.00680.00971.27641.44310.26823.44860.56580.01601.446
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