Journal of Applied Research and Technology
www.jart.ccadet.unam.mx
Journal of Applied Research and Technology 17 (2019) 126-136
P. Arun a, *, S. Abraham Lincon b, N. Prabhakaran c
xi(k)= ∑M-1l=0 w(l)x(l)e-j2πklM , 1≤i≤Q
Pi(k)
= 1
∑M−1k=0|w(k)|2|Xi(k)|2 (2)
Pi(k) = 1
∑M−1k=0|w(k)|2|Xi(k)|2 (2)
S=
[
P0(0) P0(1) P0(2) ⋯⋯ P0(Q-1) P1(0) P1(1) P1(2) ⋯⋯ P1(Q-1) P2(0) P2(1) P2(2) ⋯⋯ P2(Q-1)
⋮ ⋮ ⋮ ⋯⋯ ⋮
PM-1(0) PM-1(1) PM-1(2) ⋯⋯ PM-1(Q-1)]
(3)
SSIM(X,Y) = (2μxμy+C1) (2σxy+C2)
(μx2+μy 2+C1) (σx2+σy 2+C2) (4)
≪
μ μ σ σ σ
the contextual vibration data and baseline spectrogram image is tested for their ability to distinguish healthy, IRF, ORF and RED via Kruskal-
SSIM(X,Y) = (2μxμy+C1) (2σxy+C2)
(μx2+μy 2+C1) (σx2+σy 2+C2) (4)
≪
μ μ σ σ σ
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.8
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Bearing Vibration Normal
Time
Amplitude
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Bearing Vibration IRF
Time
Amplitude
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Bearing Vibration RED
Time
Amplitude
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-4 -3 -2 -1 0 1 2 3
Bearing Vibration ORF
Time
Amplitude
400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time Spectrogram of Healthy Bearing
Normalized Frequency ( rad/sample)
400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time Spectrogram of Inner Race Fault
Normalized Frequency ( rad/sample)
400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time Spectrogram of outer race fault
Normalized Frequency ( rad/sample)
400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time Spectrogram of roller element defect
Normalized Frequency ( rad/sample)
400 600 800 1000 1200 1400 1600 1800 2000 2200 2400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time
Normalized Frequency
( rad/sample)
Sl No: Healthy IRF RED ORF 1 0.9997 0.9997 0.9974 0.9988 2 0.9997 0.9992 0.9973 0.9990 3 0.9997 0.9994 0.9975 0.9987 4 0.9997 0.9993 0.9973 0.9945 5 0.9996 0.9997 0.9977 0.9948 6 0.9996 0.9996 0.9974 0.9987 7 0.9997 0.9994 0.9980 0.9992 8 0.9997 0.9996 0.9983 0.9990 9 0.9997 0.9993 0.9988 0.9989 10 0.9996 0.9990 0.9987 0.9991 11 0.9997 0.9994 0.9989 0.9992 12 0.9997 0.9994 0.9992 0.9979 13 0.9997 0.9993 0.9990 0.9959 14 0.9997 0.9993 0.9987 0.9951 15 0.9997 0.9992 0.9985 0.9962 16 0.9997 0.9991 0.9988 0.9981 17 0.9997 0.9990 0.9989 0.9938 18 0.9996 0.9991 0.9985 0.9937 19 0.9997 0.9994 0.9983 0.9959 20 0.9996 0.9992 0.9979 0.9936 21 0.9997 0.9972 0.9975 0.9946 22 0.9997 0.9966 0.9970 0.9898 23 0.9997 0.9950 0.9974 0.9917 24 0.9997 0.9948 0.9972 0.9893 25 0.9997 0.9938 0.9972 0.9875 26 0.9997 0.9932 0.9972 0.9818 27 0.9997 0.9930 0.9970 0.9717 28 0.9996 0.9926 0.9963 0.9852 29 0.9996 0.9920 0.9957 0.9880 30 0.9996 0.9974 0.9927 0.9795
0.975 0.98 0.985 0.99 0.995 1
HEALTHY IRF RED ORF
Four Feature classes of bearing vibration data
SSIM of spectrogram co-efficients
Box Whisker Plot
, MoASoS and selected classifiers, Measurement,
Sl No: Healthy IRF RED ORF 1 0.9960 0.9887 0.9954 0.9964 2 0.9985 0.9866 0.9946 0.9973 3 0.9986 0.9882 0.9951 0.9959 4 1.0000 0.9864 0.9953 0.9958
Source Sum of Squares (SS)
Degree of Freedom (DF)
Mean Square (MS)
Chi-Square value (H)
Probability value (p)
Columns 89438.1 3 29812.7 74.59 4.43693x10-16
Error 53251.4 116 459.1
Total 142689.5 119
