We applied the proposed PCA visualization method to the vibration data collected from the rotor
kit, shown in Figure 50.
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The testbed consists of a shaft with length of 470 mm coupled with a flexible coupling to reduce
the effect of the high frequency vibration, two discs and three bearing housings. Two
accelerometers are mounted at bearing housing along x and y directions. Channel 1 and channel 2
data were obtained from accelerometers in the y and x directions, respectively. All the experiments
are conducted at 1,700 rpm.
As shown in Table 2, 11 features, including commonly used time domain features and
frequency domain features in rotor machines, were extracted for each channel. After extracting the
features, the PCA algorithm was applied to the feature data and we obtain the results shown in
Tables 3 and 4.
Table 2: Extracted features
CH1 (Y direction) CH2 (X direction) Feature Variance Variance Mean Mean RMS RMS Kurtosis Kurtosis Skewness Skewness SRA SRA
Peak to peak Peak to peak 1X amplitude 1X amplitude 2X amplitude 2X amplitude
1X phase 1X phase
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Table 3: PCA result (eigenvectors)
PC1PC2PC3PC4PC5PC6PC7PC8PC9 PC 10 PC 11 PC 12 PC 13 PC 14 PC 15 PC 16 PC 17 PC 18 PC 19 PC 20 PC 21 PC 22 CH1- variance -0.101 0.462 -0.030 -0.019 0.008 -0.348 0.336 0.290 0.137 -0.152 -0.135 0.476 0.032 0.023 0.079 0.369 0.128 -0.055 -0.004 -0.072 0.019 -0.012 CH2- variance -0.147 -0.085 0.004 -0.004 -0.004 0.021 -0.004 -0.054 0.272 0.021 0.330 0.030 -0.353 0.594 -0.069 0.241 0.023 0.340 -0.064 0.350 -0.012 0.007 CH1-mean -0.006 -0.004 -0.002 -0.005 -0.005 0.002 -0.005 0.003 0.013 -0.007 0.011 -0.026 0.020 0.012 -0.138 0.197 -0.537 -0.404 -0.676 0.124 0.125 -0.040 CH2-mean 0.012 0.007 0.002 0.001 -0.001 -0.005 0.005 -0.006 -0.012 0.017 -0.031 0.014 -0.003 -0.036 0.105 -0.055 -0.028 0.639 -0.511 -0.554 -0.067 -0.039 CH1-RMS -0.062 0.215 -0.013 -0.009 0.003 -0.100 0.100 0.032 0.067 -0.191 0.088 0.114 -0.008 0.063 -0.334 -0.600 -0.124 0.124 0.013 0.039 0.554 0.228 CH2-RMS -0.101 -0.058 0.003 -0.003 -0.003 0.003 0.010 -0.004 0.178 0.012 0.210 0.039 -0.137 0.297 0.032 -0.191 0.027 -0.372 0.105 -0.508 0.094 -0.589 CH1- 1X amplitude 0.022 0.364 -0.022 -0.006 0.007 -0.056 0.045 -0.094 -0.077 -0.594 0.093 -0.617 -0.223 -0.030 0.169 0.129 -0.046 -0.006 0.054 -0.062 0.006 -0.012 CH2- 1X amplitude -0.020 -0.013 0.002 0.001 0.002 -0.056 0.059 0.106 0.043 0.098 -0.078 0.035 0.069 0.169 0.815 -0.246 -0.402 0.049 0.096 0.150 0.087 0.039 CH1- 2X amplitude -0.039 -0.018 -0.001 -0.005 -0.006 0.012 -0.010 -0.019 0.087 -0.019 0.211 0.109 0.065 -0.191 -0.231 0.239 -0.679 0.216 0.469 -0.203 -0.116 -0.012 CH2- 2X amplitude -0.120 -0.077 -0.001 -0.004 -0.005 0.038 -0.014 -0.047 0.254 -0.086 0.641 0.170 -0.044 -0.573 0.250 -0.031 0.177 -0.043 -0.145 0.113 0.055 0.007 CH1- Kurtosis 0.153 0.110 -0.001 0.011 0.007 0.077 -0.091 -0.332 -0.228 0.023 -0.196 0.378 -0.747 -0.166 0.070 -0.058 -0.097 -0.046 0.022 0.000 -0.007 -0.009 CH2- Kurtosis -0.076 -0.066 -0.004 0.000 -0.004 -0.253 0.233 0.525 0.022 0.438 -0.003 -0.372 -0.442 -0.231 -0.099 -0.062 -0.036 0.013 0.019 0.004 0.004 0.001 CH1- Skewness -0.269 -0.469 0.019 -0.001 -0.008 0.162 -0.178 0.501 -0.110 -0.547 -0.186 0.173 -0.148 -0.026 -0.003 -0.015 -0.017 0.014 -0.003 0.006 -0.019 -0.005 Ch2- Skewness 0.005 -0.023 -0.009 0.009 0.006 -0.166 0.108 0.099 -0.823 0.035 0.471 0.111 0.071 0.173 0.020 0.019 0.005 -0.012 -0.010 -0.016 -0.017 0.011 CH1-SRA -0.035 0.193 -0.012 -0.007 0.003 -0.098 0.096 0.036 0.049 -0.134 0.031 0.071 0.034 -0.001 -0.144 -0.467 -0.106 0.021 -0.112 0.254 -0.732 -0.222 CH2-SRA -0.069 -0.040 0.002 -0.002 -0.003 0.005 0.005 -0.007 0.139 0.008 0.135 0.017 -0.109 0.199 0.039 -0.079 0.006 -0.320 -0.012 -0.381 -0.320 0.739 CH1- Peak to peak-0.711 0.443 -0.007 -0.008 -0.007 0.318 -0.338 0.044 -0.142 0.237 -0.038 -0.041 0.021 -0.031 0.016 0.007 0.004 -0.001 0.000 -0.001 0.000 0.000 CH2- Peak to peak-0.569 -0.342 0.013 -0.005 0.000 -0.350 0.385 -0.488 -0.062 -0.049 -0.184 -0.064 0.018 -0.077 -0.003 0.001 -0.005 0.002 0.005 0.006 0.003 0.000 CH1- 1X phase -0.016 0.009 0.172 0.684 0.706 -0.047 -0.043 0.008 0.018 -0.004 0.005 0.000 0.004 -0.001 -0.005 0.003 -0.005 -0.002 -0.003 -0.001 0.000 0.000 CH2- 1X phase 0.002 -0.029 -0.306 -0.644 0.700 0.020 -0.007 -0.002 -0.003 0.011 -0.001 -0.003 -0.003 -0.001 0.001 0.000 0.000 0.001 0.000 -0.002 -0.001 0.000 CH1- 2X phase -0.010 -0.039 -0.676 0.206 -0.098 -0.490 -0.497 -0.025 0.038 0.002 -0.006 0.000 0.006 0.001 0.003 -0.002 0.003 0.001 0.000 0.000 0.001 0.000 CH2 -2X phase 0.002 0.010 0.646 -0.272 0.042 -0.511 -0.494 -0.018 0.028 -0.002 0.004 -0.002 0.003 -0.003 0.002 -0.002 0.003 -0.001 0.001 0.001 0.000 0.000
We applied the proposed PCA visualization technique to this PCA result data, which is difficult to
analyze in a table form. However, Figures 51 and 52 show the result of the proposed visualization.
Table 4 shows that the sum of the proportion of eigenvalues from PC1 to PC4 is over 90% at 90.9.
In the visualization result in Figure 51, it can be seen that more than 90% of the data can be
explained from PC1 to PC4. In this case, the corresponding principal component nodes on the right
62
largest height in the original feature node on the left, it can be considered that the ‘peak-to-peak’ is the most dominant feature in the original data.
Table 4: PCA result (eigenvalues)
Eigenvalue Proportion (%) PC1 4.6687 44.1 PC2 2.5659 24.2 PC3 1.4624 13.8 PC4 0.9347 8.8 PC5 0.6395 6.0 PC6 0.1363 1.3 PC7 0.1060 1.0 PC8 0.0344 0.3 PC9 0.0197 0.2 PC10 0.0089 0.1 PC11 0.0058 0.1 PC12 0.0039 0.0 PC13 0.0022 0.0 PC14 0.0016 0.0 PC15 0.0003 0.0 PC16 0.0001 0.0 PC17 0.0001 0.0 PC18 0.0001 0.0 PC19 0.0000 0.0 PC20 0.0000 0.0 PC21 0.0000 0.0 PC22 0.0000 0.0
63
Figure 51: Result of PCA visualization
(a) (b)
64
Based on the results of the visual analysis, we compared the results of dimension reduction of the
data along the direction of PC1 and PC2 (Figure 53), which have the largest proportions, and the
results of feature extraction with ‘peak-to-peak’ (Figure 54), which is considered to be the best
feature. As shown in Figures 53 and 54, we can figure out that the data clusters of each group are
grouped similarly. In other words, peak-to-peak in the original features contributes most to the
reduced feature space.
65
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5 CONCLUSIONS AND FUTURE RESEARCH
In this thesis, the machine learning toolbox and the PCA visualization were proposed. The machine
learning toolbox is capable of plotting raw data, selecting hand-crafted features based on an expert
knowledge, followed by a dimension reduction step if necessary. In addition, the various machine
learning algorithms are provided for the classification to diagnose current machine health
conditions. Therefore, it can quickly provide engineers a guideline to determine suitable features
and data-driven PHM algorithms. In the developed GUI software, the engineer can select the
desired features and algorithms, and visually check and compare the results so that the final
decision is made based on the experience or opinion of the engineer. In future research, we need to
develop a system that automatically selects features and algorithms by generating a indicator that
can determine the degree of classification.
PCA visualization so far has not yet been well done despite the fact that the eigenvector and
eigenvalue of PCA are important information. It was used only to reduce the dimension of high-
dimensional data, or the user had to view and interpret the result table. However, new PCA
visualization methods have made it easier for users to understand and analyze PCA results more
easily and intuitively. Users can interactively search for information they want. In addition, the
development of visualization using Web-based JavaScript has the potential to be applied to web-
based real-time monitoring platforms. The interest in machine learning algorithms such as PCA,
which was discussed in this thesis, is increasing, but it is difficult to understand the analysis results
without the help of an expert. Therefore, further works are needed to apply visualization techniques
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