In order to perform an effective fault diagnosis, input features (or vectors) must be selected appropriately. Input features should contain the critical information of each fault condition. The raw data or signal directly from sensors contains high noise and redundant information, and create the problem of dimensionality. The variation in raw signal is too small to be detected, therefore the comparison of raw data of faulty and healthy IMs is not effective in order to determine whether the component is behaving normally or exhibiting signs of a failure. The feature extraction has to be performed to convert a raw signal into compact form that can accentuate the changes and reveal the significant information or certain characteristics of the signal in order to correctly predict the machine’s health. Moreover, in order to perform the intelligent fault diagnosis, it is not possible to feed the raw data directly into the classifier for training and testing purpose because the handling
of large data is a challenging task. The feature extraction also provides reduced data sets for an effective application of the intelligent fault diagnosis.
Common statistical features such as standard deviation, skewness, and kurtosis have been used for time domain analysis. Tran et al., 2009 and Nguyen et al. 2008 used the skewness, kurtosis, variance, and crest factor of time domain vibration signals for the mechanical fault detection of IM. Bordoloi and Tiwari (2013) utilized the standard deviation, skewness and kurtosis based on time domain data, for the fault classification of gears and showed that these three features can effectively classify all gear faults. In other study, Gangsar and Tiwari (2014) have also used standard deviation, skewness and kurtosis in order to diagnose faults in the rolling element bearings and showed that the bearing faults can be successfully diagnosed using these features.
Therefore, to start with just three most preferred statistical features, i.e. the standard deviation, skewness and kurtosis are chosen to perform the comparative investigation of the vibration and current signals for the diagnosis of IM faults in this chapter. Three statistical parameters are explained as follows:
Standard Deviation (σ): The standard deviation is a dimensional quantity that measure variability of the distribution or fluctuation of signals from the mean. This is a measure of the effective energy or power content of signals. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. The standard deviation of a data set is the square root of its variance.
The standard deviation is the second standardized moment (or normalized central moment) of the data and is expressed as
2
2 1
1
1 ( )
N i i
N x
(4.1)Where,
x
i is the amplitude, N is the number of data points in the sample, 1 is the first moment or mean and 2 is the second moment or variance.Skewness (χ): The skewness is a non-dimensional feature that measure the degree of asymmetry of the probability distribution (or shape of the distribution) of a real valued variable around its mean. The skewness value can be positive or negative, or even undefined. Qualitatively, a negative skew indicates that the tail on the left side of the probability density function is longer than the right side and the bulk of the values (including the median) lie to the left of the mean. A positive skewness indicates a distribution with an asymmetric tail extending towards more positive values.
A zero value indicates that the values are relatively evenly distributed on both sides of the mean, typically but not necessarily implying a symmetric distribution. The skewness is the third standardized moment of the data and is expressed as
3 1
3 1
3 3
1 ( )
N i i
N x
(4.2)
where, 3 is the third moment and is the standard deviation.
Kurtosis (к): The kurtosis is a non-dimensional feature that reflects the flatness or the spikiness of the distribution of signal. It provides a measure of the size of the tails of the distribution and is used as an indicator of major peaks in a set of data. Its value is very high for faulty machines due to the spiky nature of the signals. It is standardized fourth moment of the data and is expressed as:
4 1 1
4
4 4
1 ( )
N i i
N x
(4.3)
where, 4 is the fourth moment and is the standard deviation..
The features extracted from the time domain vibration and current signals (i.e., x(t)) in this chapter are described in Table 4.1. The standard deviation, skewness and kurtosis are calculated from 2000 points available in one data set, which is obtained from Experiment 1. In Experiment 1, 300 raw data sets are collected, so 3×300 feature data sets are extracted for each IM fault and operating condition.
Figure 4.1 and Figure 4.2 show time domain features from the vibration and current signals of BF at 40 Hz and T3. In addition, the scatter plot or a cluster of three statistical features of the acquired vibration as well as current signals from mechanical and electrical faults (at 40 Hz speed and for the high load) are also added in Figure 4.3 and Figure 4.4, respectively. Figure 4.3 shows that features are well clustered in the case of mechanical faults using vibration signals; however, when these faults are considered with current signals the features are not clustered so well. Figure 4.4 shows that in the case of electrical fault using vibration signals, these features are not clustered
well; however, when these faults are considered with current signals the features are well clustered.
It is noted that features, which are produced by current signals, are very difficult to cluster in the case of mechanical faults and features from vibration signals are very difficult to cluster in case of electrical faults. It is evident from scatter plots of the vibration and current features that values of features are linearly inseparable, i.e. apparently it is difficult to find out a straightforward relationship between the features and the corresponding fault type. Therefore, there is a need for fast or automated feature data interpretation techniques, like the artificial intelligence. The SVM is adopted here for automated fault diagnosis of IMs using the vibration and current signals. Now in the next section, a comparative analysis of the vibration and current signals is performed in the mechanical and electrical fault diagnosis based on the SVM.
Table 4.1 The statistical feature parameters in time domain Signals Feature parameter for each
of the signals (time domain) Vibration in x-axis,
Vibration in y-axis, Vibration in z-axis, Current in Phase A, Current in Phase B, Current in Phase C
Standard deviation (σ), Skewness (χ)
and Kurtosis (к)
Figure 4.1 Time domain features of acquired vibration signal for BF at 40 Hz and T3
Figure 4.2 Time domain features of acquired current signal for BF at 40 Hz and T3
0 100 200 300
5 6 7
Standard deviation
x-axis
0 100 200 300
10 15
y-axis
0 100 200 300
6 8 10
z-axis
0 100 200 300
-0.5 0 0.5
Skewness
0 100 200 300
-0.2 0 0.2
0 100 200 300
-0.5 0 0.5
0 100 200 300
2 4 6
Data set number
Kurtosis
0 100 200 300
1 2 3
Data set number
0 100 200 300
2 4 6
Data set number
0 100 200 300
0.18 0.19 0.2
Standard deviation
Phase A
0 100 200 300
0.19 0.2
0.21 Phase B
0 100 200 300
6 8
10 Phase C
0 100 200 300
-0.05 0 0.05
Skewness
0 100 200 300
-0.05 0 0.05
0 100 200 300
-0.05 0 0.05
0 100 200 300
1.5 1.55
Data set number
Kurtosis
0 100 200 300
1.5 1.55
Data set number
0 100 200 300
1.5 1.55
Data set number
(a) Mechanical fault with vibration signal
(b) Mechanical fault with current signal
Figure 4.3 Typical scatter plots for mechanical faults using three features ( , , and ) at 40 Hz for T3
3 4 5 6 7 8 9 10 11 -0.5
0 0.5
1
2 4 6
Kurtosis
ND BF UR BR MR
Skewness
Standard deviation
0.185 0.18 0.195 0.19
0.205 0.2
-0.05
0
0.05 1.46
1.48 1.5 1.52 1.54
Kurtosis
ND BF UR BR MR
Standard deviation
Skewness
(a) Electrical fault with vibration signal
(b) Electrical fault with current signal
Figure 4.4 Typical scatter plots for electrical faults using three features ( , , and ) at 40 Hz for T3
4 2 8 6
12 10 16 14
-1 0 1 2
3 4 5 6 7 8
Standard deviation
Kurtosis
ND BRB PUF1 PUF2 SWF1 SWF2
Skewness
0.2 0.18 0.24 0.22
0.28 0.26 0.3
-0.05 0
0.05 1.5
1.55 1.6 1.65 1.7
Standard deviation
Kurtosis
ND BRB PUF1 PUF2 SWF1 SWF2
Skewness