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In Fig.4, the sample point of 689 can be considered as the violating fault
inception point as it violated both the T 2 and Q control limits. In the section
before point 689, which is also referred to the pre-fault signal, the calculated
results of T 2 and Q statistics are both under the control limit. The section
after the inception point is named post-fault signal, with high values of statistic
results. Then the unusual event can be detected by these high values of statistics.
A effective set of multiple variate control charts is therefore a T 2 chart on the five
dominant orthogonal PCs plus a SPE or Q chart. Fig.4 also indicates that these
statistics respond sharply to the abrupt changes in the voltages and currents
caused by transmission line faults.
For a verification of the PCA model working under noisy condition, the model
based on the noisy signals was identified next. In order to provide a fair compar-
ison, the same five PCs were retained in the model. Noise was generated based
on the random normal distribution, with 5% to 30% of the signal amplitude as
the fluctuation range at the interval of 5%. Fig.5 presents the entire situation
under the 10%(left part with logged ordinate) and 15%(right part with linear
ordinate)noisy condition. This indicates that the value of T 2 decrease with the
increasing amplitude of the added noise. Some spikes appeared when the noise
amplitude was bigger than 20% of the signal amplitude. The details were given
in Table.1. In general, the error caused by different range of random noises were
under 1% which was acceptable. These have led to a conclusion that the statis-
tics control limit work well in the charts under the noise condition less than 30%
except some fluctuations added.
Tabl e 1. Table of PCA monitoring error under different noise condition
Noise Condition Inception Point PCA Result Error
5%
689
703
0.3499%
10%
689
702
0.3249%
15%
689
714
0.6248%
20%
689
712
0.5749%
25%
689
728
0.9748%
30%
689
735
1.1497%
From the monitoring scheme, it is clear that PCA is capable of finding the
accurate fault inception point. Due to that PCA modelling only based on the
normal data set, any type of disturbance would result in a change in the covari-
ance structure of the observation data, which will be detected by the high value
of statistic charts. Therefore, the modelling results are able to find the violate
point, and are independent of the fault type. In the following part, the focus is
on the feature extraction according to the faults. The diagonal elements of ma-
trix S (intermediate result of PCA) consists of the eigenvalues of the covariance
matrix of the data sets, which are uncorrelated and independent, thus can be
considered as the main features of the certain fault type.
The second stage of monitoring scheme is to use SVM to classify the fault type.
The SVMs were set up using supporting vector machine toolbox in MATLAB.
 
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