Background
III. A NEW PQ Classification Algorithm
Overview of the Algorithm
Theoretical Background
In pattern recognition applications, feature extraction are usually based on
some form of time-frequency representations (TFRs). As shown in the figure below, there are
infinity number of TFRs corresponding to one given signal. Our task is to find out one
TFR that fits our classification goal best.
A TFR of a given signal is nothing but a certain type of description of the time and frequency
related information about the orignal signal. Different descriptions come from different underlying
functions. Here for our classification goal, we don't necessarily need the accurate time-frequency
description of the signal, just like the spectrogram does. Instead, we need design certain TFR that
maximizes the separability of the signals from different classes.
Time-frequency ambiguity plane has been shown to be a good base for generating desired
class-dependent TFRs,
TFR = Fourier Transform {Ambiguity Plane .* Kernel}.
In the feature extractions of our proposed algorithm, the class dependent
TFR is generated using a certain kernal function that has class-dependent properties.
Artificial neural networks (ANN) have been shown to be a very effective tools for pattern recognition
applications. In this project, ANN will be used as the classifier, accepting extracted features and outputing classification results.
Implementation Procedures
Lowpass filtering and resampling
As depicted in the figure above, the first step is to pass the original signal through a Lowpass filter and resample the signal with a downsampling rate 8. By downsampling, the signal dimension has been reduced greatly, which leads to a dramatic reduction of the computation complexity. In addition, electrical noise has also been attenuated. Using Lowpass filter is to avoid aliasing during downsampling. After this step, a new 160-point signal that keeps the signature of the original signal is obtained.
Calculating instantaneous autocorrelation function
Now we calculate the instantaneous autocorrelation function R[n,t] for the signal x,
If we express an example voltage signal as V=[v1 v2 v3 … vn-2 vn-1 vn],
The instantaneous autocorrelation function (IAF) will be,
In our case, n is equal to 160.
Calcutating the ambiguity plane
The time-frequency ambiguity plane of the original signal can be obtained by taking Fourier transform on the IAF as follows,
The ambiguity plane has very desirable properties for classification.
An individual location in this plane captures "global" information about the
time frequency structure of the signal. Points on the axis h=0 result in time-frequency structure that is stationary in time.
Similarly, points on the t=0 axis correspond to a time-frequency structure that is stationary in frequency.
Before we describe how to select features vectors, let's look at the ambiguity planes corresponding to different classes of signals in
the figure below. We find the ambiguity planes corresponding to different classes show different patterns.
In each of
the following 6 figures, the first subfigure shows the disturbance signal, the second subfigure shows the FFT of the given signal,
and the third one shows the corresponding ambiguity plane.
Applying the modified Fisher's discriminant ratio kernel (MFDK)
We design and use a Modified Fisher's Discriminant Ratio kernel (MFDK) to get those N locations.
Here the mfdk kernel is designed by a number of training example signals from each class with the equation as follows,
The overall idea of this method is shown in the following figure. We are trying to get a small number of important
data set, which are essential for the classification purpose, and ignore all other points on the plane.
Training a feedforward neural network and implementing classification
We choose an artificial neural network (ANN) with a 3-layered feedforward structure as the classifier. The inputs of the ANN are features extracted by the scheme presented in the last section. The outputs of the ANN determine which class the disturbance event belongs to. The training algorithm we used is error
backpropagation algorithm, and in the the neuronal model the activation function is bipolar sigmoid.
Fuzzy Classification Strategy
We have proposed a new classification algorithm for power quality disturbance signals. However, the philosophy behind this algorithm is to take in a disturbance signal and classify the signal to one of the disturbance classes. We call it the crisp classification approach. That means we always assume that there is only one type of disturbance in a 5-cycle waveform.
In some cases, however, there are multiple types of disturbances happening at the same time. The crisp classification strategy does not work very well for these combined events. Based on the same feature extraction scheme, we are exploring a fuzzy classification approach that will provide us more accurate, more comprehensive, and more useful information for the power system under our monitoring. The basic idea is as follows. For a given piece of 5-cycle disturbance waveform, we will give a soft evaluation of the disturbance component in this waveform. Specifically, we will determine the grade (i.e. membership function) corresponding to each disturbance class. The grade of an arbitrary class A will show us to what extent the waveform includes the disturbance of class A. For example, if we input a 5-cycle disturbance waveform, we may get an output like this -- "Harmonics 2.5, Capacitor fast switching 7.5, Capacitor slow switching 5.5, Sudden sag 0.5, Sag gradual decay 3, Swell 0.5". Thus we know this short duration disturbance is mostly capacitor switching event. But it also has slight harmonics and sag gradual decay components. This strategy serves better the goal of monitoring, analyzing, and evaluating the power quality of a given power system. We are exploring the details of the fuzzy classification idea. Multiple neural networks and statistical signal processing techniques are employed.
