Journal of Electrical and Computer Engineering

Volume 2018, Article ID 9529870, 10 pages

https://doi.org/10.1155/2018/9529870

## Change Point Detection for Piecewise Envelope Current Signal Based on Wavelet Transform

^{1}China Electric Power Research Institute, Wuhan 430074, China^{2}School of Electrical Engineering, Chongqing University, Chongqing 400044, China

Correspondence should be addressed to Huaiqing Zhang; nc.ude.uqc@gniqiauhgnahz

Received 15 August 2017; Revised 22 April 2018; Accepted 14 May 2018; Published 3 July 2018

Academic Editor: Gorazd Stumberger

Copyright © 2018 Haiyan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

One of the key issues of the accurate parameters analysis for the piecewise envelope current signal is to position the change point precisely. Discrete wavelet transform (DWT) modulus maxima method can detect change point, but the detection window of DWT will cause suspicious change point. Besides, the amount of calculated data is very large in actual process of envelope current signal. Therefore, in this paper, the envelope is used instead of the original sampling data for DWT so as to reduce the calculation amount. What is more, combined with the sliding dislocation window method, the change point can be located accurately and the pseudo-change point can be eliminated. The simulation results as well as the electric locomotive current and forging machine current examples show that it is feasible to detect the change point precisely through the proposed method, which provides possibilities for real-time online monitoring of change point.

#### 1. Introduction

The wide application of semiconductor electronic devices and distributed powers has caused harmonic content in power system and serious distortion of voltage and current waveform [1, 2]. The equipment such as fluorescent lamp and rolling machine will cause harmonic current. The running machine like electric locomotive is prone to produce oblique envelope current. Besides, the operation of electric-arc furnace and cogging mill can lead to parabolic envelope current and exponential envelope current, respectively [3–5]. The four typical envelop signals are as follows:(i)Harmonic current .(ii)Oblique envelope current .(iii)Parabolic envelope current .(iv)Exponential envelope current .

The traditional electric energy meter usually works in sinusoidal linear load condition with high precision. However, in practical terms, the current signal often has different envelopes, which is the piecewise envelope current signal actually. The harmonics and the varying amplitudes in the current signal will cause difficulties for accurate measurement of conventional energy meter [6, 7]. In order to overcome this defect, the precise analysis of signal parameters is particularly significant. Moreover, the harmonics and nonstationary amplitudes have a serious impact on power quality. Therefore, this paper focuses on the change point detection of piecewise envelope current signal.

In general, change point analysis may be performed in either parametric or nonparametric approaches. These approaches follow some statistical framework, including CUSUM (cumulative sum), GLR (generalized likelihood ratio), and the change finder. Generally, these approaches have limitation, that is, heavily relying on prespecified parametric models such as probability density models and state-space models [8]. Therefore, these methods are not flexible enough in real-world change point detection. On the other hand, wavelet transform (WT) is a promising approach for change point detection, and this paper uses discrete wavelet transform (DWT) to analyze the signal.

DWT has the ability of multiresolution analysis. It can represent local information in both time domain and frequency domain [9, 10]. It has wide applications in signal processing, image processing, digital communications, etc. According to [11–14], wavelet transform modulus maxima method has proven to be an effective approach in singularities and transient phenomena detection of image processing, statistical chatter detection, damage detection, etc. The signal change point can be determined through DWT modulus maxima method. However, the amount of calculated data is very large and the time of data processing is too long in actual process of envelope current signal, which causes difficulties for real-time online detection of change point. What is worse, DTW will result in suspicious change points at both ends of the detection window.

Therefore, this paper positions the change point through DWT of the envelope of the current signal (not the original sampling data), which aims to reduce the calculation time. Besides, The DWT modulus maxima method is applied to detect the change point, and the sliding dislocation window is introduced to eliminate the suspicious change point. Furthermore, the simulation for dynamic current signal is applied to analyze the performance of the proposed method. An electric locomotive current signal and forging machine current are analyzed in the end.

#### 2. The principle of Discrete Wavelet Transforms and Modulus Maxima

##### 2.1. Discrete Wavelet Transform

Wavelet transform includes continuous wavelet transform and discrete wavelet transform. They both can be used to detect the signal change point. However, the amount of calculated data of continuous wavelet transform is too large, which results in a long computing time. Therefore, the discrete wavelet transform is suitable for online calculation. Discrete wavelet transform decomposes the dynamic signal into the various scales of frequency bands by multiresolution analysis [15, 16].

The DWT of a signal* f*(*t*) takes this form

Furthermore, in the multiresolution analysis process, a give n signal* f*(*t*) can be completely decomposed based on scaling function *φ*(*t*) and wavelet function *ψ*(*t*). Hence the* J*-level DWT representation of* f*(*t*) can be defined as

where* a*_{j,k} is the approximation coefficients at level J.* d*_{j,k} is detail coefficients. The decomposition level of discrete wavelet transform* n* should satisfy , where is the fundamental frequency of the signal and is the sampling frequency. The frequency bands corresponding to the DWT signal are shown in Figure 1.