Optimized use of Wavelet Packet Trees for the analysis of electrical waveforms

Abstract

Wavelet packet trees represent a topic which grows in popularity when it comes to analysis of electrical waveforms. It allows for time-frequency analysis providing information on narrower ranges of frequency (as compared to the faster Discrete Wavelet Decomposition), but the computational resources are significantly greater than that involved in other types of wavelet-based analysis. In order to allow for this type of analysis to be usable in real-time applications, that is – to reduce the runtime, original algorithms were conceived and tested. In the first part of this work, previously implemented algorithms are briefly described, along with their pros and cons. Afterward, a new runtime optimization algorithm is proposed. Details on data structures, workflow, tests and study of errors are provided. This algorithm diminishes with up to 59% the runtime required by the application of the superposition theorem in order to evaluate the contribution of clustered harmonics using WPT.

Analyzing the Influence of Harmonic Parameters on Accuracy Indices When Applying Wavelet Transform

“…The extended study presented in this paper addresses the errors which characterize the determination of 4 types of harmonic signals, generated from the following pairs of harmonic orders: (3,5), (7,9), (15,17) and (31,33).…”

“…Table II shows the 4 sets of harmonic orders (HO) that were used for this analysis as well as the nodes that were affected by those sets of harmonics. The dominant harmonics and nodes [7] are represented with bold fonts.…”

“…The authors have previously studied a specific type of WT called Wavelet Packet Transform (WPT) that was proposed in 1992 [3]. WPT provides full harmonic spectrum but suffers from decimation phenomenon [4]- [7]. Detailed analysis of wavelet binary tree shown the best parameters (number of levels, wavelet mother, filter length) when applying WT.…”

“…The authors extensively studied a specific case of a wavelet tree with seven levels (T7) that uses a wavelet mother from Daubechies family and filter length of 28 ("db14") [6]. One of the important conclusions was that nodes from the bottom level of the wavelet tree exhibits cluster patterns [7]- [10]. This means that nodes can be grouped in clusters of 2, 4 or 8 nodes where each group is affected by 2, 4 and 8 harmonics respectively.…”