Harmonics Based Clustering Patterns Featured by the Final Nodes of a WPT tree


Decompositions1 of electric waveforms relying on the Wavelet Package Transform (WPT) provide numerous advantages but require a significant amount of computa-tional resources (runtime and memory). A tree topology with 7 levels, relying on a wavelet mother from Daubechies family with a filter of 28 components was studied. Studies on artificial waveforms polluted with a single harmonic were made firstly, revealing interesting aspects relative to clusters of nodes affected by the same group of harmonic orders. Different pairing patterns of odd and even harmonics were revealed, along with decisions on nodes being more relevant for certain harmonics. Nodes clustering patterns with re-spect to the most significant odd harmonic orders were de-duced as well. These patterns consist in sequences of 4, 8 and 32 nodes. Similarities in harmonic weights associated to node clustering patterns based on the most significant har-monic orders were also derived and discussed. The harmon-ics-nodes clustering properties were afterward tested with respect to capabilities related to time-frequency identifica-tion of most common harmonic orders magnitudes modifi-cation. Multi-harmonic artificial test signals, similar to those from power applications were used to validate the original WPT based algorithms relying on the special clustering and patterns-related properties derived by authors. The results were commented and conclusions were drawn. images