Wavelet packet tree selection for vibration data

Wavelets are powerful tools for extracting features from vibration data. Wavelet packet tree optimisation algorithms such as those by Coifman and Wickerhauser (IEEE Trans. Information Theory, vol. 38, pp. 713-718, 1992) establish the best basis for signal decomposition. Although most of these algorithms are suitable for signal compression, their use for pattern recognition results in at least two problems: as signals from the leaves of the trees are used as features, the pattern recognition system has to deal with extracted vectors of different length. This variability in size prevents the use of common pattern recognition methods. During our investigation it also became evident that among the same class of signals the optimized tree can differ considerably from one signal to another. A methodology to overcome these problems is proposed in this paper. An algorithm, called the gap selection algorithm (GSA) is presented which utilizes the level of improvement associated with each possible optimized tree, given all the samples in the training set. In essence a clustering approach on the levels of improvement is used for best tree selection. The proposed methodology has been successfully tested on mechanical vibrations from ball bearings. These results are presented and discussed