Application of the wavelet multifractal analysis of vibration signal for rotating machinery diagnosis

The paper proposes the WLMF (Wavelet Leaders Multifractal Formalism) method enabling the adoption of multifractal parameters mapped by vibration signal log-cumulants as diagnostic features, in the procedure of automatic classification of assembly errors and wear of demonstration gearbox. In the analysis of vibration time signals, initially, a multifractal formalism was used based on the study of time series local regularity, which is measured by Holder exponents. The presented test results relate to time-frequency multifractal analysis, the starting point of which was a continuous wavelet transform. Discrete wavelet transform allowed for much better grounded multifractal formalism and more accurate estimation of multifractal parameters using wavelet leaders, which are determined based on wavelet coefficients and are representatives of Holder exponents.