124 PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 89 NR 2b/2013 Paweł EWERT, Czesław T. KOWALSKI, Marcin WOLKIEWICZ Wroclaw University of Technology, Institute of Electrical Machines, Drives and Measurements The application of wavelet analysis and neural networks in the diagnosis of rolling bearing faults in induction motors Abstract. The paper describes a monitoring method of damage detection in induction motor rolling bearings. The method is based on wavelet transform analysis of vibration. The possibility of the application of neural networks to detect bearing faults was presented. The quality of bearing faults detection and identification methods was tested experimentally. The experiments have been conducted on induction motors with bearing faults. The correctness of the proposed methods has been confirmed by satisfactory tests results. Streszczenie. W pracy przedstawiono metodę monitorowania stanu łożysk tocznych silników indukcyjnych opartą na analizie falkowej. Omówiono dyskretną transformatę falkową oraz jej uogólnienie w postaci pełnego przekształcenia falkowego. Przedstawiono możliwość zastosowanie sieci neuronowych do wykrywania uszkodzeń łożysk tocznych. Eksperymentalnie sprawdzono możliwość wykrywania oraz identyfikowania uszkodzeń poszczególnych elementów konstrukcyjnych łożysk. Przedstawiono przykładowe wyniki badań laboratoryjnych. Dokonano oceny skuteczności wykrywania uszkodzeń łożysk tocznych w silnikach indukcyjnych przy wykorzystaniu analizy falkowej przyspieszenia drgań oraz sieci neuronowych. (Zastosowanie analizy falkowej i sieci neuronowych do diagnostyki łożysk tocznych silników indukcyjnych) Keywords: condition monitoring of rolling bearings, induction motors, wavelet analysis, neural networks. Słowa kluczowe: monitorowanie stanu łożysk tocznych, silniki indukcyjne, analiza falkowa, sieci neuronowe. Introduction The non-stationary character of the available diagnostic signals results in the fact that in recent years wavelet analysis has been used more and more frequently used to detect fault symptoms in induction motors. The approach assumes that the diagnostic signal in the time domain can be decomposed to components of various time windows and various frequency bands, and the information obtained in this way can be presented in a time-scale domain. On account of the character of the frequency response, the approach is effective for both long, low frequency signals and short, high frequency signals. The wavelet approach has advantage over the traditional Fourier transform in the case of the analysis of incoherent and short-impulse signals (non-stationary processes). The Fourier transform brings the change of signal representation from the time domain to the frequency domain, which results in a loss of time information and in consequence interpretation difficulties. The wavelet transform is free from this disadvantage as the signal it represents is shifted and rescaled in relation to the so called wavelet matrix. This allows for signal frequency information analysis during its development in time. The ability to represent the signal simultaneously in the time and frequency domains is a very important advantage of wavelet transform [1], [2]. It turns out that non-stationary signals with sharp changes may be easier recognized when an irregular wavelet is used than in decomposition to regular sinusoids [3]. This is why the choice of appropriate type of wavelet is so important when the wavelet analysis is used. Currently the most commonly used wavelet in the diagnostics of induction motors is the Daubechies wavelet [4], [5], [6]. The article presents the results of the application of the wavelet analysis of vibration acceleration in detection of rolling bearing faults in mains-electricity powered induction motors. Wavelet analysis algorithms, available in the LabVIEW programming environment, were used in the research. In addition the article presents the possibility of using neural networks, based on the information obtained from the wavelet analysis in rolling bearings fault detection. Wavelet analysis – basic information Continuous Wavelet Transform (CWT) is defined by the following equation [1]: (1)           dt t t x b a x CWT b a * , ,  where: a – scale coefficient, b – displacement coefficient, * – complex function conjugate, and (2)          a b t a t b a   1 , where: a,bR i a0. In the case of continuous wavelet transform, it is assumed that the scale coefficient a and the displacement coefficient b are continuous functions. When the transform parameters are discreet functions, transformation (1) describes the so called Discrete Wavelet Transform (DWT). Since it is assumed that the scale coefficient a and the displacement coefficient b change at multiplicity 2, displacement (1) takes the following form [2]: (3)     1 0 * ) ( ) ( N n jk jk n n x x DWT  where: (4)     k n n j j jk     2 2 2 /   It is assumed that: T n  – signal duration time x(t), T – signal sampling time x(t), N – number of samples defined by wavelet occurrence limits  jk (n). The discrete wavelet transform allows to divide the input signal x(t) into two components, whose frequency bands occupy half of the band signal x(t). The components are obtained by signal filtration with a low-pass filter and a high- pass filter respectively as well as a signal re-sampling operation, selecting only even samples, i.e. downsampling. The output signal on the low-pass filter is an approximant, and the output signal on the high-pass filter is a detail – it contains the details which complement the approximant. The approximants are the elements of signal x(t) – high scale and low frequency, while the details are the elements of low scale and high frequency. The decomposition process can be repeated to decompose the subsequent signal approximants into an approximant and a detail. Then the process is called a multilevel decomposition. The generalisation of this multi-level decomposition is a complete signal decomposition in which in the subsequent steps not only the subsequent signal approximants are filtered but also its details.