Issue 49

S. Djaballah et alii, Frattura ed Integrità Strutturale, 49 (2019) 291-301; DOI: 10.3221/IGF-ESIS.49.29 292 subject of several research studies. Most research related to the diagnosis of bearing defects uses vibration signals because they contain valuable information about defects [2, 3]. In addition, vibration analysis is considered to be the most common and reliable method in this type of analysis [4]. However, ultrasound has also been used appropriately and precisely in the detection of bearing defects [5]. There are different vibration analysis tools to detect and diagnose the appearance of defects in rotating machinery. Many publications synthesize these different methods or tools. They are generally classified into three main categories of vibration data analysis: time analysis, frequency analysis and time-scale analysis. The wavelets transform (TO) be a time- scale analysis technique suitable for both stationary and non-stationary signals [6]. The wavelet transform, offering a multi- resolution analysis, is very suitable for fault diagnosis [7]. The wavelet packet transform (WPT) is an improvement of the Multi-resolution MRA [8] since it allows decomposition of all frequency sub-bands. In this work, we focus on the diagnosis of rolling defects, using an intelligent classification system based on Artificial Neural Networks (ANN) and Wavelet Packet Transformation. The coefficients of the WPT will be used for the extraction of the indicators, in this case, the energy, and the kurtosis, which will drive the network of neurons [9]. Thus, the main objective of our work is the determination of the wavelet generating the most representative indicators of the state of the bearings for better detection and a good diagnosis of the defects. W AVELET TRANSFORM Wavelet packet transform he wavelet packet method is a generalization of wavelet decomposition that offers a range of possibilities for signal analysis in wavelet analysis; a signal is broken down into approximations and details. The approximation is then itself cut into approximation and second-level detail, and the process is repeated. For decomposition of "n" levels, there are (n + 1) possible ways to decompose or encode the signal [10]. In wavelet packet analysis, details, as well as approximations, can be decomposed. This yields more than (2n + 1) of different signal decompositions. The wavelet packet decomposition tree is shown in Fig .1. In the case of the detection of bearing defects, this technique makes it possible to obtain the same analysis fineness regardless of the frequencies investigated. Figure 1 : Representation in filter banks of the DWT at N = 3 level. The extraction of indicators Due to the complex nature of the machines and the complexity of the associated parameters, it is generally difficult to evaluate the state of a machine directly from the time data. The advent of the wavelet transform has provided an efficient tool for feature extraction of various time signals. As an extension to the discrete wavelet transform, the DWPT, in comparison with the DWT, provides more flexibility in time-frequency decomposition, especially in the high- frequency region. In particular, the DWPT allows the extraction of the indicators (for example, energy or kurtosis) from the frequency sub-bands where the indicators are concentrated[11]. Since the energy content of a signal provides a strong indicator of the signal but is not sensitive enough to incipient defects, kurtosis, on the other hand, is very sensitive to incipient defects but has low stability. Therefore, these two T