## 1 Introduction  
Rotating machines play an important role in industrial and transport applications. They have become more complicated, precise and costly. Thanks to technological progress, fault diagnosis techniques, are increasingly being used. Most rotating machines operate by means of bearings, gears and other rotating parts which can often cause defects. These defects can lead the machine to fail, reducing performance and even causing very serious accidents [1; 2; 3]. Bearings are the most critical elements parts of rotating machines because they support the dynamic forces of a shaft. Therefore they must be closely monitored to detect and locate defects at an early stage. By using some vibration signal processing methods, it is possible to obtain decisive diagnostic information. These methods are used to characterize, extract and identify fault signatures. Many conventional techniques such as time domain analysis and Fourier analysis are investigated in recent research and performed in many applications. The method, based on scalar features such as Root Mean Square,Crest Factor, and Kurtosis, can detect the presence of faults and their locations but the diagnosis is still imprecise [4; 5]. The second approach is based on the application of the Fast Fourier Transform algorithm. However, the total spectrum of the vibration signal (shaft and bearings) obtained does not exhibit an obvious characteristic frequency generated by the defects. This technique is quite limited and it works efficiently only for periodic signals [6]. The autocorrelation function is a statistical average suitable for characterizing random signals in the time domain. The Fourier transform of the autocorrelation function is the Power Spectral Density (PSD). It gives the power distribution of a signal in the frequency domain and is used to characterize random signals. The Welch power density estimation gives the spectral characteristics of signals characterized as random processes [7; 8]. However, continuous monitoring of the damage indicative variables is tedious because it is a procedure that requires a good deal of expertise to successfully apply them. It is therefore necessary to have simpler approaches that enable relatively low-skilled operators to make reliable decisions in the absence of diagnostic experts. Statistical techniques such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA) were the first to be used in this field [9; 10; 11]. The Random Forest Algorithms are based on the decision trees classifier; it has been considered significantly in development of fault machine diagnostics methods through a powerful method for classification and predictions [12; 13; 14]. Support Vector Machine (SVM) is also used; it is a very precise classifier, robust to noise and overfitting, but expensive in terms of computation [15; 16]. Subsequently, artificial intelligent techniques, such as Genetic Algorithms, Fuzzy Logic, and Artificial Neural Networks, have been applied successfully to automatic detection and to diagnosis [17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. In this paper, we aim to diagnose vibration failure occurring on a bearing mounted on the aircraft air compressor. This study concerns two aspects: we seek first to acquire the vibratory signals and to characterize the defects of the compressor bearing. The chosen signal analysis method is the Welch spectral density estimate for its efficiency on signals embedded in noise. The second part allows building a model which facilitates the monitoring and the diagnosis. We used neural networks with optimization based on genetic algorithms. The diagnostic results obtained by this approach were compared with two other traditional diagnostic methods. The first model that has been tried is based on statistical methods. The results obtained motivate the choice of another more efficient approach based on Artificial Neural Network. Then we used neural networks with the Back-Propagation algorithm to accomplish the training.