Among the advanced techniques of the predictive maintenance, the vibratory analysis proves to be very effective, in particular, for monitoring rotating components such as the bearings. Their damage creates cyclic efforts which are at the origin of the processing of vibratory measurements. This processing can be made by temporal methods, frequential methods, or by time-scale methods using the wavelets for 2 decades. The wavelet transform is a very effective processing, however, the difficulties of application and interpretation of the results slow down their employment. The determination of the parameters of the wavelets makes its use all the more difficult. Moreover, the use of these time-scale methods is very expensive in time computation. This paper proposes a wavelet adapted to the mechanical shock response of a structure with $n$ degrees of freedom. In addition, we developed a procedure for analysis of signals by this wavelet which makes it possible to accelerate the process and to improve detection in the case of disturbed signals. This methodology is compared with the traditional time-scale methods and is implemented to detect defects of different sizes on outer rings and inner rings of ball bearings.

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