Rail inspection in track maintenance: A benchmark between the wavelet approach and the more conventional Fourier analysis

Nowadays the power of data analysis tools like the wavelet decomposition of signals is well known and spread. On the other hand the theoretical advantages of such methods often fight with reality, when real field signals are collected and analysed: it sometimes comes out that this time–frequency approach somehow fails, demanding for a deeper insight into the kind of physical problem to be considered, and requiring a sort of “benchmark” between the traditional Fourier approach and the more recent time–frequency one. In this paper, sharply application-oriented, the possibilities offered by the wavelet techniques have been analysed: both the DSP specialist and the field engineer points of view have been joined to exploit the new approach of its best. A real problem has been considered, in which acceleration signals from a train bogie are collected and real-time analysed, to get a diagnostic tool to know the track condition of a subway line. This paper would like to look for a compromise point between complex mathematics based techniques, such as wavelet packet, sometimes hard to comprehend to the application engineer, and the physical meaning of these tools helping in fixing the real method limits. Therefore the aim is not just trying this analysis on an almost random process, like the accelerations measured on a running bogie, to locate defects, but rather a discussion on the development of the continuous and discrete wavelet transform, in comparison with the classical Fourier analysis or filter banks. Only the minimum mathematical background is provided in the text, with the needed references, to give tools fit for comprehending the physical meaning of the new tools, capable of sparing computing effort, while preserving or even improving the system effectiveness.