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

机译：轨道维护中的铁路检查：小波方法与更常规的傅立叶分析之间的基准

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摘要

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.rnTherefore 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.
机译：如今，诸如信号的小波分解之类的数据分析工具的功能已广为人知并得到了传播。另一方面，当收集和分析实地信号时，此类方法的理论优势通常与现实相抵触：有时会出现这种时频方法以某种方式失效的情况，需要对要解决的物理问题有更深入的了解。在传统的傅立叶方法和最新的时频方法之间需要某种“基准”。在本文中，以应用为导向，分析了小波技术提供的可能性：DSP专家和现场工程师的观点都得到了充分利用，以充分利用新方法。已经考虑了一个实际问题，其中收集来自火车转向架的加速度信号并进行实时分析，以获取诊断工具来了解地铁线路的轨道状况。本文希望在基于数学的复杂技术之间找到一个折衷点，例如小波包，有时很难为应用工程师所理解，而这些工具的物理含义有助于固定实际方法的限制。只是在几乎随机的过程（如在运行的转向架上测得的加速度）上尝试进行此分析以找出缺陷，而是与经典的傅立叶分析或滤波器组相比，对连续小波和离散小波变换的发展进行了讨论。文本中仅提供了最低限度的数学背景以及所需的参考，以提供适合理解新工具的物理含义的工具，从而能够节省计算工作量，同时还能保持甚至提高系统效率。

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