<P> In signal processing based FDI, some mathematical or statistical operations are performed on the measurements, or some neural network is trained using measurements to extract the information about the fault . </P> <P> A good example of signal processing based FDI is time domain reflectometry where a signal is sent down a cable or electrical line and the reflected signal is compared mathematically to original signal to identify faults . Spread Spectrum Time Domain Reflectometry, for instance, involves sending down a spread spectrum signal down a wire line to detect wire faults . Several clustering methods have also been proposed to identify the novel fault and segment a given signal into normal and faulty segments . </P> <P> Machine fault diagnosis is a field of mechanical engineering concerned with finding faults arising in machines . A particularly well developed part of it applies specifically to rotating machinery, one of the most common types encountered . To identify the most probable faults leading to failure, many methods are used for data collection, including vibration monitoring, thermal imaging, oil particle analysis, etc . Then these data are processed utilizing methods like spectral analysis, wavelet analysis, wavelet transform, short term Fourier transform, Gabor Expansion, Wigner - Ville distribution (WVD), cepstrum, bispectrum, correlation method, high resolution spectral analysis, waveform analysis (in the time domain, because spectral analysis usually concerns only frequency distribution and not phase information) and others . The results of this analysis are used in a root cause failure analysis in order to determine the original cause of the fault . For example, if a bearing fault is diagnosed, then it is likely that the bearing was not itself damaged at installation, but rather as the consequence of another installation error (e.g., misalignment) which then led to bearing damage . Diagnosing the bearing's damaged state is not enough for precision maintenance purposes . The root cause needs to be identified and remedied . If this is not done, the replacement bearing will soon wear out for the same reason and the machine will suffer more damage, remaining dangerous . Of course, the cause may also be visible as a result of the spectral analysis undertaken at the data - collection stage, but this may not always be the case . </P> <P> The most common technique for detecting faults is the time - frequency analysis technique . For a rotating machine, the rotational speed of the machine (often known as the RPM), is not a constant, especially not during the start - up and shutdown stages of the machine . Even if the machine is running in the steady state, the rotational speed will vary around a steady - state mean value, and this variation depends on load and other factors . Since sound and vibration signals obtained from a rotating machine which are strongly related to its rotational speed, it can be said that they are time - variant signals in nature . These time - variant features carry the machine fault signatures . Consequently, how these features are extracted and interpreted is important to research and industrial applications . </P>

Isolate an identified fault in a large software