Using filter diagonalization for fault detection in low-speed rotational machinery

Abstract

This chapter presents the application of Filter Diagonalization (FD) method for fault detection in low-speed rotational machinery. FD serves to extract frequency components from short time signals. The length of the signal can be significantly shorter than the length required by methods based on computing the similarity between the signal and the sine wave, for example, Fourier Transform (FT) and Wavelet Transform (WT). The intrinsic advantage of FT is that one can separately extract frequencies at any desired spectral range and the extraction is not impeded by the frequency content of other ranges. On the other hand, the main drawback is the direct relationship between the frequency resolution and the length of the observed signal. WT enables more balanced consideration of low and high frequencies, since it uses the same relative width of the time-window, which depends on the frequency in question. However, when trying to distinguish between two very close frequencies the same limitations as in Fourier Transform are encountered. Brief mathematical background of the FD method is outlined along with a short comparison of its performance with respect to the FT. Finally, an example of utilization of FD for fault detection is described.