Transform principle of inner product for fault diagnosis

Fourier transform, short time Fourier transform, wavelet transform and second generation wavelet transform are widely used for mechanical fault diagnosis. In this paper, it is revealed that the essence of these transforms is inner product transform for signals with various basis functions, from which fault feature being the most similar to basis function can be extracted from dynamic signals. A lot of basis functions such as trigonometric basis, Gabor basis, discrete basis, harmonic basis, Laplace basis, Hermitian basis, second generation wavelet basis, etc. have been adopted for fault feature extraction. Looseness fault feature of a turbo-generator, impulse friction symptom of gearbox, failure feature of high-pressure turbine excited by steam, and bearing defect of electric locomotive were extracted successfully. Provided that adopt reasonable basis functions or multi-bases (multiwavelet) for inner product transform of dynamic signals, effective fault features and correct fault diagnosis can be obtained.