The Mathematic Principle of Inner Product Transform for Mechanical Fault Diagnosis

摘要

An important approach in mechanical fault diagnosis is fault feature extraction from dynamic signals. Mathematical transforms like Fourier transform, short time Fourier transform, wavelet transform, second generation wavelet transform and multiwavelet are widely used. This paper reveals a concept that the mathematic principle of these transforms is inner product transform for signals with various basis functions. If fault feature in mechanical signal is similar to a basis function, the fault feature can be desirably extracted from dynamic signals based on inner product transform. Basis functions of Hermitian basis, second generation wavelet basis and multiwavelet bases have been adopted for fault feature extraction to successfully diagnose impact-rub fault, bearing defect and gear fault in key rotating machine, electric locomotive and hot strip finishing mills respectively.