Differgram: A convex optimization-based method for extracting optimal frequency band for fault diagnosis of rotating machinery

Abstract

The extraction of fault resonance bands from a full frequency band has always stood as a classical and effective strategy for fault diagnosis in rotating machinery. Among the existing techniques for capturing fault frequency bands, methods such as fast kurtogram and its variants have been prevalent. However, these methods encounter two main limitations. Firstly, they are subject to the constraints of index performance, potentially leading to the identification of incorrect frequency bands. Secondly, they do not fully harness the potential of healthy signals, thus hindering accurate fault frequency band localization. While approaches like SKRgram and accugram endeavor to leverage healthy signals to highlight differences between healthy and faulty signals, SKRgram falls short in thoroughly exploring the significance of healthy signals. Accugram relies on classifier accuracy to pinpoint fault frequency bands, rendering it less robust and less interpretable. To capitalize more effectively on healthy signals' potential, this study proposed a novel approach called differgram based on the convex optimization model. By inputting both healthy and faulty signals into the differgram, optimal fault frequency bands can be extracted. By solving the constructed convex optimization model, the optimal difference frequency bands between healthy and faulty signals are automatically identified. The method is substantiated through mathematical proofs and physical explanations, enhancing its interpretability. Through simulations and experimental validation, the proposed diffetergram demonstrates its efficiency in the extraction of fault frequency bands. In comparison to fast kurtogram, SKRgram, and accugram, the differgram showcases heightened robustness and noise immunity.