Multi-source fidelity sparse representation via convex optimization for gearbox compound fault diagnosis

Industrial automatic control systems have high requirements for manufacturing accuracy, which are often adversely affected by the compound fault of rotating machinery such as gearboxes. Compound fault diagnosis has many challenges because of its many types of faults, complex oscillation characteristics, and mutual interference between various vibration sources. Therefore, it is urgently required for the development of a method which can accurately detect gearbox complex multi-source faults. To address the compound fault problem, a novel multi-source fidelity sparse representation method is proposed, which can accurately realize multiple fault diagnosis of the gearbox without the prior knowledge regarding the number of fault sources. Moreover, to ensure the accuracy of signal reconstruction, the gearbox compound failure mechanism is analyzed, from which the sparse dictionaries are established. The multi-source penalty function is constructed to improve the fidelity of the signal and the convexity condition of the objective function is further discussed for the global minimum. Simulations and engineering signals are used to verify the versatility of the proposed method.