Improved double TQWT sparse representation using the MQGA algorithm and new norm for aviation bearing compound fault detection

The double tunable wavelet transform sparse representation realizes signal decomposition by constructing a basis function dictionary that match various characteristic waveforms of compound fault signal. However, the quality factor describing the resonance characteristic of the wavelet basis function can only be determined from practical experience, which is often subjective, and can significantly affect the matching degree between the wavelet basis function and the fault signal. To solve this problem, a new sparse representation method and a new norm are proposed. First, the multi-population quantum genetic algorithm (MQGA) is used to optimize the selected quality factor parameter combinations. The cross-correlated kurtosis of the periodic impact signal is established as the new norm and used to evaluate the optimized parameters. Then, according to the principle of energy entropy dominance, main sub-bands of the low resonance component are reconstructed to reduce noise interference and enhance the impact characteristics of the signal. Finally, Hilbert envelope demodulation analysis is performed on the reconstructed signal to obtain the instantaneous fault characteristic frequency. The proposed method was applied to diagnose compound faults of aviation bearings. The results show that the proposed method can effectively separate and extract the compound fault signal of a bearing in an aero-engine testbed. Furthermore, the compound fault of a damaged bearing in a helicopter transmission system was successfully decoupled, which verified the effectiveness and practicability of the proposed method.