Fractional-order stochastic resonance-based rescaling-frequency scanning images for early multi-frequency fault detection of machines

In engineering applications, weak multi-frequency fault signals from mechanical equipment are often masked by strong background noise. Traditional stochastic resonance (SR) methods mainly focus on enhancing fault signals into sine-like ones, but they may lose or even destroy the multi-harmonic characteristics of fault signals. To this end, this paper would propose a rescaling-frequency scanning image method using fractional-order SR (FSR-RFSI), aiming to enhance and visualize weak multi-frequency useful signals. First, the proposed method develops a fractional-order SR system with memory properties, which is designed to detect weak multi-frequency signals in complex spectral environments. Moreover, a weighted zero-crossing signal-to-noise ratio (WZCSNR) is proposed as a performance evaluation metric, which effectively overcomes the limitation of the traditional signal-to-noise ratio (SNR) that focuses solely on frequency-domain energy while neglecting time-domain multi-harmonic components. Meanwhile, to improve parameter tuning efficiency, this paper establishes an analytical relationship map between the resonant frequency and system parameters, namely rescaling-frequency scanning image. Furthermore, a quantum genetic algorithm (QGA) is used to achieve adaptive optimization of key system parameters. Simulation analyses and experiments on early rolling bearing and gearbox faults show that the proposed method can effectively boost and detect weak multi-frequency fault signals. Additionally, comparative analysis with Maximum Correlated Kurtosis Deconvolution (MCKD), Fast Kurtogram (FK), and Feature Modal Decomposition (FMD) methods further validates the superiority of the proposed method.