Fractional Diversity Entropy: A Vibration Signal Measure to Assist a Diffusion Model in the Fault Diagnosis of Automotive Machines

Real-world vibration signal acquisition of automotive machines often results in imbalanced sample sets due to restricted test conditions, adversely impacting fault diagnostic accuracy. To address this problem, we propose fractional diversity entropy (FrDivEn) and incorporate it into the classifier-guided diffusion model (CGDM) to synthesize high-quality samples. Additionally, we present a corresponding imbalanced fault diagnostic method. This method first converts vibration data to Gramian angular field (GAF) image samples through GAF transformation. Then, FrDivEn is mapped to the gradient scale of CGDM to trade off the diversity and fidelity of synthetic samples. These synthetic samples are mixed with real samples to obtain a balanced sample set, which is fed to the fine-tuned pretrained ConvNeXt for fault diagnosis. Various sample synthesizers and fault classifiers were combined to conduct imbalanced fault diagnosis experiments across bearing, gearbox, and rotor datasets. The results indicate that for the three datasets, the diagnostic accuracies of the proposed CGDM using FrDivEn at an imbalance ratio of 40:1 are 91.22%, 87.90%, and 98.89%, respectively, which are 7.32%, 11.59%, and 3.48% higher than that of the Wasserstein generative adversarial network (WGAN), respectively. The experimental results across the three datasets validated the validity and generalizability of the proposed diagnostic method.