Quantitative Fault Diagnosis of Railway Wheel Polygonization Based on Fractional-Order-Enhanced Transform-Domain Multi-Instance Learning and FiLM Modulation

Wheel polygonization is a typical out-of-roundness fault in high-speed trains, and multi-order roughness spectra can quantitatively describe its fault condition. Variations in operating speed, wheel diameter, and reprofiling state cause differences in axle-box vibration responses, making the diagnosis of multi-order roughness amplitudes difficult. A fractional-order-enhanced transform-domain multi-instance learning method with FiLM modulation is proposed for quantitative fault diagnosis of wheel polygonization. First, axle-box vibration acceleration, operating speed, and measured roughness data are jointly processed to construct multi-instance samples containing angular-domain time series, order-domain spectra, vibration statistics, and operating-condition information. Second, a model integrating transform-domain multi-instance learning and FiLM modulation is constructed, combining a state-adaptive multi-regression mechanism with order-aware correlation mapping to achieve quantitative diagnosis of roughness amplitudes across orders 1–32. Finally, the Grünwald–Letnikov fractional-order difference is introduced into the loss function to enhance the model’s ability to learn inter-order correlations and overall spectral-shape features, thereby reducing diagnostic errors in multi-order roughness amplitudes. Experimental results show that the proposed method achieves an RMSE of 1.157 dB, 60.5% lower than that of CNN-LSTM, the best-performing comparison method, providing a quantitative diagnostic method for high-speed train wheel condition assessment and reprofiling evaluation.