Modulated differentiable STFT and balanced spectrum metric for freight train wheelset bearing cross-machine transfer monitoring under speed fluctuations

TL;DR

This work tackles cross-machine bearing fault diagnosis for heavy freight train wheelsets under speed fluctuations and limited labeled data. It introduces pyDSN, a one-stage framework that fuses a physics-informed modulated differentiable STFT (MDSTFT) with a balanced spectrum quality (BSQ) loss and a domain-adaptation network to learn domain-invariant discriminative features. MDSTFT provides time-varying, differentiable windowing guided by a mask modulation, while BSQ enforces physically meaningful time-frequency representations and regularizes cross-domain learning. Empirical results across multiple datasets show that pyDSN significantly outperforms traditional DSN and STFT-based methods, achieving average accuracies around 97% and demonstrating strong generalization to real-world heavy haul data. The approach also offers interpretable improvements through quantitative spectrogram quality metrics, suggesting practical value for railway health monitoring under variable-speed operation.

Abstract

The service conditions of wheelset bearings has a direct impact on the safe operation of railway heavy haul freight trains as the key components. However, speed fluctuation of the trains and few fault samples are the two main problems that restrict the accuracy of bearing fault diagnosis. Therefore, a cross-machine transfer diagnosis (pyDSN) network coupled with interpretable modulated differentiable short-time Fourier transform (STFT) and physics-informed balanced spectrum quality metric is proposed to learn domain-invariant and discriminative features under time-varying speeds. Firstly, due to insufficiency in extracting extract frequency components of time-varying speed signals using fixed windows, a modulated differentiable STFT (MDSTFT) that is interpretable with STFT-informed theoretical support, is proposed to extract the robust time-frequency spectrum (TFS). During training process, multiple windows with different lengths dynamically change. Also, in addition to the classification metric and domain discrepancy metric, we creatively introduce a third kind of metric, referred to as the physics-informed metric, to enhance transferable TFS. A physics-informed balanced spectrum quality (BSQ) regularization loss is devised to guide an optimization direction for MDSTFT and model. With it, not only can model acquire high-quality TFS, but also a physics-restricted domain adaptation network can be also acquired, making it learn real-world physics knowledge, ultimately diminish the domain discrepancy across different datasets. The experiment is conducted in the scenario of migrating from the laboratory datasets to the freight train dataset, indicating that the hybrid-driven pyDSN outperforms existing methods and has practical value.

Figures (21)

• Figure 1: The overview of pyDSN.
• Figure 2: $\odot$ is element-wise product. Multiplying the signals with the window functions with variable window lengths, followed by DFFT yields MDSTFT. Subsequently, the balanced spectrum quality loss is calculated, the optimal window function is determined employing three evaluation metrics and backpropagation procedure.
• Figure 3: Flowchart of a PyDSN model.
• Figure 4: Equipments: (a) is double-span and double-rotor comprehensive fault experimentation platform; (b) is gearbox fault experiment platform; (c) is rotor-gear comprehensive fault experiment platform; (d) is experimental setup from University of Ottawa.
• Figure 5: Heavy haul freight train wheelset bearing related equipment: (a) is heavy haul freight train wheelset bearing experimental platform; (b)is the data collector; (c) is the sensor; (d) is the acquisition system; (e) is the bearing (352226X2-2RZ); (f) is the schematic diagram of bearing disassembly; (g) is the partial failure types of railway freight train bearing.