CTDFormer: A New Method for Bearing Fault Diagnosis Fusing Liquid Neural Networks and Transformer

CTDFormer is a new method for bearing fault diagnosis that fuses bidirectional closed-form continuous-time liquid neural networks (CfC) with Transformer. Its core innovation is replacing the multi-head attention mechanism of traditional Transformer with CfC to better capture temporal dynamic features. This method has been validated on multiple public datasets such as CWRU, MFPT, and SEU, providing an efficient and robust technical path for bearing fault diagnosis in rotating machinery.

In modern industry, bearing faults in rotating machinery account for about 40% of equipment failures, directly affecting production safety and efficiency. Traditional fault diagnosis relies on expert experience and manual feature extraction, which is difficult to adapt to complex working conditions; although deep learning has brought breakthroughs, balancing performance, computational efficiency, and temporal dynamic capture capability remains a challenge.

The core of CTDFormer is replacing the multi-head attention of Transformer with bidirectional CfC:

1. CfC is an efficient implementation of Liquid Neural Networks (LNN), which approximates ODE integration through closed-form solutions to avoid iterative computation. Its equation is h(t) = σ(-τ(t)) ⊙ h(t-1) + (1 - σ(-τ(t))) ⊙ f(x(t), h(t-1)), where τ(t) is a learnable time constant.
2. The fusion architecture includes input embedding, positional encoding, bidirectional CfC blocks, feed-forward network, layer normalization and residual connection, and classification head, balancing continuous-time modeling and parallel computing efficiency.

CTDFormer's effectiveness has been verified on three datasets:

• CWRU Dataset: A classic benchmark covering various faults and loads, with an accuracy of over 99%, comparable to state-of-the-art methods;
• MFPT Dataset: Industrial real-environment data with high noise and variable working conditions, still maintaining high diagnostic accuracy and strong generalization ability;
• SEU Dataset: Bearing/gear fault data under multi-speed loads, verifying adaptability to different working conditions.

The technical advantages of CTDFormer include:

• Computational Efficiency: CfC's linear complexity replaces the quadratic complexity of attention, suitable for real-time deployment;
• Physical Consistency: Continuous-time characteristics match the physical nature of vibration signals;
• Interpretability: The time constant τ(t) corresponds to the physical meaning of fault characteristic frequencies;
• Robustness: Strong resistance to noise and disturbances. These advantages give it important engineering value in industrial scenarios.

Application Scenarios:

• Predictive Maintenance Systems: Real-time monitoring of equipment health;
• Edge AI Devices: Deployment in resource-constrained environments;
• Digital Twin Systems: Core diagnostic module;
• Fault Mode Research: Analyzing dynamic features to understand fault mechanisms. Open Source Suggestions: Explore the application of CfC in other industrial time-series tasks, multi-modal diagnosis, custom model development, fusion with graph neural networks/physics-informed neural networks, etc.