# An Uncertainty-Aware Bayesian Deep Learning Method for Automatic Identification and Capacitance Estimation of Compensation Capacitors

## TL;DR

This paper introduces a Bayesian deep learning method to accurately identify and estimate compensation capacitors in noisy railway circuits, improving reliability and accuracy.

## Contribution

The novel contribution is a hierarchical Bayesian deep learning framework combining multi-domain signal enhancement and uncertainty-aware prediction for capacitor detection.

## Key findings

- The method achieves 97.8% state-recognition accuracy and a mean absolute error of 0.084 μF.
- It outperforms CNN and BiLSTM models in metrics like NLL and ECE, with near 95% interval coverage.
- The framework improves robustness and reliability for intelligent monitoring in railway track circuits.

## Abstract

This paper addresses the challenges of misclassification and reliability assessment in compensation capacitor detection under strong noise in high-speed railway track circuits. A hierarchical Bayesian deep learning framework is proposed, integrating multi-domain signal enhancement in the time, frequency, and time–frequency (TF) domains with bidirectional long short-term memory (BiLSTM) sequence modeling for robust feature extraction. Bayesian classification and regression based on Monte Carlo (MC) Dropout and stochastic weight averaging Gaussian (SWAG) enable posterior inference, confidence interval estimation, and uncertainty-aware prediction, while a rejection mechanism filters low-confidence outputs. Experiments on 8782 real-world segments from five railway lines show that the proposed method achieves 97.8% state-recognition accuracy, a mean absolute error of 0.084 μF, and an R2 of 0.96. It further outperforms threshold-based, convolutional neural network (CNN), and standard BiLSTM models in negative log-likelihood (NLL), expected calibration error (ECE), and overall calibration quality, approaching the theoretical 95% interval coverage. The framework substantially improves robustness, accuracy, and reliability, providing a viable solution for intelligent monitoring and safety assurance of compensation capacitors in track circuits.