Generating Bearing Vibration Signals at User-Specified Fault Probabilities Using PR-GAN and Counterfactual Methods

2026-07-21

AI Summary

This study addresses the scarcity of bearing vibration samples with intermediate fault probabilities (e.g., 0.25–0.75), which hinders research on condition-based maintenance near decision boundaries. To overcome this, the authors propose two methods for generating high-fidelity vibration signals with specified fault probabilities: first, a residual Probability-Regularized GAN (PR-GAN) based on WGAN-GP that incorporates a target probability regularization term; and second, a training-free counterfactual optimization approach that directly fine-tunes original signals to match desired probabilities. Innovatively combining probabilistic regularization with counterfactual strategies, the framework employs a heterogeneous ensemble classifier as a probability oracle and enforces time-frequency domain constraints for precise control. Experiments show the counterfactual method achieves remarkably low average probability errors (0.005–0.008), perfect success rates (1.0), and minimal perturbations, substantially outperforming PR-GAN (errors: 0.046–0.059; success rates: 0.501–0.680), though PR-GAN offers higher computational efficiency.

Abstract

In bearing vibration datasets, most samples receive predicted fault probabilities close to 0 or 1, while samples with intermediate (gray-zone) probabilities are rare. Such borderline samples are important because they reflect conditions in which maintenance decisions may require additional inspection or a conservative response and are useful for studying decision boundaries. To address this scarcity, this paper proposes and compares two approaches that generate vibration signals whose predicted fault probability matches a target probability of 0.25, 0.50, or 0.75. We use the average output of a heterogeneous ensemble classifier with different architectures and random initializations as a fixed, gradient-accessible probability oracle. The first, training-based approach, Probability-Regularized Generative Adversarial Network (PR-GAN), extends Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) and edits a real signal through a residual generator while pushing the classifier output toward the target probability. The second is a training-free, per-sample Wachter-style counterfactual (CF) procedure that directly optimizes each input signal to reach the target probability while remaining close to the source signal. We evaluate both methods on the Case Western Reserve University (CWRU) and Paderborn bearing datasets using mean absolute target-probability error, time-domain total variation, and frequency-domain log power spectral density (log-PSD) differences. Across all settings, CF reaches the target with a mean absolute probability error of 0.005-0.008 and a within-tolerance success rate of 1.000 on retained samples, whereas PR-GAN's mean error is 0.046-0.059 with success rates between 0.501 and 0.680. CF therefore steers the probability more reliably and requires smaller average L1 changes, whereas PR-GAN has a lower reported runtime in most settings.

Problem

• bearing vibration
• fault probability
• gray-zone samples
• decision boundary
• sample scarcity

Innovation

• PR-GAN
• Counterfactual generation
• Fault probability control
• Bearing vibration synthesis
• Gray-zone samples