Quadratic Time-Frequency Analysis of Vibration Signals for Diagnosing Bearing Faults (2401.01172v2)

Abstract: Diagnosis of bearing faults is paramount to reducing maintenance costs and operational breakdowns. Bearing faults are primary contributors to machine vibrations, and analyzing their signal morphology offers insights into their health status. Unfortunately, existing approaches are optimized for controlled environments, neglecting realistic conditions such as time-varying rotational speeds and the vibration's non-stationary nature. This paper presents a fusion of time-frequency analysis and deep learning techniques to diagnose bearing faults under time-varying speeds and varying noise levels. First, we formulate the bearing fault-induced vibrations and discuss the link between their non-stationarity and the bearing's inherent and operational parameters. We also elucidate quadratic time-frequency distributions and validate their effectiveness in resolving distinctive dynamic patterns associated with different bearing faults. Based on this, we design a time-frequency convolutional neural network (TF-CNN) to diagnose various faults in rolling-element bearings. Our experimental findings undeniably demonstrate the superior performance of TF-CNN in comparison to recently developed techniques. They also assert its versatility in capturing fault-relevant non-stationary features that couple with speed changes and show its exceptional resilience to noise, consistently surpassing competing methods across various signal-to-noise ratios and performance metrics. Altogether, the TF-CNN achieves substantial accuracy improvements up to 15%, in severe noise conditions.

• The paper introduces a novel TF-CNN framework that fuses quadratic time-frequency distributions with deep learning to accurately diagnose bearing faults.
• It leverages a compact kernel distribution to suppress cross-terms and effectively capture non-stationary vibration signals under variable operational conditions.
• The model, validated on the KAIST dataset, demonstrates superior noise resilience and diagnostic accuracy through feature clustering and misclassification analysis.

Quadratic Time-Frequency Analysis of Vibration Signals for Diagnosing Bearing Faults

This research presents an advanced approach to diagnosing bearing faults using a combination of time-frequency analysis and deep learning. The paper emphasizes the challenges posed by non-stationary vibration signals in rotating machinery operating under variable speeds and noise conditions. It introduces a novel methodology that leverages quadratic time-frequency distributions (TFDs) fused with convolutional neural networks (CNNs) to effectively diagnose faults in rolling-element bearings. This synthesis aims to capture dynamic patterns associated with different fault conditions, overcoming limitations in traditional methods that operate under ideal environments.

Time-Frequency Analysis Methodology

Bearing Vibrations and Signal Modeling

The paper develops a comprehensive model for bearing vibrations that considers time-varying rotational speeds and noise. These conditions are typical in real-world applications and contribute to the non-stationarity of the vibration signals. The model incorporates amplitude modulation and pulse frequency modulation, directly reflecting the bearing's geometry, operational conditions, and speed variability.

Figure 1: Example synthetic bearing vibration signal with an inner race fault following Eq. $\ref{eq:fault_model}$.

Quadratic Time-Frequency Representation

Rather than relying on conventional linear TFRs like STFT or CWT, this paper utilizes the Wigner-Ville distribution (WVD) for its high-resolution capability. However, to mitigate cross-terms, a compact kernel distribution (CKD) is employed, which balances resolution and interference suppression efficiently. This choice of TFR is pivotal in enhancing the detection and characterization of fault-induced signal patterns.

Figure 2: The CKD of the first vibration segment from the sensor mounted on the y-direction with no noise.

Implementation and Evaluation

Dataset and Preprocessing

Utilizing the KAIST dataset, which includes vibration signals recorded under varying speeds, each signal undergoes time-frequency transformation. The paper proposes a segment length of 0.1 seconds to capture relevant frequency dynamics while accommodating speed fluctuations. The resultant TFRs are standardized and serve as input for the TF-CNN model.

Figure 3: Frequency analysis of the rotational speeds in the KAIST dataset.

Time-Frequency CNN Design

The deep learning architecture, TF-CNN, processes TFRs through a series of convolutional layers optimized for feature extraction across time and frequency. The model's structure comprises five convolutional layers followed by a dense layer, dropout, and a softmax activated classification layer to output probabilities for each fault class.

Results and Discussion

The TF-CNN model demonstrated superior performance across various noise levels, outperforming baseline models by significant margins, especially under high-noise conditions. The findings confirm that the model effectively learns state-relevant features even in the presence of significant noise.

t-SNE and Grad-CAM Insights

Analyses such as t-SNE indicate distinct clustering of learned features, affirming the model's ability to differentiate between different fault states even at reduced dimensionality. Grad-CAM results further validate the relevance of the extracted features, highlighting patterns that correspond dynamically to different operational speeds.

Figure 4: The Grad-CAM maps and rotational speeds for the first 8 seconds of clean data.

Speed and Misclassification Correlation

Investigation into misclassification occurrences reveals a propensity for errors at lower speeds where fault-induced vibrations closely align with the bearing's natural resonances. This insight underscores the necessity of the TF-CNN model's sensitivity to dynamic speed conditions.

Figure 5: The link between misclassification, at 0 dB SNR, and rotational speed for the different bearing health states.

Conclusion

The integration of quadratic TFDs with CNNs in the TF-CNN model provides a robust framework for diagnosing bearing faults under realistic conditions. Through effective noise mitigation and detailed pattern analysis, the proposed approach offers significant improvements in diagnostic accuracy and reliability. Future work may incorporate advanced strategies like attention mechanisms and operational neural networks to further enhance diagnostic capabilities.