⚡ electrical engineering

Frequency-domain-based Bayesian-optimized 1-D CNN feature learning for integrated bearing fault diagnosis and remaining useful life prediction

This study proposes a unified framework that leverages Bayesian optimization to tune a frequency-domain 1-D CNN for extracting deep features, which are then utilized for high-accuracy bearing fault diagnosis and robust remaining useful life prediction across multiple NASA IMS datasets.

Original authors: Md Hedayetul Islam Chy, Charles Lowe, Sujatha Alla, Hicham Chaoui, Abdullah Al Mamun

Published 2026-09-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Md Hedayetul Islam Chy, Charles Lowe, Sujatha Alla, Hicham Chaoui, Abdullah Al Mamun

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Machines that spin, from the massive turbines in power plants to the quiet motors in factory robots, rely on a small but critical component to keep turning smoothly: the rolling-element bearing. These are the rings of steel balls or rollers that sit between a rotating shaft and a stationary housing, allowing parts to move with minimal friction. Like any mechanical part, they wear down over time. When a tiny defect forms on the surface of a ball or the track it rolls on, it creates a rhythmic, repetitive thud as the bearing spins. These thuds generate vibrations that travel through the machine. For decades, engineers have listened to these vibrations to guess when a bearing is about to fail. However, the signals are often messy and subtle, especially in the early stages of wear, making it difficult to distinguish a healthy machine from one that is slowly dying. The challenge has been to find a way to automatically and accurately read these complex vibrations to not only spot a fault but also predict exactly how much life is left in the part before it breaks.

A team of researchers at Old Dominion University has developed a new method to solve this problem by teaching a computer to listen to the vibrations in a different way. Instead of looking at the raw vibration signals as they happen over time, the researchers first convert them into a frequency map. Imagine taking a complex song and breaking it down into a list of all the specific musical notes it contains; this is what the researchers did with the machine's noise. They then used a type of artificial intelligence, specifically a one-dimensional convolutional neural network, to study these frequency maps. This computer model is designed to automatically find the most important patterns that signal a problem, such as a crack in the inner ring or a flaw on a rolling ball. The key innovation in their work is how they taught this computer model to learn. Rather than guessing the best settings for the model, they used a smart search technique called Bayesian optimization. This method systematically tests different combinations of settings, learning from each attempt to find the perfect configuration for the specific dataset, much like a chef tasting a sauce repeatedly and adjusting the spices until the flavor is just right.

The researchers tested their approach using three different sets of real-world data from NASA, where bearings were run until they completely failed. These datasets included bearings that developed cracks on their inner rings, outer rings, and on the rolling balls themselves. The new method proved to be exceptionally accurate at identifying these faults. In the first test set, it correctly diagnosed the condition of the bearings 99.85% of the time. In the second set, it achieved a perfect score of 100%, correctly identifying every single healthy and faulty bearing. In the third set, it reached 99.98% accuracy. When compared to a standard, widely used method that combines two different types of neural networks, the new approach was consistently better, particularly in spotting the subtle signs of outer-race failures, which are notoriously difficult to detect. The standard method missed a significant number of these faults, while the new system caught them all.

Beyond just diagnosing what is wrong, the researchers also used this system to predict how much time a bearing has left before it fails. They took the patterns the computer learned and turned them into a health score that tracks the bearing's condition from healthy to broken. By plotting this score over time, they could see the gradual decline of the machine's health. They then used a statistical model to draw a line through this decline and predict when the health score would hit a critical failure point. The results showed that their method produced a much smoother, more realistic picture of the degradation process. In contrast, the standard method often showed the health score jumping up and down or hitting a ceiling too early, making it hard to tell exactly when the machine would stop working. The new approach kept the signal clear and progressive, allowing for a more reliable estimate of the remaining useful life.

This work demonstrates that by combining a smart way of analyzing sound frequencies with an automated process for tuning computer models, it is possible to create a unified system that both diagnoses machine faults and predicts their future. The researchers found that letting the computer find its own best settings, rather than relying on human guesswork, leads to a much more robust and accurate tool for maintenance. This kind of technology is vital for industries that rely on heavy machinery, as it moves maintenance from a reactive practice—fixing things after they break—to a proactive one, where parts are replaced just before they fail, saving money and preventing unexpected downtime. The study confirms that with the right data and the right learning strategy, machines can be made to tell us exactly when they need help.

Technical Summary: Frequency-domain-based Bayesian-optimized 1-D CNN Feature Learning for Integrated Bearing Fault Diagnosis and Remaining Useful Life Prediction

Problem Statement
Rolling-element bearings are critical components in rotating machinery, yet their fault diagnosis and Remaining Useful Life (RUL) prediction face significant challenges. These challenges stem from the complex elastohydrodynamic contact dynamics that govern vibration signatures and the scarcity of comprehensive "run-to-failure" datasets. Furthermore, existing data-driven models often rely on empirically selected neural network hyperparameters, which can lead to suboptimal performance, overfitting, and a lack of robustness across different bearing conditions. The study addresses the need for a unified, automated framework capable of extracting discriminative features from vibration signals to simultaneously perform fault diagnosis and prognostic assessment without manual hyperparameter tuning.

Methodology
The proposed framework is a three-stage, frequency-domain-based approach utilizing Bayesian optimization (BO) to automate the learning process:

Frequency-Domain Transformation and Data Preparation:
Raw time-domain vibration signals are converted into frequency-domain representations using the Fast Fourier Transform (FFT). To capture the full spectrum of bearing degradation, the dataset is split such that the first 10% (early-stage) and last 10% (late-stage) of the run-to-failure data are used for training and validation, while the remaining 80% is reserved for feature extraction.
Bayesian-Optimized 1-D CNN Feature Learning:
A one-dimensional Convolutional Neural Network (1-D CNN) is employed to automatically extract deep features from the FFT spectra. Unlike traditional approaches, the CNN's hyperparameters are not fixed but are systematically optimized using Bayesian optimization with a Gaussian Process (GP) surrogate model. The optimization targets a multidimensional search space including:
- Initial learning rate (logarithmic range $10^{-5}$ to $10^{-2}$ ).
- L-2 regularization coefficient ( $10^{-6}$ to $10^{-2}$ ).
- Mini-batch size.
- Feature dimension.
- Adaptive numbers of filters across three convolutional layers.
  Parallel computation is integrated to accelerate candidate evaluations and reduce computational burden.
Integrated Diagnosis and Prognosis:
- Fault Diagnosis: The deep features extracted by the optimized CNN are fed into a Gaussian-kernel Support Vector Machine (SVM) for multiclass fault classification (e.g., healthy, inner-race, outer-race, roller-element). The SVM hyperparameters (box constraint and kernel scale) are also optimized via Bayesian optimization.
- RUL Prediction: Channel-wise features are fused at the bearing level to construct a degradation-sensitive Health Indicator (HI) based on Relative Squared Error (RSE). An adaptive failure threshold is determined using statistical properties of the healthy baseline and late-stage data. A Bayesian-optimized Gaussian Process Regression (GPR) model then predicts the future degradation trajectory and estimates the RUL by identifying when the predicted HI crosses the failure threshold.

Key Contributions
The paper outlines five primary technical contributions:

Adaptive Learning Rate Optimization: The framework systematically searches a wide learning rate range, allowing the 1-D CNN to adapt its learning behavior for improved convergence.
Improved Generalization via L-2 Regularization: An automated search for the optimal L-2 regularization coefficient is incorporated to control model complexity and reduce overfitting across varying bearing conditions.
Computationally Efficient Hyperparameter Optimization: By integrating Bayesian optimization with parallel computing, the method efficiently identifies optimal configurations (including adaptive filter counts) without the exhaustive cost of grid search.
High Fault-Diagnosis Performance: The Bayesian-optimized 1-D CNN feature-learning framework achieves diagnostic accuracies of 99.85%, 100.00%, and 99.98% for IMS Datasets #1, #2, and #3, respectively, outperforming the benchmark CNN-LSTM-based feature extraction method, which achieves accuracies of 99.69%, 96.69%, and 99.86% for the same datasets.
Integrated Diagnosis and Prognosis: The study provides a unified framework where optimized CNN features serve dual purposes: training SVMs for fault detection and GPR models for RUL prediction.

Experimental Results
The framework was validated using three NASA Intelligent Maintenance Systems (IMS) run-to-failure datasets representing inner-race, rolling-element, and outer-race failures.

Diagnostic Accuracy:
- IMS Dataset #1: Achieved 99.85% accuracy (vs. 99.69% for the benchmark).
- IMS Dataset #2: Achieved 100.00% accuracy (vs. 96.69% for the benchmark), demonstrating a significant 3.31 percentage point improvement, particularly in detecting outer-race faults.
- IMS Dataset #3: Achieved 99.98% accuracy (vs. 99.86% for the benchmark).
- The proposed method consistently showed higher precision and recall with lower standard deviations compared to the benchmark.
RUL Prediction and Health Indicators:
- The proposed method generated Health Indicators (HIs) that exhibited a more progressive and degradation-sensitive trajectory compared to the benchmark.
- Unlike the benchmark, which often showed abrupt changes or premature saturation near the upper limit, the proposed framework preserved the gradual evolution of degradation, providing a more interpretable basis for long-horizon extrapolation.
- t-SNE visualization confirmed that the proposed method learned a more discriminative feature space with clearer separation between healthy and faulty states.

Significance and Claims
The authors claim that this study demonstrates the viability of a unified, data-driven framework for robust fault diagnosis and RUL prediction. By integrating frequency-domain signal representation with Bayesian-optimized deep feature learning, the method overcomes the limitations of manual hyperparameter tuning and limited dataset availability. The results suggest that the framework supports the transition from conventional fault detection to intelligent predictive maintenance and condition-based decision-making. The study concludes that the proposed approach offers a more interpretable and reliable basis for assessing bearing degradation under various failure modes compared to existing benchmark methods. Future work is noted to potentially extend this framework toward agentic AI-based autonomous decision-making.

Technical Summary: Frequency-domain-based Bayesian-optimized 1-D CNN Feature Learning for Integrated Bearing Fault Diagnosis and Remaining Useful Life Prediction

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