Integrating Mathematical Modeling and Deep Learning for Uncertainty-Aware Fault Diagnosis in Industrial Rotating Machinery
DOI:
https://doi.org/10.37385/a6wnmz27Keywords:
Fault Diagnosis, Rotating Machinery, Hybrid CNN-LSTM, Monte Carlo Dropout, Uncertainty QuantificationAbstract
In Industry 4.0, reliable fault diagnosis is critical for minimizing downtime and preventing catastrophic failures in rotating machinery. However, conventional deep learning models often operate deterministically, lacking the ability to quantify prediction uncertainty—a limitation that hinders risk-based maintenance decisions. This study aims to develop a hybrid deep learning framework that integrates Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), and Bayesian inference for uncertainty-aware fault diagnosis. The model extracts spatial features from Short-Time Fourier Transform (STFT) spectrograms via CNN, models temporal dynamics from raw vibration signals via LSTM, and quantifies prediction uncertainty using Monte Carlo Dropout (T=50). Evaluated on the benchmark Case Western Reserve University (CWRU) bearing dataset with an 80/20 data partitioning under six operating conditions, the hybrid architecture achieves an accuracy of 99.14% and an F1-score of 0.9914, significantly outperforming standalone CNN (97.42%) and LSTM (84.12%) models. The integration of probabilistic inference enhances decision reliability by providing confidence estimates for each prediction. This work contributes a robust, uncertainty-aware model that effectively captures both spatial and temporal patterns, offering significant implications for safety-critical industrial predictive maintenance systems.
Downloads
References
Abdar, M., Pourpanah, F., Hussain, S., Rezazadegan, D., Liu, L., Ghavamzadeh, M., Fieguth, P., Cao, X., Khosravi, A., Acharya, U. R., Makarenkov, V., & Nahavandi, S. (2021). A review of uncertainty quantification in deep learning: Techniques, applications and challenges. Information Fusion, 76, 243–297. https://doi.org/10.1016/j.inffus.2021.05.008
Ali, B. A. A., Gorgees, H. M., & Kathim, R. I. (2020). Bayesian estimators of the scale parameter and reliability function of inverse Rayleigh distribution under three types of loss function. 040018. https://doi.org/10.1063/5.0027983
Asrol, M., & Pratama, O. (2025). Performance Improvement of Quality Monitoring Systems in Imbalanced Data Conditions for Fat-Filled Powder Quality in The Dairy Industry. Journal of Applied Engineering and Technological Science (JAETS), 7(1), 274–295. https://doi.org/10.37385/jaets.v7i1.6996
Borré, A., Seman, L. O., Camponogara, E., Stefenon, S. F., Mariani, V. C., & Coelho, L. D. S. (2023). Machine Fault Detection Using a Hybrid CNN-LSTM Attention-Based Model. Sensors, 23(9), 4512. https://doi.org/10.3390/s23094512
Cariño, J. A., Delgado-Prieto, M., Zurita, D., Picot, A., Ortega, J. A., & Romero-Troncoso, R. J. (2020). Incremental novelty detection and fault identification scheme applied to a kinematic chain under non-stationary operation. ISA Transactions, 97, 76–85. https://doi.org/10.1016/j.isatra.2019.07.025
Chen, C.-C., Liu, Z., Yang, G., Wu, C.-C., & Ye, Q. (2020). An Improved Fault Diagnosis Using 1D-Convolutional Neural Network Model. Electronics, 10(1), 59. https://doi.org/10.3390/electronics10010059
Choi, Y., & Joe, I. (2024). Motor Fault Diagnosis and Detection with Convolutional Autoencoder (CAE) Based on Analysis of Electrical Energy Data. Electronics, 13(19), 3946. https://doi.org/10.3390/electronics13193946
Desnelita, Y., Siddik, M., Lita, L., Hajjah, A., & Gustientiedina, G. (2025). Hand Pose Classification Using Mediapipe Hands and CNN-LSTM For Augmented Reality Based Intravenous Infusion Learning. Jurnal Testing Dan Implementasi Sistem Informasi, 3(2), 94-107. https://doi.org/10.55583/jtisi.v3i2.2343
Eren, L., Ince, T., & Kiranyaz, S. (2019). A Generic Intelligent Bearing Fault Diagnosis System Using Compact Adaptive 1D CNN Classifier. Journal of Signal Processing Systems, 91(2), 179–189. https://doi.org/10.1007/s11265-018-1378-3
Fan, Z., Wang, Y., Meng, L., Zhang, G., Qin, Y., & Tang, B. (2023). Unsupervised Anomaly Detection Method for Bearing Based on VAE-GAN and Time-Series Data Correlation Enhancement (June 2023). IEEE Sensors Journal, 23(23), 29345–29356. https://doi.org/10.1109/JSEN.2023.3326335
Fang, Q., Xiong, G., Shang, X., Liu, S., Hu, B., & Shen, Z. (2020). An Enhanced Fault Diagnosis Method with Uncertainty Quantification Using Bayesian Convolutional Neural Network. 2020 IEEE 16th International Conference on Automation Science and Engineering (CASE), 588–593. https://doi.org/10.1109/CASE48305.2020.9216773
Fauzan, A., Sadik, K., & Kurnia, A. (2025). Evaluating ordinal multivariate models under multicollinearity via pairwise likelihood: A simulation perspective. Advance Sustainable Science, Engineering and Technology (ASSET), 7(4), 02504024. https://doi.org/10.26877/asset.v7i4.2282
Gal, Y., & Ghahramani, Z. (2016). Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning (arXiv:1506.02142). arXiv. https://doi.org/10.48550/arXiv.1506.02142
Huang, W., Chen, Y., Chen, Y., & Zhang, T. (2024). Life prediction method of rolling bearing based on CNN-LSTM-AM. Journal of Vibroengineering, 26(5), 1027–1039. https://doi.org/10.21595/jve.2024.23793
Jia, Z., & Sharma, A. (2021). Review on engine vibration fault analysis based on data mining. Journal of Vibroengineering, 23(6), 1433–1445. https://doi.org/10.21595/jve.2021.21928
Kendall, A., & Gal, Y. (2017). What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision? (arXiv:1703.04977). arXiv. https://doi.org/10.48550/arXiv.1703.04977
Kurniawan, S., Pramayoga, A. S., Ashari, Y. F., & Amrustian, M. A. (2026). Development and evaluation of an IndoBERT-based NLP model for automated clickbait detection. Advance Sustainable Science, Engineering and Technology (ASSET), 8(1), 02601021. https://doi.org/10.26877/asset.v8i1.2637
Li, X., Bi, F., Zhang, L., Yang, X., & Zhang, G. (2022). An Engine Fault Detection Method Based on the Deep Echo State Network and Improved Multi-Verse Optimizer. Energies, 15(3), 1205. https://doi.org/10.3390/en15031205
Lokeshwaran, K., Komal Kumar, N., Senthil Murugan, J., Elanangai, V., & Sathya, S. (2025). Benchmarking Transformer Models Against Classical Approaches for Fake Review Detection on the Deceptive Opinion Spam Corpus. International Journal of Environment, Engineering and Education, 7(3), 182–195. https://doi.org/10.55151/ijeedu.v7i3.334
Lubis, A. R., Prayudani, S., Putra, P. H., & Lase, Y. Y. (2025). Optimization of Convolutional Neural Network for Classification of Hydroponic Vegetable Cultivation Using Machine Learning. Journal of Applied Engineering and Technological Science (JAETS), 7(1), 119–128. https://doi.org/10.37385/jaets.v7i1.7231
Mansor, N., Md Shah, W., & Khambari, N. (2025). Swarm Intelligence Optimisation Vs Deep Learning: Energy-Aware Strategy for Disaster Communication Networks. Journal of Applied Engineering and Technological Science (JAETS), 7(1), 211–223. https://doi.org/10.37385/jaets.v7i1.7937
Mohd Ghazali, M. H., & Rahiman, W. (2021). Vibration Analysis for Machine Monitoring and Diagnosis: A Systematic Review. Shock and Vibration, 2021(1), 9469318. https://doi.org/10.1155/2021/9469318
Muhammad, A. E., & Abdulrahman, A. A. (2025). A Comprehensive Review of Deep Learning Techniques for Intrusion Detection in the Internet of Medical Things. Journal of Applied Engineering and Technological Science (JAETS), 7(1), 745–761. https://doi.org/10.37385/jaets.v7i1.6637
Pinedo-Sánchez, L. A., Mercado-Ravell, D. A., & Carballo-Monsivais, C. A. (2020). Vibration analysis in bearings for failure prevention using CNN. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(12), 628. https://doi.org/10.1007/s40430-020-02711-w
Pralano, A. Z. P., Poovathy, F. G., & Hermana, R. (2026). Hybrid XGBoost-LSTM framework for accurate SOC, SOH, DOD and internal resistance estimation in Li-ion cells. Advance Sustainable Science, Engineering and Technology (ASSET), 8(2), 02602037. https://doi.org/10.26877/asset.v8i2.3119
Primawati, P., Ferra Yanuar, Dodi Devianto, Remon Lapisa, & Fazrol Rozi. (2026). A Hybrid Bayesian ICA–LSTM Framework for Unsupervised-Like Anomaly Detection in Rolling Element Bearings. International Journal of Mechanical Engineering and Robotics Research, 15(2), 114–122. https://doi.org/10.18178/ijmerr.15.2.114-122
Primawati, P., Qalbina, F., Mulyanti, M., Yanuar, F., Devianto, D., Lapisa, R., & Rozi, F. (2025). Predictive Maintenance of Old Grinding Machines Using Machine Learning Techniques. Journal of Applied Engineering and Technological Science (JAETS), 6(2), 874–888. https://doi.org/10.37385/jaets.v6i2.6417
Primawati, P., Yanuar, F., Devianto, D., & Rozi, F. (2026). Residual-Based Unsupervised Bearing Fault Detection Using ICA-Enhanced LSTM Autoencoder. https://doi.org/10.28919/cmbn/9688
Purbojo, T., & Wijaya, A. P. (2025). Enhancing pose-based sign language recognition: A comparative study of preprocessing strategies with GRU and LSTM. Advance Sustainable Science, Engineering and Technology (ASSET), 7(2), 02502017. https://doi.org/10.26877/asset.v7i2.1658
Rafati, A., & Shaker, H. R. (2024). Predictive maintenance of district heating networks: A comprehensive review of methods and challenges. Thermal Science and Engineering Progress, 53, 102722. https://doi.org/10.1016/j.tsep.2024.102722
Raj, K. K., Kumar, S., Kumar, R. R., & Andriollo, M. (2024). Enhanced Fault Detection in Bearings Using Machine Learning and Raw Accelerometer Data: A Case Study Using the Case Western Reserve University Dataset. Information, 15(5), 259. https://doi.org/10.3390/info15050259
Rihi, A., Baïna, S., Mhada, F.-Z., El Bachari, E., Tagemouati, H., Guerboub, M., Benzakour, I., Baïna, K., & Abdelwahed, E. H. (2024). Innovative predictive maintenance for mining grinding mills: From LSTM-based vibration forecasting to pixel-based MFCC image and CNN. The International Journal of Advanced Manufacturing Technology, 135(3–4), 1271–1289. https://doi.org/10.1007/s00170-024-14588-3
Rozi, F., Primawati, P., Komaini, A., & Handayani, S. G. (2025). Applied Mathematical Modeling For 3d Kinematic Spatial Reconstruction In A Low-Cost Monocular Webcam-Based Squat Analysis System . Jurnal Testing Dan Implementasi Sistem Informasi, 3(1), 41-53. https://doi.org/10.55583/jtisi.v3i1.2197
Sahu, D., Dewangan, R. K., & Matharu, S. P. S. (2025). Hybrid CNN-LSTM model for fault diagnosis of rolling element bearings with operational defects. International Journal on Interactive Design and Manufacturing (IJIDeM), 19(8), 5737–5748. https://doi.org/10.1007/s12008-024-02165-7
Seoni, S., Jahmunah, V., Salvi, M., Barua, P. D., Molinari, F., & Acharya, U. R. (2023). Application of uncertainty quantification to artificial intelligence in healthcare: A review of last decade (2013–2023). Computers in Biology and Medicine, 165, 107441. https://doi.org/10.1016/j.compbiomed.2023.107441
Shahin, M., Chen, F. F., Hosseinzadeh, A., & Zand, N. (2023). Using machine learning and deep learning algorithms for downtime minimization in manufacturing systems: An early failure detection diagnostic service. The International Journal of Advanced Manufacturing Technology, 128(9–10), 3857–3883. https://doi.org/10.1007/s00170-023-12020-w
Song, K. Y., Chang, I. H., & Pham, H. (2019). A Testing Coverage Model Based on NHPP Software Reliability Considering the Software Operating Environment and the Sensitivity Analysis. Mathematics, 7(5), 450. https://doi.org/10.3390/math7050450
Stroescu, V.-C., & Olcay, E. (2022). Deep Learning-Based Approaches for Fault Detection in Disc Mower. IFAC-PapersOnLine, 55(6), 217–221. https://doi.org/10.1016/j.ifacol.2022.07.132
Syah, N., Haq, S., Ashar, F., & Arbi, Y. (2026). Exploring Energy Efficiency and User Attitudes toward Green Energy Implementation in University Buildings. International Journal of Environment, Engineering and Education, 8(1), 65–78. https://doi.org/10.55151/ijeedu.v8i1.362
Tama, B. A., Vania, M., Lee, S., & Lim, S. (2023). Recent advances in the application of deep learning for fault diagnosis of rotating machinery using vibration signals. Artificial Intelligence Review, 56(5), 4667–4709. https://doi.org/10.1007/s10462-022-10293-3
Thoppil, N. M., & Vasu, V. (2025). An Industrial IoT Framework for Predictive Maintenance of CNC Lathe Spindles: Integrating Deep Learning and Cloud-Based Analytics. Journal of Vibration Engineering & Technologies, 13(8), 590. https://doi.org/10.1007/s42417-025-02144-6
Ventricci, L., Ribeiro Junior, R. F., & Gomes, G. F. (2024). Motor fault classification using hybrid short-time Fourier transform and wavelet transform with vibration signal and convolutional neural network. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 46(6), 337. https://doi.org/10.1007/s40430-024-04890-2
Wahid, A., Breslin, J. G., & Intizar, M. A. (2022). Prediction of Machine Failure in Industry 4.0: A Hybrid CNN-LSTM Framework. Applied Sciences, 12(9), 4221. https://doi.org/10.3390/app12094221
Wang, C., Peng, Z., Liu, R., & Chen, C. (2022). Research on Multi-Fault Diagnosis Method Based on Time Domain Features of Vibration Signals. Sensors, 22(21), 8164. https://doi.org/10.3390/s22218164
Yanuar, F., Abrari, T., Rahmi Hg, I., & Zetra, A. (2023). Spatial Autoregressive Quantile Regression with Application on Open Unemployment Data. Science and Technology Indonesia, 8(2), 321–329. https://doi.org/10.26554/sti.2023.8.2.321-329
Yuan, F.-G., Zargar, S. A., Chen, Q., & Wang, S. (2020). Machine learning for structural health monitoring: Challenges and opportunities. In D. Zonta, H. Sohn, & H. Huang (Eds.), Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2020 (p. 2). SPIE. https://doi.org/10.1117/12.2561610
Zhan, X., Bai, H., Yan, H., Wang, R., Guo, C., & Jia, X. (2022). Diesel Engine Fault Diagnosis Method Based on Optimized VMD and Improved CNN. Processes, 10(11), 2162. https://doi.org/10.3390/pr10112162
CITEDNESS IN SCOPUS
CITEDNESS IN WOS
