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Fault Diagnosis and Vibration Signal Processing in Rotor Systems

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A special issue of Sensors (ISSN 1424-8220). This special issue belongs to the section "Fault Diagnosis & Sensors".

Deadline for manuscript submissions: 25 April 2025 | Viewed by 18265

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Special Issue Editors

Dr. Yongfeng Yang

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Guest Editor

Institute of Vibration Engineering, Northwestern Polytechnical University, Xi’an 710072, China
Interests: fault diagnosis; vibration signal processing; rotor systems; nonlinear dynamics

Prof. Dr. Jin Zhou

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Guest Editor

College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Interests: magnetic bearings; vibration control; rotor dynamics; mechatronics; rotating machinery
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Rafael Morales

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Guest Editor

Escuela Técnica Superior de Ingenieros Industriales de Ciudad Real, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
Interests: offshore sustainable renewable energy systems; maintenance maneuvers; robotics; control; automation and sensor integration applied to offshore renewable energy systems
Special Issues, Collections and Topics in MDPI journals

Dr. Alexandre Presas

E-Mail Website
Guest Editor

Center for Industrial Diagnosis and Fluid Dynamics, Polytechnic University of Catalonia, 08028 Barcelona, Spain
Interests: fatigue failures; erosion and wear; signal processing; rotor systems; modal analysis; resonance problems; vibrations in hydraulic machinery
Special Issues, Collections and Topics in MDPI journals

Dr. Saleh Mobayen

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Guest Editor

Graduate School of Intelligent Data Science, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 640301, Taiwan
Interests: fault diagnosis; robust control; variable structure control; robotics; wind turbines
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Rotor systems are kernel components of rotating machinery and are applied in most industrial fields, such as aero-engines, gas turbines, steam turbines, generators, electric motors, and mechanical manufacturing. Meanwhile, some renewable energy systems contain a lot of rotating subsystems, such as synchronous generators, wind power systems, power-driven machines, and bearing systems. With the performance improvements of the rotating machinery, the complications of structural design are ever increasing. Vibration is integral to these rotating systems, especially in high-speed rotating systems, and the almost all the faults may show special characteristic compared with regular work. The aim of this Special Issue is to compile original research and review articles on the topics of fault diagnosis and related vibration signal processing. Submissions about the current state of dynamic analysis, as well as advances in, structural optimization of, and vibration control of nonlinear rotor systems are welcome. Research on theories, simulations, experiments, and engineering applications are all welcome. We hope that this Special Issue will create an academic discussion in the field.

Dr. Yongfeng Yang
Prof. Dr. Jin Zhou
Prof. Dr. Rafael Morales
Dr. Alexandre Presas
Dr. Saleh Mobayen
Guest Editors

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Keywords

vbiration of wind power system with faults
dynamic modeling of rotor systems
improvement of theoretical methods rotor systems
simulation methods for rotor systems
nonlinear vibration response characteristics of rotor systems with faults
vibration and stability control of rotor systems
active, semi-active, and passive control techniques applied in rotor systems
applications of intelligent controls, adaptive controls, nonlinear controls, and linear controls in rotor systems
intelligent sensing and signal analysis for rotor systems
intellignet fault diagnosis for rotor systems
rotor systems with magnetic bearings

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Published Papers (12 papers)

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Research

26 pages, 7065 KiB

Open AccessArticle

From Envelope Spectra to Bearing Remaining Useful Life: An Intelligent Vibration-Based Prediction Model with Quantified Uncertainty

by Haobin Wen, Long Zhang and Jyoti K. Sinha

Sensors 2024, 24(22), 7257; https://doi.org/10.3390/s24227257 - 13 Nov 2024

Viewed by 362

Abstract

Bearings are pivotal components of rotating machines where any defects could propagate and trigger systematic failures. Once faults are detected, accurately predicting remaining useful life (RUL) is essential for optimizing predictive maintenance. Although data-driven methods demonstrate promising performance in direct RUL prediction, their robustness and practicability need further improvement regarding physical interpretation and uncertainty quantification. This work leverages variational neural networks to model bearing degradation behind envelope spectra. A convolutional variational autoencoder for regression (CVAER) is developed to probabilistically predict RUL distributions with confidence measures. Enhanced average envelope spectra (AES) are used as network input for its physical robustness in bearing condition assessment and fault detection. The use of the envelope spectrum ensures that it contains only bearing-related information by removing other rotor-related frequencies, hence it improves the RUL prediction. Unlike traditional variational autoencoders, the probabilistic regressor and latent generator are formulated to quantify uncertainty in RUL estimates and learn meaningful latent representations conditioned on specific RUL. Experimental validations are conducted on vibration data collected using multiple accelerometers whose natural frequencies cover bearing resonance ranges to ensure fault detection reliability. Beyond conventional bearing diagnosis, envelope spectra are extended for statistical RUL prediction integrating physical knowledge of actual defect conditions. Comparative and ablation studies are conducted against benchmark models to demonstrate their effectiveness. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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16 pages, 6667 KiB

Open AccessArticle

Coupling Fault Diagnosis of Bearings Based on Hypergraph Neural Network

by Shenglong Wang, Xiaoxuan Jiao, Bo Jing, Jinxin Pan, Xiangzhen Meng, Yifeng Huang and Shaoting Pei

Sensors 2024, 24(19), 6391; https://doi.org/10.3390/s24196391 - 2 Oct 2024

Viewed by 519

Abstract

Coupling faults that simultaneously occur during the operation of mechanical equipment are widespread. These faults encompass a diverse range of high-order coupling relationships, involving multiple base fault types. Based on the advantages of hypergraphs for higher-order relationship descriptions, two coupling fault diagnosis architectures based on the hypergraph neural network are proposed in this paper: 1. In the coupling fault diagnosis framework based on feature generation, the base faults serve as the hypergraph nodes, and each hyperedge connects the base faults. The generator, which consists of the hypergraph neural network, generates coupling faults as negative samples to enforce regularization constraints for the discriminator training. 2. In the coupling fault diagnosis framework based on feature extraction, each node represents a fault mode, and each hyperedge connects nodes with common failure modes. The multi-head attention mechanism extracts the features of base faults, and the common fault features in a hyperedge are aggregated via the hypergraph neural network. The inner product correlation is used to diagnose the fault modes. The results show that the diagnostic accuracy for coupling faults with the two frameworks reaches 88.6% and 86.76%, respectively. Both frameworks can be used for the diagnosis and analysis of high-order coupling faults. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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24 pages, 22521 KiB

Open AccessArticle

GCN-Based LSTM Autoencoder with Self-Attention for Bearing Fault Diagnosis

by Daehee Lee, Hyunseung Choo and Jongpil Jeong

Sensors 2024, 24(15), 4855; https://doi.org/10.3390/s24154855 - 26 Jul 2024

Viewed by 1089

Abstract

The manufacturing industry has been operating within a constantly evolving technological environment, underscoring the importance of maintaining the efficiency and reliability of manufacturing processes. Motor-related failures, especially bearing defects, are common and serious issues in manufacturing processes. Bearings provide accurate and smooth movements and play essential roles in mechanical equipment with shafts. Given their importance, bearing failure diagnosis has been extensively studied. However, the imbalance in failure data and the complexity of time series data make diagnosis challenging. Conventional AI models (convolutional neural networks (CNNs), long short-term memory (LSTM), support vector machine (SVM), and extreme gradient boosting (XGBoost)) face limitations in diagnosing such failures. To address this problem, this paper proposes a bearing failure diagnosis model using a graph convolution network (GCN)-based LSTM autoencoder with self-attention. The model was trained on data extracted from the Case Western Reserve University (CWRU) dataset and a fault simulator testbed. The proposed model achieved 97.3% accuracy on the CWRU dataset and 99.9% accuracy on the fault simulator dataset. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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16 pages, 13007 KiB

Open AccessArticle

Coupling Fault Diagnosis Based on Dynamic Vertex Interpretable Graph Neural Network

by Shenglong Wang, Bo Jing, Jinxin Pan, Xiangzhen Meng, Yifeng Huang and Xiaoxuan Jiao

Sensors 2024, 24(13), 4356; https://doi.org/10.3390/s24134356 - 4 Jul 2024

Cited by 1 | Viewed by 699

Abstract

Mechanical equipment is composed of several parts, and the interaction between parts exists throughout the whole life cycle, leading to the widespread phenomenon of fault coupling. The diagnosis of independent faults cannot meet the requirements of the health management of mechanical equipment under actual working conditions. In this paper, the dynamic vertex interpretable graph neural network (DIGNN) is proposed to solve the problem of coupling fault diagnosis, in which dynamic vertices are defined in the data topology. First, in the date preprocessing phase, wavelet transform is utilized to make input features interpretable and reduce the uncertainty of model training. In the fault topology, edge connections are made between nodes according to the fault coupling information, and edge connections are established between dynamic nodes and all other nodes. Second the data topology with dynamic vertices is used in the training phase and in the testing phase, the time series data are only fed into dynamic vertices for classification and analysis, which makes it possible to realize coupling fault diagnosis in an industrial production environment. The features extracted in different layers of DIGNN interpret how the model works. The method proposed in this paper can realize the accurate diagnosis of independent faults in the dataset with an accuracy of 100%, and can effectively judge the coupling mode of coupling faults with a comprehensive accuracy of 88.3%. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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29 pages, 36219 KiB

Open AccessArticle

Off-Design Operation and Cavitation Detection in Centrifugal Pumps Using Vibration and Motor Stator Current Analyses

by Yuejiang Han, Jiamin Zou, Alexandre Presas, Yin Luo and Jianping Yuan

Sensors 2024, 24(11), 3410; https://doi.org/10.3390/s24113410 - 25 May 2024

Cited by 1 | Viewed by 1045

Abstract

Centrifugal pumps are essential in many industrial processes. An accurate operation diagnosis of centrifugal pumps is crucial to ensure their reliable operation and extend their useful life. In real industry applications, many centrifugal pumps lack flowmeters and accurate pressure sensors, and therefore, it is not possible to determine whether the pump is operating near its best efficiency point (BEP). This paper investigates the detection of off-design operation and cavitation for centrifugal pumps with accelerometers and current sensors. To this end, a centrifugal pump was tested under off-design conditions and various levels of cavitation. A three-axis accelerometer and three Hall-effect current sensors were used to collect vibration and stator current signals simultaneously under each state. Both kinds of signals were evaluated for their effectiveness in operation diagnosis. Signal processing methods, including wavelet threshold function, variational mode decomposition (VMD), Park vector modulus transformation, and a marginal spectrum were introduced for feature extraction. Seven families of machine learning-based classification algorithms were evaluated for their performance when used for off-design and cavitation identification. The obtained results, using both types of signals, prove the effectiveness of both approaches and the advantages of combining them in achieving the most reliable operation diagnosis results for centrifugal pumps. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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14 pages, 3713 KiB

Open AccessArticle

An Intelligent Ball Bearing Fault Diagnosis System Using Enhanced Rotational Characteristics on Spectrogram

by Gyujin Seong and Dongwan Kim

Sensors 2024, 24(3), 776; https://doi.org/10.3390/s24030776 - 25 Jan 2024

Cited by 2 | Viewed by 1432

Abstract

Faults in the ball bearing are a major cause of failure in rotating machinery where ball bearings are used. Therefore, there is a growing demand for ball bearing fault diagnosis to prevent failures in rotating machinery. Although studies on the fault diagnosis of bearing have been conducted using temperature measurements and sound monitoring, these methods have limitations, because they are affected by external noise. Therefore, many researchers have studied vibration monitoring for bearing fault diagnosis. Among these, mel-frequency cepstral coefficients (MFCCs) and 2D convolutional neural networks (CNNs) have attracted significant attention in vibration monitoring schemes. However, the MFCC in existing studies requires a high sampling rate and an expansive frequency band utilization. In addition, 2D CNNs are highly complex. In this study, a rotational characteristic emphasis (RCE) spectrogram process and an optimized CNN were proposed to solve these problems. The RCE spectrogram process analyzes a narrow frequency band and produces low-resolution images. The optimized CNN was designed with a shallow network structure. The experimental results showed an accuracy of 0.9974 for the proposed system. The optimized CNN model has parameters of 5.81 KB and FLOPs of

1.53 \times 10^{6}

. We demonstrate that the proposed ball bearing fault diagnosis system can achieve high accuracy with low complexity. Thus, we propose a ball bearing fault diagnosis scheme that is applicable to a low sampling rate and changing rotation frequency. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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40 pages, 29073 KiB

Open AccessArticle

Scale-Fractal Detrended Fluctuation Analysis for Fault Diagnosis of a Centrifugal Pump and a Reciprocating Compressor

by Ruben Medina, René-Vinicio Sánchez, Diego Cabrera, Mariela Cerrada, Edgar Estupiñan, Wengang Ao and Rafael E. Vásquez

Sensors 2024, 24(2), 461; https://doi.org/10.3390/s24020461 - 11 Jan 2024

Cited by 1 | Viewed by 1476

Abstract

Reciprocating compressors and centrifugal pumps are rotating machines used in industry, where fault detection is crucial for avoiding unnecessary and costly downtime. A novel method for fault classification in reciprocating compressors and multi-stage centrifugal pumps is proposed. In the feature extraction stage, raw vibration signals are processed using multi-fractal detrended fluctuation analysis (MFDFA) to extract features indicative of different types of faults. Such MFDFA features enable the training of machine learning models for classifying faults. Several classical machine learning models and a deep learning model corresponding to the convolutional neural network (CNN) are compared with respect to their classification accuracy. The cross-validation results show that all models are highly accurate for classifying the 13 types of faults in the centrifugal pump, the 17 valve faults, and the 13 multi-faults in the reciprocating compressor. The random forest subspace discriminant (RFSD) and the CNN model achieved the best results using MFDFA features calculated with quadratic approximations. The proposed method is a promising approach for fault classification in reciprocating compressors and multi-stage centrifugal pumps. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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15 pages, 3710 KiB

Open AccessArticle

Physics-Informed Neural Networks for the Condition Monitoring of Rotating Shafts

by Marc Parziale, Luca Lomazzi, Marco Giglio and Francesco Cadini

Sensors 2024, 24(1), 207; https://doi.org/10.3390/s24010207 - 29 Dec 2023

Cited by 5 | Viewed by 2198

Abstract

Condition monitoring of rotating shafts is essential for ensuring the reliability and optimal performance of machinery in diverse industries. In this context, as industrial systems become increasingly complex, the need for efficient data processing techniques is paramount. Deep learning has emerged as a dominant approach due to its capacity to capture intricate data patterns and relationships. However, a prevalent challenge lies in the black-box nature of many deep learning algorithms, which often operate without adhering to the underlying physical characteristics intrinsic to the studied phenomena. To address this limitation and enhance the fusion of data-driven methodologies with the fundamental physics of the system under study, this paper leverages physics-informed neural networks (PINNs). Specifically, a simple but realistic numerical case study of an extended Jeffcott rotor model, encompassing damping effects and anisotropic supports for a more comprehensive modelling, is considered. PINNs are used for the estimation of five parameters that characterize the health state of the system. These parameters encompass the radial and angular position of the static unbalance due to the disk installed on the shaft, the stiffness along the principal axes of elasticity, and the non-rotating damping coefficient. The estimation is conducted solely by exploiting the displacement signals from the centre of the disk and, to showcase the efficacy and precision provided by this novel methodology, various scenarios involving different constant rotational speeds are examined. Additionally, the impact of noisy input data is also taken into account within the analysis and the performance is compared to that of traditional optimization algorithms used for parameters estimation. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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15 pages, 9786 KiB

Open AccessArticle

Research on Circuit Breaker Operating Mechanism Fault Diagnosis Method Combining Global-Local Feature Extraction and KELM

by Qinzhe Liu, Xiaolong Wang, Zhaojing Guo, Jian Li, Wei Xu, Xiaowen Dai, Chenlei Liu and Tong Zhao

Sensors 2024, 24(1), 124; https://doi.org/10.3390/s24010124 - 26 Dec 2023

Viewed by 1224

Abstract

In response to the lack of generality in feature extraction using modal decomposition methods and the susceptibility of diagnostic performance to parameter selection in traditional mechanical fault diagnosis of high-voltage circuit breaker operating mechanisms, this paper proposes a Global-Local feature extraction method based on Generalized S-Transform (S-Translate) combined with Gray Level Co-Occurrence Matrix (GLCM) and complemented by Maximum Relevance and Minimum Redundancy (mRMR) feature selection. The GL (Global-Local)-mRMR-KELM fault diagnosis model is proposed, which employs the Kernel Extreme Learning Machine (KELM). In this model, the original time-frequency domain features and the time-frequency features of the Generalized S-Transform matrix of vibration signals under different states of the circuit breaker are first extracted as global features. Then, the GLCM is obtained to extract texture features as local features. Finally, the mRMR and KELM are comprehensively applied to perform feature selection and classification on the dataset, thereby accomplishing the fault diagnosis of the circuit breaker’s operating mechanism. In this study, the 72.5 kV SF₆ circuit breaker operating mechanism is taken as the research object, and three types of mechanical faults are simulated to obtain a vibration signal. Experimental results verify the effectiveness of the proposed GL-mRMR-KELM model, achieving a diagnostic accuracy of 96%. This research provides a feasible approach for the fault diagnosis of circuit breaker operating mechanisms. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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15 pages, 10213 KiB

Open AccessArticle

Digital Twin of a Gear Root Crack Prognosis

by Omri Matania, Eric Bechhoefer and Jacob Bortman

Sensors 2023, 23(24), 9883; https://doi.org/10.3390/s23249883 - 17 Dec 2023

Cited by 4 | Viewed by 1372

Abstract

Digital twins play a significant role in Industry 4.0, offering the potential to revolutionize machinery maintenance. In this paper, we introduce a new digital twin designed to address the open problem of predicting gear root crack propagation. This digital twin uses signal processing and model fitting to continuously monitor the condition of the root crack and successfully estimate the remaining time until immediate maintenance is required for the physical asset. The functionality of this new digital twin is demonstrated through the experimental data obtained from a planetary gear, where comparisons are made between the actual and estimated severity of the fault, as well as the remaining time until maintenance. It is shown that the digital twin addresses the open problem of predicting gear root crack propagation. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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16 pages, 4445 KiB

Open AccessArticle

Rolling Bearing Composite Fault Diagnosis Method Based on Enhanced Harmonic Vector Analysis

by Jiantao Lu, Qitao Yin and Shunming Li

Sensors 2023, 23(11), 5115; https://doi.org/10.3390/s23115115 - 27 May 2023

Cited by 3 | Viewed by 1203

Abstract

Composite fault diagnosis of rolling bearings is very challenging work, especially when the characteristic frequency ranges of different fault types overlap. To solve this problem, an enhanced harmonic vector analysis (EHVA) method was proposed. Firstly, the wavelet threshold (WT) denoising method is used to denoise the collected vibration signals to reduce the influence of noise. Next, harmonic vector analysis (HVA) is used to remove the convolution effect of the signal transmission path, and blind separation of fault signals is carried out. The cepstrum threshold is used in HVA to enhance the harmonic structure of the signal, and a Wiener-like mask will be constructed to make the separated signals more independent in each iteration. Then, the backward projection technique is used to align the frequency scale of the separated signals, and each fault signal can be obtained from composite fault diagnosis signals. Finally, to make the fault characteristics more prominent, a kurtogram was used to find the resonant frequency band of the separated signals by calculating its spectral kurtosis. Semi-physical simulation experiments are conducted using the rolling bearing fault experiment data to verify the effectiveness of the proposed method. The results show that the proposed method, EHVA, can effectively extract the composite faults of rolling bearings. Compared to fast independent component analysis (FICA) and traditional HVA, EHVA improves separation accuracy, enhances fault characteristics, and has higher accuracy and efficiency compared to fast multichannel blind deconvolution (FMBD). Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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21 pages, 1129 KiB

Open AccessArticle

Machine Fault Detection Using a Hybrid CNN-LSTM Attention-Based Model

by Andressa Borré, Laio Oriel Seman, Eduardo Camponogara, Stefano Frizzo Stefenon, Viviana Cocco Mariani and Leandro dos Santos Coelho

Sensors 2023, 23(9), 4512; https://doi.org/10.3390/s23094512 - 5 May 2023

Cited by 41 | Viewed by 4400

Abstract

The predictive maintenance of electrical machines is a critical issue for companies, as it can greatly reduce maintenance costs, increase efficiency, and minimize downtime. In this paper, the issue of predicting electrical machine failures by predicting possible anomalies in the data is addressed through time series analysis. The time series data are from a sensor attached to an electrical machine (motor) measuring vibration variations in three axes: X (axial), Y (radial), and Z (radial X). The dataset is used to train a hybrid convolutional neural network with long short-term memory (CNN-LSTM) architecture. By employing quantile regression at the network output, the proposed approach aims to manage the uncertainties present in the data. The application of the hybrid CNN-LSTM attention-based model, combined with the use of quantile regression to capture uncertainties, yielded superior results compared to traditional reference models. These results can benefit companies by optimizing their maintenance schedules and improving the overall performance of their electric machines. Full article

(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)

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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Off-design Operation and Cavitation Detection in Centrifugal Pumps Using Vibration and Motor Stator Current Analyses
Authors: Yuejiang Han, Jiamin Zou, Alexandre Presas, Yin Luo, Jianping Yuan
Affiliation: (1): Yuejiang Han (Research Center of Fluid Machinery Engineering and Technology, Jiangsu University) (2): Jiamin Zou ( Centre for Industrial Diagnostics and Fluid Dynamics, UPC ) (3): Alexandre Presas (Centre for Industrial Diagnostics and Fluid Dynamics, UPC)* (corresponding) (4): Yin Luo (Research Center of Fluid Machinery Engineering and Technology, Jiangsu University) (5): Jianping Yuan (Research Center of Fluid Machinery Engineering and Technology, Jiangsu University)
Abstract: Diagnosis of centrifugal pumps is crucial to ensure their reliable operation. This paper investigates two commonly encountered problems in centrifugal pumps: off-design operation and cavitation. A centrifugal pump was tested under off-design conditions and various levels of cavitation. Vibration and stator current signals were sampled simultaneously under each state, and both are evaluated for their effectiveness in operation diagnosis. Signal processing methods, including wavelet threshold function, variational mode decomposition (VMD), Park vector modulus transformation, and marginal spectrum are introduced for feature extraction. Seven families of machine learning-based classification algorithms are evaluated for their performance when used for off-design and cavitation identification. The obtained results, using both types of signals, prove the effectiveness of both approaches and the advantages of combining them in achieving the most reliable operation diagnosis results for centrifugal pumps.

Title: From Envelope Spectra to Bearing Remaining Useful Life: An Intelligent Vibration-based Prediction Model with Quantified Uncertainty
Authors: Haobin Wen; Long Zhang; Jyoti K. Sinha
Affiliation: The University of Manchester, UK
Abstract: Bearings are pivotal components of rotating machines where any defects could propagate and trigger systematic failures. For prognostics and health management (PHM), accurately predicting remaining useful life (RUL) is essential for optimizing predictive maintenance. Although data-driven methods demonstrate promising performance in direct RUL prediction, their robustness and practicability need further improvement regarding physical interpretation and uncertainty quantification. This work leverages variational neural networks to model bearing degradation behind envelope spectra. A convolutional variational autoencoder for regression (CVAER) is developed to probabilistically predict RUL distributions with confidence measures. Enhanced average envelope spectra (AES) are used as network input for its physical robustness in bearing condition assessment and fault detection. The use of the envelope spectrum make sure that it contains only bearing related information by removing other rotor related frequencies, hence it improves the RUL prediction. Unlike traditional variational autoencoder, the probabilistic regressor and latent generator are formulated to quantify uncertainty in RUL estimates and learn meaningful latent representations conditioned on specific RUL. Experimental validations are conducted on vibration data collected using multiple accelerometers, whose natural frequencies cover bearing resonance ranges to ensure fault detection reliability. Beyond conventional bearing diagnosis, envelope analysis is extended to statistical RUL prediction integrating physical knowledge of actual defect conditions. Comparative and ablation studies are conducted against benchmark models to demonstrate its effectiveness.

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