Remaining useful life prediction with uncertainty quantification for rotating machinery: A method based on explainable variational deep gaussian process.

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Title: Remaining useful life prediction with uncertainty quantification for rotating machinery: A method based on explainable variational deep gaussian process.
Authors: Liu, Xiuli1,2 (AUTHOR), Cui, Shuo1,2,3 (AUTHOR) 1317754704@qq.com, Qiao, Wan1,2,3 (AUTHOR), Liu, Jianyu1,2,3 (AUTHOR), Wu, Guoxin1,2,3 (AUTHOR)
Source: Neurocomputing. Jul2025, Vol. 638, pN.PAG-N.PAG. 1p.
Subjects: Remaining useful life, Sensor placement, Reliability in engineering, Gaussian processes, Statistical correlation, Rotating machinery, Monitoring of machinery
Abstract: Remaining Useful Life (RUL) prediction is one of the key technologies to ensure the safety and reliability of mechanical equipment. To address the challenges of low prediction accuracy and insufficient uncertainty quantification in rotating machinery monitoring, this paper proposes an innovative Variational Deep Gaussian Process (VDGP) method. The proposed method adopts an Adaptive Inter-layer Variational Inference (AIVI) strategy, integrating inter-layer dependency modeling, adaptive inducing point optimization, and hierarchical variational lower bound, enhancing information transfer and feature extraction in multi-layer structures while reducing redundant computation and improving training efficiency. Through Shapley Additive exPlanations (SHAP) analysis and correlation analysis between input features and hidden layer node outputs, the key factors in RUL prediction are deeply explored. The VDGP method is validated using the C-MAPSS dataset and a wind turbine planetary gearbox dataset, and it is thoroughly compared with classical methods and state-of-the-art methods from the past three years. Experimental results show that the VDGP method not only achieves superior prediction accuracy but also effectively quantifies prediction uncertainty. Additionally, through SHAP analysis and correlation analysis between input features and hidden layer node outputs, low-contribution features are identified and removed, significantly reducing the number of required sensors and deployment costs. This improves computational efficiency and real-time performance, providing strong technical support for equipment health evaluation, sensor deployment optimization in industrial applications, cost reduction, and enhanced real-time monitoring and decision-making efficiency. • Proposed an innovative VDGP method with AIVI strategy for Remaining Useful Life prediction. • Provide more accurate uncertainty quantification for predictions. • Reveal degradation mechanisms from the perspective of RUL prediction model explainability. • Obtain a wind turbine planetary gear dataset from self-conducted experiments. • Provided key guidance for sensor deployment optimization in industrial applications. [ABSTRACT FROM AUTHOR]
Copyright of Neurocomputing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
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  Data: Remaining useful life prediction with uncertainty quantification for rotating machinery: A method based on explainable variational deep gaussian process.
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  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Xiuli%22">Liu, Xiuli</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Cui%2C+Shuo%22">Cui, Shuo</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> 1317754704@qq.com</i><br /><searchLink fieldCode="AR" term="%22Qiao%2C+Wan%22">Qiao, Wan</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Jianyu%22">Liu, Jianyu</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wu%2C+Guoxin%22">Wu, Guoxin</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="DE" term="%22Remaining+useful+life%22">Remaining useful life</searchLink><br /><searchLink fieldCode="DE" term="%22Sensor+placement%22">Sensor placement</searchLink><br /><searchLink fieldCode="DE" term="%22Reliability+in+engineering%22">Reliability in engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+processes%22">Gaussian processes</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+correlation%22">Statistical correlation</searchLink><br /><searchLink fieldCode="DE" term="%22Rotating+machinery%22">Rotating machinery</searchLink><br /><searchLink fieldCode="DE" term="%22Monitoring+of+machinery%22">Monitoring of machinery</searchLink>
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  Label: Abstract
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  Data: Remaining Useful Life (RUL) prediction is one of the key technologies to ensure the safety and reliability of mechanical equipment. To address the challenges of low prediction accuracy and insufficient uncertainty quantification in rotating machinery monitoring, this paper proposes an innovative Variational Deep Gaussian Process (VDGP) method. The proposed method adopts an Adaptive Inter-layer Variational Inference (AIVI) strategy, integrating inter-layer dependency modeling, adaptive inducing point optimization, and hierarchical variational lower bound, enhancing information transfer and feature extraction in multi-layer structures while reducing redundant computation and improving training efficiency. Through Shapley Additive exPlanations (SHAP) analysis and correlation analysis between input features and hidden layer node outputs, the key factors in RUL prediction are deeply explored. The VDGP method is validated using the C-MAPSS dataset and a wind turbine planetary gearbox dataset, and it is thoroughly compared with classical methods and state-of-the-art methods from the past three years. Experimental results show that the VDGP method not only achieves superior prediction accuracy but also effectively quantifies prediction uncertainty. Additionally, through SHAP analysis and correlation analysis between input features and hidden layer node outputs, low-contribution features are identified and removed, significantly reducing the number of required sensors and deployment costs. This improves computational efficiency and real-time performance, providing strong technical support for equipment health evaluation, sensor deployment optimization in industrial applications, cost reduction, and enhanced real-time monitoring and decision-making efficiency. • Proposed an innovative VDGP method with AIVI strategy for Remaining Useful Life prediction. • Provide more accurate uncertainty quantification for predictions. • Reveal degradation mechanisms from the perspective of RUL prediction model explainability. • Obtain a wind turbine planetary gear dataset from self-conducted experiments. • Provided key guidance for sensor deployment optimization in industrial applications. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Neurocomputing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.neucom.2025.130232
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Remaining useful life
        Type: general
      – SubjectFull: Sensor placement
        Type: general
      – SubjectFull: Reliability in engineering
        Type: general
      – SubjectFull: Gaussian processes
        Type: general
      – SubjectFull: Statistical correlation
        Type: general
      – SubjectFull: Rotating machinery
        Type: general
      – SubjectFull: Monitoring of machinery
        Type: general
    Titles:
      – TitleFull: Remaining useful life prediction with uncertainty quantification for rotating machinery: A method based on explainable variational deep gaussian process.
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            NameFull: Liu, Xiuli
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            NameFull: Cui, Shuo
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            NameFull: Qiao, Wan
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            NameFull: Liu, Jianyu
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              M: 07
              Text: Jul2025
              Type: published
              Y: 2025
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