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Bayesian calibration with missing data and model discrepancies: Application to high-speed train with uncertain control.

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Title: Bayesian calibration with missing data and model discrepancies: Application to high-speed train with uncertain control.
Authors: Jorge Do Marco, R.1,2,3 (AUTHOR) romain.jorge-domarco@sncf.fr, Perrin, G.1 (AUTHOR) guillaume.perrin@univ-eiffel.fr, Soize, C.3 (AUTHOR) christian.soize@univ-eiffel.fr, Funfschilling, C.2 (AUTHOR) christine.funfschilling@sncf.fr
Source: Journal of Sound & Vibration. Sep2026, Vol. 637, pN.PAG-N.PAG. 1p.
Subjects: Calibration, Missing data (Statistics), Railroad trains, Gaussian processes, Parameter estimation, Dynamical systems, Uncertainty (Information theory)
Abstract: • We calibrate dynamic models with uncertain and missing input data. • Our method models the log-likelihood using Gaussian Process regression. • The approach accounts for both model error and input uncertainty. • We reduce solver calls using a surrogate-based Bayesian framework. • A railway case study demonstrates robustness and efficiency. With the increasing complexity of engineering systems, the calibration of physical models has become a key step in ensuring predictive accuracy for industrial applications. In practice, however, calibration is often hindered by latent environmental variables whose influence on system behavior cannot be directly observed or controlled. Standard calibration techniques typically presume full knowledge of input variables — an assumption that, when violated, can lead to biased estimates and degraded model performance. This issue is exacerbated in dynamic systems, where both inputs and outputs are time-dependent functions, and measurements are inherently noisy and approximate. To address these limitations, we formulate the calibration problem within a Bayesian framework, treating the unknown environmental variables as random inputs with an associated probability distribution. Rather than optimizing calibration parameters for a fixed set of inputs, we compute their posterior distribution and marginalize over the distribution of the unobserved variables. This approach propagates input uncertainty through the model and provides a natural mechanism for regularizing model error, thereby enhancing both robustness and interpretability. We demonstrate the practical benefits of this method on a railway dynamics case study, where it outperforms standard calibration in terms of both accuracy and reliability under uncertainty. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Sound & Vibration is the property of Academic Press Inc. 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.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 193723687
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Bayesian calibration with missing data and model discrepancies: Application to high-speed train with uncertain control.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Sound+%26+Vibration%22">Journal of Sound & Vibration</searchLink>. Sep2026, Vol. 637, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Calibration%22">Calibration</searchLink><br /><searchLink fieldCode="DE" term="%22Missing+data+%28Statistics%29%22">Missing data (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Railroad+trains%22">Railroad trains</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+processes%22">Gaussian processes</searchLink><br /><searchLink fieldCode="DE" term="%22Parameter+estimation%22">Parameter estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertainty+%28Information+theory%29%22">Uncertainty (Information theory)</searchLink>
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  Data: • We calibrate dynamic models with uncertain and missing input data. • Our method models the log-likelihood using Gaussian Process regression. • The approach accounts for both model error and input uncertainty. • We reduce solver calls using a surrogate-based Bayesian framework. • A railway case study demonstrates robustness and efficiency. With the increasing complexity of engineering systems, the calibration of physical models has become a key step in ensuring predictive accuracy for industrial applications. In practice, however, calibration is often hindered by latent environmental variables whose influence on system behavior cannot be directly observed or controlled. Standard calibration techniques typically presume full knowledge of input variables — an assumption that, when violated, can lead to biased estimates and degraded model performance. This issue is exacerbated in dynamic systems, where both inputs and outputs are time-dependent functions, and measurements are inherently noisy and approximate. To address these limitations, we formulate the calibration problem within a Bayesian framework, treating the unknown environmental variables as random inputs with an associated probability distribution. Rather than optimizing calibration parameters for a fixed set of inputs, we compute their posterior distribution and marginalize over the distribution of the unobserved variables. This approach propagates input uncertainty through the model and provides a natural mechanism for regularizing model error, thereby enhancing both robustness and interpretability. We demonstrate the practical benefits of this method on a railway dynamics case study, where it outperforms standard calibration in terms of both accuracy and reliability under uncertainty. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Journal of Sound & Vibration is the property of Academic Press Inc. 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.jsv.2026.119830
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
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      – SubjectFull: Calibration
        Type: general
      – SubjectFull: Missing data (Statistics)
        Type: general
      – SubjectFull: Railroad trains
        Type: general
      – SubjectFull: Gaussian processes
        Type: general
      – SubjectFull: Parameter estimation
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Uncertainty (Information theory)
        Type: general
    Titles:
      – TitleFull: Bayesian calibration with missing data and model discrepancies: Application to high-speed train with uncertain control.
        Type: main
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            NameFull: Jorge Do Marco, R.
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            NameFull: Perrin, G.
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            NameFull: Soize, C.
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            – D: 01
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
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              Value: 637
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