A Learnable Radial Basis Function Network–Based Method for Decomposing Shock‐Induced Vibration Signals.

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Title: A Learnable Radial Basis Function Network–Based Method for Decomposing Shock‐Induced Vibration Signals.
Authors: Long, Yiyang1 (AUTHOR), Zhu, Wei1 (AUTHOR), Wen, Jun1 (AUTHOR), Ma, Feng1 (AUTHOR) kang@bit.edu.cn, Guo, Liwen1 (AUTHOR), Park, Junhong1 (AUTHOR) parkj@hanyang.ac.kr
Source: Shock & Vibration. 7/3/2026, Vol. 2026, p1-21. 21p.
Subjects: Radial basis functions, Signal separation, Structural dynamics, Impact (Mechanics), Modal analysis, Spectrum analysis, Underwater explosions
Abstract: Structural shock responses caused by underwater explosions contain transient components with overlapping frequency contents, which makes modal decomposition difficult. This paper proposes an adaptive decomposition and reconstruction method based on a learnable radial basis function network (RBFN). The response spectrum is represented by a compact set of Gaussian kernels, whose centers, bandwidths, and amplitudes are learned in the frequency domain. Sequential parameter updates, bandwidth penalization, and pruning based on kernel overlap are used to obtain modal components with limited spectral leakage and interpretable spectral features. The method is evaluated using acceleration responses from 50 points in a stiffened plate frame underwater explosion simulation and is compared with empirical mode decomposition (EMD), variational mode decomposition (VMD), empirical wavelet transform (EWT), Hilbert vibration decomposition (HVD), and local mean decomposition (LMD). The assessment considers reconstruction fidelity, phase portrait consistency, modal correlation, spectral overlap, computational cost, and parameter stability. The results show that RBFN preserves reconstruction consistency while reducing spectral overlap under the tested conditions. The near‐zero reconstruction error of EMD is discussed as a consequence of its additive completeness rather than direct evidence of modal separation quality. Measured shock responses from unstiffened and stiffened plate frame structures are further analyzed to examine the applicability of the learned spectral partition to experimental signals with broadband spectral contents and multiple peaks. [ABSTRACT FROM AUTHOR]
Copyright of Shock & Vibration is the property of Wiley-Blackwell 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: A Learnable Radial Basis Function Network–Based Method for Decomposing Shock‐Induced Vibration Signals.
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  Data: <searchLink fieldCode="AR" term="%22Long%2C+Yiyang%22">Long, Yiyang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhu%2C+Wei%22">Zhu, Wei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wen%2C+Jun%22">Wen, Jun</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ma%2C+Feng%22">Ma, Feng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kang@bit.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Guo%2C+Liwen%22">Guo, Liwen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Park%2C+Junhong%22">Park, Junhong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> parkj@hanyang.ac.kr</i>
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  Data: <searchLink fieldCode="JN" term="%22Shock+%26+Vibration%22">Shock & Vibration</searchLink>. 7/3/2026, Vol. 2026, p1-21. 21p.
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  Data: <searchLink fieldCode="DE" term="%22Radial+basis+functions%22">Radial basis functions</searchLink><br /><searchLink fieldCode="DE" term="%22Signal+separation%22">Signal separation</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+dynamics%22">Structural dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Impact+%28Mechanics%29%22">Impact (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Modal+analysis%22">Modal analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Spectrum+analysis%22">Spectrum analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Underwater+explosions%22">Underwater explosions</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Structural shock responses caused by underwater explosions contain transient components with overlapping frequency contents, which makes modal decomposition difficult. This paper proposes an adaptive decomposition and reconstruction method based on a learnable radial basis function network (RBFN). The response spectrum is represented by a compact set of Gaussian kernels, whose centers, bandwidths, and amplitudes are learned in the frequency domain. Sequential parameter updates, bandwidth penalization, and pruning based on kernel overlap are used to obtain modal components with limited spectral leakage and interpretable spectral features. The method is evaluated using acceleration responses from 50 points in a stiffened plate frame underwater explosion simulation and is compared with empirical mode decomposition (EMD), variational mode decomposition (VMD), empirical wavelet transform (EWT), Hilbert vibration decomposition (HVD), and local mean decomposition (LMD). The assessment considers reconstruction fidelity, phase portrait consistency, modal correlation, spectral overlap, computational cost, and parameter stability. The results show that RBFN preserves reconstruction consistency while reducing spectral overlap under the tested conditions. The near‐zero reconstruction error of EMD is discussed as a consequence of its additive completeness rather than direct evidence of modal separation quality. Measured shock responses from unstiffened and stiffened plate frame structures are further analyzed to examine the applicability of the learned spectral partition to experimental signals with broadband spectral contents and multiple peaks. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Shock & Vibration is the property of Wiley-Blackwell 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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        Value: 10.1155/vib/5366468
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      – Code: eng
        Text: English
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        PageCount: 21
        StartPage: 1
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      – SubjectFull: Radial basis functions
        Type: general
      – SubjectFull: Signal separation
        Type: general
      – SubjectFull: Structural dynamics
        Type: general
      – SubjectFull: Impact (Mechanics)
        Type: general
      – SubjectFull: Modal analysis
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      – SubjectFull: Spectrum analysis
        Type: general
      – SubjectFull: Underwater explosions
        Type: general
    Titles:
      – TitleFull: A Learnable Radial Basis Function Network–Based Method for Decomposing Shock‐Induced Vibration Signals.
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            NameFull: Long, Yiyang
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            NameFull: Zhu, Wei
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            NameFull: Wen, Jun
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            NameFull: Guo, Liwen
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            – D: 03
              M: 07
              Text: 7/3/2026
              Type: published
              Y: 2026
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              Value: 2026
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            – TitleFull: Shock & Vibration
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