Uncertainty propagation of frequency response functions using a multi-output Gaussian Process model

Jun Lu, Zhenfei Zhan, Daniel W. Apley, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


Uncertainty propagation of frequency response functions (FRFs) under parameter variations is crucial for structural design and reliability analysis. However, obtaining sufficiently large samples of FRFs from a high-fidelity finite element (FE) model can easily become unaffordable. To reduce the computational cost, much interest is focused on metamodeling techniques, but how to efficiently create a metamodel over the whole frequency domain still remains challenging. In this work, a novel nonparametric approach based on multi-output Gaussian Process (MOGP) modeling to speedup uncertainty propagation is proposed. First, modal decomposition together with a low-dimensional representation method is used to address the curse of dimensionality of FRF output. Subsequently, a MOGP model is employed to provide a fast vector-output approximation of the random modal parameters, which are needed thereafter for reconstruction of the FRFs at any frequency level. To demonstrate the numerical accuracy and computational efficiency of the proposed method, both a discrete and continuous numerical example are investigated. It is shown that the proposed approach not only achieves accurate estimation of FRF variability, but also greatly improves computational efficiency.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalComputers and Structures
StatePublished - Jun 2019


  • Frequency response function
  • Functional output
  • Gaussian Process model
  • Nonparametric approach
  • Uncertainty propagation

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Modeling and Simulation
  • General Materials Science
  • Mechanical Engineering
  • Computer Science Applications


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