A Critical Assessment of Kriging Model Variants for High-Fidelity Uncertainty Quantification in Dynamics of composite Shells

  • T. MukhopadhyayEmail author
  • S. Chakraborty
  • S. Dey
  • S. Adhikari
  • R. Chowdhury
Original Paper


This paper presents a critical comparative assessment of Kriging model variants for surrogate based uncertainty propagation considering stochastic natural frequencies of composite doubly curved shells. The five Kriging model variants studied here are: Ordinary Kriging, Universal Kriging based on pseudo-likelihood estimator, Blind Kriging, Co-Kriging and Universal Kriging based on marginal likelihood estimator. First three stochastic natural frequencies of the composite shell are analysed by using a finite element model that includes the effects of transverse shear deformation based on Mindlin’s theory in conjunction with a layer-wise random variable approach. The comparative assessment is carried out to address the accuracy and computational efficiency of five Kriging model variants. Comparative performance of different covariance functions is also studied. Subsequently the effect of noise in uncertainty propagation is addressed by using the Stochastic Kriging. Representative results are presented for both individual and combined stochasticity in layer-wise input parameters to address performance of various Kriging variants for low dimensional and relatively higher dimensional input parameter spaces. The error estimation and convergence studies are conducted with respect to original Monte Carlo Simulation to justify merit of the present investigation. The study reveals that Universal Kriging coupled with marginal likelihood estimate yields the most accurate results, followed by Co-Kriging and Blind Kriging. As far as computational efficiency of the Kriging models is concerned, it is observed that for high-dimensional problems, CPU time required for building the Co-Kriging model is significantly less as compared to other Kriging variants.


Kriging Covariance Function Ordinary Kriging Marginal Likelihood Kriging Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



TM acknowledges the financial support from Swansea University through the award of Zienkiewicz Scholarship during the period of this work. SC acknowledges the support of MHRD, Government of India for the financial support provided during this work. SA acknowledges the financial support from The Royal Society of London through the Wolfson Research Merit award. RC acknowledges the support of The Royal Society through Newton Alumni Funding.


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Copyright information

© CIMNE, Barcelona, Spain 2016

Authors and Affiliations

  • T. Mukhopadhyay
    • 1
    Email author
  • S. Chakraborty
    • 2
  • S. Dey
    • 3
  • S. Adhikari
    • 1
  • R. Chowdhury
    • 2
  1. 1.College of EngineeringSwansea UniversitySwanseaUK
  2. 2.Department of Civil EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia
  3. 3.Leibniz-Institut für Polymerforschung Dresden e.V.DresdenGermany

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