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

• Published in: Archives of computational methods in engineering Vol. 24; no. 3; pp. 495 - 518
• Main Authors: Mukhopadhyay, T., Chakraborty, S., Dey, S., Adhikari, S., Chowdhury, R.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-07-2017; Springer Nature B.V
• Subjects: Composite structures; Computational efficiency; Computer simulation; Computing time; Covariance; Deformation effects; Engineering; Error analysis; Finite element method; Kriging interpolation; Mathematical and Computational Engineering; Mindlin plates; Monte Carlo simulation; Noise propagation; Original Paper; Random variables; Resonant frequencies; Shear deformation; Shells (structural forms); Uncertainty; Ordinary Kriging; Marginal Likelihood; Kriging; Covariance Function; Kriging Model
• ISSN: 1134-3060; 1886-1784
• DOI: 10.1007/s11831-016-9178-z

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.