Combining Polynomial Chaos Expansions and Kriging

Abstract

Computer simulation has emerged as a key tool for designing and assessing engineeringsystems in the last two decades. Uncertainty quantification has becomepopular more recently as a way to model all the uncertainties affecting the systemand their impact onto its performance.In this respect meta-models (a.k.a. surrogate models) have gained interest. Indeeddealing with uncertainties requires running the computer model many times,which may not be affordable for complex models. Surrogate models mimic the behaviourof the original model while being cheap to evaluate.Polynomial chaos expansion (PCE) and Kriging are two popular techniques, whichhave been developed with very little interaction so far. In this report we present a newapproach, called PC-Kriging, that combines the two tools. The algorithm is based onthe universal Kriging model where the trend is represented by a set or orthonormalpolynomials.Various aspects of the new metamodelling technique are presented and investigatedin details. The discussion starts with a survey on methods for generating anoptimal design of experiments (DOE). The PC-Kriging algorithm inherits many parametersand sub-methods such as the number of polynomial terms and the choiceof the autocorrelation kernel. A variety of kernels are presented and discussed.The methods are compared on analytical benchmark functions. The conclusionof this report is that PC-Kriging performs better or at least as well as PCE or Krigingtaken separately in terms of relative generalized error (L2-error).

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