A Non-stationary Covariance-Based Kriging Method with Adaptation to Irregularities in the Response Behavior

Meta-models are widely used to facilitate the analysis and optimization of engineering systems that involve computationally expensive simulations. Kriging is widely used as a meta-modeling technique to build surrogate models. However, the assumption of a stationary covariance structure underlying Kriging does not hold in situations where the level of smoothness of a response varies significantly. In this paper, the non-stationary covariance structure is incorporated into Kriging meta-modeling for computer simulations. To represent the non-stationary covariance structure, we adopt a non-linear mapping approach based on parameterized density functions. To avoid over-parameterizing for the high dimension problems, we use step function to represent the density function. To build a density function suited to the real function, we define the step function by the irregularity of region which is characterization by the appearance frequency of the local optima. Numerical examples show that the proposed method is superior to the conventional Kriging method in producing kriging meta-models with higher prediction accuracy and in quantifying prediction uncertainty associated with the use of meta-models.