Generalized latin hypercube design for computer experiments

Space filling designs, which satisfy a uniformity property, are widely used in computer experiments. In the present paper the performance of non-uniform experimental designs which locate more points in a neighborhood of the boundary of the design space is investigated. These designs are obtained by a quantile transformation of the one-dimensional projections of commonly used space filling designs. This transformation is motivated by logarithmic potential theory, which yields the arc-sine measure as equilibrium distribution. Alternative distance measures yield to Beta distributions, which put more weight in the interior of the design space. The methodology is illustrated for maximin Latin hypercube designs in several examples. In particular it is demonstrated that in many cases the new designs yield a smaller integrated mean square error for prediction. Moreover, the new designs yield to substantially better performance with respect to the entropy criterion

Structural model updating based on metamodel using modal frequencies

Modal frequencies are often used in structural model updating based on the finite element model, and metamodel technique is often applied to the corresponding optimization process. In this work, the Kriging model is used as the metamodel. Firstly, the influence of different correlation functions of Kriging model is inspected, and then the approximate capability of Kriging model is investigated via inspecting the approximate accuracy of nonlinear functions. Secondly, a model updating procedure is proposed based on the Kriging model, and the samples for constructing Kriging model are generated via the method of Optimal Latin Hypercube. Finally, a typical frame structure is taken as a case study and demonstrates the feasibility and efficiency of the proposed approach. The results show the Kriging model can match the target functions very well, and the finite element model can achieve accurate frequencies and can reliably predict the frequencies after model updating

Centered L2-Discrepancy of Random Sampling and Latin Hypercube Design, and Construction of Uniform Designs

Abstract. In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance. 1