īy also considering specific issues studied through computer experiments, more recently, several and interesting papers have been published, where the Kriging methodology has been further developed to also solve complex technological and engineering issues. Moreover, sliced space-filling designs based on sliced SOAs have been developed by Liu and Liu, and more recently, the so-called SOAs of strength ‘two plus’ are defined by also illustrating their connection with second-order saturated designs. Since then, the theory on SOAs of strength three has been further developed by He and Tang, where a complete characterisation of such a type of arrays is presented. They demonstrated the excellent space-filling properties of the SOA-based LH designs, also compared to OA-based-LH designs. The authors proposed LH designs based on this new class of orthogonal arrays, naming them strong orthogonal array based LH (SOA-based-LH) designs. Recently, He and Tang developed a new class of orthogonal arrays, called strong orthogonal array (SOA). extended them to the construction of LH designs based on nested and sliced orthogonal arrays respectively. LH designs based on orthogonal arrays, and called orthogonal array based LH (OA-based-LH) designs, have been developed by Tang subsequently, He and Qian and Yin et al. Despite the large number of such approaches, in this manuscript we focus on LH designs constructed through orthogonal and strong orthogonal arrays. As a result, a commonly used approach is to build LH designs that are space-filling in some low-dimensional projections. On one side, there is no guarantee that a random LH design achieves uniformity when projected in more than one dimension on the other, finding an LH design that achieves the maximum stratification in a high-dimensional design space is a challenge. Nevertheless, in most of the real applications, the design involves a large number of input variables, and therefore the uniformity should be achieved in more than one dimension. An LH design achieves the maximum uniformity when projected in any one dimension. One commonly used class of space-filling designs for computer experiments is the Latin Hypercube (LH) design introduced by McKay et al. For this purpose, space-filling designs are widely accepted as the most appropriate ones, since they spread the design points as uniformly as possible in order to observe the response in the entire experimental region. ![]() , the studies on Kriging have been largely developed by considering both theoretical and applied issues.Ī fundamental issue for computer experiments is the planning of the experimental design. In literature, after the seminal contribution of Sacks et al. Despite the large class of such surrogate models, the Kriging is the most important and widely used for the analysis of computer experiments. The complexity of the simulator requires an approximation of the system through a surrogate model or metamodel. To this end, computer experiments are increasingly used in this field where a computer code or simulator is run in order to mathematically represent the physical system under study. When dealing with complex engineering and technological issues, physical experimentation is often too expensive or, in some cases, even impossible to perform. The results are very satisfactory and confirm that our approach represents a valid method to be successfully applied by interested Railway Undertakings. ![]() Kriging models with anisotropic covariance function are subsequently applied to assess which is the best payload distribution capable of reducting the in-train forces according to the specific train-set arrangement considered. A suitable Latin hypercube design is planned for the computer experiment that achieves excellent space-filling properties with a relatively low number of experimental runs. ![]() One contribution of this manuscript is that to improve the freight train efficiency in terms of braking performance, we consider that the train is composed of several train sections with each one characterised by its own overall payload. We optimise the braking performance of freight trains through computer experiments and Kriging modelling by focussing on the payload distribution along the train, so as to reduce the effects of in-train forces among wagons during a train emergency braking. Computer experiments are analysed through suitable metamodels acting as statistical interpolators of the simulated input-output data: Kriging is the most appropriate and widely used one. Nowadays, computer experiments are used increasingly more to solve complex engineering and technological issues.
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