Abstract

Nowadays, when dealing with complex engineering and technological products and/or processes, physical experimentation may be too costly or impossible to perform. To this end, computer experiments are increasingly used in this field. When considering the analysis of computer experiments, specific surrogate models are applied, which are statistical interpolators of the simulated input and output data; in this regard, a widely used one is the Kriging. The main objective of Kriging modeling is the optimal prediction of the output (i.e., the response variable) through a statistical model involving a deterministic part, named trend function, and a stochastic part, that is, a Gaussian random field with zero mean and stationary covariance function. In this talk, we deal with a proposal for a joint multiresponse Kriging modeling and optimization by specifically considering Universal Kriging models involving a non-constant trend and anisotropic covariance functions. Our proposal is twofold. More specifically, first, we propose a joint Kriging modeling for a multiple response situation, also aiming to study the association among the responses. Second, we also deal with a proposal for an optimization procedure, involving the definition of a single objective function and taking account of the adjustment to the objective values for each response (i.e. targets), the predicted Kriging mean and variance. Moreover, rather than fixed values for the targets of the responses, we consider tolerance intervals, and weights to take care of the different importance of each response variable. We illustrate our proposal through a no-trivial case-study in the technological field, also reported in Nikiforova et al. (2021) and in Berni et al. (2022). In the case study we aim to improve the braking performance of freight trains in order to avoid train derailment or disruption of the train in two or more parts. Our approach could be successfully applied by interested Railway Undertakings in their operational practice to solve similar technical problems.
REFERENCES:

1. Berni, R., Cantone, L., Magrini, A., Nikiforova, N. D. (2022). Hierarchical optimal designs and modeling for engineering: A case-study in the rail sector. Applied Stochastic Models In Business And Industry, 38, 1061-1078.
2. Nikiforova N. D., Berni R., Arcidiacono G., Cantone L. and Placidoli P. (2021). Latin hypercube designs based on strong orthogonal arrays and Kriging modelling to improve the payload distribution of trains. Journal of Applied Statistics, 48 (3): 498-516, DOI: 10.1080/02664763.2020.1733943.