Sequential designs, sensitivity analysis and optimization of computer experiments

Sonja Kuhnt, Dortmund University of Applied Sciences and Arts, Dortmund, Germany

In production and engineering, computer experiments are nowadays widely used to analyze, model and optimize complex processes. Computer experiments simulate for example the manufacturing of components together with their resulting properties. As computer experiments are often very time consuming, so-called meta-models of these black-box functions are surrogate models easy to evaluate. The acquisition of data for the building of meta-models is usually based on space filling designs on the input space. Each run of the experimental design results in one simulation and provides measures of one or more response property.

The effect of the controllable parameters on a response variable of interest can be explored by sensitivity analysis techniques. The well-known Sobol indices quantify the influence of variables or groups of variables on the variability of the response.

We review the recently developed total interaction indices (TII) and show different ways to display them in so called FANOVA graphs. Thereby, knowledge about the unknown black-box function can be gained. New methods for the modelling and optimization of the computer experiment are developed by utilizing the additivity structure of the function implicated by the FANOVA graph.

• Fruth, J., Roustant, O., Kuhnt, S. (2015), "Sequential designs for sensitivity analysis of functional inputs in computer experiments". Reliability Engineering & System Safety 134, 260–267.
• Roustant, O., Fruth, J., Iooss, B., Kuhnt, S. (2014), "Crossed-Derivative Based Sensitivity Measures for Interaction Screening", Mathematics and Computers in Simulation, 105, 105-118.
• Fruth, J., Roustant, O., Kuhnt, S. (2014), "Total Interaction Index: A Variance-based Sensitivity Index for Second-order Interaction Screening", Journal of Statistical Planning and Inference 147, 212–223.
• Ivanov, M., Kuhnt, S. (2014), "A Parallel Optimization Algorithm based on FANOVA Decomposition", Quality and Reliability Engineering International, 30, 961-974.

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