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Abstract

Experimenting is one of the scientific approaches for the investigation of natural and physical phenomena. Because experiments cannot avoid random errors, statistical methods play an important role for the design and analysis of experiments. Often interests are to fit mathematical models to the experimental data. Then the fitted models can be used for the further prediction of studied phenomena. Another interest is to estimate the model parameters as accurately as possible. Taking into account known fact that the variances of estimated model parameters and predictions using the estimated model depend on the experimental design, thus the variances can be minimized by a well-designed experiment [1-3].

In this report a short introduction to the theory of optimal experimental planning will be given and its application on heat capacity data fitted by segmented regression model will be demonstrated. The segmented regression model is a nonlinear physically-based model which has been developed to consider several physical effects separately in low and high temperatures. The segmented regression approach has been successfully applied for modeling of several pure elements and it delivers an accurate description for entire temperature range down to 0K [4, 5]. Some new results for other pure elements as Re, Ni, Mo, Nb, W and Ir will be shortly presented in this report.

The obtained results from application of an optimal experimental planning deliver a set of recommendations for determining the experimental conditions where measurements must be collected. Furthermore, these recommendations can be generalized and applied for the planning of computer experiments for the metastable and liquid phases to save computational time and costs. The financial support from the Sino-German Center for Promotion of Science (Grant No. GZ755) is greatly acknowledged.

References:

[1] Konstantinou, M. (2013), Locally optimal and robust designs for two-parameter nonlinear models with application to survival models, PhD-Thesis, University of Southampton.

[2] Wu, X.F. (2007), Optimal designs for segmented polynomial regression models and Web-based implementation of optimal design software, PhD-Thesis, Stony Brook University.

[3] Atkinson, A., Donev, A. and Tobias, R. (2007) Optimum Experimental Designs, with SAS (Oxford Statistical Science Series). Oxford University Press, USA, 2nd edn.

[4] I. Roslyakova, B. Sundman, H. Dette, Contribution to the third generation CALPHAD databases using segmented regression approach: new description for pure Cr, Al and Fe and comparison with existing models, ICAMS Advance Discussion 2014, Ruhr-Universität Bochum, Germany

[5] I. Roslyakova, B. Sundman, H. Dette, Modelling of thermo-physic properties for pure elements using segmented regression methodology, CALPHAD 2014, Changsha, China