ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


Statistical modelling of thermo-physic materials properties using segmented regression

Date: 22.03.2013
Time: 08:50 a.m.
Place: 3rd Joint Statistical Meeting DAGStat, Freiburg, Germany

Irina Roslyakova
Holger Dette, Mathematik III, Ruhr-Universität Bochum, Bochum, Germany

Frequently in regression problems, a model is assumed to be a single parametric function throughout the entire domain of analysis. However, in many phenomena is it necessary to consider regression models which have different analytical form in different regions of domain. Such type of regression models used for the parameter estimation is called segmented regression. The proposed segmented regression was developed for modeling of the heat capacity.

Traditionally in applied thermo-physics the temperature dependence of the heat capacity is described by high-order polynomials, with adjustable parameters fitted to experimental data. This approach led to fitting coefficients that lack any physical meaning and it is not valid below 298.15K.

To overcome this difficulties, in this work we used more physical approach that requires the modeling of several contributions (e.g. electronic, vibrational, etc.). Since these contributions appear in different temperature ranges and can be described by different functions, the segmented regression methodology was applied for developing of mathematical model for heat capacity of materials. Several segmented regressions were considered, analyzed and validated by using statistical tests. Corresponding confidence intervals have been calculated using the bootstrap method.

Additionally to this practical issue, the asymptotic theory for the proposed model has being developing. The results of this study are several theorems on consistency and asymptotic normality of nonlinear least square estimator in case of independent not identically distributed random errors.

[1] G. A. F. Seber, C. J. Wild (1989). Nonlinear Regression.

[2] G. Grimvall (1986). Thermophysical properties of materials.

Supporting information:

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