Sustainable development of a thermodynamic steel database: mathematical aspects of database structure and data regression strategies
Development and application of mathematical models for the establishment of noncommercial and sustainable thermodynamic databases and maintenance tools.The construction of Gibbs energy databases is, from a mathematical point of view, an inverse problem as the available experimental information complies with derivatives of Gibbs energies. The construction of the Gibbs energies for multicomponent multiphase alloys is extremely demanding, as the configurational space with 20 or more components, more than 100 possible phases, and the dependence on temperature and pressure is of very high dimensionality. The traditional way of constructing these databases by combining unary information to binary, ternary etc., and including more and more interaction parameters urgently deserves a mathematical foundation. In particular strategies have to be investigated to reduce the dimension of the configurational space and to optimize the functional basis of the Gibbs energy functions in order to represent available experimental data and to avoid overfitting of the energy functions. In the practical part the project will contribute to the establishment of noncommercial and sustainable thermodynamic databases and maintenance tools.