A recently suggested algorithm for recursive partitioning of statistical models (Zeileis, Hothorn and Hornik, 2005), such as models estimated by maximum likelihood or least squares, is evaluated in practice. The general algorithm is applied to linear regression, logisitic regression and survival regression and applied to economical and medical regression problems. Furthermore, its performance with respect to prediction quality and model complexity is compared in a benchmark study with a large collection of other tree-based algorithms showing that the algorithm yields interpretable trees, competitive with previously suggested approaches. / Series: Research Report Series / Department of Statistics and Mathematics

Within industrial product development processes there is an increasing demand towards reliable predictions of the material behavior, which aims to promote a property driven development that can reduce the lead times. The implementation of simulation based product development with integrated casting simulation may enable the design engineers to gain an early understanding of the products with relation to castability, and orient the subsequent design refinement so as to achieve the desired mechanical properties. This work investigates the suitability of three commercial casting simulation softwares –MAGMA 5.2, NovaFlow & Solid 4.7.5 (NFS) and Click2Cast 3.0 (C2C)–, with respect to the needs of design engineers, such as prediction of shrinkage porosity and mechanical properties with relation to the design. Simplified solidification simulations suitable for this stage were thus performed for three high pressure die cast components with different geometrical constraints. The comparability between the solidification and cooling behaviour predicted by the three softwares was studied, and showed that a reasonably good agreement between predicted solidification times by MAGMA and NFS could be obtained, albeit not between predictions by MAGMA and C2C. Predictions by the three softwares of the hot spot/porosity areas showed to have a good agreement. The calculation times by each software were compared, and MAGMA was seen to have the best performance, yielding significantly shorter times than NFS and C2C. The results obtained were also compared to experimental investigations of porosity, microstructural coarseness, and mechanical properties. There was a good agreement between the predicted hot spot areas –i.e. areas in the geometry that solidify last– and the findings of porosities in the actual castings, meaning that solidification simulations might be able to provide important information for the prediction of most of shrinkage related porosity locations that are related to the casting geometry. However, the lack of a detailed knowledge at the design stage of the casting process limits the possibilities to predict all porosities. The predicted microstructure and mechanical properties by MAGMA non-ferrous were seen to have a good agreement in trend with the experimental data, albeit the predicted values showed large differences in magnitude with the experimental data. Although, the MAGMA non-ferrous module was not developed for HPDC components, it was interesting to study if it could be applied in this context. However, the models seem to need adoption to the HPDC process and alloys. In conclusion, with a limited knowledge of the manufacturing parameters, simplified solidification simulations may still be able to provide reasonably reliable and useful information during early development stages in order to optimise the design of castings.

In this thesis, several development steps for the incremental method are presented. At first, the extension of the incremental scheme to other quantities than the energy is advanced in terms of molecular dipole moments. In this context, a revised error correction as well as the template localization for the treatment of aromatic systems are introduced. As a second enhancement, a new implementation of the template localization ensures a higher stability of this algorithm step and, thus, of the incremental scheme. Finally, pair natural orbitals (PNOs) are utilized in the incremental method with the aim of an increased efficiency. The PNO approach is re-assessed in context of the incremental expansion leading to both small incremental and PNO local errors for reaction, intermolecular interaction and cluster binding energies. The higher efficiency due to the twofold reduction of the computational efforts by the PNO and the incremental approaches is demonstrated for molecular clusters. Additionally, the complete basis set (CBS) limit is targetted by using the efficient MP2-based focal-point approach to the incremental scheme (with and without PNOs). Finally, based on these improvements of the performance, the PNO-based incremental scheme is applied to support a computational study regarding the modelling of the reaction mechanism for the base-catalyzed twin polymerization.