Systematic decision making in engineering requires appropriate models. In this article, we introduce a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity constraints. Incorporating such information is particularly useful when the available datasets are small or do not cover the entire input space, as is often the case in manufacturing applications. We set up the regression subject to the considered monotonicity constraints as a semi-infinite optimization problem, and propose an adaptive solution algorithm. The method is applicable in multiple dimensions and can be extended to more general shape constraints. It was tested and validated on two real-world manufacturing processes, namely, laser glass bending and press hardening of sheet metal. It was found that the resulting models both complied well with the expert’s monotonicity knowledge and predicted the training data accurately. The suggested approach led to lower root-mean-squared errors than comparative methods from the literature for the sparse datasets considered in this work.

This article introduces a novel laboratory-scale process for the electrochemical synthesis of hydrogen peroxide (H${}_2$O${}_2$). The process aims at an energy-efficient, decentralized production, and a mathematical optimization of it is presented. A dynamic, zero-dimensional mathematical model of the reactor is set up in Aspen custom modeler^®. The proposed model constitutes a reasonable compromise between complexity and convergence. After thoroughly determining the reaction kinetics by adjustment to experimental data, the reactor unit is embedded in an Aspen Plus^® flowsheet in order to investigate its interaction with other unit operations. The downstream contains another custom module for membrane distillation. Electricity appears as a resource in the process, and optimization shows that it reaches product purities of up to 3 wt.-%. Both the process optimization and the adjustment of the reaction kinetics are treated as multi-criteria optimization (MCO) problems.

The oxygen reduction reaction (ORR) mechanism for electrochemical production of hydrogen peroxide is investigated for an Au-Pd catalyst with 25 at% palladium. The sample was prepared by chemical reduction of a precursor solution on a carbon-based substrate. Rotating ring-disk electrode (RRDE) measurements were performed for electrochemical characterization exhibiting H₂O₂ current efficiencies of about 75-78% at low disk potentials. The focus of this article is on the mathematical evaluation of the experimental data using the analytical method from Damjanovic et al. [J. Chem. Phys. 45, 4057 (1966)] and a powerful numerical data fitting technique based on RRDE simulations in MATLAB, which is capable of investigating reaction mechanisms with different structures. The latter method is presented in detail and the electro-kinetic parameters of the ORR mechanism at the considered catalyst resulting from both methods are compared quantitatively. It is found that the oxygen reductions via the 2-electron and the 4-electron pathways occur in parallel, whereas the hydrogen peroxide reduction pathway is found apparently inactive.

Increasing digitalization enables the use of machine learning methods for analyzing and optimizing manufacturing processes. A main application of machine learning is the construction of quality prediction models, which can be used, among other things, for documentation purposes, as assistance systems for process operators, or for adaptive process control. The quality of such machine learning models typically strongly depends on the amount and the quality of data used for training. In manufacturing, the size of available datasets before start of production is often limited. In contrast to data, expert knowledge commonly is available in manufacturing. Therefore, this study introduces a general methodology for building quality prediction models with machine learning methods on small datasets by integrating shape expert knowledge, that is, prior knowledge about the shape of the input-output relationship to be learned. The proposed methodology is applied to a brushing process with $125$ data points for predicting the surface roughness as a function of five process variables. As opposed to conventional machine learning methods for small datasets, the proposed methodology produces prediction models that strictly comply with all the expert knowledge specified by the involved process specialists. In particular, the direct involvement of process experts in the training of the models leads to a very clear interpretation and, by extension, to a high acceptance of the models. Another merit of the proposed methodology is that, in contrast to most conventional machine learning methods, it involves no time-consuming and often heuristic hyperparameter tuning or model selection step.

Optimization in engineering requires appropriate models. In this article, a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity constraints, is presented. Incorporating such information is particularly useful when the available data sets are small or do not cover the entire input space, as is often the case in manufacturing applications. The regression subject to the considered monotonicity constraints is set up as a semi-infinite optimization problem, and an adaptive solution algorithm is proposed. The method is applicable in multiple dimensions and can be extended to more general shape constraints. It is tested and validated on two real-world manufacturing processes, namely laser glass bending and press hardening of sheet metal. It is found that the resulting models both comply well with the expert's monotonicity knowledge and predict the training data accurately. The suggested approach leads to lower root-mean-squared errors than comparative methods from the literature for the sparse data sets considered in this work.