In this chapter, an overview is given of the research work during the years 2007 until 2016 in the field of tolerance analysis, optimization and synthesis of mechanisms ([11] and [17]). At the beginning, the challenges related to mechanisms are highlighted, especially the time-dependent behaviour of a mechanism during its operation and the different kinds of deviation occuring during the production and the operation of the mechanism. After that, the integrated approach for the statistical tolerance analysis of mechanisms is described. This approach is then enlarged to a complete tolerance analysis, optimization and synthesis approach before its applicability is demonstrated in a case study. The chapter will end with a summary.

Diese Studie beschreibt die Entwicklung eines betriebsunabhängigen Simulationsmodells für elektrifizierte Druckgießereien, die ihren Energiebedarf mit Hilfe eines Smart Grid Systems decken. Das Modell verwendet reale Wetter- und Börsenstrompreisdaten für den Simulationszeitraum. Mit Hilfe des Modells können die Stromkosten für eine Produktion zu einem bestimmten Zeitpunkt (Tages- und Jahreszeit) sowie die Wirtschaftlichkeit verschiedener PV-Anlagen- und Stromspeichervarianten ermittelt und verglichen werden. Zudem ermöglicht es die Untersuchung des Anteils der verschiedenen Energieträger für die jeweilige Konfiguration. Dies kann mit Hilfe des Modells für Standorte in ganz Deutschland durchgeführt werden. Darüber hinaus werden in dieser Arbeit beispielhafte Simulationsstudien vorgestellt, die den breiten Anwendungsbereich des Modells aufzeigen. Aus den Ergebnissen kann ein erster Überblick über Einsparungs- und Optimierungsmöglichkeiten gewonnen werden. Perspektivisch stellt das Modell eine Grundlage dar, um mittels simulationsgestützter Optimierung optimale Anlagenlayouts und Produktionszeitpunkte zu ermitteln.

Purpose - This study aims to address challenges in the Laser Powder Bed Fusion process of polymers, focusing on the considerable amount of unsintered powder left post-printing. The objective is to understand the altered properties of this powder and find solutions to improve the process, reduce waste, and explore reusing reprocessed powder.

Design/methodology/approach - A novel methodology is employed to generate reprocessed powder without traditional printing, reducing time, cost, and waste. The approach mimics the aging effects during the printing process, providing insights into particle size distribution and thermal behavior.

Findings - Results reveal insights into artificial aging, showing an 8.2% decrease in particle size (60.256 - 69.183 μm) and a 9.1% increase in particle size (17.378 - 19.953 μm) compared to unsintered powder. Thermal behavior closely mirrors used powders, with variations in enthalpy of fusion (-0.55% to 2.69%) and degree of crystallinity (0.19% to 2.64%). The proposed methodology produces results that differ from those due to printing under 3% from a thermal point of view. The
new process reduces the time needed for aged powder, contributing to cost savings and waste reduction.

Originality/value - The study introduces a novel method for reprocessed powder generation, deviating from traditional printing. The originality lies in artificially aging powders, providing comparable results to actual printing. This approach offers efficiency, time savings, and waste reduction in the Laser Powder Bed Fusion process, presenting a valuable avenue for further research.

A reformulation of the dynamical component analysis (DyCA) via an optimization-free approach is presented. The original cost function approach is converted into a numerical linear algebra problem, i.e., the computation of coupled singular-value decompositions. A simple algorithm is presented together with numerical experiments to document the feasability of the approach. This methodology is able to recover the mixing and state matrices of multivariate signals from high-dimensional measured data fully.

The manifold of essential matrices is equipped with a one-parameter family of (pseudo-)Riemannian metrics. For the whole family, explicit formulas for geodesics are derived. Moreover, specific curves, so-called quasi-geodesics, are studied and a closed form expression for a quasi-geodesic connecting two given essential matrices is obtained.

In this paper, we show an application of spatiotemporal persistence landscapes to real world time series. Spatiotemporal persistence landscapes are a recent extension of persistence landscapes to time series that capture features of the data that are persistent with respect to time and space. We perform our analysis on EEG data to detect absence epileptic seizures. Further, we compare two dimension reduction techniques (DyCA and PCA) with no dimension reduction and show that the combination of DyCA and persistent landscapes yields the best results.

This paper discusses the challenges and methods for source reconstruction of evoked potentials using deep learning in the context of electroencephalography (EEG). We propose the use of deep learning to address known challenges and improve traditional approaches. We explain the creation of a suitable dataset for solving the inverse problem, including the simulation of neural activity and the use of lead field matrices for the forward solution. Furthermore, we undertake a comparative analysis of some initial deep learning models with similar classical methods.

Dynamical Component Analysis (DyCA) and Dynamic Mode Decomposition (DMD), both data-driven dimension reduction methods, are introduced. After application to multivariate simulated signals the techniques of mode selection and the resulting amplitudes are compared with respect to noise robustness and sampling periods. The results indicate that DyCA is a useful alternative to DMD and outperforms DMD under certain conditions. These conditions are based on the underlying dynamics in the terms of differential equations and on the noise ratios of the signals.