Christoph Garth’s research while affiliated with Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau and other places

Root cause analysis in modern multistage assembly lines is a challenging, yet widely used technique to increase the product quality. Improvements – due to Industry 4.0 – aim for near-zero-defects manufacturing. Thus, we propose a novel root cause analysis: the Process Estimator neural Network (PEN) to solve the sparse, nonlinear problem of the state-space model empowering a graph convolution neural network. The contributions of this paper are: (1) study a novel problem of utilizing nonlinear deep neural networks to solve the state-space model; (2) elaborating the use of a graph convolution neural network to scope with the current limitations of linear approaches, which cannot process dense 3D point cloud data of the outer skin of the product; (3) how to analyze the trained network for fine tuning. We showed through a realistic experiment how PEN performs on huge 3D point clouds (188.000 points or higher) in form of meshed CAD models of first-order shell elements. These experiments set an example on how to overcome the fundamental performance limitations of current linear approaches.

Background Proton computed tomography (pCT) and radiography (pRad) are proposed modalities for improved treatment plan accuracy and in situ treatment validation in proton therapy. The pCT system of the Bergen pCT collaboration is able to handle very high particle intensities by means of track reconstruction. However, incorrectly reconstructed and secondary tracks degrade the image quality. We have investigated whether a convolutional neural network (CNN)-based filter is able to improve the image quality. Material and methods The CNN was trained by simulation and reconstruction of tens of millions of proton and helium tracks. The CNN filter was then compared to simple energy loss threshold methods using the Area Under the Receiver Operating Characteristics curve (AUROC), and by comparing the image quality and Water Equivalent Path Length (WEPL) error of proton and helium radiographs filtered with the same methods. Results The CNN method led to a considerable improvement of the AUROC, from 74.3% to 97.5% with protons and from 94.2% to 99.5% with helium. The CNN filtering reduced the WEPL error in the helium radiograph from 1.03 mm to 0.93 mm while no improvement was seen in the CNN filtered pRads. Conclusion The CNN improved the filtering of proton and helium tracks. Only in the helium radiograph did this lead to improved image quality.

Contemporary scientific data sets require fast and scalable topological analysis to enable visualization, simplification and interaction. Within this field, parallel merge tree construction has seen abundant recent contributions, with a trend of decentralized, task-parallel or SMP-oriented algorithms dominating in terms of total runtime. However, none of these recent approaches computed complete merge trees on distributed systems, leaving this field to traditional divide and conquer approaches. This paper introduces a scalable, parallel and distributed algorithm for merge tree construction outperforming the previously fastest distributed solution by a factor of around three. This is achieved by a task-parallel identification of individual merge tree arcs by growing regions around critical points in the data, without any need for ordered progression or global data structures, based on a novel insight introducing a sufficient local boundary for region growth.

We propose that a topological model of a real-valued function can be employed to define a spatial subdivision of the function’s domain. When multiple topologically-induced subdivisions for the same or different functions on the same domain are combined, a finer spatial subdivision arises: the topological subdivision complex. The topological subdivision graph then gives adjacency relations among the d-cells of the subdivision complex and can be used to describe similarities among topological models. We apply this idea to give new topological models for multiple real-valued functions (multifields), extending contour trees and Morse-Smale complexes to these problem settings, and we illustrate our idea for piecewise-linear functions. We also discuss how our work relates to joint contour nets.

This paper presents the theoretical foundation to approximate the Pareto set and its affiliated reachability graph through the Joint Contour Net (JCN). The theory works for multivariate scalar fields with arbitrary numbers of domain dimensions and functions. This allows us to visualize critical regions, connected component inside the Pareto set, and their connections using the efficient and noise robust JCN algorithm. With visualization application in mind, we demonstrate the feasibility of our approach on 2D examples.

The deviations between the actual geometry of a workpiece and the measured geometry are defined by the transfer function of the surface topography measuring instrument used. When the transfer characteristics of a measuring instrument are known, they can, for example, be used for the estimation of measuring results by performing virtual measurements and can subsequently be applied for the estimation of the measurement uncertainty. A technique that has been increasingly applied for the determination of the transfer function of topography measuring devices is the approach based on physical modeling. Here, mathematical models apply simplifications of the complex physical relationships to describe the transfer characteristics of measuring devices. Another method used in practice is the application of material measures for the direct measurement of transfer properties. Within this paper, an alternative approach developed by the authors that applies the ARMA model is further investigated and optimized with regard to its practical applicability. This model was described in a previous publication (Keksel et al 2018 Meas. Sci. Technol. 29 095012) and combines the advantages of theoretical modeling and the experimental determination of transfer characteristics. Within the present work, the approach is further optimized and it is demonstrated that the description of measuring devices by the ARMA model delivers reasonable results for various measuring principles that can be used for a precise virtual prediction of measurement results.

Due to the fourth industrial revolution, industrial applications make use of the progress in communication and embedded devices. This allows industrial users to increase efficiency and manageability while reducing cost and effort. Furthermore, the fourth industrial revolution, creating the so-called Industry 4.0, opens a variety of novel use and business cases in the industrial environment. However, this progress comes at the cost of an enlarged attack surface of industrial companies. Operational networks that have previously been phyiscally separated from public networks are now connected in order to make use of new communication capabilites. This motivates the need for industrial intrusion detection solutions that are compatible to the long-term operation machines in industry as well as the heterogeneous and fast-changing networks. In this work, process data is analysed. The data is created and monitored on real-world hardware. After a set up phase, attacks are introduced into the systems that influence the process behaviour. A time series-based anomaly detection approach, the Matrix Profiles, are adapted to the specific needs and applied to the intrusion detection. The results indicate an applicability of these methods to detect attacks in the process behaviour. Furthermore, they are easily integrated into existing process environments. Additionally, one-class classifiers One-Class Support Vector Machines and Isolation Forest are applied to the data without a notion of timing. While Matrix Profiles perform well in terms of creating and visualising results, the one-class classifiers perform poorly.

Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large variety of visualization techniques. In this chapter, we sample the visualization literature to provide a taxonomy of the usage of mathematics in visualization, and to identify a fundamental set of mathematics that should be taught to students as part of an introduction to contemporary visualization research. Within the scope of this chapter, we are unable to provide a full review of all mathematical foundations of visualization; rather, we identify a number of concepts that are useful in visualization, explain their significance, and provide references for further reading.

Due to the fourth industrial revolution, industrial applications make use of the progress in communication and embedded devices. This allows industrial users to increase efficiency and manageability while reducing cost and effort. Furthermore, the fourth industrial revolution, creating the so-called Industry 4.0, opens a variety of novel use and business cases in the industrial environment. However, this progress comes at the cost of an enlarged attack surface of industrial companies. Operational networks that have previously been phyiscally separated from public networks are now connected in order to make use of new communication capabilites. This motivates the need for industrial intrusion detection solutions that are compatible to the long-term operation machines in industry as well as the heterogeneous and fast-changing networks. In this work, process data is analysed. The data is created and monitored on real-world hardware. After a set up phase, attacks are introduced into the systems that influence the process behaviour. A time series-based anomaly detection approach, the Matrix Profiles, are adapted to the specific needs and applied to the intrusion detection. The results indicate an applicability of these methods to detect attacks in the process behaviour. Furthermore, they are easily integrated into existing process environments. Additionally, one-class classifiers One-Class Support Vector Machines and Isolation Forest are applied to the data without a notion of timing. While Matrix Profiles perform well in terms of creating and visualising results, the one-class classifiers perform poorly.