Statistics Group

DFG-Project: Major-Instrumentation Initiative: CT of structural elements under changing load

Computer Tomography has been used for many years in construction materials technology in order to gain knowledge, using small format samples, of the joint structure of construction materials and how they change under different conditions of exposure. However, there is lack of appropriately configured equipment that would enable by means of X-ray technology a better understanding of bearing and deformation behaviour of entire building parts. Hence, in line with the DFG offer to tender, a completely new type of Tomography Portal (TOP) has been conceived; one that can scan building components of real life dimensions under increasing load with high resolution accuracy. It makes use of a high radiation energy, which is indispensable in order for example to illuminate bar-like reinforced concrete components using cross-section dimensions of at least 30 x 30 cm, and imaging of cracks of 0.1 mm width. In addition, a second radiating source has been integrated, which in the case of smaller dimensions or less demanding materials permits higher resolutions. The design has been understood as an interdisciplinary work. The guiding factors in the design were: the needs of the construction industry, machine, X-ray and measuring technology, calibration procedure, mathematical reconstruction of raw data, with their visual preparation and further processing on high performance computers as well as the availability of the research results.



Project partner:

Professor Dr.-Ing. Jürgen Schnell

Professor Dr.-Ing. Manfred Curbach

Professor Dr.-Ing. Josef Hegger

Professorin Dr. Heike Leitte

Professor Dr.-Ing. Harald S. Müller

Professor Dr.-Ing. Ralf Müller

Professor Dr.-Ing. Matthias Pahn

Professor Dr.-Ing. Jörg Seewig

Professor Dr.-Ing. Christos Vrettos

German-French doctoral college

The goal of the research training group is to develop new methods for the analysis, modeling and simulation of complex material structures using image data. In the fourth funding period of the research training group, the following key subjects will be addressed:

  • A major focus will be on the temporal evolution of 3D image data. The interest in describing, analyzing and simulating the dynamics of big data has increased considerably in recent years, especially in materials science.
  • Another focus will be on spatially sparse data with sudden changes in structure (e. g. foams). Statistical and morphological methods for their analysis and modelling will be developed.
  • Finally, methods for the detection of anomalies in different materials, such as misorientations of fibers or cellular fractures, will be developed. To manage the corresponding classification and segmentation problems, the development and implementation of machine learning techniques, including Convolutional Neural Networks (CNN) and Random Forrests, is planned. The goal is to combine "deep learning" techniques with existing variational calculus and morphology methods by using them to support and improve intermediate results.

The inclusion of physical facts as well as prior knowledge about the structure of images will be investigated.



Project partner:

Professorin Dr. Gabriele Steidl

Dr. Katja Schladitz

Dr. François Willot

Dr. Jesús Angulo

MWG-Project: MaTBiZ - Microstructure Design and Additive Manufacturing of a Chromatography Column for the Separation of Biological Cells

The separation of biological cells (cell chromatography) plays a crucial role in many processes in the biotechnical field. For example, it is of central importance in stem cell research or the therapy of blood cancer. The current separation procedures are based on complex, sometimes multi-stage process chains.

To develop a proper filter medium, we start with a foam-like microstructure. Due to their high connectivity, foams are in general well suited for additive manufacturing processes. This filter is placed in a glass column through which a cell-enriched suspension flows. This enables cell separation in the flow, which significantly simplifies the process of cell separation. Foams are suitable as a starting point for the development of the microstructure, which is then to serve as a filter medium. Due to their high connectivity, these are generally well suited for additive manufacturing processes. We primarily consider foams based on a Laguerre mosaics. Their numerous parameters allow a high degree of flexibility regarding the structural properties. Parameters such as size of foam pores or thickness of foam struts can easily be adjusted to enable the best possible separation of the biological cells.

First, the microstructure is generated virtually and optimized with respect to its flow properties and the possibility of cell attachment. For this, we expend existing models for cell transport and interaction. Furthermore, the microstructure must meet certain connectivity criteria in order to be able to be produced in the next step using additive processes. In addition to the connectivity, the challenge lies in the size of the filter medium. The entire glass column into which the structure has to be placed in has a diameter of 1.2 mm. The average diameter of the foam struts is around 30 μm, thinner than a human hair. Hence, we use 3D laser lithography with two-photon polymerization (3D μ-printing). In the last step, the filter medium is validated in a real experiment.



Project partner:

Fraunhofer-Institute for Industrial Mathematics ITWM 

Data and experimental results for academic test examples were provided by

Merck KGAA


BMBF Project: Oho - Optimization of wood-based insulation

Wood and other cellulose fiber insulating materials are the most commonly used insulating materials made from renewable ressources. However, their thermal conductivity is generally higher than the thermal conductivity of conventional insulation materials. Due to the manufacturing process, the distribution and orientation of the cellulose fibers lead to highly anisotropic thermal conductivity. Besides single fibers, the microstructure also contains fiber bundles of different sizes. To this end, accurate prediction of thermal conductivity as well as further optimization of the board structure to achieve thermal conductivities <35 W/K is difficult.

The goal of the research project is therefore to optimize the structure of highly porous wood fiber insulation boards in order to further reduce their effective thermal conductivity. The potential for this lies precisely in exploiting anisotropy and specifically mixing fiber bundles of different sizes. To exploit this potential, machine learning methods, image based geometric structure modeling and numerical methods for the efficient simulation of heat transfer are to be combined with optimization methods.



Project partner:

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

Bergische Universität Wuppertal (BUW)

Martin-Luther-Universität Halle (LUH)


Fagus-GreCon Greten GmbH & Co. KG


BMBF Project: poST - Synthetic data for ML segmentation of FIB-SEM nanotomographs of highly porous structures

The nanostructure of complex materials can be imaged in 3D by the FIB-SEM serial sectioning technique. To analyze the material, its components must be reconstructed from the image data. In the case of high porosity, this is difficult because structures behind the current imaging plane are also visible through the pores.

Machine learning techniques have high potential here. However, training data are difficult to obtain. Manual segmentation is hardly possible, since even humans often cannot decide which structures form the foreground of the current section. Synthetic images for which the correct result is known are an attractive way out. The similarity of the simulated to the real structure has a considerable influence on the quality of the result.



Project partner:

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

DFKI Saarbrücken

BMBF Project: SynosIs - Synthetic, Optically Realistic Image Data of Surface Structures for AI-Based Inspection Systems

Artificial intelligence (AI) is used very successfully in image recognition, processing and understanding. However, training an AI-based inspection system for industrial quality assurance requires large amounts of representative annotated image data for all defect types. Manual annotation is laborious and error-prone. Many defects, especially safety-critical ones, occur very rarely.

Realistic synthetic image data help circumvent these problems.

We combine physics, mathematics and computer science to generate synthetic images of typical defects on metallic surfaces with unprecedented realism. These defect images that are guaranteed to be correctly and objectively annotated are available for training and validation of AI systems for optical surface inspection after the end of the project.

More information about the project


Project partner:

Professor Hans Hagen (TUK)

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

Fraunhofer-Institut für Angewandte Optik und Feinmechanik IOF

BMBF Project: DAnoBi

The aim of the research project is to develop methods for the detection of anomalies in large image data. This could be e. g. micro cracks in concrete beams, material densifivation in textile web goods or local fiber misalignments in components made of fiber-reinforced plastic. For this purpose, methods of machine learning, modeling of structures and imaging as well as statistical methods for the detection of abnormalities can be combined. In all this cases mentioned, the structure varies greatly.

Methods and measures must therefore be developed in order to decide objectively, robustly and repeatably what an anomaly, i. e. a significant deviation is. The anomalies to be detected rarely occur both statistically and spacially. For this reason, there is a lack of training data for purely machine learning (ML) based solutions, which annotation is also very difficult. One way out is training based on realistic, simulated data, since in this case enough data can be generated and the basic truth is immediately available.

An alternative approach is to adopt statistical methods for structure break detection in time series for the detection of spatial anomalies. The spatial component of the image data gives rise to new tasks, such as recognizing complex anomaly regions, which will also be solved in the project.

The planned research work focuses on the detection of cracks in concrete components, since this question is of great practical relevance, but also particularly difficult in a methodological sense. ML and statistical methods for solving this specific problem are expected to be transferable to the other use cases mentioned above. Models for concrete and crack structures, on the other hand, are problem-specific, but are already a major challenge in this thematic limitation.



Project partner:

Universität Ulm

Otto von Guericke-Universität Magdeburg

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM

BORAPA Ingenieurgesellschaft mbH

MKT Metall-Kunststoff-Technik GmbH & Co KG

C-Con GmbH & Co KG

Dr. Ketterer Ingenieurgesellschaft mbH

Heinze CobiaxDeutschland GmbH

Bekaert GmbH

Completed projects



Other Projects

  • Junior Endowed Professorship
    Statistics of Spatial Structures for Innovations in the Engineering Sciences of the "Carl Zeiss Foundation"

  • Project as Part of the Innovation Centre "Applied System Modeling"
    Applied System Modeling for Multi Scale Materials

  • (CM)²-Project
    Image Processing in Civil Engineering

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