@article{FrankeHeinrichReisch2024, author = {Franke, Jan and Heinrich, Florian and Reisch, Raven T.}, title = {Vision based process monitoring in wire arc additive manufacturing (WAAM)}, series = {Journal of Intelligent Manufacturing (ISSN: 1572-8145)}, volume = {36}, journal = {Journal of Intelligent Manufacturing (ISSN: 1572-8145)}, number = {3}, publisher = {Springer US}, address = {New York}, issn = {0956-5515}, doi = {10.1007/s10845-023-02287-x}, url = {http://nbn-resolving.de/urn:nbn:de:101:1-2405052141549.085870766506}, pages = {1711 -- 1721}, year = {2024}, abstract = {A stable welding process is crucial to obtain high quality parts in wire arc additive manufacturing. The complexity of the process makes it inherently unstable, which can cause various defects, resulting in poor geometric accuracy and material properties. This demands for in-process monitoring and control mechanisms to industrialize the technology. In this work, process monitoring algorithms based on welding camera image analysis are presented. A neural network for semantic segmentation of the welding wire is used to monitor the working distance as well as the horizontal position of the wire during welding and classic image processing techniques are applied to capture spatter formation. Using these algorithms, the process stability is evaluated in real time and the analysis results enable the direction independent closed-loop-control of the manufacturing process. This significantly improves geometric fidelity as well as mechanical properties of the fabricated part and allows the automated production of parts with complex deposition paths including weld bead crossings, curvatures and overhang structures.}, language = {en} } @article{FinkForsterHeinrich2023, author = {Fink, Thomas and Forster, Brigitte and Heinrich, Florian}, title = {Gabor's "complex signal" revisited: Complexifying frames and bases}, series = {PAMM (Proceedings in Applied Mathematics and Mechanics)}, volume = {23}, journal = {PAMM (Proceedings in Applied Mathematics and Mechanics)}, number = {3}, publisher = {Wiley}, address = {Hoboken}, doi = {10.1002/pamm.202300155}, url = {http://nbn-resolving.de/urn:nbn:de:101:1-2023091815015485698899}, pages = {8}, year = {2023}, abstract = {In 1946, Dennis Gabor introduced the analytic signal š‘“ + š‘–š»š‘“ for real-valued signals š‘“. Here, š» is the Hilbert transform. This complexification of functions allows for an analysis of their amplitude and phase information and has ever since given well-interpretable insight into the properties of the signals over time. The idea of complexification has been reconsidered with regard to many aspects: examples are the dual tree complex wavelet transform, or via the Riesz transform and the monogenic signal, that is, a multi-dimensional version of the Hilbert transform, which in combination with multi-resolution approaches leads to Riesz wavelets, and others. In this context, we ask two questions: - Which pairs of real orthonormal bases (ONBs), Riesz bases, frames and Parseval frames {š‘“ š‘› } š‘›āˆˆā„• and {š‘” š‘› } š‘›āˆˆā„• can be "rebricked" to complex-valued ones {š‘“š‘› + š‘–š‘” š‘› } š‘›āˆˆā„•? - And which real operators A allow for rebricking via the ansatz {š‘“š‘› + š‘–š“š‘“š‘› } š‘›āˆˆā„•? In this short note, we give answers to these questions with regard to a characterization which linear operators A are suitable for rebricking while maintaining the structure of the original real valued family. Surprisingly, the Hilbert transform is not among them.}, language = {en} } @article{FinkForsterHeinleinHeinrich2024, author = {Fink, Thomas and Forster-Heinlein, Brigitte and Heinrich, Florian}, title = {Rebricking frames and bases}, series = {Journal of Mathematical Analysis and Applications}, volume = {2025}, journal = {Journal of Mathematical Analysis and Applications}, publisher = {Elsevier}, address = {Amsterdam}, issn = {1096-0813}, doi = {10.1016/j.jmaa.2024.129051}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus4-19227}, pages = {35 Seiten}, year = {2024}, abstract = {In 1949, Denis Gabor introduced the "complex signal" (nowadays called "analytic signal") by combining a real function fwith its Hilbert transform Hfto a complex function f+iHf. His aim was to extract phase information, an idea that has inspired techniques as the monogenic signal and the complex dual tree wavelet transform. In this manuscript, we consider two questions: When do two real-valued bases or frames {fn:n∈N} and {gn:n∈N} form a complex basis or frame of the form {fn+ign:n∈N}? And for which bounded linear operators Adoes {fn+iAfn:n∈N} form a complex-valued orthonormal basis, Riesz basis or frame, when {fn:n ∈N} is a real-valued orthonormal basis, Riesz basis or frame? We call this approach rebricking. It is well-known that the analytic signals don't span the complex vector space L2(R; C), hence H is not a rebricking operator. We give a full characterization of rebricking operators for bases, in particular orthonormal and Riesz bases, Parseval frames, and frames in general. We also examine the special case of finite dimensional vector spaces and show that we can use any real, invertible matrix for rebricking if we allow for permutations in the imaginary part.}, language = {en} }