Rekonstruktionsbasierte Selektion relevanter Einflussgrößen

In diesem Beitrag wird ein Verfahren vorgestellt,das im Rahmen einer Datenvoranalyse für eine nachgeschaltete datenbasierte Modellierung aus einer gegebenen Menge von potenziellen Einflussgrößen einen Satz relevanter und nichtredundanter Einflussgrößen selektiert.Hierdurch wird der Suchraum und somit auch die Komplexität für ein nachgeschaltetes Modellierungsverfahren erheblich reduziert. Im Gegensatz zu den meisten etablierten Selektionsverfahren bewertet das Verfahren nicht nur die Relevanz einzelner Einflussgrößen, sondern auch die von gesamten Sätzen von Einflussgrößen.Die Leistungsfähigkeit des Verfahrens wird an einem Demonstrationsbeispiel verdeutlicht. Des Weiteren wird exemplarisch die Auswirkung dieser Datenvoranalyse auf eine nachgeschaltete Fuzzy-Modellierung von bekannten Benchmarkbeispielen diskutiert

Ein Verfahren zur datenbasierten Komplexitätsreduktion

Im vorliegenden Beitrag wird ein fuzzybasiertes Verfahren vorgestellt, das potentiell zu berücksichtigende Eingangsgrößen eines zu erstellenden Modells auf eindeutige Zusammenhäge mit den Ausgangsgrößen und mit den übgrigen potentiell zu berücksichtigenden Eingangsgrößen untersucht. Weist einen Eingangsgröße keinen eindeutigen Zusammenhang mit der Ausgangsgröße auf oder läßt sie sich durch eine andere Eingangsgröße eindeutig ausdrücken, ist sie zur Modellierung nicht erforderlich. Das Verfahren dient in erster Linie dazu, bei der datenbasierten Fuzzy-Modellierung die Anzahl der Eingangsgrößen des Fuzzy-Modells und damit seine Komplexität zu reduzieren

Flux penetration in slab shaped Type-I superconductors

We study the problem of flux penetration into type--I superconductors with high demagnetization factor (slab geometry).Assuming that the interface between the normal and superconducting regions is sharp, that flux diffuses rapidly in the normal regions, and that thermal effects are negligible, we analyze the process by which flux invades the sample as the applied field is increased slowly from zero.We find that flux does not penetrate gradually.Rather there is an instability in the process and the flux penetrates from the boundary in a series of bursts, accompanied by the formation of isolated droplets of the normal phase, leading to a multiply connected flux domain structure similar to that seen in experiments.Comment: 4 pages, 2 figures, Fig 2.(b) available upon request from the authors, email - [email protected]

Direct immersogeometric fluid flow analysis using B-rep CAD models

We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche\u27s method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep

Single-variable formulations and isogeometric discretizations for shear deformable beams

We present numerical formulations of Timoshenko beams with only one unknown, the bending displacement, and it is shown that all variables of the beam problem can be expressed in terms of it and its derivatives. We develop strong and weak forms of the problem. The strong form of the problem involves the fourth derivative of the bending displacement, whereas the symmetric weak form involves, somewhat surprisingly, third and second derivatives. Based on these, we develop isogeometric collocation and Galerkin formulations, that are completely locking-free and involve only half the degrees of freedom compared to standard Timoshenko beam formulations. Several numerical tests are presented to demonstrate the performance of the proposed formulations

Patch-wise quadrature of trimmed surfaces in Isogeometric Analysis

This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA should be able to deal with these models in order to fulfil its promise of closing the gap between design and analysis. Trimming operations violate the tensor-product structure of the used Non-Uniform Rational B-spline (NURBS) basis functions and of typical quadrature rules. Existing efficient patch-wise quadrature rules consider actual knot vectors and are determined in 1D. They are extended to further dimensions by means of a tensor-product. Therefore, they are not directly applicable to trimmed structures. The herein proposed method extends patch-wise quadrature rules to trimmed surfaces. Thereby, the number of quadrature points can be significantly reduced. Geometrically linear and non-linear benchmarks of plane, plate and shell structures are investigated. The results are compared to a standard trimming procedure and a good performance is observed