Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen
OPUS4-2901 Konferenzveröffentlichung Smith, Andrew Paul; Garloff, Jürgen; Werkle, Horst Gürlebeck, Klaus; Könke, Carsten VERIFIED SOLUTION OF FINITE ELEMENT MODELS WITH UNCERTAIN NODE LOCATIONS We consider a structural truss problem where all of the physical model parameters are uncertain: not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening (pruning) technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements. 15 urn:nbn:de:gbv:wim2-20170314-29010 10.25643/bauhaus-universitaet.2901 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2837 Konferenzveröffentlichung De Bie, Hendrik; Sommen, Frank Gürlebeck, Klaus; Könke, Carsten VECTOR AND BIVECTOR FOURIER TRANSFORMS IN CLIFFORD ANALYSIS In the past, several types of Fourier transforms in Clifford analysis have been studied. In this paper, first an overview of these different transforms is given. Next, a new equation in a Clifford algebra is proposed, the solutions of which will act as kernels of a new class of generalized Fourier transforms. Two solutions of this equation are studied in more detail, namely a vector-valued solution and a bivector-valued solution, as well as the associated integral transforms. 11 urn:nbn:de:gbv:wim2-20170314-28371 10.25643/bauhaus-universitaet.2837 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2872 Konferenzveröffentlichung Abu Abed, Wassim; Milbradt, Peter Gürlebeck, Klaus; Könke, Carsten UNDERSTANDING THE ASPECT OF FUZZINESS IN INTERPOLATION METHODS Fuzzy functions are suitable to deal with uncertainties and fuzziness in a closed form maintaining the informational content. This paper tries to understand, elaborate, and explain the problem of interpolating crisp and fuzzy data using continuous fuzzy valued functions. Two main issues are addressed here. The first covers how the fuzziness, induced by the reduction and deficit of information i.e. the discontinuity of the interpolated points, can be evaluated considering the used interpolation method and the density of the data. The second issue deals with the need to differentiate between impreciseness and hence fuzziness only in the interpolated quantity, impreciseness only in the location of the interpolated points and impreciseness in both the quantity and the location. In this paper, a brief background of the concept of fuzzy numbers and of fuzzy functions is presented. The numerical side of computing with fuzzy numbers is concisely demonstrated. The problem of fuzzy polynomial interpolation, the interpolation on meshes and mesh free fuzzy interpolation is investigated. The integration of the previously noted uncertainty into a coherent fuzzy valued function is discussed. Several sets of artificial and original measured data are used to examine the mentioned fuzzy interpolations. 22 urn:nbn:de:gbv:wim2-20170314-28726 10.25643/bauhaus-universitaet.2872 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2856 Konferenzveröffentlichung Khan, Farhan Manzoor Ahmed; Cong, ZiXiang; Karsten, Menzel; Stack, Paul Gürlebeck, Klaus; Könke, Carsten TRACKING OCCUPANTS AND INVENTORY ITEMS IN BUILDINGS USING RADIO FREQUENCY IDENTIFICATION (RFID) TECHNOLOGY In order to make control decisions, Smart Buildings need to collect data from multiple sources and bring it to a central location, such as the Building Management System (BMS). This needs to be done in a timely and automated fashion. Besides data being gathered from different energy using elements, information of occupant behaviour is also important for a building's requirement analysis. In this paper, the parameter of Occupant Density was considered to help find behaviour of occupants towards a building space. Through this parameter, support for building energy consumption and requirements based on occupant need and demands was provided. The demonstrator presented provides information on the number of people present in a particular building space at any time, giving the space density. Such collections of density data made over a certain period of time represents occupant behaviour towards the building space, giving its usage patterns. Similarly, inventory items were tracked and monitored for moving out or being brought into a particular read zone. For both, people and inventory items, this was achieved using small, low-cost, passive Ultra-High Frequency (UHF) Radio Frequency Identification (RFID) tags. Occupants were given the tags in a form factor of a credit card to be possessed at all times. A central database was built where occupant and inventory information for a particular building space was maintained for monitoring and providing a central data access. 13 urn:nbn:de:gbv:wim2-20170314-28562 10.25643/bauhaus-universitaet.2856 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2846 Konferenzveröffentlichung Grob, Dennis; Constales, Denis; Kraußhar, Rolf Sören Gürlebeck, Klaus; Könke, Carsten THE HYPERCOMPLEX SZEGÖ KERNEL METHOD FOR 3D MAPPING PROBLEMS In this paper we present rudiments of a higher dimensional analogue of the Szegö kernel method to compute 3D mappings from elementary domains onto the unit sphere. This is a formal construction which provides us with a good substitution of the classical conformal Riemann mapping. We give explicit numerical examples and discuss a comparison of the results with those obtained alternatively by the Bergman kernel method. 7 urn:nbn:de:gbv:wim2-20170314-28464 10.25643/bauhaus-universitaet.2846 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2866 Konferenzveröffentlichung Lavicka, Roman; Delanghe, Richard; Soucek, Vladimir Gürlebeck, Klaus; Könke, Carsten THE HOWE DUALITY FOR HODGE SYSTEMS In this note, we describe quite explicitly the Howe duality for Hodge systems and connect it with the well-known facts of harmonic analysis and Clifford analysis. In Section 2, we recall briefly the Fisher decomposition and the Howe duality for harmonic analysis. In Section 3, the well-known fact that Clifford analysis is a real refinement of harmonic analysis is illustrated by the Fisher decomposition and the Howe duality for the space of spinor-valued polynomials in the Euclidean space under the so-called L-action. On the other hand, for Clifford algebra valued polynomials, we can consider another action, called in Clifford analysis the H-action. In the last section, we recall the Fisher decomposition for the H-action obtained recently. As in Clifford analysis the prominent role plays the Dirac equation in this case the basic set of equations is formed by the Hodge system. Moreover, analysis of Hodge systems can be viewed even as a refinement of Clifford analysis. In this note, we describe the Howe duality for the H-action. In particular, in Proposition 1, we recognize the Howe dual partner of the orthogonal group O(m) in this case as the Lie superalgebra sl(2 1). Furthermore, Theorem 2 gives the corresponding multiplicity free decomposition with an explicit description of irreducible pieces. 11 urn:nbn:de:gbv:wim2-20170314-28669 10.25643/bauhaus-universitaet.2866 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2838 Konferenzveröffentlichung De Schepper, Nele; Brackx, Fred; Sommen, Frank Gürlebeck, Klaus; Könke, Carsten THE FOURIER-BESSEL TRANSFORM In this paper we devise a new multi-dimensional integral transform within the Clifford analysis setting, the so-called Fourier-Bessel transform. It appears that in the two-dimensional case, it coincides with the Clifford-Fourier and cylindrical Fourier transforms introduced earlier. We show that this new integral transform satisfies operational formulae which are similar to those of the classical tensorial Fourier transform. Moreover the L2-basis elements consisting of generalized Clifford-Hermite functions appear to be eigenfunctions of the Fourier-Bessel transform. 18 urn:nbn:de:gbv:wim2-20170314-28387 10.25643/bauhaus-universitaet.2838 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2839 Konferenzveröffentlichung Djordjevic, Djordje; Petkovic, Dusan; Zivkovic, Darko Gürlebeck, Klaus; Könke, Carsten THE APPLICATION OF INTERVAL CALCULUS TO ESTIMATION OF PLATE DEFLECTION BY SOLVING POISSON'S PARTIAL DIFFERENTIAL EQUATION This paper describes the application of interval calculus to calculation of plate deflection, taking in account inevitable and acceptable tolerance of input data (input parameters). The simply supported reinforced concrete plate was taken as an example. The plate was loaded by uniformly distributed loads. Several parameters that influence the plate deflection are given as certain closed intervals. Accordingly, the results are obtained as intervals so it was possible to follow the direct influence of a change of one or more input parameters on output (in our example, deflection) values by using one model and one computing procedure. The described procedure could be applied to any FEM calculation in order to keep calculation tolerances, ISO-tolerances, and production tolerances in close limits (admissible limits). The Wolfram Mathematica has been used as tool for interval calculation. 12 urn:nbn:de:gbv:wim2-20170314-28397 10.25643/bauhaus-universitaet.2839 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2896 Konferenzveröffentlichung Szolomicki, Jerzy Pawel Gürlebeck, Klaus; Könke, Carsten STRUCTURAL BEHAVIOUR OF MASONRY VAULTS This paper deals with the modelling and the analysis of masonry vaults. Numerical FEM analyses are performed using LUSAS code. Two vault typologies are analysed (barrel and cross-ribbed vaults) parametrically varying geometrical proportions and constraints. The proposed model and the developed numerical procedure are implemented in a computer analysis. Numerical applications are developed to assess the model effectiveness and the efficiency of the numerical procedure. The main object of the present paper is the development of a computational procedure which allows to define 3D structural behaviour of masonry vaults. For each investigated example, the homogenized limit analysis approach has been employed to predict ultimate load and failure mechanisms. Finally, both a mesh dependence study and a sensitivity analysis are reported. Sensitivity analysis is conducted varying in a wide range mortar tensile strength and mortar friction angle with the aim of investigating the influence of the mechanical properties of joints on collapse load and failure mechanisms. The proposed computer model is validated by a comparison with experimental results available in the literature. 11 urn:nbn:de:gbv:wim2-20170314-28966 10.25643/bauhaus-universitaet.2896 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2870 Konferenzveröffentlichung Malonek, Helmuth R. Gürlebeck, Klaus; Könke, Carsten SPECIAL FUNCTIONS VERSUS ELEMENTARY FUNCTIONS IN HYPERCOMPLEX FUNCTION THEORY In recent years special hypercomplex Appell polynomials have been introduced by several authors and their main properties have been studied by different methods and with different objectives. Like in the classical theory of Appell polynomials, their generating function is a hypercomplex exponential function. The observation that this generalized exponential function has, for example, a close relationship with Bessel functions confirmed the practical significance of such an approach to special classes of hypercomplex differentiable functions. Its usefulness for combinatorial studies has also been investigated. Moreover, an extension of those ideas led to the construction of complete sets of hypercomplex Appell polynomial sequences. Here we show how this opens the way for a more systematic study of the relation between some classes of Special Functions and Elementary Functions in Hypercomplex Function Theory. 3 urn:nbn:de:gbv:wim2-20170314-28702 10.25643/bauhaus-universitaet.2870 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2899 Konferenzveröffentlichung Vorechovský, Miroslav Gürlebeck, Klaus; Könke, Carsten SIMULATION OF SIMPLY CROSS CORRELATED RANDOM FIELDS BY SERIES EXPANSION METHODS A practical framework for generating cross correlated fields with a specified marginal distribution function, an autocorrelation function and cross correlation coefficients is presented in the paper. The contribution promotes a recent journal paper [1]. The approach relies on well known series expansion methods for simulation of a Gaussian random field. The proposed method requires all cross correlated fields over the domain to share an identical autocorrelation function and the cross correlation structure between each pair of simulated fields to be simply defined by a cross correlation coefficient. Such relations result in specific properties of eigenvectors of covariance matrices of discretized field over the domain. These properties are used to decompose the eigenproblem which must normally be solved in computing the series expansion into two smaller eigenproblems. Such decomposition represents a significant reduction of computational effort. Non-Gaussian components of a multivariate random field are proposed to be simulated via memoryless transformation of underlying Gaussian random fields for which the Nataf model is employed to modify the correlation structure. In this method, the autocorrelation structure of each field is fulfilled exactly while the cross correlation is only approximated. The associated errors can be computed before performing simulations and it is shown that the errors happen especially in the cross correlation between distant points and that they are negligibly small in practical situations. 13 urn:nbn:de:gbv:wim2-20170314-28995 10.25643/bauhaus-universitaet.2899 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2829 Konferenzveröffentlichung Bauer, Marek; Richter, Matthias; Weiß, Hendrik Gürlebeck, Klaus; Könke, Carsten SIMULATION MODEL OF TRAM ROUTE OPERATION From passenger's perspective, punctuality is one of the most important features of tram route operation. We present a stochastic simulation model with special focus on determining important factors of influence. The statistical analysis bases on large samples (sample size is nearly 2000) accumulated from comprehensive measurements on eight tram routes in Cracow. For the simulation, we are not only interested in average values but also in stochastic characteristics like the variance and other properties of the distribution. A realization of trams operations is assumed to be a sequence of running times between successive stops and times spent by tram at the stops divided in passengers alighting and boarding times and times waiting for possibility of departure . The running time depends on the kind of track separation including the priorities in traffic lights, the length of the section and the number of intersections. For every type of section, a linear mixed regression model describes the average running time and its variance as functions of the length of the section and the number of intersections. The regression coefficients are estimated by the iterative re-weighted least square method. Alighting and boarding time mainly depends on type of vehicle, number of passengers alighting and boarding and occupancy of vehicle. For the distribution of the time waiting for possibility of departure suitable distributions like Gamma distribution and Lognormal distribution are fitted. 19 urn:nbn:de:gbv:wim2-20170314-28295 10.25643/bauhaus-universitaet.2829 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2842 Konferenzveröffentlichung Flaig, Thomas; Apel, Thomas Gürlebeck, Klaus; Könke, Carsten SIMULATION AND MATHEMATICAL OPTIMIZATION OF THE HYDRATION OF CONCRETE FOR AVOIDING THERMAL CRACKS After mixing of concrete, the hardening starts by an exothermic chemical reaction known as hydration. As the reaction rate depends on the temperature the time in the description of the hydration is replaced by the maturity which is defined as an integral over a certain function depending on the temperature. The temperature distribution is governed by the heat equation with a right hand side depending on the maturity and the temperature itself. We compare of the performance of different time integration schemes of higher order with an automatic time step control. The simulation of the heat distribution is of importance as the development of mechanical properties is driven by the hydration. During this process it is possible that the tensile stresses exceed the tensile strength and cracks occur. The goal is to produce cheap concrete without cracks. Simple crack-criterions use only temperature differences, more involved ones are based on thermal stresses. If the criterion predicts cracks some changes in the input data are needed. This can be interpreted as optimization. The final goal will be to adopt model based optimization (in contrast to simulation based optimization) to the problem of the hydration of young concrete and the avoidance of cracks. The first step is the simulation of the hydration, which we focus in this paper. 15 urn:nbn:de:gbv:wim2-20170314-28424 10.25643/bauhaus-universitaet.2842 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2850 Konferenzveröffentlichung Harbrecht, Helmut; Eppler, K. Gürlebeck, Klaus; Könke, Carsten SHAPE OPTIMIZATION FOR FREE BOUNDARY PROBLEMS In this paper three different formulations of a Bernoulli type free boundary problem are discussed. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for discretizing the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes is proven. In combination with a fast boundary element method efficient first and second order shape optimization algorithms are obtained. 8 urn:nbn:de:gbv:wim2-20170314-28508 10.25643/bauhaus-universitaet.2850 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2828 Konferenzveröffentlichung Bauer, Marek; Dudek, Mariusz; Richter, Matthias Gürlebeck, Klaus; Könke, Carsten RELIABILITY OF TRAM - NETWORK SECTION We investigate aspects of tram-network section reliability, which operates as a part of the model of whole city tram-network reliability. Here, one of the main points of interest is the character of the chronological development of the disturbances (namely the differences between time of departure provided in schedule and real time of departure) on subsequent sections during tram line operation. These developments were observed in comprehensive measurements done in Krakow, during one of the main transportation nodes (Rondo Mogilskie) rebuilding. All taken building activities cause big disturbances in tram lines operation with effects extended to neighboring sections. In a second part, the stochastic character of section running time will be analyzed more detailed. There will be taken into consideration sections with only one beginning stop and also with two or three beginning stops located at different streets at an intersection. Possibility of adding results from sections with two beginning stops to one set will be checked with suitable statistical tests which are used to compare the means of the two samples. Section running time may depend on the value of gap between two following trams and from the value of deviation from schedule. This dependence will be described by a multi regression formula. The main measurements were done in the city center of Krakow in two stages: before and after big changes in tramway infrastructure. 16 urn:nbn:de:gbv:wim2-20170314-28281 10.25643/bauhaus-universitaet.2828 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2895 Konferenzveröffentlichung Suzuki, Osamu Gürlebeck, Klaus; Könke, Carsten RECENT RESULTS ON ITERATION DYNAMICAL SYSTEMS OF DISCRETE LAPLACIANS ON THE PLANE LATTICE The recent development on the mathematical theory and the computer simulations of iteration dynamical system of discrete Laplacian on the plane lattice is reviewed and the future problem is discussed. 13 urn:nbn:de:gbv:wim2-20170314-28954 10.25643/bauhaus-universitaet.2895 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2891 Konferenzveröffentlichung Smarsly, Kay; Hartmann, Dietrich Gürlebeck, Klaus; Könke, Carsten REAL-TIME MONITORING OF WIND CONVERTERS BASED ON SOFTWARE AGENTS Due to increasing numbers of wind energy converters, the accurate assessment of the lifespan of their structural parts and the entire converter system is becoming more and more paramount. Lifespan-oriented design, inspections and remedial maintenance are challenging because of their complex dynamic behavior. Wind energy converters are subjected to stochastic turbulent wind loading causing corresponding stochastic structural response and vibrations associated with an extreme number of stress cycles (up to 109 according to the rotation of the blades). Currently, wind energy converters are constructed for a service life of about 20 years. However, this estimation is more or less made by rule of thumb and not backed by profound scientific analyses or accurate simulations. By contrast, modern structural health monitoring systems allow an improved identification of deteriorations and, thereupon, to drastically advance the lifespan assessment of wind energy converters. In particular, monitoring systems based on artificial intelligence techniques represent a promising approach towards cost-efficient and reliable real-time monitoring. Therefore, an innovative real-time structural health monitoring concept based on software agents is introduced in this contribution. For a short time, this concept is also turned into a real-world monitoring system developed in a DFG joint research project in the authors' institute at the Ruhr-University Bochum. In this paper, primarily the agent-based development, implementation and application of the monitoring system is addressed, focusing on the real-time monitoring tasks in the deserved detail. 11 urn:nbn:de:gbv:wim2-20170314-28916 10.25643/bauhaus-universitaet.2891 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2886 Konferenzveröffentlichung Schneider, David Gürlebeck, Klaus; Könke, Carsten QUALITY OPTIMIZATION USING LOCALLY REFINED META MODELS Quality is one of the most important properties of a product. Providing the optimal quality can reduce costs for rework, scrap, recall or even legal actions while satisfying customers demand for reliability. The aim is to achieve ``built-in'' quality within product development process (PDP). The common approach therefore is the robust design optimization (RDO). It uses stochastic values as constraint and/or objective to obtain a robust and reliable optimal design. In classical approaches the effort required for stochastic analysis multiplies with the complexity of the optimization algorithm. The suggested approach shows that it is possible to reduce this effort enormously by using previously obtained data. Therefore the support point set of an underlying metamodel is filled iteratively during ongoing optimization in regions of interest if this is necessary. In a simple example, it will be shown that this is possible without significant loss of accuracy. 17 urn:nbn:de:gbv:wim2-20170314-28864 10.25643/bauhaus-universitaet.2886 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2847 Konferenzveröffentlichung Gutierrez S, Andrei; Ramirez, Marco P.; Rodriguez, Octavio; Sanchez N., V.D. Gürlebeck, Klaus; Könke, Carsten ON THE SOLUTIONS OF ELECTRICAL IMPEDANCE EQUATION: A PSEUDOANALYTIC APPROACH FOR SEPARABLE-VARIABLES CONDUCTIVITY FUNCTION Using a quaternionic reformulation of the electrical impedance equation, we consider a two-dimensional separable-variables conductivity function and, posing two different techniques, we obtain a special class of Vekua equation, whose general solution can be approach by virtue of Taylor series in formal powers, for which is possible to introduce an explicit Bers generating sequence. 11 urn:nbn:de:gbv:wim2-20170314-28478 10.25643/bauhaus-universitaet.2847 In Zusammenarbeit mit der Bauhaus-Universität Weimar
OPUS4-2863 Konferenzveröffentlichung Constales, Denis; Kraußhar, Rolf Sören Gürlebeck, Klaus; Könke, Carsten ON THE KLEIN-GORDON EQUATION ON THE 3-TORUS In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus. 10 urn:nbn:de:gbv:wim2-20170314-28639 10.25643/bauhaus-universitaet.2863 In Zusammenarbeit mit der Bauhaus-Universität Weimar