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- Architektur <Informatik> (201) (remove)
Für eine gesicherte Planung im Bestand, sind eine Fülle verschiedenster Informationen zu berücksichtigen, welche oft erst während des Planungs- oder Bauprozesses gewonnen werden. Voraussetzung hierfür bildet immer eine Bestandserfassung. Zwar existieren Computerprogramme zur Unterstützung der Bestandserfassung, allerdings handelt es sich hierbei ausschließlich um Insellösungen. Der Export der aufgenommenen Daten in ein Planungssystem bedingt Informationsverluste. Trotz der potentiellen Möglichkeit aktueller CAAD/BIM Systeme zur Verwaltung von Bestandsdaten, sind diese vorrangig für die Neubauplanung konzipiert. Die durchgängige Bearbeitung von Sanierungsprojekten von der Erfassung des Bestandes über die Entwurfs- und Genehmigungsplanung bis zur Ausführungsplanung innerhalb eines CAAD/BIM Systems wird derzeit nicht adäquat unterstützt. An der Professur Informatik in der Architektur (InfAR) der Fakultät Architektur der Bauhaus-Universität Weimar entstanden im Rahmen des DFG Sonderforschungsbereich 524 "Werkzeuge und Konstruktionen für die Revitalisierung von Bauwerken" in den letzten Jahren Konzepte und Prototypen zur fachlich orientierten Unterstützung der Planung im Bestand. Der Fokus lag dabei in der Erfassung aller planungsrelevanter Bestandsdaten und der Abbildung dieser in einem dynamischen Bauwerksmodell. Aufbauend auf diesen Forschungsarbeiten befasst sich der Artikel mit der kontextbezogenen Weiterverwendung und gezielten Bereitstellung von Bestandsdaten im Prozess des Planens im Bestand und der Integration von Konzepten der planungsrelevanten Bestandserfassung in marktübliche CAAD/BIM Systeme.
In the context of finite element model updating using vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the order of natural frequencies and mode shapes is important. As only limited spatial information is available and noise is present in the measurements, the automatic selection of the most likely numerical mode shape corresponding to a measured mode shape is a difficult task. The most common criterion to indicate corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases. In this paper, the pure mathematical modal assurance criterion will be enhanced by additional physical information of the numerical model in terms of modal strain energies. A numerical example and a benchmark study with real measured data are presented to show the advantages of the enhanced energy based criterion in comparison to the traditional modal assurance criterion.
Am Beispiel eines 3-feldrigen Durchlaufträgers wird die Versagenswahrscheinlichkeit von wechselnd belasteten Stahlbetonbalken bezüglich des Grenzzustandes der Adaption (Einspielen, shakedown) untersucht. Die Adaptionsanalyse erfolgt unter Berücksichtigung der beanspruchungschabhängigen Degradation der Biegesteifigkeit infolge Rissbildung. Die damit verbundene mechanische Problemstellung kann auf die Adaptionsanalyse linear elastisch - ideal plastischer Balkentragwerke mit unbekannter aber begrenzter Biegesteifigkeit zurückgeführt werden. Die Versagenswahrscheinlichkeit wird unter Berücksichtigung stochastischer Tragwerks- und Belastungsgrößen berechnet. Tragwerkseigenschaften und ständige Lasten gelten als zeitunabhängige Zufallsgrößen. Zeitlich veränderliche Lasten werden als nutzungsdauerbezogene Extremwerte POISSONscher Rechteck-Pulsprozesse unter Berücksichtigung zeitlicher Überlagerungseffekte modelliert, so dass die Versagenswahrscheinlichkeit ebenfalls eine nutzungsdauerbezogene Größe ist. Die mechanischen Problemstellungen werden numerisch mit der mathematischen Optimierung gelöst. Die Versagenswahrscheinlichkeit wird auf statistischem Weg mit der Monte-Carlo-Methode geschätzt.
This contribution will be freewheeling in the domain of signal, image and surface processing and touch briefly upon some topics that have been close to the heart of people in our research group. A lot of the research of the last 20 years in this domain that has been carried out world wide is dealing with multiresolution. Multiresolution allows to represent a function (in the broadest sense) at different levels of detail. This was not only applied in signals and images but also when solving all kinds of complex numerical problems. Since wavelets came into play in the 1980's, this idea was applied and generalized by many researchers. Therefore we use this as the central idea throughout this text. Wavelets, subdivision and hierarchical bases are the appropriate tools to obtain these multiresolution effects. We shall introduce some of the concepts in a rather informal way and show that the same concepts will work in one, two and three dimensions. The applications in the three cases are however quite different, and thus one wants to achieve very different goals when dealing with signals, images or surfaces. Because completeness in our treatment is impossible, we have chosen to describe two case studies after introducing some concepts in signal processing. These case studies are still the subject of current research. The first one attempts to solve a problem in image processing: how to approximate an edge in an image efficiently by subdivision. The method is based on normal offsets. The second case is the use of Powell-Sabin splines to give a smooth multiresolution representation of a surface. In this context we also illustrate the general method of construction of a spline wavelet basis using a lifting scheme.
A UNIFIED APPROACH FOR THE TREATMENT OF SOME HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS ON SPHERES
(2010)
Using Clifford analysis methods, we provide a unified approach to obtain explicit solutions of some partial differential equations combining the n-dimensional Dirac and Euler operators, including generalizations of the classical time-harmonic Maxwell equations. The obtained regular solutions show strong connections between hypergeometric functions and homogeneous polynomials in the kernel of the Dirac operator.
In this paper we study the structure of the solutions to higher dimensional Dirac type equations generalizing the known λ-hyperholomorphic functions, where λ is a complex parameter. The structure of the solutions to the system of partial differential equations (D- λ) f=0 show a close connection with Bessel functions of first kind with complex argument. The more general system of partial differential equations that is considered in this paper combines Dirac and Euler operators and emphasizes the role of the Bessel functions. However, contrary to the simplest case, one gets now Bessel functions of any arbitrary complex order.
The application of a recent method using formal power series is proposed. It is based on a new representation for solutions of Sturm-Liouville equations. This method is used to calculate the transmittance and reflectance coefficients of finite inhomogeneous layers with high accuracy and efficiency. Tailoring the refraction index profile defining the inhomogeneous media it is possible to develop very important applications such as optical filters. A number of profiles were evaluated and then some of them selected in order to perform an improvement of their characteristics via the modification of their profiles.
Design activity could be treated as state transition computationally. In stepwise processing, in-between form-states are not easily observed. However, in this research time-based concept is introduced and applied in order to bridge the gap. In architecture, folding is one method of form manipulation and architects also want to search for alternatives by this operation. Besides, folding operation has to be defined and parameterized before time factor is involved as a variable of folding. As a result, time-based transformation provides sequential form states and redirects design activity.
MICROPLANE MODEL WITH INITIAL AND DAMAGE-INDUCED ANISOTROPY APPLIED TO TEXTILE-REINFORCED CONCRETE
(2010)
The presented material model reproduces the anisotropic characteristics of textile reinforced concrete in a smeared manner. This includes both the initial anisotropy introduced by the textile reinforcement, as well as the anisotropic damage evolution reflecting fine patterns of crack bridges. The model is based on the microplane approach. The direction-dependent representation of the material structure into oriented microplanes provides a flexible way to introduce the initial anisotropy. The microplanes oriented in a yarn direction are associated with modified damage laws that reflect the tension-stiffening effect due to the multiple cracking of the matrix along the yarn.
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.
ON THE NAVIER-STOKES EQUATION WITH FREE CONVECTION IN STRIP DOMAINS AND 3D TRIANGULAR CHANNELS
(2006)
The Navier-Stokes equations and related ones can be treated very elegantly with the quaternionic operator calculus developed in a series of works by K. Guerlebeck, W. Sproeossig and others. This study will be extended in this paper. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one basically needs to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. With special variants of quaternionic holomorphic multiperiodic functions we obtain explicit formulas for three dimensional parallel plate channels, rectangular block domains and regular triangular channels. The explicit knowledge of the integral kernels makes it then possible to evaluate the operator equations in order to determine the solutions of the boundary value problem explicitly.
In classical complex function theory the geometric mapping property of conformality is closely linked with complex differentiability. In contrast to the planar case, in higher dimensions the set of conformal mappings is only the set of Möbius transformations. Unfortunately, the theory of generalized holomorphic functions (by historical reasons they are called monogenic functions) developed on the basis of Clifford algebras does not cover the set of Möbius transformations in higher dimensions, since Möbius transformations are not monogenic. But on the other side, monogenic functions are hypercomplex differentiable functions and the question arises if from this point of view they can still play a special role for other types of 3D-mappings, for instance, for quasi-conformal ones. On the occasion of the 16th IKM 3D-mapping methods based on the application of Bergman's reproducing kernel approach (BKM) have been discussed. Almost all authors working before that with BKM in the Clifford setting were only concerned with the general algebraic and functional analytic background which allows the explicit determination of the kernel in special situations. The main goal of the abovementioned contribution was the numerical experiment by using a Maple software specially developed for that purpose. Since BKM is only one of a great variety of concrete numerical methods developed for mapping problems, our goal is to present a complete different from BKM approach to 3D-mappings. In fact, it is an extension of ideas of L. V. Kantorovich to the 3-dimensional case by using reduced quaternions and some suitable series of powers of a small parameter. Whereas until now in the Clifford case of BKM the recovering of the mapping function itself and its relation to the monogenic kernel function is still an open problem, this approach avoids such difficulties and leads to an approximation by monogenic polynomials depending on that small parameter.
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.
THE FOURIER-BESSEL TRANSFORM
(2010)
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.
Designing a structure follows a pattern of creating a structural design concept, executing a finite element analysis and developing a design model. A project was undertaken to create computer support for executing these tasks within a collaborative environment. This study focuses on developing a software architecture that integrates the various structural design aspects into a seamless functional collaboratory that satisfies engineering practice requirements. The collaboratory is to support both homogeneous collaboration i.e. between users operating on the same model and heterogeneous collaboration i.e. between users operating on different model types. Collaboration can take place synchronously or asynchronously, and the information exchange is done either at the granularity of objects or at the granularity of models. The objective is to determine from practicing engineers which configurations they regard as best and what features are essential for working in a collaborative environment. Based on the suggestions of these engineers a specification of a collaboration configuration that satisfies engineering practice requirements will be developed.
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.
Reasonably accurate cost estimation of the structural system is quite desirable at the early stages of the design process of a construction project. However, the numerous interactions among the many cost-variables make the prediction difficult. Artificial neural networks (ANN) and case-based reasoning (CBR) are reported to overcome this difficulty. This paper presents a comparison of CBR and ANN augmented by genetic algorithms (GA) conducted by using spreadsheet simulations. GA was used to determine the optimum weights for the ANN and CBR models. The cost data of twenty-nine actual cases of residential building projects were used as an example application. Two different sets of cases were randomly selected from the data set for training and testing purposes. Prediction rates of 84% in the GA/CBR study and 89% in the GA/ANN study were obtained. The advantages and disadvantages of the two approaches are discussed in the light of the experiments and the findings. It appears that GA/ANN is a more suitable model for this example of cost estimation where the prediction of numerical values is required and only a limited number of cases exist. The integration of GA into CBR and ANN in a spreadsheet format is likely to improve the prediction rates.
Der Begriff der Zuverlässigkeit spielt eine zentrale Rolle bei der Bewertung von Verkehrsnetzen. Aus der Sicht der Nutzer des öffentlichen Personennahverkehrs (ÖPNV) ist eines der wichtigsten Kriterien zur Beurteilung der Qualität des Liniennetzes, ob es möglich ist, mit einer großen Sicherheit das Reiseziel in einer vorgegebenen Zeit zu erreichen. Im Vortrag soll dieser Zuverlässigkeitsbegriff mathematisch gefasst werden. Dabei wird zunächst auf den üblichen Begriff der Zuverlässigkeit eines Netzes im Sinne paarweiser Zusammenhangswahrscheinlichkeiten eingegangen. Dieser Begriff wird erweitert durch die Betrachtung der Zuverlässigkeit unter Einbeziehung einer maximal zulässigen Reisezeit. In vergangenen Arbeiten hat sich die Ring-Radius-Struktur als bewährtes Modell für die theoretische Beschreibung von Verkehrsnetzen erwiesen. Diese Überlegungen sollen nun durch Einbeziehung realer Verkehrsnetzstrukturen erweitert werden. Als konkretes Beispiel dient das Straßenbahnnetz von Krakau. Hier soll insbesondere untersucht werden, welche Auswirkungen ein geplanter Ausbau des Netzes auf die Zuverlässigkeit haben wird. This paper is involved with CIVITAS-CARAVEL project: "Clean and better transport in cites". The project has received research funding from the Community's Sixth Framework Programme. The paper reflects only the author's views and the Community is not liable for any use that may be made of the information contained therein.
Wir betrachten im ÖPNV (Öffentlichen Personennahverkehr) diejenige Situation, daß zwei Bus- oder Straßenbahnlinien gemeinsame Haltestellen haben. Ziel unserer Untersuchungen ist es, für beide Linien einen solchen Fahrplan zu finden, der für die Fahrgäste möglichst viel Bequemlichkeit bietet. Die Bedarfsstruktur - die Anzahl von Personen, die die beiden Linien benutzen - setzt dabei gewisse Beschränkungen für die Taktzeiten der beiden Linien. Die verbleibenden Entscheidungsfreiheiten sollen im Sinne der Zielstellung ausgenutzt werden. Im Vortrag wird folgenden Fragen nachgegangen: - nach welchen Kriterien kann man die "Bequemlichkeit" oder die "Synchonisationsgüte" messen? - wie kann man die einzelnen "Synchronisationsmaße" berechnen ? - wie kann man die verbleibenden Entscheidungsfreiheiten nutzen, um eine möglichst gute Synchronisation zu erreichen ? Die Ergebnisse werden dann auf einige Beispiele angewandt und mit den bereitgestellten Methoden Lösungsvorschläge unterbreitet.
In civil engineering it is very difficult and often expensive to excite constructions such as bridges and buildings with an impulse hammer or shaker. This problem can be avoided with the output-only method as special feature of stochastic system identification. The permanently existing ambient noise (e.g. wind, traffic, waves) is sufficient to excite the structures in their operational conditions. The output-only method is able to estimate the observable part of a state-space-model which contains the dynamic characteristics of the measured mechanical system. Because of the assumption that the ambient excitation is white there is no requirement to measure the input. Another advantage of the output-only method is the possibility to get high detailed models by a special method, called polyreference setup. To pretend the availability of a much larger set of sensors the data from varying sensor locations will be collected. Several successive data sets are recorded with sensors at different locations (moving sensors) and fixed locations (reference sensors). The covariance functions of the reference sensors are bases to normalize the moving sensors. The result of the following subspace-based system identification is a high detailed black-box-model that contains the weighting function including the well-known dynamic parameters eigenfrequencies and mode shapes of the mechanical system. Emphasis of this lecture is the presentation of an extensive damage detection experiment. A 53-year old prestressed concrete tied-arch-bridge in Hünxe (Germany) was deconstructed in 2005. Preliminary numerous vibration measurements were accomplished. The first experiment for system modification was an additional support near the bridge bearing of one main girder. During a further experiment one hanger from one tied arch was cut through as an induced damage. Some first outcomes of the described experiments will be presented.