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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.
Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centered around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions, called Hermitean (or h-) monogenic functions, of two Hermitean Dirac operators which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Clifford-Cauchy integral formula has proven to be a corner stone of the function theory, as is the case for the traditional Cauchy formula for holomorphic functions in the complex plane. Previously, a Hermitean Clifford-Cauchy integral formula has been established by means of a matrix approach. This formula reduces to the traditional Martinelli-Bochner formula for holomorphic functions of several complex variables when taking functions with values in an appropriate part of complex spinor space. This means that the theory of Hermitean monogenic functions should encompass also other results of several variable complex analysis as special cases. At present we will elaborate further on the obtained results and refine them, considering fundamental solutions, Borel-Pompeiu representations and the Teoderescu inversion, each of them being developed at different levels, including the global level, handling vector variables, vector differential operators and the Clifford geometric product as well as the blade level were variables and differential operators act by means of the dot and wedge products. A rich world of results reveals itself, indeed including well-known formulae from the theory of several complex variables.
In this paper the influence of changes in the mean wind velocity, the wind profile power-law coefficient, the drag coefficient of the terrain and the structural stiffness are investigated on different complex structural models. This paper gives a short introduction to wind profile models and to the approach by Davenport A. G. to compute the structural reaction of wind induced vibrations. Firstly with help of a simple example (a skyscraper) this approach is shown. Using this simple example gives the reader the possibility to study the variance differences when changing one of the above mentioned parameters on this very easy example and see the influence of different complex structural models on the result. Furthermore an approach for estimation of the needed discretization level is given. With the help of this knowledge the structural model design methodology can be base on deeper understanding of the different behavior of the single models.
Die Behandlung von geometrischen Singularitäten bei der Lösung von Randwertaufgaben der Elastostatik stellt erhöhte Anforderungen an die mathematische Modellierung des Randwertproblems und erfordert für eine effiziente Auswertung speziell angepasste Berechnungsverfahren. Diese Arbeit beschäftigt sich mit der systematischen Verallgemeinerung der Methode der komplexen Spannungsfunktionen auf den Raum, wobei der Schwerpunkt in erster Linie auf der Begründung des mathematischen Verfahrens unter besonderer Berücksichtigung der praktischen Anwendbarkeit liegt. Den theoretischen Rahmen hierfür bildet die Theorie quaternionenwertiger Funktionen. Dementsprechend wird die Klasse der monogenen Funktionen als Grundlage verwendet, um im ersten Teil der Arbeit ein räumliches Analogon zum Darstellungssatz von Goursat zu beweisen und verallgemeinerte Kolosov-Muskhelishvili Formeln zu konstruieren. Im Hinblick auf die vielfältigen Anwendungsbereiche der Methode beschäftigt sich der zweite Teil der Arbeit mit der lokalen und globalen Approximation von monogenen Funktionen. Hierzu werden vollständige Orthogonalsysteme monogener Kugelfunktionen konstruiert, infolge dessen neuartige Darstellungen der kanonischen Reihenentwicklungen (Taylor, Fourier, Laurent) definiert werden. In Analogie zu den komplexen Potenz- und Laurentreihen auf der Grundlage der holomorphen z-Potenzen werden durch diese monogenen Orthogonalreihen alle wesentlichen Eigenschaften bezüglich der hyperkomplexen Ableitung und der monogenen Stammfunktion verallgemeinert. Anhand repräsentativer Beispiele werden die qualitativen und numerischen Eigenschaften der entwickelten funktionentheoretischen Verfahren abschließend evaluiert. In diesem Kontext werden ferner einige weiterführende Anwendungsbereiche im Rahmen der räumlichen Funktionentheorie betrachtet, welche die speziellen Struktureigenschaften der monogenen Potenz- und Laurentreihenentwicklungen benötigen.
Models in the context of engineering can be classified in process based and data based models. Whereas the process based model describes the problem by an explicit formulation, the data based model is often used, where no such mapping can be found due to the high complexity of the problem. Artificial Neuronal Networks (ANN) is a data based model, which is able to “learn“ a mapping from a set of training patterns. This paper deals with the application of ANN in time dependent bathymetric models. A bathymetric model is a geometric representation of the sea bed. Typically, a bathymetry is been measured and afterwards described by a finite set of measured data. Measuring at different time steps leads to a time dependent bathymetric model. To obtain a continuous surface, the measured data has to be interpolated by some interpolation method. Unlike the explicitly given interpolation methods, the presented time dependent bathymetric model using an ANN trains the approximated surface in space and time in an implicit way. The ANN is trained by topographic measured data, which consists of the location (x,y) and time t. In other words the ANN is trained to reproduce the mapping h = f(x,y,t) and afterwards it is able to approximate the topographic height for a given location and date. In a further step, this model is extended to take meteorological parameters into account. This leads to a model of more predictive character.
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.
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.
Am 25. März 2010 veranstaltete die Professur Baubetrieb und Bauverfahren im Rahmen der jährlich stattfindenden baubetrieblichen Tagungsreihe gemeinsam mit der Arbeitsgruppe „Unikatprozesse“ in der Fachgruppe „Simulation in Produktion und Logistik“ (SPL) im Rahmen der Arbeitsgemeinschaft Simulation – ASIM einen ganztägigen Workshop mit dem Titel: „Modellierung von Prozessen zur Fertigung von Unikaten“. Viele Bauprozesse sind dadurch gekennzeichnet, dass sie Unikatcharakter besitzen. Unikate sind durch prototypische Einmaligkeit, Individualität, vielfältige Randbedingungen, einen geringen Grad an Standardisierung und Wiederholungen gekennzeichnet. Das erschwert die realitätsnahe Modellierung zur Simulation sogenannter Unikatprozesse. Dieser Besonderheit widmet sich die überwiegende Zahl der Tagungsbeiträge, die in diesem Band widergegeben sind.
Digitale Lesezeichen, Volltextsuche und Multimedia-Inhalte – die Ende des 20. Jahrhunderts durch das Internet ausgelöste Medienrevolution ließ auch das Buch nicht unberührt. Die Verbreitung des World Wide Webs parallel zur rasanten Entwicklung der Computertechnologie ermöglichte die Digitalisierung des Buches und bildete das E-Book als neue Publikationsform heraus. Seit etwa zehn Jahren können Bücher nicht mehr nur gedruckt, sondern auch elektronisch zur Verfügung gestellt werden, was für die Buchbranche und den Leser einige Veränderungen bedeutet. Moderne Lesegeräte, auch E-Reader genannt, erlauben die Speicherung einer ganzen Bibliothek auf einem einzigen mobilen Endgerät. Dabei steht das einzelne E-Book dem gedruckten Buch in seiner Lesequalität in nichts nach und ermöglicht zudem das Einfügen elektronischer Notizen und Lesezeichen, die Volltextsuche nach bestimmten Wörtern und die Verbindung von Text mit Bild, Ton und Video. Dennoch kann das E-Book seit seinem Aufkommen in Deutschland noch keine Erfolgsgeschichte schreiben. Insbesondere hohe Preise für die Lesegeräte halten immer noch viele Leser vom Nutzen der E-Books ab. Zu sehr ist das gedruckte Buch für zahlreiche Menschen noch fester Bestandteil ihres alltäglichen Lebens, als das sie es bereits durch das E-Book austauschen würden. Eine Situation, die einige Fragen aufwirft: Wird sich das EBook als Medium durchsetzen und das gedruckte Buch langfristig ablösen? Kann das EBook neben Zeitung, Radio, Fernsehen und Buch überhaupt als ein neues Medium verstanden werden? Und welche Veränderungen würde die massenhafte Verbreitung elektronischer Bücher mit sich bringen?
Visually impaired is a common problem for human life in the world wide. The projector-based AR technique has ability to change appearance of real object, and it can help to improve visibility for visually impaired. We propose a new framework for the appearance enhancement with the projector camera system that employed model predictive controller. This framework enables arbitrary image processing such as photo-retouch software in the real world and it helps to improve visibility for visually impaired. In this article, we show the appearance enhancement result of Peli's method and Wolffshon's method for the low vision, Jefferson's method for color vision deficiencies. Through experiment results, the potential of our method to enhance the appearance for visually impaired was confirmed as same as appearance enhancement for the digital image and television viewing.