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The aim of this paper is to present so-called discrete-continual boundary element method (DCBEM) of structural analysis. Its field of application comprises buildings constructions, structures and also parts and components for the residential, commercial and un-inhabitant structures with invariability of physical and geometrical parameters in some dimensions. We should mention here in particular such objects as beams, thin-walled bars, strip foundations, plates, shells, deep beams, high-rise buildings, extensional buildings, pipelines, rails, dams and others. DCBEM comes under group of semianalytical methods. Semianalytical formulations are contemporary mathematical models which currently becoming available for realization due to substantial speed-up of computer productivity. DCBEM is based on the theory of the pseudodifferential boundary equations. Corresponding pseudodifferential operators are discretely approximated using Fourier analysis or wavelet analysis. The main DCBEM advantages against the other methods of the numerical analysis is a double reduction in dimension of the problem (discrete numerical division applied not to the full region of the interest but only to the boundary of the region cross section, as a matter of fact one is solving an one-dimensional problem with the finite step on the boundary area of the region), one has opportunities to carrying out very detailed analysis of the specific chosen zones, simplified initial data preparation, simplistic and adaptive algorithms. There are two methods to define and conduct DCBEM analysis developed – indirect (IDCBEM) and direct (DDCBEM), thus indirect like in boundary element method (BEM) applied and used little bit more than direct.

The execution of project activities generally requires the use of (renewable) resources like machines, equipment or manpower. The resource allocation problem consists in assigning time intervals to the execution of the project activities while taking into account temporal constraints between activities emanating from technological or organizational requirements and costs incurred by the resource allocation. If the total procurement cost of the different renewable resources has to be minimized we speak of a resource investment problem. If the cost depends on the smoothness of the resource utilization over time the underlying problem is called a resource levelling problem. In this paper we consider a new tree-based enumeration method for solving resource investment and resource levelling problems exploiting some fundamental properties of spanning trees. The enumeration scheme is embedded in a branch-and-bound procedure using a workload-based lower bound and a depth first search. Preliminary computational results show that the proposed procedure is promising for instances with up to 30 activities.

We present an algebraically extended 2D image representation in this paper. In order to obtain more degrees of freedom, a 2D image is embedded into a certain geometric algebra. Combining methods of differential geometry, tensor algebra, monogenic signal and quadrature filter, the novel 2D image representation can be derived as the monogenic extension of a curvature tensor. The 2D spherical harmonics are employed as basis functions to construct the algebraically extended 2D image representation. From this representation, the monogenic signal and the monogenic curvature signal for modeling intrinsically one and two dimensional (i1D/i2D) structures are obtained as special cases. Local features of amplitude, phase and orientation can be extracted at the same time in this unique framework. Compared with the related work, our approach has the advantage of simultaneous estimation of local phase and orientation. The main contribution is the rotationally invariant phase estimation, which enables phase-based processing in many computer vision tasks.

Analysis of the reinforced concrete chimney geometry changes and their influence on the stresses in the chimney mantle was made. All the changes were introduced to a model chimney and compared. Relations between the stresses in the mantle of the chimney and the deformations determined by the change of the chimney's vertical axis geometry were investigated. The vertical axis of chimney was described by linear function (corresponding to the real rotation of the chimney together with the foundation), and by parabolic function (corresponding to the real dislocation of the chimney under the influence of the horizontal forces - wind). The positive stress pattern in the concrete as well as the negative stress pattern in the reinforcing steel have been presented. The two cases were compared. Analysis of the stress changes in the chimney mantle depending on the modification in the thickness of the mantle (the thickness of the chimney mantle was altered in the linear or the abrupt way) was carried out. The relation between the stresses and the chimney's diameter change from the bottom to the top of the chimney was investigated. All the analyses were conducted by means of a specially developed computer program created in Mathematica environment. The program makes it also possible to control calculations and to visualize the results of the calculations at every stage of the calculation process.

TOOL TO CHECK TOPOLOGY AND GEOMETRY FOR SPATIAL STRUCTURES ON BASIS OF THE EXTENDED MAXWELL'S RULE
(2006)

One of the simplest principle in the design of light-weight structures is to avoid bending. This can be achieved by dissolving girders into members acting purely in axial tension or compression. The employment of cables for the tensioned members leads to even lighter structures which are called cable-strut structures. They constitute a subclass of spatial structures. To give fast information about the general feasibility of an architectural concept employing cable-strut structures is a challenging task due to their sophisticated mechanical behavior. In this regard it is essential to control if the structure is stable and if pre-stress can be applied. This paper presents a tool using the spreadsheet software Microsoft (MS) Excel which can give such information. Therefore it is not necessary to purchase special software and the according time consuming training is much lower. The tool was developed on basis of the extended Maxwell's rule, which besides topology also considers the geometry of the structure. For this the rank of the node equilibrium matrix is crucial. Significance and determination of the rank and the implementation of the corresponding algorithms in MS Excel are described in the following. The presented tool is able to support the structural designer in an early stage of the project in finding a feasible architectural concept for cable-strut structures. As examples for the application of the software tool two special cable-strut structures, so called tensegrity structures, were examined for their mechanical behavior.

Subject of the paper is the realisation of a model based efficiency control system for PV generators using a simulation model. A standard 2-diodes model of PV generator is base of the ColSim model, which is implemented in ANSI C code for flexible code exporting. The algorithm is based on discretisized U-I characteristics, which allows the calculation of string topologies witch parallel and serial PV cells and modules. Shadowing effects can be modelled down to cell configuration using polar horizon definitions. The simulation model was ported to a real time environment, to calculate the efficiency of a PV system. Embedded System technology allows the networked operation and the integration of standard I/O devices. Futher work focus on the adaption of shadowing routine, which will be adapted to get the environment conditions from the real operation.

Die meisten Insolvenzen in Deutschland kommen aus der Bauindustrie. Die Gründe hierfür sind vielschichtig, jedoch kann mittels eines modern ausgerichteten M-I-S und Baustellen-Controllings frühzeitig erkannt werden, wie sich die Baustellenergebnisse entwickeln. Hierzu ist es notwendig, dass die Arbeitskalkulation ständig auf dem Laufenden gehalten wird. Nur wenn dies geschieht, sind monatliche Soll-/ Ist-Vergleiche und eine Betrachtung der cost-to-complete möglich und sinnvoll. Eine monatlich rollierende Prognose des Baustellenergebnisses zum Bauende ermöglicht, dass gravierende Veränderungen des Ergebnisses umgehend aufgedeckt werden. Nur in Kenntnis dieser Entwicklungen kann das Management frühzeitig (im Sinne eines Frühwarnsystems) agieren und Steuerungsmaßnahmen ergreifen. Die Ergebnisprognose zum Bauende ist allein als Steuerungsinstrument nicht ausreichend. Die Finanzsituation der Baustelle muß auch regelmäßig geprüft werden, d.h. der Leistungsstand mit der Rechnungsstellung an den Bauherren abgeglichen sowie die unbezahlten Rechnungen des Bauherren überprüft werden. Das beste Prognoseergebnis ist wertlos, wenn der Bauherr seine bezogenen Leistungen nicht vergütet. Die wirtschaftlichen Daten stehen den Verantwortlichen online im Baustellen-Informations-System (B-I-S) zur Verfügung. Ein Ampelsystem verdeutlicht die wirtschaftliche Lage der Baustelle.

Hinsichtlich der Integration einzelner Bauwerkslebensphasen und der verschiedenen Beteiligten, insbesondere innerhalb von Bauplanungs- und Revitalisierungsprozessen, bestehen aktuell entscheidende Defizite. Die generelle Zielstellung der in diesem Beitrag vorgestellten Forschungsarbeiten besteht in der Unterstützung und Verbesserung der Integration durch die disziplin- und lebensphasenübergreifende Bereitstellung sämtlicher bauwerksbezogener Informationen. Dies erfordert einerseits geeignete Ansätze zur Modellierung und Integration der vielfältigen disziplinspezifischen Daten, andererseits geeignete Lösungen, die einen globalen Zugriff, Navigation und Recherche im Gesamtdatenbestand ermöglichen. Die Modellierung und Verwaltung bauwerksbezogener Daten ist seit längerem Gegenstand diverser Forschungsarbeiten. Im Rahmen des SFB 524 wurde ein eigener Ansatz basierend auf einem laufzeitdynamischen Partialmodellverbund entwickelt. Dieser wird in den wesentlichen Grundzügen anderen Ansätzen gegenübergestellt. Den Schwerpunkt dieses Beitrags bildet jedoch die Entwicklung einer geeigneten flexiblen Navigations- und Rechercheschicht zu Realisierung projektglobaler Informationsrecherche. Aus der Sicht der Modellierung und Datenverwaltung wie auch aus der Sicht der Informationsrecherche und Informationspräsentation in Planungsprozessen ergeben sich verschiedene Anforderungen an derartige Recherchewerkzeuge, wobei der wesentlichste Grundsatz maximale Flexibilität hinsichtlich verfügbarer Darstellungstechniken und deren freie Kombination mit Techniken formaler Suchanfragen ist. Das entwickelte Systemkonzept basiert auf einem Framework, welches verschiedene Grundtypen von Recherchemodulen und deren Interaktionsprinzipien vorgibt. Einzelne Recherchemodule werden als Ausprägungen dieser Modultypen realisiert und können je nach Bedarf laufzeitdynamisch in die Navigationsschicht integriert werden. Die technische Realisierung des Systems erfolgt im Umfeld vorhandener Prototypen aus vorangegangenen Forschungsaktivitäten. Dieses technische Umfeld gibt verschiedene Rahmenbedingungen vor, welche im Vorfeld prototypischer Implementierungen verschiedene Adaptionen des generellen Systemkonzepts notwendig machen. Der vorliegende Beitrag stellt den aktuellen Entwicklungsstand der Systemlösung aus konzeptioneller und technischer Sicht sowie erste prototypische Realisierungen von Recherchemodulen vor.

The design of safety-critical structures, exposed to cyclic excitations demands for non-degrading or limited-degrading behavior during extreme events. Among others, the structural behavior is mainly determined by the amount of plastic cycles, completed during the excitation. Existing simplified methods often ignore this dependency, or assume/request sufficient cyclic capacity. The paper introduces a new performance based design method that considers explicitly a predefined number of re-plastifications. Hereby approaches from the shakedown theory and signal processing methods are utilized. The paper introduces the theoretical background, explains the steps of the design procedure and demonstrates the applicability with help of an example. This project was supported by German Science Foundation (Deutsche Forschungsgemeinschaft, DFG)

The reduction of oscillation amplitudes of structural elements is necessary not only for maintenance of their durability and longevity but also for elimination of a harmful effect of oscillations on people and technology operations. The dampers are widely applied for this purpose. One of the most widespread models of structural friction forces having piecewise linear relation to displacement was analysed. T The author suggests the application of phase trajectories mapping in plane "acceleration – displacement". Unlike the trajectories mapping in a plane "velocity – displacement", they don't require large number of geometrical constructions for identification of the characteristics of dynamic systems. It promotes improving the accuracy. The analytical assumptions had been verified by numerical modeling. The results show good enough coincide between numerical and analytical estimation of dissipative characteristic.

The paper is devoted to the investigation of dynamical behavior of a cable under influence of various types of excitations. Such element has a low rigidity and is sensitive to dynamic effect. The structural scheme is a cable which ends are located at different level. The analysis of dynamical behavior of the cable under effect of kinematical excitation which is represented by the oscillations of the upper part of tower is given. The scheme of cable is accepted such, that lower end of an inclined cable is motionless. The motion of the upper end is assumed only in horizontal direction. The fourth-order Runge-Kutta method was realized in software. The fast Fourier transform was used for spectral analysis. Standard graphical software was adopted for presenting results of investigations. The mathematical model of oscillations of a cable was developed by the account of the viscous damping. The analysis of dynamical characteristics of a cable for various parameters of damping and kinematical excitation was carried out. The time series, spectral characteristics and amplitude-frequencies characteristics was obtained. The resonance amplitude for different oscillating regimes was estimated. It is noted that increasing of the coefficient of the viscous damping and decreasing of the amplitude of tower's oscillations reduces the value of the critical frequency and the resonant amplitudes.

The extended finite element method (XFEM) offers an elegant tool to model material discontinuities and cracks within a regular mesh, so that the element edges do not necessarily coincide with the discontinuities. This allows the modeling of propagating cracks without the requirement to adapt the mesh incrementally. Using a regular mesh offers the advantage, that simple refinement strategies based on the quadtree data structure can be used to refine the mesh in regions, that require a high mesh density. An additional benefit of the XFEM is, that the transmission of cohesive forces through a crack can be modeled in a straightforward way without introducing additional interface elements. Finally different criteria for the determination of the crack propagation angle are investigated and applied to numerical tests of cracked concrete specimens, which are compared with experimental results.

The paper contains a description of dynamic effects in the silo wall during the outflow of a stored material. The work allows for determining the danger of construction damage due to resonant vibrations and is of practical importance by determining the influence of cyclic pressures and vibro–creeping during prolonged use of a silo. The paper was devised as a result of tests on silo walls in semi-technical scale. The model is generally applicable and allows for identification of parameters in real- size silos as well.

The paper proposes a new method for general 3D measurement and 3D point reconstruction. Looking at its features, the method explicitly aims at practical applications. These features especially cover low technical expenses and minimal user interaction, a clear problem separation into steps that are solved by simple mathematical methods (direct, stable and optimal with respect to least error squares), and scalability. The method expects the internal and radial distortion parameters of the used camera(s) as inputs, and a plane quadrangle with known geometry within the scene. At first, for each single picture the 3D position of the reference quadrangle (with respect to each camera coordinate frame) is calculated. These 3D reconstructions of the reference quadrangle are then used to yield the relative external parameters of each camera regarding the first one. With known external parameters, triangulation is finally possible. The differences from other known procedures are outlined, paying attention to the stable mathematical methods (no usage of nonlinear optimization) and the low user interaction with good results at the same time.

In this paper proposed the application of two-parameters damage model, based on non-linear finite element approach, to the analysis of masonry panels. Masonry is treated as a homogenized material, for which the material characteristics can be defined by using homogenization technique. The masonry panels subjected to shear loading are studied by using the proposed procedure within the framework of three-dimensional analyses. The nonlinear behaviour of masonry can be modelled using concepts of damage theory. In this case an adequate damage function is defined for taking into account different response of masonry under tension and compression states. Cracking can, therefore, be interpreted as a local damage effect, defined by the evolution of known material parameters and by one or several functions which control the onset and evolution of damage. The model takes into account all the important aspects which should be considered in the nonlinear analysis of masonry structures such as the effect of stiffness degradation due to mechanical effects and the problem of objectivity of the results with respect to the finite element mesh. Finally the proposed damage model is validated with a comparison with experimental results available in the literature.

This paper presents results of applying Fuzzy Inference System for estimation of the number of potential Park and Ride users. Usually it is difficult to evaluate the number of users because it depends on human factor and data in the considered system are uncertain. In such situation the traditional mathematical approaches can not take into consideration rough data. Therefore a fuzzy approach can be applied in this case. A fuzzy methodology is treated as a proper way to describe choice of mode of transport, and especially that uncertainty accompanied of choosing process has rather fuzzy character. The proposed approach is based on the Mamdani Fuzzy Inference System and for calculation there is used Matlab software with Fuzzy Logic Toolbox. Mamdani model requires, as an input data, knowledge of the shape of membership function. These functions can be calibrated taking into consideration results of questionnaires conducted among users of Park and Ride system. Due to lack of representative sample of users, one has decided to use results of experts' questionnaires as a input data for calibration the shape of membership functions. Describing factor will be generalized cost of the trip for different modes of transport. Proposed approach consists of two main stages: modeling of share of public/private transport trips and Multimodal model estimating number of Park and Ride users. Verification of presented methodology is treated as an indirect proof. Proposed approach can be applied for estimation of bi-modal split. Then the results are compared with traditional approaches based on logit functions. Comparable results of proposed fuzzy approach with traditional logit models can be treated as a confirmation of chosen methodology.

DIGITAL SUPPORT OF MATERIAL- AND PRODUCT SELECTION IN THE ARCHITECTURAL DESIGN- AND PLANNING PROCESS
(2006)

Architecture is predominantly perceived over the surfaces limiting the space. The used surface materials thereby should support the design intention and have to fulfil various technical and economical requirements. If the architect wants to select the "right" or the "best" material he has to play with very different and sometimes contradicting criteria and must weight these individually for the special purpose. This selection process is supported only insufficiently by today's digital systems. If it would be possible to illustrate all the various parameters by numerical values, the method of multidimensional scaling will offer a solution for architects to find the material which is best fitting on basis of his individual weighting of criteria. By displaying the result of the architect's multidimensional query in a spatial arrangement multidimensional scaling can support an interactive selection process with additional feedback over the applied search strategy.

The concept is presented of the sensitivity analysis of the limit state of the structure with respect to selected basic variables. The sensitivity is presented in the form of the probability distribution of the limit state of the structure. The analysis is performed by the problem-oriented Monte Carlo simulation procedure. The procedure is based on the problem's definition of the elementary event, as a structural limit state. Thus the sample space consists of limit states of the structure. Defined on the sample space the one-dimensional random multiplier is introduced. This multiplier refers to the dominant basic variable (group of variables) of the problem. Numerical procedure results in the set of random numbers. Normalized relative histogram of this set is an estimator of the PDF of the limit state of the structure. Estimators of reliability, or the probability of failure are statistical characteristics of this histogram. The procedure is illustrated by the example of sensitivity analysis of the serviceability limit state of monumental structure. It is the colonnade of Licheń Basilica, situated in central Poland. Limit state of the structure is examined with reference to the upper deck horizontal deflection. Wind actions are taken as dominant variables. An assumption is made that the wind load intensities acting on the lower and on the upper storey of the colonnade, respectively, are identically distributed, but correlated random variables. Three correlation variants of these variables are considered. Relevant limit state histograms are analysed thereafter. The paper ends with the conclusions referring to the method and some general remarks on the fully probabilistic design.

VARIATION OF ROTATIONAL RESTRAINT IN GRID DECK CONNECTION DUE TO CORROSION DAMAGE AND STRENGTHENING
(2006)

The approach to assessment of rotational restraint of stringer-to-crossbeam connection in a deck of 100-year old steel truss bridge is presented. Sensitivity of rotational restraint coefficient of the connection to corrosion damage and strengthening is analyzed. Two criteria of the assessment of the rotational restraint coefficient are applied: static and kinematic one. The former is based on bending moment distribution in the considered member, the latter one – on the member rotation at the given joint. 2D-element model of finite element method is described: webs and flanges are modeled with shell elements, while rivets in the connection – with system of beam and spring elements. The method of rivet modeling is verified by T-stub connection test results published in literature. FEM analyses proved that recorded extent of corrosion damage does not alter the initial rotational restraint of stringer-to-crossbeam connection. Strengthening of stringer midspan influences midspan bending moment and stringer end rotation in a different way. Usually restoring member load bearing capacity means strengthening its critical regions (where the highest stress levels occur). This alters flexural stiffness distribution over member length and influences rotational restraint at its connection to other members. The impact depends on criterion chosen for rotational restraint coefficient assessment.

Monitoring und Bewertung sind Hauptaufgaben im Management bzw. der Revitalisierung von Bauwerken. Unterschiedliche Verfahren können bei der Akquisition der erforderlichen geometrischen Information, wie z. B. Größe oder Verformung eines Gebäudes, eingesetzt werden. Da das Potenzial der digitalen Fotografie kontinuierlich wächst, stellt die Industriephotogrammetrie heute eine bedeutende Alternative zu den klassischen Verfahren wie Dehnmessstreifen oder anderen taktilen Sensoren dar. Moderne Industriephotogrammetrie erfasst die Bilder mittels digitaler Systeme. Dies bedeutet, dass die Information digitaler Bilder mit Hilfe der digitalen Bildverarbeitung untersucht werden muss, um die Bildkoordinaten der Messpunkte zu erhalten. Eine der Aufgaben der Bildverarbeitung für photogrammetrische Zwecke besteht somit darin, den Mittelpunkt von kreisförmigen Marken zu lokalisieren. Die modernen Operatoren liefern Subpixelgenauigkeit für die Koordinaten des Punktes. Das optische Messverfahren der Industriephotogrammetrie erfordert hinsichtlich der Hardware in erster Linie hochauflösende digitale Kameras. Dabei lassen sich die Kameras in Videokameras, HighSpeed-Kameras, intelligente Kameras sowie so genannte Consumer und Professionelle Kameras unterscheiden. Die geometrische Auflösung digitaler HighEnd-Kameras liegt heute bei über 10 Megapixel. In punkto Datentransfer zum Rechner sind verschiedene Standards am Markt verfügbar, z. B. USB2.0, GigE-Vision, CameraLink oder Firewire. Die Wahl des Standards hängt immer von der spezifischen Aufgabenstellung ab, da keine der Techniken eine führende Position einnimmt. Die moderne Photogrammetrie bietet viele neue Möglichkeiten für das Monitoring und die Bewertung von Bauwerken. Sie kann ein-, zwei-, drei- oder vierdimensionale Informationen liefern, falls erforderlich auch in Echtzeit. Als berührungsloses Messverfahren ist der Einsatz der Photogrammetrie noch möglich, wenn die taktilen Sensoren z. B. aufgrund ihres Platzbedarfes nicht mehr eingesetzt werden können. Hochauflösende Videokameras erlauben es, selbst dynamische Untersuchungen mit großer Präzision durchzuführen.

Car following models are used to describe the behavior of a number of cars on the road dependent on the distance to the car in front. We introduce a system of ordinary differential equations and perform a theoretical and numerical analysis in order to find solutions that reflect various traffic situations. We present three different variations of the model motivated by reality.

In many branches companies often lose the visibility of their human and technical resources of their field service. On the one hand the people in the fieldservice are often free like kings on the other hand they do not take part of the daily communication in the central office and suffer under the lacking involvement in the decisions inside the central office. The result is inefficiency. Reproaches in both directions follow. With the radio systems and then mobile phones the ditch began to dry up. But the solutions are far from being productive.

Die Kommunale Wohnungsgesellschaft mbH Erfurt(KoWo) ist mit ihren rund 20.000 Wohnungen in der Landeshauptstadt das größte Wohnungsunternehmen in Thüringen. Der Immobilienbestand ist heterogen in seinem technischen Zustand und im Bezug auf die unterschiedlichen Lagen der Objekte. Bedingt durch Leerstände und unterschiedliche Modernisierungsmaßnahmen und -stände unterscheidet sich die Wirtschaftlichkeit verschiedener Objekte deutlich. Ohne eine einheitliche Einwertung des Immobilienbestandes im Bezug auf die Objektattraktivität, die Standortqualität und die Objektwirtschaftlichkeit fällt eine langfristige strategische Entwicklung des Immobilienportfolios schwer. Über die Schritte der technischen Bestandserfassung, die Einwertung über ein Scorintmodell, die Abbildung in einem Portfoliomodell mit zugehöriger Normstrategie bis hin zur Weiterverarbeitung der Daten in der 20-jährigen Instandsetzungsplanung wird praxisnah aufgezeigt, wie die Vorgehensweise bei der Einwertung des Immobilienportfolios ist.

Im Bereich der Altbausanierung und der Bestandserfassung im Bauwesen ist es häufig notwendig, bestehende Pläne hinsichtlich des Bauwerkszustandes zu aktualisieren oder, wenn diese Pläne nicht (mehr) zugänglich sind, gänzlich neue Planunterlagen des Ist-Zustandes zu erstellen. Ein komfortabler Weg, diese Bauwerksdaten zu erheben, eröffnet die Technologie der Laservermessung. Der vorliegende Artikel stellt in diesem Zusammenhang Ansätze zur Teilautomatisierung der Generierung eines dreidimensionalen Computermodells eines Bauwerkes vor. Als Ergebnis wird ein Volumenmodell bereitgestellt, in dem zunächst die geometrischen und topologischen Informationen über Flächen, Kanten und Punkte im Sinne eines B-rep Modells beschrieben sind. Die Objekte dieses Volumenmodells werden mit Verfahren aus dem Bereich der künstlichen Intelligenz analysiert und in Bauteilklassen systematisch kategorisiert. Die Kenntnis der Bauteilsemantik erlaubt es somit, aus den Daten ein Bauwerks-Produktmodell abzuleiten und dieses einzelnen Fachplanern – etwa zur Erstellung eines Energiepasses – zugänglich zu machen. Der Aufsatz zeigt den erfolgreichen Einsatz virtueller neuronaler Netze im Bereich der Bestandserfassung anhand eines komplexen Beispiels.

Unconstrained models are very often found in the broad spectrum of different theories of traffic demand models. In these models there are none or only one-sided restrictions influencing the choice of the individual. However in the traffic demand different deciding dependencies of the traffic volume with regard to the specific conditions of the territory structure potentials exist. Kichhoff and Lohse introduced bi- and tri-linearly constrained models to show these dependencies. In principle, the dependencies are described as hard, elastic and open boundary sum criteria. In this article a model is formulated which gets away from these predefined boundary sum criteria and allows a free determination of minimal and maximal boundary sum criteria. The iterative solution algorithm is shown according to a FURNESS procedure at the same time. With the approach of freely selectable minimal and maximal boundary sum criteria the modeling transport planner gets the possibility to show the traffic event even better. Furthermore all common boundary sum criteria can be calculated with this model. Therewith the often necessary and sensible standard and special cases can also be modeled.

Räume und Gebäude sind heute wegen der enormen Funktionalität der technischen Gebäudeausrüstung (TGA) in Kombination mit der sonstigen Ausstattung und den diversen Anwendungsprozessen und Nutzergruppen ohne innovative Konzepte der integrierten Bedienung kaum noch beherrschbar bzw. optimal nutzbar. Dies gilt sowohl für Wohn- als auch für Zweckimmobilien. Die Gebäudeleittechnik (GLT) und die Gebäudeautomation (GA) können hier unter sinnvoller Integration der Möglichkeiten der Mikroelektronik, Multimedia-, Kommunikations- und Informationstechnik erheblich zu nutzbringenden Innovationen beitragen. Die Automobilindustrie hat in den letzten Jahren gezeigt, wie durch einen integralen Systemansatz und durch Einsatz von Elektronik, Kommunikations- und Informationstechnik eine sinnvolle technische Assistenz der Anwender machbar ist. Genannt sei hier das Konzept des Cockpits mit integrierter Funktionsbündelung und der Informationskonzentration am Armaturenbrett. Im Gegensatz zum Automobil ist der Bereich der technischen Gebäudeausstattung in Wohn- und Nutzimmobilien gekennzeichnet durch eine starke Fragmentierung in unterschiedlichste Gewerke unter Beteiligung vieler oft schlecht koordinierter Akteure. Durch das Duisburger inHaus-Innovationszentrum für Intelligente Raum- und Gebäudesysteme der Fraunhofer-Gesellschaft wurden in den letzten Jahren neuartige Konzepte der Systemintegration heterogener Technik auf der Basis von Middleware-Plattformen und Multimedia-Technologien und -Geräten entwickelt, getestet und in die Anwendung getragen. Einer der ersten Systemanwendungen dieses offenen Infrastrukturkonzepts ist die integrierte Systembedienung mit zum Teil völlig neuen Bedienkonzepten und einer starken Bedienungsvereinfachung auch komplexester Technikausrüstungen in Immobilien. Der Beitrag beschreibt nach einer Analyse der Ausgangslage die technologischen Grundzüge der integrierten Systembedienung. Es folgen einige Anwendungsbeispiele und eine zusammenfassende Bewertung mit einem Ausblick auf weiterführende Aktivitäten.

In distributed project organisations and collaboration there is a need for integrating unstructured self-contained text information with structured project data. We consider this a process of text integration in which various text technologies can be used to externalise text content and consolidate it into structured information or flexibly interlink it with corresponding information bases. However, the effectiveness of text technologies and the potentials of text integration greatly vary with the type of documents, the project setup and the available background knowledge. The goal of our research is to establish text technologies within collaboration environments to allow for (a) flexibly combining appropriate text and data management technologies, (b) utilising available context information and (c) the sharing of text information in accordance to the most critical integration tasks. A particular focus is on Semantic Service Environments that leverage on Web service and Semantic Web technologies and adequately support the required systems integration and parallel processing of semi-structured and structured information. The paper presents an architecture for text integration that extends Semantic Service Environments with two types of integration services. Backbone to the Information Resource Sharing and Integration Service is a shared environment ontology that consolidates information on the project context and the available model, text and general linguistic resources. It also allows for the configuration of Semantic Text Analysis and Annotation Services to analyse the text documents as well as for capturing the discovered text information and sharing it through semantic notification and retrieval engines. A particular focus of the paper is the definition of the overall integration process configuring a complementary set of analyses and information sharing components.

The use of virtual reality techniques in the development of educational applications brings new perspectives to the teaching of subjects related to the field of civil construction in Civil Engineering domain. In order to obtain models, which would be able to visually simulate the construction process of two types of construction work, the research turned to the techniques of geometric modelling and virtual reality. The applications developed for this purpose are concerned with the construction of a cavity wall and a bridge. These models make it possible to view the physical evolution of the work, to follow the planned construction sequence and to visualize details of the form of every component of the works. They also support the study of the type and method of operation of the equipment necessary for these construction procedures. These models have been used to distinct advantage as educational aids in first-degree courses in Civil Engineering. Normally, three-dimensional geometric models, which are used to present architectural and engineering works, show only their final form, not allowing the observation of their physical evolution. The visual simulation of the construction process needs to be able to produce changes to the geometry of the project dynamically. In the present study, two engineering construction work models were created, from which it was possible to obtain three-dimensional models corresponding to different states of their form, simulating distinct stages in their construction. Virtual reality technology was applied to the 3D models. Virtual reality capacities allow the interactive real-time viewing of 3D building models and facilitate the process of visualizing, evaluating and communicating.

Die effektive Kooperation aller beteiligten Fachplaner im Bauplanungsprozess ist die Voraussetzung für wirtschaftliches und qualitativ hochwertiges Bauen. Bauprojektorganisationen bestehen in der Regel aus zahlreichen unabhängigen Planungspartnern, die örtlich verteilt spezifische Planungsaufgaben bearbeiten und die Ergebnisse in Teilproduktmodellen ablegen. Da Planungsprozesse im Bauwesen stark arbeitsteilig ablaufen, sind die Teilproduktmodelle der einzelnen Fachplanungen in hohem Maße voneinander abhängig. Ziel des hier vorgestellten Ansatzes ist die Integration der Teilproduktmodelle der Gebäudeplanung in einem netzwerkbasierten Modellverbund am Beispiel der Brandschutzplanung. Im Beitrag werden die Probleme der Verteiltheit und insbesondere der semantischen Heterogenität der involvierten Teilproduktmodelle betrachtet. Der verteilte Zugriff wird mithilfe mobiler Software-Agenten realisiert. Die Agenten können sich dabei frei im netzwerkbasierten Planungsverbund bewegen und agieren als Vertreter der Fachplaner. Das Problem der semantischen Heterogenität der Teilproduktmodelle wird auf der Basis von Ontologien gelöst. Dazu werden erstens Domänenontologien entwickelt, die Objekte der realen Welt einer abgeschlossenen Domäne, hier des Brandschutzes, abbilden. Zweitens werden Applikationsontologien entwickelt, die die einzelnen proprietären Datenhaltungen (im Sinne von Teilproduktmodellen) der jeweiligen Fachplanungen repräsentieren. Beide Ontologien werden mit einem regelbasierten Ansatz verknüpft. Im vorgestellten Anwendungsfall Brandschutz dient die Domänenontologie als einheitliche Schnittstelle für den Zugriff auf die verteilten Modelle und abstrahiert dabei von deren Datenbankspezifika und proprietären Schemata. Mithilfe von mobilen Agenten und semantischen Technologien kann so eine Plattform zur Verfügung gestellt werden, die erstens die dynamische Integration von Ressourcen in den Planungsverbund erlaubt und zweitens auf deren Basis unabhängig von der Verteiltheit und Heterogenität der eingebundenen Ressourcen ingenieurgerechte Verarbeitungsmethoden realisiert werden können.

Durch die Betrachtung des Produktions-Prozesses als zentrales Transformationselement wird die Struktur der Bauproduktion realitätsnah gefasst. Die Integration der prozessorientierten Kostendefinition setzt relevante Kostenparameter und Produktionsfaktoren so in Beziehung, dass sie im Einklang mit der realen Kostenstruktur und Kostendynamik einer Baustelle stehen. Die Beziehung zwischen Bauzeit und Kosten wird direkt erfasst und ausgewertet. Der hohen Dynamik der Bauproduktion zwischen kapazitätsbeschränkten Einsatzmitteln und Produktionsprozessen wurde durch das Poolmodell und der Simulation als Berechnungsmethode Rechnung getragen. Eine einfache Modellierung von sich zyklusartig wiederholenden Arbeitsvorgängen (Taktplanung) ist möglich. Die Taktbildung vollzieht sich bei der Simulation durch Kapazitätsbeschränkungen ohne Zutun des Benutzers. Durch eine Optimierungsmethode kann automatisiert nach der kostengünstigsten oder zeitlich schnellsten Produktionsvariante gesucht werden

MODELLING THE PLASTIC HINGE IN THE STATICALLY INDETERMINABLE REINFORCED CONCRETE BAR ELEMENTS
(2006)

The paper presents the example numerical model to calculate the reinforced concrete bar structures. Usually applied methods of structure dimensioning do not include the case of plastic hinges occurrence under the limit load of construction. The model represented by A. Borcz is based on the differential equation of deflection line of the beam and it includes the effects of rearrangement of the internal forces and reological effects. The experimental parameters obtained in earlier investigations describe effects resulting from the rise of plastic hinges in the proposed equation.

This research focuses on the Case-based Reasoning paradigm in architectural design (CBD) and education. Initial point for further exploring this only seemingly comprehensive investigated field of research constitutes the finding that promising looking concepts exist but that they do not play a role in daily routine of designing architects or in university education. In search of reasons for this limited success a critical review of the CBR approach to architectural education and design was performed. The aim was to identify gaps in the CBD research and to discover potential fields of research within CBR research in architectural education and design to improve acceptance and practical suitability. Two major shortcomings could be identified. In the first place the way retrieval mechanisms of systems under investigation relate to the needs of architectural designers and students. At second: Successful CBD systems rely on the work of third-parties in sharing their experiences with others and filling the databases with relevant cases. Therefore two questions remain unanswered: The question of which projects become part of the database and how get existing projects not only described but evaluated. This is an essential task and prerequisite to meet the requirements of the underlying theory of CBR.

The presented method for an physically non-linear analysis of stresses and deformations of composite cross-sections and members based on energy principles and their transformation to non-linear optimisation problems. From the LAGRANGE principle of minimum of total potential energy a kinematic formulation of the mechanical problem can be developed, which has the general advantage that pre-deformations excited by shrinkage, temperature, residual deformations after unloading et al., can be considered directly. Thus the non-linear analysis of composite cross-sections with layers of different mechanical properties and different preloading becomes possible and cracks in concrete, stiffness degradation and other specifics of the material behaviour can be taken into account without cardinal modification of the mathematical model. The impact of local defects on the bearing capacity of an entire element can also be analysed in this principle way. Standard computational systems for mathematical optimisation or general programs for spreadsheet analysis enable an uncomplicated implementation of the developed models and an effective non-linear analysis for composite cross-sections and elements.

A new approach to the non-linear analysis of cross-sections loaded by normal forces and bending moments is presented in the paper. The mechanical model is based on the LAGRANGE principle of minimum of total potential energy. Deformations, stresses and limit load parameters are obtained by solving a non-linear optimisation problem. The mathematical model is independent of the specifics of material. In addition to the stress strain relation and the specific strain energy W(ε) two further functions F(ε) and Φ(ε) are introduced to describe the material behaviour. Thus cracks in concrete, non-linearity of material etc. can be taken into account without basic modification of the numerical algorithm. For polygonal cross-sections the GAUSS' integral theorem is used. Numerical solutions of the non-linear optimisation problems can be found by application of standard software. Thus the analysis of reinforced concrete cross-sections or more general composite cross-sections with non-linear behaviour of material is as simple as in the case of linear elasticity. The application of the method is demonstrated for polygonal cross-sections. Pre-stresses or pre-strains can easily be included in the mathematical model.

Major problems of applying selective sensitivity to system identification are requirement of precise knowledge about the system parameters and realization of the required system of forces. This work presents a procedure which is able to deriving selectively sensitive excitation by iterative experiments. The first step is to determine the selectively sensitive displacement and selectively sensitive force patterns. These values are obtained by introducing the prior information of system parameters into an optimization which minimizes the sensitivities of the structure response with respect to the unselected parameters while keeping the sensitivities with respect to the selected parameters as a constant. In a second step the force pattern is used to derive dynamic loads on the tested structure and measurements are carried out. An automatic control ensures the required excitation forces. In a third step, measured outputs are employed to update the prior information. The strategy is to minimize the difference between a predicted displacement response, formulated as function of the unknown parameters and the measured displacements, and the selectively sensitive displacement calculated in the first step. With the updated values of the parameters a re-analysis of selective sensitivity is performed and the experiment is repeated until the displacement response of the model and the actual structure are conformed. As an illustration a simply supported beam made of steel, vibrated by harmonic excitation is investigated, thereby demonstrating that the adaptive excitation can be obtained efficiently.

The paper presents a linear static analysis on continuous orthotropic thin-walled shell structures simply supported at the transverse ends with a random deformable contour of the cross section. The external loads can be random as well. The class of this structures involves most of the bridges, scaffold bridges, some roof structures etc. A numerical example of steel continuous structures on five spans with an open contour of the cross-section has been solved. The examination of the structure has used the following two computation models: a prismatic structure consisting of isotropic strips, a plates and ribs, with considering their real interaction, and a smooth orthotropic plate equivalent to the structure in the first model. The displacements and forces of the structure characterizing its stressed and deformed condition have been determined. The results obtained from the two solutions have been analyzed. The study on the structure is made with the force method in combination with the analytical finite strip method (AFSM) in displacements. The basic system is obtained by separating the superstructure from the understructure at the places of intermediate supports and consists of two parts. The first part is a single span thin-walled prismatic shell structure; the second part presents supports (columns, space frames etc.). The connection between the superstructure and intermediate supports is made under random supporting conditions. The forces at the supporting points in the direction of the connections removed are assumed to be the basic unknowns of the force method. The solution of the superstructure has been accomplished by the AFSM in displacements. The structure is divided in only one (transverse) direction into a finite number of plain strips connected to each other in longitudinal linear nodes. The three displacements of the points on the node lines and the rotation around those lines have been assumed to be the basic unknown in each node. The boundary conditions of each strip of the basic system correspond to the simply support along the transverse ends and the restraint along the longitudinal ones. The particular strip of the basic system has been solved by the method of the single trigonometric series. The method is reduced to solving a discrete structure in displacements and restoring its continuity at the places of the sections made in respect to both the displacements and forces. The two parts of the basic system have been solved in sequence under the action of single values of each of the basic unknowns and with the external load. The solution of the support part is accomplished using software for analyzing structures by the FEM. The basic unknown forces have been determined from system of canonic equations, the conditions of the deformations continuity on the places of the removed connections under superstructure and intermediate supports. The final displacements and forces at a random point of a continuous superstructure have been determined using the principle of superposition. The computations have been carried by software developed with Visual Fortran version 5.0 for PC.

The paper is dedicated to decidability exploration of market segmentation problem with the help of linear convolution algorithms. Mathematical formulation of this problem represents interval task of bipartite graph cover by stars. Vertices of the first partition correspond to types of commodities, vertices of the second – to customers groups. Appropriate method is offered for interval problem reduction to two-criterion task that has one implemented linear convolution algorithm. Unsolvability with the help of linear convolution algorithm of multicriterion, and consequently interval, market segmentation problem is proved.

Water resources development and management is a complex problem. It includes the design and operation of single system components, often as part of larger interrelated systems and usually on the basis of river basins. While several decades ago the dominant objective was the maximization of economic benefit, other objectives have evolved as part of the sustainable development envisaged. Today, planning and operation of larger water resources systems is practically impossible without adequate computer tools, normally being one or several models, increasingly combined with data bank management systems and multi criteria assessment procedures in decision support systems. The use of models in civil engineering already has a long history when structural engineering is considered. These design support models, however, must rather be seen as expert systems made to support the engineer with his daily work. They often have no direct link to stakeholders and the decision makers community. The scale of investigation is often much larger in water resources engineering than in structural engineering which is related to different stakeholders and decision making procedures. Still, several similarities are obvious which can be summarized as the search for a compromise solution on a complex, i.e. multiobjective and interdisciplinary decision problem. While in structural engineering e.g. aestetics, stability and energy consumption might be important evaluation criteria in addition to construction and maintenance cost other or additional criteria have to be considered in water resources planning such as political, environmental and social criteria. In this respect civil engineers tend to overemphasize technical criteria. For the future the existing expert systems should be embedded into an improved decision support shell, keeping in mind that decision makers are hardly interested in numerical modelling results. The paper will introduce into the problem and demonstrate the state of the art by means of an example.

The paper is a proposal of calculation of internal forces and dislocations in the reinforced concrete beams before and after cracking. For the ideally elastic bars transfer matrix proposed by Rakowski was applied. The effects associated with cracking were introduced by means of the Borcz's theory in the spectrally way. Numerical example was shown. The presented attitude also enables to calculate dynamic problems and those connected with the stability of the compressed and bending cracked beams and columns.

This paper deals with the development of a new multi-objective evolution strategy in combination with an integrated pollution-load and water-quality model. The optimization algorithm combines the advantages of the Non-Dominated Sorting Genetic Algorithm and Self-Adaptive Evolution Strategies. The identification of a good spread of solutions on the pareto-optimum front and the optimization of a large number of decision variables equally demands numerous simulation runs. In addition, statements with regard to the frequency of critical concentrations and peak discharges require continuous long-term simulations. Therefore, a fast operating integrated simulation model is needed providing the required precision of the results. For this purpose, a hydrological deterministic pollution-load model has been coupled with a river water-quality and a rainfall-runoff model. Wastewater treatment plants are simulated in a simplified way. The functionality of the optimization and simulation tool has been validated by analyzing a real catchment area including sewer system, WWTP, water body and natural river basin. For the optimization/rehabilitation of the urban drainage system, both innovative and approved measures have been examined and used as decision variables. As objective functions, investment costs and river water quality criteria have been used.

The Element-free Galerkin Method has become a very popular tool for the simulation of mechanical problems with moving boundaries. The internally applied Moving Least Squares approximation uses in general Gaussian or cubic weighting functions and has compact support. Due to the approximative character of this method the obtained shape functions do not fulfill the interpolation condition, which causes additional numerical effort for the imposition of the essential boundary conditions. The application of a singular weighting function, which leads to singular coefficient matrices at the nodes, can solve this problem, but requires a very careful placement of the integration points. Special procedures for the handling of such singular matrices were proposed in literature, which require additional numerical effort. In this paper a non-singular weighting function is presented, which leads to an exact fulfillment of the interpolation condition. This weighting function leads to regular values of the weights and the coefficient matrices in the whole interpolation domain even at the nodes. Furthermore this function gives much more stable results for varying size of the influence radius and for strongly distorted nodal arrangements than classical weighting function types. Nevertheless, for practical applications the results are similar as these obtained with the regularized weighting type presented by the authors in previous publications. Finally a new concept will be presented, which enables an efficient analysis of systems with strongly varying node density. In this concept the nodal influence domains are adapted depending on the nodal configuration by interpolating the influence radius for each direction from the distances to the natural neighbor nodes. This approach requires a Voronoi diagram of the domain, which is available in this study since Delaunay triangles are used as integration background cells. In the numerical examples it will be shown, that this method leads to a more uniform and reduced number of influencing nodes for systems with varying node density than the classical circular influence domains, which means that the small additional numerical effort for interpolating the influence radius leads to remarkable reduction of the total numerical cost in a linear analysis while obtaining similar results. For nonlinear calculations this advantage would be even more significant.

The modeling of crack propagation in plain and reinforced concrete structures is still a field for many researchers. If a macroscopic description of the cohesive cracking process of concrete is applied, generally the Fictitious Crack Model is utilized, where a force transmission over micro cracks is assumed. In the most applications of this concept the cohesive model represents the relation between the normal crack opening and the normal stress, which is mostly defined as an exponential softening function, independently from the shear stresses in tangential direction. The cohesive forces are then calculated only from the normal stresses. By Carol et al. 1997 an improved model was developed using a coupled relation between the normal and shear damage based on an elasto-plastic constitutive formulation. This model is based on a hyperbolic yield surface depending on the normal and the shear stresses and on the tensile and shear strength. This model also represents the effect of shear traction induced crack opening. Due to the elasto-plastic formulation, where the inelastic crack opening is represented by plastic strains, this model is limited for applications with monotonic loading. In order to enable the application for cases with un- and reloading the existing model is extended in this study using a combined plastic-damage formulation, which enables the modeling of crack opening and crack closure. Furthermore the corresponding algorithmic implementation using a return mapping approach is presented and the model is verified by means of several numerical examples. Finally an investigation concerning the identification of the model parameters by means of neural networks is presented. In this analysis an inverse approximation of the model parameters is performed by using a given set of points of the load displacement curves as input values and the model parameters as output terms. It will be shown, that the elasto-plastic model parameters could be identified well with this approach, but require a huge number of simulations.

In engineering science the modeling and numerical analysis of complex systems and relations plays an important role. In order to realize such an investigation, for example a stochastic analysis, in a reasonable computational time, approximation procedure have been developed. A very famous approach is the response surface method, where the relation between input and output quantities is represented for example by global polynomials or local interpolation schemes as Moving Least Squares (MLS). In recent years artificial neural networks (ANN) have been applied as well for such purposes. Recently an adaptive response surface approach for reliability analyses was proposed, which is very efficient concerning the number of expensive limit state function evaluations. Due to the applied simplex interpolation the procedure is limited to small dimensions. In this paper this approach is extended for larger dimensions using combined ANN and MLS response surfaces for evaluating the adaptation criterion with only one set of joined limit state points. As adaptation criterion a combination by using the maximum difference in the conditional probabilities of failure and the maximum difference in the approximated radii is applied. Compared to response surfaces on directional samples or to plain directional sampling the failure probability can be estimated with a much smaller number of limit state points.

Requires for reliability and durability of structures and their elements with simultaneous material economy have stimulated improvement of constitutive equations for description of elasto-plastic deformation processes. This has led to the development of phenomenological modelling of complex phenomena of irreversible deformation including history-dependent and rate-dependent effects. During the last several decades many works have been devoted to the development of elasto-plastic models, in order to better predict the material behavior under combined variable thermo-mechanical loading. The increase of accuracy of stress analysis and safety factors for complex structures with the help of modern finite-element packages (ABAQUS, ANSYS, COSMOS, LS-DYNA, MSC.MARC, MSC.NASTRAN, PERMAS and other) can be provided only by use of complex and special variants of plasticity theories, which are adequate for the considered loading conditions and based on authentic information about properties of materials. The areas of application of the various theories (models) are as a rule unknown to the users of finite-element packages at the existing variety loading condition sin machine-building designs. At the moment a universal theory of inelasticity is absent and even the most accomplished theories can not guarantee adequate description of deformation processes for arbitrary structure under wide range of loading programs. The classifier of materials, loading conditions, effects (phenomena) and list of basic experiments are developed by the authors. Use of these classifiers for an establishment of hierarchy of models is a first step for introduction of the multimodel analysis into computational practice. The set of the classic and modern inelasticity theories is considered, so that they are applicable for stress analysis of structures under complex loading programs. Among them there are plastic flow theories with linear and nonlinear isotropic and kinematic hardening, multisurface theories, endochronic theory, holonomic theory, rheologic models, theory of elasto-plastic processes, slip theory, physical theories (single crystal and polycrystalline models) and others. The classification of materials provides rearranging by a degree of homogeneous, chemical composition, level of strength and plasticity, behavior under cyclic loading, anisotropy of properties at initial condition, anisotropy of properties during deformation process, structural stability. The classification of loading conditions takes into consideration proportional and non-proportional loading, temperature range, combination of cyclic and monotonous loading, one-axial, two-axial and complex stress state, curvature of strain path, presence of stress concentrators and level of strain gradient. A unified general form of constitutive equations is presented for all used material models based upon the concept of internal state variables. The wide range of mentioned above inelastic material models has been implemented into finite element program PANTOCRATOR developed by authors (see for details www.pantocrator.narod.ru). Application possibility of different material models is considered both for material element and for complex structures subjected to complex non-proportional loading.

A new application of software technology is the application area of smart living or sustainable living. Within this area application platforms are designed and realized with the goal to support value added services. In this context value added services integrates microelectronics, home automation and services to enhance the attractiveness of flats, homes and buildings. Especially real estate companies or service providers dealing with home services are interested in an effective design and management of their services. Service Engineering is the approved approach for designing customer oriented service processes. Service engineering consists of several phases; from situation analysis to service creation and service design to service management. This article will describe how the method service blueprint can be used to design service processes. Smart living includes all actions to enlarge a flat to a smart home for living. One special requirement of this application domain is the use of local components (actuators, sensors) within service processes. This article will show how this extended method supports service providers to improve the quality of customer oriented service processes and the derivation of needed interfaces of involved actors. For the civil engineering process it will be possible to derive needed information from a built in home automation system. The aim is to show, how to get needed smart local components to fullfill later offered it-supported value added services. Value added services focused on inhabitants are grouped to consulting and information, care and supervision, leisure time activities, repairs, mobility and delivery, safety and security, supply and disposal.

In many applications such as parameter identification of oscillating systems in civil enginee-ring, speech processing, image processing and others we are interested in the frequency con-tent of a signal locally in time. As a start wavelet analysis provides a time-scale decomposition of signals, but this wavelet transform can be connected with an appropriate time-frequency decomposition. For instance in Matlab are defined pseudo-frequencies of wavelet scales as frequency centers of the corresponding bands. This frequency bands overlap more or less which depends on the choice of the biorthogonal wavelet system. Such a definition of frequency center is possible and useful, because different frequencies predominate at different dyadic scales of a wavelet decomposition or rather at different nodes of a wavelet packet decomposition tree. The goal of this work is to offer better algorithms for characterising frequency band behaviour and for calculating frequency centers of orthogonal and biorthogonal wavelet systems. This will be done with some product formulas in frequency domain. Now the connecting procedu-res are more analytical based, better connected with wavelet theory and more assessable. This procedures doesn’t need any time approximation of the wavelet and scaling functions. The method only works in the case of biorthogonal wavelet systems, where scaling functions and wavelets are defined over discrete filters. But this is the practically essential case, because it is connected with fast algorithms (FWT, Mallat Algorithm). At the end corresponding to the wavelet transform some closed formulas of pure oscillations are given. They can generally used to compare the application of different wavelets in the FWT regarding it’s frequency behaviour.