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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.
For assessment of old buildings, thermal graphic analysis aided with infra-red camera have been employed in a wide range nowadays. Image processing and evaluation can be economically practicable only if the image evaluation can also be automated to the largest extend. For that reason methods of computer vision are presented in this paper to evaluate thermal images. To detect typical thermal image elements, such as thermal bridges and lintels in thermal images respectively gray value images, methods of digital image processing have been applied, of which numerical procedures are available to transform, modify and encode images. At the same time, image processing can be regarded as a multi-stage process. In order to be able to accomplish the process of image analysis from image formation through perfecting and segmentation to categorization, appropriate functions must be implemented. For this purpose, different measuring procedures and methods for automated detection and evaluation have been tested.
The Lucas-Kanade tracker has proven to be an efficient and accurate method for calculation of the optical flow. However, this algorithm can reliably track only suitable image features like corners and edges. Therefore, the optical flow can only be calculated for a few points in each image, resulting in sparse optical flow fields. Accumulation of these vectors over time is a suitable method to retrieve a dense motion vector field. However, the accumulation process limits application of the proposed method to fixed camera setups. Here, a histogram based approach is favored to allow more than a single typical flow vector per pixel. The resulting vector field can be used to detect roads and prescribed driving directions which constrain object movements. The motion structure can be modeled as a graph. The nodes represent entry and exit points for road users as well as crossings, while the edges represent typical paths.
Digital models of buildings are widely used in civil engineering. In these models, geometric information is used as leading information. Engineers are used to have geometric information, and, for instance, it is state of the art to specify a point by its three coordinates. However, the traditional approaches have disadvantages. Geometric information is over-determined. Thus, more geometric information is specified and stored than needed. In addition, engineers already deal with topological information. A denotation of objects in buildings is of topological nature. It has to be answered whether approaches where topological information becomes a leading role would be more efficient in civil engineering. This paper presents such an approach. Topological information is modelled independently of geometric information. It is used for denoting the objects of a building. Geometric information is associated to topological information so that geometric information “weights” a topology.
The concept presented in this paper has already been used in surveying existing buildings. Experiences in the use of this concept showed that the number of geometric information that is required for a complete specification of a building could be reduced by a factor up to 100. Further research will show how this concept can be used in planning processes.
Optimum technological solutions must take into account the entire life cycle of structures including design procedures as well as quality assurance, inspection, maintenance, and repair strategies. Unfortunately, current design standards do not provide a satisfactory basis to ensure expected structural lifetimes. The latter may vary from only a few years for temporary structures to over a century for bridges, water dams or nuclear repositories. Consistent scientific concepts are urgently required to cover this wide spectrum of lifetimes in structural design and maintenance. This was a motivation for a group of scientists at the Ruhr-University Bochum (RUB) to start a special research program supported by the German Research Foundation (DFG) within the Cooperative Research Center SFB 398 since 1996. Institutes of the University Wuppertal and of the University Essen-Duisburg joined the research group. The goal of the Center is to study sources of damage and deterioration in materials and structures, to develop consistent models and simulation methods, to predict structural lifetimes and finally to integrate this predictions into new lifetime-oriented design strategies.
Research activities in our center are organised in three Project Groups as follows:
- Modelling of lifetime effects
- Methods for lifetime-oriented structural analyses
- Future lifespan-oriented design strategies.
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 design of challenging space structures frequently relies on the theory of folded plates. The models are composed of plane facets of which the bending and membrane stiffness are coupled along the folds. In conventional finite element analysis of faceted structures the continuity of the displacement field is enforced exclusively at the nodes. Since approximate solutions for transverse and for in-plane displacements are not members of the same function space, separation occurs in between the common nodes of adjacent elements. It is shown that the kinematic assumptions of Bernoulli are accounted for this incompatibility along the edges in facet models. A general answer to this problem involves substantial modification of plate and membrane theory, but a straight forward formulation can be derived for simply folded plates, structures, whose folds do not intersect. A broad class of faceted structures, including models of various curved shells, belong to this category and can be calculated consistently. The additional requirements to assure continuity concern the mapping of displacement derivatives on the edges. An appropriate finite facet element provides node and edge-oriented degrees of freedom, whose transformation to system degrees of freedom, depends on the geometric configuration at each node. The concept is implemented using conform triangular elements. To evaluate the new approach, the energy norm of representative structures for refined meshes is calculated. The focus is placed on the mathematical convergence towards reliable solutions obtained from finite volume models.
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
The concrete is modeled as a material with damage and plasticity, whereat the viscoplastic and the viscoelastic behaviour depends on the rate of the total strains. Due to the damage behaviour the compliance tensor develops different properties in tension and compression. There have been tested various yield surfaces and flow rules, damage rules respectively to their usability in a concrete model. One three-dimensional yield surface was developed from a failure surface based on the Willam--Warnke five-parameter model by the author. Only one general uni-axial stress-strain-relation is used for the numeric control of the yield surface. From that curve all necessary parameters for different strengths of concrete and different strain rates can be derived by affine transformations. For the flow rule in the compression zone a non associated inelastic potential is used, in the tension zone a Rankine potential. Conditional on the time-dependent formulation, the symmetry of the system equations is maintained in spite of the usage of non-associated potentials for the derivation of the inelastic strains. In case of quasi statical computations a simple viscoplastic law is used that is rested on an approach to Perzyna. The principle of equality of dissipation power in the uni-axial and the three-axial state of stress is used. It is modified by a factor that depends on the actual stress ratio and in comparison with the Kupfer experiments it implicates strains that are more realistic. The implementation of the concrete model is conducted in a mixed hybrid finite element. Examples in the structural level are introduced for verification of the concrete model.