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Many structures in different engineering applications suffer from cracking. In order to make reliable prognosis about the serviceability of those structures it is of utmost importance to identify cracks as precisely as possible by non-destructive testing. A novel approach (XIGA), which combines the Isogeometric Analysis (IGA) and the Extended Finite Element Method (XFEM) is used for the forward problem, namely the analysis of a cracked material, see [1]. Applying the NURBS (Non-Uniform Rational B-Spline) based approach from IGA together with the XFEM allows to describe effectively arbitrarily shaped cracks and avoids the necessity of remeshing during the crack identification problem. We want to exploit these advantages for the inverse problem of detecting existing cracks by non-destructive testing, see e.g. [2]. The quality of the reconstructed cracks however depends on two major issues, namely the quality of the measured data (measurement error) and the discretization of the crack model. The first one will be taken into account by applying regularizing methods with a posteriori stopping criteria. The second one is critical in the sense that too few degrees of freedom, i.e. the number of control points of the NURBS, do not allow for a precise description of the crack. An increased number of control points, however, increases the number of unknowns in the inverse analysis and intensifies the ill-posedness. The trade-off between accuracy and stability is aimed to be found by applying an inverse multilevel algorithm [3, 4] where the identification is started with short knot vectors which successively will be enlarged during the identification process.
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.
We consider a structural truss problem where all of the physical model parameters are uncertain: not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening (pruning) technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements.
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.
Adopting the European laws concerning environmental protection will require sustained efforts of the authorities and communities from Romania; implementing modern solutions will become a fast and effective option for the improvement of the functioning systems, in order to prevent disasters. As a part of the urban infrastructure, the drainage networks of pluvial and residual waters are included in the plan of promoting the systems which protect the environmental quality, with the purpose of integrated and adaptive management. The paper presents a distributed control system for sewer network of Iasi town. Unsatisfactory technical state of the actual sewer system is exposed, focusing on objectives related to implementation of the control system. The proposed distributed control system of Iasi drainage network is based on the implementation of the hierarchic control theory for diagnose, sewer planning and management. There are proposed two control levels: coordinating and local execution. Configuration of the distributed control system, including data acquisition and conversion equipment, interface characteristics, local data bus, data communication network, station configuration are widely described. The project wish to be an useful instrument for the local authorities in the preventing and reducing the impact of future natural disasters over the urban areas by means of modern technologies.
Interval analysis extends the concept of computing with real numbers to computing with real intervals. As a consequence, some interesting properties appear, such as the delivery of guaranteed results or confirmed global values. The former property is given in the sense that unknown numerical values are in known to lie in a computed interval. The latter property states that the global minimum value, for example, of a given function is also known to be contained in a interval (or a finite set of intervals). Depending upon the amount computation effort invested in the calculation, we can often find tight bounds on these enclosing intervals. The downside of interval analysis, however, is the mathematically correct, but often very pessimistic size of the interval result. This is in particularly due to the so-called dependency effect, where a single variable is used multiple times in one calculation. Applying interval analysis to structural analysis problems, the dependency has a great influence on the quality of numerical results. In this paper, a brief background of interval analysis is presented and shown how it can be applied to the solution of structural analysis problems. A discussion of possible improvements as well as an outlook to parallel computing is also given.
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.
This paper presents a methodology for uncertainty quantification in cyclic creep analysis. Several models- , namely BP model, Whaley and Neville model, modified MC90 for cyclic loading and modified Hyperbolic function for cyclic loading are used for uncertainty quantification. Three types of uncertainty are included in Uncertainty Quantification (UQ): (i) natural variability in loading and materials properties; (ii) data uncertainty due to measurement errors; and (iii) modelling uncertainty and errors during cyclic creep analysis. Due to the consideration of all type of uncertainties, a measure for the total variation of the model response is achieved. The study finds that the BP, modified Hyperbolic and modified MC90 are best performing models for cyclic creep prediction in that order. Further, global Sensitivity Analysis (SA) considering the uncorrelated and correlated parameters is used to quantify the contribution of each source of uncertainty to the overall prediction uncertainty and to identifying the important parameters. The error in determining the input quantities and model itself can produce significant changes in creep prediction values. The variability influence of input random quantities on the cyclic creep was studied by means of the stochastic uncertainty and sensitivity analysis namely the Gartner et al. method and Saltelli et al. method. All input imperfections were considered to be random quantities. The Latin Hypercube Sampling (LHS) numerical simulation method (Monte Carlo type method) was used. It has been found by the stochastic sensitivity analysis that the cyclic creep deformation variability is most sensitive to the Elastic modulus of concrete, compressive strength, mean stress, cyclic stress amplitude, number of cycle, in that order.
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.
In order to make control decisions, Smart Buildings need to collect data from multiple sources and bring it to a central location, such as the Building Management System (BMS). This needs to be done in a timely and automated fashion. Besides data being gathered from different energy using elements, information of occupant behaviour is also important for a building’s requirement analysis. In this paper, the parameter of Occupant Density was considered to help find behaviour of occupants towards a building space. Through this parameter, support for building energy consumption and requirements based on occupant need and demands was provided. The demonstrator presented provides information on the number of people present in a particular building space at any time, giving the space density. Such collections of density data made over a certain period of time represents occupant behaviour towards the building space, giving its usage patterns. Similarly, inventory items were tracked and monitored for moving out or being brought into a particular read zone. For both, people and inventory items, this was achieved using small, low-cost, passive Ultra-High Frequency (UHF) Radio Frequency Identification (RFID) tags. Occupants were given the tags in a form factor of a credit card to be possessed at all times. A central database was built where occupant and inventory information for a particular building space was maintained for monitoring and providing a central data access.
A topology optimization method has been developed for structures subjected to multiple load cases (Example of a bridge pier subjected to wind loads, traffic, superstructure...). We formulate the problem as a multi-criterial optimization problem, where the compliance is computed for each load case. Then, the Epsilon constraint method (method proposed by Chankong and Haimes, 1971) is adapted. The strategy of this method is based on the concept of minimizing the maximum compliance resulting from the critical load case while the other remaining compliances are considered in the constraints. In each iteration, the compliances of all load cases are computed and only the maximum one is minimized. The topology optimization process is switching from one load to another according to the variation of the resulting compliance. In this work we will motivate and explain the proposed methodology and provide some numerical examples.
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.
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.
The stress state of a piecewise-homogeneous elastic body, which has a semi-infinite crack along the interface, under in-plane and antiplane loads is considered. One of the crack edges is reinforced by a rigid patch plate on a finite interval adjacent to the crack tip. The crack edges are loaded with specified stresses. The body is stretched at infinity by specified stresses. External forces with a given principal vector and moment act on the patch plate. The problem reduces to a Riemann-Hilbert boundary-value matrix problem with a piecewise-constant coefficient for two complex potentials in the plane case and for one in the antiplane case. The complex potentials are found explicitly using a Gaussian hypergeometric function. The stress state of the body close to the ends of the patch plate, one of which is also simultaneously the crack tip, is investigated. Stress intensity factors near the singular points are determined.
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.
We briefly review and use the recent comprehensive research on the manifolds of square roots of −1 in real Clifford geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the complex imaginary unit j is replaced by a square root of −1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known and applied CFTs, which replaced the complex imaginary unit j only by blades (usually pseudoscalars) squaring to −1. A major advantage of real Clifford algebra CFTs is their completely real geometric interpretation. We study (left and right) linearity of the CFT for constant multivector coefficients in Cl(p,q), translation (x-shift) and modulation (w -shift) properties, and signal dilations. We show an inversion theorem. We establish the CFT of vector differentials, partial derivatives, vector derivatives and spatial moments of the signal. We also derive Plancherel and Parseval identities as well as a general convolution theorem.
Due to the amount of flow simulation and measurement data, automatic detection, classification and visualization of features is necessary for an inspection. Therefore, many automated feature detection methods have been developed in recent years. However, only one feature class is visualized afterwards in most cases, and many algorithms have problems in the presence of noise or superposition effects. In contrast, image processing and computer vision have robust methods for feature extraction and computation of derivatives of scalar fields. Furthermore, interpolation and other filter can be analyzed in detail. An application of these methods to vector fields would provide a solid theoretical basis for feature extraction. The authors suggest Clifford algebra as a mathematical framework for this task. Clifford algebra provides a unified notation for scalars and vectors as well as a multiplication of all basis elements. The Clifford product of two vectors provides the complete geometric information of the relative positions of these vectors. Integration of this product results in Clifford correlation and convolution which can be used for template matching of vector fields. For frequency analysis of vector fields and the behavior of vector-valued filters, a Clifford Fourier transform has been derived for 2D and 3D. Convolution and other theorems have been proved, and fast algorithms for the computation of the Clifford Fourier transform exist. Therefore the computation of Clifford convolution can be accelerated by computing it in Clifford Fourier domain. Clifford convolution and Fourier transform can be used for a thorough analysis and subsequent visualization of flow fields.
This paper presents a robust model updating strategy for system identification of wind turbines. To control the updating parameters and to avoid ill-conditioning, the global sensitivity analysis using the elementary effects method is conducted. The formulation of the objective function is based on M¨uller-Slany’s strategy for multi-criteria functions. As a simulationbased optimization, a simulation adapter is developed to interface the simulation software ANSYS and the locally developed optimization software MOPACK. Model updating is firstly tested on the beam model of the rotor blade. The defect between the numerical model and the reference has been markedly reduced by the process of model updating. The effect of model updating becomes more pronounced in the comparison of the measured and the numerical properties of the wind turbine model. The deviations of the frequencies of the updated model are rather small. The complete comparison including the free vibration modes by the modal assurance criteria shows the excellent coincidence of the modal parameters of the updated model with the ones from the measurements. By successful implementation of the model validation via model updating, the applicability and effectiveness of the solution concept has been demonstrated.