Refine
Document Type
- Conference Proceeding (145)
- Report (9)
- Article (1)
Institute
- In Zusammenarbeit mit der Bauhaus-Universität Weimar (82)
- Graduiertenkolleg 1462 (31)
- Professur Angewandte Mathematik (13)
- Institut für Strukturmechanik (ISM) (12)
- Professur Computergestütztes kooperatives Arbeiten (9)
- Institut für Konstruktiven Ingenieurbau (IKI) (4)
- Professur Informatik im Bauwesen (4)
- Professur Stochastik und Optimierung (3)
- Professur Computer Vision in Engineering (2)
- Professur Stahlbau (2)
Keywords
- Angewandte Informatik (155) (remove)
Non-destructive techniques for damage detection became the focus of engineering interests in the last few years. However, applying these techniques to large complex structures like civil engineering buildings still has some limitations since these types of structures are
unique and the methodologies often need a large number of specimens for reliable results. For this reason, cost and time can greatly influence the final results.
Model Assisted Probability Of Detection (MAPOD) has taken its place among the ranks of damage identification techniques, especially with advances in computer capacity and modeling tools. Nevertheless, the essential condition for a successful MAPOD is having a reliable model in advance. This condition is opening the door for model assessment and model quality problems. In this work, an approach is proposed that uses Partial Models (PM) to compute the Probability Of damage Detection (POD). A simply supported beam, that can be structurally modified and
tested under laboratory conditions, is taken as an example. The study includes both experimental and numerical investigations, the application of vibration-based damage detection approaches and a comparison of the results obtained based on tests and simulations.
Eventually, a proposal for a methodology to assess the reliability and the robustness of the models is given.
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.
In the past, several types of Fourier transforms in Clifford analysis have been studied. In this paper, first an overview of these different transforms is given. Next, a new equation in a Clifford algebra is proposed, the solutions of which will act as kernels of a new class of generalized Fourier transforms. Two solutions of this equation are studied in more detail, namely a vector-valued solution and a bivector-valued solution, as well as the associated integral transforms.
The present research analyses the error on prediction obtained under different data availability scenarios to determine which measurements contribute to an improvement of model prognosis and which not. A fully coupled 2D hydromechanical model of a water retaining dam is taken as an example. Here, the mean effective stress in the porous skeleton is reduced due to an increase in pore water pressure under drawdown conditions. Relevant model parameters are ranked by scaled sensitivities, Particle Swarm Optimization is applied to determine the optimal parameter values and model validation is performed to determine the magnitude of error forecast. We compare the predictions of the optimized models with results from a forward run of the reference model to obtain actual prediction errors.
The analyses presented here were performed to 31 data sets of 100 observations of varying data types. Calibrating with multiple information types instead of only one sort, brings better calibration results and improvement in model prognosis. However, when using several types of information the number of observations have to be increased to be able to cover a representative part of the model domain; otherwise a compromise between data availability and domain
coverage prove best. Which type of information for calibration contributes to the best prognoses, could not be determined in advance. For the error in model prognosis does not depends on the error in calibration, but on the parameter error, which unfortunately can not be determined in reality since we do not know its real value. Excellent calibration fits with parameters’ values near the limits of reasonable physical values, provided the highest prognosis errors. While models which included excess pore pressure values for calibration provided the best prognosis, independent of the calibration fit.
In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus.
MICROPLANE MODEL WITH INITIAL AND DAMAGE-INDUCED ANISOTROPY APPLIED TO TEXTILE-REINFORCED CONCRETE
(2010)
The presented material model reproduces the anisotropic characteristics of textile reinforced concrete in a smeared manner. This includes both the initial anisotropy introduced by the textile reinforcement, as well as the anisotropic damage evolution reflecting fine patterns of crack bridges. The model is based on the microplane approach. The direction-dependent representation of the material structure into oriented microplanes provides a flexible way to introduce the initial anisotropy. The microplanes oriented in a yarn direction are associated with modified damage laws that reflect the tension-stiffening effect due to the multiple cracking of the matrix along the yarn.
Electromagnetic wave propagation is currently present in the vast majority of situations which occur in veryday life, whether in mobile communications, DTV, satellite tracking, broadcasting, etc. Because of this the study of increasingly complex means of propagation of lectromagnetic waves has become necessary in order to optimize resources and increase the capabilities of the devices as required by the growing demand for such services.
Within the electromagnetic wave propagation different parameters are considered that characterize it under various circumstances and of particular importance are the reflectance and transmittance. There are several methods or the analysis of the reflectance and transmittance such as the method of approximation by boundary condition, the plane wave expansion method (PWE), etc., but this work focuses on the WKB and SPPS methods.
The implementation of the WKB method is relatively simple but is found to be relatively efficient only when working at high frequencies. The SPPS method (Spectral Parameter Powers Series) based on the theory of pseudoanalytic functions, is used to solve this problem through a new representation for solutions of Sturm Liouville equations and has recently proven to be a powerful tool to solve different boundary value and eigenvalue problems. Moreover, it has a very suitable structure for numerical implementation, which in this case took place in the Matlab software for the valuation of both conventional and turning points profiles.
The comparison between the two methods allows us to obtain valuable information about their perfor mance which is useful for determining the validity and propriety of their application for solving problems where these parameters are calculated in real life applications.
The application of a recent method using formal power series is proposed. It is based on a new representation for solutions of Sturm-Liouville equations. This method is used to calculate the transmittance and reflectance coefficients of finite inhomogeneous layers with high accuracy and efficiency. Tailoring the refraction index profile defining the inhomogeneous media it is possible to develop very important applications such as optical filters. A number of profiles were evaluated and then some of them selected in order to perform an improvement of their characteristics via the modification of their profiles.
A UNIFIED APPROACH FOR THE TREATMENT OF SOME HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS ON SPHERES
(2010)
Using Clifford analysis methods, we provide a unified approach to obtain explicit solutions of some partial differential equations combining the n-dimensional Dirac and Euler operators, including generalizations of the classical time-harmonic Maxwell equations. The obtained regular solutions show strong connections between hypergeometric functions and homogeneous polynomials in the kernel of the Dirac operator.
In the context of finite element model updating using vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the order of natural frequencies and mode shapes is important. As only limited spatial information is available and noise is present in the measurements, the automatic selection of the most likely numerical mode shape corresponding to a measured mode shape is a difficult task. The most common criterion to indicate corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases. In this paper, the pure mathematical modal assurance criterion will be enhanced by additional physical information of the numerical model in terms of modal strain energies. A numerical example and a benchmark study with real measured data are presented to show the advantages of the enhanced energy based criterion in comparison to the traditional modal assurance criterion.