Refine
Institute
- In Zusammenarbeit mit der Bauhaus-Universität Weimar (82) (remove)
Keywords
- Angewandte Mathematik (82) (remove)
Bridge vibration due to traffic loading has been subject of extensive research in the last decades. Such studies are concerned with deriving solutions for the bridge-vehicle interaction (BVI) and analyzing the dynamic responses considering randomness of the coupled model’s (BVI) input parameters and randomness of road unevenness. This study goes further to examine the effects of such randomness of input parameters and processes on the variance of dynamic responses in quantitative measures. The input parameters examined in the sensitivity analysis are, stiffness and damping of vehicle’s suspension system, axle spacing, and stiffness and damping of bridge. This study also examines the effects of the initial excitation of a vehicle on the influences of the considered input parameters. Variance based sensitivity analysis is often applied to deterministic models. However, the models for the dynamic problem is a stochastic one due to the simulations of the random processes. Thus, a setting using a joint meta-model; one for the mean response and other for the dispersion of the response is developed. The joint model is developed within the framework of Generalized Linear Models (GLM). An enhancement of the GLM procedure is suggested and tested; this enhancement incorporates Moving Least Squares (MLS) approximation algorithms in the fitting of the mean component of the joint model. The sensitivity analysis is then performed on the joint-model developed for the dynamic responses caused by BVI.
SELECTION AND SCALING OF GROUND MOTION RECORDS FOR SEISMIC ANALYSIS USING AN OPTIMIZATION ALGORITHM
(2015)
The nonlinear time history analysis and seismic performance based methods require a set of scaled ground motions. The conventional procedure of ground motion selection is based on matching the motion properties, e.g. magnitude, amplitude, fault distance, and fault mechanism. The seismic target spectrum is only used in the scaling process following the random selection process. Therefore, the aim of the paper is to present a procedure to select a sets of ground motions from a built database of ground motions. The selection procedure is based on running an optimization problem using Dijkstra’s algorithm to match the selected set of ground motions to a target response spectrum. The selection and scaling procedure of optimized sets of ground motions is presented by examining the analyses of nonlinear single degree of freedom systems.
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.
VARIATIONAL POSITING AND SOLUTION OF COUPLED THERMOMECHANICAL PROBLEMS IN A REFERENCE CONFIGURATION
(2015)
Variational formulation of a coupled thermomechanical problem of anisotropic solids for the case of non-isothermal finite deformations in a reference configuration is shown. The formulation of the problem includes: a condition of equilibrium flow of a deformation process in the reference configuration; an equation of a coupled heat conductivity in a variational form, in which an influence of deformation characteristics of a process on the temperature field is taken into account; tensor-linear constitutive relations for a hypoelastic material; kinematic and evolutional relations; initial and boundary conditions. Based on this formulation several axisymmetric isothermal and coupled problems of finite deformations of isotropic and anisotropic bodies are solved. The solution of coupled thermomechanical problems for a hollow cylinder in case of finite deformation showed an essential influence of coupling on distribution of temperature, stresses and strains. The obtained solutions show the development of stressstrain state and temperature changing in axisymmetric bodies in the case of finite deformations.
The aim of this paper we discuss explicit series constructions for the fundamental solution of the Helmholtz operator on some important examples non-orientable conformally at manifolds. In the context of this paper we focus on higher dimensional generalizations of the Klein bottle which in turn generalize higher dimensional Möbius strips that we discussed in preceding works. We discuss some basic properties of pinor valued solutions to the Helmholtz equation on these manifolds.
In this paper we present some rudiments of a generalized Wiman-Valiron theory in the context of polymonogenic functions. In particular, we analyze the relations between different notions of growth orders and the Taylor coefficients. Our main intention is to look for generalizations of the Lindel¨of-Pringsheim theorem. In contrast to the classical holomorphic and the monogenic setting we only obtain inequality relations in the polymonogenic setting. This is due to the fact that the Almansi-Fischer decomposition of a polymonogenic function consists of different monogenic component functions where each of them can have a totally different kind of asymptotic growth behavior.
For many applications, nonuniformly distributed functional data is given which lead to large–scale scattered data problems. We wish to represent the data in terms of a sparse representation with a minimal amount of degrees of freedom. For this, an adaptive scheme which operates in a coarse-to-fine fashion using a multiscale basis is proposed. Specifically, we investigate hierarchical bases using B-splines and spline-(pre)wavelets. At each stage a leastsquares approximation of the data is computed. We take into account different requests arising in large-scale scattered data fitting: we discuss the fast iterative solution of the least square systems, regularization of the data, and the treatment of outliers. A particular application concerns the approximate continuation of harmonic functions, an issue arising in geodesy.
In this note, we describe quite explicitly the Howe duality for Hodge systems and connect it with the well-known facts of harmonic analysis and Clifford analysis. In Section 2, we recall briefly the Fisher decomposition and the Howe duality for harmonic analysis. In Section 3, the well-known fact that Clifford analysis is a real refinement of harmonic analysis is illustrated by the Fisher decomposition and the Howe duality for the space of spinor-valued polynomials in the Euclidean space under the so-called L-action. On the other hand, for Clifford algebra valued polynomials, we can consider another action, called in Clifford analysis the H-action. In the last section, we recall the Fisher decomposition for the H-action obtained recently. As in Clifford analysis the prominent role plays the Dirac equation in this case the basic set of equations is formed by the Hodge system. Moreover, analysis of Hodge systems can be viewed even as a refinement of Clifford analysis. In this note, we describe the Howe duality for the H-action. In particular, in Proposition 1, we recognize the Howe dual partner of the orthogonal group O(m) in this case as the Lie superalgebra sl(2 1). Furthermore, Theorem 2 gives the corresponding multiplicity free decomposition with an explicit description of irreducible pieces.
MULTI-SITE CONSTRUCTION PROJECT SCHEDULING CONSIDERING RESOURCE MOVING TIME IN DEVELOPING COUNTRIES
(2010)
Under the booming construction demands in developing countries, particularly in Vietnam situation, construction contractors often perform multiple concurrent projects in different places. In construction project scheduling processes, the existing scheduling methods often assume the resource moving time between activities/projects to be negligible. When multiple projects are deployed in different places and far from each other, this assumption has many shortcomings for properly modelling the real-world constraints. Especially, with respect to developing countries such as the Vietnam which contains transportation systems that are still in backward and low technical standards. This paper proposes a new algorithm named Multi-Site Construction Project Scheduling - MCOPS. The objective of this algorithm is to solve the problem of minimising multi-site construction project duration under limited available conditions of renewable resources (labour, machines and equipment) combining with the moving time of required resource among activities/projects. Additionally, in order to mitigate the impact of resource moving time into the multi-site project duration, this paper proposed a new priority rule: Minimum Resource Moving Time (MinRMT). The MinRMT is applied to rank the finished activities according to a priority order, to support the released resources to the scheduling activities. In order to investigate the impact of the resource moving time among activities during the scheduling process, computational experimentation was implemented. The results of the MCOPS-based computational experiments showed that, the resource moving time among projects has significantly impacted the multi-site project durations and this amount of time can not be ignored in the multi-site project scheduling process. Besides, the efficient application of the MinRMT is also demonstrated through the achieved results of the computational experiment in this paper. Though the efforts in this paper are based on the Vietnamese construction conditions, the proposed method can be usefully applied in other developing countries which have similar construction conditions.
It is well known that complex quaternion analysis plays an important role in the study of higher order boundary value problems of mathematical physics. Following the ideas given for real quaternion analysis, the paper deals with certain orthogonal decompositions of the complex quaternion Hilbert space into its subspaces of null solutions of Dirac type operator with an arbitrary complex potential. We then apply them to consider related boundary value problems, and to prove the existence and uniqueness as well as the explicit representation formulae of the underlying solutions.
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.
Steel profiles with slender cross-sections are characterized by their high susceptibility to instability phenomena, especially local buckling, which are intensified under fire conditions. This work presents a study on numerical modelling of the behaviour of steel structural elements in case of fire with slender cross-sections. To accurately carry out these analyses it is necessary to take into account those local instability modes, which normally is only possible with shell finite elements. However, aiming at the development of more expeditious methods, particularly important for analysing complete structures in case of fire, recent studies have proposed the use of beam finite elements considering the presence of local buckling through the implementation of a new effective steel constitutive law. The objective of this work is to develop a study to validate this methodology using the program SAFIR. Comparisons are made between the results obtained applying the referred new methodology and finite element analyses using shell elements. The studies were made to laterally restrained beams, unrestrained beams, axially compressed columns and columns subjected to bending plus compression.
Portugal is one of the European countries with higher spatial and population freeway network coverage. The sharp growth of this network in the last years instigates the use of methods of analysis and the evaluation of their quality of service in terms of the traffic performance, typically performed through internationally accepted methodologies, namely that presented in the Highway Capacity Manual (HCM). Lately, the use of microscopic traffic simulation models has been increasingly widespread. These models simulate the individual movement of the vehicles, allowing to perform traffic analysis. The main target of this study was to verify the possibility of using microsimulation as an auxiliary tool in the adaptation of the methodology by HCM 2000 to Portugal. For this purpose, were used the microscopic simulators AIMSUN and VISSIM for the simulation of the traffic circulation in the A5 Portuguese freeway. The results allowed the analysis of the influence of the main geometric and traffic factors involved in the methodology by HCM 2000. In conclusion, the study presents the main advantages and limitations of the microsimulators AIMSUN and VISSIM in modelling the traffic circulation in Portuguese freeways. The main limitation is that these microsimulators are not able to simulate explicitly some of the factors considered in the HCM 2000 methodology, which invalidates their direct use as a tool in the quantification of those effects and, consequently, makes the direct adaptation of this methodology to Portugal impracticable.
In recent years special hypercomplex Appell polynomials have been introduced by several authors and their main properties have been studied by different methods and with different objectives. Like in the classical theory of Appell polynomials, their generating function is a hypercomplex exponential function. The observation that this generalized exponential function has, for example, a close relationship with Bessel functions confirmed the practical significance of such an approach to special classes of hypercomplex differentiable functions. Its usefulness for combinatorial studies has also been investigated. Moreover, an extension of those ideas led to the construction of complete sets of hypercomplex Appell polynomial sequences. Here we show how this opens the way for a more systematic study of the relation between some classes of Special Functions and Elementary Functions in Hypercomplex Function Theory.
The aim of our contribution is to clarify the relation between totally regular variables and Appell sequences of hypercomplex holomorphic polynomials (sometimes simply called monogenic power-like functions) in Hypercomplex Function Theory. After their introduction in 2006 by two of the authors of this note on the occasion of the 17th IKM, the latter have been subject of investigations by different authors with different methods and in various contexts. The former concept, introduced by R. Delanghe in 1970 and later also studied by K. Gürlebeck in 1982 for the case of quaternions, has some obvious relationship with the latter, since it describes a set of linear hypercomplex holomorphic functions all power of which are also hypercomplex holomorphic. Due to the non-commutative nature of the underlying Clifford algebra, being totally regular variables or Appell sequences are not trivial properties as it is for the integer powers of the complex variable z=x+ iy. Simple examples show also, that not every totally regular variable and its powers form an Appell sequence and vice versa. Under some very natural normalization condition the set of all para-vector valued totally regular variables which are also Appell sequences will completely be characterized. In some sense the result can also be considered as an answer to a remark of K. Habetha in chapter 16: Function theory in algebras of the collection Complex analysis. Methods, trends, and applications, Akademie-Verlag Berlin, (Eds. E. Lanckau and W. Tutschke) 225-237 (1983) on the use of exact copies of several complex variables for the power series representation of any hypercomplex holomorphic function.
In this paper, we present an empirical approach for objective and quantitative benchmarking of optimization algorithms with respect to characteristics induced by the forward calculation. Due to the professional background of the authors, this benchmarking strategy is illustrated on a selection of search methods in regard to expected characteristics of geotechnical parameter back calculation problems. Starting from brief introduction into the approach employed, a strategy for optimization algorithm benchmarking is introduced. The benchmarking utilizes statistical tests carried out on well-known test functions superposed with perturbations, both chosen to mimic objective function topologies found for geotechnical objective function topologies. Here, the moved axis parallel hyper-ellipsoid test function and the generalized Ackley test function in conjunction with an adjustable quantity of objective function topology roughness and fraction of failing forward calculations is analyzed. In total, results for 5 optimization algorithms are presented, compared and discussed.
A stress based remodeling approach is used to investigate the sensitivity of the collagen architecture in humane eye tissues on the biomechanical response of the lamina cribrosa with a particular focus on the stress environment of the nerve fibers. This approach is based on a multi-level biomechanical framework, where the biomechanical properties of eye tissues are derived from a single crimped fibril at the micro-scale via the collagen network of distributed fibrils at the meso-scale to the incompressible and anisotropic soft tissue at the macro-scale. Biomechanically induced remodeling of the collagen network is captured on the meso-scale by allowing for a continuous reorientation of collagen fibrils. To investigate the multi-scale phenomena related to glaucomatous neuropathy a generalized computational homogenization scheme is applied to a coupled two-scale analysis of the human eye considering a numerical macro- and meso-scale model of the lamina cribrosa.
Due to the complex interactions between the ground, the driving machine, the lining tube and the built environment, the accurate assignment of in-situ system parameters for numerical simulation in mechanized tunneling is always subject to tremendous difficulties. However, the more accurate these parameters are, the more applicable the responses gained from computations will be. In particular, if the entire length of the tunnel lining is examined, then, the appropriate selection of various kinds of ground parameters is accountable for the success of a tunnel project and, more importantly, will prevent potential casualties. In this context, methods of system identification for the adaptation of numerical simulation of ground models are presented. Hereby, both deterministic and probabilistic approaches are considered for typical scenarios representing notable variations or changes in the ground model.
In this paper we review two distint complete orthogonal systems of monogenic polynomials over 3D prolate spheroids. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4), and are generally assumed to be nullsolutions of the well known Riesz and Moisil Théodoresco systems in R3. This will be done in the spaces of square integrable functions over R and H. The representations of these polynomials are explicitly given. Additionally, we show that these polynomial functions play an important role in defining the Szegö kernel function over the surface of 3D spheroids. As a concrete application, we prove the explicit expression of the monogenic Szegö kernel function over 3D prolate spheroids.