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Mon, 28 Sep 2015 08:22:27 +0200Mon, 28 Sep 2015 08:22:27 +0200Application of the Finite Pointset Method to moving boundary problems for the BGK model of rarefied gas dynamics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4182
The overall goal of the work is to simulate rarefied flows inside geometries with moving boundaries. The behavior of a rarefied flow is characterized through the Knudsen number \(Kn\), which can be very small (\(Kn < 0.01\) continuum flow) or larger (\(Kn > 1\) molecular flow). The transition region (\(0.01 < Kn < 1\)) is referred to as the transition flow regime.
Continuum flows are mainly simulated by using commercial CFD methods, which are used to solve the Euler equations. In the case of molecular flows one uses statistical methods, such as the Direct Simulation Monte Carlo (DSMC) method. In the transition region Euler equations are not adequate to model gas flows. Because of the rapid increase of particle collisions the DSMC method tends to fail, as well
Therefore, we develop a deterministic method, which is suitable to simulate problems of rarefied gases for any Knudsen number and is appropriate to simulate flows inside geometries with moving boundaries. Thus, the method we use is the Finite Pointset Method (FPM), which is a mesh-free numerical method developed at the ITWM Kaiserslautern and is mainly used to solve fluid dynamical problems.
More precisely, we develop a method in the FPM framework to solve the BGK model equation, which is a simplification of the Boltzmann equation. This equation is mainly used to describe rarefied flows.
The FPM based method is implemented for one and two dimensional physical and velocity space and different ranges of the Knudsen number. Numerical examples are shown for problems with moving boundaries. It is seen, that our method is superior to regular grid methods with respect to the implementation of boundary conditions. Furthermore, our results are comparable to reference solutions gained through CFD- and DSMC methods, respectevly.Maria Kobertdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4182Mon, 28 Sep 2015 08:22:27 +0200Design and Verification of Behaviour-Based Systems Realising Task Sequences
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4181
Since their invention in the 1980s, behaviour-based systems have become very popular among roboticists. Their component-based nature facilitates the distributed implementation of systems, fosters reuse, and allows for early testing and integration. However, the distributed approach necessitates the interconnection of many components into a network in order to realise complex functionalities. This network is crucial to the correct operation of the robotic system. There are few sound design techniques for behaviour networks, especially if the systems shall realise task sequences. Therefore, the quality of the resulting behaviour-based systems is often highly dependant on the experience of their developers.
This dissertation presents a novel integrated concept for the design and verification of behaviour-based systems that realise task sequences. Part of this concept is a technique for encoding task sequences in behaviour networks. Furthermore, the concept provides guidance to developers of such networks. Based on a thorough analysis of methods for defining sequences, Moore machines have been selected for representing complex tasks. With the help of the structured workflow proposed in this work and the developed accompanying tool support, Moore machines defining task sequences can be transferred automatically into corresponding behaviour networks, resulting in less work for the developer and a lower risk of failure.
Due to the common integration of automatically and manually created behaviour-based components, a formal analysis of the final behaviour network is reasonable. For this purpose, the dissertation at hand presents two verification techniques and justifies the selection of model checking. A novel concept for applying model checking to behaviour-based systems is proposed according to which behaviour networks are modelled as synchronised automata. Based on such automata, properties of behaviour networks that realise task sequences can be verified or falsified. Extensive graphical tool support has been developed in order to assist the developer during the verification process.
Several examples are provided in order to illustrate the soundness of the presented design and verification techniques. The applicability of the integrated overall concept to real-world tasks is demonstrated using the control system of an autonomous bucket excavator. It can be shown that the proposed design concept is suitable for developing complex sophisticated behaviour networks and that the presented verification technique allows for verifying real-world behaviour-based systems.Christopher Armbrustdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4181Fri, 25 Sep 2015 09:49:05 +0200Multi-Sensory Data Analysis and On-Line Evaluation for Advanced Process Control and Yield Optimization in Polymer Film Industry
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4175
The current procedures for achieving industrial process surveillance, waste reduction, and prognosis of critical process states are still insufficient in some parts of the manufacturing industry. Increasing competitive pressure, falling margins, increasing cost, just-in-time production, environmental protection requirements, and guidelines concerning energy savings pose new challenges to manufacturing companies, from the semiconductor to the pharmaceutical industry.
New, more intelligent technologies adapted to the current technical standards provide companies with improved options to tackle these situations. Here, knowledge-based approaches open up pathways that have not yet been exploited to their full extent. The Knowledge-Discovery-Process for knowledge generation describes such a concept. Based on an understanding of the problems arising during production, it derives conclusions from real data, processes these data, transfers them into evaluated models and, by this open-loop approach, reiteratively reflects the results in order to resolve the production problems. Here, the generation of data through control units, their transfer via field bus for storage in database systems, their formatting, and the immediate querying of these data, their analysis and their subsequent presentation with its ensuing benefits play a decisive role.
The aims of this work result from the lack of systematic approaches to the above-mentioned issues, such as process visualization, the generation of recommendations, the prediction of unknown sensor und production states, and statements on energy cost.
Both science and commerce offer mature statistical tools for data preprocessing, analysis and modeling, and for the final reporting step. Since their creation, the insurance business, the world of banking, market analysis, and marketing have been the application fields of these software types; they are now expanding to the production environment.
Appropriate modeling can be achieved via specific machine learning procedures, which have been established in various industrial areas, e.g., in process surveillance by optical control systems. Here, State-of-the-art classification methods are used, with multiple applications comprising sensor technology, process areas, and production site data. Manufacturing companies now intend to establish a more holistic surveillance of process data, such as, e.g., sensor failures or process deviations, to identify dependencies. The causes of quality problems must be recognized and selected in real time from about 500 attributes of a highly complex production machine. Based on these identified causes, recommendations for improvement must then be generated for the operator at the machine, in order to enable timely measures to avoid these quality deviations.
Unfortunately, the ability to meet the required increases in efficiency – with simultaneous consumption and waste minimization – still depends on data that are, for the most part, not available. There is an overrepresentation of positive examples whereas the number of definite negative examples is too low.
The acquired information can be influenced by sensor drift effects and the occurrence of quality degradation may not be adequately recognized. Sensorless diagnostic procedures with dual use of actuators can be of help here.
Moreover, in the course of a process, critical states with sometimes unexplained behavior can occur. Also in these cases, deviations could be reduced by early countermeasures.
The generation of data models using appropriate statistical methods is of advantage here.
Conventional classification methods sometimes reach their limits. Supervised learning methods are mostly used in areas of high information density with sufficient data available for the classes under examination. However, there is a growing trend (e.g., spam filtering) to apply supervised learning methods to underrepresented classes, the datasets of which are, at best, outliers or not at all existent.
The application field of One-Class Classification (OCC) deals with this issue. Standard classification procedures (e.g., k-nearest-neighbor classifier, support vector machines) can be modified in adjustment to such problems. Thereby, a control system is able to classify statements on changing process states or sensor deviations. The above-described knowledge discovery process was employed in a case study from the polymer film industry, at the Mondi Gronau GmbH, taken as an example, and accomplished by a real-data survey at the production site and subsequent data preprocessing, modeling, evaluation, and deployment as a system for the generation of recommendations. To this end, questions regarding the following topics had to be clarified: data sources, datasets and their formatting, transfer pathways, storage media, query sequences, the employed methods of classification, their adjustment to the problems at hand, evaluation of the results, construction of a dynamic cycle, and the final implementation in the production process, along with its surplus value for the company.
Pivotal options for optimization with respect to ecological and economical aspects can be found here. Capacity for improvement is given in the reduction of energy consumption, CO\(_2\) emissions, and waste at all machines. At this one site, savings of several million euros per month can be achieved.
One major difficulty so far has been hardly accessible process data which, distributed on various data sources and unconnected, in some areas led to an increased analysis effort and a lack of holistic real-time quality surveillance. Monitoring of specifications and the thus obtained support for the operator at the installation resulted in a clear disadvantage with regard to cost minimization.
The data of the case study, captured according to their purposes and in coordination with process experts, amounted to 21,900 process datasets from cast film extrusion during 2 years’ time, including sensor data from dosing facilities and 300 site-specific energy datasets from the years 2002–2014.
In the following, the investigation sequence is displayed:
1. In the first step, industrial approaches according to Industrie 4.0 and related to Big Data were investigated. The applied statistical software suites and their functions were compared with a focus on real-time data acquisition from database systems, different data formats, their sensor locations at the machines, and the data processing part. The linkage of datasets from various data sources for, e.g., labeling and downstream exploration according to the knowledge discovery process is of high importance for polymer manufacturing applications.
2. In the second step, the aims were defined according to the industrial requirements, i.e. the critical production problem called “cut-off” as the main selection, and with regard to their investigation with machine learning methods. Therefore, a system architecture corresponding to the polymer industry was developed, containing the following processing steps: data acquisition, monitoring \& recommendation, and self-configuration.
3. The novel sensor datasets, with 160–2,500 real and synthetic attributes, were acquired within 1-min intervals via PLC and field bus from an Oracle database. The 160 features were reduced to 6 dimensions with feature reduction methods. Due to underrepresentation of the critical class, the learning approaches had to be modified and optimized for one-class classification, which achieved 99% accuracy after training, testing and evaluation with real datasets.
4. In the next step, the 6-dimensional dataset was scaled into lower 1-, 2-, or 3-dimensional space with classical and non-classical mapping approaches for downstream visualization. The mapped view was separated into zones of normal and abnormal process conditions by threshold setting.
5. Afterwards, the boundary zone was investigated and an approach for trajectory extraction consisting of condition points in sequence was developed, to optimize the prediction behavior of the model. The extracted trajectories were trained, tested and evaluated by State-of-the-art classification methods, achieving a 99% recognition ratio.
6. In the last step, the best methods and processing parts were converted into a specifically developed domain-specific graphical user interface for real-time visualization of process condition changes. The requirements of such an interface were discussed with the operators with regard to intuitive handling, interactive visualization and recommendations (as e.g., messaging and traffic lights), and implemented.
The software prototype was tested at a laboratory machine. Correct recognition of abnormal process problems was achieved at a 90\% ratio. The software was afterwards transferred to a group of on-line production machines.
As demonstrated, the monthly amount of waste arising at machine M150 could be decreased from 20.96% to 12.44% during the application time. The frequency of occurrence of the specific problem was reduced by 30% related to monthly savings of 50,000 EUR.
In the approach pertaining to the energy prognosis of load profiles, monthly energy data from 2002 to 2014 (about 36 trajectories with three to eight real parameters each) were used as the basis, analyzed and modeled systematically. The prognosis quality increased with approaching target date. Thereby, the site-specific load profile for 2014 could be predicted with an accuracy of 99%.
The achievement of sustained cost reductions of several 100,000 euros, combined with additional savings of EUR 2.8 million, could be demonstrated.
The process improvements achieved while pursuing scientific targets could be successfully and permanently integrated at the case study plant. The increase in methodical and experimental knowledge was reflected by first economical results and could be verified numerically. The expectations of the company were more than fulfilled and further developments based on the new findings were initiated. Among the new finding are the transfer of the scientific findings onto more machines and even the initiation of further studies expanding into the diagnostics area.
Considering the size of the enterprise, future enhanced success should also be possible for other locations. In the course of the grid charge exemption according to EEG, the energy savings at further German locations can amount to 4–11% on a monetary basis and at least 5% based on energy. Up to 10% of materials and cost can be saved with regard to waste reduction related to specific problems. According to projections, material savings of 5–10 t per month and time savings of up to 50 person-hours are achievable. Important synergy effects can be created by the knowledge transfer.Michael Kohlertdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4175Wed, 23 Sep 2015 12:28:30 +0200Computational Homogenization of Piezoelectric Materials using FE² Methods and Configurational Forces
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4174
Piezoelectric materials are electro-mechanically coupled materials. In these materials it is possible to produce an electric field by applying a mechanical load. This phenomenon is known as the piezoelectric effect. These materials also exhibit a mechanical deformation in response to an external electric loading, which is known as the inverse piezoelectric effect. By using these smart properties of piezoelectric materials, applications are possible in sensors and actuators. Ferroelectric or piezoelectric materials show switching behavior of the polarization in the material under an external loading. Due to this property, these materials are used to produce random access memory (RAM) for the non-volatile storage of data in computing devices. It is essential to understand the material responses of piezoelectric materials properly in order to use them in the engineering applications in innovative manners. Due to the growing interest in determining the material responses of smart material (e.g., piezoelectric material), computational methods are becoming increasingly important.
Many engineering materials possess inhomogeneities on the micro level. These inhomogeneities in the materials cause some difficulties in the determination of the material responses computationally as well as experimentally. But on the other hand, sometimes these inhomogeneities help the materials to render some good physical properties, e.g., glass or carbon fiber reinforced composites are light weight, but show higher strength. Piezoelectric materials also exhibit intense inhomogeneities on the micro level. These inhomogeneities are originating from the presence of domains, domain walls, grains, grain boundaries, micro cracks, etc. in the material. In order to capture the effects of the underlying microstructures on the macro quantities, it is essential to homogenize material parameters and the physical responses. There are several approaches to perform the homogenization. A two-scale classical (first-order) homogenization of electro-mechanically coupled materials using a FE²-approach is discussed in this work. The main objective of this work is to investigate the influences of the underlying micro structures on the macro Eshelby stress tensor and on the macro configurational forces. The configurational forces are determined in certain defect situations. These defect situations include the crack tip of a sharp crack in the macro specimen.
A literature review shows that the macro strain tensor is used to determine the micro boundary condition for the FE²-based homogenization in a small strain setting. This approach is capable to determine the consistent homogenized physical quantities (e.g., stress, strain) and the homogenized material quantities (e.g., stiffness tensor). But the application of these type of micro boundaries for the homogenization does not generate physically consistent macro Eshelby stress tensor or the macro configurational forces. Even in the absence of the micro volume configurational forces, this approach of the homogenization of piezoelectric materials produces unphysical volume configurational forces on the macro level. After a thorough investigation of the boundary conditions on the representative volume elements (RVEs), it is found that a displacement gradient driven micro boundary conditions remedy this issue. The use of the displacement gradient driven micro boundary conditions also satisfies the Hill-Mandel condition. The macro Eshelby stress tensor of a pure mechanical problem in a small deformation setting can be determined in two possible ways: by using the homogenized mechanical quantities (displacement gradient and stress tensor), or by homogenizing the Eshelby stress tensor on the micro level by volume averaging. The first approach does not satisfy the Hill-Mandel condition incorporating the Eshelby stress tensor in the energy term, on the other hand, the Hill-Mandel condition is satisfied in the second approach. In the case of homogenized Eshelby stress tensor determined from the homogenized physical quantities, the Hill-Mandel condition gives an additional energy term. A body in a small deformation setting is deformed according to the displacement gradient. If the homogenization is done using strain driven micro boundary conditions, the micro domain is deformed according to the macro strain, but the tiny vicinity around the corresponding Gauß point is deformed according to the macro displacement gradient. This implies that some restrictions are imposed at every Gauß point on the macro level. This situation helps the macro system to produce nonphysical volume configurational forces.
A FE²-based computational homogenization technique is also considered for the homogenization of piezoelectric materials. In this technique a representative volume element, which comprises of the micro structural features in the material, is assigned to every Gauß point of the macro domain. The macro displacement gradient and the macro electric field, or the macro stress tensor and the macro electric displacement are passed to the RVEs at every macro Gauß point. After determining boundary conditions on the RVEs, the homogenization process is performed. The homogenized physical quantities and the homogenized material parameters are passed back to macro Gauß points. In this work numerical investigations are carried out for two distinct situations of the microstructures of the piezoelectric materials regarding the evolution on the micro level: a) homogenization by using stationary microstructures, and b) homogenization by using evolving microstructures.
For the first case, the domain walls remain at fixed positions through out the simulations for the homogenization of piezoelectric materials. For a considerably large external loading, the real situation is different. But to understand the effects of the underlying microstructures on the macro configurational forces, to some extent it is sufficient to do the homogenization with fixed or stationary microstructures. The homogenization process is carried out for different microstructures and for different loading conditions. If the mechanical load is applied in the direction of the polarization, a smaller crack tip configurational force is observed in comparison to the configurational force determined for a mechanical loading perpendicular to the polarization. If the polarizations in the microstructures are parallel or perpendicular to the applied electric field and the applied displacement, configurational forces parallel to the crack ligament of the macro crack are observed only. In the case of inclined polarizations in the microstructures, configurational forces inclined to the crack ligament are obtained. The simulation results also reveal that an application of an external electric field to the material reduces the value of the nodal configurational forces at the crack tip.
In the second case, the interfaces of the micro structures are allowed to move from their initial positions at every step of the applied incremental external loading. Thus, at every step of the application of the external loading, the microstructures are changed when the external loading is larger than the coercive field. The movement of the interfaces is realized through the nodal configurational forces on the micro level. At every step of the application of the external loading, the nodal configurational forces per unit length on the domain walls are determined in the post-processing of the FE-simulation on the micro domain. With the help of the domain wall kinetics, the new positions of the domain walls are determined. Numerical results show that the crack tip region is the most affected area in the macro domain. For that reason a very different distribution of the macro electric displacement is observed comparing the same produced by using fixed microstructures. Due to the movement of the domain walls, the energy is dissipated in the system. As a result, a smaller configurational force appears at the crack tip on the macro level in the case of the homogenization by using evolving microstructures. By using the homogenization technique involving the evolution of the microstructures, it is possible to produce the electric displacement vs. electric field hysteresis loop on the macro level. The shape of the hysteresis loop depends on the value of the rate of application of the external electric loading. A faster deployment of the external electric field widens the hysteresis loop. Md Khalaquzzamandoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4174Wed, 16 Sep 2015 16:20:09 +0200American-style Option Pricing and Improvement of Regression-based Monte Carlo Methods by Machine Learning Techniques
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4172
In this dissertation, we discuss how to price American-style options. Our aim is to study and improve the regression-based Monte Carlo methods. In order to have good benchmarks to compare with them, we also study the tree methods.
In the second chapter, we investigate the tree methods specifically. We do research firstly within the Black-Scholes model and then within the Heston model. In the Black-Scholes model, based on Müller's work, we illustrate how to price one dimensional and multidimensional American options, American Asian options, American lookback options, American barrier options and so on. In the Heston model, based on Sayer's research, we implement his algorithm to price one dimensional American options. In this way, we have good benchmarks of various American-style options and put them all in the appendix.
In the third chapter, we focus on the regression-based Monte Carlo methods theoretically and numerically. Firstly, we introduce two variations, the so called "Tsitsiklis-Roy method" and the "Longstaff-Schwartz method". Secondly, we illustrate the approximation of American option by its Bermudan counterpart. Thirdly we explain the source of low bias and high bias. Fourthly we compare these two methods using in-the-money paths and all paths. Fifthly, we examine the effect using different number and form of basis functions. Finally, we study the Andersen-Broadie method and present the lower and upper bounds.
In the fourth chapter, we study two machine learning techniques to improve the regression part of the Monte Carlo methods: Gaussian kernel method and kernel-based support vector machine. In order to choose a proper smooth parameter, we compare fixed bandwidth, global optimum and suboptimum from a finite set. We also point out that scaling the training data to [0,1] can avoid numerical difficulty. When out-of-sample paths of stock prices are simulated, the kernel method is robust and even performs better in several cases than the Tsitsiklis-Roy method and the Longstaff-Schwartz method. The support vector machine can keep on improving the kernel method and needs less representations of old stock prices during prediction of option continuation value for a new stock price.
In the fifth chapter, we switch to the hardware (FGPA) implementation of the Longstaff-Schwartz method and propose novel reversion formulas for the stock price and volatility within the Black-Scholes and Heston models. The test for this formula within the Black-Scholes model shows that the storage of data is reduced and also the corresponding energy consumption.Songyin Tangdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4172Mon, 14 Sep 2015 09:21:08 +0200Tropical Geometry in Singular
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4169
Yue Rendoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4169Wed, 09 Sep 2015 10:34:35 +0200Stochastic Modeling and Approximation of Turbulent Spinning Processes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4168
In some processes for spinning synthetic fibers the filaments are exposed to highly turbulent air flows to achieve a high degree of stretching (elongation). The quality of the resulting filaments, namely thickness and uniformity, is thus determined essentially by the aerodynamic force coming from the turbulent flow. Up to now, there is a gap between the elongation measured in experiments and the elongation obtained by numerical simulations available in the literature.
The main focus of this thesis is the development of an efficient and sufficiently accurate simulation algorithm for the velocity of a turbulent air flow and the application in turbulent spinning processes.
In stochastic turbulence models the velocity is described by an \(\mathbb{R}^3\)-valued random field. Based on an appropriate description of the random field by Marheineke, we have developed an algorithm that fulfills our requirements of efficiency and accuracy. Applying a resulting stochastic aerodynamic drag force on the fibers then allows the simulation of the fiber dynamics modeled by a random partial differential algebraic equation system as well as a quantization of the elongation in a simplified random ordinary differential equation model for turbulent spinning. The numerical results are very promising: whereas the numerical results available in the literature can only predict elongations up to order \(10^4\) we get an order of \(10^5\), which is closer to the elongations of order \(10^6\) measured in experiments.Florian Hübschdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4168Tue, 01 Sep 2015 13:27:20 +0200Randomized Jumplists With Several Jump Pointers
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4164
In 2003, a dictionary data structure called jumplist has been introduced by Brönnimann, Cazals and Durand. It is based on a circularly closed (singly) linked list, but additional jump-pointers are added to provide shortcuts to parts further ahead in the list.
The original jump-and-walk data structure by Brönnimann, Cazals and Durand only introduces one jump-pointer per node. In this thesis, I add one more-jump pointer to each node and present algorithms for generation, insertion and search for the resulting data structure.
Furthermore, I try to evaluate the effects on the expected search costs and the complexity of the generation and insertion.
It turns out that the two-jump-pointer variant of the jumplist has a slightly better prefactor (1.2 vs. 2) in the leading term of the expected internal path length than the original version and despite the more complex structure of the two-jump-pointer variant compared to the regular jumplist, the complexity of generation and insertion remains linearithmic. Elisabeth Neumannbachelorthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4164Tue, 25 Aug 2015 13:32:46 +0200Construction of a Mittag-Leffler Analysis and its Applications
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4157
Motivated by the results of infinite dimensional Gaussian analysis and especially white noise analysis, we construct a Mittag-Leffler analysis. This is an infinite dimensional analysis with respect to non-Gaussian measures of Mittag-Leffler type which we call Mittag-Leffler measures. Our results indicate that the Wick ordered polynomials, which play a key role in Gaussian analysis, cannot be generalized to this non-Gaussian case. We provide evidence that a system of biorthogonal polynomials, called generalized Appell system, is applicable to the Mittag-Leffler measures, instead of using Wick ordered polynomials. With the help of an Appell system, we introduce a test function and a distribution space. Furthermore we give characterizations of the distribution space and we characterize the weak integrable functions and the convergent sequences within the distribution space. We construct Donsker's delta in a non-Gaussian setting as an application.
In the second part, we develop a grey noise analysis. This is a special application of the Mittag-Leffler analysis. In this framework, we introduce generalized grey Brownian motion and prove differentiability in a distributional sense and the existence of generalized grey Brownian motion local times. Grey noise analysis is then applied to the time-fractional heat equation and the time-fractional Schrödinger equation. We prove a generalization of the fractional Feynman-Kac formula for distributional initial values. In this way, we find a Green's function for the time-fractional heat equation which coincides with the solutions given in the literature.
Florian Jahnertdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4157Tue, 18 Aug 2015 08:32:00 +0200Robust storage loading problems with stacking and payload constraints
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4158
We consider storage loading problems where items with uncertain weights have
to be loaded into a storage area, taking into account stacking and
payload constraints. Following the robust optimization paradigm, we propose
strict and adjustable optimization models for finite and interval-based
uncertainties. To solve these problems, exact decomposition and heuristic
solution algorithms are developed.
For strict robustness, we also present a compact formulation based
on a characterization of worst-case scenarios.
Computational results show that computation times and algorithm
gaps are reasonable for practical applications.
Furthermore, we find that the robustness concepts show different
potential depending on the type of data being used.
Marc Goerigk; Sigrid Knust; Xuan Thanh Lepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4158Tue, 18 Aug 2015 08:23:49 +0200Spin and orbital magnetic moments of isolated single molecule magnets and transition metal clusters
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4143
In the present work, magnetic moments of isolated Single Molecule Magnets (SMMs) and transition
metal clusters were investigated. Gas phase X‐ray Magnetic Circular Dichroism (XMCD) in
combination with sum rule analysis served to separate the total magnetic moments of the
investigated species into their spin and orbital contributions. Two different mass spectrometry based
setups were used for the presented investigations on transition metal clusters (GAMBIT‐setup) and
on single molecule magnets (NanoClusterTrap). Both experiments were coupled to the UE52‐PGM
beamline at the BESSY II synchrotron facility (Helmholtz Zentrum Berlin) which provided the
necessary polarized X‐ray photons. The investigation of the given compounds as isolated molecules
in the gas phase enabled a determination of their intrinsic magnetic properties void of any influences
of e.g. a surrounding bulk or supporting surfaceMatthias Tombersdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4143Tue, 11 Aug 2015 11:46:05 +0200Aspects and Applications of the Wilkie Investment Model
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4137
The Wilkie model is a stochastic asset model, developed by A.D. Wilkie in 1984 with a purpose to explore the behaviour of investment factors of insurers within the United Kingdom. Even so, there is still no analysis that studies the Wilkie model in a portfolio optimization framework thus far. Originally, the Wilkie model is considering a discrete-time horizon and we apply the concept of Wilkie model to develop a suitable ARIMA model for Malaysian data by using Box-Jenkins methodology. We obtained the estimated parameters for each sub model within the Wilkie model that suits the case of Malaysia, and permits us to analyse the result based on statistics and economics view. We then tend to review the continuous time case which was initially introduced by Terence Chan in 1998. The continuous-time Wilkie model inspired is then being employed to develop the wealth equation of a portfolio that consists of a bond and a stock. We are interested in building portfolios based on three well-known trading strategies, a self-financing strategy, a constant growth optimal strategy as well as a buy-and-hold strategy. In dealing with the portfolio optimization problems, we use the stochastic control technique consisting of the maximization problem itself, the Hamilton-Jacobi-equation, the solution to the Hamilton-Jacobi-equation and finally the verification theorem. In finding the optimal portfolio, we obtained the specific solution of the Hamilton-Jacobi-equation and proved the solution via the verification theorem. For a simple buy-and-hold strategy, we use the mean-variance analysis to solve the portfolio optimization problem.
Norizarina Ishakdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4137Tue, 11 Aug 2015 11:06:03 +0200Interactive Visual Support for Understanding the Structural and Behavioural Aspects of Embedded Systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4142
Information Visualization (InfoVis) and Human-Computer Interaction (HCI) have strong ties with each other. Visualization supports the human cognitive system by providing interactive and meaningful images of the underlying data. On the other side, the HCI domain cares about the usability of the designed visualization from the human perspectives. Thus, designing a visualization system requires considering many factors in order to achieve the desired functionality and the system usability. Achieving these goals will help these people in understanding the inside behavior of complex data sets in less time.
Graphs are widely used data structures to represent the relations between the data elements in complex applications. Due to the diversity of this data type, graphs have been applied in numerous information visualization applications (e.g., state transition diagrams, social networks, etc.). Therefore, many graph layout algorithms have been proposed in the literature to help in visualizing this rich data type. Some of these algorithms are used to visualize large graphs, while others handle the medium sized graphs. Regardless of the graph size, the resulting layout should be understandable from the users’ perspective and at the same time it should fulfill a list of aesthetic criteria to increase the representation readability. Respecting these two principles leads to produce a resulting graph visualization that helps the users in understanding and exploring the complex behavior of critical systems.
In this thesis, we utilize the graph visualization techniques in modeling the structural and behavioral aspects of embedded systems. Furthermore, we focus on evaluating the resulting representations from the users’ perspectives.
The core contribution of this thesis is a framework, called ESSAVis (Embedded Systems Safety Aspect Visualizer). This framework visualizes not only some of the safety aspects (e.g. CFT models) of embedded systems, but also helps the engineers and experts in analyzing the system safety critical situations. For this, the framework provides a 2Dplus3D environment in which the 2D represents the graph representation of the abstract data about the safety aspects of the underlying embedded system while the 3D represents the underlying system 3D model. Both views are integrated smoothly together in the 3D world fashion. In order to check the effectiveness and feasibility of the framework and its sub-components, we conducted many studies with real end users as well as with general users. Results of the main study that targeted the overall ESSAVis framework show high acceptance ratio and higher accuracy with better performance using the provided visual support of the framework.
The ESSAVis framework has been designed to be compatible with different 3D technologies. This enabled us to use the 3D stereoscopic depth of such technologies to encode nodes attributes in node-link diagrams. In this regard, we conducted an evaluation study to measure the usability of the stereoscopic depth cue approach, called the stereoscopic highlighting technique, against other selected visual cues (i.e., color, shape, and sizes). Based on the results, the thesis proposes the Reflection Layer extension to the stereoscopic highlighting technique, which was also evaluated from the users’ perspectives. Additionally, we present a new technique, called ExpanD (Expand in Depth), that utilizes the depth cue to show the structural relations between different levels of details in node-link diagrams. Results of this part opens a promising direction of the research in which visualization designers can get benefits from the richness of the 3D technologies in visualizing abstract data in the information visualization domain.
Finally, this thesis proposes the application of the ESSAVis frame- work as a visual tool in the educational training process of engineers for understanding the complex concepts. In this regard, we conducted an evaluation study with computer engineering students in which we used the visual representations produced by ESSAVis to teach the principle of the fault detection and the failure scenarios in embedded systems. Our work opens the directions to investigate many challenges about the design of visualization for educational purposes. Ragaad AlTarawnehdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4142Tue, 04 Aug 2015 12:14:31 +0200Large Display Interaction Using Mobile Devices
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4141
Large displays become more and more popular, due to dropping prices. Their size and high resolution leverages collaboration and they are capable of dis- playing even large datasets in one view. This becomes even more interesting as the number of big data applications increases. The increased screen size and other properties of large displays pose new challenges to the Human- Computer-Interaction with these screens. This includes issues such as limited scalability to the number of users, diversity of input devices in general, leading to increased learning efforts for users, and more.
Using smart phones and tablets as interaction devices for large displays can solve many of these issues. Since they are almost ubiquitous today, users can bring their own device. This approach scales well with the number of users. These mobile devices are easy and intuitive to use and allow for new interaction metaphors, as they feature a wide array of input and output capabilities, such as touch screens, cameras, accelerometers, microphones, speakers, Near-Field Communication, WiFi, etc.
This thesis will present a concept to solve the issues posed by large displays. We will show proofs-of-concept, with specialized approaches showing the via- bility of the concept. A generalized, eyes-free technique using smart phones or tablets to interact with any kind of large display, regardless of hardware or software then overcomes the limitations of the specialized approaches. This is implemented in a large display application that is designed to run under a multitude of environments, including both 2D and 3D display setups. A special visualization method is used to combine 2D and 3D data in a single visualization.
Additionally the thesis will present several approaches to solve common is- sues with large display interaction, such as target sizes on large display getting too small, expensive tracking hardware, and eyes-free interaction through vir- tual buttons. These methods provide alternatives and context for the main contribution.Jens Bauerdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4141Tue, 04 Aug 2015 12:02:52 +0200Discrete Parallel Machine Makespan ScheLoc Problem
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4129
Scheduling-Location (ScheLoc) Problems integrate the separate fields of
scheduling and location problems. In ScheLoc Problems the objective is to
find locations for the machines and a schedule for each machine subject to
some production and location constraints such that some scheduling object-
ive is minimized. In this paper we consider the Discrete Parallel Machine
Makespan (DPMM) ScheLoc Problem where the set of possible machine loc-
ations is discrete and a set of n jobs has to be taken to the machines and
processed such that the makespan is minimized. Since the separate location
and scheduling problem are both NP-hard, so is the corresponding ScheLoc
Problem. Therefore, we propose an integer programming formulation and
different versions of clustering heuristics, where jobs are split into clusters
and each cluster is assigned to one of the possible machine locations. Since
the IP formulation can only be solved for small scale instances we propose
several lower bounds to measure the quality of the clustering heuristics. Ex-
tensive computational tests show the efficiency of the heuristics.Corinna Heßler; Kaouthar Deghdakpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4129Tue, 28 Jul 2015 09:40:15 +0200A new solution approach for solving the 2-facility location problem in the plane with block norms
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4128
Motivated by the time-dependent location problem over T time-periods introduced in
Maier and Hamacher (2015) we consider the special case of two time-steps, which was shown
to be equivalent to the static 2-facility location problem in the plane. Geometric optimality
conditions are stated for the median objective. When using block norms, these conditions
are used to derive a polygon grid inducing a subdivision of the plane based on normal cones,
yielding a new approach to solve the 2-facility location problem in polynomial time. Combinatorial algorithms for the 2-facility location problem based on geometric properties are
deduced and their complexities are analyzed. These methods differ from others as they are
completely working on geometric objects to derive the optimal solution set.Andrea Maierpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4128Fri, 24 Jul 2015 11:31:09 +0200Interactive Visual Analysis of Software Structures
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4123
Maintaining complex software systems tends to be a costly activity where software engineers spend a significant amount of time trying to understand the system's structure and behavior. As early as the 1980s, operation and maintenance costs were already twice as expensive as the initial development costs incurred. Since then these costs have steadily increased. The focus of this thesis is to reduce these costs through novel interactive exploratory visualization concepts and to apply these modern techniques in the context of services offered by software quality analysis.
Costs associated with the understanding of software are governed by specific features of the system in terms of different domains, including re-engineering, maintenance, and evolution. These features are reflected in software measurements or inner qualities such as extensibility, reusability, modifiability, testability, compatability, or adatability. The presence or absence of these qualities determines how easily a software system can conform or be customized to meet new requirements. Consequently, the need arises to monitor and evaluate the qualitative state of a software system in terms of these qualities. Using metrics-based analysis, production costs and quality defects of the software can be recorded objectively and analyzed.
In practice, there exist a number of free and commercial tools that analyze the inner quality of a software system through the use of software metrics. However, most of these tools focus on software data mining and metrics (computational analysis) and only a few support visual analytical reasoning. Typically, computational analysis tools generate data and software visualization tools facilitate the exploration and explanation of this data through static or interactive visual representations. Tools that combine these two approaches focus only on well-known metrics and lack the ability to examine user defined metrics. Further, they are often confined to simple visualization methods and metaphors, including charts, histograms, scatter plots, and node-link diagrams.
The goal of this thesis is to develop methodologies that combine computational analysis methods together with sophisticated visualization methods and metaphors through an interactive visual analysis approach. This approach promotes an iterative knowledge discovery process through multiple views of the data where analysts select features of interest in one of the views and inspect data items of the select subset in all of the views. On the one hand, we introduce a novel approach for the visual analysis of software measurement data that captures complete facts of the system, employs a flow-based visual paradigm for the specification of software measurement queries, and presents measurement results through integrated software visualizations. This approach facilitates the on-demand computation of desired features and supports interactive knowledge discovery - the analyst can gain more insight into the data through activities that involve: building a mental model of the system; exploring expected and unexpected features and relations; and generating, verifying, or rejecting hypothesis with visual tools. On the other hand, we have also extended existing tools with additional views of the data for the presentation and interactive exploration of system artifacts and their inter-relations.
Contributions of this thesis have been integrated into two different prototype tools. First evaluations of these tools show that they can indeed improve the understanding of large and complex software systems. Taimur Khandoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4123Tue, 21 Jul 2015 08:18:13 +0200Socially Enhanced Access to Digital Resources
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4120
In the digital era we live in, users can access an abundance of digital resources in their daily life. These digital resources can be located on the user's devices, in traditional repositories such as intranets or digital libraries, but also in open environments such as the World Wide Web.
To be able to efficiently work with this abundance of information, users need support to get access to the resources that are relevant to them. Access to digital resources can be supported in various ways. Whether we talk about technologies for browsing, searching, filtering, ranking, or recommending resources: what they all have in common is that they depend on the available information (i.e., resources and metadata). The accessibility of digital resources that meet a user's information need, and the existence and quality of metadata is crucial for the success of any information system.
This work focuses on how social media technologies can support the access to digital resources. In contrast to closed and controlled environments where only selected users have the rights to contribute digital resources and metadata, and where this contribution involves a social process of formal agreement of the relevant stakeholders, potentially any user can easily create and provide information in social media environments. This usually leads to a larger variety of resources and metadata, and allows for dynamics that would otherwise hardly be possible.
Most information systems still mainly rely on traditional top-down approaches where only selected stakeholders can contribute information. The main idea of this thesis is an approach that allows for introducing the characteristics of social media environments in such traditional contexts. The requirements for such an approach are being examined, as well as the benefits and potentials it can provide.
The ALOE infrastructure was developed according to the identified requirements and realises a Social Resource and Metadata Hub. Case studies and evaluation results are provided to show the impact of the approach on the user's behaviours and the creation of digital resources and metadata, and to justify the presented approach.Martin Memmeldoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4120Mon, 13 Jul 2015 11:14:48 +0200Competitive Algorithms for Multistage Online Scheduling
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4119
We study an online flow shop scheduling problem where each job consists of several tasks that have to be completed in t different stages and the goal is to maximize the total weight of accepted jobs.
The set of tasks of a job contains one task for each stage and each stage has a dedicated set of identical parallel machines corresponding to it that can only process tasks of this stage. In order to gain the weight (profit) associated with a job j, each of its tasks has to be executed between a task-specific release date and deadline subject to the constraint that all tasks of job j from stages 1, …, i-1 have to be completed before the task of the ith stage can be started. In the online version, jobs arrive over time and all information about the tasks of a job becomes available at the release date of its first task. This model can be used to describe production processes in supply chains when customer orders arrive online.
We show that even the basic version of the offline problem with a single machine in each stage, unit weights, unit processing times, and fixed execution times for all tasks (i.e., deadline minus release date equals processing time) is APX-hard. Moreover, we show that the approximation ratio of any polynomial-time approximation algorithm for this basic version of the problem must depend on the number t of stages.
For the online version of the basic problem, we provide a (2t-1)-competitive deterministic online algorithm and a matching lower bound. Moreover, we provide several (sometimes tight) upper and lower bounds on the competitive ratio of online algorithms for several generalizations of the basic problem involving different weights, arbitrary release dates and deadlines, different processing times of tasks, and several identical machines per stage.
Michael Hopf; Clemens Thielen; Oliver Wendtpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4119Thu, 09 Jul 2015 14:06:19 +0200Distributed Real-time Systems - Deterministic Protocols for Wireless Networks and Model-Driven Development with SDL
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4112
In a networked system, the communication system is indispensable but often the weakest link w.r.t. performance and reliability. This, particularly, holds for wireless communication systems, where the error- and interference-prone medium and the character of network topologies implicate special challenges. However, there are many scenarios of wireless networks, in which a certain quality-of-service has to be provided despite these conditions. In this regard, distributed real-time systems, whose realization by wireless multi-hop networks becomes increasingly popular, are a particular challenge. For such systems, it is of crucial importance that communication protocols are deterministic and come with the required amount of efficiency and predictability, while additionally considering scarce hardware resources that are a major limiting factor of wireless sensor nodes. This, in turn, does not only place demands on the behavior of a protocol but also on its implementation, which has to comply with timing and resource constraints.
The first part of this thesis presents a deterministic protocol for wireless multi-hop networks with time-critical behavior. The protocol is referred to as Arbitrating and Cooperative Transfer Protocol (ACTP), and is an instance of a binary countdown protocol. It enables the reliable transfer of bit sequences of adjustable length and deterministically resolves contest among nodes based on a flexible priority assignment, with constant delays, and within configurable arbitration radii. The protocol's key requirement is the collision-resistant encoding of bits, which is achieved by the incorporation of black bursts. Besides revisiting black bursts and proposing measures to optimize their detection, robustness, and implementation on wireless sensor nodes, the first part of this thesis presents the mode of operation and time behavior of ACTP. In addition, possible applications of ACTP are illustrated, presenting solutions to well-known problems of distributed systems like leader election and data dissemination. Furthermore, results of experimental evaluations with customary wireless transceivers are outlined to provide evidence of the protocol's implementability and benefits.
In the second part of this thesis, the focus is shifted from concrete deterministic protocols to their model-driven development with the Specification and Description Language (SDL). Though SDL is well-established in the domain of telecommunication and distributed systems, the predictability of its implementations is often insufficient as previous projects have shown. To increase this predictability and to improve SDL's applicability to time-critical systems, real-time tasks, an approved concept in the design of real-time systems, are transferred to SDL and extended to cover node-spanning system tasks. In this regard, a priority-based execution and suspension model is introduced in SDL, which enables task-specific priority assignments in the SDL specification that are orthogonal to the static structure of SDL systems and control transition execution orders on design as well as on implementation level. Both the formal incorporation of real-time tasks into SDL and their implementation in a novel scheduling strategy are discussed in this context. By means of evaluations on wireless sensor nodes, evidence is provided that these extensions reduce worst-case execution times substantially, and improve the predictability of SDL implementations and the language's applicability to real-time systems.
Dennis Christmanndoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4112Fri, 03 Jul 2015 09:52:41 +0200On the History of Differential-Algebraic Equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4106
To write about the history of a subject is a challenge that grows with the number of pages as the original goal of completeness is turning more and more into an impossibility. With this in mind, the present article takes a very narrow approach and uses personal side trips and memories on conferences,
workshops, and summer schools as the stage for some of the most important protagonists and their contributions to the field of Differential-Algebraic Equations (DAEs).Bernd Simeonpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4106Tue, 23 Jun 2015 14:32:01 +0200A nonlocal sample dependence SDE-PDE system modeling proton dynamics in a tumor
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4104
A nonlocal stochastic model for intra- and extracellular proton dynamics in a tumor is proposed.
The intracellular dynamics is governed by an SDE coupled to a reaction-diffusion
equation for the extracellular proton concentration on the macroscale. In a more general context
the existence and uniqueness of solutions for local and nonlocal
SDE-PDE systems are established allowing, in particular, to analyze the proton dynamics model both,
in its local version and the case with nonlocal path dependence.
Numerical simulations are performed
to illustrate the behavior of solutions, providing some insights into the effects of randomness on tumor acidity. Peter E. Kloeden; Stefanie Sonner; Christina Surulescupreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4104Mon, 22 Jun 2015 15:00:13 +0200Coercive functions from a topological viewpoint and properties of minimizing sets of convex functions appearing in image restoration
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4100
Many tasks in image processing can be tackled by modeling an appropriate data fidelity term \(\Phi: \mathbb{R}^n \rightarrow \mathbb{R} \cup \{+\infty\}\) and then solve one of the regularized minimization problems \begin{align*}
&{}(P_{1,\tau}) \qquad \mathop{\rm argmin}_{x \in \mathbb R^n} \big\{ \Phi(x) \;{\rm s.t.}\; \Psi(x) \leq \tau \big\} \\ &{}(P_{2,\lambda}) \qquad \mathop{\rm argmin}_{x \in \mathbb R^n} \{ \Phi(x) + \lambda \Psi(x) \}, \; \lambda > 0 \end{align*} with some function \(\Psi: \mathbb{R}^n \rightarrow \mathbb{R} \cup \{+\infty\}\) and a good choice of the parameter(s). Two tasks arise naturally here: \begin{align*} {}& \text{1. Study the solver sets \({\rm SOL}(P_{1,\tau})\) and
\({\rm SOL}(P_{2,\lambda})\) of the minimization problems.} \\ {}& \text{2. Ensure that the minimization problems have solutions.} \end{align*} This thesis provides contributions to both tasks: Regarding the first task for a more special setting we prove that there are intervals \((0,c)\) and \((0,d)\) such that the setvalued curves \begin{align*}
\tau \mapsto {}& {\rm SOL}(P_{1,\tau}), \; \tau \in (0,c) \\ {} \lambda \mapsto {}& {\rm SOL}(P_{2,\lambda}), \; \lambda \in (0,d) \end{align*} are the same, besides an order reversing parameter change \(g: (0,c) \rightarrow (0,d)\). Moreover we show that the solver sets are changing all the time while \(\tau\) runs from \(0\) to \(c\) and \(\lambda\) runs from \(d\) to \(0\).
In the presence of lower semicontinuity the second task is done if we have additionally coercivity. We regard lower semicontinuity and coercivity from a topological point of view and develop a new technique for proving lower semicontinuity plus coercivity.
Dropping any lower semicontinuity assumption we also prove a theorem on the coercivity of a sum of functions.René Ciakdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4100Tue, 09 Jun 2015 15:50:38 +0200Exploration and Design of DC MEMS Switches for Integrated Self-x Sensory Systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4090
The advances in sensor technology have introduced smart electronic products with
high integration of multi-sensor elements, sensor electronics and sophisticated signal
processing algorithms, resulting in intelligent sensor systems with a significant level
of complexity. This complexity leads to higher vulnerability in performing their
respective functions in a dynamic environment. The system dependability can be
improved via the implementation of self-x features in reconfigurable systems. The
reconfiguration capability requires capable switching elements, typically in the form
of a CMOS switch or miniaturized electromagnetic relay. The emerging DC-MEMS
switch has the potential to complement the CMOS switch in System-in-Package as
well as integrated circuits solutions. The aim of this thesis is to study the feasibility
of using DC-MEMS switches to enable the self-x functionality at system level.
The self-x implementation is also extended to the component level, in which the
ISE-DC-MEMS switch is equipped with self-monitoring and self-repairing features.
The MEMS electrical behavioural model generated by the design tool is inadequate,
so additional electrical models have been proposed, simulated and validated. The
simplification of the mechanical MEMS model has produced inaccurate simulation
results that lead to the occurrence of stiction in the actual device. A stiction conformity
test has been proposed, implemented, and successfully validated to compensate
the inaccurate mechanical model. Four different system simulations of representative
applications were carried out using the improved behavioural MEMS model, to
show the aptness and the performances of the ISE-DC-MEMS switch in sensitive
reconfiguration tasks in the application and to compare it with transmission gates.
The current design of the ISE-DC-MEMS switch needs further optimization in terms
of size, driving voltage, and the robustness of the design to guarantee high output
yield in order to match the performance of commercial DC MEMS switches.Muhammad Akmal bin Johardoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4090Wed, 03 Jun 2015 15:30:52 +0200Upscaling Approaches for Nonlinear Processes in Lithium-Ion Batteries
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4086
Lithium-ion batteries are broadly used nowadays in all kinds of portable electronics, such as laptops, cell phones, tablets, e-book readers, digital cameras, etc. They are preferred to other types of rechargeable batteries due to their superior characteristics, such as light weight and high energy density, no memory effect, and a big number of charge/discharge cycles. The high demand and applicability of Li-ion batteries naturally give rise to the unceasing necessity of developing better batteries in terms of performance and lifetime. The aim of the mathematical modelling of Li-ion batteries is to help engineers test different battery configurations and electrode materials faster and cheaper. Lithium-ion batteries are multiscale systems. A typical Li-ion battery consists of multiple connected electrochemical battery cells. Each cell has two electrodes - anode and cathode, as well as a separator between them that prevents a short circuit.
Both electrodes have porous structure composed of two phases - solid and electrolyte. We call macroscale the lengthscale of the whole electrode and microscale - the lengthscale at which we can distinguish the complex porous structure of the electrodes. We start from a Li-ion battery model derived on the microscale. The model is based on nonlinear diffusion type of equations for the transport of Lithium ions and charges in the electrolyte and in the active material. Electrochemical reactions on the solid-electrolyte interface couple the two phases. The interface kinetics is modelled by the highly nonlinear Butler-Volmer interface conditions. Direct numerical simulations with standard methods, such as the Finite Element Method or Finite Volume Method, lead to ill-conditioned problems with a huge number of degrees of freedom which are difficult to solve. Therefore, the aim of this work is to derive upscaled models on the lengthscale of the whole electrode so that we do not have to resolve all the small-scale features of the porous microstructure thus reducing the computational time and cost. We do this by applying two different upscaling techniques - the Asymptotic Homogenization Method and the Multiscale Finite Element Method (MsFEM). We consider the electrolyte and the solid as two self-complementary perforated domains and we exploit this idea with both upscaling methods. The first method is restricted only to periodic media and periodically oscillating solutions while the second method can be applied to randomly oscillating solutions and is based on the Finite Element Method framework. We apply the Asymptotic Homogenization Method to derive a coupled macro-micro upscaled model under the assumption of periodic electrode microstructure. A crucial step in the homogenization procedure is the upscaling of the Butler-Volmer interface conditions. We rigorously determine the asymptotic order of the interface exchange current densities and we perform a comprehensive numerical study in order to validate the derived homogenized Li-ion battery model. In order to upscale the microscale battery problem in the case of random electrode microstructure we apply the MsFEM, extended to problems in perforated domains with Neumann boundary conditions on the holes. We conduct a detailed numerical investigation of the proposed algorithm and we show numerical convergence of the method that we design. We also apply the developed technique to a simplified two-dimensional Li-ion battery problem and we show numerical convergence of the solution obtained with the MsFEM to the reference microscale one. Vasilena Taralovadoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4086Thu, 28 May 2015 09:01:35 +0200