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Given a finite or countably infinite family of Hilbert spaces \((H_j)_{j\in N} \), we study the Hilbert space tensor product \(\bigotimes_{j\in N} H_j\). In the general case, these tensor products were introduced by John von Neumann. We are especially interested in the case where each Hilbert space \(H_j\) is given as a reproducing kernel Hilbert space, i.e., \(H_j = H(K_j)\) for some reproducing kernel \(K_j\). We establish the following result, which is new for the case of N being infinite: If we restrict the domains of the kernels \(K_j\) properly, their pointwise product \(K\) is again a reproducing kernel, and
\[
H(K) \cong \bigotimes_{j\in N} H_j\,
\]
i.e., there is an isometric isomorphism between both spaces respecting the tensor product structure.
Industry 4.0 defines the organization of production and manufacturing processes based on technological advanced solutions and devices autonomously communicating with each other.
Within the context of this industrial revolution, the smart reconfigurable manufacturing systems are introduced. These systems shall be able to provide a dynamic level of reconfigurability based on the production demand and system availability. The introduction of the manufacturing reconfigurability constitutes a particularly important and expensive decision for the organizations and therefore scoping methods are becoming constantly essential.
The present work covers a first approach to defining reconfigurability methods and drivers for the manufacturing systems within the context of Industry 4.0. The thesis introduces five main reconfigurability use case scenarios for manufacturing systems and the description of a two – dimensional model of scoping parameters.
The first dimension is based on the potential business targets and reconfigurability drivers, while the second dimension focuses on the system functions and technologies, which are
required for the successful realization of the reconfigurability use case scenarios. Finally, the thesis concludes with a brief comparison between the traditional software product line scoping approach and purposed scoping method for the reconfigurability of manufacturing systems.
Cutting-edge cancer therapy involves producing individualized medicine for many patients at the same time. Within this process, most steps can be completed for a certain number of patients simultaneously. Using these resources efficiently may significantly reduce waiting times for the patients and is therefore crucial for saving human lives. However, this involves solving a complex scheduling problem, which can mathematically be modeled as a proportionate flow shop of batching machines (PFB). In this thesis we investigate exact and approximate algorithms for tackling many variants of this problem. Related mathematical models have been studied before in the context of semiconductor manufacturing.
Industries use software product lines as a solution to the ever-increasing variety-rich customer requirements for the software products. In order to realize the variability in the product line, several variability realization techniques are used, of which, conditional compilation and execution are more frequently used in practice. This is not without its challenges.
As the product line evolves in space and time, several versions of products are released, thereby increasing the complexity of variability code in an uncontrolled manner. In most cases, there exists no explicit variability model to provide important configuration knowledge, or the variability model and variability code do not synchronize with each other, e.g. important dependencies from the code realizations are not reflected in the variability model. When the domain experts leave the company, the product configuration knowledge will be lost. New employees will have to be trained on the domain knowledge and are left with the herculean task of tracking the code changes in the variability code for the different versions. They also have to understand the variability code to analyze the impact of code changes and how to adapt them. Overall, that lack of explicit and sound configuration knowledge results in higher efforts during the product configuration and quality assurance. Hence, industries are interested in recovering configuration knowledge via semi-automated analyses of the variability code and the existing product configurations.
This Master’s thesis investigates the various approaches that can be followed in order to recover existing configuration knowledge. It is an extension of the previous research works on the VITAL approach conducted at TU Kaiserslautern and Fraunhofer IESE. The focus of this research will be the solution space, i.e., the variability realization through variability code mechanisms like conditional compilation/execution. The goal is to analyze the preprocessor directives or respective constructs in programming languages, study respective state of the art advances in recent years and enhance the VITAL analysis method and tool. In particular, identification of configuration parameters, their values and ranges, the constraints and nesting between one parameter to the other are the primary objectives of the research. As secondary goals, visualization of the identified product configuration knowledge in the existing tool and optimization of the algorithms present in the tool will be implemented from the results of the primary goals. For the research, open source libraries and applications will be identified and used for analysis. The work will be guided by real world industrial settings.
In product line engineering tasks, the need for merging models from different product
variants emerges as the commonly used clone-and-own approach suffers from high
maintenance costs in the long run. By identifying models with a high number of similarities
we can merge them to one highly reusable model. This approach will increase the
maintainability, and further expandability of the model.
Already many works have been published aiming to solve this problem with different
N-way model Matching approaches. However, there is lack of practical evidence that the
published theories work as designed in real world cases.
In this work, we will evaluate relevant published approaches and then attempt to
integrate the most promising one in the product line analysis framework VARIOUS from
Fraunhofer IESE. Next, the implemented approach will be evaluated in comparison to the
existing mechanism for model matching that VARIOUS integrates that is called "System
Aligner". The main aspects of our evaluation are:
• Accuracy - Can it accurately find the most similar models?
• Performance - How fast is it?
• Scalability - How well does it scale in large amount of input models?
• Configurability - Can it be adapted easily for different systems?
In recent months, sustainable development and the achievement of the United Nations Sus- tainable Development Goals has gained unprecedented prominence. SDG 7 aspires to achieve access to electricity for the entire world population by 2030 and - at the same time - to significantly increase the share of renewable energy in the power mix. This target trans- lates into ambitious electricity supply and renewable energy asset growth scenarios for Sub- Saharan Africa, the least developed region worldwide. Though theoretical renewable energy potential is abundant and capital generally available, progress has been slow. Aside funds from donors and Development Finance Institutions, private commercial capital is required to accelerate the progress. Project Finance has successfully attracted private funds for renew- able energy assets in other jurisdictions but has played a negligible role in the energy tran- sition in Sub-Saharan Africa. A variety of reasons are identified that impede their implemen- tation, which are categorised into (i) unsatisfactory project pre-requisites and preparation, (ii) challenging host country conditions, (iii) elevated non-financial project risks and (iv) risky financial transaction structures. While a review of potential mitigation measures reveals that the risk factors are theoretically addressable, most require a multi-stakeholder alignment and exhibit some implementation complexity. Putting them into practice will therefore take time and will require a high level of commitment from host governments, sponsors, and fi- nancial institutions. While pressure and urgency are mounting, time will tell whether the pro- ject parties are more successful going forward.
On the one hand, Model-based Systems and Software Engineering approaches ease the development of complex software systems. On the other, they introduce the challenge of managing the multitude of different artifacts created using various tools during the system lifecycle. For understanding and maintaining these artifacts as they evolve, it is advisable to establish traceability among them. Traceability is the ability to relate the various artifacts created and evolved during the project. However, organizations often consider traceability a burden because it is time-consuming and error-prone when done manually. Hence, the objective of this thesis is to research and develop pragmatic traceability approaches that can be followed in the MBSE context. A systematic mapping study was conducted to understand and compile the various criteria that need to be followed while creating and maintaining trace links. It also provided insights on the approaches followed to ease the burden on engineers. Expert interviews with industrial companies were conducted to investigate the real-life experiences of engineers on traceability, to get an overview of best practices and known pitfalls. Based on the mapping study and the results of the interviews, various approaches and tools used to achieve traceability were discussed. A case study was conducted for state-of-the-practice traceability approaches in a toolchain consisting of Polarion, Enterprise Architect, and Doxygen. For research, open-source libraries and applications were used for analysis. A tool prototype was developed to create and maintain trace links between artifacts created in the toolchain mentioned above. The use cases in which the tool eases achieving traceability are discussed along with pros and cons.
Optimal control of partial differential equations is an important task in applied mathematics where it is used in order to optimize, for example, industrial or medical processes. In this thesis we investigate an optimal control problem with tracking type cost functional for the Cattaneo equation with distributed control, that is, \(\tau y_{tt} + y_t - \Delta y = u\). Our focus is on the theoretical and numerical analysis of the limit process \(\tau \to 0\) where we prove the convergence of solutions of the Cattaneo equation to solutions of the heat equation.
We start by deriving both the Cattaneo and the classical heat equation as well as introducing our notation and some functional analytic background. Afterwards, we prove the well-posedness of the Cattaneo equation for homogeneous Dirichlet boundary conditions, that is, we show the existence and uniqueness of a weak solution together with its continuous dependence on the data. We need this in the following, where we investigate the optimal control problem for the Cattaneo equation: We show the existence and uniqueness of a global minimizer for an optimal control problem with tracking type cost functional and the Cattaneo equation as a constraint. Subsequently, we do an asymptotic analysis for \(\tau \to 0\) for both the forward equation and the aforementioned optimal control problem and show that the solutions of these problems for the Cattaneo equation converge strongly to the ones for the heat equation. Finally, we investigate these problems numerically, where we examine the different behaviour of the models and also consider the limit \(\tau \to 0\), suggesting a linear convergence rate.
Model Identification of Power Electronic Systems for Interaction Studies and Small-Signal Analysis
(2023)
The rapid growth in offshore wind brings various challenges to power system research
and industry, such as the development of multi-terminal multi-vendor HVDC grids.
To ensure interoperability in those power converter dominated systems, suitable
models are needed to efficiently perform stability and interaction studies. With
state-space based small-signal methods stability and interaction phenomena can be
assessed globally for a complex system. Yet detailed models are needed. However,
in multi-vendor projects most likely only black-boxed models will be available to
protect the intellectual property, so that identification techniques are necessary to
obtain suitable models. This thesis contributes to the research activities on statespace
model identification of black-boxed power electronic systems.
In the first part of the thesis, a method was developed and tested, where the matrix
elements of linearized state-space models were fitted in dependency of the operating
point, based on input sweeps performed on the model of a grid forming power converter
controlled as a virtual synchronous machine. It was discussed how changes in
multiple inputs can be approximated by the superposition of the individual input
dependencies and a fully operating point dependent state-space model approximation
was created. The results were validated in time and frequency domain analyses.
It was found that the method can provide a good approximation, especially for the
operating range around the default operating point.
In the second part, identification of a power electronic system was performed based
on measurement data which was generated experimentally from a low voltage laboratory
system. A sequence of input perturbations was applied to the laboratory
system and frequency response data was calculated from the corresponding output
perturbations. The data served as basis for model identification with N4SID and a
soon to be published vector fitting method. The identified models were validated by
a visual inspection of the transfer function and by comparison of the calculated step
responses to the step responses measured in the laboratory. It was found that the
treatment of incomplete data sets, the generation of substitute data and the impact
of time delays on the identification might be worth further investigation.
This work provides a valuable contribution to the research of state-space model
identification of black-boxed power electronic systems. It points out challenges and
presents promising approaches to enable state-space based methods for stability
analysis and interaction studies in future multi-terminal multi-vendor HVDC grids.
Synapses are connections between different nerve cells that form an essential link in neural signal transmission. It is generally distinguished between electrical and chemical synapses, where chemical synapses are more common in the human brain and are also the type we deal with in this work.
In chemical synapses, small container-like objects called vesicles fill with neurotransmitter and expel them from the cell during synaptic transmission. This process is vital for communication between neurons. However, to the best of our knowledge no mathematical models that take different filling states of the vesicles into account have been developed before this thesis was written.
In this thesis we propose a novel mathematical model for modeling synaptic transmission at chemical synapses which includes the description of vesicles of different filling states. The model consists of a transport equation (for the vesicle growth process) plus three ordinary differential equations (ODEs) and focuses on the presynapse and synaptic cleft.
The well-posedness is proved in detail for this partial differential equation (PDE) system. We also propose a few different variations and related models. In particular, an ODE system is derived and a delay differential equation (DDE) system is formulated. We then use nonlinear optimization methods for data fitting to test some of the models on data made available to us by the Animal Physiology group at TU Kaiserslautern.