Refine
Document Type
- Doctoral thesis (19)
- Report (3)
- Habilitation thesis (1)
- Working paper (1)
Has Fulltext
- yes (24)
Is part of the Bibliography
- no (24)
Year of publication
Keywords
- Optimierung (24) (remove)
Institute
- FG Technische Mechanik und Fahrzeugdynamik (8)
- FG Ingenieurmathematik und Numerik der Optimierung (3)
- FG Wirtschaftsmathematik (3)
- FG Energieverteilung und Hochspannungstechnik (2)
- FG Aufbereitungstechnik und Sekundärrohstofftechnologie (ehemals) (1)
- FG Diskrete Mathematik und Grundlagen der Informatik (1)
- FG Optimale Steuerung (1)
- FG Programmiersprachen und Compilerbau (1)
- FG Prozess- und Anlagentechnik (1)
- FG Sicherheit in pervasiven Systemen (1)
This thesis summarizes the author’s developments of combustion models and multi-objective optimization methods for gasoline and diesel engines. The combustion models belong to the family of zero-dimensional stochastic reactor models introduced in the 1990s to improve the prediction of emissions with detailed chemistry in partially stirred reactors.
The first part introduces the fundamentals of the physical and chemical models describing the combustion process. As a novelty, k−ε turbulence models were implemented in the stochastic reactor model to predict the turbulent time and length scales in gasoline and diesel engines. This development allowed an improvement of the models for convective heat transfer, fuel evaporation, gas exchange across the valves, turbulent flame propagation and crevice flow, which depend on the turbulent time and length scales.
In the second part, the multi-objective optimization platform for automatic training of the stochastic reactor model is presented. The optimization method considers multiple operating points to find a set of model parameters that predict performance and emissions over the entire engine map. The Non-domination Sorting Genetic Algorithm II is combined with the stochastic reactor model and response surface models to find the best Pareto front. Multi-criteria decision making is used to select the best designs from the Pareto front.
Finally, the third part of this thesis deals with the validation of the stochastic reactor model and the multi-objective optimization platform. For this purpose, experiments of two single-cylinder research engines with spark ignition, one passenger car engine with compression ignition and one heavy duty engine with compression ignition are used. For the spark ignition engines, a set of model parameters was found that predicts well the power and emissions over the whole engine map. The calculated turbulent kinetic energy, dissipation, and angular momentum follow the trends of the three-dimensional computational fluid dynamic simulations to a good approximation for various operating points. For the two compression ignition engines, the prediction of combustion progress and nitrogen oxide emissions are in good agreement with the experiments. Larger discrepancies were found for the prediction of carbon monoxide and unburned hydrocarbon. Optimization of the soot model parameters improves the prediction of soot mass for operating points throughout the engine map.
Mit Hilfe der Constraint-Programmierung können komplexe, häufig NP-vollständige Probleme, wie zum Beispiel Graphfärbungs-, Optimierungs-, Konfigurations- sowie Schichtplanungs-, Raum- und Zeitplanungsprobleme modelliert und gelöst werden. Im Vordergrund der Constraint-Programmierung steht dabei die deklarative Modellierung, also eine Beschreibung des eigentlichen Problems und nicht dessen Lösungsvorgangs. Während es Aufgabe des Entwicklers ist, das Problem zu modellieren, wird die Lösung einem separat implementierten Solver (Löser) überlassen. Im Idealfall löst dieser Solver das Problem, unabhängig von der konkreten Modellierung, immer schnellstmöglich.
In der Praxis kann von diesem Idealfall in der Regel nicht ausgegangen werden und somit hat die Art und Weise der Modellierung ein und desselben Problems und dessen Remodellierung teilweise einen erheblichen Einfluss auf die Lösungsgeschwindigkeit. Bisher bestehende Remodellierungsverfahren transformieren entweder Constraint-Probleme im Ganzen (zum Beispiel beim Umwandeln in SAT- oder binäre Constraint-Probleme) oder erfordern eine präzise Angabe und Steuerung seitens des Nutzers der Constraint-Programmierung (zum Beispiel bei der Tabularisierung). Während die erste Variante in der Regel nur bei sehr speziellen Problemen zu einer Beschleunigung des Lösungsvorganges führt, benötigt die zweite Variante vom Constraint-Modellierer zusätzliches Expertenwissen über das Lösungsverfahren des verwendeten Solvers. Die bisherigen Verfahren erlauben somit keine (voll)-automatisierte Transformation von Constraint-Problemen, bei der Transformationen nur durchgeführt werden, wenn diese auch zu einer Beschleunigung führen.
Für das dieser Arbeit übergeordnete Ziel der automatisierten Optimierung von Constraint-Problemen mittels Remodellierung, ohne dass dafür zusätzliches Expertenwissen notwendig ist, werden ausreichend viele verschiedene, gute und gut untersuchte Remodellierungen benötigt. In dieser Arbeit werden daher sowohl bestehende Verfahren für die Transformation von Constraint-Problemen weiterentwickelt, als auch völlig neue entworfen und deren Korrektheit nachgewiesen. Die in dieser Arbeit entwickelten Transformationen werden bezüglich ihrer beschleunigenden Wirkung auf Constraint-Probleme untersucht. Anhand von generierten und von realen Praxisbeispielen wird die Wirksamkeit der Transformationen evaluiert und es werden Schlussfolgerungen darüber gezogen, wann welche Substituierungen besonders vielversprechend sind.
A cellular approach to optimize the integration of renewable generation into distribution networks
(2022)
The steady growth of the renewable-based technologies in the last twenty years has changed the character of the power systems significantly. Until today, there are more than 112 GW installed photovoltaic and wind parks in Germany and around 90% of the installed renewable generators are integrated into distribution networks. As a result, distribution networks are often facing congestion problems and more investments are needed for the required network development plans.
The political decisions in Germany for increasing the share of renewables in electricity consumption up to 65% until 2030 and the nuclear phase out until 2022 and further shutdowns of the coal power plants raised serious concerns about the reliability of power supply and feasibility of the transition plan.
The present dissertation has a look over the recent developments and offers a methodology for reduction of the resulted costs from further integration of renewable generators into the distribution networks. The suggested methodology is based on a cellular approach and helps also to postpone the unnecessary costly network expansions. Furthermore, it helps to integrate the renewable generators in an optimized way which has an added value to move towards the defined sustainability goals.
The proposed methodology has two steps. The first step is made up of the cellular approach and grey wolf optimization in MATLAB environment. In this step, the optimal combination of technologies for fulfillment of the defined goals are found out. The second step consists of the quasi dynamic simulations in PowerFactory environment. In this step, the suggested results from MATLAB optimization are investigated in semi-real situations. With the quasidynamic simulations, it is checked whether the results are tolerable from the point of view of network operation and whether it is possible to facilitate the network operation with certain strategies.
This thesis is concerned with the phenomenon of implicit variables in optimization theory. Roughly speaking, a variable is called implicit whenever it is used to model the feasible set but does not appear in the objective function. At the first glance, such variables seem to be less relevant for the purpose of optimization.
First, we provide a theoretical study on optimization problems with implicit variables. Therefore, we rely on a model program which covers several interesting problem classes from optimization theory such as bilevel optimization problems, evaluated multiobjective optimization problems, or optimization problems with cardinality constraints. We start our analysis by clarifying that the interpretation of implicit variables as explicit ones induces additional local minimizers. Afterwards, we study three reasonable stationarity systems of Mordukhovich-stationarity-type for the original problem as well as some comparatively weak associated constraint qualifications. The obtained results are applied to the three example classes mentioned above.
Second, we introduce switching- and or-constrained optimization problems. Exploiting the observation that each or-constrained optimization problem can be transferred into a switching-constrained optimization problem with the aid of slack variables, one can interpret or-constrained programs as optimization problems comprising implicit variables. Necessary optimality conditions and constraint qualifications for both problem classes are derived. Furthermore, some approaches for the numerical solution of both problem classes are discussed and results of computational experiments are presented. The shortcomings of implicit variables are highlighted in terms of or-constrained optimization.
Third, we study three different scenarios where optimality conditions and constraint qualifications for challenging optimization problems can be constructed while abstaining from the introduction of implicit variables. We start by deriving a generalized version of the linear independence constraint qualification as well as second-order necessary and sufficient optimality conditions for so-called disjunctive optimization problems, which cover several interesting but inherently irregular problem classes like mathematical programs with complementarity, switching, or-, and cardinality constraints. Afterwards, we exploit several different single-level reformulations of standard bilevel optimization problems in order to find first- and second-order sufficient optimality conditions. Finally, we study sequential stationarity and regularity conditions for nonsmooth mathematical problems with generalized equation constraints with the aid of the popular limiting variational analysis. The investigated model problem covers the one we use for the theoretical analysis of implicit variables.
In recent years parcel volumes reached record highs. The logistics industry is seeking new innovative concepts to keep pace. For densely populated areas delivery robots are a promising alternative to conventional trucking. These electric robots drive autonomously on sidewalks and deliver urgent goods, such as express parcels, medicine, or meals. The limited cargo space and battery capacity of these vehicles necessitates a depot visit after each customer served. The problem can be formulated as an electric vehicle routing problem with soft time windows and a single unit capacity. The goal is to serve all customers such that the quadratic sum of delays is minimized and each vehicle operates within its battery bounds. To solve this problem, we formulate an MIQP and present an expanded formulation based on a layered graph. For this layered graph we derive two solution approaches based on relaxations, which use less nodes and arcs. The first, Iterative Refinement, always solves the current relaxation to optimality and refines the graph if the solution is not feasible for the expanded formulation. This is repeated until a proven optimal solution is found. The second, Branch and Refine, integrates the graph refinement into a branch and bound framework avoiding restarts. Computational experiments performed on modified Solomon instances demonstrate the advantage of using our solution approaches and show that Branch and Refine outperforms Iterative Refinement in all studied parameter configurations.
Beschleunigung der Verdichterkennfeldberechnung mithilfe von Methoden des maschinellen Lernens
(2021)
In der heutigen Triebwerksentwicklung ist die Verwendung komplexer und zeitaufwändiger numerischer Strömungssimulationsverfahren (3D-CFD) unerlässlich. Dies gilt auch und insbesondere für den Bereich der Verdichterkennfeldberechnung, welcher viele zeitintensive 3D-CFD Berechnungen benötigt. Dabei sind zur qualitativen Beurteilung eines Verdichterentwurfs sowohl Betriebspunkte wie, Reiseflug, Start und Landung, hinreichend genau abzubilden, als auch die kritischen, den Verdichterarbeitsbereich limitierenden Betriebsgrenzen Pumpen und Sperren zu detektieren. Bisherige Arbeiten zur automatisierten Verdichterkennfeldberechnung basieren auf strukturierten Berechnungen von verschiedenen Drehzahllinien, auf welchen jeweils isoliert Pump- und Sperrgrenze gesucht werden. Durch die Beschränkung auf einzelne Drehzahlen wird jedoch nicht der gesamte Charakter des Kennfeldes erfasst, so dass unbekannte Betriebsbereiche aus linearer Interpolation abgeleitet werden müssen. Ein zusätzlicher Nachteil solcher auf einzelne Drehzahllinien fixierten Methoden ist ihre geringe Parallelisierbarkeit.
Der Fokus dieser Arbeit liegt daher auf der Entwicklung eines effizienten Verfahrens zur Erfassung des gesamten Verdichterkennfeldes. Die zwei wesentlichen Anforderungen an das Verfahren sind erstens die Reduktion der Anzahl der notwendigen CFD-Berechnungen zur hinreichend genauen Beschreibung des Verdichterkennfeldes sowie zweitens die Beschleunigung jeder einzelnen 3D-CFD-Berechnung. Zu diesem Zweck wird zur Kennfeldberechnung eine Strategie vorgeschlagen, welche sich von der üblichen strukturierten Berechnung einzelner Drehzahllinien löst und stattdessen mit unstrukturierten, zufällig bestimmte Stützstellen arbeitet. Dabei wird ein zweiphasiges Verfahren entwickelt, bei dem zunächst die Pump- und Sperrlinien in ihrer Gesamtheit mit einer iterativen, hoch parallelisierbaren, auf Support-Vector-Machine beruhenden Strategie bestimmt werden. Als nächster Schritt wird mit Methoden der statistischen Versuchsplanung eine ausreichende Dichte von Stützstellen innerhalb der Betriebsgrenzen des Verdichters generiert. Abschließend werden auf Basis aller verwendeten Stützstellen Antwortflächen für Verdichterdruckverhältnis, Wirkungsgrad und Eintrittsmassenstrom aufgebaut.
Zur Reduktion der Rechenzeit jeder einzelnen 3D-CFD Rechnung werden unterschiedliche Methoden zur Erzeugung von Startlösungen betrachtet. In diesem Rahmen werden Initialisierungsansätze aus reduzierten Strömungsmodellen und aus der Superposition von bereits bekannten Strömungslösungen auf Basis der Methode der Proper-Orthogonal-Decomposition (POD) untersucht.
Als Validierung wird abschließend das entwickelte Verfahren zur Kennfeldberechnung in Kombination mit dem POD-Initialisierungsansatz erfolgreich auf die Analyse eines 4.5- stufigen Forschungsverdichters angewendet.
We formulate the mission planning problem for a meet of unmanned aerial vehicles (UAVs) as a mixed-integer nonlinear programming problem (MINLP). The problem asks for a selection of targets from a list to the UAVs, and trajectories that visit the chosen targets. To be feasible, a trajectory must pass each target at a desired maximal distance and within a certain time window, obstacles or regions of high risk must be avoided, and the fuel limitations must be obeyed. An optimal trajectory maximizes the sum of values of all targets that can be visited, and as a secondary goal, conducts the mission in the shortest possible time. In order to obtain numerical solutions to this model, we approximate the MINLP by a mixed-integer linear program (MILP), and apply a state-of-the-art solver (GUROBI) to the latter on a set of test instances.
We deal with a very complex and hard scheduling problem. Several types of products are processed by a heterogeneous resource set, where resources have different operating capabilities and setup times are considered. The processing of the products follows different workflows, allowing also assembly lines. The goal is to process all products in minimum time, i.e., the makespan is to be minimized. Because of the complexity of the problem an exact solver would require too much running time. We propose a compound method where a heuristic is combined with an exact solver. Our proposed heuristic is composed of several phases applying different smart strategies. In order to reduce the computational complexity of the exact approach, we exploit the makespan determined by the heuristic as an upper bound for the time horizon, which has a direct in uence on the instance size used in the exact approach. We demonstrate the efficiency of our combined method on multiple problem classes. With the help of the heuristic the exact solver is able to obtain an optimal solution in a much shorter amount of time.
This thesis is concerned with stochastic models to manage financial risks. The first part deals with market risk and considers an investor facing a classical portfolio problem of optimal investment in log-Brownian stocks and a fixed-interest bond, but constrained to choose portfolio and consumption strategies which reduce the corresponding shortfall risk. Risk limits are formulated in terms of Value at Risk, Tail Conditional Expectation and Expected Loss and are dynamically imposed on the strategy as a risk constraint. The resulting stochastic optimal control problem is tackled using the dynamic programming approach. For both continuous-time and discrete-time financial markets the loss in expected utility of intermediate consumption and terminal wealth caused by imposing a dynamic risk constraint is investigated. The presented numerical results indicate that the loss of portfolio performance is not too large while the risk is notably reduced. Furthermore, the loss resulting from infrequent trading due to time discretization effects is typically bigger than the loss of portfolio performance resulting from imposing a risk constraint.
The second part deals with credit risk and sets up a first-passage model of corporate default risk. The default event is specified in terms of the evolution of the total value of the firm's asset and the default barrier. Short-term default risk is incorporated by modeling the default barrier at which the firm is liquidated as a random variable which is time-dependent and allowed to switch. This setup combines the two classical modeling approaches and enables to model changes in the economy or the appointment of a new firm management. Different information levels on the firm's assets are distinguished and explicit formulas for the conditional default probability given the accessible information are derived. The impact of asymmetric information on the default probability and credit yield spread is investigated. Numerical results are presented indicating that the information on the firm value has a considerable impact on the estimate of the conditional survival probability and the associated credit yield spread.
For many countries, gasturbine technology is one of the key technologies for the reduction of climate-damaging pollutant emissions. The profitability of such facilities, however, is highly dependent on the price for the utilized fossil fuel, which is why there is a constant need for increased efficiency. The potential of increasing the efficiency of the individual components is basically limited by factors which will reduce operating life. The goal of this thesis is to develop methods for improved automated structural design optimization, which shall be developed on the basis of compressor airfoils. Special attention is payed to avoid the excitation of failure critical eigenmodes by detecting them automatically. This is achieved by introducing a method based on self-organizing neural networks which enables the projection of eigenmodes of arbitrary airfoil geometries onto standard surfaces, thereby making them comparable. Another neural network is applied to identify eigenmodes which have been defined as critical for operating life. The failure rate of such classifiers is significantly reduced by introducing a newly developed initialization method based on principle components. A structural optimization is set up which shifts the eigenfrequency bands of critical modes in such a way that the risk of resonance with engine orders is minimized. In order to ensure practical relevance of optimization results, the structural optimization is coupled with an aerodynamic optimization in a combined process. Conformity between the loaded hot-geometry utilized by the aerodynamic design assessment and the unloaded cold-geometry utilized by the structural design assessment is ensured by using loaded-to-unloaded geometry transformation. Therefor an innovative method is introduced which, other than the established time-consuming iterative approach, uses negative density for a direct transformation taking only a few seconds, hence, making it applicable to optimization. Additionally, in order for the optimal designs to be robust against manufacturing variations, a method is developed which allows to assess the maximum production tolerance of a design from which onwards possible design variations are likely to violate design constraints. In contrast to the usually applied failure rate, the production tolerance is a valid requirement for suppliers w.r.t.~expensive parts produced in low-quantity, and therefore is a more suitable optimization objective.