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Nach Stand von Wissenschaft und Technik werden Komponenten hinsichtlich ihrer Eigenschaften, wie Lebensdauer oder Energieeffizienz, optimiert. Allerdings können selbst hervorragende Komponenten zu ineffizienten oder instabilen Systemen führen, wenn ihr Zusammenspiel nur unzureichend berücksichtigt wird. Eine Systembetrachtung schafft ein größeres Optimierungspotential - dem erhöhten Potential steht jedoch auch ein erhöhter Komplexitätsgrad gegenüber. Die vorliegende Arbeit ist im Rahmen des Sonderforschungsbereichs 805 entstanden, dessen Ziel die Beherrschung von Unsicherheit in Systemen des Maschinenbaus ist. Die Arbeit zeigt anhand eines realen Systems aus dem Bereich der Hydraulik, wie Unsicherheit in der Entwicklungsphase beherrscht werden kann. Hierbei ist neu, dass die durch den späteren Betrieb zu erwartende Systemdegradation eines jeden möglichen Systemvorschlags antizipiert werden kann. Dadurch können Betriebs- und Wartungskosten vorausgesagt und minimiert werden und durch eine optimale Betriebs- und Wartungsstrategie die Verfügbarkeit des Systems garantiert werden. Wesentliche Fragen bei der optimalen Auslegung des betrachteten hydrostatischen Getriebes sind dessen physikalische Modellierung, die Darstellung des Optimierungsproblems als gemischt-ganzzahliges lineares Programm, und dessen algorithmische Behandlung zur Lösungsfindung. Hierzu werden Heuristiken zum schnelleren Auffinden sinnvoller Systemtopologien vorgestellt und mittels mathematischer Dekomposition eine Bewertung des dynamischen Verschleiß- und Wartungsverlaufs möglicher Systemvorschläge vorgenommen. Die Arbeit stellt die Optimierung technischer Systeme an der Schnittstelle von Mathematik, Informatik und Ingenieurwesen sowohl gründlich als auch anschaulich und nachvollziehbar dar.
Finding a good system topology with more than a handful of components is a
highly non-trivial task. The system needs to be able to fulfil all expected load cases, but at the
same time the components should interact in an energy-efficient way. An example for a system
design problem is the layout of the drinking water supply of a residential building. It may be
reasonable to choose a design of spatially distributed pumps which are connected by pipes in at
least two dimensions. This leads to a large variety of possible system topologies. To solve such
problems in a reasonable time frame, the nonlinear technical characteristics must be modelled
as simple as possible, while still achieving a sufficiently good representation of reality. The
aim of this paper is to compare the speed and reliability of a selection of leading mathematical
programming solvers on a set of varying model formulations. This gives us empirical evidence
on what combinations of model formulations and solver packages are the means of choice with the current state of the art.
The UN sets the goal to ensure access to water and sanitation for all people by 2030. To address this goal, we present a multidisciplinary approach for designing water supply networks for slums in large cities by applying mathematical optimization. The problem is modeled as a mixed-integer linear problem (MILP) aiming to find a network describing the optimal supply infrastructure. To illustrate the approach, we apply it on a small slum cluster in Dhaka, Bangladesh.
Dieses Lehrbuch vermittelt die Grundlagen der Wärmeübertragung sowie den Umgang mit EXCEL-VBA von der Erstellung von Makros bis zu benutzerdefinierten Funktionen. Es legt damit eine Basis für die schnelle und professionelle Durchführung von Berechnungen und Simulationen. Die angeleitete Erstellung von Berechnungsmodulen mit EXCEL und VBA aus allen wichtigen Bereichen der Wärmeübertragung bildet den inhaltlichen Schwerpunkt. Dazu zählen die stationäre Wärmeleitung und der stationäre Wärmedurchgang, die instationäre Wärmeleitung, der Wärmeübergang bei freier und erzwungener Konvektion sowie die Wärmestrahlung und der Wärmeübergang beim Kondensieren und Sieden. Soweit sinnvoll und möglich werden die Stoffwertekorrelationen und die Berechnungsvorschriften aus dem VDI-Wärmeatlas verwendet. Für ausgewählte Anwendungen werden zudem komplexere Auslegungen und Simulationen von Prozessen der Wärmeübertragung sowie von Wärmeübertragern erstellt. Die Zielgruppen: Studierende in Bachelor- und Masterstudiengängen, Praktiker im Engineering
The energy-efficiency of technical systems can be improved by a systematic design approach. Technical Operations Research (TOR) employs methods known from Operations Research to find a global optimal layout and operation strategy of technical systems. We show the practical usage of this approach by the systematic design of a decentralized water supply system for skyscrapers. All possible network options and operation strategies are modeled by a Mixed-Integer Nonlinear Program. We present the optimal system found by our approach and highlight the energy savings compared to a conventional system design.
The overall energy efficiency of ventilation systems can be improved by considering not only single components, but by considering as well the interplay between every part of the system. With the help of the method "TOR" ("Technical Operations Research"), which was developed at the Chair of Fluid Systems at TU Darmstadt, it is possible to improve the energy efficiency of the whole system by considering all possible design choices programmatically. We show the ability of this systematic design approach with a ventilation system for buildings as a use case example.
Based on a Mixed-Integer Nonlinear Program (MINLP) we model the ventilation system. We use binary variables to model the selection of different pipe diameters. Multiple fans are model with the help of scaling laws. The whole system is represented by a graph, where the edges represent the pipes and fans and the nodes represents the source of air for cooling and the sinks, that have to be cooled. At the beginning, the human designer chooses a construction kit of different suitable fans and pipes of different diameters and different load cases. These boundary conditions define a variety of different possible system topologies. It is not possible to consider all topologies by hand. With the help of state of the art solvers, on the other side, it is possible to solve this MINLP.
Next to this, we also consider the effects of malfunctions in different components. Therefore, we show a first approach to measure the resilience of the shown example use case. Further, we compare the conventional approach with designs that are more resilient. These more resilient designs are derived by extending the before mentioned model with further constraints, that consider explicitly the resilience of the overall system. We show that it is possible to design resilient systems with this method already in the early design stage and compare the energy efficiency and resilience of these different system designs.
Highly competitive markets paired with tremendous production volumes demand particularly cost efficient products. The usage of common parts and modules across product families can potentially reduce production costs. Yet, increasing commonality typically results in overdesign of individual products. Multi domain virtual prototyping enables designers to evaluate costs and technical feasibility of different single product designs at reasonable computational effort in early design phases. However, savings by platform commonality are hard to quantify and require detailed knowledge of e.g. the production process and the supply chain. Therefore, we present and evaluate a multi-objective metamodel-based optimization algorithm which enables designers to explore the trade-off between high commonality and cost optimal design of single products.
To increase pressure to supply all floors of high buildings with water, booster stations, normally consisting of several parallel pumps in the basement, are used. In this work, we demonstrate the potential of a decentralized pump topology regarding energy savings in water supply systems of skyscrapers. We present an approach, based on Mixed-Integer Nonlinear Programming, that allows to choose an optimal network topology and optimal pumps from a predefined construction kit comprising different pump types. Using domain-specific scaling laws and Latin Hypercube Sampling, we generate different input sets of pump types and compare their impact on the efficiency and cost of the total system design. As a realistic application example, we consider a hotel building with 325 rooms, 12 floors and up to four pressure zones.
Given industrial applications, the costs for the operation and maintenance of a pump system typically far exceed its purchase price. For finding an optimal pump configuration which minimizes not only investment, but life-cycle costs, methods like Technical Operations Research which is based on Mixed-Integer Programming can be applied. However, during the planning phase, the designer is often faced with uncertain input data, e.g. future load demands can only be estimated. In this work, we deal with this uncertainty by developing a chance-constrained two-stage (CCTS) stochastic program. The design and operation of a booster station working under uncertain load demand are optimized to minimize total cost including purchase price, operation cost incurred by energy consumption and penalty cost resulting from water shortage. We find optimized system layouts using a sample average approximation (SAA) algorithm, and analyze the results for different risk levels of water shortage. By adjusting the risk level, the costs and performance range of the system can be balanced, and thus the
system’s resilience can be engineered