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Water distribution systems are an essential supply infrastructure for cities. Given that climatic and demographic influences will pose further challenges for these infrastructures in the future, the resilience of water supply systems, i.e. their ability to withstand and recover from disruptions, has recently become a subject of research. To assess the resilience of a WDS, different graph-theoretical approaches exist. Next to general metrics characterizing the network topology, also hydraulic and technical restrictions have to be taken into account. In this work, the resilience of an exemplary water distribution network of a major German city is assessed, and a Mixed-Integer Program is presented which allows to assess the impact of capacity adaptations on its resilience.
To maximize the travel distances of battery electric vehicles such as cars or buses for a given amount of stored energy, their powertrains are optimized energetically. One key part within optimization models for electric powertrains is the efficiency map of the electric motor. The underlying function is usually highly nonlinear and nonconvex and leads to major challenges within a global optimization process. To enable faster solution times, one possibility is the usage of piecewise linearization techniques to approximate the nonlinear efficiency map with linear constraints. Therefore, we evaluate the influence of different piecewise linearization modeling techniques on the overall solution process and compare the solution time and accuracy for methods with and without explicitly used binary variables.
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.
Pure analytical or experimental methods can only find a control strategy for technical systems with a fixed setup. In former contributions we presented an approach that simultaneously finds the optimal topology and the optimal open-loop control of a system via Mixed Integer Linear Programming (MILP). In order to extend this approach by a closed-loop control we present a Mixed Integer Program for a time discretized tank level control. This model is the basis for an extension by combinatorial decisions and thus for the variation of the network topology. Furthermore, one is able to appraise feasible solutions using the global optimality gap.
This chapter describes three general strategies to master uncertainty in technical systems: robustness, flexibility and resilience. It builds on the previous chapters about methods to analyse and identify uncertainty and may rely on the availability of technologies for particular systems, such as active components. Robustness aims for the design of technical systems that are insensitive to anticipated uncertainties. Flexibility increases the ability of a system to work under different situations. Resilience extends this characteristic by requiring a given minimal functional performance, even after disturbances or failure of system components, and it may incorporate recovery. The three strategies are described and discussed in turn. Moreover, they are demonstrated on specific technical systems.
Component failures within water supply systems can lead to significant performance losses. One way to address these losses is the explicit anticipation of failures within the design process. We consider a water supply system for high-rise buildings, where pump failures are the most likely failure scenarios. We explicitly consider these failures within an early design stage which leads to a more resilient system, i.e., a system which is able to operate under a predefined number of arbitrary pump failures. We use a mathematical optimization approach to compute such a resilient design. This is based on a multi-stage model for topology optimization, which can be described by a system of nonlinear inequalities and integrality constraints. Such a model has to be both computationally tractable and to represent the real-world system accurately. We therefore validate the algorithmic solutions using experiments on a scaled test rig for high-rise buildings. The test rig allows for an arbitrary connection of pumps to reproduce scaled versions of booster station designs for high-rise buildings. We experimentally verify the applicability of the presented optimization model and that the proposed resilience properties are also fulfilled in real systems.
In order to maximize the possible travel distance of battery electric vehicles with one battery charge, it is mandatory to adjust all components of the powertrain carefully to each other. While current vehicle designs mostly simplify the powertrain rigorously and use an electric motor in combination with a gearbox with only one fixed transmission ratio, the use of multi-gear systems has great potential. First, a multi-speed system is able to improve the overall energy efficiency. Secondly, it is able to reduce the maximum momentum and therefore to reduce the maximum current provided by the traction battery, which results in a longer battery lifetime. In this paper, we present a systematic way to generate multi-gear gearbox designs that—combined with a certain electric motor—lead to the most efficient fulfillment of predefined load scenarios and are at the same time robust to uncertainties in the load. Therefore, we model the electric motor and the gearbox within a Mixed-Integer Nonlinear Program, and optimize the efficiency of the mechanical parts of the powertrain. By combining this mathematical optimization program with an unsupervised machine learning algorithm, we are able to derive global-optimal gearbox designs for practically relevant momentum and speed requirements.
In product development, numerous design decisions have to be made. Multi-domain virtual prototyping provides a variety of tools to assess technical feasibility of design options, however often requires substantial computational effort for just a single evaluation. A special challenge is therefore the optimal design of product families, which consist of a group of products derived from a common platform. Finding an optimal platform configuration (stating what is shared and what is individually designed for each product) and an optimal design of all products simultaneously leads to a mixed-integer nonlinear black-box optimization model. We present an optimization approach based on metamodels and a metaheuristic. To increase computational efficiency and solution quality, we compare different types of Gaussian process regression metamodels adapted from the domain of machine learning, and combine them with a genetic algorithm. We illustrate our approach on the example of a product family of electrical drives, and investigate the trade-off between solution quality and computational overhead.
Ensuring access to water and sanitation for all is Goal No. 6 of the 17 UN Sustainability Development Goals to transform our world. As one step towards this goal, we present an approach that leverages remote sensing data to plan optimal water supply networks for informal urban settlements. The concept focuses on slums within large urban areas, which are often characterized by a lack of an appropriate water supply. We apply methods of mathematical optimization aiming to find a network describing the optimal supply infrastructure. Hereby, we choose between different decentral and central approaches combining supply by motorized vehicles with supply by pipe systems. For the purposes of illustration, we apply the approach to two small slum clusters in Dhaka and Dar es Salaam. We show our optimization results, which represent the lowest cost water supply systems possible. Additionally, we compare the optimal solutions of the two clusters (also for varying input parameters, such as population densities and slum size development over time) and describe how the result of the optimization depends on the entered remote sensing data.
Nahezu 100.000 denkbare Strukturen kann ein Getriebe bei gleicher Funktion aufweisen - je nach Ganganzahl und gefordertem Freiheitsgrad. Mit dem traditionellen Ansatz bei der Entwicklung, einzelne vielversprechende Systemkonfigurationen manuell zu identifizieren und zu vergleichen, können leicht innovative und vor allem kostenminimale Lösungen übersehen werden. Im Rahmen eines Forschungsprojekts hat die TU Darmstadt spezielle Optimierungsmethoden angewendet, um auch bei großen Lösungsräumen zielsicher ein für die individuellen Zielstellungen optimales Layout zu finden.
The paper industry is the industry with the third highest energy consumption in the European Union. Using recycled paper instead of fresh fibers for papermaking is less energy consuming and saves resources. However, adhesive contaminants in recycled paper are particularly problematic since they reduce the quality of the resulting paper-product. To remove as many contaminants and at the same time obtain as many valuable fibres as possible, fine screening systems, consisting of multiple interconnected pressure screens, are used. Choosing the best configuration is a non-trivial task: The screens can be interconnected in several ways, and suitable screen designs as well as operational parameters have to be selected. Additionally, one has to face conflicting objectives. In this paper, we present an approach for the multi-criteria optimization of pressure screen systems based on Mixed-Integer Nonlinear Programming. We specifically focus on a clear representation of the trade-off between different objectives.
On obligations in the development process of resilient systems with algorithmic design methods
(2018)
Advanced computational methods are needed both for the design of large systems and to compute high accuracy solutions. Such methods are efficient in computation, but the validation of results is very complex, and highly skilled auditors are needed to verify them. We investigate legal questions concerning obligations in the development phase, especially for technical systems developed using advanced methods. In particular, we consider methods of resilient and robust optimization. With these techniques, high performance solutions can be found, despite a high variety of input parameters. However, given the novelty of these methods, it is uncertain whether legal obligations are being met. The aim of this paper is to discuss if and how the choice of a specific computational method affects the developer’s product liability. The review of legal obligations in this paper is based on German law and focuses on the requirements that must be met during the design and development process.
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
Around 60% of the paper worldwide is made from recovered paper. Especially adhesive contaminants, so called stickies, reduce paper quality. To remove stickies but at the same time keep as many valuable fibers as possible, multi-stage screening systems with several interconnected pressure screens are used. When planning such systems, suitable screens have to be selected and their interconnection as well as operational parameters have to be defined considering multiple conflicting objectives. In this contribution, we present a Mixed-Integer Nonlinear Program to optimize system layout, component selection and operation to find a suitable trade-off between output quality and yield.
The transition within transportation towards battery electric vehicles can lead to a more sustainable future. To account for the development goal ‘climate action’ stated by the United Nations, it is mandatory, within the conceptual design phase, to derive energy-efficient system designs. One barrier is the uncertainty of the driving behaviour within the usage phase. This uncertainty is often addressed by using a stochastic synthesis process to derive representative driving cycles and by using cycle-based optimization. To deal with this uncertainty, a new approach based on a stochastic optimization program is presented. This leads to an optimization model that is solved with an exact solver. It is compared to a system design approach based on driving cycles and a genetic algorithm solver. Both approaches are applied to find efficient electric powertrains with fixed-speed and multi-speed transmissions. Hence, the similarities, differences and respective advantages of each optimization procedure are discussed.
The development of resilient technical systems is a challenging task, as the system should adapt automatically to unknown disturbances and component failures. To evaluate different approaches for deriving resilient technical system designs, we developed a modular test rig that is based on a pumping system. On the basis of this example
system, we present metrics to quantify resilience and an algorithmic approach to improve resilience. This approach enables the pumping system to automatically react on unknown disturbances and to reduce the impact of component failures. In this case, the system is able to automatically adapt its topology by activating additional valves. This enables the system to still reach a minimum performance, even in case of failures. Furthermore, timedependent disturbances are evaluated continuously, deviations from the original state are automatically detected and anticipated in the future. This allows to reduce the impact of future disturbances and leads to a more resilient
system behaviour.
Water suppliers are faced with the great challenge of achieving high-quality and, at the same time, low-cost water supply. In practice, the focus is set on the most beneficial maintenance measures and/or capacity adaptations of existing water distribution systems (WDS). Since climatic and demographic influences will pose further challenges in the future, the resilience enhancement of WDS, i.e. the enhancement of their capability to withstand and recover from disturbances, has been in particular focus recently. To assess the resilience of WDS, metrics based on graph theory have been proposed. In this study, a promising approach is applied to assess the resilience of the WDS for a district in a major German City. The conducted analysis provides insight into the process of actively influencing the
resilience of WDS
The chemical industry is one of the most important industrial sectors in Germany in terms of manufacturing revenue. While thermodynamic boundary conditions often restrict the scope for reducing the energy consumption of core processes, secondary processes such as cooling offer scope for energy optimisation. In this contribution, we therefore model and optimise an existing cooling system. The technical boundary conditions of the model are provided by the operators, the German chemical company BASF SE. In order to systematically evaluate different degrees of freedom in topology and operation, we formulate and solve a Mixed-Integer Nonlinear Program (MINLP), and compare our optimisation results with the existing system.
The application of mathematical optimization methods for water supply system design and operation provides the capacity to increase the energy efficiency and to lower the investment costs considerably. We present a system approach for the optimal design and operation of pumping systems in real-world high-rise buildings that is based on the usage of mixed-integer nonlinear and mixed-integer linear modeling approaches. In addition, we consider different booster station topologies, i.e. parallel and series-parallel central booster stations as well as decentral booster stations. To confirm the validity of the underlying optimization models with real-world system behavior, we additionally present validation results based on experiments conducted on a modularly constructed pumping test rig. Within the models we consider layout and control decisions for different load scenarios, leading to a Deterministic Equivalent of a two-stage stochastic optimization program. We use a piecewise linearization as well as a piecewise relaxation of the pumps’ characteristics to derive mixed-integer linear models. Besides the solution with off-the-shelf solvers, we present a problem specific exact solving algorithm to improve the computation time. Focusing on the efficient exploration of the solution space, we divide the problem into smaller subproblems, which partly can be cut off in the solution process. Furthermore, we discuss the performance and applicability of the solution approaches for real buildings and analyze the technical aspects of the solutions from an engineer’s point of view, keeping in mind the economically important trade-off between investment and operation costs.
Successful optimization requires an appropriate model of the system under consideration. When selecting a suitable level of detail, one has to consider solution quality as well as the computational and implementation effort. In this paper, we present a MINLP for a pumping system for the drinking water supply of high-rise buildings. We investigate the influence of the granularity of the underlying physical models on the solution quality. Therefore, we model the system with a varying level of detail regarding the friction losses, and conduct an experimental validation of our model on a modular test rig. Furthermore, we investigate the computational effort and show that it can be reduced by the integration of domain-specific knowledge.