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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
Cheap does not imply cost-effective -- this is rule number one of zeitgeisty system design. The initial investment accounts only for a small portion of the lifecycle costs of a technical system. In fluid systems, about ninety percent of the total costs are caused by other factors like power consumption and maintenance. With modern optimization methods, it is already possible to plan an optimal technical system considering multiple objectives. In this paper, we focus on an often neglected contribution to the lifecycle costs: downtime costs due to spontaneous failures. Consequently, availability becomes an issue.
In times of planned obsolescence the demand for sustainability keeps growing. Ideally, a technical system is highly reliable, without failures and down times due to fast wear of single components. At the same time, maintenance should preferably be limited to pre-defined time intervals. Dispersion of load between multiple components can increase a system’s reliability and thus its availability inbetween maintenance points. However, this also results in higher investment costs and additional efforts due to higher complexity. Given a specific load profile and resulting wear of components, it is often unclear which system structure is the optimal one. Technical Operations Research (TOR) finds an optimal structure balancing availability and effort. We present our approach by designing a hydrostatic transmission system.
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.
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.
Verfügbarkeit und Nachhaltigkeit sind wichtige Anforderungen bei der Planung langlebiger technischer Systeme. Meist werden bei Lebensdaueroptimierungen lediglich einzelne Komponenten vordefinierter Systeme untersucht. Ob eine optimale Lebensdauer eine gänzlich andere Systemvariante bedingt, wird nur selten hinterfragt. Technical Operations Research (TOR) erlaubt es, aus Obermengen technischer Systeme automatisiert die lebensdaueroptimale Systemstruktur auszuwählen. Der Artikel zeigt dies am Beispiel eines hydrostatischen Getriebes.
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.
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
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.
Planning the layout and operation of a technical system is a common task
for an engineer. Typically, the workflow is divided into consecutive stages: First,
the engineer designs the layout of the system, with the help of his experience or of
heuristic methods. Secondly, he finds a control strategy which is often optimized
by simulation. This usually results in a good operating of an unquestioned sys-
tem topology. In contrast, we apply Operations Research (OR) methods to find a
cost-optimal solution for both stages simultaneously via mixed integer program-
ming (MILP). Technical Operations Research (TOR) allows one to find a provable
global optimal solution within the model formulation. However, the modeling error
due to the abstraction of physical reality remains unknown. We address this ubiq-
uitous problem of OR methods by comparing our computational results with mea-
surements in a test rig. For a practical test case we compute a topology and control
strategy via MILP and verify that the objectives are met up to a deviation of 8.7%.
The conference center darmstadtium in Darmstadt is a prominent example of energy efficient buildings. Its heating system consists of different source and consumer circuits connected by a Zortström reservoir. Our goal was to reduce the energy costs of the system as much as possible. Therefore, we analyzed its supply circuits. The first step towards optimization is a complete examination of the system: 1) Compilation of an object list for the system, 2) collection of the characteristic curves of the components, and 3) measurement of the load profiles of the heat and volume-flow demand. Instead of modifying the system manually and testing the solution by simulation, the second step was the creation of a global optimization program. The objective was to minimize the total energy costs for one year. We compare two different topologies and show opportunities for significant savings.
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 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.
Booster stations can fulfill a varying pressure demand with high energy-efficiency, because individual pumps can be deactivated at smaller loads. Although this is a seemingly simple approach, it is not easy to decide precisely when to activate or deactivate pumps. Contemporary activation controls derive the switching points from the current volume flow through the system. However, it is not measured directly for various reasons. Instead, the controller estimates the flow based on other system properties. This causes further uncertainty for the switching decision. In this paper, we present a method to find a robust, yet energy-efficient activation strategy.
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.
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.
The understanding that optimized components do not automatically lead to energy-efficient systems sets the attention from the single component on the entire technical system. At TU Darmstadt, a new field of research named Technical Operations Research (TOR) has its origin. It combines mathematical and technical know-how for the optimal design of technical systems. We illustrate our optimization approach in a case study for the design of a ventilation system with the ambition to minimize the energy consumption for a temporal distribution of diverse load demands. By combining scaling laws with our optimization methods we find the optimal combination of fans and show the advantage of the use of multiple fans.
Energy-efficient components do not automatically lead to energy-efficient systems. Technical Operations Research (TOR) shifts the focus from the single component to the system as a whole and finds its optimal topology and operating strategy simultaneously. In previous works, we provided a preselected construction kit of suitable components for the algorithm. This approach may give rise to a combinatorial explosion if the preselection cannot be cut down to a reasonable number by human intuition. To reduce the number of discrete decisions, we integrate laws derived from similarity theory into the optimization model. Since the physical characteristics of a production series are similar, it can be described by affinity and scaling laws. Making use of these laws, our construction kit can be modeled more efficiently: Instead of a preselection of components, it now encompasses whole model ranges. This allows us to significantly increase the number of possible set-ups in our model. In this paper, we present how to embed this new formulation into a mixed-integer program and assess the run time via benchmarks. We present our approach on the example of a ventilation system design problem.
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.
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.