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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.
Algorithmic design and resilience assessment of energy efficient high-rise water supply systems
(2018)
High-rise water supply systems provide water flow and suitable pressure in all levels of tall buildings. To design such state-of-the-art systems, the consideration of energy efficiency and the anticipation of component failures are mandatory. In this paper, we use Mixed-Integer Nonlinear Programming to compute an optimal placement of pipes and pumps, as well as an optimal control strategy.Moreover, we consider the resilience of the system to pump failures. A resilient system is able to fulfill a predefined minimum functionality even though components fail or are restricted in their normal usage. We present models to measure and optimize the resilience. To demonstrate our approach, we design and analyze an optimal resilient decentralized water supply system inspired by a real-life hotel building.
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.
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.
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.
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.
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.
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.