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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.
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.
The recently discovered first hyperbolic objects passing through the Solar System, 1I/’Oumuamua and 2I/Borisov, have raised the question about near term missions to Interstellar Objects. In situ spacecraft exploration of these objects will allow the direct determination of both their structure and their chemical and isotopic composition, enabling an entirely new way of studying small bodies from outside our solar system. In this paper, we map various Interstellar Object classes to mission types, demonstrating that missions to a range of Interstellar Object classes are feasible, using existing or near-term technology. We describe flyby, rendezvous and sample return missions to interstellar objects, showing various ways to explore these bodies characterizing their surface, dynamics, structure and composition. Their direct exploration will constrain their formation and history, situating them within the dynamical and chemical evolution of the Galaxy. These mission types also provide the opportunity to explore solar system bodies and perform measurements in the far outer solar system.
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.
Geochemical characterisation of hypersaline waters is difficult as high concentrations of salts hinder the analysis of constituents at low concentrations, such as trace metals, and the collection of samples for trace metal analysis in natural waters can be easily contaminated. This is particularly the case if samples are collected by non-conventional techniques such as those required for aquatic subglacial environments. In this paper we present the first analysis of a subglacial brine from Taylor Valley, (~ 78°S), Antarctica for the trace metals: Ba, Co, Mo, Rb, Sr, V, and U. Samples were collected englacially using an electrothermal melting probe called the IceMole. This probe uses differential heating of a copper head as well as the probe’s sidewalls and an ice screw at the melting head to move through glacier ice. Detailed blanks, meltwater, and subglacial brine samples were collected to evaluate the impact of the IceMole and the borehole pump, the melting and collection process, filtration, and storage on the geochemistry of the samples collected by this device. Comparisons between melt water profiles through the glacier ice and blank analysis, with published studies on ice geochemistry, suggest the potential for minor contributions of some species Rb, As, Co, Mn, Ni, NH4+, and NO2−+NO3− from the IceMole. The ability to conduct detailed chemical analyses of subglacial fluids collected with melting probes is critical for the future exploration of the hundreds of deep subglacial lakes in Antarctica.
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.