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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.
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%.
A new method for improved autoclave loading within the restrictive framework of helicopter manufacturing is proposed. It is derived from experimental and numerical studies of the curing process and aims at optimizing tooling positions in the autoclave for fast and homogeneous heat-up. The mold positioning is based on two sets of information. The thermal properties of the molds, which can be determined via semi-empirical thermal simulation. The second information is a previously determined distribution of heat transfer coefficients inside the autoclave. Finally, an experimental proof of concept is performed to show a cycle time reduction of up to 31% using the proposed methodology.
Anyone who has always wanted to understand the hieroglyphs on Sheldon's blackboard in the TV series The Big Bang Theory or who wanted to know exactly what the fate of Schrödinger's cat is all about will find a short, descriptive introduction to the world of quantum mechanics in this essential. The text particularly focuses on the mathematical description in the Hilbert space. The content goes beyond popular scientific presentations, but is nevertheless suitable for readers without special prior knowledge thanks to the clear examples.
For typical cases of non-isolated lightning protection systems (LPS) the impulse currents are investigated which may flow through a human body directly touching a structural part of the LPS. Based on a basic LPS model with conventional down-conductors especially the cases of external and internal steel columns and metal façades are considered and compared. Numerical simulations of the line quantities voltages and currents in the time domain are performed with an equivalent circuit of the entire LPS.
As a result it can be stated that by increasing the number of conventional down-conductors and external steel columns the threat for a human being can indeed be reduced, but not down to an acceptable limit. In case of internal steel columns used as natural down-conductors the threat can be reduced sufficiently, depending on the low-resistive connection of the steel columns to the lightning equipotential bonding or the earth termination system, resp. If a metal façade is used the threat for human beings touching is usually very low, if the façade is sufficiently interconnected and multiply connected to the lightning equipotential bonding or the earth termination system, resp.
Modern industry and multi-discipline projects require highly trained individuals with resilient science and engineering back-grounds. Graduates must be able to agilely apply excellent theoretical knowledge in their subject matter as well as essential practical “hands-on” knowledge of diverse working processes to solve complex problems. To meet these demands, university education follows the concept of Constructive Alignment and thus increasingly adopts the teaching of necessary practical skills to the actual industry requirements and assessment routines. However, a systematic approach to coherently align these three central teaching demands is strangely absent from current university curricula. We demonstrate the feasibility of implementing practical assessments in a regular theory-based examination, thus defining the term “blended assessment”. We assessed a course for natural science and engineering students pursuing a career in biomedical engineering, and evaluated the benefit of blended assessment exams for students and lecturers. Our controlled study assessed the physiological background of electrocardiograms (ECGs), the practical measurement of ECG curves, and their interpretation of basic pathologic alterations. To study on long time effects, students have been assessed on the topic twice with a time lag of 6 months. Our findings suggest a significant improvement in student gain with respect to practical skills and theoretical knowledge. The results of the reassessments support these outcomes. From the lecturers ́ point of view, blended assessment complements practical training courses while keeping organizational effort manageable. We consider blended assessment a viable tool for providing an improved student gain, industry-ready education format that should be evaluated and established further to prepare university graduates optimally for their future careers.
Dynamic retinal vessel analysis (DVA) provides a non-invasive way to assess microvascular function in patients and potentially to improve predictions of individual cardiovascular (CV) risk. The aim of our study was to use untargeted machine learning on DVA in order to improve CV mortality prediction and identify corresponding response alterations.
Delayed cerebral ischemia (DCI) is a common complication after aneurysmal subarachnoid hemorrhage (aSAH) and can lead to infarction and poor clinical outcome. The underlying mechanisms are still incompletely understood, but animal models indicate that vasoactive metabolites and inflammatory cytokines produced within the subarachnoid space may progressively impair and partially invert neurovascular coupling (NVC) in the brain. Because cerebral and retinal microvasculature are governed by comparable regulatory mechanisms and may be connected by perivascular pathways, retinal vascular changes are increasingly recognized as a potential surrogate for altered NVC in the brain. Here, we used non-invasive retinal vessel analysis (RVA) to assess microvascular function in aSAH patients at different times after the ictus.
Purpose Vascular risk factors and ocular perfusion are heatedly discussed in the pathogenesis of glaucoma. The retinal vessel analyzer (RVA, IMEDOS Systems, Germany) allows noninvasive measurement of retinal vessel regulation. Significant differences especially in the veins between healthy subjects and patients suffering from glaucoma were previously reported. In this pilot-study we investigated if localized vascular regulation is altered in glaucoma patients with altitudinal visual field defect asymmetry. Methods 15 eyes of 12 glaucoma patients with advanced altitudinal visual field defect asymmetry were included. The mean defect was calculated for each hemisphere separately (-20.99 ± 10.49 pro- found hemispheric visual field defect vs -7.36 ± 3.97 dB less profound hemisphere). After pupil dilation, RVA measurements of retinal arteries and veins were conducted using the standard protocol. The superior and inferior retinal vessel reactivity were measured consecutively in each eye. Results Significant differences were recorded in venous vessel constriction after flicker light stimulation and overall amplitude of the reaction (p \ 0.04 and p \ 0.02 respectively) in-between the hemispheres spheres. Vessel reaction was higher in the hemisphere corresponding to the more advanced visual field defect. Arterial diameters reacted similarly, failing to reach statistical significance. Conclusion Localized retinal vessel regulation is significantly altered in glaucoma patients with asymmetri altitudinal visual field defects. Veins supplying the hemisphere concordant to a less profound visual field defect show diminished diameter changes. Vascular dysregulation might be particularly important in early glaucoma stages prior to a significant visual field defect.
The term ocular rigidity is widely used in clinical ophthalmology. Generally it is assumed as a resistance of the whole eyeball to mechanical deformation and relates to biomechanical properties of the eye and its tissues. Basic principles and formulas for clinical tonometry, tonography and pulsatile ocular blood flow measurements are based on the concept of ocular rigidity. There is evidence for altered ocular rigidity in aging, in several eye diseases and after eye surgery. Unfortunately, there is no consensual view on ocular rigidity: it used to make a quite different sense for different people but still the same name. Foremost there is no clear consent between biomechanical engineers and ophthalmologists on the concept. Moreover ocular rigidity is occasionally characterized using various parameters with their different physical dimensions. In contrast to engineering approach, clinical approach to ocular rigidity claims to characterize the total mechanical response of the eyeball to its deformation without any detailed considerations on eye morphology or material properties of its tissues. Further to the previous chapter this section aims to describe clinical approach to ocular rigidity from the perspective of an engineer in an attempt to straighten out this concept, to show its advantages, disadvantages and various applications.
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.
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.
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