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Adaptive Gaussian Process Regression for Bayesian inverse problems
No full textWe introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems
The Results of ISSI Team #547: Understanding the Activity of Comets Through 67P's Dynamics
No full textUnderstanding cometary activity gives us an insight into the materials properties, and therefore formation and evolution processes of these relatively pristine protoplanetary objects. We will present the results of an International Space Science Institute project to investigate the phenomenon through the effects of the outgassing activity on the orbit and spin-state of comet 67P/Churymov-Gerasimenko, e.g. its non-gravitational dynamics. This International Team gathered experts in orbital dynamics and trajectory reconstruction together with thermophysical modellers and comet observationalists, in order to compare the available extractions of 67P’s non-gravitational acceleration (NGA) from its trajectory. The team then fitted a combination of the NGA, the non-gravitational torque (NGT), and the total water-outgassing rate with a thermophysical activity model. The results of this model will be presented. In particular, it was found that: non-gravitational forces and torques are driven by water sublimation from the nucleus; thermal inertia and self-heating have only minor effects; spatially uniform activity cannot explain 67P's non-gravitational dynamics; spatially uniform momentum transfer cannot explain 67P's non-gravitational dynamics; and different terrain types have different instantaneous responses to insolation. The implications of these findings for the modelling of cometary material and the variety of surface types seen on 67P will be discussed
Electric Bus Scheduling with Non-Linear Charging, Power Grid Bottlenecks, and Dynamic Recharge Rates
No full textPublic transport operators are gradually electrifying their bus fleets, predominantly with battery-powered drive trains. These buses commonly have to be scheduled to recharge in-service, which gives rise to a number of challenges. A major problem is that the relationship between charging time and replenished driving range is non-linear, which is often approximately modeled. We examine the associated approximation error and show how it can result in a gross over- or underestimation of the fleet size. Moreover, we demonstrate that commonly used piecewise linear underestimations of the charge curve do not result in an underestimation of the predicted charge states in electric vehicle scheduling and routing models.
Furthermore, since power grid upgrades are currently not keeping up with an ever growing electricity demand, operators are introducing active charge management tools to dynamically adjust the charging speed depending on the amount of available energy. It is therefore imperative to extend electric bus scheduling models to account for these developments.
We propose a novel mixed-integer programming formulation for the electric bus scheduling problem featuring an improved approximation of the non-linear battery charging behavior as well as dynamic recharge speeds to accommodate grid load limits. The idea is to linearly interpolate what we call the charge increment function, which is closely related to the derivative of the commonly used charge curve. This provides very good error control and integrates easily into integer programming models. We demonstrate the practical usefulness of our model on a diverse library of real-life instances
The Tropical and Zonotopal Geometry of Periodic Timetables
No full textThe Periodic Event Scheduling Problem (PESP) is the standard mathematical tool for optimizing periodic timetables in public transport. A solution to a PESP instance consists of three parts: a periodic timetable, a periodic tension, and integer offset values. While the space of periodic tensions has received much attention in the past, we explore geometric properties of the other two components. The general aim of this paper is to establish novel connections between periodic timetabling and discrete geometry. Firstly, we study the space of feasible periodic timetables as a disjoint union of polytropes. These are polytopes that are convex both classically and in the sense of tropical geometry. We then study this decomposition and use it to outline a new heuristic for PESP, based on neighbourhood relations of the polytropes. Secondly, we recognize that the space of fractional cycle offsets is in fact a zonotope, and then study its zonotopal tilings. These are related to the hyperrectangle of fractional periodic tensions, as well as the polytropes of the periodic timetable space, and we detail their interplay. To conclude, we also use this new understanding to give tight lower bounds on the minimum width of an integral cycle basis
Integrierte Baufahrplanoptimierung auf dem Netz der S-Bahn Berlin
No full textZur Instandhaltung von Eisenbahnnetzen sind regelmäßig Baumaßnahmen erforderlich. Diese erfordern stets Anpassungen der Fahrpläne. Um den Fahrgästen trotz der Baumaßnahme weiterhin einen möglichst großen Teil des Regelangebotes bieten zu können, bewegen sich die resultierenden Baufahrpläne insbesondere in Schnellbahnnetzen mit ihren dichten Zugfolgen häufig nahe der Kapazitätsgrenze der Infrastruktur.
Etablierte Verfahren zur Taktfahrplanoptimierung können diesen Anforderungen nicht genügen, da in der Praxis Anpassungen von Laufwegen der Linien, sowie der Gleisbelegungen häufig Teil der realisierten Lösungen sind. Für diese Aufgabe haben die Autoren zuletzt ein Optimierungsmodell vorgestellt, welches diese Möglichkeiten ausschöpft. In dem vorliegenden Beitrag wird erstmalig dessen Anwendung auf ein unmittelbar der Praxis der Baufahrplanung entnommenes Beispiel aus dem Netz der Berliner S-Bahn im Detail beschrieben
Surgical planning in HTO – Alternative approaches to the Fujisawa gold-standard
No full textBACKGROUND: Presurgical planning of the correction angle plays a
decisive role in a high tibial osteotomy, affecting the loading situation in
the knee affected by osteoarthritis. The planning approach by Fujisawa et
al. aims to adjust the weight-bearing line to achieve an optimal knee joint
load distribution. While this method is accessible, it may not fully
consider the complexity of individual dynamic knee-loading profiles. This
review aims to disclose existing alternative HTO planning methods that
do not follow Fujisawa’s standard.
METHODS: PubMed, Web of Science and CENTRAL databases were
screened, focusing on HTO research in combination with alternative
planning approaches.
RESULTS: Eight out of 828 studies were included, with seven simulation
studies based on finite element analysis and multi-body dynamics. The
planning approaches incorporated gradual degrees of realignment
parameters (weight-bearing line shift, medial proximal tibial angle, hip-
knee-ankle, knee joint line orientation), simulating their effect on knee
kinematics, contact force/stress, Von Mises and shear stress. Two studies
proposed implementing individual correction magnitudes derived from
preoperatively predicted knee adduction moments.
CONCLUSION: Most planning methods depend on static alignment
assessments, neglecting an adequate loading-depending profile. They are
confined to their conceptual phases, making the associated planning
methods unviable for current clinical use
