Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.

Optimization Method for Departure Flight Scheduling Problem Based on Genetic Algorithm

Except for the bad weather or other uncontrollable reasons,a reasonable queue of departure and arrival flights is one of the important methods to reduce the delay on busy airports.Here focusing on the Pareto optimization of departure flights,the take-off sequencing is taken as a single machine scheduling problem with two objective functions,i.e.,the minimum of total weighted delayed number of departure flights and the latest delay time of delayed flight.And the integer programming model is established and solved by multi-objective genetic algorithm.The simulation results show that the method can obtain the better goal,and provide a variety of options for controllers considering the scene situation,thus improving the flexibility and effectivity of flight plan.

A NEW AND DIRECT METHOD OF ANALYSIS THE DEPARTURE PROCESSES OF SINGLE SERVER QUEUEING SYSTEMS

In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system.

Three-Dimensional Planning of Arrival and Departure Route Network Based on Improved Ant-Colony Algorithm

In order to improve safety,economy efficiency and design automation degree of air route in terminal airspace,Three-dimensional(3D)planning of routes network is investigated.A waypoint probability search method is proposed to optimize individual flight path.Through updating horizontal pheromones by negative feedback factors,an antcolony algorithm of path searching in 3Dterminal airspace is implemented.The principle of optimization sequence of arrival and departure routes is analyzed.Each route is optimized successively,and the overall optimization of the whole route network is finally achieved.A case study shows that it takes about 63 sto optimize 8arrival and departure routes,and the operation efficiency can be significantly improved with desirable safety and economy.

Urban rail departure capacity analysis based on a cellular automaton model

As an important traffic mode, urban rail transit is constantly developing toward improvement in service capacity and quality. When an urban rail transit system is evaluated in terms of its service capacity, the train departure capacity is an important index that can objectively reflect the service level of an urban rail transit facility. In light of the existing cellular automaton models, this paper proposes a suitable cellular automaton model to analyze the train departure capacity of urban rail transit under different variable factors and conditions. The established model can demonstrate the train operating processes by implementing the proposed sound rules, including the rules of train departure at the origin and intermediate stations, and the velocity and position updating rules. The properties of train traffic are analyzed via numerical experiments. The numerical results show that the departure capacity is negatively affected by the train departure control manner. In addition, （i） the real-time signal control can offer a higher train service frequency; （ii） the departure capacity gradually rises with the decrease in the line design speed to a limited extent; （iii） the departure capacity decreases with extension in the train length; （iv） the number of departed trains decreases as the train stop time increases; （v） the departure capacity is not affected by the section length. However, the longer the length, the worse the service quality of the urban rail transit line. The experiments show that the proposed cellular automaton model can be used to analyze the train service capacity of an urban rail transit system by performing quantitative analysis under various considered factors, conditions, and management modes.

Study on the Bubble Growth and Departure with A Lattice Boltzmann Method

For the growth and departure of bubbles from an orifice, a free energy lattice Boltzmann model is adopted to deal with this complex multiphase flow phenomenon. A virtual layer is set at the boundary of the flow domain to deal with the no-slip boundary condition. Effects of the viscosity, surface tension, gas inertial force and buoyancy on the characteristics of bubbles when they grow and departure from an orifice in quiescent liquid are studied. The releasing period and departure diameter of the bubble are influenced by the residual gas at the orifice, and the interaction between bubbles is taken into consideration. The relations between the releasing period or departure diameter and the gravity acceleration show fair agreements with previous numerical and theoretical results. And the influence of the gas outflow velocity on bubble formation is discussed as well. For the bubbles growing in cross-flow field, effects of the cross-flow speed and the gas outflow velocity on the bubble formation are discussed, which is related to the application in ship resistance reduction. And optimal choice of the ship speed and gas outflow velocity is studied. Cases in this paper also prove that this high density ratio LBM model has its flexibility and effectiveness on multiphase flow simulations.

Dynamic Tabu Search Algorithm for Solving Departure Scheduling Problem

The aircraft departure scheduling problem is described comprehensively. A mathematical model is built for solving this problem. Then, a local search algorithm is proposed; based on it, the dynamic tabu search technique is applied, and the related implement techniques are presented. A simulation including condition and results is performed to solve a representative problem. It is concluded that （ 1 ） departure aircrafts of each queue keep the same order comparatively all the lime, and the distribution of the departure time is well-proportioned, which accords with the ＂first-come first-serve＂ principle; （2） the total time costs are minimized, which would economize money and reduce danger; （ 3 ） the optimization result is not exclusive, which means that several approaches can be chosen at will; （4） the solution obtained is the global optimal one, which guarantees the validity of the proposed method.

Springtime migratory restlessness and departure orientation of Great Knots(Calidris tenuirostris)in the south compared to the north Yellow Sea

Background: The motivation of birds to proceed with migration is associated with both endogenous and exogenous factors. According to their migratory situation and to the characteristics of stopover sites, birds might exhibit migratory motivation differently among sites. Although migratory motivation of migrating birds has been well studied in many species, the investigation of the same species in different migratory situations and at different stopover sites is still limited. We predicted that birds at different stopover sites could differ in migratory disposition, including expression of migratory restlessness and responses to environmental cues.Methods: Here we compared migration motivation and orientation of Great Knots(Calidris tenuirostris) at two stopo ver sites, Chongming Dongtan in the south Yellow Sea, which is a temporary rest site, and Yalujiang Estuary Wetland in the north Yellow Sea, which is a critical refuelling site, during northward migration. Modified Emlen funnels, with thermal paper inside to record scratches of the birds, were used to detect activity(intensity and direction) of birds. Environmental conditions, including wind direction and speed, cloud cover, tide condition, times of the day(before and after sunset) were recorded during experiments. Generalized linear models were used to detect the effects of endogenous and exogenous factors on the migratory motivation of the birds.Results: In the south Yellow Sea, the migratory activity intensity of Great Knots was positively related to wind assistance. In the north Yellow Sea, where birds exhibited higher intensity of migratory activity than in the south, the intensity increased and the motivation to initiate migration grew stronger as the season advanced. The Great Knots exhibited wind-related orientation behaviour in the funnels at both sites.Conclusions: The results suggest that the intensity of migratory motivation differed between the two sites. Departure decisions of Great Knots appear to be affected mainly by external factors at the temporary rest site in the south Yellow Sea but possibly by endogenous factors at the final pre-breeding refuelling site in the north Yellow Sea.

Fault Geometry and Departure of Precursors From the Epicenter

Different tectonic elements may play different roles and their deformation styles and types of anomalies are also different in the process of deformation.Such differences may be the cause of the phenomena of the departure from the region with obvious anomalies from the coming epicenter,which are called "departure of precursors from epicenter." From some new experimental and numerical modeling results,five types of deformation elements are identified according to their roles in the process of deformation in a region.They are the brake(or locked),slip,yield,sensitive,and valve elements.Spatial distribution of different elements,especially sensitive and slip elements,are discussed by taking the bend fault,extension,compression,and complex en-echelon faults as examples.These elements with different roles may overlap each other in some cases or be separated in other cases.It is obvious that for different fault geometry,the spatial layout of these elements is different and thus the position and style of

Migration departure strategies of shorebirds at a final pre-breeding stopover site

Background: Departure decisions and behaviors of migratory birds at stopover sites are expected to maximize fit?ness by trade?offs among avoiding predators, optimizing refueling(energy) capacity, and matching other life?history events. We predict that species with different body sizes and migratory destinations will exhibit different behaviors when departing from the same stopover site. We also predict that with strong time constraint at the final pre?breed?ing stopover site, departure decisions may be less sensitive to exogenous factors, such as wind condition, compared to other stopover or nonbreeding sites.Methods: We recorded migratory departures of four shorebird species, i.e. Eurasian Curlew(Numenius arquata), Bar?tailed Godwit(Limosa lapponica), Great Knot(Calidris tenuirostris), and Grey Plover(Pluvialis squatarola), at Yaluji?ang Estuary Wetlands in China, a final pre?breeding stopover site in the northern Yellow Sea, from 2011 to 2014. We compared flock sizes, departure time and departure directions between species, and investigated the effects of tide and weather conditions(rain and ground wind speed and direction) on the departure decision of shorebirds.Results: We found that larger species departed in smaller flocks and were more variable in daily departure time. Departure trajectory of all four species appeared to be influenced by coastal topography. With the east–west coast?line and intertidal mudflat on the south, birds exhibited westward or eastward deflection from the shortest migra?tory routes. Bar?tailed Godwit was the only species that deviated to the southeast and did not climb over the land. Birds avoided departure during precipitation, while their departure was not related to ground wind benefit or tidal condition.Conclusions: Body size among species, which influences their vulnerability to predators, might be important in shaping shorebird departure strategies. Diverse departure directions could be the result of different wind use tac?tics in climbing stage. Narrow optimal time window of breeding might lead to reduced flexibility in departure date at a final pre?breeding site. Both endogenous and exogenous are important in shaping departure behaviors and decisions.

A Combined Arrival and Departure Scheduling for Multi-airport System

A combined arrival and departure scheduling problem is investigated for multi-airport system to alleviate the problem of airspace congestion and flight delay.Firstly,the combined scheduling problem for multi-airport system is defined through in-depth analysis of the characteristics of arrival and departure operations.Then,several constraints are taken into account,such as wake vortex separation,transfer separation,release separation,and separation in different runway operational modes.Furthermore,the scheduling model is constructed and simulated annealing algorithm is proposed by minimizing the total delay.Finally,Shanghai multi-airport system is chosen to conduct the simulation and validation.And the simulation results indicate that the proposed method is able to effectively improve the efficiency of arrival and departure operations for multi-airport system.

Departure Trajectory Design Based on Pareto Ant Colony Algorithm

Due to the ever-increasing air traffic flow,the influence of aircraft noise around the airport has become significant.As most airlines are trying to decrease operation cost,stringent requirements for more simple and efficient departure trajectory are on a rise.Therefore,a departure trajectory design was established for performancebased navigation technology,and a multi-objective optimization model was developed,with constraints of safety and noise influence,as well as optimization targets of efficiency and simplicity.An improved ant colony algorithm was then proposed to solve the optimization problem.Finally,an experiment was conducted using the Lanzhou terminal airspace operation data,and the results showed that the designed departure trajectory was feasible and efficient in decreasing the aircraft noise influence.

Sectorization Model of Terminal Airspace with Arrival and Departure Separation

Terminal airspace(TMA)is the airspace centering several military and civil aviation airports with complex route structure,limited airspace resources,traffic flow,difficult management and considerable airspace complexity.A scientific and rational sectorization of TMA can optimize airspace resources,and sufficiently utilize the control of human resources to ensure the safety of TMA.The functional sectorization model was established based on the route structure of arriving and departing aircraft as well as controlling requirements.Based on principles of sectorization and topological relations within a network,the arrival and departure sectorization model was established,using tree based ant colony algorithm(ACO)searching.Shanghai TMA was taken as an example to be sectorizaed,and the result showed that this model was superior to traditional ones when arrival and departure routes were separated at dense airport terminal airspace.

Real-time lane departure warning system based on principal component analysis of grayscale distribution and risk evaluation model

A technology for unintended lane departure warning was proposed. As crucial information, lane boundaries were detected based on principal component analysis of grayscale distribution in search bars of given number and then each search bar was tracked using Kalman filter between frames. The lane detection performance was evaluated and demonstrated in ways of receiver operating characteristic, dice similarity coefficient and real-time performance. For lane departure detection, a lane departure risk evaluation model based on lasting time and frequency was effectively executed on the ARM-based platform. Experimental results indicate that the algorithm generates satisfactory lane detection results under different traffic and lighting conditions, and the proposed warning mechanism sends effective warning signals, avoiding most false warning.

Individual departure time decision considering departure scheduling utility

The scheduling utility plays a fundamental role in addressing the commuting travel behaviours. A new scheduling utility,termed as DMRD-SU, was suggested based on some recent research findings in behavioural economics. DMRD-SU admitted the existence of positive arrival-caused utility. In addition, besides the travel-time-caused utility and arrival-caused utility, DMRD-SU firstly took the departure utility into account. The necessity of the departure utility in trip scheduling was analyzed comprehensively,and the corresponding individual trip scheduling model was presented. Based on a simple network, an analytical example was executed to characterize DMRD-SU. It can be found from the analytical example that: 1) DMRD-SU can predict the accumulation departure behaviors at NDT, which explains the formation of daily serious short-peak-hours in reality, while MRD-SU cannot; 2)Compared with MRD-SU, DMRD-SU predicts that people tend to depart later and its gross utility also decreases faster. Therefore,the departure utility should be considered to describe the traveler's scheduling behaviors better.

The Construction of an Ontology-Based Knowledge Management Model for Departure Procedures

With increased global economic development, the air traffic volume (including passengers and parcels) increases every year. Thus, the business-related load on air traffic controllers becomes heavier, which influences their need for frequent learning and training opportunities. Therefore, the only solution is to enhance the performance of the training for the air traffic controllers (ATCs) and to build uniform training procedures and standardized training content, which constitute a shared framework with ontology knowledge. Taking departure operation control processes as an example, the research analyzes an aviation organization framework, with information communication procedures and relevant knowledge assets from the viewpoint of departure processes, to explore a knowledge management model of aviation control. This research studies how explicit knowledge is transformed by CommonKADS methodology using the CommonKADS sheet, and the Unified Modeling Language (UML) graph presentation and ontology model are discussed in this research. This analysis procedure can be applied to the systematic analysis and establishment of similar business-based information systems, allowing this research result to be further shared in different industries

A Secure and Effective Energy-Aware Fixed-Point Quantization Scheme for Asynchronous Federated Learning

Asynchronous federated learning(AsynFL)can effectivelymitigate the impact of heterogeneity of edge nodes on joint training while satisfying participant user privacy protection and data security.However,the frequent exchange of massive data can lead to excess communication overhead between edge and central nodes regardless of whether the federated learning(FL)algorithm uses synchronous or asynchronous aggregation.Therefore,there is an urgent need for a method that can simultaneously take into account device heterogeneity and edge node energy consumption reduction.This paper proposes a novel Fixed-point Asynchronous Federated Learning(FixedAsynFL)algorithm,which could mitigate the resource consumption caused by frequent data communication while alleviating the effect of device heterogeneity.FixedAsynFL uses fixed-point quantization to compress the local and global models in AsynFL.In order to balance energy consumption and learning accuracy,this paper proposed a quantization scale selection mechanism.This paper examines the mathematical relationship between the quantization scale and energy consumption of the computation/communication process in the FixedAsynFL.Based on considering the upper bound of quantization noise,this paper optimizes the quantization scale by minimizing communication and computation consumption.This paper performs pertinent experiments on the MNIST dataset with several edge nodes of different computing efficiency.The results show that the FixedAsynFL algorithm with an 8-bit quantization can significantly reduce the communication data size by 81.3%and save the computation energy in the training phase by 74.9%without significant loss of accuracy.According to the experimental results,we can see that the proposed AsynFixedFL algorithm can effectively solve the problem of device heterogeneity and energy consumption limitation of edge nodes.

A Fixed-Point Iterative Method for Discrete Tomography Reconstruction Based on Intelligent Optimization

Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.

A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.