Dynamic Evolution And Nonlinearity Analysis Of Air Traffic Flow Fluctuations

Under the reality of the rapid development of air traffic,in the foreseeable future,high-traffic,high-density flight operations will become common.Under the circumstances of the reality of the slow increasing of airspace resources,in order to ensure flight growth,maintain safety and service quality level,international organizations,air traffic management authorities and research institutes of many states have proposed various operation concepts and solutions to cope with the dilemmas of this kind.Although various solutions have been proposed,in essence,they are sharing the common principle,that is based on the rules and characteristics of air traffic dynamic evolutions,various technical means are to be used to optimally allocate the required air traffic resources in temporal and spatial dimensions,so that the air traffic demand and the required resources could be matched as well as possible.The accurate description of air traffic dynamic evolution laws and operation characteristics is a key point of air traffic system optimization and control.However,the air traffic will not only be impacted by the unbalanced traffic demand of time and space,but also by the weather conditions with various uncertainties,and it is quite difficult to describe,precisely and accurately,dynamic evolution laws and operation characteristics of air traffic based on mathematical models.In addition,most of the flights operate on the airway,however,the arrival and the departure flights are the original driving forces of the complex system of the air traffic system.Therefore,this research focuses on the arrival and the departure flight flow time series of the airports,uses the time series analysis methods to explore the short term dynamic evolution laws and the long term nonlinear statistical characteristics of the air traffic from the perspectives of fluctuations,multiscale multifractality,and multiscale complexity of the air traffic flow volume in order to provide scientific theoretical bases and analysis tools for the simulation modeling,prediction analysis of air traffic flow fluctuations and the formulation of air traffic management measures.The main content of this thesis is composed of the following three parts,and the detailed research contents are listed as follows:(1)In order to characterize the dynamic evolution of air traffic flow volume fluctuations,focusing on the departure air traffic flow volume time series of a single day operation of Beijing Capital International Airport,the visibility graph and horizontal visibility graph are used to map the time series into complex networks.To analyze the time series based on the structures of the networks,the sequential motif is adopted to extract the local structures from the resulting networks to characterize the fluctuation patterns of the time series,then the state transition graphs of the fluctuation patterns are built up based on the occurrence order and the frequency of the fluctuation patterns in order to characterize the dynamic evolution trajectories of the air traffic.Based on the density of visibility lines,the community detection algorithm is used to obtain different communities of the complex networks.The sequential motif profiles are built up to characterize the fluctuation characteristics of the communities,and to quantitatively distinguish the differences among the fluctuation characteristics of the communities.From perspectives of the shifting of fluctuation patterns and fluctuation characteristics differences,this part proposes a new theoretical analysis tool for air traffic flow fluctuation research,and provides a scientific analysis tool for simulation modeling and prediction analysis of air traffic flow short term fluctuations,and for customizing air traffic flow management measures for specific periods of fluctuation characteristics.(2)In order to explore the multiscale multifractality of the air traffic flow fluctuations,focusing on the air traffic flow volume time series of the departure flights operated during the whole summer in 2017 of Beijing Capital International Airport,the multiscale multifractal analysis method is used.Based on the fluctuations of the Hurst surface,it is determined that the time series is of multiscale multifractality.The types of multifractality existing in the time series are identified.The main cause of the multifractal is also identified.The multiscale multifractal spectrum surface is proposed,and the the relationship between the parameter setting and the shape of the resulting multifractal spectrum surface is analyzed.Based on the shape features of the multifractal spectrum surface,the multiscale multifractal strength and the type of the dominate fluctuations are investigated.The time scale of the abrupt change of the dominant fluctuation type is found.In addition,based on the inter-distances of the Hurst surfaces,the relationship between the time series length and the approximation of the multiscale multifractality characterized by the Hurst surface obtained with the time series of different length is explored.The minimal length of the time series for effective analyses of the multifractality is determined.This part provides a useful analysis method for understanding the long-term statistical self-similarity characteristics of air traffic flow fluctuations,and provides a theoretical basis to use the multifractal theory to build up a simulation model of air traffic flow fluctuations,and to predict the fluctuations of air traffic flow.It also provides a theoretical basis to investigate the fluctuation characteristics of air traffic flow in different time scales,and to formulate traffic management strategies on different time scales.(3)In order to explore multiscale complexity of air traffic flow fluctuations,focusing on the air traffic flow volume time series within the whole summer in 2017 of the top ten busiest airports in China,the improved multiscale permutation entropy method is adopted,and the complexity of the arrival and the departure air traffic flow fluctuations of the ten airports is quantified from a univariate time series perspective.An improved multivariate multiscale permutation entropy method is developed,and the complexity of the total air traffic flow volume time series of the ten airports is investigated from a multivariate perspective.The concept of entropy spike is proposed,based on which the ten airports are classified into distinct groups to show the similarity among the complexity of air traffic flow fluctuations of different airports.An improved multiscale multivariate contingency quantification method is proposed,and the multiscale contingency between the arrival and the departure flow fluctuations of ten airports is investigated.Basde on the location of the maximal contingency spike,the time scale of the dominant traffic flow alternation is identified.This part provides a useful analysis method for understanding the long-term statistical regularity and uncertainty of air traffic flow fluctuations,provides a theoretical basis and an effective tool for quantitative analysis to quantify the prediction difficulty of air traffic flow fluctuations,and provides an effective measurement index for evaluating the simulation model of air traffic flow fluctuations.