ON LINKAGE-BASED CLUSTERING APPROACH AND AIR TRAFFIC PATTERN RECOGNITION

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1 ON LINKAGE-BASED CLUSTERING APPROACH AND AIR TRAFFIC PATTERN RECOGNITION Leïla ZERROUKI, INEOVA for EUROCONTROL, France Serge MANCHON, Marc DALICHAMPT, EUROCONTROL, France Abstract: The paper ntroduces a methodology and key concepts amng at dentfyng flows structures and assessng ther nterdependences. These flows structures are the bass on whch Logcal Functonal ATFCM Areas (LFAAs) are defned allowng the antcpaton of regons of strong network effect nteractons and provde a means for the defnton of a predctve functon around whch Collaboratve Decson processes can be organsed n order to reduce complexty and ncrease effcency of the Network Management. Introducton As stated n the SESAR (Sngle European Sky ATM Research) programme [1], the determnaton of solutons that cope wth capacty/demand mbalances should be desgned through a pan- European plannng and coordnaton between all stakeholders, both at the strategc and tactcal levels. To fulfl ths am, the future ATM processes should provde a predctable and stable system that smplfes and ncreases the transparency of collaboratve decson makng processes. Ths goal would be delvered through a collaboratve layered plannng [2] at local level supported by a Network Management Functon whch determnes, balances, refnes, and then optmses capacty and demand on the bass of common stuatonal awareness of the ATM pcture and network effects resultng from the stakeholders decsons. Ths fundamental prncple mples for the Network Management Functon to have the means for a clear collaboratve and nformaton sharng process, ncludng the dentfcaton of the nvolved actors, the approprate solutons, and the assessment of ther possble nterdependence enablng to antcpate the network effect resultng from these solutons. The frst part of ths paper ams to provde key concepts and approaches that enable to draw a pcture of the traffc demand structure by dentfyng the man flows and measurng ther nterdependences. The proposed approach uses data clusterng technques to group elementary sectors dependng on traffc demand connectvty crtera. The second secton shows how the dentfcaton of demand structures can be used to desgn homogeneous ATFCM areas, called Logcal Functonal ATFCM Areas whch delneate regons n whch network effect resultng from local ATFCM measures s potentally sgnfcant. A draft set of LFAAs has been dentfed so far and s presented to better llustrate the followed approach. Further work, ncludng the calbraton of the clusterng model and operatonal evaluaton s n progress. Demand Pattern Identfcaton Obectve The man obectves of the demand pattern dentfcaton s to provde a global and complete vson of the man flows structure composng the traffc demand over the ECAC area and also to quantfy the nterdependence among the flows n an antcpate way. The outcome of ths frst stage allows the manpulaton of flows that are mplctly assocated to a set of flghts and ther crossed arspace areas. Ths approach offers a rch and aggregated means for the analyss of potental nteractons between

2 arspace areas and subsequently the desgn of functonal arspace boundares. The present secton proposes an approach amng at defnng flows structures on the bass of data clusterng technques. Clusterng technques Clusterng s the process of organsng obects nto groups whose members are smlar n some way. Applyng clusterng process to flows dentfcaton conssts n groupng elementary sectors whch are connected n a certan way that determnes the shape of the flows and ther connectedness. A great number of well-known clusterng technques have been developed [3] but the approach used to cluster the sectors and defne the flows shapes s based on agglomeratve herarchcal clusterng algorthms [4]. These algorthms follow the same conceptual framework whch s presented below. Some adaptatons have been ntroduced to cope wth the flows defnton problem: 1. Start wth N elementary sectors placed nto a lst of sngleton sets S 1, S 2,, S n and an N N symmetrc connectvty matrx D = { d k }, where d k s gven by the expected common demand crossng the sectors x and x k. 2. Select a connectvty threshold (a common demand value) whch allows to trade off between the number of formed clusters and compactness of each cluster. 3. Fnd the par of clusters { S, S } that s connected at a hgher level than the connectvty threshold. Then replace S wth S S the connectvty matrx values. S and n the clusters lst and update 4. Repeat step 3 untl no more clusters can be merged. The maor dfference between the agglomeratve clusterng algorthms s the defnton of the connectvty functon used n step 3 to evaluate the connectvty level between two clusters. In the case of flows dentfcaton, connectvty functon wll determne the shape and the densty of the flows. Sngle lnkage, complete lnkage and average lnkage are the three relevant lnkage-based agglomeratve algorthms that have been mplemented n the context of demand pattern recognton and consequently determne the shape of the dentfed flows. Dependng on the lnkage mode, the connectvty functon provdng the value of between-clusters connectvty s gven for each par S, by: of clusters { } S Sngle Lnkage: d s = max x S, x S ( d, ) Complete Lnkage: dc = mn x S, x S ( d, ) Average Lnkage: d a = S 1 S x S, x S d, Sngle lnkage: wth ths method, the fuson of a sector (or a clusters of sectors) wth a cluster at a gven connectvty level, only needs that one element of each of the two clusters be lnked to one another at ths level. Complete lnkage: the algorthm allows a cluster to be merged to another at a gven level only f all the elements of the cluster are lnked to all the elements of the other cluster at ths connectvty level. Average lnkage: ths method allows two clusters to be merged at a gven level f the average of connectvty values lnks the clusters at that level. Demand structure dentfcaton ATFCM s a complex system composed of strongly nteractng elements, whch can be sectors, flows, traffc volumes or any arspace volume that s constraned by a lmted capacty and may requre beng protected by applyng an ATFCM measure such as ground delay, re-routng or level cappng. Evaluatng network effect resultng from ATFCM measures requres analyss means that

3 dentfy and quantfy the nteractons over the elements of the system. The paper focuses on the related effect among elementary sectors. An ndcator s defned to quantfy the connectvty among the sectors, the common demand, whch s gven by the number of flghts per day crossng any par of sectors. Evaluatng ths ndcator for each par of sectors over the ECAC area and representng the correspondng values n a matrx provde an overall vson of the connectvty level between the sectors. Moreover, lnkage algorthms allow the dentfcaton of structures based on the exstng man flows and assess the overall archtecture of the network provdng a quanttatve evaluaton of ts flows components and ther relatonshps. In the followng, an example of demand structure and dependences dentfcaton s descrbed n order to provde an overvew of the potental use of clusterng technques n the framework of demand pattern recognton. Lnkage algorthms have been mplemented wthn the Vsualsaton and Analyss of the Network Effect Tool (VANET) developed at EEC. Table 1 presents the experment scenaro whch s appled to a week-end day n July The experment uses the complete lnkage mechansm, whch n ths example wll merge sectors that share at least 80 flghts two by two. Algorthm Complete Lnkage Table 1. Clusterng Parameters Merged elements Elementary sectors Lnkng crtera Common demand Thresh value The complete lnkage algorthm enables to extract elongated structures (cf. Fgure 1) representng the path followed by a set of flghts representng a flow. The length of the extracted flows ncreases as the connectvty threshold relaxes. The matrx on Fgure 2 shows the result of clustered sectors and the correspondng common demand values. It can be notced that values nsde each cluster/flow are all greater than 80, 80 Fgure 1. Flows Map Fgure 2. Arranged common demand matrx The matrx on the left Fgure 3 provdes an aggregated representaton of the prevous map and matrx, where rows and columns are the flows wth ther respectve colour. The values are average common demand correspondng to the level of nternal connectedness of the sectors belongng to the same flow (the man dagonal) and the demand that two sectors belongng to two dfferent flows may share on average. Fgure 3. Flows relatonshp matrx

4 The matrx on the rght provdes an addtonal ndcaton on the number of sectors that are crossed by a par of man flows. In that case, two sectors are crossed by the flows 0 and 2: EDUUWUFLT and EDUUFFMLT, whch dependence values hghlghted n red on the matrx of fgure 2, are all greater than 80. These aggregated matrx representatons provde a meanngful means to quantfy the structure of the network and evaluate the dependence among the man flows. The followng secton wll descrbe a methodology based on average lnkage algorthm to dentfy homogeneous functonal areas for whch ATFCM measures could be appled ensurng that network effect s localsed nsde the defned area and s almost nexstent outsde. LFAAs concept defnton Ths secton presents a methodology ntally descrbed n [5], whch enable to antcpate the dentfcaton of groups of quas ndependent ATFCM bodes termed by Logcal ATFCM Functonal Areas (LFAAs). The dentfcaton of such areas ams to mprove the coordnaton wthn the ATFCM decson processes and consequently network effcency. Furthermore, the proposed method has to be calbrated and valdated wth the help of operatonal network manager experts n vew of a potental mplementaton n the framework of future ATM systems modellng. LFAAs obectves Ths secton ams at answerng the queston of what are the potental applcatons of Logcal Functonal ATFCM Areas concept n the operatonal context. The dentfcaton of two areas referred as the South-West and North-East axs n whch a set of Collaboratve Decson Makng (CDM) procedures have been set up s an llustraton of what would be the LFAAs and ther use [6]. LFAAs dentfcaton method can be generalsed to the ECAC area as a basc concept for the valdaton actvtes and more precsely for those related to NOP buldng and collaboratve decson makng processes. Therefore, the LFAA concept could contrbute to mprove the effcency of ATFCM CDM processes by provdng gudelnes for reducng the number of relevant actors nvolved n the mplementaton of pre-defned scenaros. Furthermore, for a gven pre-defned scenaro or any ATFCM measure, the defnton of LFAAs boundares together wth the evaluaton of network effect ndcators would contnuously enrch NOP processes wth structured and relevant nput data that help to mprove the network performance and effcency. Fnally, LFAAs defnton could also smplfy the CDM process n tactcal phase by quckly and fully antcpatng and evaluatng the nteractons wthn the network and consequently by applyng the approprate ATFCM measures that ensure network effcency. LFAAs defnton Regardng the ATFCM system obectves, the concept of LFAAs would be nevtably related to the dentfcaton of the traffc demand structure, whch s provded by the man flows drectons/axs. Man flows represent the strongest lnks between sectors, whle mnmsng the network effect between each other. In addton, t s also to consder the possble re-routngs of these flows. Hence, LFAAs are expected to be formed by the man flexble and relatvely ndependent flows lnked by potental re-routngs. LFAAs desgn process The desgnng process addressed n ths paper concerns the dentfcaton of LFAAs at the strategc ATFCM phase. Ths secton presents the expermental framework and the desgn process for whch each step s llustrated by the correspondng network decomposton result. Desgnng prncples Desgnng LFAAs wll follow an teratve process based essentally on a statstcal approach but also on the expertse of network managers that

5 help to refne and valdate the frst statstcal modellng teratons. It s mportant to recall that the desgnng approach presented n ths paper, concerns the strategc phase of ATFCM system. Ths wll requre the defnton of stable enttes based on the dentfcaton of exstng demand patterns. Experments Parameters In table 2 are gven the parameters for the frst two teratons of the desgn process. The use of those parameters wll be explaned when detalng the process teratons. Iteraton 1 Table 2. Clusterng Parameters Merged elements Elementary sectors Lnkng crtera Common demand Iteraton 2 Man Flows Average common demand Thresh value Iteraton 1: Groupng the elementary sectors The frst step ams to dentfy the basc flows correspondng to the strongly connected sectors. Hence, the dentfcaton of a basc flow conssts n mergng the hghly connected sectors wthn a same group (man flow). In order to ensure the stablty of the clusterng process, the average lnkage prncple wll be used: for a gven common traffc demand threshold average lnkage method allows a sector to on a group (man flow) f the average common demand between ths sector and all members of the group s greater than the gven threshold. It s worth to notce the mportance of selectng an approprate common demand threshold value, snce t determnes the characterstcs of the decomposton and the connectvty of the formed flows Several experments have been acheved so as to determne the best threshold value regardng the number of sectors merged and the nternal connectvty of the formed flow. The connectvty ndcator s gven by the average common demand of the sectors composng the flow and s dsplayed n the man dagonal of the nterdependence matrx. The selected threshold for dentfyng the basc flows at the frst teraton s establshed at 320 flghts for the eght days scenaro (or 40 flghts per day on average), as presented n Table 2. Therefore, the man flows resultng from the average lnkage clusterng process would be composed of sectors havng shared demand hgher than 320 flghts on average. The mans flows and ther remanng nterconnectvty values (.e. average common demand) are dsplayed n the map and the matrx of Fgure 7 respectvely. The large values of the nternal connectvty dsplayed on the man dagonal of the matrx can be compared to the nter flows connectvty values. In addton, teraton 1 seems to succeed n the dentfcaton of the basc flows that compose the North-East (NE) axs (Cf. Flows number: 0, 3, and 6 n Fgure 6) and the South-West (SW) axs (Cf. Flows: 1, 9, and 10). These axes are two regons currently managed through collaboratve decson processes to resolve the arspace bottlenecks occurrng n these areas. The dentfcaton of such regons based on structure of the demand wll be the nput for the assessment of LFAAs dentfcaton approach. More detals wll be provded further. Fgure 4. Basc Flows Identfcaton Process Iteraton 2: Groupng the basc flows Havng the set of basc flows and ther nterdependence matrx the second teraton wll merge the hghly connected basc flows and form the man flows. The process uses the average lnkage prncple to group the basc flows wth a threshold of average common demand of 120 flghts.

6 The resultng man flows are dsplayed n Fgure 7. It could be notced that the nterdependent flows of South-West and North-East axs, prevously dentfed, have been merged at the second teraton, snce ther nterdependence values, at the frst teraton were hgher than the fxed average demand threshold. Fgure 5. Man Flows Identfcaton Process Iteraton 3: Groupng the man flows Startng from elementary sectors and arrvng to man flows, the mergng process wll carry on recursvely untl the LFAAs are formed. At the current stage, most of the possble re-routng should have been ncluded wthn ther respectve man flow. However, some possble re-routngs occurrng between two man flows and establshng a functonal relatonshp between these flows wll complete the LFAAs desgn process by groupng the re-routable man flows. Two groupng approaches can be used dependng on the avalablty of expertse concernng each man flow. The frst approach s operatonal: snce the number of flows s reduced, the flows could be merged on the bass of network manager experence and knowledge. Fgure 6. Iteraton 1 - Basc Flows Identfcaton and Resultng Interdependence Matrx Fgure 7. Iteraton 2 - Man Flows Identfcaton and Resultng Interdependence Matrx

7 If the possble re-routngs between the man flows cannot be assessed by operatonal expertse, a statstcal approach wll be used. Ths approach s dsplayed on Fgure 8: startng from past traffc demand, the process dentfes all the possble reroutngs by orgn/destnaton par. Then, all the scenaros wll be used to buld a vrtual traffc demand fle and ts assocated common demand matrx. When ths matrx s ordered accordng the man flows matrx, the possble routes between the man flows wll be dentfed. Fgure 10. SW and NE axs ssued from the LFAAs desgn process (Iteraton 2) Fgure 8. Composng the LFAA s Iteraton 4: Calbraton of the model When LFAAs desgn process s completed, the am of the calbraton phase s to compare the ATFCM regons dentfed operatonally (SW and NE regons) wth those calculated by the desgn process (Cf. Fgure 10) and adust the common demand threshold value accordng an teratve process, descrbed below, untl the approprate thresholds are dentfed. Fgure 9. Calbratng the LFAAs model LFAAs operatonal assessment The obectve of ths phase s to valdate the operatonal feasblty of the LFAAs desgn approach. Whle, the calbraton phase compares calculated LFAAs wth exstng ATFCM regons, the operaton assessment wll confront new calculated LFAAs to the operatonal pont of vew. When the desgned LFAAs are not n adequacy regardng operatonal consderatons, the desgn process must be refned n order to take nto account the relevant operatonal constrants that have been dentfed durng ths phase. LFAAs sectors typology Fnally, after the dentfcaton of new LFAAs and ther operatonal valdaton, each resultng LFAAs s then composed of re-routable man flows whch n turn are formed by strongly dependent elementary sectors ensurng a hgh nternal functonal connectvty. However, even f the mergng process s based on the maxmsaton of nternal dependences and the exstence of potental re-routngs, t wll reman some nter LFAAs connectons correspondng to the common demand of sectors that belong to several LFAAs at the same tme. In order to assess the nterconnectvty between LFAAs, a typology of the sectors composng the LFAAs s proposed. Two categores of sectors are dstngushed: weakly connected sectors named flow orented sector and strongly nterconnected sectors named connectng sectors.

8 Connectng sectors wll be assgned a sector/lfaa connectvty ndcator value whch assesses the degree of membershp of the sector to each LFAA. The result of the overall LFAAs desgn process s llustrated wthn the model of Fgure 11. ACC Sectors Flow struct. Re-routng Connectng LFAA Lnks sectors Fgure 11. A model for LFAAs Structure Concluson The paper proposes an ntal research work representng a key modellng approach for the dentfcaton of arspace regons that strongly ft the ar traffc pattern. The desgn of the LFAAs s a frst applcaton of ths approach amng to antcpate the dentfcaton of groups of homogeneous ATFCM bodes and the dentfcaton of the nherent collaboratve networks. Besdes LFAAs desgn, the approach offers a structured nformaton related to network effect whch would contrbute to create more explct and effcent Collaboratve Decson processes. Bography Leïla Zerrouk s graduated Master n ndustral engneerng of the INPG (French Natonal Polytechnc Insttute of Grenoble) and has a PhD of the unversty of Pars VI n She has ganed 8 years experence n Ar Traffc Flow Management workng on a varety of topcs at EUROCONTROL Experment Centre. Her current nterests nclude the development and assessment of new concepts, metrcs and prototypng computer assstance tools related to network analyss for the European ATFCM system. Serge Manchon s a graduated engneer of the ENAC (French Cvl Avaton School). He spent 9 years at CENA (natonal research center for the French CAA) as ar traffc flow management proect leader. In 1999, he worked for the SCTA (Ar Traffc Control Servces) as head of the flow management and plannng subdvson. He oned the EUROCONTROL Expermental Center n July 2000 as expert n Ar Traffc Flow & Capacty Management. He s currently workng on the SESAR Sngle European Sky ATM Research concept. Marc Dalchampt s graduated engneer of the ENAC (French Cvl Avaton School). He oned EUROCONTROL Expermental Center n 1987 where he worked as expert, proect leader, head or deputy head of Ar Traffc Flow and Capacty Management. He s currently responsble of several actvtes wthn SESAR Sngle European Sky programme. References [1] SESAR Consortum, SESAR Defnton Phase, July 2006, D1: Ar Transport Framework the Current Stuaton. [2] C-ATM Co-operatve Ar Traffc Management, a European Commsson 6 th Framework Proect, 2005, Medum Term Concept of Operatons. [3] D Fasulo, Aprl 2001, An Analyss of Recent Work on Clusterng Algorthms. Unversty of Washngton, Department of Computer Scence & Engneerng, Techncal Report # [4] E. Y. Cheu, C. K. Kwoh, Z. Zhou, On the Two-level Hybrd Clusterng Algorthm, n IASAT 2004: Internatonal Conference on Artfcal Intellgence n Scence and Technology. [5] L. Zerrouk, S. Manchon, M. Dalchampt, A Data Clusterng Approach to Identfy Logcal Functonal ATFCM Area, to appear n the 26th DASC proceedngs, Dallas, October 21-25, 2007 [6] CFMU, Aprl 2007, Network Operatons Plan