Hierarchical Colored Timed Petri Nets for Maintenance Process Modeling of Civil Aircraft

International Joumal of Plant Enginoering and MansgermentVol,13 No.3 September 2008Hierarchical Colored Timed Petri Nets forMaintenance Process Modeling of Civil AircraftFU Cheng -cheng ,SUN You-chao ,LU ZhongCollege of Civil Aviation, Nanjing University of Aeronautics andAstronautics, Nanjing 210016, P. R. ChinaAbstract: Civil aircraft maintenance process simulation model is an efecive method for analyzing themaintainability of a civil airergf. First, we present the Hierarchical Colored Timed Petri Nets for ma-intenance process modeling of civil airergft. Then, we expound a general method of civil aircraft main-tenance activities , determine the maintenance level for decomposion, and propose the methods of de-scribing logic of relations betveen the maintenance actirities based on Petri Ner. Finally, a time Col-ored Petri muli-level network modeling and simulation procedures and steps are given with the mainte-nance example of the landing gear burst tire of a certain type of aircrf. The feasibiliy of the methodis proved by the example.Key words: hierarchical timed colored petri nets ( HTCPN), civil aircraft, maintenance proceasmodel, maintainability1 IntroductionMaintenance means the capacity of maintaining or restoring its provisioned state when the product isrepaired in provided conditions and within the secified time, in accordance with the regulations,procedures and methods. The maintenance of existing mature model on the whole can be dividedinto two categories: one is based on the factors afecting the maintenance of the model by analyingthe various faectors of the impact of designing maintenance, and establishing the mapping betweenproduct standards and various factors of maintenance, the typical models include score samplingmodel, retum model and weighted distribution model considering the design characterstic and so on;the other is based on the basic operating time of the maintenance of models and the basic modelbased on the time statistics, it analyzes the basic maintenance operations time covered with the ey8-tem maintenance, and seeks rehabilitation time further, the typical models include probability simu-lation model, tal time model and s0 on. Both models do not consider the relevant factors of systemmaintenance, the corresponding work process of system maintenance activities, the interrelationshipof the incident maintenance repair operations, and the interrelationship between the maintenance 0vents and conditions trigger. Therefore, it cannot support the maintenance process simulation, andcannot support the simulation of maintenance operations in virtual environment.The maintenance process is esentially a discrete system,中国煤化工d simulation ofdiscrete system usually contain CPM/PERT, DEF3，Petri:MYHCNMHGand8oon[23).Petri nets which are widely used in modeling are directly accessible due to the ability of the model toReceived 6 September 2008160Intermational Jourmal of Plant Engineering and MansgementVol.13 No.3September 2008describe the powerful graphics and flexible analysis capabilities in discrete systems. This paper con-structed multi-level network time Colored Petri based on maintenance process model of a civil air~craft. We take the maintenance of "a certain type of aircraft landing gear burst tire " as an example,and establish the maintenance process model for simulation modeling and analysis through CPNTools[4].2Basic principles of Petri NetsThe essential elements of Petri Net are Places and Transitions; the links between them can be repre-sented by the arc. Places represent states, or conditions; Transitions represent changes or events.The object or condition of Place can be denoted by a token. But basic Petri nets have many inade-quacies in the course of development, 80 that people cannot understand the system. Therefore re~searchers produce many advanced Petri Net, add the concept of "color" and "hierarchical" into it,JensenES) and others analyze the methods of Colored Petri network and develop the analysis sofware.This paper recommends Hierarchical Timed Colored Petri Nets ( HTCPN) , which can establish ma-intenance process simulation model of a civil aircraft effectively.Definition: An HTCPN is a tuple HTCPN = {PG,Z ,P,T,A,C,N,G,E,I}where:(1) PGis a finite set of pages such that: each pagepg ∈PG is a non-hierarchical CPN;(2) E isa finite set of non empty timed or unimed types , also clled color sets;(3) Pis a finite set of places; Tis a finite set of tansitions ;the relationship isP∩T= φ,P∪T≠φ;(4)Aisa finite set of arces such asP∩T=P∩A= T∩A= φ;(5) Cisa color function, is a finite set of color, such thatC = {c, e,"","n};(6) Nis a node function, which is defined fromA into(PxT) U(TxP);(7) Gis a guard function, the expression of the value is Boolean;(8) Eis an arc expression function, it is defined from A into timed or untimed;(9) I is an ialization function, it is defined from A into timed or untimed;In the graph, a circle represents Places and a rectangle represents Transtions and the arcs are usedto connect them. CPN use the color token with similar "data structure" to replace the value of a sin-gle token in general Petri Net.Petri net-based maintenance process modelMaintenance process includes all activities of maintaining or restoring products to their designedstate. Generally it involves the maintenance personnel; and according to certain components of therelationship, it involves a variety of support resources colleatrtiei[4. Main-中国煤化工。tenance process contains four levels: maintenance, mairactivity, ele-mental maintenance activity. The integrity of maintenanceJYH. CN M H Gorlely maintenance work, the maintenance work can be refined into a series of maintenance activity, and the ma-intenance activity also can be refned into a series of elemental maintenance activity ; the irelation-Hierarchica Colored Timed Petri Nets for Maintenance Process Modeling o Civil Aireraft61ship can be considered as a logical constraint relations which contain serial, parallel, selective orcyclic and 80 on. When we establish HTCPN based on the maintenance process model, the key issueis how to refine the maintenance process into elemental maintenance activity. The concept of Hierar-chical can explain maintenance process clearly. The procedure of establishing maintenance processmodel is a8 follows:(1) For study of maintenance activities, first we should make clear the maintenance work;(2) Refine maintenance works into elemental maintenance activity , representing the maintenanceprocess by a flow chart;(3) Describe the elemental maintenance activitie between the logic of relations by Petri nets, obtai.ning the bottom Petri Network model;(4) Analyue elemental maintenance activity , establish sub-Petri Net model;(5) Model simulation analysis.3.1 Analysis of maintenance workThe basis of establishing maintenance process model is analyzing the maintenance work. After ascer-taining maintenance work, we can determine the factors of maintenance, personnel, device andanalysis time, the aim of which is to confirm the type of maintenance work and to define the require-ments and maintenance projects. Normally the maintenance of civil aircraft can be divided into themaintenance of preventive maintenance and repair maintenance according to the pupose and time.The object of them is diferent, the former is for important function products, and the infuence ofthem is serious; the latter is confirmed by fault mode effect and criticality analysis( FMECA). In or~der to consider the failure mode as much as possible, and determine the cause of the fault, we mustanalyze the system from bottom to top, 80 it is very complicate for a civil aircraft, and the worloadwill be great. In this paper, we try to establish a model for a civil aircraft.3.2 Decomposition of maintenance work and maintenance process flow chartThe decomposition of maintenance work is the premise of establishing maintenance simulation mod-el. Maintenance proce8s contains four levels: maintenance , maintenance work , maintenance activi-y, elemental maintenance activity. The decomposition of maintenance process results in the flowchart of maintenance, which reflects the basic logjcal relationship between the elemental mainte-nance activities.3.3 Maintenance activity relationship described by Petri NetsThe integrity of maintenance consists of a series of orderly maintenance work , the maintenance workcan be refined into a series of maintenance activities , and the maintenance activity can be refined in-to a series of elemental maintenance activities, the relationship of them can be considered as a logj-cal constraint relations which contain serial, parallel, selective or cyclic and 80 on(2]. In examiningthe content of maintenance process, it is necessary to consider the Darameters . the auantitative indi-cators of maintenance are used for most of the time value中国煤化工Peri Nets mustintroduce the time factor into the basic Petri Nets.MYHCNMHG3.3. 1 Elementary maintenance activity relationship described by Petri NetsMaintenance work consists of a series of elementary maintenance activity , no matter what relationship162Intermational Joumal of Plant Engineering and MansgementVal.13 No. 3Soptember 2008can be described by Petri Nets. But there are sorme difference in network, see Figure 1.T2 Pz◎PI 1>0-0Po TT3 Ps2T2P4a) Serial(b) Prilel1P3 P3PoT。PPw0-OTT3 P:(C) Selective(d) CyclicFigure 1 Relationship of elementary maintenance activitySerial is used to describe the orders of the implementation operation, that is, the latter transitiontrigger is constrained by the formner transition, in Figure 1(a), T; is trigged first, and T, second, Tand T2 is serial; parallel is used to describe the coincidence of many operations, that is, the lattertransition trigger is constrained by many transition, in Figure 1(b) , Tgis trigged after T] and T2 trig-ger at the same time, Tp and Tz is parallel; selective is used to describe selective enforcement opera-tion between the number of transtions, that is, allow excution of arbitrary choice of a trigger tomeet the changing conditions, to & target state, in Figure 1(c) , T; is trigged only ifT, or T, tiggers,T and Tz is selective; cyelic is used to describe the competition, the rule of competition is constrain-ed by conitions, in Figure 1(d), if the condition W is not satisfied, T2 is responsible for changingthe system back to the T, before changing the state. The other relationships can be atained by thesebasic logical relationships.3.3.2 The introduction of the time factorThe basic Petri Nets only relet the structure or flow, not considering the time factor. In order todescribe a series of maintenance activities in the process and analyze the time, time must be intro-duced. According to the diference among the elements of Petri Nets, there are 4 methods to intro-duce time to a Petri net, i. e. in the Transitions; in the Arcs; in the Tokens;This paper uses Token and Transition method for the time factor. The time in Transition means thedelay of the transtion, that is, the Transition trigger needs time , not instantaneous. The time in To-ken means the work time, work load, and many others.3. 3.3 Hierarchical Petri NetsThere are two methods for Hierarchical Petri Nets, one is the decomposition based on Places and theother is the decomposition based on Transition. Establishing of maintenance process simulation mod-el of a civil aireraft "maintenance activities" as the center, we describe the maintenance activities byTransition. Therefore, decompostion based on transition is practicable. A simple double Petri Net isshown in Figure 2.中国煤化工YHCNMHG4 ExamplesTaking the maintenace of "a certain type of aircraft landing gear burst tire" as an example, we ex-Hienarchical Colored Timed Petri Nets for Mainenance Process Modeling o Civil Aircnaft163plain the methods for establishing the model.◎+O1 Complex transitionWe assume that there are two types ofDocemposition transitioomaintenance resources, one is A-resources,o-0-040 0 Basic mnstioand the other is B-resources. Maintenance r地Figure2 The cxample of double Petri Netsources usually include maintenance tools andequipment, spare parts and maintenance personnel, and 80 on; among these entties , maintenancetools and equipment, maintenance personnel belong to A-esources which are permanent entties;spare parts belong to B-resources, which are provisional entities.-Pailure「Waiting tanalyze faultDemolition| Determine mainte-(refining)]nance programmefor the replacementReplacement andassembly(refine); 2660GM1< A-resources>n r SufnictentLpressure ]A0 2659GM。Woaurse WareAdjustA-resources nB-resources inQualifedStartThe end]Figure 3 Maintenance procss flow chartFigue4 Structure of a tire4.1 Description of maintenance processesThe front-wheel of a civil aircralft in the land-Demolition Ibegininging process is broken down because of braking--Nontoo fast or tire use of longtime. After the faultSlcevedetection and analysis, according to "Mainte~icrew demolitiondemolition- _Ncnance Manual Requirement" , we decide to 比Ye-No-placement the front tire, at the same time weHub buildigNuts demolition>can attain the maintenance flow chart, sceYes-Non Yes-NonFigure 3; the structure of a front landing gearUpenpinTire demolition. demoltiontireof a certain type of aircraft is shown inFigure 4; decompose the process of replace-Nuts and, boltsment, several sub-process will be achieved,e. g. disassembly, assembly and so on; ana-lyze the disassembly-process, decompose it toFigure 5中国煤化工ocess flow chartthe elemental maintenance activities， andMHCNMHGthen maintenance process flow chart will beobtained, see Figure 5, the other proceses is similar.164International Joumal of Plant Engineering and ManagementVol.13 No.3September 20084.2 Petri Net examplesAnalyze the maintenance process clearly ; establish the base-level and the disassembly-process PetriNet by CPN Tools, see Figure 6.(name-="Tom".workime-=0.id="pliers" 1 ++1 name=' "Jack ,worktime=0,id=”spanner")AS@+Z@ +delay⑦回的°⑥涸④图EE_-⑧resB●回°[而国3^e。回°D°血eSTART-CT F面°年的D●回e●回Tname="Tom" .worktime-=01++(name="Jack",worktime =0 I2°s 。i'ch LOF°D°T°Dm°FINISH .Figure 6 The base-level and the dissembly-process Petri Netwhere:A_ xres is A - resources; B. .res is B. resources; P。is waiting to analyze fault; P is determinemaintenance programme; P2 isA, B_ resources in; Ps is state of waiting maintenance; P, is demoli-tion complete; Ps is replacement and assembly complete; End is the end of maintenance.To is analyze fault; T is genernate demand for resources; T2 is inspection maintenance of state; T isdemlition( Complex transtion) ; T is replacement and 8embly( Complex transition) ; T, is adjust;START is the process of demolition to be started state ; Pu ,P12,P13 are the three screws and washersto be demolished state; D. is screws and washers state of completion of demolition; P4 is hub demo-lition to be covered 8tate; D2 is hub cover demolitin finished state; Ps ,P16 are two openings sellstate to be demolished; D31 ,Dz2 are two of open pin demolitin. fniPa are two nuts,washers, bolts to be demolished state; D, is two nuts,中国煤化工: demolition fin-ished state; P, is sleeve to be demolished state; Ds is sle.C.N.MHGate;Pno is axdcnuts to be dermolished state; D。is axle nuts of demolition finished state; P1 is tire to be demolishedstate; FINISH is tire demolition finished state.Hierurchical Colrod Timed Petri Nets for Maintenance Proccee Modeling of Civil Aireraft65T ,Tr, Trs is demolition of three screws and washers; T14 is hub demolition; TIs ,Tr6 is demolition ofthe two opening sales; Tr7 ,Trg is demolition of the two nuts, washers, bolts; Tr9 is demolition sleeve;T1 is demolition axle nuts; Tm1 is demolition wheels.4.3 Analysis of maintenance timeEstablish the Petri Net based model for disassembly sub-process by CPN Tools, trigger the executa-ble transition in the model, change the distribution of token by the rule which is regulated by themodel, After that, we can explain the features of the Bystem, and then implement the simulation. Inorder to calculate quantitatively, we frstly assume that the working hours of each step of the demoli-tion activities, see Table 1, but we must point out that, the data is only used to simulate the meth-ods of calculation, not entirely consistent with the actual situation. The unit of the work time is mi-nute( min). Figure 7 Records the curve of the maintenance work time changing with the mainte~nance process.Table 1 The time of the demolition of activiticsPartsScrewHubOpen salesNuts&accessoriesSleeveAxle nutsTireTime( min)21510 1WorkingcTom)名1. Working(Jack)←4Ready TI T12 T3 TI4 TIs Ti6 TI7 TI8 TI9 Tr1o T11Figure 7 The curve of the maintenance work timeAfter the simulation, we can obtain the time of demolition, also we can obtain other time of everyprocess according to the similar method. If we have the time of every sub-process, we can add theminto the basic-level, and then the entire maintenance will be achieved. Through the process of build-ing maintenance Petri Net model for analysis and simulatio, we can also achieve the following fea-tures: calculation of resource utilization, the maintenance process of adjustment, and optimization ofthe maintenance process.5 ConclusionsIn this paper, we discussed the methods of establishing the model for maintenance rocess of a civilAireraft, approved the Hierarchical Colored Timed Petri中国煤化工DHCNMH G.(1) Given procedures for establishing a Hierarchical Colo..h.. m, Vic aalyze the task ofmaintenance in the context of a civil aircraft maintenance, make clear the levels of maintenance,propose the methods of depicting the logic relationship between basic actities;166Vol.13 No.3 Sptemaber 2008(2) Take the maintenance of "a certain type of aircraft landing gear burst tire" as an example, wepresent the methods of establishing the simulation model, and the method is proved to practicable.References[1] M. Z. Gan, Maintainability design and verification. Beijng: Defense Industry Press, 1995(In Chinese)[2] L. Ma, C. Lu,The application of PeriNer in analyzing maintenance work. Joumal of BeijingUniversity of Aeronautics and Astronautics,No. 3 ,pp.249 ~ 253 ,2004( In Chinese)[3] z. C. Xu,Y. H. Pu,Y. L. Liu,Petri nets based maintenance system-building programmers, Sy8-tems Engineering Theory and Practice , No.8,pp.141 ~ 144 ,2004( In Chinese)[4] CPN Tools version 2. 2. 0. Mera Sofrvare Corporation [ EB/OL]. Cambridge MA. Alo avail-able fom the Department of Computer Science, University of Aarhus at http://wiki. daimi.au. dk/cpntools, 2006[5] Kut Jensen. Colored Petri Nets Basic Concepts Analysis Methods and Pracical Use. NewYork: Springer -Verlag, 1992Brief BiographiesFU Cheng-cheng is a post graduate student in the College of Civil Ariation, Nanjing University ofAeronautics and Astronautics. Her researching areas are in rlaility and maintainability engineer~ing, maintainability vitual design, etc.SUN You-chao is a professor in the College of Civil Aviatioo, Nanjing University of Aeronautics andAstronautics. His researching areas are in reliability and maintainability engineering, maintainabiityvirtual design, etc.LU Zhong is a Ph. D candidate in the College of Civil Aviation, Nanjing University of Aeronauticsand Astronautics. His researching areas are in relibility and maintainability engineering, maintain-ability vitual design, etc.中国煤化工MYHCNMHG