Reliability Analysis of Aircraft Condition Monitoring Network Using an Enhanced BDD Algorithm

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1 Chnese Journal of Aeronautcs 25 (2012) Contents lsts avalable at ScenceDrect Chnese Journal of Aeronautcs journal homepage: Relablty Analyss of Arcraft Condton Montorng Network Usng an Enhanced BDD Algorthm ZHAO Changxao, CHEN Yao, WANG Halang, XIONG Huagang * School of Electroncs and Informaton Engneerng, Behang Unversty, Bejng , Chna Receved 29 August 2011; revsed 23 November 2011; accepted 13 February 2012 Abstract The arcraft condton montorng network s responsble for collectng the status of each component n arcraft. The relablty of ths network has a sgnfcant effect on safety of the arcraft. The arcraft condton montorng network works n a real-tme manner that all the data should be transmtted wthn the deadlne to ensure that the control center makes proper decson n tme. Only the connectedness between the source node and destnaton cannot guarantee the data to be transmtted n tme. In ths paper, we take the tme deadlne nto account and buld the task-based relablty model. The bnary decson dagram (BDD), whch has the mert of effcency n computng and storage space, s ntroduced when calculatng the relablty of the network and addressng the essental varable. A case s analyzed usng the algorthm proposed n ths paper. The expermental results show that our method s effcent and proper for the relablty analyss of the real-tme network. Keywords: relablty; bnary decson dagram; arcraft condton montorng network; real-tme; network calculus 1. Introducton 1 Modern physcal systems used n arcraft are becomng more and more complex. Ths ncreased complexty n system has led to an ncreased desre for automated prognostc and health montorng system [1]. In order to reduce the lfe cycle cost of the arcraft and enhance the safety of flght, many programs have been proposed. The predctve falures and advanced dagnostcs (PFAD) program and the passve arcraft status system (PASS) program are targetng arcraft avoncs n general [2]. The jont strke fghter (JSF) program has ncorporated prognostcs health management (PHM) nto ts desgn, usng sensors, advanced processng and a fully ntegrated system of nformaton and supples management [3]. The ntegrated vehcle health management (IVHM) project s to develop valdated tools, *Correspondng author. Tel.: E-mal address: hgxong@ee.buaa. edn.cn Foundaton tem: Natonal Natural Scence Foundaton of Chna ( ) Elsever Ltd. Open access under CC BY-NC-ND lcense. do: /S (11) technologes and technques for automated detecton, dagnoss and prognoss that enable mtgaton of adverse events durng flght [4]. All the programs mentoned above am to enable the rapd detecton and dagnoss of adverse events to ensure the safety of the arcraft. The startng pont for any dagnostcs or prognostcs capablty, however, s accurate and approprate data that detals the performance, status and envronment of the components of the arcraft [5]. So a well-desgned arcraft condton montorng network s the essental system for these works and the relablty of the network becomes crucal. The condton montorng network s a hybrd network composed of wred and wreless components, and the network should work n a real-tme manner to ensure that the data of arcraft s condton collected by sensors could be processed n tme. The relablty of network s defned as the probablty that the network performs ts ntended functon under specfed condtons [6]. Many algorthms ncludng exact and approxmate algorthms have been presented to solve network relablty problems. Tradtonal algorthms nclude the mnmal paths/cuts [7], factorng

2 926 ZHAO Changxao et al. / Chnese Journal of Aeronautcs 25(2012) No.6 theorem [8] and the ncdent edge substtuton. Recent lteratures [9-10] show that the bnary decson dagram (BDD) method s an effcent approach for relablty evaluaton. The algorthms mentoned above concentrate on the relablty of lnk connectve, whle the condton montorng network requres the real-tme character. In ths paper, we consder the delay constrant of tasks n condton montorng networks and propose a task-based algorthm to compute the relablty of the network. delvered to the central processor through bus. The central processor would estmate the current status of the arcraft. Fgure 1 s an example of the arcraft condton montorng network. 2. Prelmnares 2.1. BDD method The BDD method [11] s based on a dsjont decomposton of a Boolean functon called the Shannon expanson. Gven a Boolean functon f (x 1, x 2,, x n ), then for any {1, 2,, n}, f = xf + xf (1) x = 1 x = 0 Defnton 1 (apply operaton of BDD) If f 1 and f 2 are two Boolean functons wth the same varable order and Δ s a logc operaton such as AND or OR, then [ f1δ f2]( x1, x2,, xn ) = f1( x1, x2,, xn) Δ f2( x1, x2,, x n) (2) The functon can be recursvely defned as [ f1δ f2]( x1, x2,, xn ) = x( f1 x = 1Δ f2 = 1) + ( 1 = 0Δ 2 = 0) x x f x f x (3) The fact that all the paths from the root to the leaves are mutually dsjont s a useful property of BDD. If f represents the Boolean expresson of the system relablty, then, based on the property of the dsjont decomposton of BDD, the relablty of a system can be recursvely evaluated by Pr{ f} = Pr{ x}pr{ f } + Pr{ x}pr{ f } (4) x = 1 x = 0 Fg. 1 An example of arcraft condton montorng network Model of the network The data of arcraft condton should be transferred wthn the tme deadlne. Data that exceeds the tme deadlne s useless even f t s correctly receved by central processor. A task denotes a data flow transfers from a node to another node. We use an array t(s, T, D) to descrbe the task of arcraft condton network. S s the source of the task, T the destnaton of the task, and D the tme deadlne. If the task s correctly fnshed wthn the tme D, we say the task s successful, otherwse the task fals. The network s modeled by a probablstc graph. A probablstc graph G (V, E) conssts of a set V of nodes representng network elements such as sensors and processors, and a set E of lnks representng communcaton paths whch would be wred or wreless. Fgure 2 s an example of probablstc graph. In ths paper, we assume that the nodes are perfect and only lnk falures are consdered Arcraft condton montorng network The montorng of arcraft condton s acheved by several sensors and avonc devces that contnuously detect envronmental condton, flght operatons and arcraft system health state n dfferent approaches [12]. Tradtonally, the cable-based montor for arcraft condton usually nvolves large numbers of wres employed for communcaton among sensors and centralzed data acquston systems. These wres, whch brng hgh nstallaton costs and neffcent mantenance, can be cumbersome. In order to avod complex wrng for power supply and data communcaton, a hybrd network s the most promsng soluton. Sensors are equpped to gather varous parameters of the components. The front-end processng unts collect the data and do some pretreatment, and then the data would be Fg. 2 An example of probablstc graph. As the network calculus theory [13] ndcates, each component of the network can be modeled as a specfc network element whch represents the tme consumed at ths component. Each element of the network s valued wth a real number ω(p), p V E. ω(p) represents the lnk delay f p E, and t represents the delay caused by transmsson, recepton and queung when p V. We defne ω(p) as the cost of lnk or node. We use the adjacent matrx to store the cost. Then the adjacent matrx of Fg. 2 can be expressed as

3 No.6 ZHAO Changxao et al. / Chnese Journal of Aeronautcs 25(2012) S v v T 1 2 S ω( S) ω( e1) ω( e2) 0 1 ω( 1) ω( 1) ω( 3) ω( 4) v e v e e v 2 ω( e2) ω( e3) ω( e2) ω( e5) T 0 ω( e4) ω( e5) ω( T) 3. Task-based Edge Expanson Dagram Algorthm (5) In ths secton, we propose a task-based approach that analyzes the relablty of the network usng BDD algorthm. Each component s represented by a set of Boolean varables that ndcate the falure states when usng the task-based edge expanson dagram (TEED) algorthm. In Fg. 2, we use a Boolean varable to represent each edge x e (=1, 2,,5). The algorthm ncludes two steps, constructng BDD for orgnal network and computng the relablty along BDD of orgnal network. The man dea, whch makes the TEED algorthm more effcent than other algorthms, s that the BDD representng the Boolean relablty expresson of a network can be constructed by avodng the redundant computaton of the somorphc sub-problems durng the mergng process. Snce the arcraft condton montor network s a delay constrant network, the tme deadlnes of tasks are consdered when the algorthm s appled. Our algorthm borrows the concept of edge expanson dagram [14] (EED). We extend the EED algorthm to meet the real-tme demand of the arcraft condton montorng network. return as the BDD expresson of the graph. If the graph has been evaluated and found n the Hash table, then return the result of ts BDD from the Hash table. Otherwse, expand the graph accordng to the edge e connected to the source and get some new subgraph. The BDD expresson of the orgnal graph s constructed through ntegratng the BDD expresson of subgraph usng apply operaton. Fgure 3 s the BDD constructng algorthm. In order to descrbe the algorthm ntutvely, we apply the algorthm to the graph mentoned n Fg. 2. Fgure 4 s the decomposton process of the graph Varable orderng The sze of a BDD and the effcency of the whole methodology depend strongly on the varable orderng. Unfortunately, the problem n determnng the optmal orderng s NP-complete [15]. However, approxmate solutons are relatvely easy to fnd. The orderng obtaned by a breadth-frst (BFS) traversal of the network startng from ts source always performs well [16]. Therefore, we choose the orderng obtaned by BFS, and consequently the varable orderng for Fg. 2 s x 1 <x 2 <x 3 <x 4 <x BDD expresson constructon The procedure of the EED s to expand, recursvely, successful edges of the source. The algorthm expands the gven network G nto k new sub-networks accordng to k edges (e 1, e 2,, e k ) connected to the source. For term, t performs the contractng operaton to obtan a new network G * e, wheren the vertces orgnally connected to e are merged nto a vertex as a new node, and all edges orgnally connected to the source are deleted. The sum of all cost along the lnk s set as the cost of the new node. If the cost of the component exceeds the tme deadlne D of the task, the decomposton of the graph termnates. And BDD_Zero wll Fg. 3 BDD constructng algorthm Calculatng relablty from BDD The BDD s based on Shannon expanson (the set of dsjont decomposed functons). Thus, the BDD can be recognzed as a graph-based set of dsjont products. Gven the probablty of each varable, the relablty of a BDD-based functon f can be recursvely evaluated. Each node of the BDD corresponds to a subgraph and the relablty of the graph s equvalent to the successful probablty of the node. If the node has been calculated and found n the hash-table, then drectly return the value of probablty. Otherwse, recursvely call the procedure wth negatve cofactor and postve cofactor. The algorthm s shown n Fg. 5. The probablty calculatng process of the graph mentoned n Fg. 2 s shown n Fg. 6.

4 928 ZHAO Changxao et al. / Chnese Journal of Aeronautcs 25(2012) No.6 crucal component [17]. RG ( ) = mn( RG ( )) x, x V E (6) x = 0 x = 0 j j Fg. 6 Probablty calculatng process. Fg. 4 Decomposton process of the graph mentoned n Fg.2. In other words, an essental varable of a network s a component whose falure has a domnatng effect on network relablty. Tradtonal method to fnd the essental varable s recalculatng the relablty of the network after removng each component. However, makng full use of the potental of the BDD composton operaton may be a better way. Frst, the relablty expresson of the orgnal ordnary network graph s encoded n the BDD. Then each component n the network s substtuted by a varable. So we only need to set each varable as 0 and recalculate the relablty. The BDD composton operaton s very effcent, whch makes ths approach hghly effcent. Usng ths method, we try to fnd the essental varable of the graph mentoned n Fg. 2, and the result s shown n Table 1. The relablty probablty of the component e s set as p and q =1 p. Table 1 Relablty of the network after the component s nvald Name of component Relablty of the network Fg. 5 Probablty calculatng algorthm Essental varable In the desgn of a network, t s mportant to dentfy the most crucal component of a network so that efforts can be made to keep t functonal. The essental varable s defned wth Eq. (6) to help dentfy the most e 1 p 2 p 3 p 4 +p 2 p 3 q 4 p 5 +p 2 q 3 p 5 e 2 p 1 q 4 e 3 p 1 p 2 p 4 +p 1 p 2 q 4 p 5 +p 1 q 2 p 4 + q 1 p 2 p 5 e 4 p 1 p 2 q 5 +q 1 p 2 q 3 p 5 e 5 p 1 p 4 +q 1 p 2 q 3 p 5 4. Experments Arcraft s a complex system that contans thousands

5 No.6 ZHAO Changxao et al. / Chnese Journal of Aeronautcs 25(2012) of components, so the number of nodes n the arcraft condton montorng network s large. In ths secton we ntroduced a larger network to valdate the algorthm proposed n ths paper. The probablstc graph s shown n Fg. 7. Table 2 ndcates the task nformaton, and Table 3 shows other parameters used n the experments. The probablty of nvaldaton of each component s set to 0.1. Table 2 Informaton of tasks Task name Source Destnaton Tme deadlne/ms t 1 n 1 n 16 1 t 2 n 1 n 16 6 t 3 n 3 n 5 3 t 4 n 3 n 14 3 Table 3 Delay parameters of each component Type of component Delay parameters/μs Lnk 50 Sensor 50 Processng unt 150 Task t 1 and t 2 have the same source and destnaton n the same network, whle the relablty of network for task t 2 s hgher than that for task t 1 because task t 1 has a more rgorous tme constrant than task t 2. Some paths are connectve for task t 2, whle they are dsconnected for task t 1 because the total delay exceeds the tme deadlne of task t 1. Task t 3 and t 4 have the same delay constant, whle the relablty of network for task t 3 s hgher than that for task t 4. The reason s that the number of hops of task t 4 s larger than that of task t 3. The total delay of some long path may exceed the tme deadlne, whch reduces the relablty. Table 5 shows the essental component for each task. Task t 1 and t 2 have the same source and destnaton n the same network, whle the essental component for each task s dfferent. The number of connectve paths for the task that has a more rgorous tme constrant s smaller, so the component belongng to the shortest path has serous effect on the relablty. 5. Conclusons Ths paper proposes a relablty methodology for the arcraft condton montorng network. Frstly, ths task-based algorthm uses the BDD wth the consderaton of the tme-constran. It keeps the merts of the BDD and meanwhle s sutable for the real-tme requrement networks. Secondly, the way to dentfy the most crucal component s more effcent than the tradtonal way for t makes full use of the potental of the BDD composton operaton. Thrdly, the experment results show that our algorthm s helpful n determnng the relablty of the network and addressng the essental varable for each task. References Fg. 7 Example graph of the experment. Table 4 s the relablty of the example network for each task. The essental component for each task s shown n Table 5. Table 4 Relablty of the network for each task Task name Relablty t t t t Table 5 Essental component for each task Task name Essental component t 1 e 1, e 10 t 2 e 9 t 3 e 12 t 4 e 9 [1] Ba H, Atquzzaman M, Llja D. Wreless sensor network for arcraft health montorng. Proceedngs of the Frst Internatonal Conference on Broadband Networks, 2004: [2] Faas P, Schroeder J B, Smth G. Vehcle health management research for legacy and future operatonal envronments. IEEE AESS System Magazne 2002; 25(4): [3] Belcastro C M. Avaton safety program:ntegrated vehcle health management techncal plan summary. NASA Technology Report, 2006: [4] Srvastava A N, Mah R W, Meyer C. Integrated vehcle health management. Natonal Aeronautcs and Space Admnstraton Aeronautcs Research Msson Drectorate Avaton Safety Program, [5] Yan C L, Lu K. Theory of economc lfe predcton and relablty assessment of arcraft structures. Chnese Journal of Aeronautcs 2011; 24 (2): [6] Broln A. Relablty engneerng: theory and practce. 5th ed. Berln: Sprnger, [7] Soh S, Ra S. Expermental results on preprocessng of path/cut terms n sum of dsjont products technque. IEEE Transactons on Relablty 1993; 42(1): [8] Theologou O R, Carler J G. Factorng & reductons for

6 930 ZHAO Changxao et al. / Chnese Journal of Aeronautcs 25(2012) No.6 networks wth mperfect vertces. IEEE Transactons on Relablty 1991; 40(2): [9] Chang Y R, Amar S V, Kuo S Y. OBDD-based evaluaton of relablty and mportance measures for multstate systems subject to mperfect fault coverage. IEEE Transactons on Dependable and Secure Computng 2005; 2 (4): [10] Xng L. An effcent bnary-decson-dagram-based approach for network relablty and senstvty analyss. IEEE Transactons on Systems, Man and Cybernetcs. Part A: Systems and Humans 2008; 38(1): [11] Ln M S, Chang M S, Chen D J. Effcent algorthms for relablty analyss of dstrbuted computng systems. Informaton Scences 1999; 117(1): [12] Wu J, Yuan S F. Desgn and evaluaton of a wreless sensor network based arcraft strength testng system. Sensors 2009; 9(6): [13] Cruz R. A calculus for network delay, part I: network elements n solaton. IEEE Transactons on Informaton Theory 1991;37 (1): [14] Kuo S Y, Lu S K, Yeh F M. Determnng termnal par relablty based on edge expanson dagrams usng OBDD. IEEE Transactons on Relablty 1999; 48(3): [15] Bollgand B, Wegener I. Improvng the varable orderng of OBDDs s NP-complete. IEEE Transactons on Relablty 1996; 45(9): [16] Hardy G, Lucet C, Lmnos N. K-termnal network relablty measures wth bnary decson dagrams. IEEE Transactons on Relablty 2007; 56(3): [17] Kuo S, Yeh F, Ln H. Effcent and exact relablty evaluaton for networks wth mperfect vertces. IEEE Transactons on Relablty 2007; 56(2): Bographes: ZHAO Changxao receved B.S. degree from Behang Unversty n 2004, and he s currently workng towards hs Ph.D. degree n the same unversty. Hs man research nterest s performance evaluaton of avoncs. E-mal: zhaochangxao@yeah.net CHEN Yao receved B.S. degree from Behang Unversty n 2005, and he s currently workng towards hs Ph.D. degree n the same unversty. Hs man research nterest s swtchng fabrc and real-tme network. E-mal: chenyao_kevn@163.com WANG Halang receved B.S. degree from Behang Unversty n 2002, and he s currently workng towards hs Ph.D. degree n the same unversty. Hs man research nterest s UWB and real-tme network. E-mal: gabbar@163.com XIONG Huagang s a professor n School of Electroncs and Informaton Engneerng at Behang Unversty, Bejng, Chna. Hs major research felds are avoncs and dgtal communcaton. E-mal: hgxong@ee.buaa.edu.cn