Safety analysis for integrated modular avionics based on blueprints

Transcription

1 Safety aalysis for itegrated modular avioics based o blueprits Jiayu Chu, Xiaohog Bao, Tigdi Zhao a ad Fuchu re School of Reliability ad Systems Egieerig, Beihag Uiversity, Chia Abstract. The Itegrated Modular Avioics System (IMA) has bee a core techology for the ew geeratio of aircrafts i recet years. It cosists of a set of reusable ad iteroperable commo fuctioal modules. However, the highly coupled relatioship of resources makes it difficult to idetify ad cotrol dagers. As a effective ad efficiet way, the blueprits are used to describe ad maage the IMA system. Owig to the system maagemet fuctios provided by the blueprits, we ca accurately determie the system resources cofiguratio status, which is very crucial for safety aalysis. I this paper, we explore the possibilities to coduct safety aalysis based o blueprits. A safety aalysis method based o blueprits is proposed, which applies mathematical logic to describe the logical relatioship betwee targets ad resources provided by the blueprits ad uses semi-tesor product of matrix theory to simplify the logical expressios. Based o the mathematical model, we ca coduct the fail safety aalysis ad idetify resources failures that may udermie the IMA system safety. 1 Itroductio The avioics system is a comprehesive cotrol iformatio-itesive system cosistig of hardware ad software such as missio maagemet, display cotrol, detectio sesors ad weapos [1].From the ed of the last cetury, the itegrated modular avioics system is gradually applyig to the moder aircraft desig process, such as F, A380. Differet from the origial discrete or federated avioics system, the IMA system implemets a wide rage of physical sythesis ad fuctioal itegratio. As show i Figure 1, each fuctio is ot located withi special processor or lie replacemet uit (LRUs) i the IMA system []. While the system is ruig, the resources are dyamically allocated to differet targets, ad it ca be regarded that there are may variable virtual subsystems. Although there are may beefits offered by the resources sharig mechaism, such as improvig the missio performace ad operatioal performace, reducig the life cycle cost [3], several problems eed to be solved urgetly. Oe of the most importat problem is how to coduct safety aalysis after sharig resources widely. Ad the allocatio of the applicatios to hardware i a effective ad efficiet way is also a critical issue. I order to solve the problems above, a cocept called blueprits is used to describe the IMA system. a Correspodig author : ztd@buaa.edu.c The Authors, published by ED Scieces. This is a ope access article distributed uder the terms of the Creative Commos Attributio Licese 4.0 (

2 MATEC Web of Cofereces Figure 1. The Basic Schematic Graph of IMA System I 1997, A.Marchetto [4] proposed a IMA system maagemet methods usig blueprits. He described blueprits as a meas of cetralizig ad orgaizig the system defiitio iformatio i such a way that chages of system itegratio decisios ca be trasferred, i a cotrolled ad automatic or semi-automatic way, to the target system, simply alterig the appropriate blueprits. Allied Stadards Avioics Architecture Coucil (ASAAC) icorporated the blueprits ito the recommeded techology for IMA system maagemet i its guidelies, ad fault moitorig ad maagemet fuctios were added to the blueprits. I the same year, Graham Jolliffe ad DM Nicholsa [] explored the possibilities towards a prelimiary safety case for IMA blueprits. Li Qia etc. [5] applied the blueprits techology to TV-commad-guided system i 009. Furthermore, there are also may researches o the IMA system blueprits desig iteratioally. She Y [6] proposed a method for the desig ad implemetatio of IMA system blueprits usig AADL i 008, while Haotia Wag etc. [7] modelled the IMA system blueprits based GSN ad L i 013. Recetly, the blueprits techology is widely regarded as a method to cetrally orgaize ad maage the system defiitio iformatio. Ad the blueprits are implemeted by oe or a group of maagemet software located i the operatig system. Except the system maagemet fuctios, blueprits ca also provide support for the safety aalysis due to the defiitio of system iformatio. I this paper, we apply mathematical logic to describe the logical relatioship betwee targets ad resources provided by the blueprits. Ad semi-tesor product of matrix theory is used to simplify the logical expressios. Based o the mathematical model, we ca coduct the fail safety aalysis ad idetify resources failures that may udermie system safety. The rest of the paper is orgaized as follows. I Sectio, a brief itroductio of the IMA blueprits is give. Sectio 3 discusses some basic cocepts ad related properties of matrix algebra at first. Ad the accordig to the semi-tesor product theory, the IMA systems model based o blueprits is proposed. I Sectio 4, we apply the method proposed above to a simple IMA system case. Sectio 5 is the cocludig remarks. IMA blueprits

3 Blueprits techology is a method to cetrally orgaize ad maage the system defiitio iformatio. Ad they are implemeted by oe or a group of maagemet software located i the operatig system. The blueprits ca implemet the resources cofiguratio ad recofiguratio automatically or semiautomatically, which meas the determiistic maagemet of system resources. The IMA blueprits ca be desiged by AADL or ADA tools. As show i Figure, the blueprits are usually subdivided ito three parts recetly, icludig software blueprits, hardware blueprits ad system blueprits. Ad the system blueprits ca be further divided ito static cofiguratio blueprits ad dyamic rutime blueprits. Figure. The IMA System Blueprits The software blueprits describe the fuctio software resources i terms of rutime requiremets, processig ad memory requiremets ad commuicatio requiremets. Ad the hardware blueprits describe the physical system [8]. The software blueprits ad hardware blueprits together describe the resources set of the IMA system, which ca be also called as resources pool [9]. The system blueprits guarateed the safe operatio of the IMA system. System desigers make decompositio of system targets ad determie the resources eeded to complete the targets. The decompositio result ca be give i the form of a tree as show i Figure 3. Accordig to the decompositio result ad the resources capacity i the resources pool, the iitial resources cofiguratio pla is determied, ad desigers record it i the cofiguratio blueprits. System desigers also record the recofiguratio plas whe some resources fail i the cofiguratio blueprits. The moitorig ad maagemet of the ruig process are completed by the ruig blueprits. For example, while the resources R1.3 fails i the Figure 4, the system cofiguratio chages ito the cofiguratio. Figure 3. Target Decompositio Diagram 3

4 MATEC Web of Cofereces Figure 4. The Cofiguratio Blueprits 3 The IMA system model based o blueprits 3.1 Matrix algebra This paper is aimed at the logical relatioship betwee targets ad resources provided by the blueprits, ad tries to simply the logic expressios usig semi-tesor product of matric theory. I this sectio, we preset some basic cocepts ad related properties of matrix algebra first [10-1]. Defiitio 1: Assume that A ( aij ) Mm ad B ( bij ) Mp. The the Kroecker product of q A ad B is represeted as A Bad defied by a11b a1b a1 B = a B a B a B am1b amb amb 1 A B Mmpq Defiitio : Assume that A ( aij ) Mm ad r B ( bij ) M. The the Khatri-Rao product of r A ad B is represeted as A Bad defied by A B= Col1( A) Col1( B) Col( A) Col( B) Colr ( A) Colr ( B) M mp q () Defiitio 3: Assume that A ( aij ) Mm ad r B ( bij ) M.the the left semi-tesor product r A ad B is represeted as A B ad defied by / / / / AB AI BI M (3) = t t p mt tq p While t lcm(, p) is the least commo multiple of ad p, ad I k is the k degree idetity matrix. A B, A B ad A B testify the associative law ad the distributive law. Furthermore, because the poit product is a special case of the left semi-tesor product, this paper makes the followig assumptio: A B AB (4) t t Theorem 1: Assume that X R is a colum vector, Y R is a row vector, ad, A is a arbitrary matrix. The we have 4 (1)

5 Defiitio 4: Assume that W W as traspositio matrix if it safeties W, XA I A X AY Y I A (5) IJ,, ij, t Mm m t, ad it raks with double idex mark i tur. We defie 1 I i ad J j (6) 0 else m m Theorem : Assume that X R, YR are two colum vectors, ad AR, BR are two row vectors. Tha we have Defiitio 5: Assume that 1, 0 W XY YX, ABW BA (7) [ m, ] [ m, ] mappig f : D Dis defied as a logic fuctio below D, ad x( i 1,,, k) Dis a group of logic variable. A i y f x1, x,, x Mx (8) x x, x,, x While M is defied as structure matrix, 1. Ad M is called as logic operator whe. Defiitio 6: Assume that M c, M ad d M respectively represet ad( ),or ( ) ad ot( ). The we have Mc, Md, = M (9) 1 k Defiitio 7: Assume that Rk diag k, k, k defie R as reductio matrix if it safeties k i with k 0,0,,1,0 i. The we x k R x (10) k 3. IMA blueprits model ad safety aalysis Based o the matric algebra theory show i Sectio 3.1, we propose a method to model the IMA blueprits. Ad with the IMA blueprits model, we ca fid the combiatio of dagerous faults which may ifluece the system safety. Refer to defiitio 5, we represet the logical odes (targets, fuctios ad resources) as biary logical variables. Accordig to the logical relatioship betwee the odes provided by the blueprits, we build the logical expressios, ad simply them with the help of semi-tesor product of matrix theory. As log as we idetify the structure matrix of the key targets which may ifluece the system safety, we ca discuss the combiatio of dagerous failures by solvig the logical equatios. The flow chart of modellig ad aalysig is show i Figure 5. 5

6 MATEC Web of Cofereces Figure 5. The Flow Chart of Modellig ad Aalysig Takig a simply example show i Figure 6 to preset the process of fidig structure matrix, we represet the logical odes as t 1, f 1, f, r 1, r. Figure 6. A Simple Example of Logical Graph The we ca describe the logical relatioship as follows t f f r r r (11) Accordig to the theory itroduced i Sectio 3.1, we ca covert formula 11 to formula 1. t f f M M rr r M rr M rr r M I R rr (1) 1 1 c c 1 c 1 c 1 c 1 While M c, R are defied i defiitio 6 ad 7, ad I is a idetity matrix. The structure matrix of t 1 is represeted as M t 1, ad the we have M M I R t c (13) 4 A simple IMA system case I this sectio, we take the radio data processig fuctio as a example. As show i Figure 7, the AA1 represets voice data processig fuctio while the A represets geeral data processig fuctio. Ad the A1 has a higher priority tha the A. Ad we cosider the A1 as the key target. 6

7 Figure 7. A Simple IMA System Case Accordig to the order of fuctios priority, the pre-set recofiguratio strategies which are record i the blueprits are as follows: 1) The A1 has a higher priority tha the A; ) While the AIU+DCTR1 fails, stop the A ad reallocate the AIU+DCRT to A1; 3) While the SM1 fails ad the SM does t fail, use the SM3 to replace the SM1; While the SM1 does t fail ad the SM fails, use the SM3 to replace the SM; while the SM1 ad the SM fail together, there is t ay chage; 4) While the NSM1 fails, use the NSM to replace the NSM1; Similar to Figure 4, we describe the iitial cofiguratio pla as follows. F1 F R3 R R1 R6 R5 R4 R9 R8 R7 R10 R11 Figure 8. Iitial Cofiguratio la While the meaigs of each ode i Figure 8 are show i Table 1. Table 1. The Meaigs of Nodes Number Item Number Item f 1 A 1 r 6 SM 3 f A r 7 NSM 1 r 1 AIU+DCTR 1 r 8 NSM r AIU+DCTR r 9 AM r 3 IF r 10 DM r 4 SM 1 r 11 SCM 1 r 5 SM 7

8 MATEC Web of Cofereces Because we oly cosider the A1 as the key target, we ca build the followig logical expressio accordig to the iitial cofiguratio pla. f1 r1r3r4r7 r9 r11 (14) As we cosider the pre-set recofiguratio strategies, we ca modify formula 14 to formula 15. f r r r r r r r r r r r r r (15) Ad the we covert the logical expressio to matrix represetatio. f M MrMMrr r MrMMrrr MrMMrr rr (16) 5 1 c d 1 c 1 3 d 4 c d 7 c The simplificatio process is as follows M rm M rr = M I M M R rr = rr M rr d 1 c 1 d c M rm M rrr= rrr M rrr d 4 c (17) (18) M rm M rr= M rr= rr M rr c 7 d 7 8 c The fial simplificatio result is show as formula 0. f M MrrrM rrrm rrrr M M I M I M rrrrrrrrrr (0) 5 5 1= c c The structure matrix of f 1 is represeted as M, ad the we have f1 5 c f (19) M MM IM I M (1) If we oly cosider the possible safety problems caused by SM resources failures, we make, ad solve the equatio f r1 r r3 r7 r8 r9 r T = rrr T, that is Accordig to the equatio solutio, we ca fid that oly whe r4 0 1 T, ad at least oe of r ad f fails. The aalysis result is i lie with T expectatios. r6 0 1 T holds, the the 1 () 5 Coclusios I this paper, we propose a method of safety aalysis for the IMA system based o blueprits, which applies mathematical logic to describe the logical relatioship betwee targets ad resources provided 8

9 by the blueprits ad uses semi-tesor product of matrix theory to simplify the logical expressios. Based o the mathematical model, we ca coduct the fail safety aalysis ad idetify resources failures that may udermie system safety. Adoptig the method proposed above, the value of the blueprits is further tapped. Owig to the system maagemet fuctios provided by the blueprits, we ca accurately determie the system resources cofiguratio status, which is very crucial for safety aalysis. Refereces 1. I. Moir, A. Seabridge ad M. Jukes, Civil Avioics Systems (West Sussex, UK, 013). G. Jolliffe ad DM. Nicholso, Costituets of Moder System-safety Thikig, (005) 3. C. Yi, Y. Reliag ad Z. Li, Itegrated Techology of Avioics Modular Itegrated System (Beijig, Chia, 013) 4. A. Marchetto, Dasc. Aiaa/ieee. IEEE, 18, (1997) 5. L. Qia, F. Jifu,. Bo ad Z. Jiaqiag, Computer Egieerig, 35, 5-7 (009) 6. Y. She, Computer Egieerig, 34, (008) 7. W. Haotia, H. Feg ad X. Huagag, Aerosp. Sci. Techol., 6, (013) 8. D. Suo, J. A ad J. Zhu, Digital Avioics Systems Coferece. IEEE, 1C4-1-1C4-1 (011) 9. Y. Wokeu ad Y. Baeck-ju, Computer Stadards & Iterfaces, 36(6), (014) 10. C. Daizha, X. Yuaqig, M. Hogbi, Y. lipig, Matrix Algebra, Cotrol ad Game (Beijig, Chia, 016) 11. C Daizha, Q Hogsheg ad X Acheg, Joural of Systems Sciece & Complexity, 0, (007) 1. C Daizha ad Q Hogsheg, IEEE Tras. Autom. Cotrol, 55, (010) 9