Fault-tolerant Sensor Network Based on Fault Evaluation Matrix and Compensation for Intermittent Observation

Transcription

1 Vol.48, No.10, 1/ Fault-tolerant Sensor Networ Based on Fault Evaluaton Matrx and Compensaton for Intermttent Observaton Kazuya Kosug and Toru Namerawa Ths paper deals wth a fault-tolerant sensor networ confguraton by ntroducng a fault evaluaton matrx and a compensaton method of ntermttent observaton. A networed sensor system s desgned by embedded local Dstrbuted Kalman flters n each sensor, and the sensor agent has to estmate plant s state under the condton of sensor falure and ntermttent observaton. We propose two KF estmaton algorthms whch are based on a fault detecton swtchng reles on a fault evaluaton matrx and an mputaton method by usng estmate observaton, respectvely. Fnally we show expermental results to analyze effectveness of the proposed method. Key Words: fault tolerant system, fault detecton, ntermttent observaton, swtchng Kalman flter 1. (WSN) 1) 3) 4), 5) WSN WSN 6) 7) WSN WSN Graduate School of Scence and Engneerng, Keo Unversty, Hyosh, Kohou-u, Yoohama Faculty of Scence and Engneerng, Keo Unversty, Hyosh, Kohou-u, Yoohama Receved November 22, 2011 Revsed May 28, ) 9) WSN WSN 11) 12) 13), 14) (KF) 14) KF TR 0010/12/ c 2011 SICE

2 2 T. SICE Vol.48 No.10 October Fg. 1 Fg. 1 Problem formulaton N 1 1 N 2 2 (1) LTI x +1 = Ax + Bu + w =1,...,N 1 1 x R n u R r w R n W 0, 0 u = Lˆx j 2 L R r n LQG ˆx j j y j y j = Cj x + D j vj + F j gj j =1,...,N 2 3 Rm j 1 v j Rp V j 0, 0 15) D j := Dj (x ) R m p j F j Rm n, g j Rn F j gj > 0 j Fg (1) (3) E{v j vjt s } = E{ww s T } =0( s) E{v j wt } =0,E{g j wt } =0,E{g j vjt } =0 E{x 0w T } =0,E{x 0v jt } =0,E{x0gjT } =0 v E{ww T } = W > 0, E{v j vjt } = V j > 0, E{[g j E(gj )][gjt E(gj )]} = Gj 0 2 (A, W 1 2 ) 3 (C j,a) 1 2, 3 Rccat ( y j F j gj yj ) (3) F j gj > 0 j 2 1, 2 j y j

3 KF j f 1 = j0 1, ˆx 1 1 j0 j 0 ˆx +1 ˆx ỹ +1 K S = Aˆxj0 + Buj0 = ˆxj0 = y 1 + γj0 C ˆxj0 1 = AP AT + W = P = Kj0 {ỹj0 } 1 γj0 Kj0 Cj0 1 T 1 Cj0 {S } = cov(ỹ ) 6 S S 16) (4) (6) 14) KF γ R 1 14) γ γ j 0 M [ 1] M := S Cj0 = D + E{C E[C T 1 Cj0 V D T ˆD ηj0 (g j0 T F j0 T ηj0 ](g j0 T F j0 T ˆD ˆV ˆV ˆD T ˆD T +F j0 F j0 T F j0 T Gj0 F j0 T E[g j0 T ]) E[g j0 T ])} E[η j0t C T ]) T ](ηj0 C T E[η j0t C T ])} 7 + E{F T gj0 (ηj0 C T E[F j0 gj0 η j0 := x ˆx 1 j0 ˆD ˆV := D (ˆxj0 1 ) v 0 (7) ˆv (5) x ˆx 1 x,ˆx 1 D, ˆDj 0 D V D T ˆD ˆV ˆD T F j0 Gj0 F j0 T ˆV V V M 2 γ [ 2] γ 1 f M mn tracem M max := 8 0 otherwse M mn, M max P 1, P +1 M +1 M x, ˆx 1 J g j0 F 1 G j0 F 1T F 2 G j0 F 2T M 1 M 2 Proof F j0 gj0 γj0 =0 ˆx F j0 gj0 x u u ˆx x F j0 gj0 yj0 ˆx ˆxj0 1 F j0 gj0 x,ˆx 1 (7) (9) F j0 Gj0 F j0 T 0 M = S Cj0 = D T 1 Cj0 V D T ˆD + F j0 Gj0 F j0 T ˆD ˆV ˆV ˆD T ˆD T 9 2

4 4 T. SICE Vol.48 No.10 October 2012 (5) (10) KF (5) = 1 Kj0 Cj Proof γ =0 (5) = 1 <Pj0 γ =1 KF (5) (10) = (10) <Pj j 0 y KF = 1 2 [ 3] K := {( 1 ) 1 + α 2 C T := T 1 Cj0 {C ( ˆD ˆV j 0 T 1 Cj0 ˆD j0t ) 1 C } α 2 ˆD j ˆV 0 ˆD j0t } 1 12 (11) D j0 V DT ˆD ˆV ˆD T (13) ˆx =ˆxj0 1 + Kj0 ( ŷ + l ) 13 ŷ ŷ l = C ˆxj0 = C x ŷ 1 + ˆD =(1+α ) ˆD j0ˆv ˆv, 14 E{Cj0 (x ˆx 1 )} 15 (13) y ŷ (15) α R 1 (16) α = ɛα 1,ɛ>1 16 (11) = 1 Proof (11) ˆD ˆV ˆD T > 0 1 α (11) 2 0 (13) C x ŷ (17) ±( ŷ cov( ŷ )=C = E{( ŷ T 1 Cj0 E[ ŷ E[ ŷ ]) + ˆD ˆV ˆD T ])( ŷ E[ ŷ ])T } 17 ỹ (18) β (19) cov{ỹ ( ŷ =cov{d j0 v E[ ŷ ]+β )} + ˆD β :=(1+α ) ˆD j0ˆv ˆv +E[ ŷ ] β } 18 + E[C ˆxj0 1 ŷj0 ] 19 β α (17), (19) (20) ŷ = ŷ E[ ŷ ]+β +(1+α ) ˆD j0ˆv E[Cj0 ηj0 ] = ŷ +lj ), 18) 1 j 0 j 0 (5) KF M r j0 1,, +1,ˆxj0 1,ˆxj0 (Fg. 2 ). j 0 j 1 y j ( r j ).

5 v j KF r j ˆx j 1, P j 1,ˆxj, P j, P j +1 j v j v j u j, P j +1 v (11) v j j+1 0 (Fg. 3 ). Fg. 4 Expermental system T 1 0 T A = T ,B = T T T 22 Fg. 2 Neghbor dscovery strategy Fg. 3 Networ update P j +1 ( ) KF 17) (DKF) j 0 j 0 ˆx 1 d j r max r j0 = δdj, δ > 1 21 (21) r max j 1 j 0 r j = rj0 4. Fg (N 1 =1), (1) 18), 19) x =[x y ẋ ẏ ] T A, B T =0.1s Q = I 4 9 (N 2 =9) 2 ζ j =(X j, Y j ) ζ 1 =(0, 0), ζ 2 =(0, 0.5), ζ 3 =(0, 1.0) ζ 4 =(1.0, 0), ζ 5 =(1.0, 0.5), ζ 6 =(1.0, 1.0) =(2.0, 0), ζ 8 =(2.0, 0.5), ζ 9 =(2.0, 1.0) 23 ζ 7 C j, ] C j [1 = 1 1 1, (j =1,...,9) 24 V j =dag{0.8, 1.4, , } 25 Leutron Vson PcPort-color CCD Halcon PC 19) D j := Dj (x ) 4 4 D j := Dj (x ) x D j = Xj y Yj D (x ) dspace DS

6 6 T. SICE Vol.48 No.10 October x 1 0 = [2100] T, P0 1 =0.1 I Fg. 5 Fg. 6 Fg. 9 Trace P for sensor 4 Fg. 10 Trace P for sensor 6 Fg. 5 Vehcle s trajectory 1 Fg. 6 Sensor swtchng x 1 0 = [ ] T, x 2 0 = [0100] T, x 3 0 = [ ] T, P0 1 3 =0.1 I δ =1.5, r max =1.0 Fg. 11, Fg. 12 Fg. 6 1, 4, 6, 9 4, 6 4: 0, 25 step 1.5, 6: 0, 15 step 1.5 Fg. 6 4, 6 M mn =0.36, M max =0.76 Fg. 7 Fg. 8 A C (A: B: C: + ) 4, 6 Fg. 11 Vehcles trajectory Fg. 12 Sensor swtchng Fg Fg. 7 Trace M for sensor 4 Fg. 8 Trace M for sensor 6 Fg. 13 Vehcle 3 s trajectory Fg. 14 Trace P for vehcle 3 Fg. 9, Fg. 10 Fg. 13, Fg

7 r max = x 0 = [ ] T Fg Fg Fg. 17, Fg. 18 = 1 (11) 2 Fg. 21, Fg. 22 Fg. 21 Fg. 22 Fg. 19 Observaton corrupton Fg. 20 Trace P for vehcle Fg. 15 Vehcle s trajectory Fg. 16 Fault sgnal n sensor 1 Fg. 21 Vehcle s trajectory Fg. 22 Trajectory of estmaton 5. Fg. 17 Trace M for sensor 1 Fg. 18 Trace P for sensor step x 0 = [ ] T Fg. 19, Fg. 20

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