Condition Monitoring and Fault Detection of Railway Vehicle Suspension using Multiple-Model Approach

Proceedings of the 17th World Congress The International Federation of Autoatic Control Condition Monitoring and Fault Detection of Railway Vehicle Suspension using Multiple-Model Approach Hitoshi Tsunashia Yusuke Hayashi Hirotaka Mori Yoshitaka Maruo Nihon Uniersity, 1-2-1 Izui-cho, Narashino-shi, Chiba 275-8575, Japan (Tel: +81-47-474-2339; e-ail: tsuna@cit.nihon-u.ac.jp). Graguate School of Nihon Uniersity, 1-2-1 Izui-cho, Narashino-shi, Chiba 275-8575, Japan (Tel: +81-47-474-2339). Graguate School of Nihon Uniersity, 1-2-1 Izui-cho, Narashino-shi, Chiba 275-8575, Japan (Tel: +81-47-474-2339). Nihon Uniersity, 1-2-1 Izui-cho, Narashino-shi, Chiba 275-8575, Japan (Tel: +81-47-474-2339; e-ail: yaru@cit.nihon-u.ac.jp). Abstract: This paper deonstrates the possibility to detect suspension failures of railway ehicles using a ultiple-odel approach fro on-board easureent data. The railway ehicle odel used includes the lateral and yaw otions of the wheelsets and bogie, and the lateral otion of the ehicle body, with sensors easuring the lateral acceleration and yaw rate of the bogie, and lateral acceleration of the body. The detection algorith is forulated based on the Interacting Multiple-Model (IMM) algorith. The IMM ethod has been applied for detecting faults in ehicle suspension systes in a siulation study. The ode probabilities and states of ehicle suspension systes are estiated based on a Kalan Filter (KF). This algorith is ealuated in siulation exaples. Siulation results indicate that the algorith effectiely detects on-board faults of railway ehicle suspension systes. 1. INTRODUCTION Railway aintenance is iportant for ensuring safety and aoiding accidents. An inspection to detect faults in railway ehicles is especially iportant. Soe faults could cause serious accidents while the ehicle is traelling. Condition onitoring is necessary in order to iediately detect ehicle faults. For condition onitoring, it is necessary to detect the fault fro the signals of sensors attached to the ehicles. Condition onitoring can be considered to be a part of the well-established and well-deeloped area of Fault Detection and Isolation (or Identification) (FDI). Many research works on FDI are suarized in nuerous publications, Patton et al. [2000], Gustafsson. [2001]. Condition onitoring is ainly applicable to systes that deteriorate with tie and seeks to detect and identify deterioration before it causes a failure. This is a key eleent of condition-based aintenance, Buruni et al. [2007]. Often, only output signals can be easured, in which case signal-based ethods can be applied. A easured signal, essentially the response to a disturbance input(s), is analyzed in the tie doain, frequency doain, or tiefrequency doain. Band-pass filters, spectral analysis, axiu-entropy estiation, and waelet analysis can all be used as signal-processing ethods. If the relation This study was supported by the Progra for Prooting Fundaental Transport Technology Research fro the Japan Railway Construction, Transport and Technology Agency (JRTT). between the input signal and the output signal is known, abrupt faults can be detected using the odel-based fault detection ethod, which can be defined as detection and decision-aking based on the ealuation of residuals. A recent project has recognized the alue of odel-based processing, exaining both residual-based (i.e. using the estiation errors) and direct paraeter estiation for identifying degradation in lateral dapers, yaw dapers and the wheel profile, the three aspects industry has identified as the ost coon causes of aintenance actiity. The paraeter estiation technique in particular has been inestigated using data collected fro a set of inertial sensors fitted to a serice ehicle, and it has been possible to obtain good, representatie alues for both lateral and secondary anti-yaw dapers, Li et al. [2007]. This study deonstrates the possibility to detect railway ehicle suspension failures using the ultiple-odel approach. The railway ehicle odel used includes the lateral and yaw otions of the wheelsets and bogie, and the lateral otion of the ehicle body, with sensors easuring lateral acceleration and yaw rate of the bogie, and lateral acceleration of the body. The IMM ethod, Bar-Shalo et al. [1993], Bar-Shalo et al. [2001], has been applied for detecting ehicle suspension faults in a siulation study. 2. VEHICLE MODEL Figure 1 depicts the railway ehicle odel Li et al. [2004]. Lateral and yaw otion of wheelsets and bogie are consid- 978-1-1234-7890-2/08/$20.00 2008 IFAC 8299 10.3182/20080706-5-KR-1001.1923

ered. Lateral otion is considered for a ehicle body. The equations of otion for a ehicle traeling on a straight track can be written as follows: w1 ÿ w1 + 2f 22 ẏ w1 + K y y w1 = (1) 2f 22 ψ w1 + K y y b + a 0 K y ψ b I w1 ψw1 + 2f 11l0 2 ψ w1 + K ψ ψ w1 = 2f 11λl 0 y w1 + K ψ ψ b + 2f (2) 11λl 0 y t1 r 0 r 0 w1 ÿ w2 + 2f 22 ẏ w2 + K y y w2 = (3) 2f 22 ψ w2 + K y y b + a 0 K y ψ b I w2 ψw2 + 2f 11l0 2 ψ w2 + K ψ ψ w2 = 2f 11λl 0 y w2 + K ψ ψ b + 2f (4) 11λl 0 y t2 r 0 r 0 b ÿ b + (C ylb + C yrb )ẏ b +{2K y + (K ylb + K yrb )}y b = K y y w1 + K y y w2 (5) +(C ylb + C yrb )ẏ bd + (K ylb + K yrb )y bd I b ψb +(C ψlb + C ψrb ) ψ b + {2a 2 0K y + 2K ψ }ψ b = a 0 K y y w1 + K ψ ψ w1 a 0 K y y w2 + K ψ ψ w2 (6) bd ÿ bd +(C ylb + C yrb )ẏ bd + (K ylb + K yrb )ẏ bd = (C ylb + C yrb )ẏ b + (K ylb + K yrb )y b (7) Anti-yaw daper C ψrb K y / 2 C yrb K yrb a Vehicle body y bd the odel j is correct, can be calculated by the following equation. p( j Y t ) = p(y t j, Y t 1 )p( j Y t 1 ) p(yt j, Y t 1 )p( j Y t 1 (8) ) Here, p(y t j, Y t 1 ) is the likelihood function of odel j at tie t. Assuing a Gaussian distribution, the likelihood function can be ealuated by residual and coariance fro odeatched filter j. An oerall estiate can be obtained by using the ode-conditioned state estiate obtained fro each filter and ode probability as p(x t Y t ) = p(x t j, Y t )p( j Y t ) (9) Figure 2 illustrates the basic concept of the ultiple-odel approach. y t u t y t u t y t u t Model1 basedfilter Model2 basedfilter Modeli basedfilter 1 xˆt 2 xˆt xˆi t Fusion xˆt K ψ y w 1 y b ψ ψ b w1 2 Bogie frae C yrb Fig. 1. Railway ehicle odel ψ w Wheelset Kyrb y w2 C ψrb Here, y w1 and y w2 are the lateral displaceents of the leading and trailing wheelsets, y b is the lateral displaceent of the bogie, y bd is the lateral displaceent of the ehicle body, ψ w1 is the yaw angle of leading wheelsets, ψ w2 is the yaw angle of the trailing wheelsets, and ψ b is the yaw angle of the bogie. y t1 represents the lateral track displaceent at the leading wheels, and y t2 represents the lateral track displaceent at the trailing wheels. 3. MULTIPLE-MODEL APPROACH The ultiple-odel approach is an adaptie-estiation technique proposed in the field of target tracking. This approach enables a wide ariety of adaptie estiation to be used while changing both paraeters and the odel structure. In the ultiple-odel approach, it is assued that the syste obeys one of a finite nuber of odels M { j },, that include possible odes. Using Bayes forula, the ode probability, a posteriori probability that Fig. 2. Concept of ultiple-odel approach When the syste ode (odel) switches in tie, it is necessary to forulate the ultiple-odel approach dynaically. In the dynaic forulation, the ode-jup process, which is considered the ode-transition probability, should be taken into account. The possible odel history through tie t is denoted by the ode history, M t = {M 1, M 2,, M t}. The ode probability based on the ode history is p(m t Y t ) = p(y t M t, Y t 1 )p( t M t 1, Y t 1 ) p(yt M t, Y t 1 )p(m t, Y t 1 ) p(m t 1 Y t 1 ) (10) The oerall estiate is obtained by the ode-conditioned estiate and the ode probability as p(x t Y t ) = p(x t M t, Y t )p(m t Y t ) (11) t The nuber of the ode history M t increases exponentially with tie, which is a fatal proble for ipleentation. In order to aoid the exponentially increasing nuber of ode history, generalized pseudo-bayesian of first order(gpb1) and second order(gpb2) and Interacting Multiple-Model(IMM) algorith, Blo et al. [1988], Li et al. [1993], are proposed. 8300

4. FAULT DETECTION OF VEHICLE SUSPENSION USING IMM ESTIMATOR Figure 3 illustrates the concept of fault detection of ehicle coponents using the ultiple-odel approach. Disturbance d( t) P 0j = i=1 + { ρ i j( t 1) P i [ ] [ ] T } (13) ˆx i ˆx0j ˆx i ˆx0j Here, ρ i j is the ixed probability at tie t, and is expressed by u( t ) y( t) Mode 1 Spring failure odel based estiator Mode Probability Fault where ρ i j = 1 c p ij ρ i j i, j = 1,..., (14) c j = p ij ρ i j = 1,..., (15) i=1 Mode 2 Daper failure odel based estiator Fig. 3. Multiple-odel approach for ehicle suspension fault detection Figure 4 depicts the algorith of the IMM estiator. Estiations were conducted using the Kalan filter (KF) described below. u ( t) Vehicle y( t) Mixing ˆ, 01 01 x( t P 1) ( t 1) ˆ, 02 02 x( t P 1) ( t 1) ˆ, 0 0 x( t P 1) ( t 1) Fig. 4. IMM estiator Model 1 based KF Model 2 based KF Model based KF Probability Mode 1 p 2 p p Fusion 1 1 x ˆ, P ( t) ( t) 2 2 x ˆ, P ( t) ( t) x ˆ, P ( t) ( t) Fusion sets of odels were considered as the syste odes. The (i, j) eleent of the ode transition atrix p ij representing ode transition probabilities aong the odes expresses the transition probability fro Mode i to Mode j. The following sections describe the details of the IMM estiator for railway ehicle suspension systes. 4.1 Mixing Expressing the estiated alue obtained by the KF for Mode i(i = 1,, ) as ˆx i and that obtained at tie t(t = 0, 1, 2, ) as P i, the ixed estiated alue ˆx0j and the ixed estiated coariance atrix as P 0j can be expressed by the following equations. ˆx 0j = ˆx i ρ i j j = 1,..., (12) i=1 ˆp xˆ ( t ) 4.2 Mode-Matched Filtering In this study, the KF was designed based on the reducedorder linear odel, where the otions of wheelsets are excluded. The discrete syste is expressed by x (t+1) = F x + Gu + w (16) y = Hx + Lu + (17) where x = [ ] T ẏ b y b ψ b ψ b ẏ bd y bd, u = [ u 1 u ] T 2, w = [ w 1 w 2 w 3 w 4 w 5 w 6 ] T, y = [ ] T ÿ b ψ b ÿ bd, = [ 1 2 3 ] T The following KF algoriths are then obtained. Filter equations ˆx j (t t 1) = F j (ˆx 0j (t 1 t 1) ) + Dj u (18) ˆx j (t t) = ˆxj (t t 1)[ )] y (H j (ˆx j(t t 1) ) + (19) Lj u Kalan gain +K j K j = P j (t t 1) Hj T S j 1 (20) S j = Hj P j (t t 1) Hj T + R j (21) Coariance equations P j (t t 1) = F j P 0j (t t 1) F j T +G j Qj Gj T (22) P j (t t) = P j (t t 1) Kj Sj Kj T (23) Here, ˆx j is the estiated state obtained by using the KF. The syste noise w and easureent noise are assued to be white Gaussian with a zero ean and coariance of Q(w ) and R( ). 8301

4.3 Calculation of Mode Probability The likelihood function for the each ode is expressed as Λ j = 2πS j 1 2 exp[ 1 2 e T S 1 j e ] (24) e = y (H j ˆx j (t t 1) + Lj u ) Therefore, the ode probability for Mode j at tie t is gien by Λ j c j ρ j = i=1 Λ (25) i c i The ode probabilities obtained ary with tie and are soothed by using a oing-aerage window. 4.4 Estiate and Coariance Cobination The estiated state ˆx and cobination of coariance P are finally obtained by weighting the estiated state ˆx j and the ixed coariance P j for each ode with the ode probabilities. ˆx = ˆx j ρ j (26) P = ρ j [P ] j + [ˆxj ˆx ] [ˆx j ˆx ] T (27) 5.1 Siulation Condition 5. SIMULATION EXAMPLE We erified the alidity of the proposed ethod for two cases: (1) a secondary lateral daper failure (the daping coefficient reduced fro its noinal alue) occurs while the train is running; (2) a lateral acceleroeter failure occurs when the train is running. In this siulation, the ehicle response is generated when passing along a track with an irregularity. We created a track irregularity by using white Gaussian noise passed through a shaping filter. In case 1, the daping coefficient changes as shown in Fig. 5. Fig. 6. Measureent noise Mode 2 A secondary lateral spring failure (100% reduction in spring rate) Mode 3 A secondary lateral daper failure (20% reduction) Mode 4 A secondary lateral daper failure (40% reduction) Mode 5 A secondary lateral daper failure (60% reduction) Mode 6 Failure of lateral acceleroeter of bogie. Mode 7 Failure of yaw rate sensor of bogie. Mode 8 Failure of lateral acceleroeter of body. In Modes 6, 7 and 8, we proide a different coariance odel of the easureent noise. First, we assued that the bogie lateral daper and lateral acceleroeter were noral. In case 1, the estiated alue of the daping coefficient at tie t, was obtained by equation (28) by weighting the daping coefficient C j ylb for each ode with the ode probabilities. Ĉ ylb = C j ylb ρ j t (28) 5.2 Siulation Result Detection of a Secondary Lateral Daper Failure Figures 7,8 and 9 present the easureent data of this case used for the suspension fault detection. Fig. 5. Noralized daping coefficient In case 2, we odeled a sensor failure for increasing coariance of the easureent noise. Figure 6 depicts the easureent noise used in the siulation. IMM estiator is designed based on following odels. Mode 1 No alfunction in ehicle Fig. 7. Lateral acceleration of bogie Figures 10 and 11 depict the calculation results of ode probabilities; the odes where the probability was alost zero are excluded. It is difficult to directly detect a lateral daper failure fro these easureent data. Howeer, ode probabilities indicate that a lateral daper failure can be detected 8302

Fig. 8. Lateral acceleration of body Mode 1 to Mode 1) of the transition atrix is uch higher than that of other odes. The estiation delay can be iproed by changing the transition atrix, but there is a trade-off between delay and estiation accuracy. Figure 12 presents the estiated alue of the lateral daper coefficient. It can be seen that the proposed ethod exhibited good estiation perforance. In addition, we estiated the paraeter using EKF for coparison. Fig. 9. Yaw rate of bogie Fig. 10. Mode probabilities for odes 1 and 2 Fig. 12. Estiation of daping coefficient EKF is the ost widely applied state-estiation algorith for nonlinear systes. EKF can be used to estiate unknown paraeters in dynaic systes. When using EKF for paraeter estiation, it should be noted that selecting the state ector and initial alues of paraeters is iportant as partial linearization is eployed and that the conergence of estiated paraeters is not always guaranteed, Ljung. [1979]. It should be noted that the estiation using EKF failed in this siulation exaple. Detecting a Lateral Acceleroeter Failure Figure 13 illustrates the lateral acceleration of bogie data of this case used for the sensor fault detection as an exaple. Figures 14 and 15 present the calculation results of ode probabilities; odes where the probability was alost zero are excluded. Fig. 11. Mode probabilities for odes 3, 4 and 5 in 3s with an estiation delay of 1s. This can be supported by the fact that Modes 3, 4 and 5 (lateral daper failure ode) exhibited higher ode probabilities after 3s, and Mode 1 (no alfunction ode) indicated a lower ode probability after 3s. It should be noted that the type of failure (lateral spring failure or lateral daper failure) can be detected because Mode 2 (lateral spring failure) exhibited lower ode probabilities. The reason for the delay in ode probabilities is that the weight of the p 11 eleent (transition probabilities fro Fig. 13. Lateral acceleration of bogie data for case 2 We can see that ode probabilities indicate a lateral acceleration sensor failure after 2s. 6. CONCLUSIONS We studied ethods of detecting alfunctions in ehicle suspension systes using on-board easureent data. We adapted the IMM ethod, which is a ultiple-odel based estiation ethod, for detecting faults in railway ehicles. 8303

Fig. 14. Mode probabilities for odes 1 and 2 Y. Bar-Shalo, X. R. Li and T. Kirubarajan. Estiation with Application to Tracking and Naigation. Wiley. H. A. Blo and Y. Bar-Shalo. The Interacting Multiple Model Algorith for Syste with Markoian Switching Coefficient. IEEE Trans. Autoatic Control, olue AC-33, No.8, pages 780-783, 1988. R. L. Li and Y. Bar-Shalo. Design of an Interacting Multiple Model Algorith for Air Traffic Control Tracking. IEEE Trans. Control Syst. Tech., olue 1, No.3, pages 186-194, 1993. L. Ljung. Asyptotic behaior of the extended Kalan filter as a paraeter estiator for linear syste. IEEE Trans. Autoatic Control, olue AC-24, No.1, pages 36-50, 1979. Fig. 15. Mode probabilities for odes 6, 7 and 8 We described the interacting ultiple-odel(imm) ethod for detecting faults in railway ehicles fro the easured lateral acceleration of the bogie and body and fro the yaw rate of the bogie. A paraeter-estiation technique using EKF was also copared with the IMM-based ethod. We exained the alidity of the proposed approach by perforing two siulations, a secondary lateral daper failure (the daping coefficient reduced fro its noinal alue) and a lateral acceleroeter failure (coariance of the easureent noise is increase) in railway ehicle suspension systes. Siulation results indicate that the IMM-based ethod is an effectie on-board fault detection technique for railway ehicle suspension systes. REFERENCES R. J. Patton, P. M. Frank and R. N. Clark. Issues of Fault Diagnosis for Dynaic Syste Springer, 2000. F. Gustafsson. Adaptie Filtering and Change Detection Wiley, 2001. S. Buruni, R. M. Goodall, T.X. Mei and H. Tsunashia. Control and onitoring for railway ehicle dynaics. Vehicle Syste Dynaics, olue 45, No. 7-8, pages 765-771, 2007. P. Li, R. M. Goodall, R. Weston, C. S. Ling, C. Goodan and C. Roberts. Estiation of railway ehicle suspension paraeters for condition onitoring. Control Engineering Practice, olue 15, pages 43-55, 2007. P. Li, R. M. Goodall and Kadirkaanathan. Estiation of paraeters in linear state space odel using Rao- Blackwellised particle filter. IEE Proceedings-Control Theory and Application, olue 151, No. 6, pages 727-738, 2004. Y. Bar-Shalo and X. R. Li. Esitiation and Tracking Principles, Techniques, and Software Artech House. 8304