Fault Diagnosis of Autonomous Underwater Vehicles

Transcription

1 Research Journal of Appled Scences, Engneerng and Technology 5(6): , 03 SSN: ; e-ssn: Maxwell Scentfc Organzaton, 03 Submtted: March 3, 0 Accepted: January, 03 Publshed: Aprl 30, 03 Fault Dagnoss of Autonomous Underwater Vehcles Xao Lang, Jundong Zhang and 3 We L College of Traffc Equpment and Ocean Engneerng, College of Marne Engneerng, 3 College of Envronmental Scence and Engneerng, Dalan Martme Unversty, Dalan, Chna Abstract: n ths study, we propose the least dsturbance algorthm addng scale factor and shft factor. The dynamc learnng rato can be calculated to mnmze the scale factor and shft factor of wavelet functon and the varaton of net weghts and the algorthm mprove the stablty and the convergence of wavelet neural networ. t was appled to buld the dynamcal model of autonomous underwater vehcles and the resduals are generated by comparng the outputs of the dynamcal model wth the real state values n the condton of thruster fault. Fault detecton rules are dstlled by resdual analyss to execute thruster fault dagnoss. The results of smulaton prove the effectveness. Keywords: Autonomous underwater vehcle, least dsturbance, thruster fault dagnoss, wavelet neural networ NTRODUCTON Wth the development of the actvtes n deep ocean, the applcaton of underwater vehcles s wdespread (Xu and Xao, 007; Bldberg, 99). Underwater vehcles are frequently performng msson n unstructured, complcated and hazardous envronment (Adam, 985). For autonomous underwater vehcles, the ablty to detect and tolerate fault s a crucal ssue to realze ts autonomy. Model-based technque has the merts such as low cost, hgh relablty and easy realzaton for autonomous underwater vehcles, so t s a sutable approach. However, for the nfluence of model error, measurement nose, outer dsturbance and so on, t s dffcult enogh to buld up the accurate model for autonomous underwater vehcles. Neural networ has the characters of strong nput-output nonlnear mappng, dstrbuted store of nformaton, parallel process and especally strong self-organzng and selflearnng ablty, whch mae neural networ become an effectve method for fault dagnoss. Moreover, t has been appled n practce (Alessandr et al., 999). Wavelet neural networ s a new radal bass functon neural networ developed from wavelet transform. The orthonormalty of wavelet functon used as the hdden layer functon maes wavelet neural networ more sutable n learnng functon of local varaton and dscontnutes. By adustng scale factor and shft factor of wavelet functon and weghts of networ to affect output of networ, wavelet neural networ has strong ablty of dstllng sgnal detals and mappng nonlnear functon (L and We, 998; Zhao and Zhou, 003). n ths study, we propose a least dsturbance wavelet neural networ to buld up the dynamc model of underwater vehcles and add scale factor and shft factor of wavelet functon to dynamc learnng rate algorthm based on steepest descent method. Then, we compare the output of model wth the real state value to acheve resduals and dstll the fault nformaton from the resduals to detect fault. n ths study, we propose the least dsturbance algorthm addng scale factor and shft factor. The dynamc learnng rato can be calculated to mnmze the scale factor and shft factor of wavelet functon and the varaton of net weghts and the algorthm mprove the stablty and the convergence of wavelet neural networ. t was appled to buld the dynamcal model of autonomous underwater vehcles and the resduals are generated by comparng the outputs of the dynamcal model wth the real state values n the condton of thruster fault. Fault detecton rules are dstlled by resdual analyss to execute thruster fault dagnoss. The results of smulaton prove the effectveness. LEAST DSTURBANCE WAVELET NEURAL NETWORK The common tranng algorthm of wavelet neural networ s steepest descent method and learnng rate s extremely sgnfcant for the convergence and stablty of c networ. The hdden layer functon of wavelet neural networ s wavelet functon and ts scale factor and shft factor are also adusted to mnmze the least square error. For wavelet neural networ, outputs of neural networ are affected by both net weghts and scale factor and shft factor of wavelet functon. From the perspectve, we add scale factor and shft factor of wavelet functon to the least dsturbance dynamc learnng rate algorthm based on steepest descent method (Lu et al., 00). Correspondng Author: Xao Lang, Dalan Martme Unversty, Dalan 606, Chna 407

2 Res. J. Appl. Sc. Eng. Technol., 5(6): , 03 Defne the nput-output relatonshp of wavelet neural networ as: ( ) y w h = () (( )/ ) h = f net b a () ( ) net w x = (3) The error functon s gven by: E = d y ( ) (4) where, y s the th component of an output vector and h denotes the output of th wavelet n hdden layer and net denotes the nput of th wavelet n hdden layer, x s the th component of nput vector. d s the th desred target output. a, b s scale factor and shft factor of wavelet functon n hdden layer. Mae dfference operaton for (4) as follows: ( ) E = ( d y) y = ( d y) h w ( ) ( ) ( ) + w / a f () x w w / a f () ( ) ( ) ( xw b ) a w / a f () b (5) f we mae ΔE = - E through the modfyng weght, nput-output relatonshp wll satsfy the need of the goal functon. However, owng to frst-order approxmaton of the dfference operaton; there wll be errors for nonlnear neural networ and t s very hard to get ΔE = - E through once modfcaton, so η s ntroduced whch s usually gven by 0< η <. ΔE. s defned as: E = η E = Ω (6) where η has the same meanng as the tranng rato of the steepest descent method, but the hgher certanty s obtaned compared wth the standard steepest descent method. f the tranng rato s selected n the adacent area of, the smlar results can be obtaned. From (5) and (6), the varaton of net weghts can be descrbed as: The soluton of (7) s ndefnte, namely, there are nfnte approprate solutons. To obtan the defnte soluton condton, we construct a performance functon: ( ) ( ) J = w + w + a + b,, (8) The sgnfcance to mnmze the performance functon s to adust net weghts and scale factor and shft factor of wavelet neural networ as small as possble and mae the current error be zero. The smaller the adustable value s, the less the dsturbance of the prevous learnng nowledge would be. Therefore, the performance functon s called least dsturbance functon. The equvalent expresson of (7) s: ( ) ( ) J = w + w + a,, ( ) + b λ ( ) d y h w ( ) ( ) ( ) + w / a f ( net ) x w w / a f () ( ) ( ) ( xw b ) a w / a ) b Ω (9) where, λ s an unnown coeffcent. We can use Lagrange extreme value theory to get the soluton whch satsfes (7) and mnmzes J. The algorthm n detal s as follows. To mae the dervatve of the weght modfed value be zero, we can obtan: J ( ) = w ( ) ( ) 0 λ d y h = w J ( ) ( ) = w ( ) ( ) / () 0 λ d y w a f x = w (0) () J ( ) = a +λ ( d y ) w / a f ( net ) a ( ) ( xw b ) = 0 J ( ) = b +λ d y w a f ( net ) = () ( ) / 0 (3) b ( ) ( ) d y h w w / a f + ( net ) ( ) ( ) ( ) ( ) ( ) x w w / a f net ( x w b ) ( ) a w / a ) b Ω= 0 (7) 407 (0) to (3) can be rewrtten as: ( ) ( ) () w = λ d y h = λδ h (4) ( ) (5) ( ) ( ) ( ) w = λ d y w / a ) x = λδ x / a

3 Res. J. Appl. Sc. Eng. Technol., 5(6): , 03 ( ) ( ) a = λ ( d y ) w / a ) ( xw b ) ( ) ( ) = λδ ( xw b )/ a (6) b = λ d y w a f net = λδ a ( ) ( ) ( ) / ( ) / (7) Substtutng (4), (5), (6) and (7) nto (7): That s: (9) ( ) ( ) xλδ x + w / a ) ( ) ( ) ( ) ( xw b ) λδ ( xw b )/ a ( ) ( ) + w / a ) λδ / a = Ω ( ) ( ) ( ) δ hλδ h + w / a ) ( ) ( ) λ δ h +λ δ x / a + ( ) ( ) ( ) λ δ [( xw b ) / a ] +λ δ / a =Ω We can obtan: Ω λ= ( ) ( ) δ h + δ x / a + ( ) ( ) ( ) δ (( xw b ) / a ) + δ / a (8) (0) Substtutng (0) nto (4), (5), (6) and (7), we can obtan the sutable varaton of net weghts, scale factor and shft factor. Consderng when error approaches zero, the numerator and denomnator of (0) wll both approach zero, we add a small value ε > 0 nto the denomnator, then we can obtan: Ω λ= ( ) ( ) δ h + δ x / a +ε+ ( ) ( ) ( ) δ (( xw b ) / a ) + δ / a () The varaton of net weghts, scale factor and shft factor also use steepest descent method, but snce λ wll change tmely wth the current state and the current nput of the system, t wll be of beneft to the convergence and robustness of the networ. From (), we can conclude that ths change wll lead to that the reducng of error s always at the sutable level whch s 4073 Fg. : Effect of traned networ n two methods determned by η of (6), that s, the reducng of error wll not be large to cause unnecessary oscllaton and wll not be small to cause the convergence too low. On the other hand, snce η s equal to the expected reducton rato of the error, whose value s a lttle less than whch wll not nfluence the convergence of networ serously, but n steepest descent method the convergence s senstve to the learnng rato. n the standard steepest descent method, when the number of hdden layer ponts s added, t s necessary to reduce the learnng rato to assure the convergence of the networ. n (), when Σ h s added, λ s reduced smultaneously. Whle addng the number of hdden layer ponts means to add Σ h and thus λ s reduced. Ths dynamc learnng rato s helpful for the convergence stablty of the networ. Wth the same ntal value of neural networ, the effect of two dfferent algorthms s shown as Fg.. The tranng data are from a certan yawng moton of one underwater vehcle. As can be seen, the convergence velocty of the networ usng least dsturbance algorthm s much better. MODELNG USNG LEAST DSTURBANCE WAVELET NEURAL NETWORK The proposed approach has been verfed on a certan autonomous underwater vehcle named ZS4 (made n HEU, Chna) for smulaton study. The vehcle has eght thrusters and they can be dvded nto four groups based on the functon of the thrusters: horzontal plane thrusters, vertcal plane thrusters, sde thrusters and vertcal thrusters. Each group has two thrusters. Horzontal and vertcal plane thrusters are the ducted thrusters and sde and vertcal thrusters are the tunnel thrusters. As the velocty ncreases n the surge drecton, thruster deducton becomes serous enough, thus we close four tunnel thrusters n the hgh velocty to save energy. So n ths study, we manly dscuss the thruster fault dagnoss for four man thrusters. Fgure shows the thruster confguraton of ZS4.

4 Res. J. Appl. Sc. Eng. Technol., 5(6): , 03 Fg. : Thruster confguraton of ZS4 The autonomous underwater vehcle s a hgh couplng system and for dentfyng each degree, wavelet neural networ should be a mult-nput and mult-output system. The hdden layer functon s defned as the Morlet wavelet: Fg. 3: North velocty output of traned networ ( /) = () gx ( ) cos(.75 xe ) x ZS4 autonomous underwater vehcle s equpped wth Doppler Velocty Log (DVL) to measure threedmensonal lnear velocty and compass to measure three-dmensonal angles. Consderng the sensors and the executon equpments and smplfyng the approxmatng model of neural networ, we defne the nput and output as: Fg. 4: South velocty output of traned networ [ ] u( ) = X ( ) Y ( ) Z ( ) M ( ) N ( ) K ( ) T T T T T T y( ) = [ u( ) v( ) w( ) roll( ) ptch( ) yaw( )] T (3) where, u, v w are lnear velocty n surge, sway and heave drecton. roll, ptch, yaw are angular velocty n roll, ptch and yaw drecton. X T, Y T, Z T, N T, K T, are force/moment n surge, sway, heave, roll, ptch and yaw drecton. From the nput and output, we can realze 6- DOF nonlnear model dentfcaton. The neural networ structure s We tran wavelet neural networ offlne. ntalzng the parameters of wavelet neural networ s an mportant ssue and for the parameter learnng rate, we use the dynamc approach above. For the scale factor and shft factor, we apply the approach n Zhao and Zhou (003). Accordng to the wavelet theory, gven t*as the tme doman center, Δψ as the mother wavelet radus. The tme doman s gven by: * * [ b at b, b at b ] + ψ + + ψ (4) Fg. 5: Yaw output of traned networ n order to guarantee that the wavelet extends ntally over the whole nput doman, the scale factor and shft factor should satsfy the followng equatons: Thus: b at a w x b + at + a ψ = w x * + ψ = mn = * max = w x max w x mn = = a = ψ * * w x max ( ψ t ) w x mn ( ψ + t ) = = b = ψ (5) (6) 4074

5 Res. J. Appl. Sc. Eng. Technol., 5(6): , 03 Fg. 6: North velocty of left thruster fault experment Fg. 7: Yaw of left thruster fault experment The net weghts s less crtcal and the parameters are ntalzed to small random value between [-, + ]. The tranng data are from the smulaton experments such as surgng, yawng, swayng and so on. The traned neural networ can smulate the moton of the autonomous underwater vehcle very well. The Fg. 3, 4 and 5 show the results and we can see that the least dsturbance wavelet neural networ can approxmate the whole functon outlne and also dstll the change detal. ANALYSS OF SMULATON RESULTS Comparng the outputs of wavelet neural networ wth the real state values, we can obtan the resduals and analyze them to dstll fault nformaton. To mnmze the effect of envronment nose, the resduals are analyzed as: n a sold perod of gatherng a group of resduals, max value and mn value are cut and the mean valve of the left data s used as the threshold value. The perod and the threshold value are based on plenty of experments. f the resdual s beyond the threshold value, we consder there occurs a fault. n smulaton, the faults of the thrusters are consdered as zero outputs of the controller. Smulaton s shown as the example of settng a fault of a certan thruster n certan tme and then analyzng the resduals. Fgure 6, 7, 8 and 9 show the real state values and the outputs of wavelet neural networ n the fault of the left or the rght thruster when the autonomous underwater vehcle surges. We can see when the man thruster has a fault, the surge velocty changes and the change ncreases to a steady value as tme goes. Meanwhle, the yaw value ncreases nfntely. For the fault of the left thruster, the yaw s negatve. For the fault of the rght thruster, the yaw s postve. So we can set one threshold value for each degree. f both the resdual of the real velocty and the estmated velocty and the resdual of the real yaw and the estmated yaw are beyond the separate threshold value and the yaw resdual s negatve, the left thruster has a fault. f both 4075 Fg. 8: North velocty of rght thruster fault experment Fg. 9: Yaw of rght thruster fault experment the resdual of the real velocty and the estmated velocty and the resdual of the real yaw and the estmated yaw are beyond the separate threshold value and the yaw resdual s postve, the rght thruster has a fault. For the other thrusters, the approach s the same. CONCLUSON Amng at the character that hdden layer wavelet functon of wavelet neural networ can adust scale factor and shft factor to affect output of the networ, the least dsturbance algorthm addng scale factor and shft factor s proposed. The algorthm can calculate the dynamcal learnng rato to mprove the stablty and the

6 Res. J. Appl. Sc. Eng. Technol., 5(6): , 03 convergence of the wavelet neural networ. Meanwhle, for strong ablty of dstllng sgnal detals and mappng nonlnear functon of wavelet neural networ, the algorthm s appled to buld the dynamcal model of the autonomous underwater vehcle and the resduals are acheved by comparng the outputs of the neural networ wth the real state values. Fault detecton rules are dstlled from the resduals to execute actuator fault dagnoss. The results of smulaton prove the approach s effectve. ACKNOWLEDMENT Ths study s supported by the Natonal Natural Scence Foundaton of Chna (Grant No ) and the Chna Postdoctoral Scence Foundaton (Grant No ) and Fundamental Research Funds for the Central Unverstes of Chna (Grant No. 0QN30) and Specal Fund for Marne Scentfc Research n the Publc nterest (Grant No ). REFERENCES Adam, J.A., 985. Probng beneath the sea. EEE Spectrum, (4): Alessandr, A., M. Cacca and G. Veruggo, 999. Fault detecton of actuator fault n unmanned underwater vehcles. Control Eng. Practce, 7(): Bldberg, D.R., 99. Autonomous underwater vehcles: A tool for the ocean. Unmanned Syst., 9(): 0-5. L, X. and G. We, 998. Dynamc system dentfcaton and ts applcaton usng wavelet neural networ. Control Theory Appl., 5(4): Lu, X., J. Lu and Y. Xu, 00. Moton control of underwater vehcle based on least dsturbance bp algorthm. J. Harbn Eng. Unv., (9): 0-3. Xu, Y. and K. Xao, 007. Technology development of autonomous ocean vehcle. Robot, 33(5): Zhao, X. and C. Zhou, 003. A research on ntalng parameter of wavelet neural networ. J. South Chna Unv. Technol., 3():