Analytical Redundancy and Fuzzy Inference in AUV Fault Detection and Compensation

Transcription

1 Analytical Redundancy and Fuzzy Inference in AUV Fault Detection and Compenation A. J. Healey Profeor and Director Center for AUV Reearch Naval Potgraduate School Monterey, CA ABSTRACT Thi paper will addre the reult of a recent tudy developing model baed technique uing analytical redundancy in the production of obervation reidual that are proceed for the on-line, real time detection of dynamic fault during the operation of AUV. AUV are being developed for oceanographic urvey, a well a military, miion. Now that underwater navigation to ufficient preciion within cot limit i poible, the remaining technical iue i to improve the reliability of the miion completion. Increaing miion reliability implie many thing-ome having nothing to do with automatic fault detection. However, auming that the vehicle i equipped with highly reliable enor uite, connection, and computing component, it i of interet to ee if unexpected fault could be detected reliably o that ytem reconfiguration could be accomplihed to allow miion to be continued in ome fahion. A urvey of fault detection method indicate that alarm can be eaily monitored if ignal are tatic. Thi i done uing limit and trend analyi with threhold et for variou level of everity. With dynamic ignal, uch a thoe induced by an actuator fault in the form of a tuck fin, or a looe fin, or fouling of a propeller, the tranient nature of the ignal make limit and trend analyi invalid. In thee cae, ignal are ought that include ervo error, and the reidual error in obervation filter. Deigning obervation filter build analytical redundancy into the deciion making. Additionally, ince there i alway the difficulty of eparating the fault repone from diturbance repone, operation near the urface under wave require the development of a wave detector. A fault detection architecture i propoed that i baed on uing imple detection circuit that look for fault ignal magnitude a well a length of time periting in the fault mode that produce the fault declaration. Adjutment in the threhold parameter are able to ditinguih between wave diturbance and fault condition. The architecture allow for the recommended accommodation repone uing a fuzzy inference ytem linking reidual fault declaration ignal a input that are mapped to recommended action uing fuzzy rule. Example repone are dicued, and in particular, the fault detection and accommodation due to lo of control at low peed under wave action with tuck fin, i given. INTRODUCTION Long term deployment of autonomou ytem in the ocean require replenihment of energy upplie and reliable, fault free operation. It i recognized that fault free operation will not alway be

2 Report Documentation Page Form Approved OMB No Public reporting burden for the collection of information i etimated to average 1 hour per repone, including the time for reviewing intruction, earching exiting data ource, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding thi burden etimate or any other apect of thi collection of information, including uggetion for reducing thi burden, to Wahington Headquarter Service, Directorate for Information Operation and Report, 1215 Jefferon Davi Highway, Suite 124, Arlington VA Repondent hould be aware that notwithtanding any other proviion of law, no peron hall be ubject to a penalty for failing to comply with a collection of information if it doe not diplay a currently valid OMB control number. 1. REPORT DATE REPORT TYPE 3. DATES COVERED - 4. TITLE AND SUBTITLE Analytical Redundancy and Fuzzy Inference in AUV Fault Detection and Compenation 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Potgraduate School,Center for AUV Reearch,Monterey,CA, PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 1 SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public releae; ditribution unlimited 13. SUPPLEMENTARY NOTES The original document contain color image. 11. SPONSOR/MONITOR S REPORT NUMBER(S)

3 14. ABSTRACT Thi paper will addre the reult of a recent tudy developing model baed technique uing analytical redundancy in the production of obervation reidual that are proceed for the on-line, real time detection of dynamic fault during the operation of AUV. AUV are being developed for oceanographic urvey, a well a military, miion. Now that underwater navigation to ufficient preciion within cot limit i poible, the remaining technical iue i to improve the reliability of the miion completion. Increaing miion reliability implie many thing-ome having nothing to do with automatic fault detection. However, auming that the vehicle i equipped with highly reliable enor uite, connection, and computing component, it i of interet to ee if unexpected fault could be detected reliably o that ytem reconfiguration could be accomplihed to allow miion to be continued in ome fahion. A urvey of fault detection method indicate that alarm can be eaily monitored if ignal are tatic. Thi i done uing limit and trend analyi with threhold et for variou level of everity. With dynamic ignal, uch a thoe induced by an actuator fault in the form of a tuck fin, or a looe fin, or fouling of a propeller, the tranient nature of the ignal make limit and trend analyi invalid. In thee cae, ignal are ought that include ervo error, and the reidual error in obervation filter. Deigning obervation filter build analytical redundancy into the deciion making. Additionally, ince there i alway the difficulty of eparating the fault repone from diturbance repone, operation near the urface under wave require the development of a wave detector. A fault detection architecture i propoed that i baed on uing imple detection circuit that look for fault ignal magnitude a well a length of time periting in the fault mode that produce the fault declaration. Adjutment in the threhold parameter are able to ditinguih between wave diturbance and fault condition. The architecture allow for the recommended accommodation repone uing a fuzzy inference ytem linking reidual fault declaration ignal a input that are mapped to recommended action uing fuzzy rule. Example repone are dicued, and in particular, the fault detection and accommodation due to lo of control at low peed under wave action with tuck fin, i given. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclaified b. ABSTRACT unclaified c. THIS PAGE unclaified 18. NUMBER OF PAGES 6 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Precribed by ANSI Std Z39-18

4 poible, o that ytem deign mut pay attention to a tudy of failure mode and their effect. In pite of the ue of good engineering practice, fault can occur. Two kind of fault identified are, 1) thoe that arie from malfunction in the hardware and oftware ubytem in the vehicle, 2) thoe that arie from environmental condition that are viewed a diturbance, and while thee may not be directly fault, they have the effect that the completion of a miion i jeopardized. An example of a hardware fault would be the lo of teering reulting from a tuck or looe fin. An example of a type 2 fault would the inability of the vehicle to take a data meaurement becaue of high ea tate in hallow water operation. To deign a ytem that will automatically detect the preence of a fault i the ubject of many paper. Thi problem i common to the aircraft, pacecraft, and proce indutrie, and much ha been written about method available. In general we can claify the method into thoe that ue imple limit and trend analyi, thoe that ue detection technique but which are without the ue of analytical model, and thoe that provide analytical model a the bai for detection filter [1,2]. The detection of tatu ignal uch a battery voltage, motor winding temperature, computer bay temperature, i relatively eay and accomplihed by the comparion of the meaured ignal with a previouly et threhold. Exceeding thoe threhold would indicate a fault condition for which ome action i taken for intance either to low down the vehicle peed or to abort the miion and urface. It i more difficult i to detect thoe fault that give rie to dynamic ignal uch a udden change in pitch rate that are caued by actuator fault where ome form of model free, or model baed reidual generation mut be included. Model Free Detection Threhold detection i appropriate when the ignal are tatic or lowly varying and uch that a ingle excedence mean that a fault will be peritent for the remainder of the voyage. Such method are not uitable for dynamic ignal that could arie for intance from eaway wave action. The propenity of dynamic ignal to exceed a threhold but later to come within bound caue threholding alone to be a problem. We reort to model free method where ome contant feature of the ignal can be extracted and then that feature i compared againt the threhold. Such i the cae when a pectral analyi i performed on ignal and pectral level in pecified frequency band can be compared againt threhold. Thi methodology i ueful to detect the preence of frequency component in ervo error ignal caued by wave motion and could be ued to identify level of eaway induced diturbance conidered a fault. Model Baed Detection The overall problem of AUV fault detection i complex. Handling complexity by decompoition, the author recommend limiting the detection of fault to the primary ubytem in the vehicle, including, the peed control, teering, diving, roll control, navigation, powering, and computer ubytem. A far a motion capabilitie are concerned the peed, teering, diving, and (if preent) active roll control ubytem hould be monitored. Fault that impair the capability of thee ubytem need to be detected o that control reconfiguration may help to mitigate an unneceary miion abort. Some graceful degradation of miion could be continued if partial depth control or ped control could be maintained. Dynamic ignal uch a thoe developed by autopilot error become hard to detect, a error are naturally large when teering to new command, yet are mall if correct final heading i maintained. Wave motion caue wave period ocillatory motion in ervo error. Model baed method have been found to be ueful in detecting dynamic fault. A model-baed oberver i ued to generate a reidual between the enor meaured value and that predicted from the model. Fault can arie from a bad enor a well a a faulty actuator (fin / propeller).

5 The reidual provide a ignal that i not enitive to ervo error caued by command change, and repond primarily to non ideal load, diturbance from wave, and enor ignal error. Analyi of the reidual provide the key to ubytem failure. The diving ubytem of an AUV i analyzed for example. The diving ub-ytem dynamic for an AUV may be modeled by the ytem [3,4, 5 ]. x' ( t ) = [ w r( t ),q( t ), θ( t ),Z( t )];u( t ) = δ x& ( t ) = Ax( t ) + Bu( t ) + Ef ( t ) + Fd( t ); y( t ) = Cx( t ) + f ( t ) a ( t) with With a high quality inertial ytem, all tate variable are meaured with little noie and the output matrix, C, may conidered to be identity. f a( t ), f ( t ) are conidered to be added force caued by fin fault, and enor error repectively. In the above, w r, q, θ, and Z are the heave velocity of the vehicle relative to the water, the pitch rate, pitch angle, and the depth. B and E are the input vector for the control plane and added force and moment caued by imbalance of commanded and actual load on the vehicle, caued by actuator fault and F i the input vector aociated with diturbance from wave and upwelling current. It i important to note that ince the relative velocity definition for vehicle tate i ued, E and F are ditinct and diturbance from wave and current can be ditinguihed from actuator fault. A model-baed oberver i ued given by xˆ ' ( t ) = [ ŵ r( t ),qˆ( t ), θˆ( x ˆ & ( t ) = ( A KC )ˆ( x t ) + ν( t ) = y( t ) Cxˆ( t ); t ),Ẑ( t )];u( t ) Bu( t ) + = δ Ky( t ); ( t) with The reidual, ν(t), are the difference between the meaured tate and the etimate from the oberver. It follow that, the tate obervation error, ε x i given by, ε& ( t ) = ( A KC ) ε x ν( t ) = Cε x ( t ) + f x ( t ) + Ef ( t ) + Fd( t ) + Kf ( t ) Unlike tate obervation, reidual generation require a different balance in the choice of filter gain, K. Too high a choice lead to the reidual being mall, dominated by enor fault and noie. A lower gain et i needed conitent with bandwith requirement. Of coure, tability mut be obtained. The reidual can be analyzed in the frequency domain by, ν( t ) = C( I A A = ( A KC ) c a ( t ); c ) Efa( ) + C( I Ac ) Fd( ) + C( I Ac ) Kf ( ); One oberver deign (low gain) hould therefore find a gain et that maximize the influence of actuator fault, minimize the influence of wave diturbance, and the enor fault, while a econd (high gain) oberver could be deigned to emphai enor fault. It i noted that ince the direction of E direction of F (E, F are orthogonal), eparation of wave effect and actuator fault i poible. In fact, deigning a weight matrix, W, for the reidual detecting actuator fault, the ratio, WC( I A c ) E / WC( I A c ) F ;

6 hould be maximized over the frequency range appropriate. A method for the maximal decoupling of diturbance from fault uing eigenvector aignment i dicued in [6]. SIMULATION RESULTS Uing a model of the US Navy DSRV vehicle [6], running at a forward peed of 6 ft/ec., x ' = [ wr,q, θ, Z]. For a low forward peed of 6 feet per econd, the dynamic and input matrice are, 1959 = 483 A ; B = In thi example, the vehicle i in forward way with a command to dive. The autopilot for depth control may be deigned a number of different way, but here, a liding mode deign i ued which yield the control law, delta=-k*x-4*ign(inv(('*b)))*tanh((ig/phi)); if ab(delta)>.4; delta=4*ign(delta); end; The placed pole are elected to include a ingle pole at the origin (required by the method) giving, λ=[ -4, -41, -42, ] k=[ ] =[ ] The oberver gain are found uing the Matlab place algorithm to get put the oberver pole at real value cloe to the control pole, at [-5, -56,-53,-44]. The olution for K yield, K =, and the fault input matrix i in the ame direction a the input matrix, B, E=B, while the diturbance from wave velocitie appear a an additive input to the lat of the tate equation, o that F=[;;;1]. A quick check how that perfect diturbance decoupling ha been achieved. At a time given by t=1 econd, an added fault at the tern plane i inerted, on the top of a inuoidal wave diturbance which perit from the tart, t= The weighting matrix, W = I produce the following reidual repone a hown in Figure 1.

7 Depth Changing Control Repone With Actuator Fault at 1 ec.'control Command in Rad * De pth Ch an 1 ge, Ft Depth Reidual Heave and Pitch Rate Reidual Time, Sec. (4 Knot Speed) Time, Sec. Figure 1. Fault Detection Decoupled Reidual For Each Diving State V Time. Figure 1 how that the heave velocity reidual i highly reponive to the impoed actuator fault and will eaily detect the fault when compared againt a threhold. It appear that heave relative velocity i inenitive to wave motion which appear trongly in the depth reidual repone. In contrat, the wave diturbance i detected by the depth reidual without influence from the actuator fault. Detecting fault and iolating their origin i the ubject of robut reidual generator deign and thi oberver with a relatively low bandwidth illutrate that ome iolation i poible. However, robutne i improved when reidual from a variety of different ource are compared. For intance, the fin activation level, the level of ervo error, and the oberver-baed reidual are all ueful in the final determination of fault. The combination of all ource of information i illutrated with the fault detection architecture illutrated in Figure 2. Control Input Vehicle Controller Senor Output Command Adjutment Health Aement To Higher Level Control - Fin troke detector - Servo error detector Fault Detector Fuzzy Inference Sytem - Oberver reidual detector - Wave activity detector Figure 2 Fault Detection Architecture Including Fuzzy Inference Sytem for Reolution of Fault State CONCLUSION

8 The paper ha demontrated that actuator fault can be detected in the preence of wave induced diturbance. However, becaue of the complexity of the environmental diturbance and the variety of poible fault, a more comprehenive detection ytem i being propoed that include aement of actuator level, ervo error level, and oberver baed reidual to make the overall determination of ub ytem health for AUV. ACKNOWLEDGEMENTS The author wihe to recognize the Office of Naval Reearch for financial upport during the conduct of thi continuing tudy. REFERENCES [1 Intelligent Control: Fault Detection and Compenation, ONR Workhop, Naval Potgraduate School Monterey, March 1997 [2] Gertler, J., Failure Detection and Iolation in Complex Plant A Survey, IFAC Sympoium on Microcomputer Application in Proce Control, Itanbul, Turkey, [3] Healey, A. J., Coure Note Marine Vehicle Dynamic, 1995 [4] Healey, A. J., Lienard, D., "Multivariable Sliding Mode Control for Autonomou Diving and Steering of Unmanned Underwater Vehicle", IEEE Journal of Oceanic Engineering Vol. 18, No. 3, July 1993 pp [5] Criti, R., Healey, A.J., Papoulia, F.A., "Adaptive Sliding Mode Control of Autonomou Underwater Vehicle in the Dive Plane" IEEE Journal of Oceanic Engineering, July 199 [6] Patton, R. J., Chen, J., Robut Fault Detection Uing Eigentructure Aignment: A Tutorial Conideration And Some New Reult, Proceeding of 3 th. Conference on Deciion and Control, 1991, pp [7] Young, D. B., Model Invetigation of the Stability and Control Characteritic of the Contract Deign for the Deep Submergence Recue Vehicle (DSRV), NSRDC Report # 33, April, 1969.