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Yang, Xilin, Mejias Alvarez, Luis, Warren, Michael, Gonzalez, Felipe, &Upcroft, Ben(2014)Recursive actuator fault detection and diagnosis for emergency landing ofUASs.In Xia, X & Boje, E (Eds.) Proceedings of the19th World Congress of theInternational Federation of Automatic Control.International Federation of Automatic Control (IFAC), http://www.ifac-papersonline.net/, pp. 2495-2502.

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https://doi.org/10.3182/20140824-6-ZA-1003.00087

Recursive Actuator Fault Detection andDiagnosis for Emergency Landing of UASs

X. Yang ∗ L. Mejias ∗ M. Warren ∗ F. Gonzalez ∗ B. Upcroft ∗∗

∗ Australian Research Center for Aerospace Automation (ARCAA) andQueensland University of Technology (QUT), Brisbane, Australia.

(e-mail: {xilin.yang, luis.mejias, michael.warren,felipe.gonzalez}@qut.edu.au).

∗∗ School of EECS, QUT, Brisbane, Australia.(e-mail:ben.upcroft@qut.edu.au)

Abstract: This paper presents a practical recursive fault detection and diagnosis (FDD) schemefor online identification of actuator faults for unmanned aerial systems (UASs) based on theunscented Kalman filtering (UKF) method. The proposed FDD algorithm aims to monitorhealth status of actuators and provide indication of actuator faults with reliability, offeringnecessary information for the design of fault-tolerant flight control systems to compensate forside-effects and improve fail-safe capability when actuator faults occur. The fault detection isconducted by designing separate UKFs to detect aileron and elevator faults using a nonlinearsix degree-of-freedom (DOF) UAS model. The fault diagnosis is achieved by isolating truefaults by using the Bayesian Classifier (BC) method together with a decision criterion to avoidfalse alarms. High-fidelity simulations with and without measurement noise are conductedwith practical constraints considered for typical actuator fault scenarios, and the proposedFDD exhibits consistent effectiveness in identifying occurrence of actuator faults, verifying itssuitability for integration into the design of fault-tolerant flight control systems for emergencylanding of UASs.

Keywords: Fault diagnosis and isolation; unscented Kalman filter; multiple-model adaptiveestimation; emergency landing; unmanned aerial system.

1. INTRODUCTION

UASs have proved effective in a number of civilian op-erations such as power line inspection, bush fire inves-tigation and urban traffic monitoring. They also havegreat potential to reduce cost and requirements for lifesupport due to recent development in UAS technology(Kendoul (2013); Bernard et al. (2011)). However, one ofthe key issues which remains unresolved is the demandfor an emergency landing system in case of accidentalactuator faults, especially when UASs are operating overpopulated areas. In such situations, UASs are expected tobe equipped with sufficient capability to identify suitablelanding sites and accommodate faults to achieve safe emer-gency landing. This requires automated implementation ofseveral systems onboard the UAS. A landing site decisionmethod is required which aims to provide feasible landinglocations given information about land texture, surfaceflatness and turning rate constraints. A fault-tolerant flightcontrol system is also necessary which can detect, isolateand accommodate online actuator faults.

Emergency landing of UASs has received increasing atten-tion in the past decades due to occurrence of accidentalcrash caused by mechanical failures (engine, actuator,etc.) or loss of stability in extreme weather conditions(strong gusts, storm, etc.). Several important aspects ofemergency landing has been investigated in the literature.

Development of a fault-tolerant guidance, navigation andcontrol system to improve emergency landing reliabilityand minimize threat to the community has been addressedin a number of references (Ducard (2009); Zhang and Jiang(2000); Calise et al. (2001); Brinker and Wise (2001)).Ducard (2009) designed a fault-tolerant control systemwhich focuses on the FDD of faults among sensors andactuators and on development of a reconfigurable con-trol allocation module. A fault-tolerant control systemwas proposed by Zhang and Jiang (2000) which possessesthe ability to accommodate system component failures.This system comprises a FDD scheme, a reconfigurablecontroller and a control reconfiguration mechanism. Also,Identification of appropriate landing sites for trajectoryplanning in emergency situations has been addressed bysome researchers (Williams and Crump (2012); Mejiaset al. (2009); Mejias and Fitzgerald (2013)). Mejias et al.(2009) proposed a computer vision based procedure toidentify emergency landing sites based on size, shape, slopeand texture of surfaces to achieve automatic classificationof the candidate landing sites. Williams and Crump (2012)provided flight-test results of a landing system which uti-lizes prior location information to decide the most feasiblelanding sites.

Onboard fault detection and diagnosis has also been inves-tigated in the literature for several aerospace applications.The multiple-model adaptive estimation (MMAE) scheme

has proven to be effective and been applied to dealingwith FDD problems in various flight scenarios (Maybeck(1999); Eide and Maybeck (1996); Meskin et al. (2013);Amirarfaei et al. (2013)). A bank of parallel Kalman filterswas adopted with each matched to a specific hypothesison the failure status by Maybeck (1999). The authors alsodeveloped a hierarchical structure to keep the number ofonline filters to a minimum. However, linear Kalman filtersonly function effectively around operating conditions, anda series of linearized flight models are required for theFDD purpose to cover the whole flight envelope. Thiswould greatly aggravate onboard computational burden.Further, this algorithm would collapse in situations wherelinearized models do not exist. The MMAE with extendedKalman filters (EKF) incorporated has been proposed forfault estimation in Ducard (2009); Ducard and Geering(2008). The validity of EKFs is based on the existence ofJacobian matrices of the system model under all possibleflight conditions. Moreover, in situations where systemdynamics change abruptly, Jacobian matrices might notexist or have singular issues (Julier and Uhlmann (2004)),and EKF-based MMAE would fail to detect occurrence offaults. Therefore, in our case where flight dynamics aresubject to abrupt changes when accidental faults occur,we will develop a UKF-based FDD procedure. Campbelland Brunke (2001) demonstrate that the UKFs show per-formance improvement when compared with the EKFs fora nonlinear F-16 like aircraft model. Another possible so-lution to the online FDD is the interactive multiple model(IMM) method. The IMM employs parallel filters whichinteract with each other for performance improvement atthe expense of high computational and storage require-ments (Zhang and Li (1998); Kim et al. (2008); Lee et al.(2005)). This is due to the fact that the initial estimateat the beginning of each cycle is a mixture of all mostrecent estimates (Zhang and Li (1998)). In our work, weare aimed at a feasible estimation approach which can beimplemented at the cost of limited flight computer memoryand provide sufficient estimation accuracy. Thus, we usethe MMAE with UKFs to perform the FDD of actuatorfaults.

The current research is part of the ResQu project whichaims to develop automated safety technologies for UASsafe recovery by providing a feasible emergency landingsystem with autonomous vision-based site decision androbust navigation, guidance and control capabilities. Inthis research, we aim to develop an online FDD procedureto monitor occurrence of actuator faults with minimumtime delay, and conduct fault detection when a UAS op-erates in a wide range of flight envelopes. The proposedalgorithm should also consider computational burden andFDD reliability. To this end, a nonlinear 6-DOF dynamicmodel in consideration of aerodynamic forces and mo-ments is explored. The UKF algorithm is designed basedon the nonlinear model and excludes the need for cal-culating the Jacobian matrices. The aileron and elevatorare treated as additional system states in the augmentedstate vector, and are estimated by the UKF algorithm.To avoid false alarms of faulty actuators, a recursive faultdiagnosis algorithm is designed based on the measurementresiduals and error covariance of the UKF. Performanceof the FDD is evaluated using a high-fidelity 6-DOF UASmodel. Simulations are conducted to verify performance

of the proposed FDD scheme, and it is demonstrated thatactuator faults can be identified with guarantees.

2. FLIGHT DYNAMICS OF A UAS

In practice, emergency landing is required as a result ofoccurrence of possible actuator faults under various flightscenarios (steady-state, bank-to-burn, skid-to-turn, etc).In the considered application which requires a detectionand diagnosis procedure to cover entire flight regions,the nonlinear 6-DOF dynamic model is developed inconsideration of aerodynamic and propulsive forces andmoments. Details of the nonlinear dynamics are given inYang et al. (2013). We are concerned with a UAS modelwith variable flight speeds as faults might occur during anyphase of flight. Thus, the current model is different fromthe one which assumes constant flight speeds in Yang et al.(2013).

The continuous-time system model is discretized using theEuler integral method, and can be described by

x(k + 1) = f(x(k), u(k)) + ϵ(k) (1)

where state vector x refers to 8 state variables

x = [u, v, w, p, q, r, ϕ, θ]T (2)

and actuator inputs are u = [δa, δe]T . Process noise ϵ =

[ϵ1, · · · , ϵ8]T is mutually independent Gaussian distribu-tions and satisfies

E[ϵ(k)] = 0, E[ϵ(k)ϵT (i)] = δ(k − i)Q(k) (3)

where δ(·) is the Kronecker function and Q(k) is processerror covariance.

The measurement equation is

y(k) = C · x(k) + ξ(k) (4)

The constant matrix C = I8×8 and measurement noisewith Gaussian distribution ξ = [ξ1, ..., ξ8]

T satisfies

E[ξ(k)] = 0, E[ξ(k)ξT (i)] = δ(k − i)R(k) (5)

where R(k) is the measurement noise covariance.

3. UKF-BASED FAULT DETECTION

The MMAE is an effective approach to online detectionof system faults/failures. This method relies on a bankof Kalman filters with each matching a particular systemmode (faulty or non-faulty). In our case, we are aimed atdeveloping a UKF-based MMAE scheme to cover a widerange of flight conditions with reasonable computationalefficiency. Given this requirement, it is desired that acomplete set of system modes are to be explored, and eachis associated with evident separation properties. Measure-ment residuals are a key factor to determine proper systemmodes and distinct differences in them make the modesidentifiable by the UKF models. Furthermore, fault isola-tion is achieved by computing model probabilities whichalso rely on measurement residuals. Therefore, we willbuild UKF models with each accompanied with notableseparation properties.

In our case, there are three possible modes: non-fault,aileron fault and elevator fault. Thus, the filter designprocess is formulated as the construction of filter models

to represent dynamics of possible system behaviors byemploying the following N pairs of equations:

xi(k + 1) = fi(xi(k), ui(k)) + ϵi(k) (6)

yi(k) = Ci(k)xi(k) + ξi(k) (7)

Here, subscript i ∈ N relates to the mode mi ∈ Z. Themodel set Z = {m0,ma,me} contains N(N = 3) possiblesystem modes where m0 refers to the non-fault mode, ma

the aileron fault and me the elevator fault. Also, fi(·) andCi(·) are of different structures for different system modes.

There are several recursive filter options available (EKFand UKF, etc.) for nonlinear systems. The UKF-basedfilters are preferred as singular issues can be avoided. Inthe considered application, three single-filter-based UKFsare developed with the first one for non-fault mode andthe other two for actuator faults. The two UKFs foractuator fault detection are derived with each monitoringthe health status of one actuator. System model (Eq. (1))and measurement model (Eq. (4)) can only be used forstate estimate in the non-fault scenario, and an augmentedsystem model is required with adequate modifications todetect a specific actuator fault. We follow the strategy inDucard (2009) and augment the state vector as

xj = [xTi , δj ]

T (8)

where δj , j = a, e refers to the aileron or elevator. This def-inition considers the monitored actuator as an additionalstate variable. Thus, control action from the δj to flightperformance is neglected and the status of the δj actuatoris estimated through conducting the UKF procedure.

The fault detection is conducted by designing separateUKFs for ailerons and elevators, as shown in Fig. 1. Inputsto each UKF are measured system states and other avail-able information (angle-of-attack, sideslip, thrust, etc.).The UKF algorithm is able to detect actuator faults with-out knowledge of health status of any actuator. Whendetecting aileron fault, the estimated elevator signal fromUKF2 is considered as a replica of the actual elevator com-mand. Thus, UKF1 is able to estimate status of aileron.Similarly, UKF2 takes estimated aileron command fromUKF1 as actual aileron and outputs estimate of elevatorstatus. Thus, the detection algorithm can be consideredas a black-box which takes measured states as inputs andoutputs status of actuators.

4. RECURSIVE FAULT DIAGNOSIS

4.1 Calculation of Fault Probability

Fault diagnosis refers to isolation of true faults whichcan be used to trigger fault-tolerant control strategies.Occasionally, actuator faults occur instantly and disappearrapidly. These expeditious faults are often of low magni-tude and cause ignorable effect on the handling qualityof a UAS due to the short duration. Thus, flight stabilitycan still be maintained by existing proportional-integral-derivative (PID) controllers. However, in the event of trueactuator faults characterized by an evident time dura-tion and significant magnitude, it is required that thesefaults are identified with maximum probability such thatconfident fault isolation is achieved which can trigger theemergency landing procedure timely.

In the MMAE framework, each UKF generates an estimateof the system states, and the actual system states arethe summation of these state vectors weighted by thecorresponding conditional probability (Maybeck (1999)),

x̂(k) =

N∑i=1

Pi(k)xi(k) (9)

Here, the index i covers all possible faulty modes includingthe non-fault mode. The probability Pi(k) is the posteriorconditional probability that declares the faulty mode m =mi given the observed measurements up to the timeinstant k,

Pi(k) = Pr[m = mi|Yk], Yk = {y0, · · · , yk} (10)

where measurement history vector Yk contains availablemeasurements at different time instants t0, · · · , tk.For online fault isolation, Pi(k) can be computed bythe recursive Bayesian Classifier (BC) (Ducard (2009);Maybeck (1999))

Pi(k) =P [y = yk|m = mi, Yk−1]Pi(k − 1)∑N

j=0 P [y = yk|m = mj , Yk−1]Pj(k − 1)(11)

with the conditional probability density for the currentmeasurement yk given by

P [y = yk|m = mi, Yk−1] = αi(k)e−Si(k) (12)

where

αi(k) = (2π)−m2 |Σi(k)|−

12 (13)

Si(k) =rTi (k)Σ

−1i (k)ri(k)

2(14)

Here, i is actuator fault mode, N is number of actuatorfaults. Residual is ri(k) = yi(k)−µi(k) where yi(k) is mea-surement vector and µi(k) predicted mean of measurementfrom the UKF. Therefore, the complete recursive form tocompute fault probabilities at time instant k is

Pi(k) =αi(k)e

−Si(k) · Pi(k − 1)∑Nj=0 αj(k)e−Sj(k) · Pj(k − 1)

(15)

where j ∈ {0, a, e} indicates an actuator fault. In practice,it is found that the leading term αi(k) can be neglected inthe recursive process (Eide and Maybeck (1996)).

In our case, the BC approach conducts hypothesis testingby assuming Gaussian distributions of the measurementresiduals. This method functions effectively when systemdynamics are contaminated by noise with Gaussian distri-butions. Essentially, the UKF corresponding to the truefault scenario would generate an estimated measurementvector most close to the the observed measurement vector,and yield the minimum residuals which result in the largestprobability to indicate the proper UKF in consonance withthe true fault scenario.

Remark 1. To avoid false alarms, the detected fault isclaimed to be true when the corresponding fault proba-bility exceeds 0.95 for ten consecutive sampling points.

Remark 2. As we are concerned with emergency situationswhere actuator faults occur abruptly, the UAS is assumedsteady-state flight conditions at the initial stage. Thus, theinitial probability for non-fault case is set to be unity andprobabilities for faulty actuators are set to be zero. Theprobability will converge to declare the fault mode onceactuator fault occurs.

UKF1

Aileron Fault

UKF2

Elevator Fault

Fault Detection

UKF

Non-Fault

Fault Isolation

Prob.

weights

ad

ad

ad

ed

ed

ed

MAF

Prob.

weights

Prob.

weights

Decision

criterion

Hypothesis

testing

P0

Pa

Pe

Fig. 1. UKF-based fault detection and diagnosis scheme

Remark 3. In the recursion process, low bounds for theprobabilities are set to be 0.001 to prevent locking intozero which would prevent the recursion algorithm fromconverging to true probabilities.

4.2 Design of moving average filters

The probabilities generated from the BC are subject toshort-term fluctuations which obscure probability trend.A proper filter is required to highlight the long-term trendof probability without causing significant time delay forfault identification. Three moving average filters (MAFs)are designed to smooth out the raw probabilities from theBC with proper window widths. These filters cannot beinitiated efficiently until sufficient raw probability samplesare collected and stored in the computer memory. In ourcase, a window width of 20 points was chosen after a fewtrails.

4.3 Actuator Fault Isolation

Even though the filtered probabilities become less noisyand performance of fault isolation has been improved, theisolation performance is yet to be satisfactory. For sometime instant, it is observed that the true fault probability isambiguous and not notably dominant over other probabili-ties. This causes difficulties in distinguishing true actuatorfaults and would result in false alarms. Ducard (2009)imposed an supervision module to monitor probabilitysignals which assists in confirmation of actuator faults byadding excitation signals. There was also an additionalfiltering stage with lower and upper bounds to isolatetrue faults. These bounds are chosen empirically to extractdominant probabilities.

In our case, we employ a decision criterion proposed byZhang and Li (1998):

Pj(k) = maxmi∈Z

Pi(k), i = {0, a, e} (16)

where Z refers to actuator fault model space Z ={m0,ma,me}.

PH(k) =Pj(k)

maxi ̸=j,mi∈Z Pi(k)(17)

if PH(k) ≥ PT ⇒ Hj : Fault j occurs, (18)

if PH(k) < PT ⇒ H0 : No fault occurs (19)

where PT is the probability threshold. This decision logic isbased on determination of a single threshold and facilitatesthe implementation in practice. The choice of thresholdPT is problem-dependent, and different values are used fordifferent systems. Practically, the threshold begins with anempirical value and is determined after a few trials. Theproper threshold is selected to reduce isolation time delayand avoid missing detection.

The block diagram of the proposed FDD is illustratedin Fig. 1. Based on the available measurements, thefault detection part constructs three UKFs which eachmonitoring a particular type of fault (including the non-fault scenario). The residuals and error covariance ofeach UKF are input into the hypothesis testing block togenerate raw probabilities, which are then filtered by theMAFs to highlight long-term trends. The true probabilityweights for each mode are obtained after the filteredprobabilities are regulated by the decision criterion. Theestimated system states are the probabilistically weightedsum of the states from each UKF.

5. SIMULATION RESULTS

In this section, we test performance of the proposed FDDprocedure for typical actuator faults which are likely tooccur during flight. To identify and remedy possible defi-ciencies of the procedure before real-time implementation,we set up a high-fidelity simulation model based on param-eters of one of ARCAA UASs by using the AeroSim simu-lation blockset. The AeroSim library provides a complete

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MeasuredEstimated

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0.3

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φ (r

ad)

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0

0.5

Time (s)

θ (r

ad)

Fig. 4. Estimated states for floating faults

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−5

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5

10

AIL

(D

EG

)

TrueEstimated

10 20 30 40 50 60 70 80−20

−10

0

10

20

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ELE

(D

EG

)

TrueEstimated

Fig. 2. Comparison of true and estimated actuator com-mand for single floating faults

set of tools for developing nonlinear aircraft models foroverall evaluation of the FDD. Aerodynamic parametersof our UAS platform can be found in Yang et al. (2013).

In simulations, our UAS is controlled to be within theoperational velocity range of [20.83m/s, 57.78m/s]. Also,operational limits on elevators and ailerons are imposed(δe ∈ [−25o, 25o] and δa ∈ [−15o, 15o]). The angle ofattack and sideslip are stabilized to change within thescope of −5o ≤ α ≤ 5o and − 28o ≤ β ≤ 28o. Moreover,measurement noise in velocities, attitudes and angular

20 40 60 800

0.5

1

Non

−fa

ult P

r

Raw prob

20 40 60 800

0.5

1

AIL

Pr

20 40 60 800

0.5

1

Time (s)

ELE

Pr

20 40 60 800

0.5

1

Non

−fa

ult P

r

Prob after isolation

20 40 60 800

0.5

1

AIL

Pr

20 40 60 800

0.5

1

Time (s)

ELE

Pr

Fig. 3. Probabilities generated by the fault isolation deci-sion criterion for single floating faults

rates are considered with progressive increasing levels totest the performance of the FDD procedure. Two PIDcontrollers are designed for aileron and elevator to achievesteady-state flight conditions. A group of control gainsare selected to satisfy performance specifications such assettling time (< 100s) and steady-state errors (< %5).Empirically, the proper control gains were found after afew trails with kap = 0.2279, kai = 0.0027 and kad =

0.2 for the aileron control, and kep = −0.055, kei =−0.01 and ked = −0.1 for the elevator control.

5.1 Detection and Diagnosis of Single Actuator Faults

Performance evaluation for single faults is firstly con-ducted for sequential occurrence of actuator faults. Thereare two typical actuator faults: floating fault and lock-in-place (LIP) fault. The floating fault describes a fluctuatingactuator surface moving up and down without staying ata desired position. The LIP fault refers to the situationwhere the actuator is stuck at an unexpected location. Insimulations, both faults occur and last for a certain periodof time. Numerous simulations have been carried out andperformance for single floating fault scenarios is illustratedin Fig. 2 and Fig. 3. As we are only concerned withfaults during steady-state flight, the transient responsein the first 10s is removed for observation convenience.Two separate floating faults are generated with an aileronfault occurring at time interval [30s, 40s] and an elevatorfault at [50s, 65s]. It is observed that the aileron fault isconsistently estimated when floating fault occurs within[−7o, 7o]. In the time interval where elevator fault occurswithin [−8o, 8o], the UKF is able to detect the fault withrapid response. The estimate time delay is approximately0.4s for aileron fault and 0.5s for the elevator fault. Thisis considered to be sufficient to conduct fault isolationonboard to distinguish true faults.

The fault isolation performance is shown in Fig. 3. It isseen that the raw probabilities from the BC are sensitiveand will lead to false alarms. In the initial stage, proba-bilities for both aileron and elevator are zero. When theprobabilities for aileron increase abruptly (shown as spikesin Fig. 3), these probabilities are set to zero after the filter-ing stage to avoid false alarms as they are less than 0.95 orlast for less than 10 consecutive points. Only probabilitieslarger than 0.95 with a duration of 10 successive pointsare treated true faults. The decision threshold is chosen tobe PT = 14 after a few trials for fault isolation purpose.It is noticed that the actual aileron and elevator faultsare effectively detected and isolated with rapid response.The estimated system states calculated from Eq. (9) areillustrated in Fig. 4. They are probabilistically weightedsum of the estimated states from different UKFs. It isobserved that the proposed FDD is able to consistentlyestimate local velocities, angular rates and attitudes witha sufficient accuracy from the noisy measurements. Whenthe estimated system states deviate from the steady-statevalues, our FDD procedure can detect and isolate truefaults within a short period of time.

Performance of the FDD method is also tested for LIPactuator faults. Two individual LIP faults are created foraileron and elevator as shown in Fig. 5. It is observed thatwhen LIP faults occur, it takes longer time to recover tothe nominal values. Further, the coupling effect has thepotential to result in an elevator fault when the aileronfault occurs. It is found that our procedure is able to detectand isolate an aileron fault within [−5o, 5o]. It is shown inFig. 5 that single LIP fault in aileron is accurately detectedand isolated with a time delay of 0.4s. For a continuousLIP fault, it is seen that the estimate error increases dueto the fact that it takes time for the UKFs to track the

20 40 60 80 100 120 140−10

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0

5

10

AIL

(D

EG

)

20 40 60 80 100 120 140−20

−10

0

10

20

Time (s)

ELE

(D

EG

)

TrueEstimated

TrueEstimated

Fig. 5. Comparison of true and estimated actuator com-mand for single LIP faults

20 40 60 80 100 120 1400

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ult P

r

Raw prob

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Pr

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AIL

Pr

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Pr

Fig. 6. Probabilities generated by the fault isolation deci-sion criterion for LIP faults

system dynamics. Thus, this leads to transient responses.However, the LIP fault is still identified with a short timedelay as can be seen in Fig. 6. It is shown in Fig. 7 thatthe estimated system states are accurately estimated fromnoisy measurements and can be used to evaluate flightconditions of a UAS.

5.2 Performance Evaluation for Measurement Noise

Measurement noise is an inevitable factor affecting esti-mate performance in real-time applications. The sensitiv-ity analysis of our FDD method indicates that detectionand isolation performance would degrade with an increasein measurement noise levels. To assess the tolerable limitfor the proposed FDD, Gaussian random noise is imposedwith progressively increasing levels in simulations. The fol-lowing quantitative specifications are employed to evaluatethe estimate performance:

σ =

√√√√ 1

N

N∑k=1

(x(k)− x̄(k))2 (20)

The estimate capacity factor γ is

γ = 20 log10σ

xmax(21)

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/s)

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θ (r

ad)

Fig. 7. Estimated states for LIP faults

Here, x̄(k) is the average value of the estimated actuatorcommand. The mean squared error (MSE) σ aims tocheck the standard deviation of the estimate. γ is usedto assess the estimation capacity when measurement noiseis present.

For single floating actuator faults, 100 simulations areconducted with each lasting for 150s (simulation step is0.01s). The single faults occur within the time interval[0, 150s] when the standard deviation of measurementnoise increases. The estimate performance is illustrated inFig. 8 and Fig. 9. For single aileron faults with magnitudevariations between [−7o, 7o], it is observed that the MSEis less than 1.05o which indicates an accurate estimateof the faulty aileron. To quantify the acceptable estimatecapacity, a threshold for the estimate capacity factor isrequired. The threshold is set to −13.97 dB in our case,which means the MSE is 20% of the maximum estimatedaileron command. It is noticed in Fig. 8 that the estimatecapacity factor γ remains less than the threshold untilnoise standard deviation is 0.16 m/s in velocities, 0.13o

in attitudes and 0.13o/s in angular rates. This indicatesthe FDD can tolerate measurement noise with standarddeviations lower than these limit values. Similarly, singlefloating elevator fault is generated with increasing mea-surement noise to test estimate capacity of the FDD pro-cedure. The elevator changes within [−4o, 4o]. It is shownin Fig. 9 that the MSE is less than 0.97o for the estimatedelevator. Also, the estimate capacity factor remains lessthan −13.97 dB until noise standard deviation reaches

0 50 1000.85

0.9

0.95

1

1.05

1.1

Num of simulations

MS

E (

Deg

)

Simulations for single aileron fault

0 50 100−20

−18

−16

−14

−12

−10

Sim index

Est

imat

e ca

paci

ty (

Aile

ron)

Esti. capacity factorThreshold

Fig. 8. MSE and estimate capacity factor for single floatingaileron faults

0.53 m/s for velocities, 0.42o for attitudes and 0.42o/s forangular rates. It is seen that the proposed FDD procedurefunctions effectively when the measurement noise is withinthese limit values. Due to small measurement noise yieldedby available sensors in the considered application, ourFDD method can be applied to identification of singleactuator faults.

6. CONCLUSION AND FUTURE WORK

In this paper, we present a recursive FDD scheme foridentifying actuator faults with improved reliability. Thefault detection is performed by using the UKF algorithm

0 50 1000.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Num of simulations

MS

E (

Deg

)

Simulations for single elevator fault

0 50 100−16

−15.5

−15

−14.5

−14

−13.5

−13

Sim index

Est

imat

e ca

paci

ty (

Ele

vato

r)

Esti. capacity factorThreshold

Fig. 9. MSE and estimate capacity factor for single floatingelevator faults

and the fault diagnosis is conducted by the BC method.Performance of the proposed FDD is evaluated by us-ing aerodynamic parameters of an ARCAA UAS and itis demonstrated in simulations that our method can ef-fectively detect and isolate typical single actuator faultswhen measurement noise is present within certain levels.Future work includes assessment of our procedure for dualactuator fault scenarios (simultaneous occurrence of twoactuator faults) and flight validation of the proposed FDDmethod. Also, performance of the proposed FDD frame-work will be tested for windy conditions.

ACKNOWLEDGEMENTS

The research presented in this paper forms part ofProject ResQu led by the Australian Research Centre forAerospace Automation (ARCAA). The authors gratefullyacknowledge the support of ARCAA and the project part-ners, Queensland University of Technology (QUT); Com-monwealth Scientific and Industrial Research Organisation(CSIRO); Queensland State Government Department ofScience, Information Technology, Innovation and the Arts;Boeing and Insitu Pacific.

REFERENCES

Amirarfaei, F., Baniamerian, A., and Khorasani, K.(2013). Joint kalman filtering and recursive maximumlikelihood estimation approaches to fault detection andidentification of boeing 747 sensors and actuators. InAIAA Aerospace Science Meeting.

Bernard, M., Kondak, K., Maza, I., and Ollero, A. (2011).Autonomous transportation and deployment with aerialrobots for search and rescue missions. Journal of FieldRobotics, 28, 914–931.

Brinker, J.S. and Wise, K.A. (2001). Flight testing ofreconfigurable control law on the X-36 tailless aircraft.Journal of Guidance, Control, and Dynamics, 24, 903–909.

Calise, A.J., Lee, S., and Sharma, M. (2001). Developmentof a reconfigurable flight control law for tailless aircraft.Journal of Guidance, Control, and Dynamics, 24, 896–902.

Campbell, M.E. and Brunke, S. (2001). Nonlinear estima-tion of aircraft models for on-line control customization.In IEEE Aerospace Conference.

Ducard, G. and Geering, H.P. (2008). Efficient nonlinearactuator fault detection and isolation system for un-

manned aerial vehicles. Journal of Guidance, Controland Dynamics, 31(1), 225–237.

Ducard, G.J.J. (2009). Fault-tolerant Flight Control andGuidance Systems: Practical Methods for Small Un-manned Aerial Vehicles. Springer, 1st edition.

Eide, F. and Maybeck, P. (1996). An MMAE failuredetection system for the F-16. IEEE Transactions onAerospace and Electronics Systems, 32, 1125–1136.

Julier, S.J. and Uhlmann, J.K. (2004). Unscented filter-ing and nonlinear estimation. In Proc. of the IEEE,volume 92, 401–422.

Kendoul, F. (2013). Towards a unified framework for uasautonomy and technology readiness assessment (atra).Autonomous Control Systems and Vehicles, 55–71.

Kim, S., Choi, J., and Kim, Y. (2008). Fault detection anddiagnosis of aircraft actuators using fuzzy-tuning IMMfilter. IEEE Transactions on Aerospace and ElectronicSystems, 44, 940–952.

Lee, B.J., Park, J.B., Lee, H.J., and Joo, Y.H. (2005).Fuzzy-logic-based IMM algorithm for tracking a ma-noeuvring target. IEE Proceedings on Radar SonarNavigation, 152, 16–22.

Maybeck, P.S. (1999). Multiple model adaptive algo-rithms for detecting and compensating sensor and ac-tuator/surface failures in aircraft flight control systems.International Journal of Robust and Nonlinear Control,9, 1051–1070.

Mejias, L. and Fitzgerald, D. (2013). A multi-layeredapproach for site detection in UAS emergency landingscenarios using geometry-based image segmentation. InInternational Conference on Unmanned Aerial Systems.

Mejias, L., Fitzgerald, D., Eng, P., and Liu, X. (2009).Forced Landing Technologies for Unmanned Aerial Vehi-cles: Towards Safer Operations, chapter Aerial Robotics,415–442. InTech.

Meskin, N., Naderi, E., and Khorasani, K. (2013). Amultiple model-based approach for fault diagnosis ofjet engines. IEEE Transactions on Control SystemsTechnology, 21, 254–262.

Williams, P. and Crump, M. (2012). Intelligent landingsystem for landing uavs at unsurveyed airfields. In 28thInternational Congress of the Aeronautical Sciences.

Yang, X., Mejias, L., and Molloy, T. (2013). NonlinearH∞ control of UAVs for collision avoidance in gusty en-vironment. Journal of Intelligent and Robotic Systems,69, 207–225.

Zhang, Y. and Jiang, J. (2000). Integrated design ofreconfigurable fault-tolerant control systems. Journalof Guidance, 24, 133–136.

Zhang, Y. and Li, Z.R. (1998). Detection and diagnosisof sensor and actuator failures using IMM estimator.IEEE Transactions on Aerospace and Electronic Sys-tems, 34(4), 1293–1313.