sensor and control surface/actuator failure detection and isolation applied to f‐16 flight dynamic

Sensor and control surface/actuator failuredetection and isolation applied to F-16 flight

dynamicChingiz Hajiyev

Faculty of Aeronautics and Astronautics, Istanbul Technical University, Istanbul, Turkey, and

Fikret CaliskanFaculty of Electrical and Electronics, Istanbul Technical University, Istanbul, Turkey

AbstractPurpose – The purpose of the paper is to present an approach to detect and isolate the aircraft sensor and control surface/actuator failures affectingthe mean of the Kalman filter innovation sequence.Design/methodology/approach – The extended Kalman filter (EKF) is developed for nonlinear flight dynamic estimation of an F-16 fighter and theeffects of the sensor and control surface/actuator failures in the innovation sequence of the designed EKF are investigated. A robust Kalman filter (RKF)is very useful to isolate the control surface/actuator failures and sensor failures. The technique for control surface detection and identification is appliedto an unstable multi-input multi-output model of a nonlinear AFTI/F-16 fighter. The fighter is stabilized by means of a linear quadratic optimal controller.The control gain brings all the eigenvalues that are outside the unit circle, inside the unit circle. It also keeps the mechanical limits on the deflections ofcontrol surfaces. The fighter has nine state variables and six control inputs.Findings – In the simulations, the longitudinal and lateral dynamics of an F-16 aircraft dynamic model are considered, and the sensor and controlsurface/actuator failures are detected and isolated.Research limitations/implications – A real-time detection of sensor and control surface/actuator failures affecting the mean of the innovationprocess applied to the linearized F-16 fighter flight dynamic is examined and an effective approach to isolate the sensor and control surface/actuatorfailures is proposed. The nonlinear F-16 model is linearized. Failures affecting the covariance of the innovation sequence is not considered in the paper.Originality/value – An approach has been proposed to detect and isolate the aircraft sensor and control surface/actuator failures occurred inthe aircraft control system. An extended Kalman filter has been developed for the nonlinear flight dynamic estimation of an F-16 fighter. Failures in thesensors and control surfaces/actuators affect the characteristics of the innovation sequence of the EKF. The failures that affect the mean of theinnovation sequence have been considered. When the EKF is used, the decision statistics changes regardless the fault is in the sensors or in the controlsurfaces/actuators, while a RKF is used, it is easy to distinguish the sensor and control surface/actuator faults.

Keywords Aerodynamics, Failure (mechanical), Control systems

Paper type Research paper

Nomenclature

A ¼ aircraft dynamic matrix

B ¼ aircraft control matrix

Du ¼ covariance matrix of control input error

Dd ¼ covariance matrix of system disturbance

F ¼ matrix that represents the nonlinear part of

aircraft equations

G ¼ transfer matrix of system disturbance

H ¼ measurement matrix

K ¼ Kalman filter gain matrix

M ¼ covariance matrix of extrapolation error

Q ¼ process noise intensity matrix

Q(qr) ¼ process noise intensity matrix parameterized

by qr

S ¼ covariance matrix

p ¼ roll rate

P ¼ covariance matrix of estimation error

q ¼ pitch rate

r ¼ yaw rate

u ¼ aircraft control vector

x ¼ state vector

v ¼ forward velocity

ve ¼ estimated forward velocity by EKF

v ¼ measurement disturbance vector

w ¼ system noise

z ¼ measurement vector

a ¼ angle of attack

b ¼ side-slip angle

dC ¼ canard deflection

dFL ¼ left flap deflection

dFR ¼ right flap deflection

dHL ¼ left stabilizer deflection

dHR ¼ right stabilizer deflection

dR ¼ rudder deflection

u ¼ pitch angle

The Emerald Research Register for this journal is available at

www.emeraldinsight.com/researchregister

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/0002-2667.htm

Aircraft Engineering and Aerospace Technology: An International Journal

77/2 (2005) 152–160

q Emerald Group Publishing Limited [ISSN 0002-2667]

[DOI 10.1108/00022660510585992]

152

www.emeraldinsight.com/researchregister

www.emeraldinsight.com/0002-2667.htm

c ¼ yaw angle

w ¼ roll angle

f ¼ state transition matrix~D ¼ normalized innovation sequences2 ¼ variance

Subscripts

FDI ¼ fault detection and isolation

GLR ¼ generalized likelihood ratioEKF ¼ extended Kalman filter

RKF ¼ robust Kalman filter

FTC ¼ fault tolerant control

IMM ¼ interacting multiple-modelMMAE ¼ multiple model adaptive estimation

1. Introduction

Many fault detection filters have been developed to detect and

identify sensor and actuator faults by using analytical

redundancy (Larson et al., 2002; Lee and Lyou, 2002;Zhang and Li, 1997; Rago et al., 1998; Maybeck, 1999).

In Larson et al. (2002), an analytical redundancy-based

approach for detecting and isolating sensor, actuator, and

component (i.e. plant) faults in complex dynamical systems,

such as aircraft and spacecraft is developed. The method isbased on the use of constrained Kalman filters, which are able

to detect and isolate such faults by exploiting the functional

relationships that exist among various subsets of available

actuator input and sensor output data. A statistical changedetection technique based on a modification of the standard

generalized likelihood ratio (GLR) statistic is used to detect

faults in real time. The GLR test requires the statistical

characteristics of the system to be known before and after thefault occurs. As this information is usually not available after

the fault, the method has limited applications in practice.An integrated robust fault detection and isolation (FDI)

and fault tolerant control (FTC) scheme for a fault in

actuators or sensors of linear stochastic systems subjected to

unknown inputs (disturbances) is presented in Lee and Lyou

(2002). The FDI modules are constructed using banks of

robust two-stage Kalman filters, which simultaneouslyestimate the state and the fault bias, and generate residual

sets decoupled from unknown disturbances. All elements of

residual sets are evaluated by using a hypothesis statistical

test, and the fault is declared according to the prepareddecision logic. In this work, it is assumed that a single fault

occurs at a time and the fault treated is of random bias type.

The diagnostic method presented in the article is valid only

for the control surface FDI.In Zhang and Li (1997) and Rago et al. (1998) the

algorithms for the detection and diagnosis of multiple failures

in a dynamic system are described. They are based on theinteracting multiple-model (IMM) estimation algorithm,

which is one of the most cost-effective adaptive estimation

techniques for systems involving structural as well as

parametric changes. The proposed algorithms provide anintegrated framework for fault detection, diagnosis, and state

estimation.In Maybeck (1999) multiple model adaptive estimation

(MMAE) methods have been incorporated into the design ofa flight control system for the variable in-flight stability test

aircraft (VISTA) F-16, providing it with the capability to

detect and compensate for sensor and control surface/actuator

failures. The algorithm consists of a “front end” estimator for

the control system, composed of a bank of parallel Kalmanfilters, each matched to a specific hypothesis about the failure

status of the system (fully functional or a failure in any onesensor or surface/actuator), and a means of blending the filter

outputs through a probability-weighted average. In themethods described in Zhang and Li (1997), Rago et al.(1998) and Maybeck (1999), the faults are assumed to beknown, and the Kalman filters are designed for the known

sensor/actuator faults. As the approach requires severalparallel Kalman filters, and as the faults should be known, it

can be used in limited applications.In Napolitano et al. (1993, 1996), Raza et al. (1994),

Borairi and Wang (1998) and Alessandri (2003), the neuralnetwork based methods to detect sensor, control surface/

actuator failures are developed and discussed. In Napolitanoet al. (1993), a neural network is proposed as an approach to

the task of failure detection following a damage to anaerodynamic surface of an aircraft flight control system.

This structure, used for the state estimation purpose, can bedesigned and trained online in flight and generates a residual

signal indicating the damage as soon as it occurs.In Raza et al. (1994) the problem of detecting control

surface failures of a high performance aircraft is considered.The detection model is developed using a linear dynamic

model of an F/A-18 aircraft. Two parallel models detect theexistence of a surface failure, whereas the isolation and

magnitude of any one of the possible failure modes isestimated by a decision algorithm using either neural

networks or fuzzy logic.Napolitano et al. (1996) describe a study related to the

testing and validation of a neural-network based approach forthe problem of actuator failure detection and identification

following battle damage to an aircraft control surface. Onlinelearning neural architectures, trained with the extended back-

propagation algorithm, have been tested under nonlinearconditions in the presence of sensor noise.In Borairi and Wang (1998), an approach for the fault

detection and diagnosis of the actuators and sensors in

nonlinear systems is presented. First, a known nonlinearsystem is considered, where an adaptive diagnostic model

incorporating the estimate of the fault is constructed. Further,unknown nonlinear systems are studied and a feedforward

neural network is trained to estimate the system under healthyconditions. Genetic algorithms are proposed as a means of

optimising the weighting connections of neural network andto assist the diagnosis of the fault.In Alessandri (2003), a neural network based method to

detect the faults in nonlinear systems is proposed. Fault

diagnosis is accomplished by means of a bank of estimators,which provide estimates of parameters that describe actuator,

plant, and sensor faults. The problem of designing suchestimators for general nonlinear systems is solved by searching

for optimal estimation functions. These functions areapproximated by feed forward neural networks and the

problem is reduced to find the optimal neural weights.The methods based on artificial neural networks and geneticalgorithms do not have physical bases. Therefore, according

to the different data corresponding to the same event, themodel gives different solutions. Thus, the model should

continuously be trained by using the new data.Perhinschi et al. (2002) focus on specific issues relative to

the real-time online estimation of aircraft aerodynamic

Sensor and control surface/actuator FDI applied to F-16 flight dynamic

Chingiz Hajiyev and Fikret Caliskan


Volume 77 · Number 2 · 2005 · 152–160

153

parameters at nominal and post-actuator failure flight

conditions. A specific parameter identification method,based on Fourier transform, has been applied to an

approximated mathematical model of the NASA IFCS F-15

aircraft. The direct evaluation of stability and controlderivatives versus the estimation of the coefficients of the

state space system matrices evaluation has been considered.This method may not produce good results, when the number

of the stability and control derivatives is high.One of the diagnosis approaches based on Kalman filtering

is the analysis of the innovation sequence (Mehra andPeschon, 1971; Willsky, 1976; Bsseville and Benveniste,

1986; Gadzhiev, 1992, 1994). These approaches do notrequire a priori statistical characteristics of the faults, and the

computational burden is not very heavy. If the systemoperates normally, the normalized innovation sequence in a

Kalman filter is a Gaussian white noise with a zero mean and

a unit covariance matrix. Faults that change the systemdynamics by causing surges of drifts of the state vector

components, abnormal measurements, sudden shifts in themeasurement channel, and other difficulties such as decrease

of instrument accuracy, an increase of background noise,reduction in control surface/actuator effectiveness etc., effect

the characteristics of the normalized innovation sequence bychanging its white noise nature, displacing its zero mean, and

varying unit covariance matrix. Thus, the problem is how todetect as quickly as possible any change of these parameters

from their nominal value.Methods of testing the agreement between the innovation

sequence and white noise, and the detection of any change inits mathematical expectation have been discussed in the

literature (Mehra and Peschon, 1971; Willsky, 1976; Bsseville

and Benveniste, 1986; Hajiyev and Caliskan, 2003).The approaches that verify the covariance matrix of the

innovation process are addressed in Mehra and Peschon(1971), Gadzhiev (1992, 1994) and Hajiyev and Caliskan

(2003).In this paper, a real-time detection of sensor and control

surface/actuator failures effecting the mean of the innovationprocess applied to F-16 fighter flight dynamic is examined

and an effective approach to isolate the sensor and controlsurface/actuator failures is proposed.

2. F-16 aircraft model description

The technique for control surface detection and identification

is applied to an unstable multi-input multi-output model ofan AFTI/F-16 fighter. The fighter is stabilized by means of a

linear quadratic optimal controller. The control gain brings allthe eigenvalues that are outside the unit circle, inside the unit

circle. It also keeps the mechanical limits on the deflections ofcontrol surfaces. The model of the fighter is as follows

(Lyshevski, 1997):

xðk þ 1Þ ¼ AxðkÞ þ BuðkÞ þ FðxðkÞÞ þ wðkÞ ð1Þ

The aircraft state variables are:

x ¼ ½v;a; q; u;b; p; r;f;c �T;

where v is the forward velocity, a is the angle of attack, q is the

pitch rate, u is the pitch angle, b is the side-slip angle, p is theroll rate, r is the yaw rate, f is the roll angle, c is the yaw

angle, w(k) is the system noise with zero mean and the

correlation matrix E½wðkÞwTð jÞ� ¼ QðkÞdðkjÞ; d(kj) is the

Kronecker symbol:

dðkjÞ ¼1; k ¼ j

0; k – j

(

The fighter has six control surfaces and hence the six control

inputs are:

u ¼ ½dHR; dHL; dFR ; dFL; dC; dR�;

where dHR and dHL are the deflections of the right and left

horizontal stabilizers, dFR and dFL are the deflections of the

right and left flaps, and dC and dR are the canard and rudder

deflections.We assume the following hard bounds (mechanical limits)

on the deflections of control surfaces: jdHRdHLj # 0:44 rad;jdFRdFLj # 0:35 rad; jdCj # 0:47 rad and jdRj # 0:52 rad:

A, B, and F(x) for the sampling period of 0.03 s are:

A¼

0:9995 0:2457 20:0273 20:2885 20:0391 20:0075 20:002 0 0

20:0001 0:9663 0:0291 0 0:0011 0:0017 0:0003 0 0

0 0:1135 0:9765 0 0:0007 0:0002 0:0012 0 0

0 0:0017 0:0296 1 0 0 0 0 0

20:0001 0:0048 0:0011 0:0288 0:977 0:0037 20:0268 0 0

0:0001 0:0165 0:0005 20:0198 21:3515 0:8977 0:025 0 0

0 20:0268 0:0015 0:0041 0:2716 20:0003 0:9811 0 0

0 0:0003 0 20:0002 20:0207 0:0285 0:0003 1 0

0 20:0004 0 0 0:0041 0 0:0297 0 1

266666666666666666664

377777777777777777775

B¼

0:071 0:0067 20:011 20:0117 20:0004 20:0001

20:009 20:0088 20:0091 20:009 0 0

20:2818 20:2819 20:0746 20:0746 0 0

20:0042 20:0042 20:0011 20:0011 0 0

20:001 0:0007 20:0006 0:0005 0:0123 0:0018

20:0822 0:0819 20:0881 0:0879 0:0122 0:025

0:0921 20:0924 0:0233 20:0232 0:02 20:0132

20:0013 0:013 20:013 0:013 0:0002 0:0004

0:0014 20:0014 0:0003 20:0003 0:0003 20:0002

266666666666666666664

377777777777777777775

FðxÞ¼

Fn

Fa

Fq

Fu

Fb

Fp

Fr

Ff

Fc

266666666666666666664

377777777777777777775

¼

0

20:03pcosatanb20:03r sinatanb

0:028pr20:00018p2þ0:00018r2

0:03qcosf20:03r sinf

0:03psina20:03rcosa

0:00026qp20:017qr

20:025qp20:00026qr

0:03qtanusinfþ0:03r tanucosf

0:03qcos21usinfþ0:03rcos21ucosf

266666666666666666664

377777777777777777775

3. Design of the EKF for the F-16 aircraft modelestimation

Below the extended Kalman filter (EKF) to estimate the F-16

aircraft motion is designed.Let us define the estimated vector as:




Volume 77 · Number 2 · 2005 · 152–160

154

xTðkÞ ¼ ½nðkÞ;aðkÞ; qðkÞ; uðkÞ;bðkÞ; pðkÞ; rðkÞ;fðkÞ;cðkÞ�

and apply the Kalman filter to estimate this vector. The

nonlinear mathematic model for the longitudinal and lateral

F-16 aircraft motion is given in (1).

The measurement equations can be written as:

zðkÞ ¼ HxðkÞ þ vðkÞ; ð2Þ

where H is the measurement matrix, which is 9 £ 9 unit

matrix, v(k)-measurement noise and its mean and correlation

matrix, respectively, are:

E½vðkÞ� ¼ 0; E½vðkÞvTð jÞ� ¼ RðkÞdðkjÞ:

By using quasi-linearization method let us linearize the

equation (1):

xðkÞ ¼ Axðk 2 1Þ þ Buðk 2 1Þ þ Fðxðk 2 1ÞÞ

þ A½xðk 2 1Þ2 xðk 2 1Þ� þ Fxðk 2 1Þ

£ ½xðk 2 1Þ2 xðk 2 1Þ� þ B½uðk 2 1Þ2 uðk 2 1Þ�

þ wðk 2 1Þ

ð3Þ

where

Fx ¼ ›F

›x

� �xðk21Þ

:

Among the procedures of estimation theory, the Bayes

procedure has the most accuracy because it is based on both

the experimental data in likelihood function and a priori data

expressed by a priori density of the estimated parameters. The

more data, the more accuracy yields. Moreover, the Bayes

procedure does not require the system to be linear and

stationary, and produces a solution for the filtering when the

initial conditions of the state vector are unknown (Gadzhiev,

1996). Therefore, we prefer the Bayes procedure to filter the

state vector of the aircraft motion. A posteriori distribution

density of the state vector is given by the Bayes formula:

PxðkÞZk

� �¼ P

xðkÞZk21; zðkÞ

� �¼

PxðkÞZk21

h iP

zðkÞZk21

h iPzðkÞ

xðkÞ;Zk21

� �; ð4Þ

where Zk ¼ {zð1Þ; zð2Þ; zð3Þ; . . . ; zðkÞ}; Zk21¼{zð1Þ; zð2Þ; . . . ;zðk 2 1Þ}:When the probability density functions in (4) are

substituted and the conditional mathematical expectation of

the a posteriori probability density function is taken as the

optimum estimation value, the following recursive EKF

algorithm for the state vector estimation of the F-16 aircraft

motion is obtained as Caliskan and Hajiyev (2003):

xðkÞ ¼ Axðk 2 1Þ þ Buðk 2 1Þ þ Fðxðk 2 1ÞÞ

þ PðkÞHTR21ðkÞ{zðkÞ2 H ½Axðk 2 1Þ

þ Buðk 2 1Þ þ Fðxðk 2 1ÞÞ�}

ð5Þ

PðkÞ ¼ MðkÞ2 MðkÞHT½RðkÞ þ HMðkÞHT�21HMðkÞ ð6Þ

MðkÞ ¼ APðk 2 1ÞAT þ BDuðk 2 1ÞBT

þ Fxðk 2 1ÞPðk 2 1ÞFTx ðk 2 1Þ þ GQðk 2 1ÞGT

ð7Þ

where P(k) is the covariance matrix of the estimation error,

M(k) is the covariance matrix of the extrapolation error, Du is

the covariance matrix of the control input error; G is the

transfer matrix of the system noise.

4. Sensor/control surface failure detection andisolation via innovation sequence

Sensor/control surface failures may be caused by sensor drift,

step changes, scale factor errors changing the mean, incorrect

calibration of the sensors, friction between moving parts of

the sensors and control surfaces, etc. To detect failures

changing the mean of the innovation sequence, the following

statistical function is used (Willsky, 1976)

bðkÞ ¼Xk

j¼k2Mþ1

~DTð jÞ ~Dð jÞ ð8Þ

where ~Dð jÞ is the normalized innovation sequence of Kalman

filter. This statistical function has x2 distribution with Msdegree of freedom. Now consider the following two

hypotheses:

H0: System operates normally, and

H1: Fault occurs in the system.

If the hypothesis H1 is correct then x2 level for a confidence

probability a will be greater than x2 level found for the

hypothesis H0, i.e.:

H0 : bðkÞ # x2a;Ms ;k

H1 : bðkÞ . x2a;Ms ’k:

A robust Kalman filter may be designed in order to isolate the

detected sensor and control surface failures. A Kalman filter

that satisfies the Doyle-Stein condition is referred to as

Robust Kalman Filter (RKF). The Doyle-Stein condition is,

KðI þ HfKÞ21 ¼ BðHfBÞ21 ð9Þ

where K is the filter gain, I is unit matrix, f ¼ ðsI 2 AsÞ21,

and As is the system matrix in continuous time, H is the

system measurement matrix and B is the control distribution

matrix in continuous time. The use of the RKF is very useful

in the isolation of sensor and control surface failures as it is

insensitive to the latter failures. If the Kalman filter process

noise intensity matrix is chosen as,

QðqrÞ ¼ Q þ q2BVBT; ð10Þ




Volume 77 · Number 2 · 2005 · 152–160

155

where Q is process noise intensity matrix for the nominal

plant, qr approaches to infinity, V is any positive definite

symmetric matrix, then the RKF is obtained (Caliskan,

1997).If the fault is detected as a sensor fault rather than a control

surface fault, then it is necessary to determine what sensor is

faulty. For this purpose, the s-dimensional sequence ~D is

transformed into s one-dimensional sequences to isolate the

faulty sensor, and for each one-dimensional sequence ~Diði ¼1; 2; . . . ; sÞ; corresponding monitoring algorithm is run. The

statistics of the faulty sensor is assumed to be affected much

more than those of the other sensors. Let the statistics be

denoted as jiðkÞ. When max{jiðkÞ=i ¼ 1; 2; . . . ; s} ¼ jmðkÞ fori – j, and jiðkÞ – jjðkÞ; it is judged thatmth control channel has

failed.Let the statistics which is a rate of sample and theoretical

variances, s2i =s

2i be used to verify the variances of one

dimensional innovation sequences ~DiðkÞ; i ¼ 1; 2; . . . ; s.When ~Di , Nð0;siÞ it is known that,

ni

s2i

, x2a;M21; ;i; i ¼ 1; 2; . . . ; s ð11Þ

where ni ¼ ðM 2 1Þs2i :

As s2i ¼ 1 for normalized innovation sequence it follows

that,

ni , x2a;M21; ;i; i ¼ 1; 2; . . . ; s: ð12Þ

When a fault affecting the variance of the innovation

sequence occurs in the system, the statistics ni exceeds the

threshold value x2a;M21 depending on the confidence

probability a, and degree of freedom ðM 2 1Þ. Using (12)

it can be proved that any change in the mean of the

normalized innovation sequence can be detected. Let a

change in the mean of the innovation sequence occur at the

time t, and let ~D�ðkÞdenote the unchanged normalized

innovation sequence, then the changed normalized

innovation sequence is given by,

~DðkÞ ¼ ~D�ðkÞ k ¼ 1; 2; . . . ; t2 1 ð13Þ

~DðkÞ ¼ ~D�ðkÞ þ mðk 2 tÞ k ¼ t; tþ 1; . . . ð14Þ

where mð·Þ is an unknown change and may vary with respect

to time, but there exists a quantity L . 0 such that jmð jÞj ,L; for ;j. (13) and (14) yield,

~DðkÞ , Nð0; 1Þ k ¼ 1; 2; . . . ; t2 1 ð15Þ

~DðkÞ , Nðmðk 2 tÞ; 1Þ k ¼ t; tþ 1; . . . ð16Þ

Let the number of shifted values from j ¼ k 2 M þ 1 to k in

a window be denoted by N. When k , t it can be easily

shown that the mathematical expectation of (5) is

E½ni � ¼ M 2 1. When a fault occurs, the mathematical

expectation of (12) can be determined by the following

theorem.

Theorem. When k$t, i.e. the hypothesis H1 is true, thefollowing equation is also true,

E½yðkÞ� ¼ ðM 2 1Þs2

þ EXk

j¼k2Mþ1

mð j 2 tÞ2

Xk

j¼k2Mþ1

mð j 2 tÞ

M

266664

377775

28>>>>><>>>>>:

9>>>>>=>>>>>;ð17Þ

where

mð j 2 tÞ ¼0 j , t

m� ¼ constant j $ t

(

The proof is given in (Hajiyev and Caliskan, 1999).

Let the number of shifted innovation values from j ¼k 2 M þ 1 to k in a window be denoted by N. Two distinctcases may be considered;1 N¼M, in this case,

EXk

j¼k2Mþ1

mð j 2 tÞ2

Xk

j¼k2Mþ1

mð j 2 tÞ

M

266664

377775

28>>>>><>>>>>:

9>>>>>=>>>>>;

¼ 0 ð18Þ

and so, E½vðkÞ� ¼ ðM 2 1Þs2. When the values ~Dð jÞ haveshifted by the same amount mð j 2 tÞ in a window, it isimpossible to detect the change by using (12).

2 N , M; in this case

mð j 2 tÞ2

Xk

j¼k2Mþ1

mð j 2 tÞ

M

266664

377775

2

¼ mð j 2 tÞ2 Nm�M

� �2$ 0 ð19Þ

and a shift in the innovation sequence will cause anasymptotic increase in the expected value of the statisticsn(k), and n(k) will exceed the threshold x2a;M21. The larger

m� the faster detection is.

The sample variances si are the diagonal components of theselection covariance matrix SðkÞ. Therefore there is no needto make heavy additional computation in the existent

algorithm, but only the diagonal components of the matrixSðkÞ are multiplied by ðM 2 1Þ; and compared with x2a;M21

and with one another at each iteration. The decision-makingfor isolation is done as follows; if the hypothesis H1 is trueand SiiðkÞ – SjjðkÞ; i – j and max{SiiðkÞ=i ¼ 1; 2; . . . ; s} ¼SmmðkÞ where SiiðkÞ is the iith component of SðkÞ, then it isjudged that there is a fault in the mth channel.

5. Simulation results of failure isolation algorithm

The technique for detecting and isolating sensor/control surface failures is applied to an unstable multi-input




Volume 77 · Number 2 · 2005 · 152–160

156

multi-output model of an AFTI/F-16 fighter. The fighter isstabilized by means of a linear quadratic optimal controller.The control gain brings all the eigenvalues that are outside theunit circle, inside the unit circle. It also keeps the mechanicallimits on the deflections of control surfaces.In the simulations, M ¼ 20, s ¼ 9, and a ¼ 0:95 are taken,

and the threshold values x2a;M21 and x2a;Ms are found as 31.4and 212 from the table, respectively.1 A sensor failure at iteration 30, changing the mean value

of the innovation sequence in the third measurementchannel (pitch rate gyroscope fault) is considered asfollows:

zqðkÞ ¼ zqðkÞ þ 3; ðk $ 30Þ:

The graph of statistical values of bðkÞ is shown in Figure 1,when a shift occurs in the pitch rate gyroscope. As seen inFigure 1, until the sensor failure occurs, bðkÞ is lower thanthe threshold, and when a failure occurs in the pitch rategyroscope, bðkÞ grows rapidly and after two iterations itexceeds the threshold. Hence, H1 hypothesis is judged tobe true. This failure causes a change in the mean of theinnovation sequence. The innovation sequence of thirdmeasurement channel ~DqðkÞ is presented in Figure 2.Other innovation sequences are not presented here.

2 The control input dHR (deflection of the right horizontalstabilizer) has been changed to dHRðkÞ ¼ dHRðkÞ þ 10;ðk $ 30Þ at iteration 30. The graph of statistical values ofb(k) is shown in Figure 3 when a shift occurs in theactuator motor at the step 30. This failure causes a changein the mean of the innovation sequence. As seen inFigure 3, until the actuator failure occurs, b(k) is lowerthan the threshold, and when a failure occurs in theactuator, b(k) grows rapidly and after five steps it exceedsthe threshold. Hence H1 hypothesis is judged to be true.The innovation sequence ~DqðkÞ in the case of actuatormotor failure is shown in Figure 4.

3 The first control surface (right horizontal stabilizer) hasbeen changed as follows at iteration 30;

Bði; 1Þ ¼ Bði; 1Þ þ 0:08; i ¼ 1; 9

The graph of statistical values of bðkÞ is shown in Figure 5when a shift occurs in the control surface. As seen in

Figure 1 Detection of pitch rate gyroscope failure

Figure 2 Normalized innovation sequence ~DqðkÞ in the case of pitchrate gyroscope failure

Figure 3 Behavior of statistic b(k) in the case of actuator motor failure

Figure 4 Normalized innovation sequence ~DqðkÞ in the case of actuatormotor failure




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Figure 5, until the control surface failure occurs, bðkÞ is

lower than the threshold, and when a fault occurs in the

control surface, bðkÞ grows rapidly, after 30 iterations it

exceeds the threshold. Hence H1 hypothesis is judged to

be true. This failure causes a change in the mean of the

innovation sequence. The innovation sequence ~DqðkÞ in

the case of control surface failure is shown in Figure 6.

The simulations show that both sensor failures and

control surface/actuator failures affect the innovation

process.

Figures 7-9 illustrate a good isolation of the sensor and

control surface/actuator failures.As shown in Figure 10(a)-(c) only the (3,3) element of the

covariance matrix S(S(3,3)) exceeds the threshold x2a;M21,

which indicates a failure in the pitch rate gyro. S( j, j), j – 3

elements do not exceed the thresholds.The RKF which is insensitive to control surface/actuator

failures and sensitive to sensor failures, is employed to isolate

the sensor and control surface/actuator failures. It is shown

that the RKF can detect sensor failures, and cannot detect

Figure 5 Behavior of statistic b(k) in the case of control surface failure

Figure 6 Normalized innovation sequence ~DqðkÞ in the case of controlsurface failure

Figure 7 Detection of pitch rate gyroscope failure when the RKF is used

Figure 8 Detection of actuator motor failure is not possible when theRKF is used

Figure 9 Detection of control surface failure is not possible when theRKF is used




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control surface/actuator failures, in other words the RKF still

estimates the actual plant states even in case of a control

surface/actuator failure.

6. Conclusion

In this paper, an approach has been proposed to detect and

isolate the aircraft sensor and control surface/actuator failures

occurred in the aircraft control system. An extended Kalman

filter has been developed for nonlinear flight dynamic

estimation of an F-16 fighter. Failures in the sensors and

control surfaces/actuators affect the characteristics of the

innovation sequence of the EKF. The failures that affect

the mean of the innovation sequence have been considered.

When the EKF is used, the decision statistics changes

regardless the faults in the sensors or in the control surfaces/

actuators, while a RKF is used, it is easy to distinguish the

sensor and control surface/actuator faults. Assuming that the

effect of the faulty sensor on its channel is more significant

than on the other channels, a sensor isolation method is

presented by transforming s-dimensional innovation process

to s one-dimensional processes. The theoretical results are

confirmed by the simulations carried out on a nonlinear

dynamic model of the F-16 aircraft.

References

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Figure 10 Pitch rate gyro failure isolation




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About the authors

Chingiz Hajiyev graduated from Moscow Aviation

University (Moscow, Russia) with honour diploma on the

field of “Automatic and Information Systems” (MSc) in

1981. He received his PhD and DSc (Eng) degrees in Process

Control from Superior Certifying Commission at the Council

of Ministers of the USSR from Azerbaijanian Scientific and

Production Association (ASPA) “Neftgazavtomat” (Sumgait,

Azerbaijan), in 1987 and 1993, respectively. From 1987 to

1994 he worked as a Scientific Worker, Senior Scientific

Worker, Chief of the Information Measurement Systems

Department at the ASPA “Neftgazavtomat”. From 1994 to

1996 he was a Leading Scientific Worker at the Institute of

Cybernetics of the Academy of Sciences of Azerbaijan

Republic. From 1995 to 1996 he was a Professor in the

Department of Electronically-Calculated System Design,

Azerbaijan Technical University. Since 1996 he has been

with Department of Aeronautics and Astronautics, Istanbul

Technical University (Istanbul, Turkey), where he is currently

a Professor. He has more than 200 technical publications

including five books. He is a full Member of the International

Academy of Navigation and Motion Control (Russia, Saint

Petersburg). He was awarded a grant from the International

Science Foundation (USA) (1993). He is an adviser editor

and on the executive editorial boards of a number of journals.

His research interest include system identification, fault

detection and isolation, fault tolerant aircraft control system

design, aircraft parameter estimation and integrated

navigation systems.

Fikret Caliskan received his BSc (1984) and MSc (1987)

degrees from the Technical University of Istanbul, Turkey, in

electrical, electronics and control systems engineering, and

PhD (1993) from the University of London, United

Kingdom, in control systems engineering. He was a lecturer

at the technical university of Istanbul between 1993 and 1997,

and has been an assistant professor at the same university

since 1997. He was involved with various research and

teaching activities at Oakland University and Washington

University, USA between 1999 and 2001. He is a referee for

several international journals. He published a book together

with Chingiz Hajiyev and has more than 30 publications. His

research interest includes fault tolerant control systems,

robust control, neural networks, and estimation.




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sensor and control surface/actuator failure detection and isolation applied to f‐16 flight dynamic

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