A Statistical Decision-Making Scheme for
Automated Detection and Identification of
Faults in Aircraft Systems
D.G. Dimogianopoulos1, J.D. Hios1, S.D. Fassois1
1
Stochastic Mechanical Systems & Automation (SMSA) Group, Dept of Mechanical &
Aeronautical Engineering, University of Patras, GR 265 00 Patras, Greece, Tel/Fax:
(++30 2610) 997130, 997405, Email:{dimogian,hiosj,fassois}@mech.upatras.gr
Internet site: http://www.mech.upatras.gr/~sms
This paper introduces a Fault Detection and Identification (FDI) scheme well suited to
aircraft systems. The scheme is extensively based on nonlinear modeling of purposely
chosen Input/Output (I/O) relationships among available flight data. Advanced pooled
nonlinear representations, are used to model these relationships in two stages for a nofault (“healthy”) aircraft. Due to their pooled form, these representations are able to
accurately describe the modeled I/O dynamics for various aircraft operating conditions
and flight envelope areas. When the aircraft is affected by fault(s), the nominal
representation parameters must be updated to accurately describe the current (faultaffected) I/O dynamics. Thus, these parameter changes point to fault occurrence and
may be statistically evaluated to obtain automated onboard FDI results. The scheme’s
performance and robustness are checked via flights conducted in a nonlinear flight
simulator under light or intense aircraft maneuvering in various envelope points.
1. Introduction
The design of modern aircraft systems has stressed the importance of automated
Fault Detection and Identification (FDI) techniques for two reasons: (i) Reliability
and security, which are critical for such complex systems, should be acquired at the
lowest cost, and (ii) a fault, which is a deviation from the normal behavior of a
certain component or subsystem, usually leads to less efficient operation of the
entire closed-loop system. For instance, fault-affected sensors may lead to
discrepancies between measured and actual values of individual system variables:
Forwarding erroneous values to the flight control system can be downright
dangerous. Similarly, fault-affected actuator components may (at best) compromise
the operational characteristics of the actuator and deteriorate the handling qualities.
Detecting faults affecting aircraft systems is, thus, a critical task, which should rely
more on the smart use of the existing hardware rather than its (ponderous and
costly) duplication. Over the past years, considerable research efforts have resulted
in novel automated FDI algorithms for main (engines and actuators) and secondary
components (sensors). Relevant schemes [1]-[3] are based upon the Interactive
Multiple Model (IMM) principle: Kalman filters provide linear “healthy” and “faulty”
models for the monitored sensors and actuators, and the one corresponding to the

Research supported by the European Commission [STREP project No. 503019 on ``Innovative
Future Air Transport System (IFATS)''].
current aircraft state is selected by means of a probabilistic principle. The study in
[4] relies on the Multiple Model Switching and Tuning (MMST) concept to provide
linear adaptive models, each one covering an area of the aircraft dynamics under
specific failure scenarios. All model outputs are used to find the model closest to the
current plant dynamics, switch to that and adapt from there. Although complicated
(many filters per component, adaptive design), the application of these schemes is
reportedly successful. In order to avoid using detailed aircraft models for FDI, a
weak model-based approach is proposed in [5]: A single sensor signal (Angle-ofAttack) is processed via non-stationarity removal and whitening by suitably
estimated filters. Then, statistically testing the resulting signal allows for detecting
abrupt sensor faults. The method is successfully validated with real data.
Recent approaches in sensor and actuator FDI, take into account the potentially
nonlinear aircraft dynamics, e.g. when operating near the flight envelope
boundaries. The schemes in [6] and [7] use Neural Networks (NN) for modeling the
aircraft dynamics related to the monitored sensors. The detection of failed sensors
relies on monitoring the residual sequence, that is, the difference of the signal
(obtained by the physical sensor), and its estimated counterpart (obtained by the
NN model). The NN-based approaches are able of capturing the nonlinear aircraft
dynamics with good precision. Yet, a higher level of complexity is introduced, and
training is time consuming. Other nonlinear model-based schemes [8],[9] rely on
identifying Pooled Nonlinear AutoRegressive with eXogenous (P-NARX) excitation
representations with either constant [8], or time-varying [9] parameters. In [9], the
parameters depend upon functions of flight envelope-related quantities (Mach
number and Altitude). Via these representations, part of the healthy aircraft
dynamics is modeled for broad envelope areas and in various external conditions.
The healthy (modeled) dynamics are statistically compared with those of an aircraft
in unknown health state, to achieve rapid and reliable FDI results (validated by
several hundreds of flights examined). Finally, in [10] a system is modeled as a set
of I/O Differential Algebraic Equations (DAE). Then, statistical hypothesis tests on
the model parameters, check for changes pointing to subsystem failures.
The aim of this study is to introduce an effective automated FDI scheme based on
nonlinear modeling of carefully chosen I/O relationships between available recorded
flight data. In this case, the I/O relationship from the (auto)pilot stick input to the
aircraft pitch-rate signals is considered: It is modeled in two stages by combing a
Pooled Nonlinear AutoRegressive Moving Average with eXogenous excitation (PNARMAX) representation (first stage) with a P-NAR one (second stage), for a
“healthy” aircraft. Due to the pooled form, the I/O dynamics are accurately
described for various aircraft operating conditions and flight envelope areas. When
the aircraft is affected by faults, the nominal representation parameters are updated
in order to accurately describe the current (fault-affected) I/O dynamics. Clearly
these parameter changes result from fault occurrence, meaning that they may be
statistically evaluated to achieve automated onboard FDI results. The scheme’s
performance and robustness are checked via flights conducted in a nonlinear flight
simulator under light or intense aircraft maneuvering in various envelope points.
2. The Aircraft System and the Faults
A 6 Degree-Of-Freedom (DOF) nonlinear aircraft model in MATLAB Simulink©
environment, is used. Model inputs are the (auto)pilot commands (stick, wheel and
pedal), while outputs are the attitudes, the resulting accelerations on the body axes
2nd Stage
1st Stage
Figure 1: The FDI scheme’s operational principle with the aircraft model schematic in detail (left) and
the aircraft pitch rate under the considered faults for stick input equal to step of 15 lbs at 5 s (right).
and the corresponding angular rates (Fig. 1, detail left). The turbulence and wind
effects are regarded as system disturbances.
2.1 The faults considered
Faults affecting the elevator, the aileron and the engine subsystems are considered.
All faults are reproduced by altering the corresponding component blocks in the
aircraft simulator, and are denoted as FkA with A being the fault type and k the fault
magnitude. The elevator fault, referred to as F5A , is a Lost Of Effectiveness (LOE)
one, corresponding to reducing the elevator deflection range by 5%. It simulates
partial loss of feedback in the elevator circuit, leading to a small deflection reduction
(for safety). In Fig. 1 right (a), the pitch rate step response of an F5A -affected aircraft
is close to that of the healthy one, except for the small steady state chattering.
Two aileron faults are also considered. The first one, which is also a LOE fault,
simulates a constant bias added to the aileron deflection. The overall pitch rate step
response of the faulty aircraft is reduced by 10% at steady state [see Fig. 1 right
(b)], and thus, this fault is referred to as F10B . Moreover, Fig. 1 right (b) reveals that
the effect of F10B faults is a slow drift of the aileron response after t=7 s, pointing to a
B
“slowly evolving” fault. The second aileron fault, referred to as F0.0005
, is an “abrupt''
one. It corresponds to a small additive noise (with variance σ2=0.0005) added to the
aileron deflection, and simulates circuit wear [Fig. 1 right (b)].
Finally, the engine fault is of the One Engine Inoperative (or malfunctioning) type
(OEI). A throttle reduction of 38% (referred to as F38C ), is reproduced by lowering the
amplitude saturation limits of the throttle mechanism. This reduction leads to a quite
slow drift of the aircraft pitch rate response, following a specific step input [Fig. 1
right (c)]. Note that this drift is so slow that the aircraft may continue to fly safely
without any flight control law reconfiguration.
3. The Fault Detection and Identification Method
3.1 Overview of the Main Ideas
Aircrafts may exhibit approximately linear behavior, when operating inside limited
flight envelope areas, but nonlinearities may occur when an entire flight regime is
considered and/or the envelope boundaries are (instantly) crossed. To avoid using
many (local) models for globally modeling the aircraft dynamics, the proposed FDI
scheme makes use of:
a) Two stage nonlinear modeling: The first stage represents part of the healthy
system I/O dynamics, via a P-NARMAX representation providing a first set of
residuals e[t] (Fig. 1). The second stage uses a P-NAR representation to describe
the remaining part of the dynamics in various system states (healthy or faulty).
b) A feature vector1 θ containing the parameters of the previous P-NAR
representation. It is used to obtain system representations for healthy (θ0) and
various faulty states (θF) considered. Hereafter, the subscript (0) refers to an aircraft
in healthy state and the subscript (F) to that affected by the respective fault.
c) A Kullback distance metric providing a measure of the distance between the
current parameter vector θu (unknown system health state) and vectors θF
corresponding to the “benchmark” health states in b (healthy or the considered
faulty ones). This metric in the Gaussian case is given as:
1
T
D(θ F , θu )  tr  Pθu  Pθ F Pθu1  PθF1   tr  θ u  θ F  Pθu1  PθF1  θ u  θ F  
(1)




2
with θF and θu denoting random vectors with Gaussian probability density functions,
and Pθ F and Pθu the corresponding covariance matrices of the parameters. More
information on this metric in the general (non Gaussian) case may be found in [11].






3.2 Baseline Modeling Phase (Off-Line)
a) First Stage P-NARMAX Modeling
For a healthy aircraft, the relationship among the considered I/O signals (pilot stick
and pitch rate, respectively), is represented as follows:
L
y j [t ]  i  pi , j [t ]  e j [t ]  j
i 0
E e j [t ]  ei [t   ]   e [i, j ] [ ]  i, j
e j [t ]
(2)
NID  0,  e2 ( j )   j
with t designating the normalized discrete time, y j [t ] and e j [t ] the model's output
and one-step-ahead prediction error [or residual, assumed to be a zero-mean
uncorrelated sequence with variance  e2 ( j ) ] signals for the j-th flight, respectively.
E   designates statistical expectation, NID  ,  Normally Independently
Distributed (with the indicated mean and variance),  [ ] the Kronecker delta
(  [ ]  1 when   0 and  [ ]  0 when   0 ) and  e [i, j ] the cross covariance [14].
The terms pi , j [t ] are referred to as regressors and involve the output y j [t ] , the (not
explicitly shown) input u j [t ] , and past values of the residual e j signals. They are
nonlinear terms, that is, products of the output, the input, and the prediction error or
even powers of these signal values (with p0, j [t ] 1 , by definition). The nonlinearity
degree of the representation is equal to nl (that is, the sum of powers of the signal
values involved in each regressor, is less than or equal to nl). The maximum lags
1
Lower case/capital bold symbols designate column vector/matrix quantities, respectively.
of the signals y j [t ] , u j [t ] and e j [t ] in (2) (representation orders) are n y nu and ne ,
respectively. The i-th regressor coefficient (parameter) is denoted as  i .
During the baseline phase the objective is to identify the P-NARMAX
representation, that is: (a) To choose the regressors pi , j [t ] that most accurately
describe the system dynamics, and (b) to estimate the associated parameters θi .
For this purpose, the top equation in (2) may be rewritten as:
(3)
y j [t ]  φTj [t ]  θ  e j [t ]
pL, j [t ] and θ[t ]   0 [t ]
 L [t ] the parameter vector.
T
with φ j [t ]   p0, j [t ]
T
The j-th flight data (N samples) is then rewritten as a matrix equation:
y j  Φ j θ  e j
(4)
T
T
T
 y j [1] ... y j [ N ]  N1 , e j
 e j [1] ... e j [ N ]  N1 and Φ j φ j [1] ... φ j [ N ]
  N ( L 1) If M flights (each of N recorded data samples) are available for the
baseline modeling phase, for each of them, a matrix equation (4) may be defined.
Pooling all M sets together (that is, stacking one on top of the others) yields:
y  Φθ  e
(5)
with y j
T
T
 y1T ... y TM   NM 1 and e  e1T ... eTM   NM 1 . The matrix Φ Φ1T ...
ΦTM   NM ( L 1) involves the terms pi , j [t ] for all (M) flights at all (N) time instants.
with
y
The selection of pi , j terms in (5) should be carried out via a two Step Least Squares
(2SLS) method, since the regressor matrix  clearly contains past values of e j [t ] .
During the first step, an initial residual sequence e is obtained by identifying an
auxiliary P-NARX representation (of sufficiently high orders ny and nu): It features a
form similar to that in (2)-(5), except that its regressors do not include any past e j [t ]
values. The selection of the P-NARX regressors as well as the estimation of the
corresponding parameter vector is based upon an orthogonal parameter estimation
algorithm (see [12] and [13]). Briefly, an initial regressor set including all possible
product combinations (of nonlinearity up to nl) formed by the I/O signal values [yj[t1]...yj[t-ny]] and [u,j[t-1]... u,j[t-nu]], is considered. Then, an iterative procedure starts
searching for the most significant regressor term in this set. Each term's
significance is evaluated by its contribution to the reduction of the Residual Sum of
Squares to Signal Sum of Squares (RSS/SSS) ratio. The term leading to the most
significant RSS/SSS reduction at each iteration, is chosen. When a term is selected
and stored, the second most significant one is sought until a user-defined number of
regressors is obtained. This auxiliary identified P-NARX representation is used with
the available signals y and u for obtaining a first set of residuals e.
During the second step of the 2SLS procedure, another initial regressor set (similar
to that in the previous P-NARX representation) is formed. However, now all three
signal sequences y, u and e are utilized to form this new regressor set containing all
possible combinations of products (of nonlinearity up to nl). Then, P-NARMAX
identification is performed using this regressor set, the recorded data y, u and e, and
the orthogonal algorithm in [12] and [13], as in the P-NARX case.
b) Second Stage P-NAR Modeling
For an aircraft operating in healthy state, the P-NARMAX-obtained residuals should
be uncorrelated and stationary. However, due to a number of factors, such as
unmodeled nonlinearities, aircraft abrupt maneuvering and changing flight
conditions and so on, the residual sequence may be slightly correlated and nonstationary. On the other hand, if a fault has affected the system, then the residual
signal must be both correlated and non-stationary, since the initial P-NARMAX
representation is identified using data from a healthy system.
In order to enhance robustness with respect to the aforementioned factors, the
residual sequence e[t] (see Fig. 2) is further modeled via a P-NAR representation
following the procedure described for the P-NARMAX identification. Based on the
identified P-NAR representation, a feature vector containing the P-NAR parameters
is constructed for the healthy system case. Using the same P-NAR regressors, this
procedure is repeated in order to construct feature vectors θF for the fault cases as
described in section 3.1. Consequently, the second stage P-NAR modeling involves
one separate feature vector per fault considered.
3.3 Operational (Diagnostic) Phase (On-Line)
For a flight conducted under unknown aircraft health state, FDI results may be
obtained by using the procedure described in section 3.1. The parameter vector θu
of the P-NAR representation (with regressors selected in section 3.2.b) for the
aforementioned flight, is obtained in-flight, at each time instant, using recursive type
parameter estimation procedures [14]. Then, FDI results are obtained by comparing
the Kullback metric distance in (1) between the parameter vector θu corresponding
to the current (unknown state) flight, and the vectors corresponding to benchmark
faulty states, obtained during the baseline phase (see section 3.2). A fault is
declared once the Kullback distance between the healthy θ0 and the parameter
vector θu ceases to be minimal. Furthermore, fault identification is achieved once
the distance between the parameter vector θu and one of the predetermined
parameter vectors of “faulty states” becomes minimal. Hence, this method offers
simultaneous fault detection and identification.
4. Fault Detection and Identification Results
4.1 Preliminaries
The testing procedure involves a total number of 40 flights, all different from those
employed in the baseline phase, for the P-NARMAX and P-NAR identifications. The
duration of each flight is equal to 50 seconds with sampling at 100 Hz, and may
B
have been conducted with a healthy, or a F5A / F10B / F0.0005
/ F38C fault-affected aircraft.
The I/O relationship from the pilot stick input to the aircraft pitch rate is modeled, as
it heavily depends upon faults affecting both the elevator and the aileron surfaces.
The engine malfunction effects are also clearly visible through this I/O relationship.
In the next subsections the modeling and FDI results are presented.
4.2 Baseline Phase Modeling Results
The healthy system is represented by a P-NARMAX(15,15,15) representation with
nonlinearity degree nl equal to 2. The representation includes 25 regressors, shown
in Table 2. The parameters (estimated by the procedure of section 3.2) are based
P-NARMAX Regressors
y[t-1]
e[t-8]
y[t-3]
e[t-9]
y[t-8]
u2[t-15]
y[t-9]
Health State
Number of
Mean Time
test flights
for FDI (s)
Healthy
7
N/A
u[t-8]u[t-15]
F5A
11
0.10
y[t-13]
u[t-11]u[t-14]
F10A *
2
0.10
y[t-15]
u[t-3]e[t-15]
F10B
12
18.82
u[t-6]
u[t-14]e[t-15]
2
8.50
u[t-7]
u[t-14]e[t-2]
F15B *
u[t-8]
e[t-2]e[t-7]
B
F0.0005
3
0.05
u[t-9]
e[t-1]e[t-15]
F38C
3
9.90
u[t-10]
e[t-14]e[t-5]
u[t-13]
e2[t-15]
e[t-2]
Table 1: Structure of P-NARMAX(15,15,15)
with 25 terms
Table 2: Number of test flights conducted in various
aircraft health states and FDI results [N/A stands for
Not Applicable- no fault detection for healthy aircraft;
the asterisk (*) indicates fault of different magnitude
with respect to that in section 2.1]
upon 40 flights (other than those used for the FDI scheme’s testing) of 5001 samples
each, conducted in the landing regime for a given aircraft configuration (no faults,
constant weight-distribution and weather conditions). For the second stage modeling, a
P-NAR(25) representation with 35 regressors and nl also equal to 2 is identified. As
noted in section 3.1, P-NAR parameters for both healthy (θ0) and benchmark faulty (θF)
health states are estimated.
4.3 Operational (Diagnostic) Phase Results
For flights conducted with an aircraft in unknown state, the parameter vector θu is
obtained using a Recursive Least Square algorithm (RLS) [14] with forgetting factor
=0.995, chosen after extensive testing. The RLS algorithm becomes operational
after the first 1000 time samples of the flight (10 seconds). The results are collected
in Table 2, where the test flights are classified according to the aircraft health state
under which they have been conducted. The mean time of detection for each fault
class (measured from the time instant the algorithm is operational) is also
presented. All faults are successfully detected, and in most cases the Kullback
distance between the parameter vector θu and the specific θF is considerably lower
(2 orders of magnitude at times) than the differences corresponding to other faults.
Hence, no ambiguity with respect to the type or the occurrence of faults is possible.
Note that the detection mean time depends on the fault type (abrupt or slowly
B
evolving): Abrupt faults ( F5A and F0.0005
) are detected significantly earlier than slowly
evolving ones ( F10B and F38C ), whose effects build up gradually and are, thus, less
noticeable. Note also that different magnitudes of a given fault type be detected, as
in faults marked with an asterisk in Table 2. This is very promising since all
considered faults of various origins, are detected from the same I/O relationship.
Hence, the automated FDI task is simpler, allowing for surveillance of many
components, through modeling a small number of I/O relationships.
5. Conclusion
In this study, a scheme for the simultaneous automated FDI in aircraft systems has
been presented. It is designed for extracting maximum information from minimal
amounts of available I/O data, while avoiding hardware duplication. The scheme is
based upon the extensive pooled nonlinear modeling (in two stages) of the
relationship from the pilot stick input to the aircraft pitch rate signal. Subsequently,
automated FDI was achieved through the monitoring of the recursively estimated
parameter vectors involved. Validation flights, conducted with aircrafts affected by
both abrupt and slowly evolving faults (of different magnitudes and origins), showed
promising results: All faults were reliably detected and identified onboard from the
(previously mentioned) single I/O relationship, thus greatly simplifying the FDI task.
Acknowledgements
Thanks are due to the IFATS project partners, especially to M. Attar from IAI (Israeli
Aircraft Industries) and G. Peiller from EADS France for their useful comments.
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