=Paper=
{{Paper
|id=Vol-1507/dx15paper18
|storemode=property
|title=A General Process Model: Application to Unanticipated Fault Diagnosis
|pdfUrl=https://ceur-ws.org/Vol-1507/dx15paper18.pdf
|volume=Vol-1507
|dblpUrl=https://dblp.org/rec/conf/safeprocess/WangHZL15
}}
==A General Process Model: Application to Unanticipated Fault Diagnosis==
https://ceur-ws.org/Vol-1507/dx15paper18.pdf
Proceedings of the 26th International Workshop on Principles of Diagnosis
A General Process Model：Application to Unanticipated Fault Diagnosis
Jiongqi WANG1, Zhangming HE2, Haiyin ZHOU3 and Shuxing LI1
1
College of Science, National University of Defense Technology, Changsha, Hunan, P. R. China
email: wjq_gfkd@163.com
2
Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Duisburg, Germany
email: hezhangming2008@sina.com
2
Beijing Institute of Control Engineering, Beijing, P. R. China
email: gfkd_zhy@sina.com
1
College of Science, National University of Defense Technology, Changsha, Hunan, P. R. China
email: lishuxingok@163.com
Abstract (2006) [16] proposed that the UF diagnosis was carried out
by utilizing particle filter for incomplete patterns. As a
The improvement of the detection and diagnosis transmission mechanism of the UF could not be obtained in
capability for the unanticipated fault is a tendency
advance, the UF diagnosis could not be realized based on
in the research and application of fault diagnosis. model inference. George Vachtsevanos etc. (2008) [17]
In this paper, some notions and the basic principles proposed an UF robust detection method, however, the
for the unanticipated fault detection and diagnosis
isolation on the UF could not be realized. Furthermore, Z.
are given. A general process model applied to the M He (2012) [18] proposed a one-class principal compo-
diagnosis for the unanticipated fault is designed, nent analysis (OC-PCA) method, which could only be used
by adopting a three-layer progressive structure,
for processing the system with stable data in a normal pat-
which is comprised of an inherent detection layer, tern, and did not relate to the UF diagnosis at all. The ma-
an unanticipated isolation layer and an unantici- jority of currently published articles involve only UF de-
pated recognition layer. Several key problems in
tection. However, the fault isolation between the UF and the
the general process model are analyzed. The model AF as well as the recognition (i.e. identification) of the UF
and methods proposed in this paper are driven by has not yet been performed.
pure data and they can detect and diagnose the
For actual system, some impacts such as nonlinearity,
unanticipated fault. The approach is evaluated by uncertainty and external interference are inevitable in its
using an example of a satellite’s attitude control actual operation, which will result difficulties in setting up a
system, and excellent results have been obtained.
precise model for the system. Consequently, the application
of the methods for fault detection and diagnosis based on
1 Introduction model inference will be very limited [19-20]. With the
At present, in the research field of fault diagnosis, a great development of sensor technology, the input and output
majority of methods proposed are based on the premise of a data or the system’s status under real-time monitor is easier
perfect fault pattern database. The treatment on the fault to obtain. The data are redundant, real-time and reliable. As
detection and diagnosis are carried out for anticipated fault a result, the fault diagnosis ideology of extracting data
(AF) [1-3]. However, due to the high complexity and un- instead of establishing a system’s model will play a positive
certainty of the technical structure, the process environment role.
and the working state of the system etc, the occurrence of This paper proposes a data-driven fault diagnosis method
some faults which cannot be anticipated in advance (Un- for UF. Combined with the fault diagnosis process, a gen-
anticipated Fault, UF) is inevitable in actual work [4]. The eral process model (GPM) is advanced, which is comprised
UF is not included in the anticipated fault database, and the of an inherent detection layer (IDL), an unanticipated iso-
occurrence of the UF affects normal operation of the system lation layer (UIL) and an unanticipated recognition layer
and even possibly leads to thorough failure of the system. (URL). Firstly, according to different characteristics of the
The improvement of unanticipated fault detection and monitoring data, the corresponding residual statistics are
diagnosis (UFDD) capability is a difficult issue, as well as a built and a detection criterion of the IDL is provided for
developing direction in the research and application for the fault detection. Secondly, the statistic of angle similarity is
fault diagnosis [5-8]. constructed on the basis of the fault feature direction, the
In retrospect to the existing researches, rather little at- isolation between the UF and the AF is realized in the UIL.
tention has been paid to research UF detection and diagno- Finally, in the URL, by the adoption of the contribution
sis. Therefore, no mature solve scheme has been shaped for factor, the UF is recognized. The method, as a fault diag-
either the problem itself or the technical realization [9-12]. nosis method driven by pure data, is capable of carrying out
Most research on the UF focus on the recognition and the detection, isolation and recognition for the UF.
match between different patterns based on the known fault The paper is organized as follows. In Section 2, some
pattern database [13-14]. For example, Tom Brotherton and notions and the basic principles for UF and UFDD are
Tom Johnson (2001) [15] proposed a neural network discussed. A three-layer GPM for UFDD is introduced in
anomaly detector, which was essentially a single neural Section 3. Sections 4 analyzes some key problems in the
network classifier and could not identify the UF. Z. H. Duan GPM and advances the corresponding solutions. In Section
137
Proceedings of the 26th International Workshop on Principles of Diagnosis
5, performance evaluation of the proposed GPM and cess model (GPM) for UF diagnosis on the basis of pure
methods for the satellite’s attitude control system is pre- data-driven method. The structure of GPM is shown in
sented. Conclusions are drawn in Section 6. Figure 1. The first layer is the IDL, which establishes a
detection discriminator for fault detection; the second layer
2 Notions and Basic Principles for UFDD is the UIL, which applies the detection residual to establish
a fault feature direction so as to build an isolation discrim-
inator to realize the isolation of the AF and the UF; the third
2.1 Notion of UF layer is the URL, which applies a contribution factor to
The fault can be divided into the anticipated fault (AF) and analyze the variant which is most relevant to the current UF
the unanticipated fault (UF). and to realize the fault recognition based on superficial data
Explanation 1: Anticipated fault (AF) is the fault which characteristics.
has been recognized by people, existing in the fault pattern
database with the relevant monitoring data and the pro-
cessing strategy.
Explanation 2: Unanticipated fault (UF) is the fault
which lacks prior knowledge without any fault samples or
with few fault data. UF does not exist in the fault pattern
database, and the corresponding elimination strategy for it
has not been detected.
A perfect fault pattern database should be a set including
all AF patterns and UF patterns. However, due to some
objective reasons, the acquisition of the perfect fault pattern
database is extremely difficult. The AF rarely occurs, and
most of faults occurs in the actual working process are UF
[21]. At present, to detect the UF and moreover to diagnose
the UF is one of the most difficult issues in fault diagnosis
region, and it is also a great challenge for fault diagnosis
technology.
2.2 Notion for UF Detection
Explanation 3: UF detection is a process for judging
whether UF occurs.
The tasks of UF detection and AF detection are different.
The two methods apply previous normal monitoring data to
train a discriminator, and then the current monitoring data is
used as the testing data to be input into the discriminator to
judge whether the current status is a fault. However, the UF
detection is carried out after the completion of fault detec-
tion, and the fault is further judged whether to be UF. Ob-
viously, for AF detection, all faults are always assumed to
be anticipated. Consequently, if the UF occurs, it will be Figure 1 The GPM for UFDD
misjudged as a certain anticipated fault.
3.1 Inherent Detection Layer (IDL)
2.3 Notion for UF Diagnosis The first issue that a diagnosis system faces is to carry out
Explanation 4: UF diagnosis is a process of determining normal/abnormal recognition for a feature vector of the
whether the UF occur (i.e. UF detection). In addition, the monitoring data. The task of the IDL is to determine
UF diagnosis further includes the isolation and the recog- whether the monitoring data is normal or abnormal. The
nition of the UF after the UF detection is completed. detection discriminator can be used for reflecting the
Compared with the AF diagnosis, due to lack of prior characteristics of the normal system. In a given threshold,
knowledge of the UF, the mapping relationship from fault the testing data is inputted to the detection discriminator for
data to fault part (essentially, the fault pattern is a function judging whether the fault exists. If a value of the discrimi-
between fault data and fault part) cannot be found. There- nator is smaller than the given threshold, the system is
fore, the key for UF diagnosis is to quickly establish a thought to be normal; otherwise, a fault is thought to occur.
cognition process. The cognition comprises the recognition Meanwhile the occurrence time (Fault time) and the feature
of superficial data characteristics or the mapping recogni- direction of the fault (Current fault direction) should be
tion from data to a physical layer. Based on a fault diagnosis determined, and the testing data is presented to the UIL.
method driven by pure data, this paper focuses on the Essentially, the IDL is a single discriminator, which can
recognition of superficial data characteristics. be applied to catch the characteristics of the system in a
normal pattern as well as to complete the detection and
3 General Process Model (GPM) for UFDD discrimination of the testing data. Two key problems are
involved, the first is the residual generation and the second
By combining the notion and basic principles of the UF and is the residual evaluation. The specific techniques can be
the UFDD, this paper proposes a multi-layer general pro- seen in Section 4.1.
138
Proceedings of the 26th International Workshop on Principles of Diagnosis
3.2 Unanticipated Isolation Layer (UIL) is suitable for the system capable of obtaining the baseline
The task of the UIL is to finish the isolation between the UF data, its calculation amount is small, the detection speed is
fast, and the detection effect is the best [23]. The time-series
and AF. After detected, the current fault shall be judged
whether to be the AF or the UF. If it is, the current fault will modeling prediction is suitable for the system with con-
be classified as some sort of AF. All AF patterns are saved tinuous output and without input; it is also suitable for it-
eration update of the pattern, while the defect is that the
in the pattern database of AF. The isolation discriminator
matches the feature of the current fault pattern with all those prediction time is short [25].
of the AF patterns successively, so as to realize the isolation In practical application, the characteristics of the moni-
toring system and the monitoring data can be applied to
between the UF and AF. If the feature of the current fault
cannot be matched with any AF pattern, it indicates that the select the corresponding detection method.
UF occurs. The testing data is presented to the URL. The Besides, for the three methods analyzed above, only the
characteristics of data output are considered. However, for
key problem of the UIL lies in the establishment of an iso-
lator and the design of an isolation criterion. The specific some systems (such as the satellite’s attitude control sys-
techniques can be seen in Section 4.2. tem), the object of the fault detection always comprises
control input as well as measuring output, and the control
3.3 Unanticipated Recognition Layer (URL) input has a certain responding relationship with the meas-
uring output. In the situation where there is no baseline
The task of the URL is to perform online learning and training data, an input-output system identification method
analysis for the UF data, so as to generate the fault pattern. is needed to search a model structure for the system, and
The function of the URL is to learn and summarize the thus the fault detection both on control input and measuring
pattern found in unknown pattern. As it is different from the output will be performed in the IDL.
AF, it is difficult to find the mapping relationship from the If we assume that (U n −1 ,Yn −1 ) ∈ ( R ( n −1)× p , R ( n −1)× m ) are re-
fault data to the fault part for the UF. Therefore, the key spectively as system input and system output before the nth
point of recognition lies in establishing the corresponding time period, take them as the training data and make
relationship between the data and the unknown fault. Due to
insufficient recognition on the UF and lack of historical
( un , yn ) ∈ ( R1× p , R1×m ) as the current testing data. The train
purpose is to find the model structure of the system, usually
information and prior knowledge, it is usually more difficult with the rule as follows
to establish the mapping relationship on the physical layer.
The key point of this paper is to analyze the UF recognition min Yn −1 − f (U n −1 ) (1)
f
based on the superficial data layer. According to contribu-
tion factor, the variant which is mostly relevant to the cur- Let Yˆn −1 = f (U n −1 ) is the tendency term,
rent UF can be found, so that the UF recognition is finished.
Yn −1 = Yn −1 − Yˆn −1 = Yn −1 − f (U n −1 ) is the residual term;
The specific techniques can be seen in Section 4.3.
yˆ n = f ( un , U n −1 , Yn −1 )
T
is one-step prediction, and
4 Some Key Problems in GPM
rn = yn − yˆ n is the prediction residual, then the key point
In the above section, a basic framework of the UF diagnosis
for the minimum problem in (1) is to construct the function
is provided. The task of the UF diagnosis is to detect, isolate
f between the system input and system output.
and recognize the UF. The detection is a starting point of
fault diagnosis, and the target of the fault detection is to If a mathematical model can be obtained for the system
equation by the physical mechanism, the estimation of f can
judge whether the UF occurs; the isolation is the core of
be converted into the parameter estimation (Gray-Box
fault diagnosis; and the recognition is a terminal point of
fault diagnosis. Additionally, the recognition is also the Model); and if there is no physical background, f can be
estimated only according to the experiment and the system
starting point of fault-tolerant control (fault processing).
identification (Black-Box Model). Common linear black
The specific techniques on detecting, isolating and recog-
nizing the UF can be seen below. box models comprise an autoregression model (AR Model)
with external input, an autoregressive moving average
4.1 Detection Statistic Construction model (ARMA Model) with external input, an output error
model (OE Model), a Box-Jenkins model (BJ Model) and a
Just as Section 3 shows, the basic task of the IDL is to judge prediction error minimized model (PEM Model); and
whether the testing data is normal. If it is a fault, simulta- common nonlinear black box models comprise a nonlinear
neously the occurrence time and the feature direction of the autoregression moving average model (NLARMA Model)
fault shall be determined. The key point of the IDL lies in and a nonlinear Hammerstein-Wiener model (NLHW
the detection residual generation as well as the residual Model) [26-29] with external input.
evaluation. The detection statistic is established according After obtaining the prediction residual, the detection sta-
to the residual, and the fault detection is performed ac- tistics are as below:
cording to the given criterion. For different monitoring data,
( ) r
-1
different residual generation approaches exist, including T 2 ( yn ) = rnT cov Y n (2)
simple T2 detection [18, 22], baseline data smoothing de-
tection [23], and time-series modeling and predicting de- where cov (Y ) is the covariance of the residual term Y , and
tection [24-25]. a judging threshold is set to be
The characteristics of the monitoring system and moni- m ( n )( n − 2 )
toring data can be applied to select the corresponding de- Tα2 = F ( m, n − 1 − m ) (3)
( n − 1) ( n − 1 - m ) (1−α )
tection method. The simple T2 statistic detection is applied
to a stable data [22]. The baseline data smoothing detection
139
Proceedings of the 26th International Workshop on Principles of Diagnosis
where F(1−α ) ( m, n − 1 − m ) indicates a quantile of F distri- current directions from the same pattern. ξ 2 is another true
bution function when a significance level is α , the degree direction, corresponding to another fault pattern. The origin
of freedom is ( m, n − 1 − m ) . of the coordinates can be regarded as the true direction for
If T 2 ( yn ) > Tα2 , yn−1 is considered as the fault point. the normal pattern.
However, a false alarm is inevitable because of noise, thus
we need a more reliable criterion for detection as follows.
Criterion 1: If T 2 ( yn ) > Tα2 holds continuously for W
times, then the fault has really happened, where W is ξ2
ξ1
called time threshold. The W-th alarm time is considered as
the fault time (tf) (i.e. the occurrence time of the fault) and
the residual r of the fault time is called the current fault
direction or current direction (i.e. the feature direction of
the fault).
The detection statistic threshold is decided by Equation ξ1
(3). The time threshold should not be too large (usually 2 to ξ2
4) to avoid any false alarms. A larger time threshold makes
a more reliable decision, but it will cause some detection
delay which will cause harm to the system. Current fault Figure 2 True detections and current directions
direction is the key information of each fault, and it is the
base for the isolation fault. According to Criterion 1, the Denote θ ( r , ξ ) is the angle between the current direction
current fault is detectable if and only if and the true direction, Ddisc ( r , ξ ) = 1 − cos (θ ( r , ξ ) ) is
called the directional discrepancy between them. We can
( )
−1
| rn ||> Tα2 rn T cov(Y ) −1 rn (4) find that if they are from the same pattern, Ddisc ( r , ξ ) will
be small, otherwise, it will be large.
In the IDL, the fault detection is realized by the adoption Suppose that ε ∼ N ( 0, Ω ) , the current direction is
of the input-output system identification method. Moreover,
r = ε + r ξ , and {ξ i }i =1 is all anticipated true directions, and
q
the occurrence time and feature direction of the fault can
also be obtained. {
ξ i0 = arg min 1 − cos ( r , ξi ) }
q
, then the isolation statistic is
i =1
Obviously, the input-output system identification method ξ
is provided with all the advantages of the time-series mod- given as follows
eling prediction method. It is particularly suitable for the
Iso( r ) =
( (
r 1 − cos r , ξ i0 )) (7)
system with discontinuous input and discontinuous output T
ξ Ωξ i0
at the same time, its defect is that the calculation amount is i0
large, and the iteration process is relatively difficult. Theorem 1: If Iso(r ) is defined in Equation (7), then
Iso(r ) ∼ N ( 0,1) (8)
4.2 Directional Similarity and Isolation Criterion
The basic task of the UIL is to utilize the feature direction of Proof: Suppose that the current direction is r = ε + r ξ ,
the fault obtained in the IDL to establish the isolation dis- where ξ is the true direction and ε is the observation
criminator, and then to realize the isolation between the AF noise, and ε ∼ N ( 0, Ω ) . According to Explanation 5 we
and the UF. The key point lies in the isolator establishment. have ξ = 1 . If cos(r , ξ ) ≥ 0 , we can approximately obtain
Here the concept of direction similarity is induced, and a that
fault isolation criterion is given. In Criterion 1, the defini-
tion of current fault direction or current direction (i.e. the
cos(r , ξ ) =
ξ Tr
ξ r
=
ξ Tε
r
−2
+ 1 ∼ N 1, r ξ T Ωξ ( ) (9)
feature direction of a fault) is given. We adopt the true fault i.e. cos(r , ξ ) satisfies truncated normal distribution.
feature direction as defined below to be the fault’s pattern
characteristics on superficial data layer. Thus
Explanation 5: True (fault) direction of a fault pattern is ( ) (
r 1 − cos(ξ i0 , r ) ∼ N 0 ,ξ iT0 Ωξ i0 ) (10)
defined as the unified mean of all possible current fault
directions from the same pattern. Similarly, if cos(r , ξ ) < 0 , we can prove that
The relationship between the current directions and the r (1 + cos(ξ , r ) ) ∼ N ( 0 ,ξ T Ωξ ) (11)
true direction is just like that between discrete random
variable and its expectation. It is easy to understand that According to Equation (10) and Equation (11), we obtain
1 1
r (1 − cos(ξ , r ) ) ∼ N ( 0,ξ T Ωξ )
n n
ξ = lim
n →∞
∑ ri / n ∑
n i =1 i =1
ri (5) (12)
2
r = r ξ +ε (6) Then
where {ri }i =1 are all possible current directions from the
n
Iso( r ) =
(
r 1 − cos r , ξ i0 ( ))
∼ N ( 0,1) (13)
same pattern, and ε is the noise and r is the magnitude T
ξ Ωξ i0
i0
of the current direction.
It is shown in Figure 2 that there are two opposite true and thus the theorem is proved. Therefore, the threshold for
directions for each fault pattern, e.g. the true direction , ξ1 , Iso(r ) is Φ (1−α ) , where α is the significance level, and Φ
is in the center of a symmetric cone, around which are the is the inverse of the normal cumulative distribution function.
We provide the isolation criterion as follows.
140
Proceedings of the 26th International Workshop on Principles of Diagnosis
Criterion 2: If Iso(r ) > Φ1−α holds true, the current fault The monitoring data comprises of not only the output
is unanticipated; otherwise, it is anticipated. data of the measuring mechanism, but also the control input
Criterion 2 indicates that UF with too small a magnitude of the execution mechanism. The dimension of the data
cannot be isolated. If the current fault is unanticipated, a output by the measuring mechanism is m = 7 , The dimen-
new fault pattern is found and the unified current direction sion of the data input by the execution mechanism is p = 4 ,
is regarded as its true direction. If the current fault is an- which can be seen in Table 1. There are altogether 10
ticipated, then the current direction should be added to the batches of monitoring data, which can be seen in Table 2.
corresponding AF direction database in UIL of the GPM, The first batch is the normal data, and the normal pattern
and the true direction shall be updated. data is discontinuous and unstable (Figure 3). The subse-
quent 9 batches are used for testing, and different fault
4.3 Calculation for Contribution Factor patterns (a sudden-change fault, a gradual-change fault and
The basic task of the URL is to carry out online learning and so on) are given. In Figure 3, the comparison of the moni-
analysis for UF data. The key point of recognition or iden- toring data in the fault with drift-increasing of gyro at roll
tification is to establish the corresponding relationship from axis and the normal pattern is given. The time of each batch
the monitoring data to the unknown fault or the character- of data is 45000s-48000s; each piece data is collected per
istics of the unknown fault. The UF diagnosis discussed in second, and the data length n = 3000 .
this paper is an approach driven by pure data, thus the Additionally, the public parameters used in the simulation
characteristic recognition on the data layer is more focused. are assigned as follows: The significance level α = 0.01
According to the contribution factor, the variant which is and the time threshold defined in Criterion 1 is W=3.
most relevant to the current UF can be found, and then the Table 1 Data explain of attitude control system
UF recognition is completed.
Known from Criterion 1 that after the residual detection Variable
Code Sensor
statistic is established, if T 2 ( yn ) > Tα2 , it is thought that a subscript
1 Wheel1 Output of the first momentum wheel
fault occurs at time period n-1. For the system with the
2 Wheel2 Output of the second momentum wheel
control input and measure output, firstly a residual covari- Input
3 Wheel3 Output of the third momentum wheel
ance matrix R (i.e. cov(Y ) in Equation (2)) is subjected to 4 Wheel4 Output of the fourth momentum wheel
the singular value decomposition, which is 1 Output EarthPhi Output of earth sensor at roll axis
R = P T diag ( λ) P (14) 2 EarthTheta Output of earth sensor at pitch axis
where λ = ( λ1 , … , λm ) , P = ( p1 , … , pm ) , pi indicates the 3 SunPhi Output of sun sensor at roll axis
4 SunTheta Output of sun sensor at pitch axis
ith column of P , and p ji indicates the jth component of
pi . Let ti = r T pi , and rj indicates the jth component of 5 GeoPhi Output of gyro at roll axis
the current fault feature direction r, where 1 ≤ j ≤ m . 6 GeoTheta Output of gyro at pitch axis
Explanation 6: The contribution factor of the jth variant 7 GeoPsi Output of gyro at yaw axis
to the current fault feature direction r is Table 2 Batch number of monitoring data
Cont ( j ) = ∑ ( ti rj p ji / λi )
m
(15) Batch Fault
i =1 Data description
number time
From the aspect of characteristic recognition in the data 1 Normal data Null
layer, the variant with the largest contribution factor is the 2 Sudden-change fault data of earth sensor at roll axis 46000s
fault variant. If it is a sensor fault, the sensor corresponding 3 Gradual-change fault data of earth sensor at roll axis 46000s
to the variant with the largest contribution factor is the 4 Sudden-change fault data of earth sensor at pitch axis 46000s
sensor hardware with the fault. 5 Gradual-change fault data of earth sensor at pitch axis 46000s
6 Loss fault data of sun sensor at roll axis 46000s
5 Simulation and Performance Evaluation 7 Loss fault data of sun sensor at pitch axis 46000s
8 Drift-increasing fault data of gyro at roll axis 46000s
The effectiveness of the proposed GPM and the corre- 9 Drift-increasing fault data of gyro at pitch axis 46000s
sponding UF fault detection, isolation and recognition 10 Drift-increasing fault data of gyro at yaw axis 46000s
method are demonstrated in this section through a satellite’s
attitude control system model. 5.2 Performance Evaluation
5.1 Input and Output of Satellite Control System The monitoring data are relatively more complex, com-
prising of the output data of the measuring mechanism and
The satellite’s attitude control system is a main part of a the control input of the execution mechanism (seen in Table
satellite, which consists of four main parts: a satellite body, 1). The normal pattern data is discontinuous and unstable
a controller, an execution mechanism and a measuring (seen in Figure 3), and the fault pattern is diversified (with
mechanism [30]. sudden-change fault, gradual-change fault and so on).
As the complexity of the satellite’s attitude control sys- Therefore, the normal pattern data is difficult to be dis-
tem, faults particularly for the measuring mechanism and criminated from the fault pattern data (seen from Figure 3).
the execution mechanism occur rather frequently. With the input-output system identification method, the
Here on consideration of the monitoring data for the sat- Hammerstein-Wiener model (NLHW) is adopted. Equation
ellite’s attitude control system. The monitoring data are (1) is optimized, and the responding function f between the
provided by China Aerospace Science and Technology input and output is estimated. Similarly, for the same data
Corporation (CASA). (Drift-increasing fault data of gyro at roll axis (the batch
number is 8) in Table 2), the detection result of the IDL is
141
Proceedings of the 26th International Workshop on Principles of Diagnosis
given in Figure 4, which can be seen that the fault detection tion is delayed caused by the time threshold, W = 3 .
is timely, the detection effect is remarkable, and 4s detec-
-3
x 10
-0.6 1.4 100 100 10
-0.8 1.2 50 50
5
-1 1 0 0
0
-1.2 0.8 -50 -50
-1.4 -100 -100 -5
4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8
es-x 4 es-y 4 ss-x 4 ss-y 4 w-x 4
x 10 x 10 x 10 x 10 x 10
-0.054 0.01 0.15 0.15 0.1
0.005 0.1 0.1 0.05
-0.056
0 0.05 0.05 0
-0.058
-0.005 0 0 -0.05
-0.06 -0.01 -0.05 -0.05 -0.1
4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8
w-y 4 w-z 4 T-wheel-1 4 T-wheel-2 4 T-wheel-3 4
x 10 x 10 x 10 x 10 x 10
0.04 0.3 0.05 0.4
0.2 0 0.2
0.02
0.1 -0.05 0
0
0 -0.1 -0.2
-0.02 -0.1 -0.15 -0.4
4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8 4.5 4.6 4.7 4.8
T-wheel-4 4 x-esti-attitude 4 y-esti-attitude 4 z-esti-attitude 4
x 10 x 10 x 10 x 10
Figure 3 Drift-increasing fault of gyro at roll axis (Blue line shows the output in the normal pattern while green line shows the output in the
fault patter
By adopting the input-output system identification method, ture direction and the direction similarity is valid, and the
the detection results in the IDL for the data in Table 2 are isolation between the UF and the AF can be truly realized.
shown in Table 3. The fault detection is timely, and the
detection effect is more obvious (both of the FAP (false
alarm probability) and the MAP (missing alarm probability)
are much lower).
In the IDL, the fault detection can be realized, and the t f2 : 1004
ln(T2 ): 5.483
fault time and the current fault direction are also determined.
In the UIL, Criterion 2 is adopted to realize the isolation
between the UF and the AF. In the initial stage, the AF
pattern is assumed to be empty, therefore, when the second
batch of data in Table 2 is filled into the UIL, the detected
fault must be the UF, and then the isolation result is trans-
ferred into the URL. When the third batch of data in Table 2
is filled into the IDL, the fault time is that t = 1001s , the
statistic of the directional similarity is
r (1− cos(r,ξ1 ) ) / ξ1T Rξ1 = 7.3179 , and the isolation threshold
of the UF is also Φ 0.99 = 2.3263 . Obviously
r (1− cos(r,ξ1 ) ) / ξ1T Rξ1 > Φ0.99 , the current fault pattern is
different from the first fault pattern, and an UF occurs. Then Figure 4 The detection result (with input-output system
the UF is transferred into the URL. The fault isolation result identification method) for drift-increasing fault data of gyro at roll
for all the tested data in Table 2 can be seen in Table 4. axis
From Table 4, we know that the isolator with the fault fea-
Table 3 Unanticipated fault diagnosis—IDL
Inherent Detection Layer (IDL)
Batch Normal FAP MAP Fault
Current fault direction
number or Fault (%) (%) time (s)
1 N 5 0 0 0 0 0 0 0
2 F 3 2 1000+2 0.9876 -0.0042 0.041 -0.053 0.0453 -0.1342 0.0678
3 F 4 1 1000+1 -0.9997 0.0005 -0.034 0.049 0.0049 -0.0036 0.0222
4 F 5 1 1000+2 -0.1510 -0.9747 -0.0097 0.0105 0.0442 -0.1550 0.0345
5 F 4 1 1000+2 -0.0018 1.0000 0.0007 0.0006 -0.0009 -0.0022 -0.0077
6 F 5 1 1000+2 0.0086 -0.0093 -0.9752 0.0046 -0.0007 0.0003 0.0008
7 F 3 2 1000+3 -0.0067 0.0052 0.0016 -0.9925 -0.1553 0.0028 -0.0016
8 F 5 1 1000+4 -0.0769 0.0051 0.0037 0.0018 0.9682 -0.0139 -0.0549
9 F 3 1 1000+2 -0.0742 0.0215 -0.0029 0.0016 0.0454 -0.9968 0.0447
10 F 3 1 1000+2 0.0627 -0.0201 -0.0079 0.0086 -0.0476 -0.0441 -0.9849
142
Proceedings of the 26th International Workshop on Principles of Diagnosis
Table 4 Unanticipated fault diagnosis—UIL
Unanticipated Isolation Layer (UIL)
Batch Anticipated or Fault Pattern
Updated true fault direction
number Unanticipated code
1 Null 0 0 0 0 0 0 0 0
2 U 1 1 -0.0043 0.0415 -0.0537 0.0459 -0.1359 0.0687
3 U 2 -1 0 -0.0340 0.049 0 0 0.0223
4 U 3 -0.1549 -1 -0.01 0.0108 0.0453 -0.1590 0.0354
5 U 4 -0.0018 1 0 0 0 -0.0022 -0.0077
6 U 5 0.0088 -0.0095 -1 0.0047 0 0 0
7 U 6 -0.0068 0.0052 0.0016 -1 -0.1565 0.0028 -0.0016
8 U 7 -0.0794 0.0053 0.0038 0.0019 1 -0.0144 -0.0567
9 U 8 -0.0744 0.0216 0.0029 0.0016 0.0455 -1 0.0447
10 U 9 0.0637 -0.0204 -0.0080 0..0087 -0.0483 -0.0448 -1
In the IDL, the fault detection can be realized, and the
fault time and the current fault direction are also determined. 6 Conclusion
In the UIL, Criterion 2 is adopted to realize the isolation The paper firstly takes the UF as a main diagnosis object.
between the UF and the AF. In the initial stage, the AF The detection and diagnosis method based on data driven
pattern is assumed to be empty, therefore, when the second for the UFs has been researched. The GPM for the UF di-
batch of data in Table 2 is filled into the UIL, the detected agnosis has been designed. The GPM is comprised of the
fault must be the UF, and then the isolation result is trans- IDL, the UIL and the URL. This GPM has provided a
ferred into the URL. When the third batch of data in Table 2 framework support for the UF diagnosis. According to the
is filled into the IDL, the fault time is that t = 1001s , the system both with the control input and the measure output,
statistic of the directional similarity is the system identification detection method corresponding to
r (1− cos(r,ξ1 ) ) / ξ1T Rξ1 = 7.3179 , and the isolation threshold the IDL has been provided. The current fault feature direc-
of the UF is also Φ 0.99 = 2.3263 . Obviously tion and the feature direction of the AF pattern have been
r (1− cos(r,ξ1 ) ) / ξ1T Rξ1 > Φ0.99 , the current fault pattern is used to establish the statistic of directional similarity. The
different from the first fault pattern, and an UF occurs. Then isolation between the AF and the UF has been realized in
the UF is transferred into the URL. The fault isolation result the UIL. According to the singular value decomposition, the
for all the tested data in Table 2 can be seen in Table 4. fault contribution factor of each variance has been obtained,
From Table 4, we know that the isolator with the fault fea- and the fault recognition in data layer has been completed.
ture direction and the direction similarity is valid, and the The application to fault diagnosis of the satellite’s control
isolation between the UF and the AF can be truly realized. system has demonstrated its validity.
After isolating the UF, the recognition of the UF should Our research shall be furthered in two directions. Firstly,
be carried out on the data layer. For the data in Table 2, the based on the framework of the GPM, the fault detection,
recognition result is that: the fault feature direction isolation and recognition method on the foundation of
is ( 0.9876,-0.0042,0.041,-0.053,0.0453, -0.1342, 0.0678 ) . The
T
model inference shall be researched. Secondly, the GPM
variance with the largest contribution factor is the first and methods shall be applied to the diagnosis of other
dimension. According to Explanation 6, the contribution complex system for both military and civil use.
factor reaches 97 percent, and it indicates that the fault
occurs for the earth sensor at the roll axis. Similarly, the Acknowledgments
result of the UF recognition in the URL for other batches of
data is shown in Table 5. From Table 5, the recognition of This work was supported in part by National Natural Sci-
the UF corresponding to the fault variance is correct, and ence Foundation of China (NSFC) under Grant No.
the UF recognition of the data layer is reached. 61304119. Besides, we would like to especially thank
China Aerospace Science and Technology Corporation
Table 5 Unanticipated fault diagnosis—URL
(CASA) for providing the satellite control system data.
Unanticipated Recognition Layer
Batch
Anticipated Fault
Variable subscript
References
or pattern
number
Unanticipated code
in Table 3 [1] P. Nomikos, J. F. Macgregor. Monitoring of batch processes
using multiday principal component analysis. AIChE J, 1994,
1 Null 0 0
40(8): 1361-1375.
2 U 1 1
3 U 2 1 [2] R. Isermann. Supervision, Fault detection and fault diagnosis
4 U 3 2 methods-an introduction. Journal of Control Engineering
5 U 4 2 Practice, 1997, 5(5): 639-652.
6 U 5 3 [3] D. M. J. Tax. One-class classification. Ph.D., Delft University
7 U 6 4 of Technology, Holland, 2001.
8 U 7 5 [4] S. Gayaka1, B. Yao. Accommodation of unknown actuator
9 U 8 6 faults using output feedback-based adaptive robust control.
10 U 9 7 International Journal of Adaptive Control and Signal Pro-
cessing, 2008, 25(11): 965-982.
143
Proceedings of the 26th International Workshop on Principles of Diagnosis
[5] P. Smyth. Markov monitoring with unknown States. IEEE detection of unanticipated faults. International Conference on
Journal on Selected Areas in ConununiCationS, 1994, Prognostics and Health Management, 6-9, Oct, Denver, CO,
12(9):1600-1610. 2008: 1-8.
[6] Hofbaur, B.C. Williams. Hybrid diagnosis with unknown [18] Z. M He, H. Y. Zhou, J. Q. Wang. Model for Unanticipated
behavioral modes. Proceedings of the 13th International Fault Detection by OCPCA. Advanced Materials Research,
Workshop on Principles of Diagnosis (DX02), May, 2002. Vols. 591-593, 2012: 2108-2113.
[7] V.J. Hodge, J. Austin. A survey of outlier detection method- [19] J. Chen, R.J. Patton. Robust model-based fault diagnosis for
ologies. Artificial intelligence review. Kluwer Academic Pub- dynamic systems. Boston: Kluwer Academic Publishers, 1999.
lishers, Vol. 22, 2004, 85-124. [20] B. Zhang, S. Chris, B. Carl. A probabilistic fault detection
[8] Patcha, J. M Park. An overview of anomaly detection tech- approach: application to bearing fault detection. IEEE Trans-
niques: existing solutions and latest technology trends. Com- actions on Industrial Electronics, 2010, 58(5): 2011-2018.
puter Networks, 2007, 51: 3448-3470. [21] Pierre Sens. An unreliable failure detector for unknown and
[9] K. Kojima, K. Ito. Autonomous learning of novel patterns by mobile networks. OPODIS 2008, LNCS 5401, 2008, 555–559.
utilizing chaotic dynamics. IEEE International Conference on [22] Anna M. Bartkowiak. Anomaly, novelty, one-class classifi-
Systems, Man, and Cybernetics, IEEE SMC '99, 1999, cation: a short introduction. Computer Information Systems
1:284-289. and Industrial Management Applications (CISIM), 2010 In-
[10] Petra Perner. Concepts for Novelty Detection and Handling ternational Conference, Wrocław, Poland, 8-10, Oct, 2010,
Based on a Case-Based Reasoning Process Scheme. Spring- 1-6.
er-Verlag Berlin Heidelberg, 2007. [23] F. N. Zhou. Extended DCA method for unknown multiple
[11] Satnam Singh, Haiying Tu, William Donat. Anomaly detec- faults diagnosis. Huazhong Univ. of Sci. & Tech. (Natural
tion via feature-aided tracking and Hidden Markov Models. Science Edition), 2009, 37(4): 84-94 [in Chinese].
IEEE Transactions on Systems, Man, and Cybernetics, Part A: [24] N. Gebraeel, J. Pan. Prognostic degradation models for
Systems and Humans, 2009, 39(1): 144-159. computing and updating residual life distributions in a
[12] Ching-Fang Lin. Predictive fault diagnosis system for intel- time-varying environment. IEEE Trans. Rel., 2008, 57(4):
ligent and robust health monitoring. AIAA In- 539–550.
fotech@Aerospace, 20-22, April, 2010, Atlanta, Georgia. [25] Wang Z M, Yi D Y, Duan X J. Measurement data modeling
[13] E. Sobhani-Tehrani, H. A. Talebi, K. Khorasani1. Neural and parameter estimation. CRC Press, 2011.
parameter estimators for hybrid fault diagnosis and estimation [26] Adrian Wills, Brett Ninness. On gradient-based search for
in nonlinear systems. IEEE International Conference on Sys- multivariable system estimates. IEEE Trans. Automat. Control,
tems, Man and Cybernetics, Montreal, 7-10, Oct, 2007, 2008, 53(1): 298–306.
3171-3176.
[27] E. Wernholt, S. Moberg. Nonlinear gray-box identification
[14] Amitabh Barua. Hierarchical fault diagnosis and health using local models applied to industrial robots. Automatica,
monitoring in satellites formation flight. IEEE Transactions on 2011, 4(47): 650-660.
Systems, Man and Cybernetics-Part C: Applications and Re-
views, 2011, 41(2): 223-239. [28] Lennart Ljung. System identification: Theory for the User.
Linkoping University, Sweden Published, 1998.
[15] B. Tom and J. Tom: Anomaly detection for advanced military
aircraft using neural networks. Aerospace Conference, IEEE [29] Goethals, K. Pelckmans, J. A. K. Suykens, B. De Moor.
Proceedings, 2001, 6: 3113-3134. Sup-space identification of Hammerstein systems using least
squares support vector machines. IEEE Transactions on Au-
[16] Z. H. Duan: Theoretic and methodological research on fault tomatic Control, 2005, 50(10): 1509-1519.
diagnosis of mobile robots based on adaptive particle filters.
Ph.D., Central South University, 2007, 63-89. [in Chinese]. [30] Tu S C. Satellite attitude dynamics and control. Beijing:
Chinese Astronautic Publishing House, 2003; 125-168 [in
[17] B. Zhang, Chris Sconyers, Carl Byington, Romano Patrick, Chinese].
Marcos Orchard. Anomaly detection: A robust approach to
144