Sequential Probability Ratio Test Based Fault Detection Method for
Actuators in GNC System
LI Dan, ZHANG Miao
1
, LAI Zhenzhou, SHEN Yi
Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001
1. E-mail: zm1840@hit.edu.cn
Abstract: This paper proposes a fault diagnosis method of satellite actuator based on parameters sequential probability ratio test.
Sequential probability ratio test is a hypothesis test based on statistical learning, whose greatest advantages is that it does not need
to prescribed the number of observed sample group, but compare each hypothesis test data to the set threshold value. Firstly, give
the hypothesis testing and drawn threshold based on the given false alarm rate and missed alarm rate. Secondly, extract the
characteristic parameters of the signal to be inspected, Finally, calculate the likelihood values and compare to threshold value, so
that we can judge whether there is a fault signal. This article made verification experiment based on actuator fault detection of
Autonomous GNC system of deep space probes, as can be seen from the simulation results, sequential probability ratio detection
method can made a real-time detection of the fault signal. Compared with the fault diagnosis method based on state observer, this
method reduces the average inspection time of the fault greatly.
Key Words: GNC system, sequential probability ratio test, actuator, fault detection
1 Introduction
As the continuous development of astronautical
technology, the structure of spacecraft becomes complex
increasingly. However, the complexity brings more
possibility of fault. A chain reaction caused by the failure
of a very small component can cause huge losses for the
whole project. Therefore, the security and reliability are
of great importance for a spacecraft, which can be
improved by making use of the fault detection and
diagnosis technologies.
Fault detection [1] is a very important part of the fault
diagnosis [2]. Once a fault is discovered by the fault
detection, effective measures will be taken to avoid
greater impact for the system, then the diagnosis
subsystem will locate and diagnose the fault. Traditional
fault diagnosis methods need to pre-set the number of
sample group, which need to select a large number of
samples in order to guarantee the accuracy of the
diagnosis. This article proposes a fault diagnosis method
based on parameter sequential probability ratio test.
The sequential probability ratio test [3] is hypothesis
testing based on statistical, raised by Illinois [4] from the
Chicago Argonne National Laboratory. The biggest
advantage of sequential probability ratio test method is
that it does not need to
predetermine the number of
observed sample groups, while each hypothesis test data
is compared with the set threshold. And sequential
probability ratio test method requires fewer samples, and
the smaller dynamic changes can be judged under the
premise of ensuring the strength of test.
Sequential probability ratio test detects subtle changes
of the statistical characteristics of residual signal, and
compared with the
conventional method, it also has a
significant characteristic in the improvement of
*
This work is supported by the National Natural Science Foundation of
China (No. 61273162 and No. 61201310), the Fundamental Research
Funds for the Central Universities (HIT.NSRIF.201160) and China
Postdoctoral Science Foundation (No. 20110491067).
sensitivity and reliability. Even the signals are with
characteristics such as rapid change and harsh fault,
sequential probability ratio test can alarm rapidly acting
as traditional threshold test. because this method
monitors signal all the time. For these signals varying
slowly for a long period of time, sequential probability
ratio test is able to predict the trajectory of the changing
signals before a failure occurs, thus it will be more
conducive for the fault detection. According to the idea of
hypothesis
testing based on the accumulated information,
SPRT method can achieve better results with professional
knowledge and adequate prior information.
2 The principle of sequential probability ratio
detection
Sequential probability ratio test also known as Wald
test is statistical inference method based on sequential
analysis and probability ratio test. This method firstly
gives hypothesis on the overall distribution and
parameters,
then construct sequential probability
likelihood ratio on the basis of the prior knowledge and
the measured sample. Lastly, the sequential probability
likelihood ratio is used as the decision function to
determine the correctness of the assumptions under
certain reliability [5].
Give two hypotheses
for the two states of the system
(normal or fault): state
0
and state
1
. According to the
observations and maximum posteriori criterion, make a
judgment from
0
and
1
:
If
1
0
(/)
1
(/)
PH x
PH x
!
, then decision
1
is established;
If
1
0
(/)
1
(/)
PH x
PH x
, then decision
0
is established.
Transform
the equations above by the multiplication
formula:
3URFHHGLQJVRIWKHQG&KLQHVH&RQWURO&RQIHUHQFH
-XO\;LDQ&KLQD
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