Scholarly article on topic 'Application of Analytic Redundancy-based Fault Diagnosis of Sensors to Onboard Maintenance System'

Application of Analytic Redundancy-based Fault Diagnosis of Sensors to Onboard Maintenance System Academic research paper on "Electrical engineering, electronic engineering, information engineering"

CC BY-NC-ND
0
0
Share paper
Keywords
{"fault detection" / "analytic redundancy" / "sequential probability ratio test (SPRT)" / "onboard maintenance system (OMS)" / "redundancy management" / sensors}

Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — Chengzhi CHI, Weiguo ZHANG, Xiaoxiong LIU

Abstract Analytic redundancy-based fault diagnosis technique (ARFDT) is applied to onboard maintenance system (OMS). The principle of the proposed ARFDT scheme is to design a redundancy configuration using ARFDT to enhance the functions of redundancy management and built in test equipment (BITE) monitor. Redundancy configuration for dual-redundancy and analytic redundancy is proposed, in which, the fault diagnosis includes detection and isolation. In order to keep the balance between rapid diagnosis and binary hypothesis, a filter together with an elapsed time limit is designed for sequential probability ratio test (SPRT) in the process of isolation. Diagnosis results would be submitted to central maintenance computer (CMC) together with BITE information. Moreover, by adopting reconstruction, the designed method not only provides analytic redundancy to help redundancy management, but also compensates the output when both of the sensors of the same type are faulty. Our scheme is applied to an aircraft's sensors in a simulation experiment, and the results show that the proposed filter SPRT (FSPRT) saves at least 50% of isolation time than Wald SPRT (WSPRT). Also, effectiveness, practicability and rapidity of the proposed scheme can be successfully achieved in OMS.

Academic research paper on topic "Application of Analytic Redundancy-based Fault Diagnosis of Sensors to Onboard Maintenance System"

Chinese Journal of Aeronautics 25 (2012) 236-242

ELSEVIER

Contents lists available at ScienceDirect

Chinese Journal of Aeronautics

journal homepage: www.elsevier.com/locate/cja

JOURNAL OF

AERONAUTICS

Application of Analytic Redundancy-based Fault Diagnosis of Sensors to Onboard Maintenance System

CHI Chengzhi, ZHANG Weiguo, LIU Xiaoxiong*

School of Automation, Northwestern Polytechnical University, Xi'an 710072, China Received 28 March 2011; revised 27 May 2011; accepted 23 August 2011

Abstract

Analytic redundancy-based fault diagnosis technique (ARFDT) is applied to onboard maintenance system (OMS). The principle of the proposed ARFDT scheme is to design a redundancy configuration using ARFDT to enhance the functions of redundancy management and built in test equipment (BITE) monitor. Redundancy configuration for dual-redundancy and analytic redundancy is proposed, in which, the fault diagnosis includes detection and isolation. In order to keep the balance between rapid diagnosis and binary hypothesis, a filter together with an elapsed time limit is designed for sequential probability ratio test (SPRT) in the process of isolation. Diagnosis results would be submitted to central maintenance computer (CMC) together with BITE information. Moreover, by adopting reconstruction, the designed method not only provides analytic redundancy to help redundancy management, but also compensates the output when both of the sensors of the same type are faulty. Our scheme is applied to an aircraft's sensors in a simulation experiment, and the results show that the proposed filter SPRT (FSPRT) saves at least 50% of isolation time than Wald SPRT (WSPRT). Also, effectiveness, practicability and rapidity of the proposed scheme can be successfully achieved in OMS.

Keywords: fault detection; analytic redundancy; sequential probability ratio test (SPRT); onboard maintenance system (OMS); redundancy management; sensors

1. Introduction

Fault detection and isolation (FDI) based on analytic redundancy (AR) originated in the early 1970s, which was aimed at solving the problems with hardware redundancy, such as extra cost, maintenance, software, additional space required to place the equipment and additional weight. With continuously research [1-9], FDI has been widely applied to aviation, aerospace and complex industry systems. Among these applications, an onboard failure detection and identification system for dual redundancy with analytic redundancy on the NASA F8C digital fly-by-wire (dFBW) is presented in

^Corresponding author. Tel.: +86-29-88431398. E-mail address: liuxiaoxiong@nwpu.edu.cn Foundation item: Aeronautical Science Foundation of China (20100753009)

1000-9361/$ - see front matter © 2012 Elsevier Ltd. All rights reserved. doi: 10.1016/S1000-9361(11)60383-X

Ref. [4]. Also, AR based FDI technique is involved in detecting failures between similar instruments, as well as between dissimilar instruments [10]. Moreover, a new concept of "equivalent bias" is proposed to model the sensor faults [6]. Both of the states and equivalent bias are online estimated by a pseudo separate-bias estimation algorithm. The estimated equivalent bias is evaluated via a modified Bayes' classification-based algorithm to detect and diagnose sensor faults. In addition, new classification framework for fault diagnosis approaches is proposed. Zhou and Hu [7] divided fault diagnosis approaches into two classes: qualitative analysis approaches and quantitative analysis approaches, with analytic redundancy classified as the latter.

Sequential probability ratio test (SPRT) is a statistical hypothesis test, which is generally more efficient than the fixed-sample size likelihood ratio test for the problem of detecting a constant signal in additive noise, and has drawn the attentions of researchers. SPRT is

applied to diagnosis of faulty sensors for F-8 DFBW [4]. Chien and Adams [11] defined a feedback control law in the process of SPRT to reduce the time delay of Wald SPRT (WSPRT) suffers in detecting a fault, and applied it to the problem of second sensor failure isolation. So they use the information of sensors separately but not all the redundant sensors in detection. In their law, whenever the joint likelihood ratio function state Xk is negative, Xk at any sampling instant k is reset to zero by the control C*(^k); if h > 0, no control is applied. Also, the Shiryayev SPRT (SSPRT) is proposed to detect the occurrence of a failure in the data sequence in minimum time (in contrast to the WSPRT) if certain parameters such as k, Ft and p are given [10], where n is the probability that a failure occurs prior to the beginning of the test, FT the probability that a failure has occurred, and p the probability of failure occurring at any time. However, so many parameter conditions limit its application in some situations. Moreover, SSPRT can be extended to on-line multiple hypotheses SSPRT by adopting a dynamic programming approach, and it can be optimal even in the asymptotic sense and the theoretical results have been extended to the detection and identification of changes with unknown parameters [12]. In addition, the maximized sequential probability ratio test (MaxSPRT) is developed in response to direct vaccine safety surveillance needs, which is based on maximum likelihood principles that generalizes the optimality of SPRT over all possibilities [13], and MaxSPRT models are established for poisson and binomial distribution in drug and vaccine safety surveillance [14].

A standard for aircraft onboard maintenance system (OMS) was proposed in 1993 [15]. OMS provides users with the functions including automatic isolation of faults and failures (by central maintenance computer (CMC)), system integrity judging, onboard maintenance document (OMD), aircraft condition monitor system (ACMS), and event function. The CMC provides users with the ability to perform many kinds of maintenance related task including ground tests, data loading and input monitoring. The ACMS provides the user with the ability to gather and report airplane performance data.

In this paper, analytic redundancy-based fault detection technique is applied to OMS for built in test (BIT) assistant monitor and redundancy management. Section 2 concerns integrated system with analytic redundancy -based fault detection technique. Section 3 addresses analytic redundancy-based fault diagnosis by utilizing all the redundancy information. First, the time delay of detection is corrected, then a filter function is designed for SPRT to achieve rapid fault diagnosis, and an elapsed time limit (ETL) [4] is also used, aimed at keeping the balance between rapid diagnosis and binary hypothesis. In Section 4, a simulation comparison between the proposed filter SPRT (FSPRT), WSPRT and MaxSPRT is carried out by application to an aircraft

model. Section 5 provides some conclusions. 2. Integrated System Description

A redundancy management work with dual redundancy and AR redundancy is addressed to assist in built in test equipment (BITE) monitor for OMS. A simplified diagram is given in Fig. 1 (see Ref. [15], Appendix 1). Rectangle shown in dashed lines provides function of fault diagnosis and redundancy management, which uses AR sensor output and real sensor outputs to diagnose faults, and then monitor results are given.

Fig. 2 shows the redundancy management. First, the detection process uses residuals generated by dual redundancy outputs to detect alarm of fault. After a fault is detected, two isolation processes work with output of hardware redundancy and AR are started. Finally, the results of isolation would be submitted to decision-making, and the rule of which is listed as follows:

1) If either of the detection results is fault, cut off the corresponding sensor.

2) If both of detection results are fault, cut off both of sensors and use the AR output instead of real sensor output, which is called reconstruction.

MAT: Maintenance access terminal; PMAT: Portable maintenance access terminal; APU: Auxiliary power unit; ECS: Environmental control system; HS: Hydraulic system.

Fig. 1 Integrated OMS with AR technique.

Fig. 2 ARFDT based redundancy management for OMS.

3. Analytic Redundancy-based Fault Diagnosis

In this paper, many types of analytic redundancy are available, such as rotational kinematics redundancy,

altitude kinematics redundancy, translational dynamics redundancy, and translational kinematics redundancy [16]. Take rotational kinematics redundancy as an example:

p = (/) -\p sinö q = 0 cos^ + i/> cosösinf; r = i/> cosöcos^-9 sin^

where p, q, r are roll, pitch, and yaw angular rates respectively, and 0, </>, y are pitch angle, yaw angle and roll angle respectively. So hardware redundancy sensor outputs ph, qh, rh together with AR outputs pa, qa, ra, and the residual Rp, Rq, Rr of p, q, r are available.

The following theoretical works are mainly on the basis of Refs. [17]-[18].

3.1. Detection

The residuals for detection are generated by dual redundancy outputs, which in no-failure hypothesis H0 and failure hypothesis Hi are consist of

H0 : R(k) = N(k) Hi : R(k) = f + N(k)

Ho : p[R(k) | Ho] = exp(-R2/2a2)

Hi : p[R(k)|Hi] = -=Uexp[-(R - f )2/2a2]

where u2 « a^ + cr2 is variance of N(k) with mean zero. The variance of N(k) includes variance of sensor noise nm (k) (^m ) and system noise ns (k) ( cr2 ).

Suppose the latest k sample sequences are mutually independent, and the log likelihood ratio of R, = [R(1) R(2) ••• R(k)]Tis defined as

ln l (Rk) = ln n l (R(n)) = E

fR(n) f

4 (¿RC) -t fl" ti

V n=1 n=1

where l1 is double threshold under two-sided test (set false alarm probability Pf equal to missing probability Pm). Usually, we hope to keep a low false alarm probability, meanwhile with a low missing probability. However, when Pf is given, Pm depends on the sample size of detection [18]. Huang, et al. [18] discussed the choice of a sample size which restricts Pm and Pf within a given range by using ^-test method of operating characteristic (OC) function. Then, Eq. (4) is rewritten by

--1 ¿R(«)* I2 ■ li - 7 ±f

The conditional probability mean and corrected variance of Sh are given by

E (Sh|H o) = 0 E (Sh|Hi) = f

var(Sh) = ah2 = a2/k + k^s2

The two-sided test for a given false alarm probability Pf is

Hq: |Sh|< lh H1: |Sh| >lh

where lh (> 0) is test threshold, which is defined as

Pf = 2

I p^^o^h =

(-SL 2 ^

V 2CTh J

where ca is a constant determined by Pf, and

3.2. Isolation

The residual for isolation is generated by a hardware redundancy and analytic redundancy, similar to Eq. (4), we have

Sa =E|R(«) -

f \ * ^

■ l,

The conditional probability mean and corrected variance of Sa are given by

E(Sa | Ho) =-kfl2

E (Sa | H,) = kfl 2 var(Sa) = CT? «k+ k^s2)

According to the Chebyshev's form of the law of large numbers, Sh converges in probability to the real residual of the sensor (normal or fault) [19]. However, for fault diagnosis, k should not be big enough. In order to limit sampling times, a minimum detectable fault signal (MDFS) fmm under a certain noise should be given. Suppose f = |fmin| and a MDFS under one-sided test is fmin/2. Via Eq. (9), there is

C^ = l/ CT = fmj2c

The MDFS fmm for M (ETL) is given by

2ca-&a(M) (13)

f =-J mm

Now, we discuss the calculation of M. Consider the two-sided test [18]

H0: E (Sa) = Sa0 Hi: E (Sa) * Sao where Sa0=-Mfl2. The OC function is given by

E ( Sa)) = PE ( Si)( H 0) = P

Sa - Sao

f 2 Z s Sa ~E (Sa) ^ 3 + Z ^

"Zf2 oj4m Zf2

0(ZPtl2 -1) -0(-Zpf/2 -2) =

0(ZPil2 -A) + 0(Zpi/2 +2)-1

where 2 =

E (Sa) - Sao

oj4u '

As M reaches a certain value, we have 0(ZPf/2 +2) « 1

Then, M satisfies

Zf2 -4MS/aA<-ZPm

where 8 is a constant value set to 8= Mfll. Through Eq. (17), we get Mwhen E(Sa)eH1 and |E(Sa)-Sa0| > ¿is

tenable, which can restrict Pf and Pm in a given range.

Then, we compute fmin within M for SPRT. fmn satisfies

1 - Pm P

m 2 fj__

2o-a2(M) ~ 2(M^ + M2a2)

So Eq. (10) can be rewritten as

Sa =Z Î R(n) - 4

b=1 V 2

Then, threshold la is the failure conditional probability mean at sampling instant M:

la = E[ Sa(M )|H1] = 2 Mfm

When Pf =Pm, there is a dual threshold +la and the test criterion is

I Ho: Sa < -la

! Hj: Sa > la

[go on check: - la <Sa < la

Now, we discuss the filter for SPRT, i.e. FSPRT. Suppose Ta is alarm instant, and Sa for sensor 1 and sensor 2 are Sa1 and Sa2, respectively. In view of detecting delay, suppose the minimum delay is Td , and the failure time should be corrected by Tf =Ta-Td. Then, a filter for Sa between [Tf , Tf +M] is defined.

Suppose Sal and Saa2 are absolute values of Sa1 and Sa2, respectively. Larger Saa is more likely to be

faulty, so "adding" larger one with smaller one, then (sample instant k is removed from the following equation)

Sa1 - Sa1 ± Sa2 '

Sa2 - Sa2 ± ■

Sa1 - Sa1 Sa2 = Sa2

Saa > S^and Sa! > 0

Saa > Saa2 and Sa1 < 0 Saa2 > Saaand Sa2 > 0 Saa2 > Saaand Sa2 < 0

oa _ r*a

Sa1 - Sa2

When k = Tf +M, i.e. the time of isolation comes to M and if -la< Sa(k)< la is tenable, then accept H0. We get the new test criterion

[H0: Sa (k) <-la ,or k = Tf + M and Sa (k) < la

|Hi : Sa(k)>la (23)

[go on check: - la < Sa (k) < la and Tf <k < Tf + M

Compared to traditional SPRT, four characteristics of the proposed method can be found here. First, the time delay of detection is corrected. Second, M is introduced to ensure that the process of isolation would not keep running if the condition for accepting H0 or H1 is not tenable. Third, assuming that a fault has been alarmed and the residual of faulty sensor is larger than normal ones, the isolation time for accepting hypothesis H1 for faulty sensor can be decreased by designing filter for Sa. Meanwhile, because of the existence of M, if in a given time, the condition for H1 is not tenable, then the hypothesis H0 should be accepted. Fourth, redundancy information interaction is used to reinforce the likelihood information of fault sensor.

After detecting a fault in one type of sensors, the isolation processes are started. A failure can be declared if the function Sa of the sensor exceeds a threshold, and then, the monitor result will be submitted to CMC together with BITE information. The process of BITE information and monitor result will not be detailed here.

4. Numerical Example

In this section, an aircraft initially trimmed to horizontal flight at Mach 0.6 and 20 000 ft is simulated with a sensor failure occurring at exactly 10 s and the system is sampled with the sampling interval 0.05. The initial conditions of the states are

[v a p p q r y/ 0 <f> h] = [204 0.046 5 0 0 0 0 0 0.046 5 0 6 096]

where v is airspeed, and h altitude, a, p are angles of attack and sideslip, respectively. The units for the states are mls (v), rad (a, p, 0, <f>), radls (p, q, r) and m (h). The measure noise of 0, <f> is Gaussian-distributed

with zero mean and standard deviation o=1 X 10 the standard deviations of p, q, r are

p = 3.162 3 x10~ q :am = 3.162 3 x10~" r = 3.162 3x 10"4

= 1.454 7 x10" <rs = 1.364 2 x10": <r = 1.3814 x 103

The sample size of detection is set to 5 and the M is 4, according to Eq. (17). The minimum delay Td is set to 1. Moreover, Pf is set equal to Pm, which is 0.05. Then, we have fmin and la for SPRT:

p : fmin=3.5510x 103, la=7.1019x 103

q : f =3.332 6x10~3, la=6.665 2x10~3

■i j mi^i y a

r : f - =3.374 2x10~3, la=6.748 3x10~3

j mill y a

fmin and la for MaxSPRT are given as follows:

p : /min = 1.173 9 x10-q : fmin = 1.1016 x 10-: r : /min = 1.115 4 x10-:

la = 5.869 7 x10" la =5.508 0 x 10"; la =5.576 8x 10~;

Because of the detection, there is an alarm of fault before isolation starts to isolate a fault. So the feedback control law in Ref. [11] has the same effect as WSPRT in isolating a faulty sensor. Table 1 indicates a simulation comparison among the proposed FSPRT, WSPRT and MaxSPRT applications to sensors with different type of failures, where DT is the detection time, WIT, MIT and FIT are the isolation time of WSPRT, MaxSPRT and FSPRT, respectively. Results show that FITs are smaller than WITs and MITs in every group, and FSPRT saves at least 50% (at most 66.7%, bias fault of yaw rate sensor) of isolation time than WSPRT. Moreover, WSPRT or MaxSPRT cannot isolate the failure but FSPRT works in group 8 and 9, especially, both WSPRT and MaxSPRT cannot isolate the failure but FSPRT works in group 3. Furthermore, among all the nine groups, FSPRT can isolate a failure before the M is reached and the rapidity is satisfying.

Table 1 Summary of simulation results

No. Sensor Failure type DT/s WIT/s MIT/s FIT/s

1 Roll rate Stuck, 0.006 rad/s 10.30 10.40 10.65 10.35

2 Roll rate Bias,0.010 rad/s 10.20 10.30 10.30 10.25

3 Roll rate Bias,0.006 rad/s 10.20 — — 10.35

4 Pitch rate Stuck, 0.010 rad/s 10.15 10.25 10.25 10.20

5 Pitch rate Stuck, 0.005 rad/s 10.60 10.70 10.70 10.65

6 Pitch rate Bias,0.007 rad/s 10.90 11.00 11.20 10.95

7 Yaw rate Stuck, 0.010 rad/s 10.15 10.25 10.25 10.20

8 Yaw rate Stuck, 0.005 rad/s 10.30 — 10.40 10.35

9 Yaw rate Bias,0.005 rad/s 11.90 12.05 — 11.95

The output of roll rate sensor with bias fault of 0.01 rad/s is shown in Fig. 3. Also, the outputs of pitch rate sensor with stuck fault of 0.01 rad/s and bias fault of 0.007 rad/s are shown in Fig. 4 and Fig. 5, respectively. Moreover, the output of yaw rate sensor with stuck dead fault of 0.010 rad/s is shown in Fig. 6. In addition, after both redundancies of the sensor are confirmed

Fig. 3 Roll rate sensor bias fault of 0.010 rad/s occurring at 10 s and reconstructed at 10.30 s.

— Normal Failure Reconstruction

Fig. 4 Pitch rate sensor stuck fault of 0.01 rad/s occurring at 10 s and reconstructed at 10.25 s.

Fig. 5 Pitch rate sensor bias fault of 0.007 rad/s occurring at 10 s and reconstructed at 11 s.

faulty, the output of faulty sensors would be reconstructed by the corresponding AR output. The reconstruction of failure is also shown in the figures, and we can see that the AR output can catches up with the output of normal sensor in 2-3 s for most faults.

Then, we discuss the effect of faulty sensor on AR output if the faulty one is not cut off, which is shown in Fig. 7. We can see the AR output of roll rate sensor is not divergent, but this will affect the diagnosis of remaining roll rate sensor if the faulty one is not cut off. Moreover, the AR output of pitch rate sensor matches the normal signal under bias fault, but its AR output is

divergent under stuck fault, and this will cause the instability on the system if the AR output is used in the reconstruction without faulty sensor being cut off. And the situation of yaw rate sensor is similar to pitch rate sensor.

Fig. 6 Yaw rate sensor stuck dead fault of 0.010 rad/s occurring at 10 s and reconstructed at 10.25 s.

(a) Bias fault of 0.010 rad/s stuck fault of 0.006 rad/s

(b) Bias fault of 0.020 rad/s, stuck fault of 0.010 rad/s

Fig. 7 AR output without cutting off the corresponding faulty sensor.

Compared to traditional analytic redundancy-based fault diagnosis technique, there are three characteristics of the technique mentioned here. First, kinematics redundancy relations are available for almost all kinds of aircraft. Second, because of the redundancy management, the method proposed in this paper may fasten the process of isolation. Third, the reconstructed outputs for faulty sensors can be used in the event of emergency.

5. Conclusions

1) This paper describes analytic redundancy-based fault diagnosis technique which is applied to OMS. A redundancy management for dual redundancy and analytic redundancy has been detailed, and the diagnosis result would be involved in BITE system, which would be the direction of future research.

2) The reconstruction of sensor outputs indicates the great role that analytic redundancy plays when hardware redundancies are all faulty. In fact, its performance satisfies our requirement.

3) Note that, the AR output will not match the output of the normal sensor if the faulty sensor is not cut off, and this will affect the diagnosis of remaining sensors, even cause the instability on the system if the AR output is used in the reconstruction without faulty sensor being cut off.

4) Simulation experiment shows the effectiveness, practicability and rapidity of the method applied to OMS.

References

[1] Beard R V. Failure accommodation in linear systems through self-reorganization. PhD thesis, Massachusetts Institutes of Technology, 1971.

[2] Isermann R. Process fault detection based on modeling and estimation methods—a survey. Automatica 1984; 20(4): 387-404.

[3] Isermann R. Model-based fault-detection and diagnosis-status and applications. Annual Reviews in Control 2005; 29(1): 71-85.

[4] Desai M N, Deckert J C, Deyst J J, et al. Dual redundant sensor FDI techniques applied to NASA F8C DFBW aircraft. AIAA-1976-1976, 1976.

[5] Frank P M. Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: a survey and some new results. Automatica 1990; 26(3): 459474.

[6] Zhou D H, Frank P M. Fault diagnostics and fault tolerant control. IEEE Transactions on Aerospace and Electronic Systems 1998; 34(2): 420-427.

[7] Zhou D H, Hu Y Y. Fault diagnosis techniques for dynamic systems. Acta Automatic Sinica 2009; 35(6): 748-758. [in Chinese]

[8] Zhang Y M, Jiang J. Integrated design of reconfigurable fault-tolerant control systems. Journal of Guidance, Control, and Dynamics 2001; 24(1): 133-136.

[9] Faller W, Hess D, Fu T, et al. Analytic redundancy for automatic control systems: recursive neural network based virtual sensors. AIAA-2007-156, 2007.

[10] Speyer J L, White J E. The shiryayev sequential probability ratio test for redundancy management. AIAA-1982-1623, 1982.

[11] Chien T T, Adams M B. A sequential failure detection technique and its application. IEEE Transactions on Automatic Control 1976; 21(5): 750-757.

[12] Malladi D P, Speyer J L. A generalized shiryayev sequential probability ratio test for change detection and isolation. IEEE Transactions on Automatic Control 1999; 44(8): 1522-1534.

[13] McClure D L, Glanz J M, Xu S, et al. Comparison of epidemiologic methods for active surveillance of vaccine safety. Vaccine 2008; 26(26): 3341-3345.

[14] Kulldorff M, Davis R L, Kolczak M, et al. A maximized sequential probability ratio test for drug and vaccine safety surveillance. Sequential Analysis 2011; 30(1): 58-78.

[15] ARINC624-1. Design guidance for onboard maintenance system-includes supplement 1. Aeronautical Radio Inc. (ARINC), 1993.

[16] Yang W, Zhang W G, Yang C X, et al. Fault-tolerant flight control system. Xi'an: Northwestern Polytechnical University Press, 2007. [in Chinese]

[17] Wang M X. The theory research and real time software developing of fault detection and isolation (FDI) for flight control system. Master thesis, Northwestern Polytechnical University, 2002. [in Chinese]

[18] Huang G, Han Y J, Li F. A quantitative analysis on the relation of Pf and Pm and samples based on the application of OC function. Journal of Guilin University of Electronic Technology 2003; 23(5): 46-48. [In Chinese]

[19] Liu K P, Zeng Q H. An improved sequential probability ratio test method for residual test. Electronics Optics & Control 2009; 16(8): 36-39. [in Chinese]

Biographies:

CHI Chengzhi received B.S. and M.S. degrees from Northwestern Polytechnical University in 2005 and 2009 respectively. Currently, he is a Ph.D. student at the School of Automation, Northwestern Polytechnical University. His main research interests include flight control and simulation,

intelligence fault diagnosis, fault-tolerance control and information fusion. E-mail: chengzhi.chi@gmail.com

ZHANG Weiguo received Ph.D. degree in navigation, guidance and control from Northwestern Polytechnical University in 1997. Currently, he is a professor at the School of Automation, Northwestern Polytechnical University. His research interests include control theory and its application, flight control system design and optimization, system modeling and simulation and fault tolerance control. E-mail: zhangwg@nwpu.edu.cn

LIU Xiaoxiong received Ph.D. degree in navigation, guidance and control from Northwestern Polytechnical University in 2006. Currently, he is an associate professor at the School of Automation, Northwestern Polytechnical University. His research interests include flight control and simulation, fault-tolerance control and intelligence computation. E-mail: liuxiaoxiong@nwpu.edu.cn