Scholarly article on topic 'Sensor Optimization Selection Model Based on Testability Constraint'

Sensor Optimization Selection Model Based on Testability Constraint Academic research paper on "Mechanical engineering"

CC BY-NC-ND
0
0
Share paper
Academic journal
Chinese Journal of Aeronautics
OECD Field of science
Keywords
{"prognostics and health management" / "design for testability" / "fault predictable rate" / "sensor selection and optimization" / "generic algorithm"}

Abstract of research paper on Mechanical engineering, author of scientific article — Shuming YANG, Jing QIU, Guanjun LIU

Abstract Sensor selection and optimization is one of the important parts in design for testability. To address the problems that the traditional sensor optimization selection model does not take the requirements of prognostics and health management especially fault prognostics for testability into account and does not consider the impacts of sensor actual attributes on fault detectability, a novel sensor optimization selection model is proposed. Firstly, a universal architecture for sensor selection and optimization is provided. Secondly, a new testability index named fault predictable rate is defined to describe fault prognostics requirements for testability. Thirdly, a sensor selection and optimization model for prognostics and health management is constructed, which takes sensor cost as objective function and the defined testability indexes as constraint conditions. Due to NP-hard property of the model, a generic algorithm is designed to obtain the optimal solution. At last, a case study is presented to demonstrate the sensor selection approach for a stable tracking servo platform. The application results and comparison analysis show the proposed model and algorithm are effective and feasible. This approach can be used to select sensors for prognostics and health management of any system.

Academic research paper on topic "Sensor Optimization Selection Model Based on Testability Constraint"

Chinese Journal of Aeronautics 25 (2012) 262-268

ELSEVIER

Contents lists available at ScienceDirect

Chinese Journal of Aeronautics

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

JOURNAL OF

AERONAUTICS

Sensor Optimization Selection Model Based on Testability Constraint

YANG Shuming, QIU Jing*, LIU Guanjun

Laboratory of Science and Technology on Integrated Logistics Support, College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha 410073, China Received 7 July 2011; revised 11 August 2011; accepted 19 October 2011

Abstract

Sensor selection and optimization is one of the important parts in design for testability. To address the problems that the traditional sensor optimization selection model does not take the requirements of prognostics and health management especially fault prognostics for testability into account and does not consider the impacts of sensor actual attributes on fault detectability, a novel sensor optimization selection model is proposed. Firstly, a universal architecture for sensor selection and optimization is provided. Secondly, a new testability index named fault predictable rate is defined to describe fault prognostics requirements for testability. Thirdly, a sensor selection and optimization model for prognostics and health management is constructed, which takes sensor cost as objective function and the defined testability indexes as constraint conditions. Due to NP-hard property of the model, a generic algorithm is designed to obtain the optimal solution. At last, a case study is presented to demonstrate the sensor selection approach for a stable tracking servo platform. The application results and comparison analysis show the proposed model and algorithm are effective and feasible. This approach can be used to select sensors for prognostics and health management of any system.

Keywords: prognostics and health management; design for testability; fault predictable rate; sensor selection and optimization; generic algorithm

1. Introduction

Testability is a design characteristic which allows the status (operable, inoperable, or degraded) of an item to be determined and the isolation of faults within the item to be performed in a timely manner [1]. Testability is of great significance to improve diagnostic efficiency and to reduce false alarm, and has been widely used in maintenance support domain [2-3]. Sensor (test) selection and optimization (SSO) is one of the important parts in design for testability (DFT) [4]. The main contents and proceedings of SSO in DFT are [5-7]:

Corresponding author. Tel.: +86-731-84573305. E-mail address: qiujing@nudt.edu.cn Foundation item: National Natural Science Foundation of China (51175502)

1000-9361/$ - see front matter © 2012 Elsevier Ltd. All rights reserved. doi: 10.1016/S1000-9361(11)60386-5

A) defining a series of testability indexes to describe testability requirements; B) constructing sensor optimization selection model based on system testability model and indexes; C) designing an effective algorithm to obtain the optimal solution. At present, SSO in DFT is mainly used for fault detection and isolation. In the aspect of testability index, fault detectable rate (FDR) and fault isolatable rate (FIR) are usually used to describe the fault diagnostics requirements for testability [4-10]; in the aspect of testability model, dependency model [11], multi-signal flow graph [12], information flow model [13] and quantitative directed graph [14] are popular; in algorithm aspect, generic algorithm [6-7], binary particle swarm [5], Boolean logic analysis [8] are usually adopted.

Catastrophes caused by aerospace system faults in recent years impel people to explore fault mechanism and the corresponding countermeasures. Prognostics

and health management (PHM), which generally combines sensing and interpretation of environmental, operational, and performance-related parameters to assess the health of a product and predict the remaining useful life[15], is significant to improve aerospace system safety and reliability [16-17]. With the rapid development of PHM concept and PHM-related technologies (i.e., fault prognostic technology, health state evaluation technology), PHM has been an important part in complex aerospace systems such as helicopter, aircraft engine, missile and so on. PHM extends the embedded diagnostics, while testability and embedded diag-nosability contribute to PHM performance [18]. So, sensors should also be selected based on PHM especially fault prognostics needs rather than only on fault detection and isolation requirements.

The topic of SSO for PHM has attracted the attention of many scholars and institutes. NASA has been studying sensor optimization configuration technology for engine health management since 2005 and proposed a famous system sensor selection strategy (S4); the researchers there have also paid much attention to some experiment validation and verification for health monitoring and health management of some aerospace systems, such as turbo engine and RS-68 rocket engine [19-22]. Cheng, et al. have studied SSO for PHM systematically and proposed the state-of-art sensor systems for PHM and further discussed the emerging trends in technologies of sensor systems for PHM [15, 23-24]. Kwon, et al. also paid much attention to SSO for

PHM [25]. The existing studies can be summarized as the design for reliability (DFR), and the main contents and procedures are: A) constructing diagnostic/prognostics model of system; B) defining an objective function or figure of merit (FOM); C) designing an effective algorithm. However, at early system design stage, the available knowledge usually includes failure modes, available sensors and schematic structure drawing, etc. It is very difficult to construct system diagnostic/prognostic model with the limited knowledge. Alternatively, SSO for PHM can be realized from DFT view rather than from DFR view.

The paper mainly studies SSO for PHM of aerospace systems from DFT view, and the remainder is organized as follows. In Section 2, a universal SSO architecture is proposed. Fault predictable rate (FPR) is defined in Section 3 and the SSO model is constructed in Section 4. A case study and analysis is provided in Section 5. Finally, conclusions are drawn in Section 6.

2. SSO Architecture for PHM

As stated previously, SSO for PHM should be realized in parallel with system design, and should take the requirements of PHM for testability into account comprehensively. Furthermore, a scheme is needed to validate and verify the selected sensors. So the architecture of the SSO for PHM can be represented by Fig.1. In the figure, FMMEA is failure modes, mechanisms and effect analysis.

Sensor iterative selection

Fig.1 A universal SSO architecture for PHM.

The proposed architecture can be segmented into four parts: knowledge base, testability requirement analysis, sensor iterative selection and sensor final selection.

1) Knowledge base mainly includes failure mode-related information, sensor-related information, system structure, function and so on. FMMEA can be used to analyze system failure modes and their essential causes, and to determine the parameters to be monitored and the locations to place the sensors [15, 26]. Sen-

sor-related information may be sensor cost, signal to noise rate (SNR), sensor reliability and sensor resolution, etc. Besides, expert knowledge and similar system knowledge are also useful to aid testability modeling and testability requirement analysis.

2) Testability requirement analysis mainly refers to defining a series of testability indexes which can describe the requirements of PHM for testability comprehensively. PHM is a complex integrated system, and diagnosis and prognosis are two key technologies in

PHM, so FDR and FIR are usually used to describe the fault diagnostics requirements for testability [2-4] and FPR to describe the fault prognostics requirements for testability. The detailed contents can be referred to Section 3.

3) Sensor iterative selection is an iterative procedure to select a group of sensor suites in order to satisfy PHM's requirements for testability. The procedure usually includes system testability model (fault-sensor dependency model), SSO model and SSO algorithm. This part is the main content of the paper and the details can be referred to Section 4.

4) Sensor final selection can generate an optimal sensor suite. The processes are: A) designing the selected sensors and locations; B) reconstructing testability model and injecting simulation faults; C) collecting fault information such as detectable faults, predictable faults; D) evaluating testability level and generating an optimal sensor suite. The details of fault simulation and injection as well as testability level evaluation can be referred to Ref. [27].

The proposed architecture is model-based, so it is very important to construct an accurate system testability model. At present, many approaches such as dependency model, multi-signal flow graph, information flow model can be used to describe system testability model. In order to shorten system development cycle and reduce system development cost, the constructed testability model should be of two distinct characteristics. One is the model should support testability requirement analysis, sensor selection and optimization, fault simulation and injection, testability analysis and evaluation; the other is the model should be of knowledge reusability for different engineers at different design stages, which enables testability design to be developed concurrently and consistently.

3. Testability Indexes for PHM

The main testability indexes for fault diagnosis (fault detection and fault isolation) are FDR and FIR. In Ref. [4], FDR and FIR are defined as follows.

Definition 1 FDR is the ratio of the number of faults detected correctly by sensors to the total number of system faults during the stated time span.

Definition 2 FIR is the ratio of the number of faults isolated correctly to no more than the stated replaceable units by sensors during the stated time span to the number of the detected faults during the same time span.

In order to describe the requirements of fault prognostics for testability, FPR is defined. As we know, fault prognostics techniques, which relate to information acquisition, signal process, prognostics models and algorithms, are always the key and difficult points in PHM domain. Testability for fault prognostics mainly enables faults predictable at information level. The predictability of a fault depends on two basic factors. One is the fault should be progressive in nature, the other is the fault should be a key fault.

Definition 3 Possible predictable fault (PPF) is a progressive key fault.

A fault satisfying Definition 3 may not be predictable, and the predictability of a fault is also related to timely detection and evolution track. If a fault is detected by some sensor when or after the fault leads to a failure, fault prognostics becomes insignificant; if the evolution process of a fault cannot be tracked by some sensor, fault prognostics (data driven-based fault prognostics) may not be realized.

Definition 4 Predictable fault (PF) is a PPF whose early state is detectable and the evolution process is trackable.

PF can be obtained by FMMEA, and in applications, we suppose that if a sensor can detect the early state of a fault, it also means the sensor can track the fault evolution process.

Based on Definition 3 and Definition 4, FPR can be defined as follows.

Definition 5 FPR is the ratio of the number of PFs determined correctly by sensors to the total number of PPFs of system during the stated time span.

4. SSO for PHM

4.1. System testability model

Testability model is the base of SSO in DFT, and dependency model is an effective modeling method [28]. Based on dependency model, fault-sensor dependency can be obtained by reachability analysis or fault simulation. Given the fault set of certain equipment system is F={fi, f2, •••, fm}, and the corresponding failure rate vector is i=[Aj, X2, •", ^m]. FPP denotes possible predictable faults of the system. The complete sensor set used for selection is T={tu t2, •••, tn}, the corresponding cost vector is C=[ci, c2, •••, cn], and sensor failure rate vector is FR=[ru r2, •••, rn]. Sensor selection situation vector is X=[xi, x2, •••, xn], where Xj (1<j<n) denotes the number of the selected sensor tj, and the vector Q=[q] the upper limit of X. A matrix B=[bj]mxn is used to denote dependency between faults and sensors. The rows of B correspond to faults, and the columns correspond to sensors. Element bj is a two-tuple, bj =(«,v). If sensor tj can detect fault f and its early state, then bj =(1,1). If sensor tj can detect fault fi but cannot detect its early state, bj=(1,0). If sensor tj cannot detect fault f nor its early state, then bj=(0,0) (bj =0 for short). Generally, if a sensor can detect early state of a fault, it also means that the sensor can detect the fault, so the case by = (0,1) would not exist.

4.2. Testability indexes modeling

Suppose that there exists, at most, a single fault in the system at any given time. Given the selected sensor set is Ts, which is a subset of T, the corresponding de-

pendency matrix becomes D=[dj\mxn., the rows of D are still faults and the columns are the selected sensors, i.e., V tj, tje Ts. The meanings of d, is the same as bj, d, =(w,v); n'=\ Ts | denotes the number of sensors in Ts. Detectable faults FD, isolable faults FI and predictable faults FP are formulated respectively by

Fd = {f \f e F, U dp (1) = 1} F = { f \ f e Fd, Tfi ® Tj = 1,yfj e F, fj * ft} (1)

Fp = {fl\fl e Fpp fi Fd

, U d (2) = 1}

t,eT. J

where U denotes Boolean variable or operation, djk) the kth item of the two-tuple d, =(u,v), k =1,2. Tfi and Tj denote sensor sets which can detect fault f and fault fj respectively. © denotes set exclusive or (XOR) operation.

dj(k)=1 has two meanings. One is that sensor tj relates to fault f; the other is that sensor tj can detect fault f with probability 1 when fault f occurs. Due to a variety of uncertainties in complex aerospace systems, a sensor relating to a fault may not mean that the fault can be detected by the sensor with probability 1. Fault detection probability is dependent on many factors, which can be generalized into sensor function attributes and performance attributes in the present research. Function attributes mainly refer to sensor reliability which is usually affected by hard faults; performance attributes mainly include sensor SNR, sensor sensitivity, sensor timely detection and symptom duration, which are usually determined by sensor design indexes and manufacture level. The impact of sensor function attributes on detectability and predictability of fault fi can be formulated respectively by

' R1 = 1 (1)

R2 = 1 ^ rXJdJ(2)

The impact of sensor performance attributes on de-tectability and predictability of fault f can be formulated respectively by

Z pj(1)

p1 =■

p2 =•

E xjdj (1)

J]ppXjdj(2) Xjdj (2)

Pj can be calculated according to Ref. [14].

-1 / /^m

(1+e-10(^j-a5);

( TTD.. V' 1 - j

TTF„

x a + e ( SyD. ^

- (SNR.-0.5) N

TTD.. < TTFv (4) ij ij

TTD... > TTF.

where V, denotes detection sensitivity of sensor tj to fault f, SNR, SNR of sensor j TTD, the time span between the initiation of fault fi (potential failure) and the detection of the fault by the sensor tj, TTFj the duration between the initiation of the fault fi and the time when the failure occurs, and SyD j symptom duration time span of sensor tj to fault f.

TTD, TTF and SyD can be obtained by fault simulation or fault propagation timing analysis method [29] .

According to Eq. (2) and Eq. (3), the total detectable and predictable probability of fault fi can be formulated respectively by

ÎFD1 = r1 X p1

FD2 = R,2 X p2

According to Definitions 1, 2 and 5, and considering the impact of sensor attributes on detectability and predictability, FDR, FIR and FPR can be formulated by

FDR = FD'. /

f ' eFd / f.eF

FIR = FDW FD1 (6)

f. eFi / f. eFd

FPR FD2 I

f. eFp / f. eFPp

4.3. SSO model

SSO model can be formulated by Eq. (7), which takes sensor cost as optimization objective, and FDR, FIR and FpR as constraint conditions.

Ts* = argmin y, cjxj

s.t. FDR>rd,FIR > ri,FpR > rp

where rd, ri and rp are testability requirements that equipment system will satisfy.

4.4. SSO algorithm

SSO problem is a combination optimization problem and is of NP-hard property. Generic algorithm (GA) is usually used to obtain the optimal solution. The steps of SSO algorithm based on a GA are as follows.

Step 1 Parameter initialization, including population size, PopSize, generic crossover and mutation probability, pc, pm, max iterative number, Nmax. The initialization population, Pop=(Xj)Nxn, is randomly generated, where n denotes the number of sensors used for selection. When tj is selected, x, =1, otherwise, xiJ =0.

Step 2 Define fitness function FitFun = C0/( Y Cj +Y Cj ) " C,max(0, rd - FDR) -

C2max(0, ri - FIR) - C3max(0, rp - fpr)

where C0, C1, C2 and C3 are constants. Individual fitness is calculated according to Eq. (8).

Justify whether the iterative number satisfies the max iterative number. If true, output the optimal individual and the corresponding optimal solution, and end the program; otherwise, go to Step 3.

Step 3 Select individuals using roulette wheel selection method based on individual fitness, and execute crossover operation with probability pc, hence produce population Pop'.

Step 4 Execute mutation operation with probab-

ility pm on the individuals in population Pop', hence produce population Pop". Return to Step 2.

5. Case Study

Stable tracking servo platform (STSP) has been widely used in advanced aerospace systems such as cruise missile and fighter. The structure of some STSP is shown in Fig.2.

Fig.2 Structure of some STSP.

The failure mode information and sensor information of the STSP are listed in Table 1 and Table 2 respectively.

Table 1 Failure mode information

Failure mode Prior failure rate/10-6 Resolution

Abnormal operation in actuator fi 1.0 1

Non-uniform gap between stator and i r> i

rotor f2 1.0 1

Open in motor's stator coil f 1.0 1

Short in motor's stator coil f 1.0 1

Grounding in motor's stator coil f 1.0 1

Wearing in motor's bearing f 1.5 1

Fatigue wear in gearbox'gear f 2.5 1

Fatigue wear in gearbox'bearing f 2.5 1

No output in gearbox f9 1.0 1

Table 2 Sensors and sensor attributes

Sensor Failure rate/10 6 Cost/dollar SNR/dB Resolution

Level signal 1 detection ti 6.0 10 0.01

Vibration sensor t2 1 6.6 10 0.01

Current detection t3 1 4.5 10 0.01

Optical-electricity 1 encoder t4 7.0 10 0.01

Temperature 1 sensor t5 8.2 10 0.01

Vibration sensor t6 1 5.7 10 0.01

Optical-electricity 1 encoder t7 8.6 10 0.01

Rate gyroscope tg 1 15.2 10 0.01

Strap-down inertial 1 14.6 10 0.01

navigation system t9

Refer to Ref. [10] and combine with FMMEA, and the dependency matrix can be obtained in Table 3.

According to Definition 3, Fpp = f1, f2, f6, f7, f8}. In order to satisfy PHM needs of STSP for testability, the required testability indexes are under the following conditions: FDR is no less than 0.98, FIR, 0.95 and FPR, 0.99.

Table 3 Fault-sensor dependency matrix

Sensor

raun t1 t2 t3 t4 t5 t6 t7 t8 t9

f1 (1,1) 0 0 0 0 0 0 0 0

f2 0 (1,0) (1,1) (1,1) 0 0 0 0 0

f3 0 0 (1,0) (1,0) 0 0 0 0 0

f4 0 0 0 (1,0) (1,0) 0 0 0 0

f5 0 0 (1,0) 0 (1,0) 0 0 0 0

f6 0 (1,1) 0 (1,0) 0 0 0 0 0

f7 0 0 0 0 0 (1,1) (1,0) (1,1) (1,1)

f8 0 0 0 0 0 (1,1) 0 0 0

f9 0 0 0 0 0 0 (1,0) (1,0) (1,0)

The SSO model is

Ts* = argmin ^ CjXj

Ts tj eTs

s.t. FDR>0.98,FIR > 0.95,FPR > 0.99

A GA is used to solve the problem, and the parameters are set as PopSize=40, pc=0.7, pm=0.02, Nmax=50, C0=10, C1=C2=C3=0.5. The optimization results are shown in Table 4 and Table 5, and the total sensor cost is 68.7 dollars.

Table 4 Testability requirement results for STSP

Parameter Requirement Optimization

FDR 0.98 0.995 1

FIR 0.95 0.982 7

FPR 0.99 0.999 2

Table 5 SSO scheme for STSP (scheme I)

Sensor ti t2 Í3 t4 t6 t9

Number 3 2 1 1 2 1

Table 4 and Table 5 show that the selection scheme I can satisfy STSP testability requirements for PHM with a small number of sensors, and sensor resources can be economized greatly, so GA is effective to sensor optimization selection problem. In order to further validate the rationality of the proposed model, STSP is used again as a case. The optimization objective is still sensor cost but the constraint conditions are only FDR and FIR, and sensor practical attributes are not considered either. In this situation, testability indexes can be represented by

FDR Z^

f, eFD / f, eF

FIR =£4/ Z4

f, ^Fd

And the corresponding SSO model is TS* = argmin Y <

Ts tj^T;

s.t. FDR > 0.98,FIR > 0.95

The linear interactive and general optimizer (LINGO) software package is used to obtain the optimal selection scheme, the results are shown in Table 6 and Table 7, and the total sensor cost is 56.6 dollars.

Table 6 Testability requirement results with FDR and FIR constraints

Parameter Requirement Optimization

FDR 0.98 0.997 3

FIR 0.95 0.992 1

Table 7 SSO scheme with FDR and FIR constraints

(scheme II)

Sensor t1 t3 t4 t5 t7 t9

Number 2 111 1 1

From Table 6 and Table 7, one can see that the cost of scheme II is lower than that of scheme I. The reasons are: A) the sensor actual attributes are not considered. Namely, a sensor can detect a fault with probability 1 when the fault occurs, so higher FDR and FIR can be reached with fewer sensors; B) scheme II does not take FPR as a constraint. Namely, fault early state detection ability and fault evolution process track ability of sensor are not necessary, so the sensors with low cost would have priority for selection. Scheme II is very suitable for fault detection and isolation of digital

systems. However, as stated previously, the practical attributes of the sensors used in complex aerospace systems should be taken into account. Furthermore, for aerospace system PHM, testability should provide state information for fault prognostics besides satisfying fault diagnostics requirements, so FPR should be considered in the optimization selection model. In STSP system, FPP = {f, f2, f6, f7, f8}, but in scheme II, due to the sensor t5 and t7 do not have the ability of fault early state detection and/or fault evolution process track, fault prognostics will not be realized for the key fault f6 and f8. In other words, although scheme II can satisfy fault diagnostics requirements with lower cost, it cannot satisfy PHM needs. The comparison analytical results show that the proposed model, which adds FPR to the constraint conditions and takes sensor practical attributes into account, can guide sensor selection and optimization for aerospace system PHM very well and hence can provide sufficient state information for PHM.

6. Conclusions

The main contributions of the paper are as follows: A) a SSO architecture is proposed that would provide a justifiable sensor suite to address PHM requirements of aerospace systems and support concurrent design methodology; B) testability indexes for PHM i.e., FDR, FIR and FPR are defined; C) a SSO model for PHM is constructed, which adds FPR to constraint conditions and considers the impact of sensor actual attributes on fault detectability; aimed at the NP-hard property of the model, a generic algorithm is introduced to solve the problem; D) a case is provided to validate and verify the proposed model and algorithm.

In engineering applications, SSO is an iterative loop process. At initial design stage, people can construct dependency model based on prior knowledge and obtain fault-sensor dependency matrix by reachability analysis; then, the proposed SSO model is used to obtain a near-optimal sensor suite; after that, testability level is evaluated by fault simulation and injection. If the evaluated testability level satisfies the system's requirements for testability, the selected sensor suite is optimal; otherwise, the testability model, testability index even prior knowledge should be readjusted and the process should be repeated until generating the optimal sensor suite that satisfies system testability requirements.

System knowledge such as fault information, sensor attribute information and system testability model has a great impact on the SSO results. However, at system design state, it is hard to obtain much information or the cost is very high, so people should not rely on the SSO results completely. The proposed model and algorithm are not object-related and can be applied to SSO for PHM of any system.

References

[1] Testability program for electronic systems and equip-

ments. MIL-STD-2165, 1985.

[2] Qiu J, Liu G J, Lv K H. Build in test false alarm reducing technologies in electromechanical systems. Beijing: Science Press, 2009. [in Chinese]

[3] Zeng Z D. Test and testability of digital systems. Changsha: National University of Defense Technology Press, 1992. [in Chinese]

[4] Tian Z, Shi J Y. System testability design, analysis and verification. Beijing: Beihang University Press, 2003. [in Chinese]

[5] Jiang R H, Wang H J, Long B. Test selection based on binary particle swarm optimization. Journal of Electronic Measurement and Instrument 2008; 22(2): 11-15. [in Chinese]

[6] Chen X X, Qiu J, Liu G J. Optimal test selection based on hybrid BPSO and GA. Chinese Journal of Scientific Instrument 2009; 30(8): 1674-1680. [in Chinese]

[7] Lv X M, Huang K L, Lian G Y. Research on the problem of test selection optimization based on chaos genetic algorithm. Journal of Projectiles, Rockets, Missiles and Guidance 2009; 29(3): 265-272. [in Chinese]

[8] Yang P, Qiu J, Liu G J, et al. The test selection algorithms based on Boolean logic. Journal of Test and Measurement Technology 2007; 21(5): 386-390. [in Chinese]

[9] Zhang L, Zhang F M. Research on optimal sensor placement in equipment health management. Transducer and Micro-system Technologies 2008; 27(7): 18-20. [in Chinese]

[10] Yang G , Liu G J, Li J G , et al. Optimal sensor placement based on various fault detectability and reliability criteria. Acta Electronica Sinica 2006; 34(2): 348-351. [in Chinese].

[11] Nair R, Lin C J, Haynes L, et al. Automatic dependency model generation using SPICE event driven simulation. Proceedings of the IEEE Automatic Test Conference. 1996; 318-328.

[12] Deb S, Pattipati K R, Raghavan V, et al. Multi-signal glow graphs: a novel approach for system testability analysis and fault diagnosis. IEEE AES Magazine 1995; 20(5): 14-25.

[13] Sheppard J W. Maintaining diagnostic truth with information flow models. Proceedings of the IEEE Automatic Test Conference. 1996; 447-454.

[14] Zhang G F. Optimum sensor localization/selection in a diagnostic/prognostic architecture. PhD thesis, Georgia Institute of Technology, 2005.

[15] Cheng S, Azarian M, Pecht M. Sensor systems for prognostics and health management. Sensors 2010; 10(4): 5774-5797.

[16] Kalgren P W, Byington C S, Roemer M J, et al. Defining PHM, a lexical evolution of maintenance and logistics. Systems Readiness Technology Conference. 2006; 353-358.

[17] Orsagh R F, Brown D W, Kalgren P W, et al. Prognostic health management for avionic systems. Proceedings of the IEEE Aerospace Conference. 2006; 1-7.

[18] GJB2547A-2009. The general requirements of equipment testability work. [in Chinese]

[19] Santi L M, Sowers T S, Aguila R B. Optimal sensor selection for health monitoring systems. NASA/TM-2005-213955, 2005.

[20] Sowers S, Kopasakis G, Simon D L. Application of the systematic sensor selection strategy for turbofan engine diagnostics. NASA/TM-2008-215200, 2008.

[21] Maul W A, Kopasakis G. Sensor selection and optimization for health assessment of aerospace systems. NASA/TM-2007-214822, 2007.

[22] Simon D L, Garg S. A systematic approach to sensor selection for aircraft engine health estimation. NASA/ TM-2009-215839, 2009.

[23] Cheng S, Tom K, Pecht M. Failure precursors for polymer resettable fuses. IEEE Transactions on Devices and Materials Reliability 2010; 10(3): 374-380.

[24] Cheng S, Tom K, Thomas L, et al. A wireless sensor system for prognostics and health management. IEEE Sensors Journal 2010; 10(4): 856-862.

[25] Kwon D, Azarian M H, Pecht M. Nondestructive sensing of interconnect failure mechanisms using time domain reflectometry. IEEE Sensors Journal 2011; 11(5): 1236-1241.

[26] Kumar S, Dolev E, Pecht M. Parameter selection for health monitoring of electronic products. Microelectronics Reliability 2010; 50(2): 161-168.

[27] Li T M. Research on optimization design and integrated evaluation of testability verification test for equipments. PhD thesis, National University of Defense Technology, 2010.

[28] Yang P. Optimization technology of design for diagnostic strategy based on dependency model. PhD thesis, National University of Defense Technology, 2008.

[29] Johnson J R. Fault propagation timing analysis to aid in the selection of sensors for health management systems. PhD thesis, Missouri University of Science and Technology, 2008.

Biographies:

YANG Shuming received B.S. degree from Central South University in 2005, and now is a Ph.D. candidate in National University of Defense Technology. His main research interests are design for testability, prognostics and health management, as well as fault diagnostics and prognostics. E-mail: ysmcsu@163.com

QIU Jing received B.S. degree from Beihang University in 1985, M.S. and Ph.D. degrees from National University of Defense Technology (NUDT) in 1988 and 1998 respectively, and now he is a professor in NUDT. His main research interests are condition monitoring and fault diagnostics, design for testability, prognostics and health management. E-mail: qiujing@nudt.edu.cn