Sensor Optimization Selection Model Based on Testability Constraint

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1 Chinese Journal o Aeronautics 25 (202) Contents lists available at ScienceDirect Chinese Journal o Aeronautics ournal homepage: Sensor Optimization Selection Model Based on Testability Constraint YANG Shuming, QIU Jing*, LIU Guanun Laboratory o Science and Technology on Integrated Logistics Support, College o Mechatronics Engineering and Automation, National University o Deense Technology, Changsha 40073, China Received 7 July 20; revised August 20; accepted 9 October 20 Abstract Sensor selection and optimization is one o the important parts in design or testability. To address the problems that the traditional sensor optimization selection model does not take the requirements o prognostics and health management especially ault prognostics or testability into account and does not consider the impacts o sensor actual attributes on ault detectability, a novel sensor optimization selection model is proposed. Firstly, a universal architecture or sensor selection and optimization is provided. Secondly, a new testability index named ault predictable rate is deined to describe ault prognostics requirements or testability. Thirdly, a sensor selection and optimization model or prognostics and health management is constructed, which takes sensor cost as obective unction and the deined testability indexes as constraint conditions. Due to NP-hard property o 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 or a stable tracking servo platorm. The application results and comparison analysis show the proposed model and algorithm are eective and easible. This approach can be used to select sensors or prognostics and health management o any system. Keywords: prognostics and health management; design or testability; ault predictable rate; sensor selection and optimization; generic algorithm. Introduction Testability is a design characteristic which allows the status (operable, inoperable, or degraded) o an item to be determined and the isolation o aults within the item to be perormed in a timely manner []. Testability is o great signiicance to improve diagnostic eiciency and to reduce alse alarm, and has been widely used in maintenance support domain [2-3]. Sensor (test) selection and optimization (SSO) is one o the important parts in design or testability (DFT) [4]. The main contents and proceedings o SSO in DFT are [5-7] : *Corresponding author. Tel.: address: qiuing@nudt.edu.cn Foundation item: National Natural Science Foundation o China (575502) /$ - see ront matter 202 Elsevier Ltd. All rights reserved. doi: 0.06/S () A) deining a series o testability indexes to describe testability requirements; B) constructing sensor optimization selection model based on system testability model and indexes; C) designing an eective algorithm to obtain the optimal solution. At present, SSO in DFT is mainly used or ault detection and isolation. In the aspect o testability index, ault detectable rate (FDR) and ault isolatable rate (FIR) are usually used to describe the ault diagnostics requirements or testability [4-0] ; in the aspect o testability model, dependency model [], multi-signal low graph [2], inormation low model [3] and quantitative directed graph [4] 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 aults in recent years impel people to explore ault mechanism and the corresponding countermeasures. Prognostics

2 No.2 YANG Shuming et al. / Chinese Journal o Aeronautics 25(202) and health management (PHM), which generally combines sensing and interpretation o environmental, operational, and perormance-related parameters to assess the health o a product and predict the remaining useul lie [5], is signiicant to improve aerospace system saety and reliability [6-7]. With the rapid development o PHM concept and PHM-related technologies (i.e., ault prognostic technology, health state evaluation technology), PHM has been an important part in complex aerospace systems such as helicopter, aircrat engine, missile and so on. PHM extends the embedded diagnostics, while testability and embedded diagnosability contribute to PHM perormance [8]. So, sensors should also be selected based on PHM especially ault prognostics needs rather than only on ault detection and isolation requirements. The topic o SSO or PHM has attracted the attention o many scholars and institutes. NASA has been studying sensor optimization coniguration technology or engine health management since 2005 and proposed a amous system sensor selection strategy (S4); the researchers there have also paid much attention to some experiment validation and veriication or health monitoring and health management o some aerospace systems, such as turbo engine and RS-68 rocket engine [9-22]. Cheng, et al. have studied SSO or PHM systematically and proposed the state-o-art sensor systems or PHM and urther discussed the emerging trends in technologies o sensor systems or PHM [5, 23-24]. Kwon, et al. also paid much attention to SSO or PHM [25]. The existing studies can be summarized as the design or reliability (DFR), and the main contents and procedures are: A) constructing diagnostic/prognostics model o system; B) deining an obective unction or igure o merit (FOM); C) designing an eective algorithm. However, at early system design stage, the available knowledge usually includes ailure modes, available sensors and schematic structure drawing, etc. It is very diicult to construct system diagnostic/prognostic model with the limited knowledge. Alternatively, SSO or PHM can be realized rom DFT view rather than rom DFR view. The paper mainly studies SSO or PHM o aerospace systems rom DFT view, and the remainder is organized as ollows. In Section 2, a universal SSO architecture is proposed. Fault predictable rate (FPR) is deined 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 SSO Architecture or PHM As stated previously, SSO or PHM should be realized in parallel with system design, and should take the requirements o PHM or testability into account comprehensively. Furthermore, a scheme is needed to validate and veriy the selected sensors. So the architecture o the SSO or PHM can be represented by Fig.. In the igure, FMMEA is ailure modes, mechanisms and eect analysis. Fig. A universal SSO architecture or PHM. The proposed architecture can be segmented into our parts: knowledge base, testability requirement analysis, sensor iterative selection and sensor inal selection. ) Knowledge base mainly includes ailure moderelated inormation, sensor-related inormation, system structure, unction and so on. FMMEA can be used to analyze system ailure modes and their essential causes, and to determine the parameters to be monitored and the locations to place the sensors [5, 26]. Sensor-related inormation may be sensor cost, signal to noise rate (SNR), sensor reliability and sensor resolution, etc. Besides, expert knowledge and similar system knowledge are also useul to aid testability modeling and testability requirement analysis. 2) Testability requirement analysis mainly reers to deining a series o testability indexes which can describe the requirements o PHM or testability comprehensively. PHM is a complex integrated system, and diagnosis and prognosis are two key technologies in

3 264 YANG Shuming et al. / Chinese Journal o Aeronautics 25(202) No.2 PHM, so FDR and FIR are usually used to describe the ault diagnostics requirements or testability [2-4] and FPR to describe the ault prognostics requirements or testability. The detailed contents can be reerred to Section 3. 3) Sensor iterative selection is an iterative procedure to select a group o sensor suites in order to satisy PHM s requirements or testability. The procedure usually includes system testability model (ault-sensor dependency model), SSO model and SSO algorithm. This part is the main content o the paper and the details can be reerred to Section 4. 4) Sensor inal selection can generate an optimal sensor suite. The processes are: A) designing the selected sensors and locations; B) reconstructing testability model and inecting simulation aults; C) collecting ault inormation such as detectable aults, predictable aults; D) evaluating testability level and generating an optimal sensor suite. The details o ault simulation and inection as well as testability level evaluation can be reerred to Re. [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 low graph, inormation low 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 o two distinct characteristics. One is the model should support testability requirement analysis, sensor selection and optimization, ault simulation and inection, testability analysis and evaluation; the other is the model should be o knowledge reusability or dierent engineers at dierent design stages, which enables testability design to be developed concurrently and consistently. 3. Testability Indexes or PHM The main testability indexes or ault diagnosis (ault detection and ault isolation) are FDR and FIR. In Re. [4], FDR and FIR are deined as ollows. Deinition FDR is the ratio o the number o aults detected correctly by sensors to the total number o system aults during the stated time span. Deinition 2 FIR is the ratio o the number o aults isolated correctly to no more than the stated replaceable units by sensors during the stated time span to the number o the detected aults during the same time span. In order to describe the requirements o ault prognostics or testability, FPR is deined. As we know, ault prognostics techniques, which relate to inormation acquisition, signal process, prognostics models and algorithms, are always the key and diicult points in PHM domain. Testability or ault prognostics mainly enables aults predictable at inormation level. The predictability o a ault depends on two basic actors. One is the ault should be progressive in nature, the other is the ault should be a key ault. Deinition 3 Possible predictable ault (PPF) is a progressive key ault. A ault satisying Deinition 3 may not be predictable, and the predictability o a ault is also related to timely detection and evolution track. I a ault is detected by some sensor when or ater the ault leads to a ailure, ault prognostics becomes insigniicant; i the evolution process o a ault cannot be tracked by some sensor, ault prognostics (data driven-based ault prognostics) may not be realized. Deinition 4 Predictable ault (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 i a sensor can detect the early state o a ault, it also means the sensor can track the ault evolution process. Based on Deinition 3 and Deinition 4, FPR can be deined as ollows. Deinition 5 FPR is the ratio o the number o PFs determined correctly by sensors to the total number o PPFs o system during the stated time span. 4. SSO or PHM 4.. System testability model Testability model is the base o SSO in DFT, and dependency model is an eective modeling method [28]. Based on dependency model, ault-sensor dependency can be obtained by reachability analysis or ault simulation. Given the ault set o certain equipment system is F={, 2,, m }, and the corresponding ailure rate vector is λ=[λ, λ 2,, λ m ]. F PP denotes possible predictable aults o the system. The complete sensor set used or selection is T={t, t 2,, t n }, the corresponding cost vector is C=[c, c 2,, c n ], and sensor ailure rate vector is FR=[r, r 2,, r n ]. Sensor selection situation vector is X=[x, x 2,, x n ], where x ( n) denotes the number o the selected sensor t, and the vector Q=[q ] the upper limit o X. A matrix B=[b i ] m n is used to denote dependency between aults and sensors. The rows o B correspond to aults, and the columns correspond to sensors. Element b i is a two-tuple, b i =(u,v). I sensor t can detect ault i and its early state, then b i =(,). I sensor t can detect ault i but cannot detect its early state, b i =(,0). I sensor t cannot detect ault i nor its early state, then b i =(0,0) (b i =0 or short). Generally, i a sensor can detect early state o a ault, it also means that the sensor can detect the ault, so the case b i = (0,) would not exist Testability indexes modeling Suppose that there exists, at most, a single ault in the system at any given time. Given the selected sensor set is T s, which is a subset o T, the corresponding de-

4 No.2 YANG Shuming et al. / Chinese Journal o Aeronautics 25(202) pendency matrix becomes D=[d i ] m n, the rows o D are still aults and the columns are the selected sensors, i.e., t, s. The meanings o d i is the same as b i, d i =(u,v); n = T s denotes the number o sensors in T s. Detectable aults F D, isolable aults F I and predictable aults F P are ormulated respectively by n ' FD = { i i F, di() = } t Ts FI = { i i FD, Ti T =, F, i} () n ' FP = { i i FPP FD, di(2) = } t Ts where denotes Boolean variable or operation, d i (k) the kth item o the two-tuple d i =(u,v), k =,2. T i and T denote sensor sets which can detect ault i and ault respectively. denotes set exclusive or (XOR) operation. d i (k)= has two meanings. One is that sensor t relates to ault i ; the other is that sensor t can detect ault i with probability when ault i occurs. Due to a variety o uncertainties in complex aerospace systems, a sensor relating to a ault may not mean that the ault can be detected by the sensor with probability. Fault detection probability is dependent on many actors, which can be generalized into sensor unction attributes and perormance attributes in the present research. Function attributes mainly reer to sensor reliability which is usually aected by hard aults; perormance attributes mainly include sensor SNR, sensor sensitivity, sensor timely detection and symptom duration, which are usually determined by sensor design indexes and manuacture level. The impact o sensor unction attributes on detectability and predictability o ault i can be ormulated respectively by xd () i Ri = r t Ts (2) 2 xd i(2) Ri = r t Ts The impact o sensor perormance attributes on detectability and predictability o ault i can be ormulated respectively by ρi xd i () i P = P = 2 i s s s s xd i ρ xd i i xd i () (2) (2) ρ i can be calculated according to Re. [4]. 0( V 0.5) ( ) (SNR 0.5) e ( e ) i TTDi SyDi ρi = TTDi < TTFi TTF i TTF i 0 TTDi TTF i (3) (4) where V i denotes detection sensitivity o sensor t to ault i, SNR SNR o sensor t, TTD i the time span between the initiation o ault i (potential ailure) and the detection o the ault by the sensor t, TTF i the duration between the initiation o the ault i and the time when the ailure occurs, and SyD i symptom duration time span o sensor t to ault i. TTD, TTF and SyD can be obtained by ault simulation or ault propagation timing analysis method [29]. According to Eq. (2) and Eq. (3), the total detectable and predictable probability o ault i can be ormulated respectively by FDi = Ri Pi (5) FDi = Ri Pi According to Deinitions, 2 and 5, and considering the impact o sensor attributes on detectability and predictability, FDR, FIR and FPR can be ormulated by 4.3. SSO model FDR = λifdi λi i FD i F FIR = FD FD i I i D 2 FPR = λifdi λi i FP i FPP λi i λi i F F (6) SSO model can be ormulated by Eq. (7), which takes sensor cost as optimization obective, and FDR, FIR and FPR as constraint conditions. * Ts = argmin cx Ts t Ts (7) s.t. FDR rd,fir ri,fpr rp where rd, ri and rp are testability requirements that equipment system will satisy SSO algorithm SSO problem is a combination optimization problem and is o NP-hard property. Generic algorithm (GA) is usually used to obtain the optimal solution. The steps o SSO algorithm based on a GA are as ollows. Step Parameter initialization, including population size, PopSize, generic crossover and mutation probability, p c, p m, max iterative number, N max. The initialization population, Pop=(x i ) N n, is randomly generated, where n denotes the number o sensors used or selection. When t is selected, x i =, otherwise, x i =0. Step 2 Deine itness unction FitFun = C0 ( c + c) Cmax(0, rd FDR) t Ts t T (8) C max(0, ri FIR) C max(0, rp FPR) 2 3 where C 0, C, C 2 and C 3 are constants. Individual itness is calculated according to Eq. (8).

5 266 YANG Shuming et al. / Chinese Journal o Aeronautics 25(202) No.2 Justiy whether the iterative number satisies the max iterative number. I 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 itness, and execute crossover operation with probability p c, hence produce population Pop. Step 4 Execute mutation operation with probab- ility p m on the individuals in population Pop, hence produce population Pop. Return to Step Case Study Stable tracking servo platorm (STSP) has been widely used in advanced aerospace systems such as cruise missile and ighter. The structure o some STSP is shown in Fig.2. Fig.2 Structure o some STSP. The ailure mode inormation and sensor inormation o the STSP are listed in Table and Table 2 respectively. Table Failure mode inormation Failure mode Prior ailure rate/0 6 Resolution Abnormal operation in actuator.0 Non-uniorm gap between stator and rotor 2.0 Open in motor s stator coil 3.0 Short in motor s stator coil 4.0 Grounding in motor s stator coil 5.0 Wearing in motor s bearing 6.5 Fatigue wear in gearbox gear Fatigue wear in gearbox bearing No output in gearbox 9.0 Table 2 Sensors and sensor attributes Sensor Failure rate/0 6 Cost/dollar SNR/dB Resolution Level signal detection t Vibration sensor t Current detection t Optical-electricity encoder t Temperature sensor t Vibration sensor t Optical-electricity encoder t Rate gyroscope t Strap-down inertial navigation system t Reer to Re. [0] and combine with FMMEA, and the dependency matrix can be obtained in Table 3. According to Deinition 3, F PP = {, 2, 6, 7, 8 }. In order to satisy PHM needs o STSP or testability, the required testability indexes are under the ollowing conditions: FDR is no less than 0.98, FIR, 0.95 and FPR, Fault Table 3 Fault-sensor dependency matrix Sensor t t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 (,) (,0) (,) (,) (,0) (,0) (,0) (,0) (,0) 0 (,0) (,) 0 (,0) (,) (,0) (,) (,) (,) (,0) (,0) (,0) The SSO model is * Ts = argmin cx Ts t Ts (9) 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, p c =0.7, p m =0.02, N max =50, C 0 =0, C =C 2 =C 3 =0.5. The optimization results are shown in Table 4 and Table 5, and the total sensor cost is 68.7 dollars.

6 No.2 YANG Shuming et al. / Chinese Journal o Aeronautics 25(202) Table 4 Testability requirement results or STSP Parameter Requirement Optimization FDR FIR FPR Table 5 SSO scheme or STSP (scheme I) Sensor t t 2 t 3 t 4 t 6 t 9 Number Table 4 and Table 5 show that the selection scheme I can satisy STSP testability requirements or PHM with a small number o sensors, and sensor resources can be economized greatly, so GA is eective to sensor optimization selection problem. In order to urther validate the rationality o the proposed model, STSP is used again as a case. The optimization obective 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 = λi λi i FD i F (0) FIR = λi λi i FI i FD And the corresponding SSO model is * Ts = argmin cx Ts t Ts () s.t. FDR 0.98, FIR 0.95 The linear interactive and general optimizer (LINGO) sotware 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 FIR Table 7 SSO scheme with FDR and FIR constraints (scheme II) Sensor t t 3 t 4 t 5 t 7 t 9 Number 2 From Table 6 and Table 7, one can see that the cost o scheme II is lower than that o scheme I. The reasons are: A) the sensor actual attributes are not considered. Namely, a sensor can detect a ault with probability when the ault occurs, so higher FDR and FIR can be reached with ewer sensors; B) scheme II does not take FPR as a constraint. Namely, ault early state detection ability and ault evolution process track ability o sensor are not necessary, so the sensors with low cost would have priority or selection. Scheme II is very suitable or ault detection and isolation o digital systems. However, as stated previously, the practical attributes o the sensors used in complex aerospace systems should be taken into account. Furthermore, or aerospace system PHM, testability should provide state inormation or ault prognostics besides satisying ault diagnostics requirements, so FPR should be considered in the optimization selection model. In STSP system, FPP = {, 2, 6, 7, 8 }, but in scheme II, due to the sensor t 5 and t 7 do not have the ability o ault early state detection and/or ault evolution process track, ault prognostics will not be realized or the key ault 6 and 8. In other words, although scheme II can satisy ault diagnostics requirements with lower cost, it cannot satisy 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 or aerospace system PHM very well and hence can provide suicient state inormation or PHM. 6. Conclusions The main contributions o the paper are as ollows: A) a SSO architecture is proposed that would provide a ustiiable sensor suite to address PHM requirements o aerospace systems and support concurrent design methodology; B) testability indexes or PHM i.e., FDR, FIR and FPR are deined; C) a SSO model or PHM is constructed, which adds FPR to constraint conditions and considers the impact o sensor actual attributes on ault detectability; aimed at the NP-hard property o the model, a generic algorithm is introduced to solve the problem; D) a case is provided to validate and veriy 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 ault-sensor dependency matrix by reachability analysis; then, the proposed SSO model is used to obtain a near-optimal sensor suite; ater that, testability level is evaluated by ault simulation and inection. I the evaluated testability level satisies the system s requirements or testability, the selected sensor suite is optimal; otherwise, the testability model, testability index even prior knowledge should be readusted and the process should be repeated until generating the optimal sensor suite that satisies system testability requirements. System knowledge such as ault inormation, sensor attribute inormation and system testability model has a great impact on the SSO results. However, at system design state, it is hard to obtain much inormation or the cost is very high, so people should not rely on the SSO results completely. The proposed model and algorithm are not obect-related and can be applied to SSO or PHM o any system. Reerences [] Testability program or electronic systems and equip-

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