Deep Learning-based Multimodal Control Interface for Human-Robot Collaboration

10th IFAC Symposium on Fault Detection, 10th IFAC Symposium on Fault Detection, Supervision and Safetyon forFault Technical Processes 10th Detection, 10th IFAC IFAC Symposium Symposium Detection, Supervision and Safetyon forFault Technical Processes Warsaw, Poland, Augustfor 29-31, 2018 Available Supervision and Safety Safety for Technical Processesonline at www.sciencedirect.com Supervision and Technical Processes Warsaw, August 10th IFACPoland, Symposium on29-31, Fault 2018 Detection, Warsaw, August 29-31, 2018 Warsaw, Poland, Poland, Augustfor 29-31, 2018 Processes Supervision and Safety Technical Warsaw, Poland, August 29-31, 2018

ScienceDirect

A A A A

IFAC PapersOnLine 51-24 (2018) 1373–1378

New New New New

Strategy of Adaptive Observer Strategy Strategy of of Adaptive Adaptive Observer Observer  Based Fault Isolation Based Fault Isolation Strategy of Adaptive Observer Based Fault Isolation   ∗∗ ∗∗ Fault Isolation HaiBased Liu ∗∗ Maiying Zhong ∗∗ Yang Liu ∗∗

Hai Liu ∗∗ Maiying Zhong ∗∗ Yang Liu ∗∗ Hai Hai Liu Liu Maiying Maiying Zhong Zhong ∗∗ Yang Yang Liu Liu ∗∗ ∗∗ ∗∗ Department of Inertia Technology and Navigation Instrumentation, Hai Liu ∗ Maiying Zhong Yang Liu Department of Inertia Technology and Navigation Instrumentation, Department of Inertia Technology and Navigation Instrumentation, Beihang University, Beijing 100191, China. DepartmentBeihang of Inertia Technology and Navigation Instrumentation, University, Beijing 100191, China. Beihang University, Beijing 100191, China. ∗ ∗∗ of Engineering Automation, Shandong ∗∗ CollegeBeihang University, Beijing 100191, China. Department ofElectrical Inertia Technology andand Navigation Instrumentation, College of Electrical Engineering and Automation, Shandong ∗∗ ∗∗ College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China (e-mail: College of Electrical Engineering and Automation, Shandong Beihang University, Beijing 100191, China. University of Science and Technology, Qingdao 266590, China (e-mail: University of Science and Technology, Qingdao 266590, China (e-mail: ∗∗ [email protected]) University of Science and Technology, Qingdao 266590, China (e-mail: College of Electrical Engineering and Automation, Shandong [email protected]) [email protected]) [email protected]) University of Science and Technology, Qingdao 266590, China (e-mail: [email protected]) Abstract: The problem of fault isolation (FI) for kind of nonlinear discrete time varying Abstract: The problem of fault isolation (FI) for for aaa kind kind of of nonlinear nonlinear discrete discrete time time varying varying Abstract: The problem of fault isolation (FI) (NDTV) systems is investigated. A bank of adaptive observers are designed for the considered Abstract: The problem of fault Aisolation (FI) for aobservers kind of nonlinear discrete time varying (NDTV) systems is investigated. bank of adaptive are designed for the considered (NDTV) systems is investigated. investigated. Aisolation bank of (FI) adaptive observers aretransformed designed forinto the considered system with different potential faults, and the isolation work is finding out (NDTV) systems is A bank of adaptive are designed for the considered Abstract: The problem of fault for aobservers kind of nonlinear discrete time varying system with with different potential faults, and the isolation work is transformed into finding out system different potential faults, and the isolation work is transformed into finding out which observer matches the current system best. The idea of reconstruction-based contribution system with different potential faults, and the isolation work is transformed into finding out (NDTV) systems is investigated. A bank of adaptive observers are designed for the considered which observer matches the current system best. The idea of reconstruction-based contribution which observer matches the system best. The idea of reconstruction-based (RBC) analysis is introduced to construct indicator variables of the observers and the one which matches the current current system best. The ideawork of for reconstruction-based contribution system with different potential faults, and the isolation isall intocontribution finding out (RBC)observer analysis is introduced introduced to construct construct indicator variables for alltransformed of the the observers observers and the one one (RBC) analysis is to indicator variables for all of and the with the largest indicator variable is declared as the isolation result. In this method, knowledge (RBC) analysis is introduced to construct indicator variables for all of the observers and the one which observer matches the currentis system best. Theisolation idea of reconstruction-based contribution with the largest indicator variable declared as the result. In this method, knowledge with the largestmodel indicator variable is while declared asidea thevariables isolation result. In this method, knowledge of the system is fully the of contribution analysis is typically datawith largest variable is declared the isolation result. this method, knowledge (RBC) analysis isindicator introduced toused, construct indicator for all ofIn the observers and the one of the thethe system model is fully fully used, while theasidea idea of contribution analysis is typically typically dataof system model is used, while the of contribution analysis is datadriven. Finally, simulation study is carried out with a nonlinear unmanned aerial vehicle (UAV) of the system model is fully used, while the idea of contribution analysis is typically datawith the largest indicator variable is declared as the isolation result. In this method, knowledge driven. Finally, simulation study is carried out with a nonlinear unmanned aerial vehicle (UAV) driven. Finally, simulation study is out with unmanned aerial vehicle (UAV) model, and the results demonstrate that the proposed method provides us with new promising driven. Finally, simulation study is carried carried with nonlinear unmanned aerial vehicle (UAV) of the system is fully used, while the idea aaofnonlinear contribution analysis isaa typically datamodel, and the model results demonstrate that theout proposed method provides us with with new promising model, and the results demonstrate that the proposed method provides us a new promising strategy for FI. model, and the results demonstrate that the proposed method provides us with a new promising driven. Finally, simulation study is carried out with a nonlinear unmanned aerial vehicle (UAV) strategy for FI. strategy for strategyand for FI. FI. results demonstrate that the proposed method provides us with a new promising model, © 2018, IFACthe (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: fault adaptive observer, contribution analysis, nonlinear system. strategy for FI. isolation, Keywords: fault isolation, adaptive adaptive observer, observer, contribution contribution analysis, analysis, nonlinear nonlinear system. system. Keywords: fault fault isolation, isolation, Keywords: adaptive observer, contribution analysis, nonlinear system. Keywords: fault isolation, adaptive observer, contribution analysis, nonlinear 1. INTRODUCTION or filters are designed for aa system. considered set of and 1. INTRODUCTION INTRODUCTION or filters are designed for set of faults faults and 1. or filters are designed for aa considered considered set faults FI is accomplished by finding out which or 1. INTRODUCTION or filters are designedbyforfinding considered set of ofobserver faults and and FI is accomplished out which observer or FI is accomplished by finding out which observer or filter matches the current system best. Usually, residual To fulfill the increasing demands on safety and reliability FI is accomplished by finding out which observer or 1. INTRODUCTION or filters are designed for a considered set of faults and filter matches the current system best. Usually, residual To fulfill fulfill the the increasing increasing demands demands on on safety safety and and reliability reliability filter matches the current system best. Usually, residual evaluation function is adopted as the indicator variable for To for modern industrial systems, fault diagnosis becomes a filter matches the current system best. Usually, residual FI is accomplished by finding out which observer or To theindustrial increasingsystems, demandsfault on safety andbecomes reliability function is adopted as the indicator variable for for fulfill modern diagnosis a evaluation evaluation function is adopted as the indicator variable for FI. However, due to the influence of disturbance, finding for modern industrial systems, fault diagnosis becomes a vital issue, especially for these safety critical systems. In evaluation function is adopted as the indicator variable for filter matches the current system best. Usually, residual for modern industrial systems, fault diagnosis becomes a To theespecially increasing on safety andsystems. reliability However, due to the influence of disturbance, finding vitalfulfill issue, fordemands these safety safety critical In FI. FI. However, due influence of disturbance, finding the best matching one is not an task. vital issue, especially for these critical systems. In recent years, there has been research activity FI. However, due to toisthe the influence ofeasy disturbance, finding evaluation function adopted as the indicator variable for vital issue, especially for thesesignificant safety critical systems. Ina out for modern industrial systems, fault diagnosis becomes out the best matching one is not an easy task. recent years, there has been significant research activity out the best matching one is not an easy task. recent years, there has been significant research activity in design and analysis of fault diagnosis schemes, see Ding out the best matching one is not an easy task. FI. However, due to the influence of disturbance, finding recent years, there has been significant research activity vital issue, especially for these safety critical systems. In Data-driven fault diagnosis methods have drawn increasin design design and and analysis analysis of of fault fault diagnosis diagnosis schemes, schemes, see see Ding Ding Data-driven fault diagnosis methods have drawn increasin (2013); Yin al. (2016); Zhou et al. (2016); Zhong et al. the best fault matching one ismethods not an shown easy in design andet analysis fault diagnosis schemes, see Ding recent years, there hasofbeen significant research activity Data-driven diagnosis have drawn increasing attention in recent years and strong ability (2013); Yin et al. (2016); Zhou et al. (2016); Zhong et al. out Data-driven fault diagnosis methods havetask. drawn increasing attention in recent years and shown strong ability (2013); Yin et al. (2016); Zhou et al. (2016); Zhong et al. (2016, 2017); Hu et al. (2017); Naderi and Khorasani (2013); Yin et al. (2016); Zhou et al. (2016); Zhong et al. in design and analysis of fault diagnosis schemes, see Ding ing ing attention in recent years and shown strong ability in dealing with FI problems, see Alcala and Qin (2011); (2016, 2017); Hu et al. (2017); Naderi and Khorasani attention in recent years and shown strong ability Data-driven fault diagnosis methods have drawn increasin dealing with FI problems, see Alcala and Qin (2011); (2016, 2017); Hu et al. (2017); Naderi and Khorasani (2017) and As stated in Ding (2013), (2016, 2017); et therein. al. Zhou (2017); Naderi and Khorasani (2013); Yinreferences et Hu al. (2016); etis al. (2016); Zhong et al. in dealing with FI problems, see Alcala and Qin (2011); Naderi and Khorasani (2017); Delpha et al. (2017) and ref(2017) and references therein. As is stated in Ding (2013), in dealing with FI problems, see Alcala and Qin (2011); ing attention in recent years and shown strong ability Naderi and Khorasani (2017); Delpha et al. (2017) and ref(2017) and references therein. As stated in (2013), the overall concept of fault diagnosis consists of three es(2017) and references therein. As is isNaderi stated in Ding Ding (2013), (2016, 2017); Hu et al. (2017); and Khorasani Naderi and Khorasani (2017); Delpha et al. (2017) and references therein. The most familiar data-driven FI method the overall concept of fault diagnosis consists of three esNaderi and Khorasani (2017); Delpha et al. (2017) and refin dealing with FI problems, see Alcala and Qin (2011); erences therein. The most familiar data-driven FI method the overall concept of fault diagnosis consists of three essential tasks: fault detection (FD), fault isolation (FI) and the overall concept of therein. fault diagnosis consists of three es- are (2017) and references As isfault stated in Ding (2013), erences therein. The most familiar data-driven FI method the contribution plots and the reconstruction-based sential tasks: fault detection (FD), isolation (FI) and erences therein. The most familiar data-driven FI method Naderi and Khorasani (2017); Delpha et al. (2017) and refare the contribution plots and the reconstruction-based sential tasks: fault (FD), fault isolation (FI) fault identification. The problem FI lies in localization sential tasks: fault detection detection (FD),of isolation (FI) and and the concept of fault diagnosis of three es- are are the therein. contribution plotsfamiliar and the reconstruction-based contribution (RBC) analysis. In contribution plots methfaultoverall identification. The problem offault FIconsists lies in localization localization the contribution plots and the reconstruction-based erences The most data-driven FI method contribution (RBC) analysis. In contribution plots methfault identification. The problem of FI lies in or classification of different faults. When compared fault identification. The problem FI lies in localization sential tasks: fault (FD), isolation (FI)with and contribution (RBC) analysis. In contribution plots methods, it is suggested faulty should have high or classification classification of detection different faults.offault When compared with contribution (RBC)that analysis. Invariables contribution plots methare the contribution plots and the reconstruction-based ods, it is suggested that faulty variables should have high or of different faults. When compared with FD and single fault estimation, FI requires an additional or classification of different faults. When compared with fault identification. The problem of FI lies in localization ods, it is suggested that faulty variables should have high contributions to the FD index, thus the fault is located. FD and single fault estimation, FI requires an additional ods, it is suggested that faulty variables should have high contribution (RBC) analysis. In contribution plots methcontributions to the FD index, thus the fault is located. FD and single fault estimation, FI requires an additional analysis of the system behavior to distinguish the effects FD and single fault estimation, FI requires an additional or classification of different faults. When compared with Latter, contributions to the FD index, thus the fault is located. to solve the fault smearing problem that caused analysis of the system behavior to distinguish the effects contributions to the FD index, thus the fault is located. ods, it is suggested that faulty variables should have high Latter, to solve the fault smearing problem that caused analysis of system behavior to distinguish effects of different faults and thus is much more difficult. analysis of the the system behavior to requires distinguish the effects Latter, FD and single fault FI an the additional Latter, to solve solve the fault smearing problem that caused by the contribution method, the so-called apof different different faults andestimation, thus is much much more difficult. difficult. to fault smearing problem caused contributions to the the plots FD index, thus the faultthat isRBC located. by the contribution plots method, the so-called RBC apof faults and thus is more of different faults and thus is much more difficult. analysis ofthe the system behavior to distinguish thecan effects by the contribution plots method, the so-called RBC approach is proposed in Alcala and Qin (2009) and generRoughly, existing model-based FI methods be by the contribution plots method, the so-called RBC apLatter, to solve the fault smearing problem that caused proach is proposed in Alcala and Qin (2009) and generRoughly, the existing model-based FI methods can be of different faults and thus is much more difficult. proach is proposed in Alcala and Qin (2009) and generalized in Alcala and Qin (2011). Accurate isolation result Roughly, the existing model-based FI methods can be divided into two categories. The first kind of methods proach is proposed in Alcala and Qin (2009) and generby the contribution plots method, the so-called RBC apRoughly, the existing model-based FI methods can be in Alcala and Qin (2011). Accurate isolation result divided into into two two categories. categories. The The first first kind kind of of methods methods alized alized in Alcala and Qin (2011). Accurate isolation result is guaranteed in the RBC method with large fault magdivided is based on decoupling techniques so that one-to-one alized in Alcala and Qin (2011). Accurate isolation result proach is proposed in Alcala and Qin (2009) and generdivided into two categories. The first kind of methods Roughly, the existing model-based FI methods can be is guaranteed in the RBC method with large fault magis based based on on decoupling decoupling techniques techniques so so that that one-to-one one-to-one nitude. is guaranteed inand the RBC(2011). method with large large fault result magdata-driven fault diagnosis methods also is mappings from faults to components of the residual are guaranteed the RBC method with fault magalized inHowever, Alcalain Qin Accurate isolation is basedinto on decoupling techniques so that divided two categories. The first kind ofone-to-one methods nitude. However, data-driven fault diagnosis methods also mappings from faults to components of the residual are is nitude. However, data-driven fault diagnosis methods also suffer problems. For example, signatures used in conmappings from faults to components of the residual are achieved, thus each component of the residual is only nitude. However, data-driven fault diagnosis methods also is guaranteed in the RBC method with large fault magmappings from faults to components of the residual are is based on decoupling techniques so residual that one-to-one suffer problems. For example, fault signatures used in conachieved, thus each component of the is only suffer problems. For example, fault signatures used in contribution or RBC calculation are not rigorously defined, achieved, thus each component of the residual is only sensitive to a corresponding fault, see Persis and Isidori suffer problems. For example, signatures used in connitude. However, data-driven fault diagnosis methods also achieved, thus each component of the residual is only mappings from faults to components of the residual are or calculation are not rigorously defined, sensitive to to aa corresponding corresponding fault, fault, see see Persis Persis and and Isidori Isidori tribution tribution or RBC RBC calculation are not rigorously defined, because propagation of faults in dynamic systems leads to sensitive (2001); Meskin and Khorasani (2009). Though this kind of tribution or RBC calculation are not rigorously defined, suffer problems. For example, fault signatures used in consensitive to a corresponding fault, see Persis and Isidori achieved, thus each component of the residual is only because propagation of faults in dynamic systems leads to (2001); Meskin Meskin and and Khorasani Khorasani (2009). (2009). Though Though this this kind kind of of because propagation of faults in dynamic systems leads to complicated fault signatures and data-driven approaches (2001); methods is theoretically graceful, strict design conditions because propagation of faults in dynamic systems leads to tribution or RBC calculation are not rigorously defined, (2001); Meskin and Khorasani (2009). this kind of complicated fault signatures and data-driven approaches sensitive to theoretically a corresponding fault, seeThough Persis and Isidori methods is graceful, strict design conditions complicated fault signatures and data-driven approaches are hardly able to define rigorous fault signatures without methods is theoretically graceful, strict design conditions limit their applications. The second category is the model complicated fault signatures and data-driven approaches because propagation of faults in dynamic systems leads to methods is theoretically graceful, strict design conditions (2001); Meskin and Khorasani (2009). Thoughisthis of are hardly able to define rigorous fault signatures without limit their their applications. The second second category thekind model are hardly able to define rigorous fault signatures without adequate faulty data. limit applications. The category is the model matching scheme, see for instance, Ma and Yang (2013); are hardly able to define rigorous fault signatures without complicated fault signatures and data-driven approaches limit their applications. The second category is the model methods is theoretically graceful, strict design conditions adequate faulty data. matching scheme, scheme, see see for instance, instance, Ma Ma and and Yang Yang (2013); (2013); adequate faulty data. matching Du and Mhaskar (2014); Pourbabaee et al. (2016); Keliris faulty data. are this hardly able to to definethe rigorous faultofsignatures matching scheme, see for forThe instance, and Yang limit their applications. second Ma category is the(2013); model adequate In study, solve problem FI for aa without kind of Du and Mhaskar (2014); Pourbabaee et al. (2016); Keliris In this study, to solve the problem of FI for kind of Du and Mhaskar (2014); Pourbabaee et al. (2016); Keliris et al. (2017). In this kind of methods, a group of observers adequate faulty data. Du and Mhaskar (2014); et al. (2016); Keliris nonlinear matching scheme, see forPourbabaee instance, Ma and Yang (2013); In this study, to solve the problem of FI for a kind of discrete time varying (NDTV) systems, a bank et al. (2017). In this kind of methods, a group of observers In this study, to solve the problem of FI for a kind of nonlinear discrete time varying (NDTV) systems, a bank et al. (2017). In this kind of methods, a group of observers et al. (2017). In this kind of methods, a group of observers Du and Mhaskar (2014); Pourbabaee et al. (2016); Keliris nonlinear nonlinear discrete time varying (NDTV) systems, a bank of adaptive observers are designed. Then, inspired by the discrete time varying (NDTV) systems, a bank In adaptive this study, to solvearethe problemThen, of FIinspired for a kind of  This work is partially supported by the National Natural Science of observers designed. by the  etThis al. (2017). In this kind of methods, a groupNatural of observers of adaptive observers designed. Then, inspired the work about how faults make contribution to filter work is partially supported by the National Science of adaptive observers are designed. Then,systems, inspired byinnothe  nonlinear discrete timeare varying (NDTV) aby bank work about how faults make contribution to filter innoFoundation of China (Grant No. 61333005, 61733009, 61703244), ReThis work is partially supported by the National Natural Science  This workofisChina partially supported by the National Science work about how make contribution to filter Foundation (Grant No. 61333005, 61733009,Natural 61703244), Revations in Zhang and Basseville (2014), of RBC work about how faults faults make contribution toidea filter innoof adaptive observers are designed. Then,the inspired byinnothe search Fundof the Taishan Scholar Project of Shangdong Province Foundation offor China (Grant No. No. 61333005, 61733009, 61703244), Revations in Zhang and Basseville (2014), the idea of RBC  Foundation (Grant 61333005, 61733009, 61703244), Research the Taishan Scholar Project of Shangdong Province This Fund work for isChina partially supported by the National Natural Science vations in Zhang and Basseville (2014), the idea of RBC is employed to construct indicator variables. Finally, FI is vations in Zhang and Basseville (2014), the idea of RBC work about how faults make contribution to filter innoof China search Fund for the Taishan Scholar Project of Shangdong Province is employed to construct indicator variables. Finally, FI is search Fundoffor the Taishan Scholar Project of Shangdong Province of China Foundation China (Grant No. 61333005, 61733009, 61703244), Reis employed to construct indicator variables. Finally, FI is is employed to construct indicator variables. Finally, FI is of China vations in Zhang and Basseville (2014), the idea of RBC of China search Fund for the Taishan Scholar Project of Shangdong Province is employed to construct indicator variables. Finally, FI is Copyright 1373 of China © 2018 IFAC ∗ ∗ ∗ ∗

2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2018, 2018 IFAC 1373Hosting by Elsevier Ltd. All rights reserved. Copyright ©under 2018 responsibility IFAC 1373Control. Peer review© of International Federation of Automatic Copyright 2018 IFAC 1373 10.1016/j.ifacol.2018.09.555 Copyright © 2018 IFAC 1373

IFAC SAFEPROCESS 2018 1374 Warsaw, Poland, August 29-31, 2018

Hai Liu et al. / IFAC PapersOnLine 51-24 (2018) 1373–1378

accomplished by finding out the observer with the largest indicator variable. When compared with the traditional RBC method, advantage of the proposed method lies in the fact that fault signatures and fault estimates applied to construct indicator variables are obtained from the corresponding adaptive observers, with knowledge of the model being fully used. The rest of the paper is organized as follows. In section II, problem statement is presented. Design of the adaptive observer and the new idea for FI is detailed in section III. In section IV, simulation studies are carried out with a nonlinear unmanned aerial vehicle (UAV) model. Finally, conclusions are made in Section V.

where γ is a given constant, x ˜0 is the initial estimation error and (5) η(k) = x ˜(k) − Υ(k)f˜j (k) ˜ ˆ where x ˜(k) = x(k) − x ˆ(k), fj (k) = fj (k) − fj (k). While in Zhang (2002), linear systems with zero mean noises is considered. After the adaptive observers are established and employed, the rest work of FI is to determine which observer matches the current system best. Usually, as is presented in Ma and Yang (2013); Du and Mhaskar (2014); Keliris et al. (2017), residual evaluation functions such as

2. PROBLEM STATEMENT Consider a class of NDTV systems as follows,  x(k + 1) = A(x(k)) + B(x(k))u(k) + Bw (x(k))w(k) +Bf,j (k)fj (k) (1) y(k) = C(k)x(k) + v(k) + Df,j (k)fj (k) where x(k) ∈ Rn is state, u(k) ∈ Rp is control input, y(k) ∈ Rq is measurement output, w(k) ∈ Rm and v(k) ∈ Rq are disturbance and measurement noise, respectively, and fj (k) ∈ R1 is fault that belongs to a known fault set F = {f1 , f2 , · · · , fl }. Without loss of generality, w(k), v(k) and fj (k) are assumed to be l2 [0, N ]-norm bounded and fj (k) is assumed to be slowly time varying. In the above nonlinear system (1), A(·), B(·) and Bw (·) are smooth functions with respect to x(k). For each fault fj , a nonlinear adaptive observer is constructed as follows.  x ˆ(k + 1) = A(ˆ x(k)) + B(ˆ x(k))u(k) + Bf,j (k)fˆj (k) +K(k)rj (k) + ω(k) (2)  ˆ rj (k) = y(k) − C(k)ˆ x(k) − Df,j (k)fj (k)

  fˆ (k + 1) = fˆj (k) + µ(k)ΩTj (k)rj (k)   j   ω(k) = Υ(k + 1)(fˆj (k + 1) − fˆj (k)) (3) Ωj (k) = C(k)Υ(k) + Df,j (k)    (k) Υ(k + 1) = (A(k) − K(k)C(k))Υ(k) + B f,j   −K(k)Df,j (k) where variables with the superscript ˆ denote their estimates, rj (k) is residual of the j th adaptive observer and ω(k) is employed to compensate the estimation error made by fˆj (k), Υ(k) ∈ Rn , Ωj (k) ∈ Rq are bounded vector sequences obtained by linearly filtering Bf,j (k) and Df,j (k). Usually, Υ(0) = 0 and fˆj (0)) are adopted in applications. Besides, the scalar sequence µ(k), system matrix A(k) and observer gain K(k) are designing parameters that will be specified in the next section. Note that the proposed nonlinear adaptive observer is an extension of the one proposed in Zhang (2002), the ability of simultaneous state and fault estimation is desired. Differently, to deal with norm bounded disturbance, it is desired that the observer gain K(k) is selected such that the following performance specification (4) is fulfilled: sup x ˜0 ,w,v∈l2

k

k 

Jr,j (k) =

T T i=0 η (i)C (i)C(i)η(i) ≤ γ 2 (4)  k−1 x ˜T0 x ˜0 + i=0 (wT (i)w(i) + v T (i)v(i))

rjT (i)rj (i),

j = 1, 2, ..., l

(6)

i=k−N +1

are adopted(for the discrete time case), where N is the length of a sliding window. The basic idea to use Jr,j (k) is that in the matched case, Jr,j (k) keeps small after the fault occurs, while for other mismatched ones, Jr,j (k) grows quickly and exceed a threshold. However, Jr,j (k) is usually ineffective because the little difference between the matched and unmatched case in Jr,j (k) is often masked by the influence of disturbance. Besides, the fault estimates obtained from the observers are improper for FI because fault estimates of different observers may response to a same fault simultaneously. Therefore, the purpose of this investigation consists in designing of a new indicator variable so that fault can be isolated effectively. 3. MAIN RESULTS 3.1 Adaptive observer design for NDTV systems This subsection is dedicated to adaptive observer design. As the problem of FI is not considered yet, the subscript j is temporarily omitted for easy presentation. First, the following assumption and lemmas are introduced. Assumption 1. For all k ≥ 0, there exits a constant  > 0 and an integer N > 0 such that the following inequality holds: 1 N

k+N −1 i=k

µ(i)ΩT (i)C T (i)C(i)Ω(i) ≥ I

where µ(k) > 0 is a scalar gain sequence such that  (7)  µ(k)Ω(k) ≤ 1 with  ·  denotes the matrix spectral norm. Lemma 1. (Guyader and Zhang, 2003, Lemma 2) For all k ≥ 0, let φ(k) ∈ Rq×l be a matrix sequence such that φ(k) ≤ 1. If there exist a real constant  > 0 and an integer N > 0 such that the following inequalities hold: 1 N

k+N −1 i=k

φT (i)φ(i) ≥ I

then the linear time varying system z(k) = (I − φT (k)φ(k))z(k) is exponentially stable.

1374

IFAC SAFEPROCESS 2018 Warsaw, Poland, August 29-31, 2018

Hai Liu et al. / IFAC PapersOnLine 51-24 (2018) 1373–1378

η(k + 1) = (A(k) − K(k)C(k))η(k) + Bw (k)w(k)

Lemma 2. (Hassibi et al., 1996, Lemma 7) For the following dynamics system 

x ˜(k + 1) = (A(k) − K(k)C(k))˜ x(k) +Bw (k)w(k) − K(k)v(k) z˜(k) = T (k)˜ x(k) and a given constant γ > 0, the H∞ performance sup

˜T (k)˜ z (k) i=0 z

x ˜T0 x ˜0 + is achieved with x ˜0 ,w(k),v(k)∈l2

k

k−1

T T i=0 (w (i)w(i) + v (i)v(i))

(8)

− K(k)v(k)

On the other hand, when the fault is slowly time varying, f˜(k + 1) − f˜(k) ≈ fˆ(k) − fˆ(k + 1)

= −µ(k)ΩT (k)r(k) where r(k) = C(k)˜ x(k) + Df (k)f˜(k) + v(k). Use (3) and (5) again,

≤ γ2

−γ 2 I + T (k)P (k)T T (k) < 0 I + C(k)P˜ (k)C T (k) > 0 where x ˜0 is the initial guess error, P˜ −1 (k) = P −1 (k) − γ −2 T T (k)T (k), P (0) = I, and P (k) satisfies the Riccati recursion T (k) P (k + 1) = A(k)P (k)AT (k) + Bw (k)Bw

− A(k)P (k)M (k)P (k)AT (k)

    C(k) M (k) = C T (k) T T (k) Re−1 (k) T (k)       T I 0 C(k) T P (k) C (k) T (k) + Re (k) = T (k) 0 −γ −2 I

Then we begin to design adaptive observer for NDTV system (1), the following Taylor expansions are considered. A(x(k)) + B(x(k))u(k) = A(ˆ x(k)) + B(ˆ x(k))u(k) + A(k)(x(k) − x ˆ(k)) + ...

where

(12)

If (A(k) − K(k)C(k)) is stable, η(k) will be bounded in a region near zero as w(k), v(k) are bounded.

K(k) = A(k)P˜ (k)C T (k)(C(k)P˜ (k)C T (k) + I)−1 if and only if

where

1375

f˜(k + 1) = f˜(k) − µ(k)ΩT (k)C(k)(η(k) + Υ(k)f˜(k)) − µ(k)ΩT (k)Df (k)f˜(k) − µ(k)ΩT (k)v(k) = (I − µ(k)ΩT (k)Ω(k))f˜(k)

− µ(k)ΩT (k)C(k)η(k) − µ(k)ΩT (k)v(k)

Combining Assumption 1 and Lemma 1, it is concluded that the homogeneous part of (13) is stable. Thus the adaptive observer is established. Furthermore, in observation of the fact that the system (12)has the same form with (8) in Lemma 2, the robust performance specification (4) is directly achieved if the observer gain K(k) is calculated as is presented in Lemma 2. Based on the above analysis, the adaptive observer for NDTV system (1) is presented in the following proposition. Proposition 3. Under Assumption 1, extended adaptive observer for NDTV system (1) is constructed as (2) and (3), where A(k) and Bw (k) are defined in (9) and(10), respectively, and µ(k) can be easily selected according to the inequality (7). Further more, for a given constant γ, if the observer gain K(k) is chosen as the one presented in Lemma 2, then the H∞ performance (4) is fulfilled. 3.2 Contribution analysis for FI

Bw (x(k)) = Bw (k) + ...

  ∂ (A(x(k)) + B(x(k))u(k)) (9) A(k) = ∂x(k) x(k)=ˆ x(k)

x(k)) (10) Bw (k) = Bw (ˆ Subtract (2) from (1), with the higher order terms of the Taylor expansions being neglected, it is easy to get the error dynamic system as follows.

As is mentioned before, the traditional residual evaluation function Jr,j (k) usually fails to accomplish the isolation work, a more effective indicator variable is desired. Inspired from Zhang and Basseville (2014) about how faults make contribution to filter innovations, the idea of RBC proposed in Alcala and Qin (2009) is adopted for FI in a model-based way with the proposed adaptive observers. First, the following lemma is introduced. Lemma 4. For the following error dynamic system 

x ˜(k + 1) = (A(k) − K(k)C(k))˜ x(k) + Bw (k)w(k) − K(k)v(k) + (Bf (k) − K(k)Df (k))f˜(k)

− ω(k) (11) Introduce η(k) defined in (5) and substitute it into (11), it is straight forward that η(k + 1) = (A(k) − K(k)C(k))η(k) + N (k)f˜(k) + Υ(k + 1)(fˆ(k + 1) − fˆ(k)) − ω(k)

(13)

x ˜(k + 1) = (A(k) − K(k)C(k))˜ x(k) + Bw (k)w(k) −K(k)v(k) + (Bf,τ (k) − K(k)Df,τ (k))fτ (k) y˜(k) = C(k)˜ x(k) + v(k) + Df,τ (k)fτ (k)

when fτ (k) is slowly time varying, it is concluded that y˜(k) = y˜0 (k) + Ωτ (k)fτ (k) where y˜0 (k) is y˜(k) in the fault free case, and Ωτ (k) is defined in (3).

+ Bw (k)w(k) − K(k)v(k) where N (k) = (A(k) − K(k)C(k))Υ(k) + Bf (k) − K(k)Df (k) − Υ(k + 1). Together with (3), it yields

The proof follows the same way as the one presented in (Zhang and Basseville, 2014, Proof of Proposition1), thus is omitted. It is observed that Ωτ (k) plays the role of fault direction in y˜(k).

1375

IFAC SAFEPROCESS 2018 1376 Warsaw, Poland, August 29-31, 2018

Hai Liu et al. / IFAC PapersOnLine 51-24 (2018) 1373–1378

Now, the idea of RBC is introduced. In Alcala and Qin (2009), RBCj (k) is constructed as RBCj (k) = Ωj fˆj (k)2M

(14)

to locate the faulty component, where Ωj is a artificial fault signature of fj , fˆj (k) is reconstructed to minimize some specific index, and the matrix M is determined by the index that is chosen. Then, the fault is isolated as the one with the largest RBCj (k). Similarly, in this study, the new indicator variables are constructed as follows. Jf,j (k) =

k 

fˆjT (i)ΩTj (i)Ωj (i)fˆj (i),

i=k−N +1

j = 1, 2, ..., l

(15)

where fˆj (t) and Ωj (t) are obtained from the corresponding adaptive observers directly. It is expected that when fault fτ occurs, Jf,τ (k) will have the largest value among Jf,j (k), j = 1, 2, ..., l, that is, Jf,τ (k) ≥ Jf,j (k),

j = 1, 2, ..., l

(16)

When fτ occurs and the adaptive observer designed for fj is employed, following a similar procedure in Proof of Proposition 3, the error dynamic system is obtained as follows.   η(k + 1) = (A(k) − K(k)C(k))η(k) + Bw (k)w(k) −K(k)v(k) + E(k)fτ (k) (17)  rj (k) = C(k)η(k) + v(k) + Ωj (k)f˜(k) + F (k)fτ (k) where E(k) = Bf,τ (k) − K(k)Df,τ (k) − (Bf,j (k) − K(k)Df,j (k)), F (k) = Df,τ (k) − Df,j (k). Compared with the error dynamic system (12) of the matched case, it is concluded that Jr,j (k) ≥ Jr,τ (k)

(18)

N is reasonable to expect that i=k−N +1 2rjT (k)Ωj (k)fˆj (k) is relatively small with a large N . If it is the case that Jy˜(k) is dominated by the first two terms, that is, Jy˜(k) ≈ Jr,j (k) + Jf,j (k) ≈ Jr,τ (k) + Jf,τ (k)

then together with (18), we get (16) straightforwardly. Based on the above analysis, the following proposition is proposed. Proposition 5. With a group of adaptive observers defined in (2) and (3) being applied, it is concluded that (16) holds true when fτ occurs and the approximation (20) is valid, where Jr,j (k) and Jf,j (k) are defined in (6) and (15), respectively. Finally, when a fault is detected, the FI result is declared as fj ∗ , where j ∗ = arg max Jf,j (k), j

4. SIMULATION STUDY 4.1 Description of UAV model A three degree-of-freedom model of a fixed-wing UAV is employed in the simulation study. The model is introduced from Frost and Bowles (1984) and presented as follows.  1    V˙ = (P cos α − D − mg sin(θ − α))  m    −w˙ x cos(θ − α) − w˙ z sin(θ − α)    1   (−L + P sin α + mg cos(θ − α)) + q  α˙ = mV sin(θ − α) cos(θ − α)  −w˙ x + w˙ z    V V   My  ˙  θ = q q ˙ =   Iy    ˙ H = V sin(θ − α) + wz

On the other hand, according to Lemma 4, rj (k) in (17) can be rewritten as rj (k) = C(k)η0 (k) + v(k) + Ωj (k)f˜(k) + Ωτ (k)fτ (k) − Ωj (k)fτ (k)

= y˜(k) − Ωj (k)fˆj (k)

where η0 (k) is η(k) in (17) of the fault free case. Then we have Jy˜(k) = Jr,j (k) + Jf,j (k) +

N 

2rjT (k)Ωj (k)fˆj (k)

i=k−N +1

(19)

for j = 1, ..., l. Different from Jr,j (k) and Jf,j (k), it is observed that the third term in (19) is not quadric. Thus it

j = 1, 2, ..., l

Remark 6. Jf,j (k) but not Jr,j (k) is adopted for FI in this study because for system (17), Jr,j (k) is usually dominated by the contribution of disturbance w(k) and v(k), especially in cases of small or incipient fault. Thus (Jr,j (k) − Jr,τ (k))/Jr,τ (k) is too small and the little difference between Jr,j (k) and Jr,τ (k) are ineffective to isolate the fault. On the contrary, Jf,j (k) mainly contains the energy of the fault and is much smaller than Jr,j (k), thus (Jf,τ (k) − Jf,j (k))/Jf,j (k) is large enough. Therefore, Jf,j (k) is more sensitive to fault when compared with Jr,j (k).

in most of the situations, because the additional terms E(k)fτ (k) and F (k)fτ (k) make additional contribution to Jr,j (k) in the mismatched case.

= C(k)η0 (k) + v(k) + Ωτ (k)fτ (k) − Ωj (k)(fτ (k) − f˜(k))

(20)

where V is true air speed (m/sec), α is angle of attack (rad), q is pitch rate (rad/sec), θ is pitch angle (rad), H is altitude (m), Iy is vehicle rotational inertia, w˙ x , w˙ z are wind gradients in horizonal and vertical directions, respectively, and wz is the wind speed in vertical direction. P , D, L and My are Propulsion, air resistance, lift and pitching moment, respectively. Set the state vector x(t) = [V α q θ H]T , the disturbance vector w(t) = [wz w˙ x w˙ z ]T , and the input vector u(t) = [δe δp ]T , where δe and δp are elevator deflection and the throttle setting, respectively. The UAV model in a state space form is obtained.

1376

wx (m/s)

IFAC SAFEPROCESS 2018 Warsaw, Poland, August 29-31, 2018

Hai Liu et al. / IFAC PapersOnLine 51-24 (2018) 1373–1378

2

50

1

45

0

40

−1

35

−2

30 0

50

100

150

1377

normalized Jf,Ele(k) normalized Jf,Thr(k) normalized J

(k)

f,Pit

normalized Jf,Gyr(k) Threshold

200

wz (m/s)

25 2

20

1

15

0

10

−1

5

−2

0

50

100 Time (s)

150

0

200

Fig. 1. Wind speed in horizonal and vertical directions

20

40

60

80

100 120 Time(s)

140

160

180

200

140

160

180

200

140

160

180

200

Fig. 2. FI result of Scenario I

Table 1. Noise Characteristics of Sensors 140

σ



Vm 0.2 m/s

qm 0.05 rad/s

θm 0.05 rad

normalized J

Hm 2m

x(t) ˙ = F (x(t)) + B(x(t))u(t) + Bw (x(t))w(t) y(t) = Cx(t) + v(t)

normalized J

(k)

f,Ele

(k)

f,Thr

(k)

f,Pit

normalized Jf,Gyr(k)

100

Threshold

80

where y(t) = [Vm qm θm Hm ]T are sensor measurements available in the feed-back control loop of the FCS, and v(t) is the sensor noise. Then the model is discretized. With actuator faults and sensor faults being considered, a nonlinear discrete time UAV model in the form of (1) is obtained. Simulations are carried out for the UAV model under closed-loop control. All parameters of the model are coincide with a real UAV and aerodynamic coefficients are identified by wind tunnel test. The simulation time is 200s, with the sampling time Ts = 0.02s. Turbulent condition is considered and wind speeds in horizonal and vertical directions are shown in Fig. 1. Standard deviations of Sensor noises are presented in Table 1. The initial condition ˆ0 = [ 24 0 0 0 200 ]T . is x0 = [ 24.2 0.1 0.2 0.01 201 ]T , x The length of the sliding window is N = 100.

60 40 20 0

20

40

60

80

100 120 Time(s)

Fig. 3. FI result of Scenario II 80 normalized Jf,Ele(k) normalized Jf,Thr(k)

70

normalized Jf,Pit(k) normalized J

60

(k)

f,Gyr

Threshold 50 40

4.2 FI results

30

Four different fault scenarios listed in Table 2 are considered as representations of actuator and sensor faults, where the subscript 0 and f stand for the nominal value and faulty value, respectively. A group of adaptive observers correspond to these four faults are constructed, and Jf,j (k) correspond to those four faults are calculated. Since different fault estimates fˆj (k) are affected by disturbance with different levels, Jf,j (k)s are normalized before employed for FI, specifically, J¯f,j (k) =

normalized J

120

Jf,j (k) 0 (k)) , E(Jf,j

j = 1, · · · , l

0 where E(Jf,j (k)) is the empirical mean of Jf,j (k) obtained from historical fault free data. Furthermore, to illustrate the different behaviors of J¯f,j (k) before and after fault occurs, a threshold is also introduced. As is depicted in Fig. 2, J¯f,T hr (k) increase quickly after the throttle fault occurs, while J¯f,Ele (k), J¯f,P it (k) and J¯f,Gyr (k) show no response to the fault and keep small. Thus the throttle fault is successfully isolated.

20 10 0

20

40

60

80

100 120 Time(s)

Fig. 4. FI result of Scenario III FI results of Scenario II and Scenario III are demonstrated in Fig. 3 and Fig. 4, respectively. In these two scenarios, both J¯f,Ele (k) and J¯f,P it (k) grow quickly after fault occurs and show little difference from each other. Therefore, it is concluded that the elevator fault and pitot fault are hardly isolable by the proposed method. Meanwhile, it is observed that there is a impulse of J¯f,T hr (k) in Fig. 4 at the instant when the pitot fault occurs. Reasons of these phenomenons need further studies. The authors expect that studies about fault isolability analysis may help us to answer these questions. As is depicted in Fig. 5, time varying fault of the rate gyro is also isolated successfully, which shows the ability of the proposed method in dealing with the time varying fault.

1377

IFAC SAFEPROCESS 2018 1378 Warsaw, Poland, August 29-31, 2018

Hai Liu et al. / IFAC PapersOnLine 51-24 (2018) 1373–1378

Table 2. Fault scenarios Scenarios I II III IV

Component Throttle Elevator Pitot tube Rate gyro

Fault time 100s 100s 100s 100s

60 normalized Jf,Ele(k) normalized Jf,Thr(k)

50

normalized Jf,Pit(k) normalized J

(k)

f,Gyr

Threshold

40

30

20

10

0

20

40

60

80

100 120 Time(s)

140

160

180

200

Fig. 5. FI result of Scenario IV 5. CONCLUSION A new strategy of adaptive observer based FI is proposed in this study. Existing result about adaptive observer design is extended to a kind of NDTV systems, then the idea of RBC is employed to construct the indicator variable for FI. The proposed method is a combinative application of model-based and data-driven approaches, and provides us with a new promising way to deal with fault detection and isolation problems. On the other hand, several problems are still unclear. For example, how to choose the observer gain so that the best isolation performance can be achieved, and wether the fault signature will be changed by the closed control loop. Further studies about isolability analysis should be carried out to make this study more completed. REFERENCES Alcala, C.F. and Qin, S.J. (2011). Analysis and generalization of fault diagnosis methods for process monitoring. Journal of Process Control, 21, 322–330. Alcala, C.F. and Qin, S.J. (2009). Reconstruction-based contribution for process monitoring. Automatica, 45, 1593–1600. Delpha, C., Diallo, D., and Youssef, A. (2017). Kullbackleibler divergence for fault estimation and isolation: Application to gamma distributed data. Mechanical Systems and Signal Processing, 93, 118–135. Ding, S.X. (2013). Model-based fault diagnosis techniques: design schemes, algorithms, and tools. Springer, Berlin. Du, M. and Mhaskar, P. (2014). Isolation and handling of sensor faults in nonlinear systems. Automatica, 50, 1066–1074. Frost, W. and Bowles, R.L. (1984). Wind shear terms in the equations of aircraft motion. Journal of Aircraft, 21(11), 866–872. Guyader, A. and Zhang, Q.H. (2003). Adaptive observer for discrete time linear time varying system. In Proceedings of the 13th Symposium on System Identification, Rotterdam, Holland, 1743–1748.

Fault model δp,f = 0.7δp,0 δe,f = δe,0 + 1◦ Vm,f = 1.05Vm,0 qm,f = qm,0 − 0.05 sin(0.1πt)rad/s

Hassibi, B., Sayed, A.H., and Kailath, T. (1996). Linear estimation in krein spaces. ii. applications. IEEE Transactions on Automatic Control, 41(1), 34–49. Hu, Y., Palme, T., and Fink, O. (2017). Fault detection based on signal reconstruction with auto-associative extreme learning machines. Engineering Applications of Artificial Intelligence, 57, 105–117. Keliris, C., Polycarpou, M.M., and Parisini, T. (2017). An integrated learning and filtering approach for fault diagnosis of a class of nonlinear dynamical systems. IEEE Transactions on Neural Networks and Learning Systems, 28(4), 988–1004. Ma, H. and Yang, G. (2013). Residual generation for fault detection and isolation in a class of uncertain nonlinear systems. International Journal of Control, 86(2), 263– 275. Meskin, N. and Khorasani, K. (2009). Robust fault detection and isolation of time-delay systems using a geometric approach. Automatica, 45, 1567–1573. Naderi, E. and Khorasani, K. (2017). A data-driven approach to actuator and sensor fault detection, isolation and estimation in discrete-time linear systems. Automatica, 85, 165–178. Persis, C.D. and Isidori, A. (2001). A geometric approach to nonlinear fault detection and isolation. IEEE Transactions on Automatic Control, 46(6), 853–867. Pourbabaee, B., Meskin, N., and Khorasani, K. (2016). Sensor fault detection, isolation, and identification using multiple-model-based hybrid kalman filter for gas turbine engines. IEEE Transactions on Control Systems Technology, 24(4), 1184–1200. Yin, S., Ding, S.X., and Zhou, D. (2016). Diagnosis and prognosis for complicated industrial systems-part i. IEEE Transactions on Industrial Electronics, 63(4), 2501–2505. Zhang, Q. (2002). Adaptive observer for multiple-input multiple-output (mimo) linear timevarying systems. IEEE Transactions on Automatic Control, 47(3), 525– 529. Zhang, Q. and Basseville, M. (2014). Statistical detection and isolation of additive faults in linear time-varying systems. Automatica, 50, 2527–2538. Zhong, M.Y., Ding, S.X., and Zhou, D.H. (2016). A new scheme of fault detection for linear discrete time-varying systems. IEEE Transactions on Automatic Control, 61(9), 2597–2602. Zhong, M., Zhang, L., Ding, S.X., and Zhou, D. (2017). A probabilistic approach to robust fault detection for a class of nonlinear systems. IEEE Transactions on Industrial Electronics, 64(5), 3930–3939. Zhou, Z., Wen, C., and Yang, C. (2016). Fault isolation based on k-nearest neighbor rule for industrial processes. IEEE Transactions on Industrial Electronics, 63(4), 2578–2586.

1378