Fault Diagnosis of Interconnected Cyber-Physical Systems

Transcription

1 Fault Diagnosis of Interconnected Cyber-Physical Systems Marios M. Polycarpou Professor, IEEE Fellow, IFAC Fellow Director, KIOS Research and Innovation Center of Excellence Dept. Electrical and Computer Engineering University of Cyprus 7 th ocps PhD School on Cyber-Physical Systems Lucca, Italy, 14 th June 2017

2 Presentation Outline Motivation for fault diagnosis Interconnected cyber-physical systems Foundations of fault diagnosis Sensor fault diagnosis Application example: Smart Buildings Concluding Remarks

3 The Smart Revolution Smart Phones Smart Cars Smart Grids Smart Buildings Smart Cities Smart Camera Networks Smart Water Networks

4 The Smart Revolution Smart Phones Smart Cars Smart Grids Smart Buildings Smart Cities Smart Camera Networks Smart Water Networks Smart-X

5 Characteristics of Smart-X HARDWARE Sensing & actuation devices Embedded computing Wide area connectivity SOFTWARE Data management Decision making algorithms Learning algorithms Optimization and control

6 Smart-X vs Smart-ready-X Digital advances provide the ICT infrastructure not the INTELLIGENCE (so far) Infrastructure will be further enhanced via the IoT Smart-X vs. Smart-ready-X

7 Smart-X vs Smart-ready-X Digital advances provide the ICT infrastructure not the INTELLIGENCE (so far) Infrastructure will be further enhanced via the IoT Smart-X vs. Smart-ready-X Control systems and machine learning are at the heart of transforming Smart-ready-X to Smart-X

8 Control Systems in the Smart-X Era More proactive, more planning ahead More discrete-event, more event-triggered More machine learning, handling of larger volume of data, more heterogeneous data Handling of more uncertainty, fault tolerance Handling of human-machine interaction

9 Fragility The technological trend is towards: more complex and large-scale systems more interconnected systems more automation and autonomy However if the data is faulty/inconsistent/missing, this may lead to: wrong decisions or escalation to a catastrophic failure fault propagation from one subsystem to another Unreliable and untrustworthy automation procedures

10 Fragility The technological trend is towards: more complex and large-scale systems more interconnected systems more automation and autonomy more FRAGILE However if the data is faulty/inconsistent/missing, this may lead to: wrong decisions or escalation to a catastrophic failure fault propagation from one subsystem to another Unreliable and untrustworthy automation procedures

11 Fragility of Interconnected Systems Fragility is a crucial issue in an interconnected cyber-physical-social world Fault Monitoring and Fault Tolerance are necessary components of Smart-X architectures Black Swan Theory Nassim Nicholas Taleb metaphor that describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight (extreme outliers)

12 Monitoring and Control Fault Monitoring and Diagnosis d f u System y

13 Monitoring and Control r u y Controller System d f

14 Monitoring and Control Control Algorithm Supervisory Algorithm Fault Accommodation Fault Monitoring and Diagnosis d f r Controller u System y

15 Fault Scenarios System/Process Faults Actuator Faults Sensor Faults Communication Faults Controller Faults Environment Faults Malicious Attacks (cyber-security) FA C FD P

16 Fault Diagnosis Steps fault detection fault isolation fault identification and risk assessment fault accommodation

17 Key Challenges for Fault Diagnosis distinguish between faults and modeling uncertainty or measurement noise exploit spatial and temporal correlations between variables handle multiple faults isolate faults in a large-scale system (needle in a haystack) prevent small faults from escalating into a major failure accommodate the fault what to do in the presence of information about a fault? Design smart SOFTWARE to handle faulty HARDWARE

18 Key Books on Fault Diagnosis J. Gertler. Fault Detection and Diagnosis in Engineering Systems. CRC Press, J. Chen and R. J. Patton. Robust Model-based Fault Diagnosis for Dynamic Systems. Kluwer Academic Publishers, R. Isermann. Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance. Springer Verlag, S. X. Ding. Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools. Springer-Verlag London, M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki. Diagnosis and Fault-Tolerant Control. Springer-Verlag Berlin Heidelberg, 2016.

19 N interconnected CPS. I th CPS: described by the pair ( ) I ( I ) : cyber part of the I th CPS. : physical part of the I th CPS, Interconnected CPS, ( I) ( I)

20 Interconnected CPS Single Agent

21 Interconnected CPS Objective: Detect and isolate multiple faults that may occur in one or more CPS

22 Problem Formulation where: state vector input vector Nominal state dynamics Modeling uncertainty Change in the system due to fault Time profile of the fault Interconnection dynamics

23 Modeling Uncertainty The modeling uncertainty includes external disturbances as well as modeling errors. where for each i = 1,., n, the bounding function is known, integrable and bounded for all (x, u) in some compact region of interest The handling of the modeling uncertainty is a key design issue in fault diagnosis architectures: - need to distinguish between faults and modeling uncertainty - structured vs. unstructured modeling uncertainty - trade-off between false alarms and conservative fault detection schemes

24 Fault Modeling The term represents the deviations in the dynamics of the system due to a fault. is the fault function The matrix characterizes the time profile of a fault which occurs at some unknown time where denotes the unknown fault evolution rate.

25 Fault Influence for Distributed Systems Local Faults Distributed Faults Distributed Faults with Overlapping Signature Propagating Faults

26 Types of FAULT ISOLATION: identify the type of fault that has occurred identify the physical location of the fault Class of fault functions : Fault Isolation where: is an unknown parameter vector, which is assumed to belong to a known compact set is a known smooth vector field

27 Fault Diagnosis Architecture There are N+1 Nonlinear Adaptive Estimators (NAEs) One of the NAEs is used for detecting and approximating faults The remaining N NAEs are isolation estimators used only after a fault has been detected for the purpose of fault isolation. Fault Detection and Isolation Architecture Fault Detection and Approximation Estimator Activation Bank of Fault Isolation Estimators Fault Detection Decision Scheme Fault Isolation Decision Scheme Alarm Identification of the fault that has occurred reference input Feedback Controller u Nonlinear Plant x

28 Fault Handling Monitoring Module x (t) x d (t) fault occurred fault detected fault isolated T 0 T d T isol t 0 < t < T 0 : system is operating in a healthy condition. T 0 < t < T d : period in which there is a fault, which however has not yet been detected. T d < t < T isol : period during which the fault has been detected, but it is not yet known which particular fault has occurred. t > T isol : the fault has been isolated.

29 Fault Detection and Approximation Estimator where: estimated state vector Adaptive approximation model adjustable weights of the on-line neural approximator estimation poles The initial weight vector is chosen such that (healthy situation)

30 Adaptive Approximation Model Nonlinear approximation model with adjustable parameters (e.g., neural networks) Linearly parameterized vs. nonlinearly parameterized It provides the adaptive structure for approximating online: Local modeling errors interconnection dynamics unknown fault functions

31 Learning Algorithm where: state estimation error The projection operator restricts the parameter estimation vector to a predefined compact and convex region. regressor matrix Positive definite learning rate matrix Dead-zone operator

32 Detection Threshold where: Robustness of the fault detection scheme is the ability to avoid false alarms. The above threshold make the FD scheme robust. In the special case of a uniform bound on the modeling uncertainty the detection threshold becomes:

33 Detectability Conditions [ t 1, t2] If there exists an interval of time such that at least one component ( x, u) of the fault vector satisfies the condition f i then a fault will be detected. Result holds for the special case of constant bound on the modeling uncertainty. We are also able to obtain more simplified detectability conditions, but they are more conservative. In general there is an inherent trade-off between robustness and fault detectability.

34 Fault Isolation Estimators N NAEs are activated for isolation (isolation estimators) after the detection of a fault Each isolation estimator corresponds to one of the possible types of parametric faults Learning Algorithm Adaptive threshold are designed based on the available information, similar to the concept of a matching filter isolation is achieved if every threshold is exceeded, except one (the one corresponding to the fault)

35 Intuitively, fault are easier to isolate if they are sufficiently mutually different in terms of a suitable measure Incipient Fault Isolability Fault isolability condition Fault Mismatch Function The difference between the actual fault function and the estimated fault function associated with any isolation estimator

36 Sensor Fault Diagnosis System/Process Faults Actuator Faults Sensor Faults Communication Faults Controller Faults Environment Faults Malicious Attacks (cyber-security) FA C FD P

37 N interconnected CPS. I th CPS: described by the pair ( ) I ( I ) : cyber part of the I th CPS. : physical part of the I th CPS, Interconnected CPS, ( I) ( I)

38 Interconnected CPS ( ) I (physical part) a nonlinear system ( I ) ( I ) ( I ) ( I ) ( I ) ( I ) ( I ) x A x ( x, u ) ( I ) ( I ) ( I ) known local dynamics ( I ) ( I ) ( I ) ( I ) ( I ) h ( x, u, Cz z ) known interconnection dynamics ( I ) ( I ) ( I ) ( x, u, t) modeling uncertainty : local state vector : local input vector generated by a feedback control agent x u z : interconnection vector using r ( I ) ( I )

39 Interconnected CPS ( ) I (physical part) ( I ) Sensor set used for measuring the linear I combination of states C x ( ) ( I) ( I ) ( I ) ( I ) ( I ) ( I ) y t C x t d t f t () () () () y d f ( I ) ( I ) ( I ) : local output vector : measurement noise : fault vector

40 Interconnected CPS ( I ) (cyber part) ( I ) control agent that ( I ) generates the input u based on some reference ( I ) signal r, the measured output and the transmitted ( I ) sensor information z y () t C z () t d () t f () t ( I) ( I) ( I) ( I) ( I) z z z z

41 Interconnected CPS Objective: Detect and isolate multiple sensor faults that may occur in one or more CPS

42 Distributed Sensor Fault Diagnosis Architecture ( I )(cyber part) ( I ) monitoring agent allowed to exchange information with the ( I ) neighboring agents z Task: Detection & isolation of multiple ( I ) sensor faults in Detection of propagated sensor faults in I () z

43 Distributed Sensor Fault Diagnosis Architecture G : global decision logic collects and processes combinatorially the decisions of the monitoring agents Task: Isolation of sensor faults propagated in the cyber layer due to the information exchange between monitoring agents

44 Monitoring Agent monitoring agent ( I )

45 Monitoring Agent The monitoring of the local sensor set is decomposed into N I modules ( I, q) The module monitors the group of sensors : y ( I ) C x d f ( I, q ) ( Iq, ) ( Iq, ) ( I ) ( Iq, ) ( Iq, ) ( Iq, )

46 Monitoring Agent ( I, q) : q th module of the I th monitoring agent Task: Detection of sensor faults in (, Iq) and/or () I z

47 Monitoring Agent The decisions of the N I modules are aggregated and processed combinatorially for isolating the combination of multiple sensor faults that have occurred and inferring the presence of propagated sensor faults

48 Monitoring Module j th residual, ( I, q) y j ˆ y y C x, j ( Iq, ) ( I) ( I) ( Iq, ) ( I, q) j j j (, ) ˆ Iq x (1) : estimation model based on the nonlinear observer ( Iq, ) ( I) ( Iq, ) ( I) ( Iq, ) ( I) xˆ A xˆ ( xˆ, u ) h xˆ u L ( I) ( I, q) ( I) ( I ) (,, yz ) y C xˆ ( Iq, ) ( Iq, ) ( Iq, ) ( Iq, ) (2)

49 Monitoring Module The j th adaptive threshold is designed to bound the j th ( Iq, residual ) y () t under healthy jh conditions () t () t ( Iq, ) ( Iq, ) y y jh j y t ( Iq, ) () j

50 The j th adaptive threshold can be implemented using linear filters () t H() s ( xˆ (), t u (),) t t Z ( t) Y ( t) ( Iq, ) ( Iq, ) ( I) ( Iq, ) ( Iq, ) y I j j Adaptive Threshold Computation ( Iq, ) ( Iq, ) ( Iq, ) Z () t E () t H1() s E () t E t H s xˆ t u t ( Iq, ) ( Iq, ) ( I) ( Iq, ) () 2() ( (), (),) B () H() s, H () s, H () s s I ( Iq, ) ( I, q) ( Iq, ) j I ( I, q) 1 ( Iq, ) ( Iq, ) 2 ( I, q) j s s I h I I I t E t,

51 Monitoring Module Decision Logic based on a set of Analytical Redundancy Relations (ARRs) ( I, q) (, ) : I q j ( Iq, ) j : ( t) ( t) 0, ( Iq, ) ( Iq, ) ( Iq, ) j y y j j residual adaptive threshold Under healthy conditions, (, ) I q is always satisfied

52 Robustness and Structured Fault Sensitivity Theorem: The distributed sensor fault diagnosis design guarantees that: (, I q) (a) Robustness: If neither the local sensor set nor the () I transmitted sensor information y z are affected by sensor faults, then the set of ARRs I q is always satisfied. (, ) (b) Structured fault sensitivity: If there is a time instant at which (, I q) is not satisfied, then the occurrence of at least one sensor fault in (, I q) () I is guaranteed. z V. Reppa, M. Polycarpou and C. Panayiotou, Distributed Sensor Fault Diagnosis for a Network of Interconnected Cyber-Physical Systems, IEEE Transactions on Control of Network Systems, vol 2, no. 1, pp , March 2015.

53 Monitoring Agent

54 Local Multiple Sensor Fault Isolation Example: ( ) I y z ( I,1) ( I) ( I,3) ( I) {1}, ( I,2) ( I) ( I) {2}, {3} {3} (,1) I (,2) I (,3 I ) (),,, 3 1, 2, 3 z z, c f f f f f f f f f f f f f f () I () I () I () I () I () I () I () I () I () I () I () I () I () I I

55 Local Multiple Sensor Fault Isolation (,1) I (,2) I (,3 I ) (),,, 3 1, 2, 3 z z, c f f f f f f f f f f f f f f ( I) ( I) ( I) ( I) ( I) ( I) ( I) ( I) ( I) ( I) ( I) ( I) ( I) ( I) I ( I ) D () t 1 0 Diagnosis Set: s () t f, f ( ) ( ) ( ) I I I 1 2 Decision on the presence of sensor faults in D ( I) ( I) ( I ) 0, fz s ( t) z () t ( I) ( I) fz s t 1, ( ) y ( I ) z

56 Local Multiple Sensor Fault Isolation (,1) I (,2) I (,3 I ) (),,, 3 1, 2, 3 z z, c f f f f f f f f f f f f f f () I () I () I () I () I () I () I () I () I () I () I () I () I () I I D Diagnosis Set: D ( I ) 1 () t ( t) f, f, f, f, f, f, f, ( ( ( ( ( ( ( ( ( s z z c Decision on the presence of sensor faults in ( I) ( I) ( I ) 0, fz s ( t) z () t ( I) ( I) fz s t 1, ( ) y ( I) z

57 Global Multiple Sensor Fault Isolation

58 Global Multiple Sensor Fault Isolation Observed pattern of sensor faults in transmitted sensor information: (1) (2) ( N) Dz() t Dz () t Dz () t Dz () t (1) (2) (3),,,,, 4 f f f f f f f f f f f f (1) (2) (3) (1) (2) (1) (3) (2) (3) (1) (2) (3) * 1 1 * * 1 * 1 1 * * 1 * Semantics of * : the sensor fault involved in the ARR can explain why the ARR is violated, while the ARR may be satisfied although the corresponding fault has occurred

59 Learning Approaches for Fault Diagnosis Reduce adaptive thresholds by reducing the bound of the modeling uncertainty using learning techniques. Design and analysis of an adaptive approximation methodology to learn the modeling uncertainty V. Reppa, M. Polycarpou and C. Panayiotou, Adaptive approximation for multiple sensor fault detection and isolation of nonlinear uncertain, IEEE Transactions on Neural Networks and Learning Systems, vol 25, no. 1, pp , January 2014.

60 Fault Diagnosis and Cybersecurity Targeted faults Early detection is crucial Sensor placement is a key issue Need to consider the impact dynamics

61 Application Example: Smart Buildings

62 How critical are buildings? 48% of energy consumption is for buildings (27% for transportation; 25% for factories) 76% of electricity consumption is for buildings (23% for factories; 1% for transportation) 87% of our time is spent indoors

63 How critical are buildings? 48% of energy consumption is for buildings (27% for transportation; 25% for factories) 76% of electricity consumption is for buildings (23% for factories; 1% for transportation) 87% of our time is spent indoors 6% in automobiles and public transportation 7% outdoors

64 The Transformation of Buildings

65 The Transformation of Buildings

66 The Electronic Transformation Inside Sensors (more self-aware) Actuators (more automation) Intelligent decision making (energy efficiency, safety and security, fault diagnosis, etc.) Communication devices (building to user; user to building; building to building; etc.)

67 The Electronic Transformation Inside Sensors (more self-aware) Actuators (more automation) Intelligent decision making (energy efficiency, safety and security, fault diagnosis, etc.) Communication devices (building to user; user to building; building to building; etc.) Internet of Things (IoT)

68 Motivation for Smart Buildings Need to monitor and control: indoor living conditions and safety of the occupants energy consumption of large-scale buildings The technology is available (smart-ready): building automation is well established Cyber-physical systems for smart buildings sensing and actuation devices are widely available Need to develop smart software to enable the coordination and scheduling of actions for handling dynamic and uncertain environments

69 Topics pursued at KIOS Research Center KIOS Research Center for Intelligent Systems and Networks was founded in 2008 Currently about 50 researchers working on Monitoring, Control and Security of Critical Infrastructure Systems Awarded a TEAMING project from H2020 to upgrade to a Center of Excellence for Research and Innovation (more than 40M)

70 Smart Buildings Topics pursued at KIOS Distributed fault diagnosis and control of HVAC systems Contamination event detection and isolation in large-scale buildings Security surveillance using smart camera networks Cognitive agents for on-line reconfiguration of in smart buildings

71 Topics pursued at KIOS Research Center Distributed control and fault diagnosis of largescale HVAC systems V. Reppa, P. Papadopoulos, M. Polycarpou and C. Panayiotou, A Distributed Architecture for HVAC Sensor Fault Detection and Isolation, IEEE Transactions on Control Systems Technology, vol. 23, pp , July V. Reppa, P. Papadopoulos, M. Polycarpou, and C. Panayiotou, A Distributed Virtual Sensor Scheme for Smart Buildings based on Adaptive Aproximation, Proceedings of the International Joint Conference on Neural Networks, World Congress on Computational Intelligence (IJCNN 2014), pp , July Zone 1 u 1 Zone 2 Zone 3 Storage Tank Zone N-2 A d,12 A A d,13 d,23 u 3 un 2 Zone N Zone N-1 u u N N 1 Condenser u2 Zone 5 5 A A d,24 d,45 Zone 4 A d,34 u 4 Heat Pump Zone 6 u 6 A d,46 Zone 7 A d,47 u A d,56 A d,67 u 7 u st

72 Topics pursued at KIOS Research Center Contamination event detection and isolation in large-scale buildings M. Michaelides, V. Reppa, M. Christodoulou, C. Panayiotou and M. Polycarpou, Contaminant Event Monitoring in Multi zone Buildings Using the State Space Method, Building and Environment, vol. 71, pp , January (2014 Best Paper Award). D. Eliades, M. P. Michaelides, C. Panayiotou and M. Polycarpou, Security Oriented Sensor Placement in Intelligent Buildings, Building and Environment, vol. 63, pp , March 2013.

73 Topics pursued at KIOS Research Center Security surveillance using smart camera networks C. Laoudias, P. Tsangaridis, M. Polycarpou, C. Panayiotou, C. Kyrkou and T. Theocharides, 'Cooperative Fault Tolerant Target Tracking in Camera Sensor Networks," Proceedings of the IEEE International Conference on Communications (ICC 2015), June C. Kyrkou, C. Laoudias, T. Theocharides, C. Panayiotou and M. Polycarpou, "Adaptive Energy Oriented Multi Task Allocation in Smart Camera Networks", IEEE Embedded Systems Letters, vol. 8, no. 2, pp , June 2016.

74 Topics pursued at KIOS Research Center Cognitive agent for on-line reconfiguration in smart buildings G. Milis, D. Eliades, C.G. Panayiotou and M. Polycarpou, A Cognitive Fault Detection Design Architecture, in Proceedings of IEEE World Congress on Computational Intelligence (WCCI 2016), July G. Milis, C.G. Panayiotou and M. Polycarpou, Semantically Enhanced Online Configuration of Feedback Control Schemes, IEEE Transactions on Cybernetics, 2017 (to appear).

75 Topics pursued at KIOS Research Center Distributed fault diagnosis and control of HVAC systems Contamination event detection and isolation in large-scale buildings Security surveillance using smart camera networks Cognitive agent for on-line reconfiguration of in smart buildings

76 HVAC systems consist of: A number of electrical and mechanical components for Heating (i.e., boilers, heating coils, heat pump) Cooling (i.e., cooling towers, chillers, cooling coils) Ventilating (i.e., fans, supply/return ducts, mixing boxes) A number of building zones (i.e., interconnected or not) HVAC Description the dynamics of a zone in the building are affected by the dynamics of their neighbouring zones Types of faults in HVAC systems: actuator/process faults (i.e., fouled heat exchangers, stuck dampers, leaking valves, broken fans) sensor faults (i.e., drifting, stuck at zero), communication faults (i.e., wire break).

77 Faulty Situations in HVAC Systems The recovery of faulty situations in HVAC systems: shutting down the operation of the system (inconvenient and possibly ineffective from the viewpoint of energy) reconfiguring the controller(s) via a fault tolerant control scheme, using the outcome of a fault detection and isolation mechanism Early diagnosis and accommodation of faults is critical since local faults effects may propagate from a local subsystem to neighbouring subsystems the physical interconnections the distributed control scheme (local controllers may use information transmitted from neighbouring controllers to achieve the best possible tracking performance)

78 HVAC System Description Electromechanical part u 1 u2 u5 u st For cooling operation: Replace Heat pump with Chiller A d,12 A A d,24 d,45 Building Zones A A d,13 d,23 u 3 Zone 4 A d,34 A d,46 A d,56 u 6 Door un 2 u 4 Fan coil unit A d,67 u u N N 1 u 7 A d,47

79 Zone 1 u 1 HVAC System Description Heat Pump Storage Tank A d,12 A d,13 Condenser u st Zone 1 u1 Zone 2 u2 Zone 5 u d st t st a 5 dtz () t U i sz imax, a a Psz z s st () ust( t) ui( i ( T t) Ui, max( z () t T ()) i st t dt C A st ( t) Tz () t ) u ( ) ( () ( )) d,12 i i t T st C A A d,24 st i d z t T,45 i amb t dt Cz C i zi ast ast haa A d,13,23 ( wt st ( t) Tpl ( t)) d 1T st ( t), a i zi Zone C3 ( Ti 1( t) Tz () t ) st C ( Zone () 6 A st d,56 ()) ( ) i u 3 az T ij z t T i z t T j z t i Cz C i z ja d,34 C i i zi u Tst () t To () t A 6 d,46 Zone 1 N-2 a irc p p 1 u, Tst ( t) To ( t) T N 2 max Ps ( Ts t () t ) ( sgn T z () t T () u) j z t i C max 4 z j i i Zone N Zone 1, N-1 TZone st ( t) 7A T d,67 o( t) Tm ax A max( T ( t), T ( t) ) 2( C C ) T ( t) T () t, Zone 4 udi j z u N i zjn p v 1 A d,47 z j u 7 z i

80 Temperature nonlinear dynamics for water in the storage tank: Performance coefficient of the heat pump HVAC System Modelling dtst () t U a P( T ()) t u () t u () t U ( T () t T ()) t dt C C st, max sz s st st i i, max z i st st st i ast ast ( Tst ( t) Tpl ( t)) T st ( t), C C st Tst () t To () t 1 p1, T ( t) T ( t) T Ps( Tst( t)) Tmax 1, T () t T () t T st 1,..., N st o max st o max M. Zaheer Uddin and R. Patel, Optimal tracking control of multizone indoor environmental spaces, Journal of Dynamic Systems, Measurement and Control, vol. 117, no. 3, pp , 1995.

81 HVAC System Modelling Temperature nonlinear dynamics of air in the i th zone dtz () t U a a i ( T ( t) T ( t)) u ( t) ( T ( t) T ( t)) dt C C imax, sz zi st zi i z i amb z z i ha 1 a ( T ( t) T ( t)) ( ( ) ( )) ( ) i a T t T t T t ij i j i C C C wi zi i1 z z z z z z z j z i i i i i airc p sgn( Tz ( t) T ( )) ( ) 2( ) ( ) ( ), j z t A i d T ij z t C i p Cv Tz t T j z t i C z i j i C z air p z i C V air heat capacity i

82 HVAC System with Feedback Control (1) y ref local linear and nonlinear dynamics () i 1 () i () i (1) i() y () i () i () i s() () i () i u t A x t c () i s () i x () t g A( x ( xt), x t( t)) g ( x (), t x ()) t u () t () i () i ( j) h x t x t ( N ) y ref (1) ( ) N (1) u c interconnection dynamics () i () i () i () i () i ( j) h( d ( xt)) ( yt ref ),( xt) ( t )) (2) (2) y ref (2) u known disturbances mod eling uncertainty c (2) (2) () i () i () i () () (2) () i ref () i () i y reference ( dsignal ( t)) r ( t), ( ( ), ( )) k y t x t u tt u ut t f t t () i () i i ( i) () () i c () c () () a f, a ( ), : y () t x () t n () t f (), t s s s permanent s s actuator permanent fault s () i () i () i actuator () i fault ( i) : y () t x () t n () t fs () t, permanent sensor fault ( N) y ( N ) u c (1) (1) ( ) N ( N ) y y y (1) (2) ( N )

83 HVAC System Modelling HVAC temperature dynamics represented in nonlinear state space form local linear and nonlinear dynamics s s s s s s s s : x () t A x () t g ( x (), t d ()) t u () t interconnection dynamics known disturbances modeling uncertainty s s s s s h ( x (), t x(), t u()) t d () t r () t, local linear and nonlinear dynamics () i () i () i () i () i s () i () i : x () t A x () t g ( x (), t x ()) t u () t interconnection dynamics known disturbances modeling uncertainty () i () i ( j) () i () i () i h ( x ( t), x ( t)) ( d ( t)) r () t,

84 Distributed control laws: Control law for : Control law for : Sensor s Structure: : y () t x () t n () t f (), t s s s s s s () i () i () i () i ( i) : y () t x () t n () t fs () t, Nominal Distributed Control s 1 s s s s uc () t A x () t h ( x (), t x(), t u()) t s s s g ( x ( t), d ( t)) s s s s s s ( d ()) t k yref () t x () t y ref () t reference signal () i 1 () i () i () i () i ( j) uc () t A x () t h ( x (), t x ()) t () i s () i g ( x ( t), x ( t)) () i () i () i () i () i () i ( d ()) t k yref () t x () t y ref () t reference signal permanent sensor fault Faults in Actuators: s s s u () t u () t f (), t c () i () i ( i) u () t uc () t fa () t, a permanent actuator fault

85 Distributed Sensor Fault Diagnosis Scheme (1) (1) (1) (1) (1) s (1) (1) : x () t A x () t g ( x (), t x ()) t u () t (1) (1) ( 2) (1) ( 1 ) ( 1) h ( x ( t), x () t ) ( d ( t)) r ( t) (2) (2) (2) (2) (2) s (2) (2) : x () t A x () t g ( x (), t x ()) t u () t (2) (2) ( 1) (2) ( 2 ) ( 2) h ( x ( t), x () t ) ( d ( t)) r ( t)

86 Distributed Sensor Fault Diagnosis Scheme ARR: Boolean decision signal: D () i : () t (), t () i () i () i y y () i 0, t td () t, () i 1, t td t inf { t 0: () t ()} t () i () i () i D y y Residual generation: () i () i () i () () ˆ y t y t x () t Distributed nonlinear estimator: xˆ () t A xˆ () t g ( y (), t y ()) t u () t () i () i () i () i s () i () i c ( (), ()) ( ()) () i () i () i () i h y t y t d t () i () i () i ˆ ( j) [ ] L y () t x (), t y () t y (): t j, i i i

87 Distributed Fault Detection: Distributed Sensor Fault Diagnosis Scheme Analytical redundancy relation (ARR): Boolean decision signal: D () i () i 0, t td () t, () i 1, t td : () t (), t () i () i () i y y t inf { t 0: () t ()} t () i () i () i D y y Residual generation: () i () i () i () () ˆ y t y t x () t Distributed nonlinear estimator: xˆ () t A xˆ () t g ( y (), t y ()) t u () t h ( y (), t y ()) t () i () i () i () i s () i () i () i () i c i () i () i () i () i () i ( d ()) t L y () t xˆ (), t [ ] ( j) () (): i, y t y t j i

88 Adaptive threshold: Distributed Sensor Fault Diagnosis Scheme g () i () i n () i n s g () i ( n () i, n s ), ( i) t ( i) () i () i t () i () i () i ( t) () i () i () i y e x n e L n r 0 g ( n, n, u ) h ( n, n, y, y ) d, () i () i s () i () i () i () i c 1 () i () i () i () i ( j) ( j) () i () i () i h p Ad ( y, y ) a (,,, ) ij z n h n n ij y y i i j Cz j i ( j) ( i) ( i) 2y 3y y () i () i ( j) () i ( j) () i ( y, y ) n n, ( j) ( i) ( j) ( i) e 2 y y 2 y y () i () i x ( t) x ( i ) ( i ) L () e A t i t e i i i ( i )

89 ˆ Distributed Sensor Fault Diagnosis Scheme nonlinear estimator () i () i () i () i s () i () ˆ () ˆ () ( (), () ˆ i x s t A xs t g y t y t f () t ) uc () t () i ˆ () i () i () i ARR s: Ea : y ( t) y ( t), () () () ( s i (), ())( s () ) () i () i () i () i () i () i x t A x t g y t y t u t a a a a c () i () i () i ( i() i) () i (( ( E), ) s: f y ( ) ), s)) (), y( t s t s( )) ( )) () i () i () i () i hh y t y t y t d t i () iboolean () i decisions i () functions: i () i () i () i () i () i ˆ i L a ( d y t()) tl () ( i ) ( ), a () i a styf() t a t () (), s s t f t 0, t t 0, () i I t t adaptive filter a () i Is Ia () t adaptive, filter I (), () i s t () i 1, t t ( ) ( ii) ( i) ( i) 1, t t a I i i () i () i s () is A() L a ts A() t () ( (), ()) () i a () i () i () i ti inf L Ls t guc () ty t y t { t () it : ( ) ( )} a D y t a y t a adaptive law () i () i () i () i () i ˆ () i ( j) p () i t I A inf d { t t y: ( ) ( )} s D y tf, s y t, ij () i s ˆ () i j K () i () i () i () i fa () Residual t a generation: a () t D s y x y () t i, adaptive law a () t () i () i i s () i () i () i ˆ () i () i () i () ˆ y t y t () ix (), a a ti fs () t s ( s () t 1) D y () t, s () i () i () i ˆ () i ˆ y t y t xs t fs s ˆ i () () (), ˆ fˆ () t, a

90 Local Fault Identification: ARR s: Distributed Sensor Fault Diagnosis Scheme E : ( t) ( t), () i () i () i a y y a E : ( t) ( t), () i () i () i s y y Boolean decisions functions: () i () i 0, 0, () i t t Ia () i t tis Ia () t, I (), () i s t () i 1, t ti 1, t t a Is Residual generation: s () i () i () i y a a a s () t y () t xˆ (), t () t y () t xˆ () t fˆ, () i () i () i () i y s s s t inf{ t t : ( t) ( t)} () i () i () i () i I D y y a a a t inf{ t t : ( t) ( t)} () i () i () i () i I D y y s s s

91 Local Fault Identification: Distributed Sensor Fault Diagnosis Scheme Distributed adaptive nonlinear estimation scheme: nonlinear estimator () i () i () i () i s () i () i () () () () () ˆ () ˆ () ( (), ())( () ˆ i i i i i x a t A xa t g y t y t uc t fa ( t) ) h ( y (), t y ()) t ( d ()) t () () ˆ L t t f (), t () i () i () i () i a y a a a adaptive law adaptive filter () i () i () i () i s () i () () () () () a () t A ˆ i i i i i L a () t g ( y (), t y ()), t fa () t a a () t D y () t, a i nonlinear estimator () i () i () i () i s () i () () () () () () () ˆ () ˆ () ( (), () ˆ i i i i ()) () ( () ˆ i i i x s t A xs t g y t y t fs t uc t h y t fs () t, y ()) t ( d ()) t () () ˆ L t t f (), t () i () i () i () i s y s s adaptive filter adaptive law () i () i () i () i () i () i () i () i () i () ( ) ( ) ( ) ( ) ( ) ( ) () () () () ˆ i j,, ˆ i i i i i s t AL s t Ls uc t p Ad y f () ( () 1) (), ij i s y fs t s s t D y t s x jk i i

92 Distributed Sensor Fault Diagnosis Scheme Fault Isolation () i () i () i Observed fault pattern: I () t [ Ia (), t Is ()] t () i Fault isolation signature matrix F I () i K i () t () i () i (i) (i) 0, if fs I ( t) f K i I (t) or D (t)=0 (i) (i) (i) 1, if f s I (t) or f K i I (t)

93 Distributed Sensor Fault Diagnosis Scheme Distributed Fault Isolation: ( j) Observed fault pattern of propagated sensor faults: IK () t I (): {} i K t jk j i i () i Fault isolation signature matrix F i (1,3) (1) (3) (2,3) (2) (3) (1,2,3) (1) (2) (3) s, s fs fs, fs fs fs, fs fs fs, fs, fs f f f (1,2) (1) (2) s

94 Simulation Results Consider a seven zone HVAC system where the architectural arrangement of the seven zones is presented by the diagram PARA METERS OF THE SEV EN-ZONE HVAC SY STEM u 1 A d,12 A A d,13 d,23 u 3 un 2 u u N N 1 u2 u5 A A d,24 d,45 Zone 4 A d,34 u 4 A d,46 A d,47 A d,56 u 6 A d,67 u 7 u st Symbol Value Units a zi, i {1,2,3,4,5,6,7} 740 kj/h o C a z12, a z13, a z24, a z34, a z45, a z46, a z47, a z56, a z67 50 kj/h o C a st 12 kj/kg o C a sz 0.6 kj/kg o C C st 837 kj/ o C C p kj/kg o C C v kj/kg o C r air kg/m 3 C zi, i {1,2,3,4,5,6,7} 370 kj/ o C U i,max, i {1,2,3,4,5,6,7} 3700 kg/h U st,max kj/h P max 3.5 DT max 45 o C A w,i, i {1,2,3,4,5,6,7} 120 m 2 h 8.29 W/m o C A d,12, A d,13, A d,24, A d, m 2 A d,45, A d,46, A d,47, A d,56, A d, m 2

95 Simulation Results Consider a seven zone HVAC system where the architectural arrangement of the seven zones is presented by the diagram u 1 u2 u5 u st Sensor fault A d,12 A A d,24 d,45 A d,13 A d,23 Zone 4 u 3 A d,34 A d,46 A d,56 u 6 un 2 u 4 A d,67 u u N N 1 A d,47 u 7 Sensor fault

96 Simulation Results s (1) (2) (3) (4) (5) (6) (7)

97 Simulation Results (2) (3) s (1) (4) (6) (5) (7)

98 Simulation Results Consider a 83 zone HVAC system where the architectural arrangement of the 83 zones is presented by the diagram Papadopoulos M. P., Reppa V., Polycarpou M. M., Panayiotou C., Distributed Diagnosis of Actuator and Sensor Faults in HVAC systems, IFAC World Congress 2017.

99 Simulation Results Multiple Faults occurring consecutively Actuator fault f ( t 2) 30% u (1) (1) (1) a f n Sensor fault fs t y (3) (3) (3) ( f 2. 5) 20% ref

100 Simulation Results Multiple Fault Scenario (1) Actuator fault in : (3) Sensor fault in : f ( t 2) 30% u (1) (1) (1) a f n (3) (3) (3) ( f 2. 5) 20% ref fs t y The parameters of each subsystem are: a 740, i{1,, N}, a 50, a 12, a 0.6, C 83700, C 1.004, z z st sz st p i ij C C U i N U p 5 v 0.717, air 1.22, z 370, i, max 3700, {1,, }, st, max , 2.5, i T 45, A 120, i{1,, N}, h8.29, A 1.95, i{1,, N}, j max w d i i It is assumed that the exogenous uncontrollable signals are constant d 10 C, d 5 C, d 5 C, d 10 C, i{1,, N} s o s o () o () o ij The modeling uncertainty in each subsystem s r 10% d sin(0.1 t), s 1 r 10% d sin(0.1 t) () i () i 1

101 Have a look at the distributed monitoring agents located at: Zones { 1 10, 81, 82, 83} Simulation Results

102 Simulation Results

103 Simulation Results

104 Local Fault Identification in Zone 1: Simulation Results

105 Local Fault Identification in Zone 3: Simulation Results

106 Remarks on Fault Diagnosis for HVAC Systems A distributed fault diagnosis (FD)methodology for isolating actuator and sensor faults in a multi zone HVAC system is presented. The proposed architecture relies on the deployment of several distributed monitoring agents, which are allowed to exchange information. Every agent is designed to detect the presence of faults, identify the type and infer the number and location (local or propagated faults).

107 Concluding Remarks Monitoring and security of interconnected cyber-physical systems is a key area of growth Fault diagnosis will play a key role in big data computing and Internet of Things (IoT) Trend towards more sensors but cheaper sensors more susceptible to faults Need for smart software to address faulty behavior of hardware

108 Acknowledgements Colleagues and Graduate Students: Vasso Reppa, Christos Panayiotou, Thomas Parisini, Xiaodong Zhang, Panayiotis Papadopoulos, Demetris Eliades, Michalis Michaelides, Chris Keliris, Stelios Timotheou, Riccardo Ferrari. This work is funded by the European Research Council Advanced Grant FAULT-ADAPTIVE (ERC-AdG )