1. Lecture 2 Model-based Diagnosis of Hybrid Systems
Gautam Biswas
Dept. of EECS and ISIS
Vanderbilt University
Acknowledge
Gabor Karsai, Pieter Mosterman, Sriram Narasimhan, Eric Manders,
Nag Mahadevan, John Ramirez
Supported by DARPA SEC, NASA-IS, NASA-ALS, & NSF-ITR
Copyright © Vanderbilt University, 2006.

2. Overview Lecture 1: Diagnosis of continuous (dynamic) systems
Lecture 2: Diagnosis of hybrid systems to accommodate more real-world applications (physical processes with supervisory (discrete) control)
Lecture 3: Online diagnosis? What’s the use – extend to fault-adaptive control
Look at the bigger picture – fault-adaptive control, different fault profiles, prognosis, maintenance, safety, etc. …
11/13/2018

3. Lecture 2 Hybrid Modeling and Diagnosis of Hybrid Systems
Combining Qualitative FDI with Quantitative parameter estimation methods for more informed and more refined diagnosis
Example Applications
Generation of Toolsuite
Simulation experiments
Run time system
11/13/2018

4. Fault Adaptive Control Technology
The FACT Paradigm

5. Overview FACT – Fault Adaptive Control Technology
Goal: systematic model-based approaches to maintain system operations under degraded and failure conditions
Expanded goals: reliable, safe, autonomous operation for long-duration missions
Approach: Develop the technology and required tool-suite using Model-Integrated Computing approach to achieve this
Components:
Modeling Approaches – hybrid dynamic processes of the plant + reconfigurable controllers
Online monitoring of system behavior
Online fault detection, isolation, and identification
Adaptive models – update plant model after failure
Model-predictive fault-adaptive control
11/13/2018

6. Definitions FACT = Toolsuite for constructing software that performs
fault diagnostics and reconfigurable control
Fault Diagnostics + Reconfigurable Control
Fault Diagnostics =
Fault Detection + Fault Source Isolation
Reconfigurable Control=
Controller alternatives + Reconfiguration Logic
Fault-Adaptive control
controller adapts its strategy to changing model of system
Toolsuite =
Design time tools + Run-time support system
Application areas:
Fault detection/Isolation/Reconfiguration/Adaptation
Intelligent Vehicle Health Management
Intelligent System Health Management
11/13/2018

7. Model-based Tools and System Development
Visual modeling tool for creating:
Hybrid bond-graph models
Timed failure propagation graph models
Controller models (including reconfiguration)
Controller
Models
Strategy
Models
Hybrid
Diagnostics
Active
Model
Modular run-time environment contains:
Hybrid observer and fault detectors
Hybrid and Discrete diagnostics modules
Controller and reconfiguration strategy model library
Controller selector and reconfiguration manager
Active controller modules
Modules can be used standalone
Can use an RTOS as the platform
Failure Propagation
Controller
Diagnostics
Selector
Fault Detector
Plant
Models
Hybrid Observer
Interface & Controllers
Reconfiguration
Manager
Run-time Platform (RTOS)
11/13/2018

8. Fault-Adaptive Control Architecture
Process
Hybrid
Observer
Fault
Detector
Qualitative
Fault Isolation
Parameter
Estimation
Fault Diagnoser
Controller 2 1 3
Supervisor
Hybrid Bond Graph
(HBG) Models
Models s1 s3 s2
State
Space
Temporal
Causal
Graph
Discrete
Time
Modes
Active State Model
11/13/2018

9. FACT Components Modeling environment: Plant + controllers
hierarchical, multi-aspect
Three views
HBG view
Plant I/O view: Sensors + Actuators
Controller view (finite state machine, extend to MPC)
parameterize faults
TFPG view: specialized discrete-event diagnosis approach with time intervals
Simulation environment: simulates physical system behavior including fault scenarios
Run-time environment: implements fault detection, isolation, identification, and fault adaptive control algorithms
11/13/2018

10. Model building using GME
Building HBG models for diagnosis

11. Bond Graphs Models Impacting Trains Two tank system Two Tank System
Sf1
Two tank system
Tank1
Tank2 C1 C2
R12 R1 R2
Lumped parameter Topological Modeling
C: C1
R: R12
C: C2
Compact Representation
across domains
Sf: Sf1 1
R: R1
R: R2
Two Tank System
11/13/2018

12. Hybrid Bond Graph Models
Notion of Switched junctions
Operate in two modes:
(1) On: traditional junction
(2) Off: deactivated, inhibit transfer of
energy
Local control mechanism implemented
as finite state automata
Two types:
(1) Controlled – by external signals
(2) Autonomous – switching function
depends on system variables
CSPEC:
OFF C1 C2 ON
11/13/2018

13. Hybrid Bond Graph Models (contd…)
Notion of Switched junctions
Autonomous Junction –
switching function depends on system
variables
Flow between tanks depends on height
of fluid in the two tanks.
Four conditions:
11/13/2018

14. Formal Definition of HBGs
Based on Hybrid Bond Graphs
Bond graphs – generic elements (C, I, R, TF, GY), sources, junctions, and bonds
Hybrid Bond Graphs – allow for discrete changes in model configuration (at meta level): idealized switches at junctions that turn energy connections on and off
11/13/2018

15. Building Models in GME
Define modeling paradigm (Hybrid Bond Graphs, in our case) as a meta language
Create model fragments for typical components
In and Out ports defining input to and output from components (both energy transfer and signal communication)
Build system components from model fragments by composition
Establish connections between in and out ports of different components to specify interactions
Switching signals for hybrid systems (controlled + autonomous)
11/13/2018

16. Modeling Language Physical system models Hybrid Bond Graphs
A topological model containing dissipative, storage, and source elements, connected as a reconfigurable network. (discrete changes in model configuration (at meta level): idealized switches at junctions that turn energy connections on and off)
Bonds = energy flows
Signal flows = information
Fault model:
Abrupt changes in plant parameters (C,R,I,.. values)
Diagnostic problem:
Given the deviation between the predicted and observed behavior, which plant parameter has changed?
Components
C,R,I,Gy,Tr Sf,Se
Variables: e/f, u/x/y
Energy/Signal ports
Switched junctions
11/13/2018

17. Specifying Modeling Paradigm for HBGs
Define HBG elements - (Sf, Se, R, C, I, Tf, Gy, 0, and 1) as
atoms
Associated properties – e.g., parameter values; C, I have initial values
Define Bonds as connections
Restrictions on what connects to what
Define control signals as atoms and switching connection to
0 or 1 junction
Define autonomous signals as boolean decision functions
Decision functions can include variables from the system
11/13/2018

18. Modeling Paradigm Example
11/13/2018

19. Bond Graph Aspect: Model building
Component: subsystem block
with I/O ports; component –
HBG fragment
Control Signal: continuous value
link between components or
external input to system
DecisionIn(Out)Port: transmits
switching values (binary) between
signals
EnergyIn(Out)Port: BG connect-
ions
In/OutPorts: pass real values into
or out of subsystem
ModFunction: Modulates BG com-
ponent parameter values
Plant: Collection of components +
sensor & actuator elements
(appear as ports)
SwitchingSignal: Boolean value that
turns junction on/off
11/13/2018

20. HBGs: Switching Junctions + Decision Signals
BG DecisionFunction.
Modulating Function
11/13/2018

21. Modeling Fluid System Components
Typical components -Tanks, Pipes, and Pumps
Tanks – C (Capacitance) connected to 0 junction
Pumps – energy source (Se) + transformer (TF) connected via 0 junction
Pipes – R (Resistance) connected to 1 junctions
Two ports for pipes
One port for tanks
Switching Signal for valves
11/13/2018

22. Water Recovery System
Reverse
Osmosis
11/13/2018

23. Model Building Environment
 Graphical Component-based Modeling environment (GME)
 Under each component model
– hybrid bond graph model
 Modeling environment:
compositional
tools for generating
simulation models,
hybrid observers, &
diagnosis models
11/13/2018

24. ALS – HBG model Topological Compact Multi-domain First principles
Conductivity
Conductivity calculations
Topological
Compact
Multi-domain
First principles
Incorporates nonlinearities
Easily linked to
Supervisory (event-based controller models) can be easily integrated
Feed Pump
Membrane
Feedback
Loop
Recirc Pump
Purge to
AES
Mechanical
Hydraulic
11/13/2018

25. Fault Diagnosis + Reconfiguration/Fault Adaptive Control
FACT
Fault Diagnosis + Reconfiguration/Fault Adaptive Control

26. Model-Predictive Control Architecture TRANSCEND + Utility-Based Control
Fault-Adaptive Control
Reconfigurable
Control
<par, mag>
Utility-based
Control
Discrete-Time
Simulator
Residual Evaluation (Qualitative)
Quantitative
Residual Generation
Fault
Detection u
Qualitative
Fault Isolation
Switching
EKF ŷ f1
Parameter
Estimation f2
Process + r y
Symbol
Generation s
Temporal Causal Graph
Hybrid Bond Graph (HBG) s1
Mode 1
State Space s3
Mode 2 s2
Mode 3
EKF – Extended Kalman Filter
11/13/2018

27. Run-time System Hybrid Observer
FINITE
AUTOMATON
MODELS
2N modes
CONTROL EVENTS
AUTONOMOUS EVENTS
RECALCULATE
EXTENDED
KALMAN FILTER
Tracks plant behavior, estimates discrete and continuous state
Handles modulated (non-linear components
Observer is constructed from component models automatically
EST:
xk ,yk uk
CONTROLLER yk
PLANT
11/13/2018

28. Run-time System Fault Detection n
Faults
Residual: Gaussian white with zero mean
To detect a fault, the generalized likelihood ratio test (LR) is used for hypothesis testing
System + + +
residual
Model 
Extended Kalman Filter 
Residuals deviate from zero because of
Noise (n)
Separation of effects necessary!
Modeling errors () X
Sensor inaccuracies ()
Faults !
11/13/2018

29. Run-time System Hybrid (TCG) Diagnostics
Plant Models
(Hybrid Bond Graphs)
TCG
Diagnostics
Temporal
Causal Graph
Parameterized
State Space
Model
State Space Models +
Hybrid Automaton
Fault Isolation
Symbol
Generation
Fault Identification
Hybrid
Observer
Kalman Filter
Fault
Detector
Hypotheses
Generation
Signature
Generation
Progressive
Monitoring Hr
Parameter
Estimation
Residual
Hybrid
Automaton
Mode change
Roll Back
Hypothesize
Autonomous
Transitions
Roll Forward
11/13/2018

30. Hybrid Diagnosis Problem
Piecewise linear hybrid dynamical systems
Presence of fault invalidates
tracked mode trajectory
Time Line
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Fault Occurs
Fault Detected
Tracked Trajectory
Actual Trajectory T1 T2 T3 T4 T5 T6
Mode 6
Mode 7
Fault Hypothesis: <mode,parameter>
Roll Back to find fault hypotheses
Known Controlled Transition
Catch up to current system mode to verify hypotheses against measurements
Note: Controller transitions known
Autonomous transitions have to be hypothesized
Hypothesized Autonomous Transition
Possible current modes
Hypothesized fault mode
Hypothesized intermediate modes
Roll Forward to confirm fault hypotheses
11/13/2018

31. Hybrid Diagnosis: Issues
Sometimes fault detection occurs after mode change occurs
Requires fast roll back process to identify correct model for fault isolation
k-diagnosability: system is k-diagnosable if the effects of a fault manifest themselves in k mode transitions.
Issues:
Fast roll back process up to k modes
What to propagate across mode-change boundaries?
Lemma 1: If controller model is “correct”, fault must have occurred in one of the modes in the mode trajectory
11/13/2018

32. Hybrid Diagnosis: Issues
To compare against current behavior, fault signatures have to be generated by a quick roll forward process
Issue: Autonomous changes cannot be correctly predicted.
Tracking process invokes multiple paths
11/13/2018

33. Fault Isolation & Identification
Roll Back Process
Candidate Set
<fault,mode>
Hypothesis Generation
(Back Propagation)
Signal to Symbol
Generator
Past Mode
Trajectory
Mode mi
Qualitative Hypotheses Refinement
Forward Prop + Prog Monitoring
Quick Roll Forward
Refined
Candidate Set
<fault,mode>
current mode
From Hybrid Bond Graphs
Temporal Causal
Graphs (TCGs)
Observations
Quick Roll Forward
Quantitative Hypotheses Refinement
Parameter Estimation
State Space
Models
Refined
Candidate Set
<fault,mode>
current mode
Online estimation
11/13/2018

34. Roll Back Process Qualitative Hypotheses Generation
Fault: Leak in Drain Pipe
Qualitative Hypotheses Generation
Back propagate through TCG in current mode to identify candidates
Back propagate across mode transitions using transition conditions (need to account for reset conditions, and change in plant configuration – invert qualitatively)
Repeat same process for previous modes to identify more candidates
Tank 1 Pressure
Tank 2 Pressure
Tank 3 Pressure
Transition
Fault Occurred
Fault Detected
System Autonomous Transition
At time of fault detection,
Current Mode Candidates = C2+(0-+ ,-+- ,000 ), C1+(-+- ,0-+ ,000 ), R1- (0-+ ,00- ,000 ), R12- (0-+ ,0+- ,000 )
Previous Mode Candidates = C1+(-+- ,000 ,000 ), R1- (0-+ ,000 ,000 )
11/13/2018

35. Quick Roll Forward
In continuous case, mismatch implies fault hypothesis is not consistent. However, in hybrid tracking, it may imply that we are not in the right mode. We need to identify the current mode (roll forward)
All controlled transitions are known, but we have to hypothesize autonomous transitions since observer can no longer predict them correctly
Use fault signatures to hypothesize mode transitions
Tank 1 Pressure
Tank 2 Pressure
Tank 3 Pressure
Transition
Fault Occurred
Fault Detected
System Autonomous Transition
At time of fault detection,
Current Mode Candidates = C1-(+-+ ,000 ,000 ), R1+ (0+- ,000 ,000 )
No Previous mode candidates
11/13/2018

36. Real-life example: Aircraft Fuel System
New models built based on feedback from Boeing
MATLAB simulation for the system
Experiments in tracking and FDI
Model:
22 components
6 state variables
7 measured variables
6 control signals
60+ symbolic equations
11/13/2018

37. Fuel System Experiments: Parameter values
Component
Parameter
Name
Value
Kalman Filter
Sensor Accuracy
0.05
Modeling Error
0.001
Fault Detector
Fault Detection Threshold
2-3
Window Size (Variance Estimation) 50
Window Size (Mean Estimation) 5
Fault Isolation: Symbol Generation
Slope Detection Sensitivity 1
Window Size 11
Fault Identification: Parameter Estimation
Number of Samples
<=400
Error Function
Parabolic
FDI system: Design Parameters
11/13/2018

38. Real-life example: Aircraft Fuel System
Left Wing Tank Pump Degradation at t = 150
Pump fault 433 sec
Transfer manifold
pressure
Left Wing Tank
pressure
Initial Set
= 13 candidates
11/13/2018

39. Real-life example: Aircraft Fuel System
Left Wing Tank Pump Degradation at t = 150
Left Wing Tank
Pressure: - (below nominal)
4 candidates
11/13/2018

40. Real-life example: Aircraft Fuel System
Left Wing Tank Pump Degradation at t = 150
After parameter estimation
True fault: LWTTF-
value=0.66
Observer updated: Tracking
Again successful
11/13/2018

41. Real-life example: Aircraft Fuel System
Left Wing Tank Pump Degradation at t = 150
TCG LOG
11/13/2018

42. Aircraft Fuel System Time Measured Deviation Fault Set 433 434 439 465
Left Wing Tank Pump Degradation at t = 150
Time
Measured Deviation
Fault Set
433
Transfer Manifold Pressure (XMP)
13 candidates
434
XMP: discontinuous
10 candidates
439
465
Mode Change: Left Feed Tank
Mode Change: Left Feed Tank Off
469
Left Wing Tank Pressure ++
LWT_Pipe.R+, LWT.TF-
LWT.R+, Leg26.R-
471
Mode Change: Left Wing Tank: Pump On
489
Left Feed Tank Pressure --
LWT.R+
528
Mode Change: Left Feed Tank On
Parameter Estimation started
LWT.TF-: fault coefficient: 0.658
Summary of
Results
11/13/2018

43. Fuel System: Experimental Results
Faults
Performance Parameters
Fault Type
Fault Magnitude
Fault Detection Time
Fault Isolation Time
Initial/Final Candidate Set
Parameter Estimation Error
Noise level 2% 3%
LTT-Pump
Efficiency Drop
33%
422
555
225
398
14/3
13/4
2.19
5.43
60%
182
183
144
240
1.28
1.79
80%
134
124
197
13/5
0.88
1.49
RWT-Pump
117
285
170
211
2.15
6.11 83 93
139
1.52
1.67 5 55
106
13/3
0.68
RLCV –Block
(valve)
 1.5 63 65 97
103
25/2
0.62
0.5
 1.75 51 58 86
23/1
0.28
0.46
 2.00 52 46 79
0.2
Leg21-Pipe
(Block) 99
100
136
350
1.58
1.65 95 90
303
14/2
0.78
0.57 76
202
0.19
0.34
11/13/2018

44. Diagnosability of Faults
Aircraft Fuel System
Diagnosability of Faults
Using simulated data
Measured Variables for experiment:
output pressures at the wing,transfer, and feed tanks,
& pressure at transfer manifold.
2% noise in measured signals (Gaussian)
WTP
WTR
TTP
TTR
TMR
SPR
FTP
FTR – X 
WT – Wing Tank
TT – Transfer Tank
TM – Transfer Manifold
FT – Feed Tank
P: Pump, R: Resistance
Using TCG diagnostics -- cannot differentiate between pump degradation and pipe leak on a segment
Need additional measurements: e.g., flow rates, pump output
11/13/2018

45. Summary Modeling of Physical Hybrid Systems using Hybrid Bond Graphs
Computational models derived –
Hybrid Automata
State Space Equations
Temporal Causal Graph
Fault Diagnosis: Process parameter based using qualitative + quantitative methods
Hybrid Observers
Robust Fault Detection + Symbol Generation
Fault Isolation (Qualitative)
Fault Identification (Parameter estimation)
Toolset for modeling, tracking, FDI, and fault-adaptive control
11/13/2018

46. Tool chain development
Software Components
Tool chain development

47. Software Generation FML file:
Model Database
for
Plant, Components,
and Controller
FML file:
Compact, textual representation of the models
Desktop
Run-time
package
Generator
(Model
Interpreter)
CPP/H files:
Models in the form of executable C++ code
Platform Run-time
package
Generator produces
Loadable model file for desktop experiment environment
Executable C++ code for embedded platform
11/13/2018

48. Tool Operations 2. Desktop experimentation, validation 1. Modeling
3. Feedback
Model
Interpretation
4. Deployment on embedded platform
11/13/2018

49. Application options Hybrid diagnosis in a user application
Data
Collection
Component failures, magnitudes
Fault Diagnostics Application:
IVHM Monitoring and Fault Isolation
11/13/2018

50. Application options Fault diagnostics, monitoring, and control
IVHM Fault Diagnostics,
Monitoring and Control
Data
Collection
Output
Interface
Component failures, magnitudes
11/13/2018

51. Application options Fault diagnostics and reconfigurable control
IVHM – Fault-adaptive Control
Data
Collection
Root failure modes
Output
Interface
Component failures, magnitudes
11/13/2018

52. FACT Integration with other tools
Diagnosability Analysis
Detectability
Distiniguishability
Ambiguity sets
Simulation Tools
Discrete-event:
Failure propagation
Continuous time:
Hybrid system (Simulink/Stateflow)
FACT Toolsuite
Modeling Tool
Desktop Environment
Deployment Platform
FMECA
Import Translator
Failure modes
Monitors
Components
Memory usage estimator
Based on platform
Integration with autocoder
Connection towards Matrix-X
11/13/2018

53. FACT: Interpeters
Generate task specific analysis tools and synthesize software components from the models
Simulink/Stateflow models for simulation/
experimental testbed
Hybrid automata (state-space)
models for system observers
Hybrid TCG models for FDI
Discrete Time models for
model-predictive control
Models
Interpreters
Tools
Systems
11/13/2018

54. Building Simulation Models using Simulink (original method)
Preserves component based hierarchy of the model
Utilizes bond graph component model library
Mode switching triggers new causal assignments in
the model using the SCAP algorithm
Fault scenarios easily created using graphical
utility
Sensors in the model mapped to Simulink scopes
Collect nominal + fault data for experimental
studies
Problems with this approach:
Junction switching implemented as standard Simulink switches
All input output signals had to rerouted dynamically at all junctions
Number of switches required very large
Solution:
Clean separation between continuous simulation and control structure for model reconfiguration
Implement switching function as C S-functions
11/13/2018

55. Bond Graphs (BG)  Computational Models
BG to Block Diagram Computational Model
Constituent element blocks + algebraic relations at junctions
Facilitated by exploiting causality in BG structure
Well defined causality assignment procedures (e.g., SCAP: Rosenberg and Karnopp, and others)
Determining Bond (DB)
One per junction, derived from causality at junction
Determines algebraic relations
11/13/2018

56. BG  block diagram conversion (Ignore switching junctions)
– Each BG element, i.e., sources, capacities,
inertias and resistive elements replaced by a
block expressing effort-flow relations
– Each bond replaced by two links
– Each junction replaced by block that models
algebraic constraints imposed by bond
Assumptions:
no algebraic loops
no elements in
derivative causality
11/13/2018

57. Example BG  Block Diagram
Bond Graph Model
BG Component Library
Computational Structure: BG Junction
Translated Block Diagram Model
11/13/2018

58. Issues in HBG  Block Diagram Translation Process
HBG Complexities
Junction switches (on and off) may cause causality changes at runtime, thus block diagram may change
Only changes in DBs will change algebraic relations at junction
These changes can propagate
Both Junctions, a and b On
Junction a turned Off
Determining bond for adjacent 0
junction changes
Changes propagate through all other
junctions
11/13/2018

59. Possible Approaches to Simulation Model Generation
Pre-generation of model configurations results in 2n possibilities
Online generation of models at every mode change can be computationally expensive
Our approach: derive new block diagram incrementally from old
Start with block diagram in initial mode
Look for changes in DBs
Update block diagram at changes
11/13/2018

60. Our Approach Details Model Creation in Simulink Run time
First build library of BG components as Simulink blocks: implemented as Matlab scripts
Implement Junctions as C S-function
Use add-block function to build hierarchy of connected component models along with determining bond information (SCAP algorithm)
Run time
11/13/2018

61. I-Element Component Construction
% Input Port
add_block('built-in/Inport',[sys,'/','Effort'])
set_param([sys,'/','Effort'],...
'Port','1',...
'position',[30,30,50,45])
% Initial Condition
add_block('built-in/Constant',[sys,'/','InitialCondition'])
set_param([sys,'/','InitialCondition'],...
'position',[30, 110, 50, 130])
% Inertia
add_block('built-in/Constant',[sys,'/','Inductance'])
set_param([sys,'/','Inductance'],...
'position',[30, 220, 50, 240])
% Math Function (Reciprocal)
add_block('built-in/Math',[sys,'/','Reciprocal'])
set_param([sys,'/','Reciprocal'],...
'Function','Reciprocal',...
'position',[125, 215, 145, 245])
% Product1
add_block('built-in/Product',[sys,'/','Product1'])
set_param([sys,'/','Product1'],...
'position',[120, 112, 150, 143])
% Integrator
add_block('built-in/Integrator',[sys,'/','Integrator'])
set_param([sys,'/','Integrator'],...
'InitialConditionSource','External',...
'position',[210, 72, 250, 123])
% Output Port
add_block('built-in/Outport',[sys,'/','Flow'])
set_param([sys,'/','Flow'],...
'Port','1',...
'position',[435, 142, 455, 158])
% Product2
add_block('built-in/Product',[sys,'/','Product2'])
set_param([sys,'/','Product2'],...
'position',[320, 132, 350, 163])
% Add connections
add_line(sys, 'Effort/1','Integrator/1')
add_line(sys, 'InitialCondition/1','Product1/1')
add_line(sys, 'Inductance/1','Product1/2')
add_line(sys, 'Product1/1','Integrator/2')
add_line(sys, 'Integrator/1','Product2/1')
add_line(sys, 'Inductance/1','Reciprocal/1')
add_line(sys, 'Reciprocal/1','Product2/2')
add_line(sys, 'Product2/1', 'Flow/1')
11/13/2018

62. Junction implementation
/* Function: mdlOutputs
* Abstract:
* This function computes the outputs of the S-function block.
* Generally outputs are placed in the output vector, ssGetY(S). */
static void mdlOutputs(SimStruct *S, int_T tid) {
const real_T *in1 = (const real_T*) ssGetInputPortSignal(S,0);
const real_T *in2 = (const real_T*) ssGetInputPortSignal(S,1);
real_T *out1 = ssGetOutputPortSignal(S,0);
real_T *out2 = ssGetOutputPortSignal(S,1);
real_T *control_output = ssGetOutputPortSignal(S,2);
const mxArray *determiningbonds;
double *dbdata;
int dbond;
// First, get the determining bond:
determiningbonds = mexGetVariablePtr("global", "determiningbonds");
// determiningbond == -1 means junction is off
if(dbond == -1) {
…} else { …
// get array of effort/flow inputs: …
// sum all dependent inputs with appropriate signs }
// output resulting sum on determinte bond,
// determinite bond's input on remainding:
// put outputs to out#:
out1[0] = outputs[0]; ….
1  determining bond
Junction switching on  off
11/13/2018

63. Our Approach Details Model Creation Run time ….
If junctions change state at a particular time step (implemented as a separate Simulink block)
Apply causality propagation update function, i.e., find new determining bonds (efficient algorithm)
Send new information to junction blocks & simulate next time step
11/13/2018

64. Causality Propagation Details
Causality update triggered by change in discrete state
Start at junctions which switch
If they cause changes in adjacent junction DBs then
update DB’s algebraic constraints
Continue till no DB change or all junctions visited
For efficiency, junctions implemented as S-functions; use global variables (cf. Ptolemy’s director function)
Causality
Update
one 1
System.one
zero
S-function 2 3
S-function 2
S-function 3
S-function 4
S-function 5
System.zero 5 4
11/13/2018

65. Example – Junction Switching
11/13/2018

66. Conclusions and Future Work
Successful demonstrations of FACT – Hybrid Diagnosis on desktop environments
Desktop simulation environments using Simulink as a design and analysis tool
Now working on interface to hardware systems ( instrumented 3 tank system)
Next: Multi-level decision-theoretic controller for managing resources in hierarchical, distributed, interacting subsystems
Global system operates system within resource constraints while optimizing performance of subsystems
Safety, robustness, and reliability based on dynamic models
Tighter bounds on sizing problems at design time
Other Work
Incipient fault diagnosis
Distributed diagnosis
Diagnosis of multiple faults
11/13/2018

67. References
P. J. Mosterman and G. Biswas, “A theory of discontinuities in physical system models,” Journal of the Franklin Institute: Engineering and Applied Mathematics, 335B(3): , January 1998.
P.J. Mosterman and G. Biswas, “Building Hybrid Observers for Complex Dynamic Systems using Model Abstractions,” Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, vol. 1569, Springer Verlag, The Netherlands, pp , March 1999.
E.J. Manders, G. Biswas, P.J. Mosterman, L. Barford, and J. Barnett, ``Signal Interpretation for Monitoring and Diagnosis: A Cooling System Testbed,’’ IEEE Trans. on Instrumentation and Measurement, vol. 49(3), pp , 2000.
S. McIllraith, G. Biswas, D. Clancy, and V. Gupta, ``Hybrid Systems Diagnosis,'' Hybrid Systems: Computation and Control -- Third Intl. Workshop, HSCC 2000, Lecture Notes in Computer Science, vol. 1790, N. Lynch and B. H. Krogh, eds., Springer Verlag, Berlin, Germany, pp , March 2000.
P.J. Mosterman and G. Biswas, “A Hybrid Modeling and Simulation Methodology for Dynamic Physical Systems, SIMULATION: Transactions of the Society for Modeling and Simulation International, vol.78, no.1, pp.5-17, Jan
S. Narasimhan and G. Biswas, “An Approach to Model-Based Diagnosis of Hybrid Systems,'' Hybrid Systems: Computation and Control, Fifth Intl. Workshop, Stanford, CA, Lecture Notes in Computer Science, vol. LNCS 2289, C.J. Tomlin and M.R. Greenstreet, eds., Springer Verlag, Berlin, pp , March 2002.
S. Narasimhan, G. Biswas, G. Karsai, T. Szemethy, T. Bowman, M. Kay, and K. Keller, “Hybrid Modeling and Diagnosis in the Real World: A Case Study,'' Intl. Workshop on Principles of Diagnosis, Simmering, Austria, May 2002.
G. Karsai, G. Biswas, S. Narasimhan, T. Szemethy, G. Peceli, G. Simon, and T. Kovacshazy, “Towards Fault-Adaptive Control of Complex Dynamic Systems,” Software-Enabled Control: Information Technologies for Dynamical Systems, T. Samad and G. Balas, eds., IEEE Press, pp , 2003.
E.J. Manders and G. Biswas, “FDI of abrupt faults with combined statistical detection and estimation and qualitative fault isolation,” 5th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (SAFEPROCESS), Washington, D.C., pp , June 2003.
S. Narasimhan and G. Biswas, “Model-based Diagnosis of Hybrid Systems,” to appear IEEE Transactions on Systems, Man, and Cybernetics, Part A, to appear Sept
E.J. Manders, G. Biswas, N. Mahadevan, G. Karsai, "Component-oriented modeling of hybrid dynamic systems using the Generic Modeling Environment," pp ,  Fourth Workshop on Model-Based Development of Computer-Based Systems and Third International Workshop on Model-Based Methodologies for Pervasive and Embedded Software (MBD-MOMPES'06),  2006.
11/13/2018

68. Lecture 3 Limited Lookahead + Hierarchical Control
Distributed Diagnosis
Diagnosis of Incipient Faults
11/13/2018