[PDF] - 11/22/2006 Massachusetts Institute of Technology Software-Extended PDF Document

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Massachusetts Institute of Technology

Diagnosing Complex Systems with Software-Extended Behavior using Constraint Optimization

Tsoline Mikaelian Brian C. Williams, Martin Sachenbacher 16th International Workshop on Principles of Diagnosis June 1, 2005

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Software-Extended Systems

Mars Polar Lander MERS Rover Testbed Earth Observing One

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Vision-based Navigation Scenario

MERS Rover Testbed

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Vision-based Navigation Scenario

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Vision-based Navigation Scenario

MERS Rover Testbed

Probability Time

Power=off

Power On and Take Picture 6

Vision-based Navigation Scenario

MERS Rover Testbed

Probability Time

Power=off

Power On and Take Picture

1

Nominal Cam=Broken Battery=low Sensor=Broken

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Vision-based Navigation Scenario

MERS Rover Testbed

Probability Time

Power=off

1

Nominal Cam=Broken Battery=low

Power On and Take Picture

2

Observe Sensor voltage = low

Battery=low Sensor=Broken Cam=Broken Sensor=Broken

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Vision-based Navigation Scenario

MERS Rover Testbed

Probability Time

Power=off

1

Nominal Cam=Broken Battery=low

Power On and Take Picture

2

Observe Sensor voltage = low

Battery=low Sensor=Broken Cam=Broken Sensor=Broken

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Vision-based Navigation Scenario

MERS Rover Testbed

Probability Time

Power=off

1

Nominal Cam=Broken Battery=low

Power On and Take Picture

2

Observe Sensor voltage = low

Battery=low Sensor=Broken Cam=Broken Sensor=Broken

………………..……………. 6

Image not corrupt S/W => Sensor=Broken Battery=low Cam=Broken

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Problem and Challenges

Problem: Given observations, commands, and behavior models: Track the most likely state trajectories of the software-extended system over time Challenges: 1. Monitor hardware and software behavior 2. Delayed symptoms 3. Efficiency

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Modeling Framework

Probabilistic, Hierarchical Constraint Automata (PHCA) [Williams, Chung, Gupta 2001]

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Modeling Framework

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Diagnosis Process

PHCA H/W models S/W specs

(code)

[Williams, Chung, Gupta 2001]

HW + SW Behavior

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Diagnosis Process

Offline compilation phase

N-Stage COP PHCA H/W models S/W specs

(code)

Delayed Symptoms

parameter N

Online solution phase

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Encoding PHCA as COP

Constraint Optimization Problem (COP):

Variables
Location variables, PHCA variables, Auxiliary variables
Domains
Example: {Marked, Unmarked} for location variables
Soft constraints/ Valued constraints*
Encode PHCA + Execution semantics
Solve for Location Variables, maximizing value of State Trajectory

N-Stage COP PHCA

*[Schiex, Fargier, Verfaillie,1995] 16

PHCA Encoding Example

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PHCA Encoding Constraints

(AND) (AND)

T1 <source1,guard1,targets1, probability1> T2 <source1, guard2, targets2, probability2>

choice targets1 targets2 (XOR)

(AND)

Categories of Constraints: 1. State consistency and transition guard consistency 2. Initial (t=0) constraints 3. Transition constraints 4. Marking constraints ⇒ We derive a total of 14 constraints (rules) ⇒ Instantiated for any PHCA, for any N-Stage time horizon

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Diagnosis Process

Offline compilation phase

N-Stage COP PHCA parameter N H/W models S/W specs

(code)

Delayed symptoms
Model Simulation
Soft constraints

Online solution phase

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Diagnosis Process

Tree Decomposition

Offline compilation phase

N-Stage COP PHCA H/W models S/W specs

(code)

Efficiency

[Gottlob, Leone, Scarcello 2000; Kask, Dechter, Larossa 2003]

Online solution phase

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Diagnosis Process

Tree Decomposition

bservations

commands

Offline compilation phase Online solution phase

N-Stage COP Optimal Constraint Solver Dynamic update of COP PHCA H/W models S/W specs

(code) 21

Online Diagnosis Phase

Trellis diagram showing PHCA State Evolutions
Online Loop

– Update the COP – Solve the COP – Repeat t0 t1 t2 t5 t6 t3 … t4

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Online Diagnosis Phase

N-Stage K-Best Trajectory Enumeration

N=3 time steps; K=2 trajectories t0 t1 t2 t5 t6 t3 … t4

Obs1, Cmd1 Obs2, Cmd2 Obs3 Obs0, Cmd0 1st Iteration – Update COP

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Online Diagnosis Phase

N-Stage K-Best Trajectory Enumeration

N=3 time steps; K=2 trajectories

1st Iteration – Solve COP

t0 t1 t2 t5 t6 t3 … t4

Obs1, Cmd1 Obs2, Cmd2 Obs3 Obs0, Cmd0

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Online Diagnosis Phase

N-Stage K-Best Trajectory Enumeration

N=3 time steps; K=2 trajectories

2nd Iteration – Update COP

t0 t1

Obs1, Cmd1 Obs2, Cmd2 Obs3, Cmd3

t2 t5 t6 t3 … t4

Obs4

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Online Diagnosis Phase

N-Stage K-Best Trajectory Enumeration

N=3 time steps; K=2 trajectories

2nd Iteration – Solve COP

t0 t1

Obs1, Cmd1 Obs2, Cmd2 Obs3, Cmd3

t2 t5 t6 t3 … t4

Obs4

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Online Diagnosis Phase

N-Stage K-Best Trajectory Enumeration

N=3 time steps; K=2 trajectories

3rd Iteration – Update COP

t0 t1

Obs2, Cmd2

t2

Obs3, Cmd3 Obs5 Obs4, Cmd4

t5 t6 t3 … t4 Delayed Symptom

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Online Diagnosis Phase

N-Stage K-Best Trajectory Enumeration

N=3 time steps; K=2 trajectories

3rd Iteration – Solve COP

t0 t1

Obs2, Cmd2

t2 t5 t6 t3 … t4

Obs3, Cmd3 Obs5 Obs4, Cmd4

Delayed Symptom

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Demonstration Scenarios

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Demonstration Scenarios

MIT SPHERES Testbed Models NASA Earth Observing One (EO-1) Models

Advanced Land Imager
Hyperion Instrument
Wideband Advanced Recorder Processor

EO-1 (12 components)

Global Metrology Subsystem

SPHERES 1 (5 components) SPHERES 2 (18 components)

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Results: Offline

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Results: Online

(1.6 GHz Pentium M) Solver: [Sachenbacher and Williams, 2004]

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Summary and Related Work

Tree Decomposition

bservations

commands

Offline compilation phase Online solution phase

N-Stage COP Optimal Constraint Solver Dynamic update of COP PHCA H/W models S/W specs

(code)

PHCA: [Williams, Chung, Gupta] Delayed Symptoms: Livingstone2 [Kurien and Nayak] Structure: [Darwiche and Provan; Dechter et al.]