10/4/2006 Massachusetts Institute of Technology Diagnosing Complex - PDF document

10/4/2006 Massachusetts Institute of Technology Diagnosing Complex Systems MERS Rover Testbed Model-based Monitoring and Diagnosis of Systems with Software-Extended Behavior Mars Polar Lander Tsoline Mikaelian Brian C. Williams, Martin Sachenbacher 20 th National Conference on Artificial Intelligence July 13, 2005 Earth Observing One 2 Vision-based Navigation Scenario Vision-based Navigation Scenario MERS Rover Testbed 3 4 Vision-based Navigation Scenario Vision-based Navigation Scenario MERS Rover Testbed MERS Rover Testbed Power=off Power=off Nominal Probability Probability Battery=low Cam=Broken Sensor=Broken Time Time 0 0 1 Power On and Take Picture Power On and Take Picture 5 6 1

10/4/2006 Vision-based Navigation Scenario Vision-based Navigation Scenario MERS Rover Testbed MERS Rover Testbed Power=off Power=off Nominal Nominal Battery=low Battery=low Probability Probability Battery=low Battery=low Cam=Broken Cam=Broken Cam=Broken Sensor=Broken Cam=Broken Sensor=Broken Sensor=Broken Sensor=Broken Time Time 0 1 0 1 Observe 2 Observe 2 Sensor Sensor Power On and Take Picture Power On and Take Picture voltage = low voltage = low 7 8 Vision-based Navigation Scenario Problem and Challenges Problem: MERS Rover Testbed Given observations, commands, and behavior models: Track the most likely state trajectories of the software-extended system over time Challenges: 1. Monitor complex behavior Power=off Sensor=Broken Nominal Battery=low Probability Battery=low Cam=Broken 2. Delayed symptoms Battery=low Cam=Broken Sensor=Broken 3. Efficiency Cam=Broken Sensor=Broken Time 1 0 Observe 2 ………………..……………. 6 Sensor Power On and Take Picture voltage = low Image not corrupt S/W => 9 10 Modeling Framework Modeling Framework Probabilistic, Hierarchical Constraint Automata (PHCA) [Williams, Chung, Gupta 2001] 11 12 2

10/4/2006 Diagnosis Process Diagnosis Process parameter N Complex Delayed [Williams, Chung, Gupta 2001] Behavior Symptoms S/W specs S/W specs PHCA PHCA N-Stage H/W models H/W models COP (code) (code) Offline compilation phase Online solution phase 13 14 Encoding PHCA as COP Valued COP PHCA N-Stage COP Valued Constraint Optimization Problem (COP): - Variables - Location variables, PHCA variables, Auxiliary variables - Domains Probabilistic Valuation: - Example: {Marked, Unmarked} for location variables - Valued constraints* *[Schiex, Fargier, Verfaillie,1995] Value of solution: - Encode PHCA + Execution semantics - Solve for Location Variables, maximizing value of State Trajectory 15 16 PHCA Encoding Example PHCA Encoding Constraints targets1 (AND) T1 <source1,guard1,targets1, probability1> choice (XOR) targets2 T2 <source1, guard2, targets2, probability2> (AND) (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 17 18 3

10/4/2006 Diagnosis Process Diagnosis Process [Gottlob, Leone, Scarcello 2000; Efficiency Kask, Dechter, Larossa 2003] observations commands S/W specs S/W specs Tree Tree Dynamic update of COP PHCA N-Stage PHCA N-Stage H/W models Decomposition H/W models Decomposition COP COP Optimal (code) (code) Constraint Solver Offline compilation phase Online solution phase Offline compilation phase Online solution phase 19 20 Online Diagnosis Phase Online Diagnosis Phase • Trellis diagram showing PHCA State Evolutions • N-Stage K-Best Trajectory Enumeration N=3 time steps; K=2 trajectories t0 t6 t1 t2 t3 t4 t5 … t0 t6 t1 t2 t3 t4 t5 … Obs0, Obs1, Obs2, Obs3 • Online Loop Cmd0 Cmd1 Cmd2 – Update the COP – Solve the COP 1st Iteration – Update COP – Repeat 21 22 Online Diagnosis Phase Online Diagnosis Phase • N-Stage K-Best Trajectory Enumeration • N-Stage K-Best Trajectory Enumeration N=3 time steps; K=2 trajectories N=3 time steps; K=2 trajectories t0 t1 t2 t3 t4 t5 t6 … t0 t1 t2 t3 t4 t5 t6 … Obs0, Obs1, Obs2, Obs3 Obs1, Obs2, Obs3, Obs4 Cmd0 Cmd1 Cmd2 Cmd1 Cmd2 Cmd3 1st Iteration – Solve COP 2nd Iteration – Update COP 23 24 4

10/4/2006 Online Diagnosis Phase Online Diagnosis Phase • N-Stage K-Best Trajectory Enumeration • N-Stage K-Best Trajectory Enumeration N=3 time steps; K=2 trajectories N=3 time steps; K=2 trajectories t0 t1 t2 t4 t5 t6 t0 t1 t2 t4 t5 t6 t3 … t3 … Obs1, Obs2, Obs3, Obs4 Obs2, Obs3, Obs4, Obs5 Cmd1 Cmd2 Cmd3 Cmd2 Cmd3 Cmd4 Delayed Symptom 2nd Iteration – Solve COP 3rd Iteration – Update COP 25 26 Online Diagnosis Phase Demonstration Scenarios • N-Stage K-Best Trajectory Enumeration N=3 time steps; K=2 trajectories t0 t6 t1 t2 t3 t4 t5 … Obs2, Obs3, Obs4, Obs5 Cmd2 Cmd3 Cmd4 Delayed Symptom 3rd Iteration – Solve COP 27 28 Demonstration Scenarios Results: Offline MIT SPHERES Testbed Models NASA Earth Observing One (EO-1) Models - Advanced Land Imager -Global Metrology Subsystem - Hyperion Instrument SPHERES 1 (5 components) - Wideband Advanced Recorder Processor SPHERES 2 (18 components) EO-1 (12 components) 29 30 5

10/4/2006 Results: Online Summary and Related Work PHCA: [Williams, Chung, Gupta] Delayed Symptoms: Livingstone2 [Kurien and Nayak] Structure: [Darwiche and Provan; Dechter et al.] (1.6 GHz Pentium M) observations commands S/W specs Tree Dynamic update of COP PHCA N-Stage H/W models Decomposition COP Optimal (code) Constraint Solver Offline compilation phase Online solution phase Solver: [Sachenbacher and Williams, 2004] 31 32 6