Challenges in Modeling Continuous Measurements and Quantitative Constraints in Discrete Techniques

1. Continuous Measurements and Quantitative ConstraintsChallenge Problems for Discrete Modeling Techniques Charles H. Goodrich Dynacs, Inc. Kennedy Space Center James Kurien NASA, Ames Research Center

2. Modeling Real-world Processes • Capabilities and benefits of models • Challenge posed by continuous processes • Discrete abstractions • Hybrid models • A Successful discrete model • Examples of discrete unconformity • Features of non-conforming processes • Suggestions for hybrid solutions

3. Benefits of Model-based Reasoning • State identification • Diagnosis • Sensor validation • Control • Planning

4. open Discrete Model Compatibility closed Ranges Qualities • Binary

5. Challenges for Discrete Abstractions Quantity Time Capacity

6. Continuous Model:Heating -20oC T(t)=25-45e-0.05t

7. Continuous Model:Cooling -20oC T(t)=-10+35e-0.05t

8. Discrete Thermostat Abstraction T < Low Set Point Heating T’ >= 0 Heater On Cooling T’ < 0 Heater Off T > High Set Point

9. CassiniPropulsionSystem Oxidizer Tank Heliumtank Main Engines Fuel tank

10. Discrete Diagnosis & Control • Component modes • Transitions • Normal modes • Failure modes

11. Basic Discrete Algorithm • Diagnosis: Search for a failure mode consistent with observations • Control: Search for normal component transition(s) that enforce desired conditions Valve Model

12. Diagnosing Propulsion Failure O2 V1 V3 He Fuel V2

13. Normal Pressure P P P P P P P P P P P P P P Larger System Magnifies impact of observations Oxidizer Tank ? Heliumtank Main Engines Fuel tank

14. Reverse Water Gas Shift

15. reactor CO2 FLOW: Input > 50? “high” “expected” +/- ?? H2 FLOW: Problems for Discrete-only Models • “low/expected/high” characterization • “zero” = “expected” ? • Calculate “expected” externally • Comparison between real-value parameters

16. Unidirectional flows No need to adjust continuous parameters No closed loop control No time factor in diagnosis Only discrete control factors; e.g. open/close Branching or multi-directional fluid flows Storage tanks or other capacity items Real-valued control factors Closed loop control Cassini vs. RWGS

17. Constraint Net - Hybrid Solution

18. Diagnosis: Suspend one constraint at a time Calculate value using other constraints Consistent value? = valid suspect Control: Express goal as set of constraints Use constraint net - calculate commands Outline of a Hybrid Solution

19. X 15 ampsP M M M Hybrid Diagnosis • Suspend one constraint at a time 4.95 gMol/hr 8 gMol/hr H2 feed rate F1 1.5 cc/min 1.5 cc/minP electrolyzer H2O use rate Legend: X command O2 flow rate Electrolyzer current M measurement 2.55 gMol/hr 2.55 gMol/hrP 24/15 amps 15 amps

20. F1 X 11.76 amps M M Hybrid Control • Express goal as set of constraints • Use constraint net - calculate commands H2 feed rate electrolyzer H2O use rate O2 flow rate Electrolyzer current 2.0 gMol/hr

21. Challenge Problems for Discrete Modeling Techniques • Benefits of model-based reasoning • Discrete abstractions of continuous processes • Successful • Problematic • Features of non-conforming processes • Suggestions for hybrid solutions