SQSIM: A simulator for imprecise ODE models

Computers and Chemical Engineering

Volumn 23, Issue 1, 1998, Pages 27-46

  Kay, Herbert ^a,b   Kuipers, Benjamin ^b  

^a NASA AMES RESEARCH CENTER   (United States)

^b University of Texas at Austin   (United States)

Author keywords

CSTR; Imprecision; ODE; Robustness; Semiquantitative; Simulation

Indexed keywords

COMPUTER SIMULATION; INFERENCE ENGINES; MATHEMATICAL MODELS; PROBABILITY;

FUNCTIONAL UNCERTAINTY; IMPRECISION; SEMIQUANTITATIVE SIMULATOR;

ORDINARY DIFFERENTIAL EQUATIONS;

ACCURACY; ENGINEERING; MATHEMATICAL MODEL; PREDICTION; REVIEW; SIMULATION;

EID: 0032535836     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0098-1354(98)00268-3     Document Type: Article

References (29)

1. Aubin, J. P., & Cellina, A. (1984). Differential Inclusions. Springer: Berlin.
2. Berleant, D., & Kuipers, B. (1992). Combined qualitative and numerical simulation with Q3. In: Faltings, B., & Struss, P. (Eds), Recent advances in qualitative physics. Cambridge, MA: MIT Press.
3. Bothe, D. (1992). Multivalued differential equations on graphs. Nonlinear Anal. Theory Methods Appl., 18(3), 245-252.
4. Corliss, G. F. (1995). Guaranteed error bounds for ordinary differential equations. In: Theory of numerics in ordinary and partial differential equations. Oxford: Oxford University Press. Also available at ftp://boris.mscs.mu.edu/pub/corliss/ValidODE.
5. Corliss, G. F. (1995). Introduction to validated ODE solving. Technical Report 416, Department of Mathematics, Statistics and Computer Science - Marquette University, Milwaukee, WI 53233.
6. Dalle Molle, D. (1989). Qualitative simulation of dynamic chemical processes. Technical Report AI89-107, Artificial Intelligence Laboratory, University of Texas at Austin, Austin, TX 78712.
7. Danès, P., Travè-Massuyès, L., & Aguilar-Martin, J. (1993). A generic method for computing the response of a numerically-known dynamic system to qualitative inputs. Proc. IEEE-SMC'93, Le Touquet, France.
8. Dvorak, D. L., & Kuipers, B. (1989). Model-based monitoring of dynamic systems. Proc. 11th Int. Joint Conf. on Artificial Intelligence, pp. 1238-1243.
9. Gazi, E., Kay, H., Kuipers, B., Seider, W. D., & Ungar, L. H. (1993). Controller verification using qualitative reasoning (extended abstract). American Institute of Chemical Engineers.
10. Gazi, E., Seider, W. D., & Ungar, L. H. (1997). A non-parametric Monte-Carlo technique for controller verification. Automatica 33 (5), 901-906.
11. Gelb, A. (1974). Applied optimal estimation. Cambridge, MA: MIT Press.
12. Hüllermeier, E. (1995). Numerical simulation methods for uncertain dynamics. Technical Report tr-ri-95-170, Heinz Nixdorf Institut, Universität-GH-Paderborn, Fürstenaallee 11, D-33102 Paderborn, Germany.
13. Kahaner, D., Moler, C., & Nash, S. (1989). Numerical methods and software. Englewood Cliffs, NJ: Prentice-Hall.
14. Kay, H. (1991). Monitoring and diagnosis of multi-tank flows using qualitative reasoning. Master's thesis, The University of Texas at Austin.
15. Kay, H., & Kuipers, B. (1993). Numerical behavior envelopes for qualitative models. Proc. 11th National Conf. on Artificial Intelligence (AAAI-93), pp. 606-613.
16. Kay, H., & Ungar, H. (1993). Deriving monotonic function envelopes from observations. Working Papers of the 7th Int. Workshop on Qualitative Reasoning about Physical Systems. Orcas Island, Washington, pp. 117-123.
17. Kuipers, B. (1984). Commonsense reasoning about causality: deriving behavior from structure. Artificial Intell, 24, 169-204.
18. Kuipers, B. (1986). Qualitative simulation. Artificial Intell., 29, 289-338.
19. Kuipers, B. (1994). Qualitative reasoning - modeling and simulation with incomplete knowledge. Cambridge, MA: MIT Press.
20. Kuipers, B., & Berleant, D. (1988). Using incomplete quantitative knowledge in qualitative reasoning. Proc. 7th National Conf. on Artificial Intelligence, pp. 324-329.
21. Lohner, R. (1988). Einschließung der Lösung gewöhnlicher Anfangs-und Randwertaufgaben und Anwendungen. Ph.D. Thesis, Universität Karlsruhe.
22. Lunze, J. (1989). Robust multivariable feedback control. Englewood Cliffs, NJ: Prentice-Hall.
23. Markov, S., & Angelov, R. (1986). An interval method for systems of ODE. In: Lecture Notes in Computer Science, 212, 1985. pp. 103-108. Berlin, Springer.
24. Moore, R. E. (1979). Methods and applications of interval analysis. Philadelphia: SIAM.
25. Reckhow, K. H. (1987). Error analysis, first order. In: Singh, M.O. (Ed), Systems and control encyclopedia - theory, technology, applications, Vol. 6, pp. 1552-1553. Oxford: Pergamon Press.
26. Richards, L., Kraan, I., & Kuipers, B. (1992). Automatic abduction of qualitative models. Proc. 10th National Conf. on Artificial Intelligence (AAAI-92), pp. 723-728.
27. Vescovi, M., Farquhar, A., & Iwasaki, Y. (1995). Numerical interval simulation: combined qualitative and quantitative simulation to bound behaviors of non-monotonic systems. Proc. 11th Int. Joint Conf. on Artificial Intelligence, pp. 1806-1812.
28. Walter, W. (1970). Differential and integral inequalities. Berlin: Springer.
29. Zukowski, C. A. (1986). The bounding approach to VLSI circuit simulation. Boston: Kluwer.