## Higher-Order Derivative Constraints in Qualitative Simulation (1991)

Venue: | Artificial Intelligence |

Citations: | 7 - 3 self |

### BibTeX

@ARTICLE{Kuipers91higher-orderderivative,

author = {Benjamin Kuipers and Charles Chiu and David T. Dalle Molle and David Throop},

title = {Higher-Order Derivative Constraints in Qualitative Simulation},

journal = {Artificial Intelligence},

year = {1991},

volume = {51},

pages = {343--379}

}

### OpenURL

### Abstract

Qualitative simulation is a useful method for predicting the possible qualitatively distinct behaviors of an incompletely known mechanism described by a system of qualitative differential equations (QDEs). Under some circumstances, sparse information about the derivatives of variables can lead to intractable branching (or "chatter") representing uninteresting or even spurious distinctions among qualitative behaviors. The problem of chatter stands in the way of real applications such as qualitative simulation of models in the design or diagnosis of engineered systems. One solution to this problem is to exploit information about higherorder derivatives of the variables. We demonstrate automatic methods for identification of chattering variables, algebraic derivation of expressions for second-order derivatives, and evaluation and application of the sign of second- and third-order derivatives of variables, resulting in tractable simulation of important qualitative models. Caution is requir...

### Citations

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(Show Context)
Citation Context ...ption of a single maximum for netf lowB(t) were used at t = 150 to predict the minimum time until amountB = 2000, a significant error would result. AIJ, 1991 30 OutflowA = M+(AmountA) (1) (2) (3) (4) =-=(5)-=- Outflow 3 Amount x 10-2.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.00 26.00 28.00 30.00 32.00 34.00 36.00 38.00 40.00 42.00 44.00 0.00 0.50 1.00 1.50 2.00 2.50 3.00 Netf... |

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(Show Context)
Citation Context ...he assumption of a single maximum for netf lowB(t) were used at t = 150 to predict the minimum time until amountB = 2000, a significant error would result. AIJ, 1991 30 OutflowA = M+(AmountA) (1) (2) =-=(3)-=- (4) (5) Outflow 3 Amount x 10-2.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.00 26.00 28.00 30.00 32.00 34.00 36.00 38.00 40.00 42.00 44.00 0.00 0.50 1.00 1.50 2.00 2.50 3... |

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(Show Context)
Citation Context ...branching due to chatter In a qualitative model of two cascaded tanks (A and B), Netf lowB(t) = Inf lowB(t) \Gamma Outf lowB(t) is constrained only by continuity as long as it remains in the interval =-=(0; 1). Thus, the sim-=-ulation branches on all possible trajectories of Netf lowB(t), while all other variables have completely uniform behavior. AIJ, 1991 7 " \Psi " \Psi # j j j3 j j3 - Q Qs (a) " \Psi # j ... |

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(Show Context)
Citation Context ...ssumption of a single maximum for netf lowB(t) were used at t = 150 to predict the minimum time until amountB = 2000, a significant error would result. AIJ, 1991 30 OutflowA = M+(AmountA) (1) (2) (3) =-=(4)-=- (5) Outflow 3 Amount x 10-2.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.00 26.00 28.00 30.00 32.00 34.00 36.00 38.00 40.00 42.00 44.00 0.00 0.50 1.00 1.50 2.00 2.50 3.00 ... |

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(Show Context)
Citation Context ...If the assumption of a single maximum for netf lowB(t) were used at t = 150 to predict the minimum time until amountB = 2000, a significant error would result. AIJ, 1991 30 OutflowA = M+(AmountA) (1) =-=(2)-=- (3) (4) (5) Outflow 3 Amount x 10-2.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 22.00 24.00 26.00 28.00 30.00 32.00 34.00 36.00 38.00 40.00 42.00 44.00 0.00 0.50 1.00 1.50 2.00 2.... |

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