Kuipers, B., Chiu, C., Molle, D. D., & Throop, D. [1991]. Higher--order derivative constraint in qualitative simulation. Artificial Intelligence, 51, 343--379.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a combination of these two behaviors. This distinction helps to answer the question: Is chatter an actual behavior of the modeled system While in certain instances, chatter may be the result of spurious behaviors 3 , in general chatter reflects potential behaviors of the modeled system (Kuipers, Chiu, Molle, Throop, 1991). Since chatter is a property of a 3 A qualitative behavior is spurious if there does not exist a corresponding real valued trajectory. 0 std) 0 dec) 0 inc) 0 inf) std) 0 inf) dec) 0 inf) inc) inf inc) inf std) inf dec) minf inc) minf std) minf dec) minf 0) inc) minf 0) ....

....system. a This example is taken from (Kuipers, 1994) page 256. Figure 4.5: Numerical Simulation of a Two Tank Cascade comparison of the two techniques is provided. 4.2 Previous Solutions Two previous methods have been developed for eliminating chatter. The higher order derivative (HOD) (Kuipers et al. 1991) technique uses the second and third order derivatives of the chattering variables to determine the direction of change; the ignore qdirs approach simply ignores distinctions in the derivative of variables identified by the modeler as chattering. Neither of these techniques provide a general ....

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Kuipers, B., Chiu, C., Molle, D. D., & Throop, D. (1991). Higher--order derivative constraint in qualitative simulation. Artificial Intelligence, 51, 343--379.

....trajectories, whereas others turn out to be physically impossible. QSIM is therefore incomplete (for QSIM is unable to provide only true behaviors) To reduce the number of such spurious behaviors, during recent years, several extensions have been added to QSIM: the use of higher order derivatives [Kuipers et al. 1991], energy functions [Fouch e and Kuipers, 1990] phase space criteria [Lee and Kuipers, 1993] and abstraction techniques [Clancy and Kuipers, 1993] each contributes to a significant reduction (yet not a complete elimination) of spurious behaviors. In the semi quantitative framework employed by ....

....on the appropriate QSIM switches to achieve it, and have SQPC compute an attainable envisionment, obtaining however much less detailed predictions. Fortunately, several techniques have been developed for coping with such problems when producing qualitative simulations [Fouch e and Kuipers, 1990; Kuipers et al. 1991; Lee and Kuipers, 1993; Clancy and Kuipers, 1993] In the context of SQPC, what is needed is: ffl a mechanism for selecting the most appropriate tool, on a model by model basis, for handling these problems when they appear; for example when chattering variables are recognized in a model, SQPC ....

B. Kuipers, C. Chiu, D. Dalle Molle, and D. Throop. Higher--order derivative constraint in qualitative simulation. Artificial Intelligence, 51:343--379, 1991.

....or initial states. Another reason is that the simulation algorithm is too weak to discard behaviors which are inconsistent. Especially, spurious behaviors can mislead the diagnosis algorithm. The large number of behaviors can be at least partially reduced by (i) improved filtering algorithms [KCMT91] CK93] ii) using semi quantitative or numerical information [KK93] BK92] and (iii) hierarchical structuring of the behaviors [Kui88] ffl Running time requirements: QSim as a research tool is implemented in Lisp and executed on general purpose computers. The running time is not a major ....

Benjamin J. Kuipers, Charles Chiu, David T. Dalle Molle, and D. R. Throop. Higher-order derivative constraints in qualitative simulation. Artificial Intelligence, 51:343--379, 1991.

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Kuipers, B., Chiu, C., Molle, D. D., & Throop, D. [1991]. Higher--order derivative constraint in qualitative simulation. Artificial Intelligence, 51, 343--379.

....tree. Similar behaviors are combined into a single aggregate behavior during simulation to eliminate occurrence branching. Occurrence branching is due to the complete temporal ordering of events whose order is not constrained by the QDE. This builds on work done by Williams [1986] and Fouch e and Kuipers [1991]. Chatter Box Abstraction eliminates chatter from a behavior tree simulation by performing a limited envisionment when A1 4 A2 1 1 2 3 4 5 6 7 (a) 1 3 10 10 11 12 13 (b) c) B1 B2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 (d) Figure 1: Partial ....

....the state variables. The behavior tree representation along with the new landmarks are used by behavior based filters [Fouch e and Kuipers, 1992, Lee and Kuipers, 1988] to eliminate spurious behaviors from the tree. Semi quantitative reasoning techniques [Kuipers and Berleant, 1988, Berleant and Kuipers, 1991, Kay and Kuipers, 1992] provide a more detailed description of the behaviors by inferring quantitative bounds for the newly introduced landmarks within the behavior tree. Williams [1986] describes an alternate simulation technique based upon individual variable histories. A history defines a ....

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B. J. Kuipers, C. Chiu, D. Dalle Molle and D. R. Throop. Higher-order derivative constraints in qualitative simulation. Artificial Intelligence, 51:343-379, 1991.

....ffl Other techniques (higher order derivatives and ignoring qdirs) are unable to eliminate chatter in NetflowB. Figure 2: Intractable branching due to chatter in the simulation of a W tube. around zero as its integral chatters. While chattering behaviors may describe a real behavior of the system (Kuipers et al. 1991), a disjunctive enumeration of all possible combinations of values provides no information. Furthermore, this enumeration obscures other distinctions within the description and can result in an infinite simulation. Eliminating this source of distinctions is essential if qualitative simulation is ....

....Eliminating this source of distinctions is essential if qualitative simulation is to be used to reason about complex dynamical systems. Previous Solutions Two previous methods have been developed for eliminating chatter within a QSIM behavior tree simulation. The higher order derivative (HOD) (Kuipers et al. 1991) technique uses the second and third order derivatives of the chattering variables to determine a unique direction of change for unconstrained variables and eliminate spurious behaviors. When possible, higher order derivatives expressions are derived via algebraic manipulation of the ....

[Article contains additional citation context not shown here]

B. J. Kuipers, C. Chiu, D. Dalle Molle and D. R. Throop, 1991. Higher-order derivative constraints in qualitative simulation. Artificial Intelligence, 51:343-379, 1991.

....chatter around zero, occurs when a variable and its derivative are represented explicitly within a model and both of them exhibit chatter. In this case, the derivative variable will chatter around zero as its integral chatters. While chattering behaviors may describe a real behavior of the system (Kuipers et al. 1991), a disjunctive enumeration of all possible combinations of values provides no information. Furthermore, this enumeration obscures other distinctions within the description and can result in an infinite simulation. Eliminating this source of distinctions is essential if qualitative simulation is ....

....Eliminating this source of distinctions is essential if qualitative simulation is to be used to reason about complex dynamical systems. Previous Solutions Three previous methods have been developed for eliminating chatter within a QSIM behavior tree simulation. The higher order derivative (HOD) (Kuipers et al. 1991) technique uses the second and third order derivatives of the chattering variables to determine a unique direction of change for unconstrained variables and eliminate spurious behaviors. When possible, higher order derivatives expressions are derived via algebraic manipulation of the ....

[Article contains additional citation context not shown here]

B. J. Kuipers, C. Chiu, D. Dalle Molle and D. R. Throop. Higher-order derivative constraints in qualitative simulation. Artificial Intelligence, 51:343-379, 1991.

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Kuipers Benjamin. Higher-order Derivative Constraints in Qualitative Simulation. Artificial Intelligence 51 (1991) 343-379.

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