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SQsim: A Simulator for Imprecise ODE Models
 COMPUTERS AND CHEMICAL ENGINEERING 23 (1998) 2746
, 1998
"... This article describes a method for representing and simulating ordinary differential equation (ODE) systems which are imprecise  that is, where the ODE model contains both parametric and functional uncertainty. Such models, while useful in engineering tasks such as design and hazard analysis, are ..."
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Cited by 15 (3 self)
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This article describes a method for representing and simulating ordinary differential equation (ODE) systems which are imprecise  that is, where the ODE model contains both parametric and functional uncertainty. Such models, while useful in engineering tasks such as design and hazard analysis, are not used in practice because they require either special structures which limit the describable uncertainty or produce predictions which are extremely weak. This article describes SQSIM (for SemiQuantitative SIMulator), a system which provides a general language for representing and reasoning about many common forms of engineering uncertainty. By defining the model both qualitatively and quantitatively and by using a simulation method that combines inferences across the qualitativetoquantitative spectrum, SQSlM produces predictions that maintain a precision consistent with the model imprecision.
A customized logic paradigm for reasoning about models, in
 Farquhar (Eds.), Proc. 10th International Workshop on Qualitative Reasoning (QR96), Stanford Sierra Camp, CA, AAAI
, 1996
"... Abstract Modeling is the process of constructing a model of a target system that is suitable for a given task. Typically, in the hierarchy from moreabstract to lessabstract models, the model of choice is the one that is just detailed enough to account for the properties and perspectives of interes ..."
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Cited by 7 (4 self)
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Abstract Modeling is the process of constructing a model of a target system that is suitable for a given task. Typically, in the hierarchy from moreabstract to lessabstract models, the model of choice is the one that is just detailed enough to account for the properties and perspectives of interest for the task at hand. The main goal of the work described here was to design and implement a knowledge representation framework that allows a computer program to reason about physical systems and candidate models (ordinary differential equations, specifically) in such a way as to find the right model at the right abstraction level as quickly as possible. A key observation about the modeling process is the following. Not only is the resulting model the least complex of all possible ones, but also the reasoning during model construction takes place at the highest possi61e level at any time. Because of this, the knowledge representation framework was designed to allow easy formulation of knowledge and meta knowledge relative to various abstraction levels. Candidate models are constructed via simple, powerful domain rules. The customized knowledge representation framework is then used to generate new knowledge about the physical system and new knowledge about the candidate model. A candidate model is valid if the facts about the system that is to be modeled are consistent with the facts about the candidate model. Any inconsistency is a reason to discard the candidate model. The implemented framework is the core of PRET, a program currently under development that automates the modeling process. Introduction Models are powerful tools that are used to understand physical systems. Abstract models are simple: they account for major properties of the physical system. Lessabstract models are more complicated, allowing them to capture the features of the physical system
A Fuzzy Simulation Method
 International Symposium on Soft Computing
, 1996
"... In this paper we propose a method for the simulation of uncertain dynamical systems. Uncertainty is taken into account by replacing crisp functions by fuzzy functions on the righthand side of differential equations. Crisp initial conditions are replaced with fuzzy ones. As an application of the met ..."
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Cited by 3 (2 self)
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In this paper we propose a method for the simulation of uncertain dynamical systems. Uncertainty is taken into account by replacing crisp functions by fuzzy functions on the righthand side of differential equations. Crisp initial conditions are replaced with fuzzy ones. As an application of the method we consider the prediction of object trajectories in spatiotemporal reasoning. 1 Introduction Knowledge about dynamical systems modelled by differential equations is often incomplete or vague. For example, parameter values, functional relationships, or initial conditions may not be known precisely. In this situation, wellknown methods for solving initial value problems analytically or numerically can only be used for finding selected system behaviors, e.g., by fixing unknown parameters to some plausible values. However, in this way it is not possible to characterize the whole set of system bahaviors compatible with our partial knowledge. To replace functions and initial values in the p...
Reasoning about structure of interval systems: An approach by sign directedgraph
 In Proceedings of the 10th International Workshop on Qualitative Reasoning (QR96
, 1996
"... Abstract This paper deals with qualitative and structural reasoning on linear interval systems whose parameters are specified by intervals. We formalize the systems of reasoning about structures of interval systems by the qualitative perturbation principle: the interval system would have the interv ..."
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Abstract This paper deals with qualitative and structural reasoning on linear interval systems whose parameters are specified by intervals. We formalize the systems of reasoning about structures of interval systems by the qualitative perturbation principle: the interval system would have the interval property when its underlying sign structure include the component that has the corresponding sign property and the norm of the rest of component (considered qualitative perturbation) is small enough. Several interval properties of interval matrix such as nonsingularity, rank and inverse stability will be discussed by applying the principle to the graphical conditions for the corresponding sign properties. The Klein model in economics is used as an illustrative example.
A semiqualitative methodology for reasoning about dynamic systems
 13 th International Workshop on Qualitative Reasoning. Loch Awe
"... A new methodology is proposed in this paper in order to study semiqualitative models of dynamic systems. It is also described a formalism to incorporate qualitative information into these models. This qualitative information may be composed of. qualitative operators, envelope functions, qualitati ..."
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A new methodology is proposed in this paper in order to study semiqualitative models of dynamic systems. It is also described a formalism to incorporate qualitative information into these models. This qualitative information may be composed of. qualitative operators, envelope functions, qualitative labels and qualitative continuous functions. This methodology allows us to study all the states of a dynamic system: the stationary and the transient states. It also allows us to obtain behaviours patterns of semiqualitative dynamic systems. The main idea of the methodology follows: a semiqualitative model is transformed into a family of quantitative models. Every quantitative model has a different quantitative behaviour, however they may have similar qualitative behaviours. A semiqualitative model is transformated into a set of quantitative models. The simulation of every quantitative model generates a trajectory in the phase space. A database is obtained with these quantitative behaviours. It is proposed a language to carry out queries about the qualitative properties of this database of trajectories. This language is also intended to classify the different qualitative behaviours of our model. This classification helps us to describe the semiqualitative behaviour of a system by means of hierarchical rules obtained by means of machine learning. The completeness property is characterized by statistical means. A theoretical study about the reliability of the obtained conclusions is presented. The methodology is applied to a logistic growth model with a delay.
UK.
"... The subject of this paper is a novel synchronous fuzzy qualitative simulator developed within the Mycro]t fuzzy quaditative reasoning framework. Synchronous fuzzy qualitative simulation involves replacing the transition rules of Mycro # with an integration phase utilising a qualitative version of Eu ..."
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The subject of this paper is a novel synchronous fuzzy qualitative simulator developed within the Mycro]t fuzzy quaditative reasoning framework. Synchronous fuzzy qualitative simulation involves replacing the transition rules of Mycro # with an integration phase utilising a qualitative version of Eulcrs first order approximation to the Taylor series: Qualitative Euler Integration (QEI). The simulation process described utilises constraintbased fuzzy qualitative models, the variables of which take their values from a predefined fuzzy quantity space. The simulation proceeds, driven by an externally defined integration time step (chosen to ensure the continuity of the magnitudes of the state variables), by means of an explicit Euler integration operation. This provides the set of possible successor values for the magnitudes of the state variables. After this the constraints of the model are solved to provide the whies of the nonstate variables of the model. As each constraint is solved the same transition rules as for asynchronous simulation are applied to constrain the generation of the behaviour tree. At the end of this process a number of successor states will be generated This number will be less than or equal to the number generated by semiconstructive or nonconstructive simulators such as Mycro # or FuSim, and a great deal less than if the transition filters had not been applied. The advantage of this approach is that it permits the utilisation of multiple precision models in which the information concerning the values of system variables may be expressed in vague terms but with precise time stamp information. The system has already been utilised in a research exploring the use of qualitative models for parameter identification, diagnosis, (Steele and Leitch 1997) and control (Keller and Leitch 1994).
Refining Imprecise Models and Their Behaviors
 Austin
, 1996
"... v List of Tables x List of Figures xi Chapter 1 Introduction 1 1.1 The Need for Reasoning with Imprecision . . . . . . . . . . . . . . . . . . . 1 1.2 Existing Methods for Dealing With Imprecision and Why They are Insufficient 2 1.2.1 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . ..."
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v List of Tables x List of Figures xi Chapter 1 Introduction 1 1.1 The Need for Reasoning with Imprecision . . . . . . . . . . . . . . . . . . . 1 1.2 Existing Methods for Dealing With Imprecision and Why They are Insufficient 2 1.2.1 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.2 Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Goals of this Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Summary of Key Contributions of this Research . . . . . . . . . . . . . . . 4 1.4.1 Nsim  A Numerical Simulator for Imprecise Models . . . . . . . . . 4 1.4.2 SQsim  A Semiquantitative Simulator for Imprecise Models . . . . 4 1.4.3 MSQUID  A Monotonic Function Estimator with Confidence Bands 4 1.4.4 SQUID  A System Identification Method Using Semiquantitative Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Guide to this Dissertation . . . . . . . . . . . . . . . ....
Scotland
"... The subject of this paper is a novel synchronous fuzzy qualitative simulator developed within the Mycroft fuzzy qualitative reasoning framework. Synchronous fuzzy qualitative simulation involves replacing the transition rules of Mycroft with an integration phase utilising a qualitative version of Eu ..."
Abstract
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The subject of this paper is a novel synchronous fuzzy qualitative simulator developed within the Mycroft fuzzy qualitative reasoning framework. Synchronous fuzzy qualitative simulation involves replacing the transition rules of Mycroft with an integration phase utilising a qualitative version of Eulers first order approximation to the Taylor series: Qualitative Euler Integration (QEI). The simulation process described utilises constraintbased fuzzy qualitative models, the variables of which take their values from a predefined fuzzy quantity space. The simulation proceeds, driven by an externally defined integration time step (chosen to ensure the continuity of the magnitudes of the state variables), by means of an explicit Euler integration operation. This provides the set of possible successor values for the magnitudes of the state variables. After this the constraints of the model are solved to provide the values of the nonstate variables ofthe model. As each constraint is solved the same transition rules as for asynchronous simulation are applied to constrain the generation of the behaviour tree. At the end of this process a number of successor states will be generated This number will be less than or equal to the number generated by semiconstructive or nonconstructive simulators such as Mycroft or FuSim, and a great deal less than if the transition filters had not been applied. The advantage of this approach is that it perinits the _ utilisation of multiple precision models in which the information concerning the values of system variables may be expressed in vague terms but with precise time stamp information. The system has already been utilised in a research exploring the use of qualitative models for parameter identification, diagnosis, (Steele and Leitch 1997) and control (Keller and Leitch 1994).