Bradley, E., and Stolle, R. 1996. Automatic construction of accurate models of physical systems. Annals of Mathematics of Artificial Intelligence 22 17:1--28.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....structures constrained by the physical and modeling assumptions, a subset of plausible candidate models, and in determining in such a set the best model which reproduces the measured data. Recent research work carried out within the Qualitative Reasoning (QR) framework (Addanki et al. 1991; Bradley and Stolle, 1996; Capelo et al. 1998; Falkenhaier and Forbus, 1991; Ironi and Stefanelli, 1994; Low and Iwasaki, 1992) has addressed the general problem of model space automated construction. In this paper, our focus is on automated model selection and parameter estimation. The subset of plausible candidate ....

Bradley, E. and Stolle, R. (1996). Automatic construction of accurate models of physical systems. Annals of Mathematics and Artificial Intelligence, Vol. 17, pp. 1--28.

....for parameter estimation which may terminate at local extrema if the numerical search for the optimal value is not properly initialized. Recent work within the Qualitative Reasoning (qr) research framework has addressed the problem of the parameter estimation phase in the model building process (Bradley 1994; Bradley, O Gallagher, Rogers 1997; Capelo, Ironi, Tentoni 1996; 1998) namely the crucial issue of automatically providing a good initial guess to start the optimization procedure. The implemented qr techniques proposed in the mentioned papers are components of computational environments ....

....integrate a variety of techniques with the goal of automating model building. Such papers consider ode models which are automatically generated by exploiting physical knowledge either of a specific physical domain (Capelo, Ironi, Tentoni 1996; 1998) or explicitely supplied by the user s input (Bradley 1994; Bradley, O Gallagher, Rogers 1997) The candidate ode models for parametric si are selected in accordance with their consistency with the observations. An interesting method, based on semi quantitative infer ences, to reduce the candidate model space is given in (Kay 1996) In the same ....

Bradley, E. 1994. Automatic construction of accurate models of physical systems. In Proc. 8th International Workshop on Qualitative Reasoning, 13--23.

....QR techniques for SI is not new. Most of the work done addresses the problem of the automation of the traditional process of SI, that is the automation of both structural identification and the choice of the most appropriate numerical techniques for parameter estimation and their initialization [6, 5, 11, 7, 8, 12]. Another piece of work deals with a method for SI capable to deal with states of incomplete knowledge [15] in which both the candidate model space and the stream of observations are defined semi quantitatively. What distinguishes this piece of work from the other ones is its capability to deal ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artificial Intelligence, 17:1--28, 1996.

....models to the observation. TrenDx [ Haimowitz and Kohane, 1993 ] is a monitoring system which uses a semi quantitative representation of a behavior and attempts to fit data to this behavior representation. Since TrenDx uses predefined behavior templates no refinement can be performed. PRET [ Bradley and Stolle, 1996 ] automatically constructs a precise ODE model of a physical system. PRET focuses on system identification and not on monitoring. Loiez and Taillibert [ Loiez and Taillibert, 1997 ] use piecewise polynomial functions, so called temporal band sequences, to bound the observation stream. The behavior ....

E. Bradley and R. Stolle. Automatic Construction of Accurate Models of Physical Systems. Annals of Mathematics of Artificial Intelligence, 17:1--28, 1996.

....scale space portrait , although this is not necessary for SQUID. 40 is more exible than a behavioral model in that one can change the structural model and then predict the consequences. This is particularly important in monitoring where faults are manifested as structural changes. PRET [3] uses qualitative, symbolic, algebraic and geometric reasoning to automate the process of system identi cation. Given a set of hypotheses, observations and speci cations PRET constructs an ODE model of the physical system. PRET is based on a library of traditional system identi cation methods and ....

Elizabeth Bradley and Reinhard Stolle. Automatic Construction of Accurate Models of Physical Systems. Annals of Mathematics of Articial Intelligence, 17:1-28, 1996.

....If all one term models fail, two term models 1 Future incarnations of the program will simplify and or refine the model returned by the generateand test cycle. The simplifier and refiner modules will also be guided by the observations. See Section 2.3. 2 For a more elaborate discussion consult [9, 11]. 5 are tried, and so on. 3 Multiple hypotheses about a single effect can and should exist; the program will automatically determine which one(s) are appropriate. The order in which candidate models are generated is a handle that can be used to make the program smart. This corresponds ....

E. Bradley. Automatic construction of accurate models of physical systems. In Proceedings of the International Workshop on Qualitative Reasoning about Physical Systems, 1994. Nara, Japan.

....describing its behavior. Furthermore, a structural model (with a simulator) is more flexible than a behavioral model in that one can change the structural model and then predict the consequences. This is particularly important in monitoring where faults are manifested as structural changes. PRET [4] uses qualitative, symbolic, algebraic and geometric reasoning to automate the process of system identification. Given a set of hypotheses, observations and specifications PRET constructs an ODE model of the physical system. PRET is based on a library of traditional system identification methods ....

Elizabeth Bradley and Reinhard Stolle. Automatic Construction of Accurate Models of Physical Systems. Annals of Mathematics of Artificial Intelligence, 17:1--28, 1996.

....structural identi cation, in which the number and types of terms forming the equation that govern the unknown dynamics are determined, and parameter estimation, in which values for the undetermined coecients in that equation are derived via comparisons with the data. The computer program Pret[4, 6] automates the SID process. Its inputs are a set of observations of the outputs of a lumped parameter continuous time nonlinear dynamic system, together with a modeling speci cation that includes resolutions for important variables and an optional list of hypotheses about the physics involved. ....

....has successfully constructed models of real systems in multiple domains, ranging from textbook problems (R ossler, Lorenz, simple pendulum, pendulum on a spring, etc. to interesting and dicult real world examples like shock absorbers, well aquifer systems, and a commercial radio controlled car[5, 6, 9, 12]. The thermistor example treated in this paper is signi cant for three reasons. First, it involves direct, autonomous interaction with a physical system. Second, it is a particularly good demonstration of the issues and diculties involved in the actual physical level implementation of ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Arti cial Intelligence, 17:1-28, 1996.

....entire spectrum, making signal separation a dicult proposition. Nonlinearity is even more of a hurdle in system identi cation: constructing dynamic models of linear systems is nontrivial, but human practitioners consider nonlinear system identi cation to be a black art, and automating the process[6] is quite dicult. 2 Nonlinear Dynamics Basics A dynamical system is something whose behavior evolves with time: binary stars, transistor radios, predator prey populations, di erential equations, the air stream past the cowl of a jet engine, and myriad other examples of interest to scientists and ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Articial Intelligence, 17:1-28, 1996.

....system identi cation process, structural identi cation, identi es the form of the model, or skeleton of the equation, such as a b sin = 0 for a simple pendulum. In the second system identi cation stage, parameter estimation, the parameter values a and b are determined. The program Pret (Bradley Stolle 1996) automates both stages of the system identi cation process; it nds a system of ODEs that models a given physical system. Inputs are observations about that system, user supplied hypotheses about the desired model, and speci cations. Fig. 1 shows a physical system that consists of two masses and ....

....in the knowledge base. The special predicate scheme eval provides the link between the inference engine and Pret s model observer functions. It also provides the link to all modules that implement other reasoning modes. For a more detailed discussion of Pret s logic system, see (Stolle Bradley 1996). Declarative Meta Level Control The control strategy of a SLD resolution theorem prover is de ned by the function that selects the literal that is resolved and by the function that chooses the resolving clause. Pret provides meta level language constructs that allow the implementer of the ODE ....

Bradley, E., and Stolle, R. 1996. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artif. Intell. 17:1-28.

.... span the spectrum between highly speci c frameworks that work well in a single, limited domain (e.g. a spring dashpot vocabulary for modeling simple mechanical systems) and abstract frameworks that rely heavily upon general mathematical formalisms at the expense of huge search space sizes (e.g. [17]) 9 2.1 The CBM Paradigm: Representation In the late 1950s and early 1960s, inspired by the realization that the principles underlying Newton s third law and Kirchho s current law were identical 7 , researchers began combining multi port methods from a number of engineering elds into a ....

....outputs using cell dynamics, bifurcation analysis, and a new representation called the qualitative state parameter space. Pret has successfully constructed models of a dozen or so textbook problems (R ossler, Lorenz, simple pendulum, pendulum on a spring, predator prey, Chua s circuit, etc. see [16,17,33]) as well as several interesting and dicult 48 real world examples, such as the well, shock absorber, and driven pendulum in the previous section, and a commercial radio controlled car, which is covered in [16] These examples are representative of wide classes of mechanical systems, both linear ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Articial Intelligence, 17:1-28, 1996.

....termed qualitative bifurcation analysis, that make it possible to automate this task. 1 Input Output Modeling System identi cation (SID) is the process of inferring an internal ordinary differential equation (ODE) model from external observations of a system. The computer program pret[5] automates the SID process, using a combination of arti cial intelligence and system identi cation techniques to construct ODE models of lumped parameter continuous time nonlinear dynamic systems. As dimath domain actuators sensors PRET system target ODE model specification modeling ....

....dynamical systems. To set the context, the following section gives a brief overview of pret. We then focus in on the input output modeling phase, describe our representation and reasoning framework, and show how pret exploits that framework. 2 PRET As outlined in the previous section, pret[5] is an automated tool for nonlinear system identi cation (SID) Its inputs are a set of observations of the outputs of a black box system, and its output is an ordinary di erential equation (ODE) model of the internal dynamics of that system. pret s architecture wraps a layer of arti cial ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Articial Intelligence, 17:1-28, 1996.

....If all one term models fail, two term models 1 Future incarnations of the program will simplify and or refine the model returned by the generateand test cycle. The simplifier and refiner modules will also be guided by the observations. See Section 2.3. 2 For a more elaborate discussion consult [9, 11]. 5 are tried, and so on. 3 Multiple hypotheses about a single effect can and should exist; the program will automatically determine which one(s) are appropriate. The order in which candidate models are generated is a handle that can be used to make the program smart. This corresponds ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artificial Intelligence. In press.

....Phase Portrait Analysis in Model Building System identification (SID) the process of inferring an internal ordinary di#erential equation (ODE) model from external observations of a system, is an ideal test case for hybrid phase portrait analysis using the QS P space. The computer program pret(Bradley Stolle 1996), a QR modeling tool that automates the SID process by building an AI layer around a set of traditional system identification techniques, constructs ODE models of lumped parameter continuous time nonlinear dynamic systems. It first uses domain knowledge to combine model fragments into ODEs, then ....

Bradley, E., and Stolle, R. 1996. Automatic construction of accurate models of physical systems. Annals of Math. & Artif. Intel. 17:1--28.

....this process using artificial intelligence techniques. One of the aims of qualitative reasoning (QR) 10, 26] a branch of artificial intelligence (AI) is to automate the modeling process by abstracting knowledge, information, and reasoning to a qualitative level. The computer program pret[4] is an example of a QR modeling tool. It automates the SID process that is diagrammed in Figure 1 by building an AI layer around a set of traditional SID techniques. This layer automates the high level stages of the modeling process that are normally performed by a human expert. pret combines ....

....to the accurate deployment of the space shuttle s manipulator arm[16] Figure 6 shows how a user instructs pret to build an ODE model of this system. The full details and implications of both input and output syntax (and the GUI that facilitates entry of the find model call) are covered elsewhere[4, 13]; here, we will concentrate on the parts of the call that pertain to the intelligent data analyzer. The first line of the find model call specifies the domain of the problem and causes the program to instantiate the associated domain theory here, a single rule specifying that forces at a point ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artificial Intelligence, 17:1--28, 1996.

.... Maintenance Based Inference System for Generalized Horn Clause Logic) at the University of Erlangen [BST96, BT92] The logic system presented in this paper is the core of Pret, an automated modeling tool that finds ordinary di#erential equations (ODEs) that model black box dynamical systems [BS96, SB98] The achievement of the three goals listed above is crucial to the success of this modeling task. The contributions described here generalize well beyond this particular application domain. The third goal, in particular, is significant for any automated reasoning system that integrates ....

....example described in the next section, the inference engine s task is to find the first proof of the query falsum. 6 An Example The logic system presented in this paper has successfully been used as a knowledge representation and reasoning framework in the domain of ODE theory. The program Pret [BS96, SB98] automates system identification [Lju87] given hypotheses, observations, and specifications, it constructs an ODE model of a black box dynamical system. Pret uses the given hypotheses to construct a sequence of candidate models and checks each candidate against the observations. The first ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artificial Intelligence, 17:1--28, 1996.

....spectrum, making signal separation a difficult proposition. Nonlinearity is even more of a hurdle in system identification: constructing dynamic models of linear systems is nontrivial, but human practitioners consider nonlinear system identification to be a black art, and automating the process[6] is quite difficult. 2 Nonlinear Dynamics Basics A dynamical system is something whose behavior evolves with time: binary stars, transistor radios, predator prey populations, differential equations, the air stream past the cowl of a jet engine, and myriad other examples of interest to scientists ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artificial Intelligence, 17:1--28, 1996.

....system identification process, structural identification, identifies the form of the model, or skeleton of the equation, such as a # b sin # = 0 for a simple pendulum. In the second system identification stage, parameter estimation, the parameter values a and b are determined. The program Pret (Bradley Stolle 1996) automates both stages of the system identification process; it finds a system of ODEs that models a given physical system. Inputs are observations about that system, user supplied hypotheses about the desired model, and specifications. Fig. 1 shows a physical system that consists of two masses ....

....in the knowledge base. The special predicate scheme eval provides the link between the inference engine and Pret s model observer functions. It also provides the link to all modules that implement other reasoning modes. For a more detailed discussion of Pret s logic system, see (Stolle Bradley 1996). Declarative Meta Level Control The control strategy of a SLD resolution theorem prover is defined by the function that selects the literal that is resolved and by the function that chooses the resolving clause. Pret provides meta level language constructs that allow the implementer of the ODE ....

Bradley, E., and Stolle, R. 1996. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artif. Intell. 17:1--28.

....The first stage of this task, structural identification, identifies the form of the model, or skeleton of the equation, such as a b sin = 0 for a simple pendulum. In the second system identification stage, parameter estimation, the parameter values a and b are determined. The program Pret [ Bradley and Stolle, 1996 ] automates both stages of the system identification process; its goal is to find a system of ODEs that models a given physical system. Inputs are observations about that system, user supplied hypotheses about the desired model, and specifications. Observations are measured automatically by ....

....framework used in this model checker and then we show how this paradigm valid if not proven invalid is able to combine several heterogeneous mechanisms into a powerful framework that is well suited for reasoning about models of physical systems. For a more elaborate discussion consult [ Bradley and Stolle, 1996 ] 2 Generating Candidate Models Pret generates candidate models by combining user hypotheses into ODEs of the form f( x; t) 0. Hypotheses are ODE fragments that contain special keywords that act as links to the domain and ODE rules. In Fig. 1, for example, Pret uses the domain rule ....

E. Bradley and R. Stolle. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artificial Intelligence, 17:1--28, 1996.

....We describe the basic paradigm of the reasoning framework used in this model checker and discuss how this framework can be expanded to incorporate additional reasoning mechanisms. The next section outlines the major features of the modeling program Pret. For a more elaborate discussion consult (Bradley Stolle 1996). Then we describe how the paradigm valid if not proven invalid is able to combine several heterogeneous mechanisms into a powerful framework that is well suited for reasoning about models of physical systems. After describing the current status of the reasoning framework, we illustrate the ....

Bradley, E., and Stolle, R. 1996. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artificial Intelligence. Forthcoming.

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Bradley, E., and Stolle, R. 1996. Automatic construction of accurate models of physical systems. Annals of Mathematics of Artificial Intelligence 22 17:1--28.

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Bradley, E., and Stolle, R. 1996. Automatic construction of accurate models of physical systems. Annals of Mathematics of Artificial Intelligence 17:1--28.

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Bradley, E. and Stolle, R. Automatic construction of accurate models of physical systems. Annals of Mathematics and Artificial Intelligence, 17:1--28, 1996.

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Bradley, E. and Stolle, R. (1996). Automatic Construction of Accurate Models of Physical Systems. Annals of Mathematics of Artificial Intelligence(to appear).

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Bradley, E., and Stolle, R. Automatic construction of accurate models of physical systems. Annals of Mathematics of Artificial Intelligence. In press. Buntine, W. L. 1994. Operations for learning with graphical models. Journal of Artificial Intelligence Research 2:159--225.

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