Hybrid Dynamic Systems:
A hybrid bond graph modeling paradigm and its application in diagnosis

Pieter J. Mosterman
Vanderbilt University


Physical system behavior follows the general principles of conservation of energy and continuity of power, but may exhibit nonlinearities that result from small, parasitic, effects, or occur on a time scale much smaller than the time scale of interest. At a macroscopic level, the detailed continuous behavior may appear to be discontinuous, thus the system is efficiently described by a mixed continuous/discrete, hybrid, model. In continuous modes the energy distribution describes the system state. Discrete configuration changes in the model may cause discontinuities in the energy distribution governed by the principle of conservation of state, and may trigger further configuration changes till a new real mode is achieved where no further changes occur. The intermediate, mythical, modes between two real modes have no physical representation. The principle of invariance of state applies to derive the energy distribution in a mode as a function of the energy distribution in the preceding real mode. When a loop of consecutive instantaneous mode changes occurs time stops progressing. This conflicts with known physical system behavior, therefore, the principle of divergence of time forms an important model verification mechanism. The principle of temporal evolution of state requires the energy state to be continuous in left-closed time intervals to ensure proper causal attribution.

From another viewpoint, abrupt faults in process components can be modeled as discontinuities that take system behavior away from its nominal, steady state, operation. To quickly isolate the true faults, well constrained hybrid models avoid the inherent intractability problems in diagnostic analyses by integrating and facilitating the (1) generation of behavioral constraints from physical laws, (2) expression of system dynamics as energy transfer between constituent elements, and (3) modeling of steady state behavior as a special case of dynamic behavior. The analysis of transients is paramount to accurate and precise fault isolation. However, this is a difficult problem which can be further complicated by operator intervention, and intermittent and cascading faults, therefore, quick capture and analysis of transients is the key to successful diagnosis.

This thesis develops a formal hybrid modeling theory based on physical principles, a model verification method, and a physically correct behavior generation algorithm. Next, it describes a methodology for monitoring, prediction, and diagnosis of dynamic systems from transient behavior, based on the developed hybrid bond graph modeling paradigm. Simulation results from diagnosing a high-order, nonlinear, model of a liquid sodium cooling system in a nuclear reactor demonstrates the success of the approach.

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JANOS SZTIPANOVITS Professor of Electrical and Computer Engineering
213 Jacobs Hall, Box 6306 Station B, Nashville, TN 37235
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GAUTAM BISWAS Associate Professor of Computer Science
Vanderbilt University, 455 The Village at Vanderbilt, Box 1679 Station B, Nashville, TN 37235
(615) 343 6204

GEORGE E. COOK Professor of Electrical and Computer Engineering
Vanderbilt University, 401b The Village at Vanderbilt, Box 1826 Station B, Nashville, TN 37235
(615) 343 5032

GABOR KARSAI Assistant Professor of Electrical and Computer Engineering
233 Jacobs Hall, Box 1824 Station B, Nashville, TN 37235
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KENNETH A. DEBELAK Associate Professor of Chemical Engineering
307 Olin Hall, Box 1700 Station B, Nashville, TN 37235
(615) 322 2088

MICHAEL GOLDFARB Assistant Professor of Mechanical Engineering
505A Olin Hall, Box 1592 Station B, Nashville, TN 37235
(615) 343 6924