Our current research in this area is in developing hybrid models for analyzing mixed continuous and discrete behavior of engineering systems. Mixed behaviors are inherent in embedded systems, i.e., continuous processes controlled by discrete elements, such as PLCs (programmable logic arrays) and computers. Also, discontinuities may emerge in models of continuous physical systems as an artifact of abstracting physical phenomena that operate on a temporal or spatial scale much smaller than that of interest to the modeller. In this case, physical laws such as *continuity of power* and *conservation of energy* appear to be violated whendiscontinuities occur. Much of our research has been geared towards finding physical laws that govern the resulting discrete behavior.

Nonlinear behaviors of real-world physical systems are often abstracted into piecewise linear models by simplifying component parameters (*parameter abstraction*) or coarsening the time scale of behavior analysis (*time scale abstraction*). These two abstraction types correspond to two distinctly different discrete event iteration mechanisms that are active in between continuous modes. An important result of this research is an ontology of phase space transitions types in hybrid physical system models.

We have developed a hybrid bond graph modeling paradigm that combines energy based bond graph models with finite state automata for discrete meta-level control of model configuration changes. This provides a systematic framework for behavior generation based on the physical principles of *conservation of state* and *invariance of state*. The principle of *divergence of time* verifies consistency of models using phase space analysis.

Current research is focused on the development of compositional modeling techniques, and efficient simulators based on these principles, and the application of this approach for control, prediction, monitoring, and diagnosis of complex embedded processes. We have developed a tool suite for efficiently simulating hybrid bond graph models using the Matlab Simulink simulation environment. The tool suite encompasses both model translation tools and a runtime support code. Hybrid bond graphs are modeled in GME/FACT, and then interpreted to generate Simulink models. The HBGSimulink Library is a collection of Matlab and C++ code to support model construction and runtime execution in Simulink. The models support parameterized, component-level fault injection through an automatically constructed user interface. When the Simulink models are executed, they use specialized code for efficient simulation of hybrid bond graphs.

Members of the MACS group also participate in the new NSF sponsored consortium: Foundations of hybrid and embedded software systems (FOUNTAIN). Our core research objectives are directly applicable in the context of the FOUNTAIN program. More information can be found at: http://macs.isis.vanderbilt.edu/link_icon.gif) 0px 1px no-repeat transparent;">http://fountain.isis.vanderbilt.edu

Current research is geared toward the development of schemes for monitoring, prediction, and diagnosis of complex dynamic continuous systems. Earlier work applied diagnosis based on steady state models. Recent work has focused on monitoring and diagnosis from transient behaviors as faults occur in a system. Modeling nominal and faulty behavior starts from bond graphs and derives a *temporal causal graph* of dynamic system behavior. This model is used to identify system faults from deviating measurements and predict future behavior of the observed variables in terms of *fault signatures*which are expressed as parameter deviations and their magnitude and higher order derivatives. Behavior and diagnostic analysis is performed in a qualitative reasoning framework.

Current work in this area focuses on

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- extensions of continuous diagnosis algorithms to hybrid diagnosis schemes
- using temporal orders of measurement deviations to improve diagnosability of continuous systems
- extensions of continuous diagnosis algorithms to multiple fault scenarios
- developing fault detection and isolation methods for incipient faults using dynamic Bayesian networks, and
- developing distributed diagnosis schemes for continuous systems.

In other work, focused on medical diagnosis, we have looked upon diagnosis as an abductive reasoning process on associational symptom-cause models - given a set of observations, hypothesize a state of the system that can account for them. Whereas the truth value of a *deductive* inference can be determined directly from the truth of its implicants, an *abductive* inference is only possible but not necessarily true - there can be many ways to explain the same set of observations.

Unlike model-based approaches in engineering systems, functional dependencies between observations can be difficult to elicit and quite time consuming across the number of cause-effect relationships present in an extensive domain of physiological relations. Our work has focused on inductively determining such dependencies which can be used to improve the efficiency and and accuracy of diagnosis. A number of experiments have been conducted on the QMR Knowledge Base to demonstrate the effectiveness of our approach.

The new fault-adaptive control technology (FACT) will be able to: (A) detect discrepancies between expected and observed behavior, (b)perform mode identification, (c) generate and verify fault hypotheses, (d) analyze the expected consequences of controller actions on system behavior, (e) derive system configuration and control law alternatives that maintain critical functionalities, (f) select a new control law among the alternatives based on predicted transient behavior and performance, and (g) manage reconfiguration, and take control actions to confine the fault and restore system operation with resources available.

Current work on FACT includes:

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- extensions of Hybrid Bond Graph modeling paradigm to allow for multi-domain modeling
- extending the observers, and fault detection and fault isolation algorithms.