Modeling and Analysis of Complex Systems



Vanderbilt University conducts research to study the behavior of embedded and hybrid physical systems. These systems are characterized by mixed discrete/continuous behaviors that are effectively described using the theory of hybrid systems. From new theoretical results we construct tools to support modeling and analysis of hybrid systems in the context of embedded system realizations. Specifically, we develop capabilities for 

  • Modeling and analysis of complex systems
  • Advanced model-based fault detection and isolation (FDI) and diagnosis
  • Fault adaptivity
  • Simulation-based prognosis systems
  • Integrated systems health management (ISHM) of high availability and mission critical engineering applications. 

The MACS group is based in the Department of Electrical Engineering and Computer Science of the School of Engineering. It is affiliated with the Institute for Software Integrated Systems (ISIS). Resources available to the group includes a three tank system process control testbed that is located in Room 314, Featheringill Hall.

The research summary gives an overview of our research objectives and core strengths. We apply our work in a number of projects, both in a laboratory setting, and in collaboration with government and industry sponsors on real-world problems. Current principal sponsored research applications include the development of hierarchical  diagnosis and prognosis schemes for civil engineering structures, aircraft and spacecraft power generation and power distribution systems, and Fault Adaptive Control Technology (FACT) for aerospace applications.

In the past, we have worked on projects that include the development of Advanced Life Support System (ALS) technology for human space exploration, fuel transfer systems for aircraft, the secondary sodium cooling loop for nuclear reactors, and the cooling system for automobile engines. 

 Please see our publication list at:  Publications are also listed on this ISIS website under the Publications tab at the top of the screen.



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: 0px 1px no-repeat transparent;">

Fault detection and isolation (FDI), and diagnosis

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 signatureswhich 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; list-style-type: square; font-family: 'Lucida Grande', Verdana, Lucida, Helvetica, Arial, sans-serif;">
  • 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:; list-style-type: square; font-family: 'Lucida Grande', Verdana, Lucida, Helvetica, Arial, sans-serif;">
  • extensions of Hybrid Bond Graph modeling paradigm to allow for multi-domain modeling
  • extending the observers, and fault detection and fault isolation algorithms.





Current sponsored research projects


Distributed Monitoring and Diagnosis of Embedded Systems Using Hierarchical Abstractions

Sponsor: NSF EHS program

The objective of this project is to develop systematic, scalable, robust, online model-based FDI schemes for distributed embedded systems. The novelty of the research centers on (i) hierarchical abstraction schemes for managing the complexity of the FDI task and enabling the design and development of online model-based FDI algorithms that are provably robust and reliable, (ii) a unified framework for diagnosis of multiple types of faults that occur in the physical and the computational parts of embedded systems as well as faults with different fault profiles (abrupt and incipient faults), and (iii) the development of a tool suite for distributed embedded systems for online FDI. Experimental test-beds are used to demonstrate and verify the effectiveness of the developed methods. The impact of the project lies on providing guarantees for reliable safe operation of complex, distributed safety-critical systems.


Aircraft Electrical Power System Diagnostics and Health Management

Sponsor: Navy STTR; in conjunction with Qualtech Systems, Inc.

The objective of this project is to improve the availability and reliability of aircraft power generator systems using health monitoring techniques that combine diagnostic and prognostic algorithms. We propose an innovative scheme for diagnosis and prognosis that combines the use of dynamical physical system models augmented with signal models for analyzing vibration signatures and physics of failure models for electrical, electronic, and mechanical generator components, such as rectifiers, transformers, batteries, converters, and bearings. These schemes estimate degrading device behavior as the system is involved in its regular operation. The fault diagnostic scheme uses innovative model-based approaches for root cause analysis, and the prognostic reasoning framework is based on simulation of the failing device (identified by diagnostic analysis) for relevant usage scenarios. Continued monitoring of system variables along with the degradation estimates will form the basis of algorithms that compute reliable estimates of the remaining life curve for the degrading components. The figure on the left illustrates the architecture of our diagnostic and prognostic system.


Online Statistical Methods for Robust State Estimation, Anomaly Detection, and Degradation Analysis in Complex, Embedded Systems 

Sponsor: NASA Aeronautics Program

Complex, safety-critical systems in aircraft, such as power generation systems have interacting subsystems that operate in multiple physical domains. A number of catastrophic accidents have demonstrated that these systems can degrade and fail in ways that are hard to predict at design time. The drive for increased safety, reliability, and autonomy imposes stringent requirements on system operation and performance, even in the presence of degradation and faults in components. Such requirements can be addressed only by accurate assessment of system health, and this has generated increased demands for onboard monitoring, analysis, and decision making schemes. Our proposed approach will combine model-based and statistical algorithms to provide robust schemes that manage modeling uncertainties, measurement noise, and the computational complexities associated with online tracking, estimation, detection, and analysis of nonlinear hybrid behaviors. The theoretical underpinnings for tracking and analysis of nominal and faulty system behavior will be centered on the use of approximate Dynamic Bayes Net (DBN) techniques. Anomaly detection methods that work in conjunction with the DBN tracker will focus on signal analysis and statistical techniques that include time-frequency representations, and maximum likelihood methods for accurate fault detection while keeping the false alarm rate low. Our detection and analysis algorithms will be tuned to analyze different fault types (sensor, actuator, and process) and different fault profiles (abrupt, incipient, and intermittent). Anomaly detection will trigger an innovative fault isolation scheme that combines qualitative reasoning and quantitative analysis of the fault dynamics to isolate and identify the root cause for the observed anomalies.

Advanced Diagnostics & Prognostics Techniques applied to NASA Spacecraft and Testbeds

Sponsor: NASA Ames

This project covers the following tasks: (1) Model building for the ADAPT Testbed subsystems. These models will form the basis for building a simulation testbed for offline experiments (VIRTUAL-ADAPT), as well as the basis for running online model-based monitoring, fault detection, and fault isolation studies, (2) Model-based Diagnosis ExperimentsA run time environment will be developed for monitoring of nominal behavior (observer-based schemes), fault detection (statistical techniques), fault isolation (TRANSCEND), and fault identification (TRANSCEND). This will involve the use of hybrid techniques because the test-bed systems combine continuous and discrete behaviors. Implement runtime infrastructure for FACT (Fault Adaptive Control Technology)1 on ADAPT in a way that we can plug in different observers, different fault detectors, and different fault isolation schemes for diagnosis. (3) Participate in the comparison of different diagnosis algorithms. (4) Formal analysis of Hybrid Diagnosis schemes and development of new approaches that address the development of hybrid diagnosis schemes for NASA applications.


Past sponsored research projects


Within the MACS laborarory we employ a three tank fluid system test-bed to evaluate tools and techniques on a real physical system.

You may also browse Completed Projects.


Fault Adaptive Control Technology (FACT)

Sponsor: DARPA Software Enabled Control (SEC) program

Dependability and safety of military systems is a common goal mandating increased component reliability and the use of physical redundancy in fault-tolerant architectures. In future military systems, affordability will preclude this approach. Dependability and mission readiness must be achieved by new robust control techniques that exploit on-line diagnostic capabilities combined with advanced control mechanisms rather than by ultra-reliable components and physical redundancy. In this project we develop techniques that will enable fault-adaptive real-time control of heterogeneous dynamic systems, such as those found in avionics applications.

Robust Hybrid Diagnosis and Reconfiguration

Sponsor: NASA Intelligent Systems (IS) program (2000-2003)

The essence of the proposed project is to develop autonomous, fault-adaptive, real-time control technology for complex dynamic systems. These control systems will be capable of autonomously detecting and isolating faults in system operation and reconfiguring the control paradigm in order to ensure stable and effective system operation. In this context, faults refer to drifts or failures in actuators, sensors and system components. The detection and isolation of these faults will be accomplished through dynamic system observers, which serve the dual purpose of estimating system states for feedback control. A key novelty of this project will be the development of fault observers and adaptive control systems for hierarchical hybrid systems, i.e., systems containing both continuous dynamics and discrete events. Hierarchical models at different levels of abstraction will be employed to efficiently deal with interacting subsystems that operate on widely differing time scales. The primary challenge in developing the overall scheme for fault-adaptive control will be the seamless integration of the various components of the system: (i) hybrid observers for tracking of continuous system behavior through discrete mode changes, (ii) fault detection schemes linked to the hybrid observers, (iii) multi-paradigm fault isolation schemes based on the hierarchical hybrid models, and (iv) controller selection and reconfiguration schemes to maintain system functionality, safety, and reliability. Model-based techniques will provide the overarching framework for developing the individual component technologies. The primary advantage of such systems will be the dramatic reduction of manually intensive monitoring and control. Another distinct advantage will be improved safety due to the continuous fault detection and adaptation capability.

Advanced Life Support System (ALS) technology

Sponsor(s): NASA Advance Human Support Technology Program (2003-2006)

The support of human life in the hostile environment of space critically depends on a set of complex technical systems that contain or interact with biological and chemical processes. The NASA Advanced Life Support Systems (ALS) program, itself a component of the larger Advanced Human Support Technology (AHST) Program, was created to explore new technologies required to support extended manned missions in space. Potential applications include a Lunar base, a manned mission to Mars, and the International Space Station (ISS). An ALS must exhibit a high level of autonomy, so as not to detract from the mission specific tasks of the crew. This requirement translates to a high level of availability of the individual components of the ALS. It also requires that the integrated system have the ability to adapt to changing mission objectives and crew configurations, mainly in response to unplanned events.





Graduate Students

  • Joshua Carl
  • Hamed Khorasgani
  • Yi Dong
  • Gan Zhou


  • Daniel Mack, Ph.D. 2013
  • Chetan Kulkarni, Ph.D. 2013
  • Ashraf Tantawy, Ph.D 2011
  • Stephanie L Wright, MS 2010
  • Srikanth P Srinivasan, MS 2010




The International Workshop on Principles of Diagnosis is an annual event that started in 1989 rooted in the Artificial Intelligence (AI) community. Its current focus is broader covering of a variety of theories, principles, and computational techniques for diagnosis, monitoring, testing, reconfiguration, fault-adaptive control, and repair of complex systems. Application of these theories, principles, and techniques to industry-related disciplines and other domains is amongst the important topics of the workshop.

Like the previous workshops in this series, DX-07 encourages the interactions and the exchange of theories, techniques, applications, and experiences amongst researchers and practitioners from different backgrounds: Artificial Intelligence, Control Theory, Systems Engineering, Software Engineering and other related areas, who share an interest in different aspects of diagnosis, and the related fields of testing, reconfiguration, maintenance, prognosis, and fault-adaptive control.

DX is a lively forum that has traditionally adopted a single-track program with a limited number of participants in order to promote detailed technical exchange and debate while at the same time making efforts to develop synergistic approaches to solving real-world problems.




Three lectures covering (i) continuous diagnosis, (ii) hybrid diagnosis, and (iii) fault adaptive control given at the Spanish Summer School on Diagnosis in Penaranda de Duero, Spain, June 2006.



Software developed by MACS

MOTHS: MOdeling and Transformation of Hybrid Bond Graphs for Simulation Tool Suite

Current Research

Current Research

 This is our current research.