Overview of the Activity Index

As the size and number of parameters of a dynamic model grow, the computational expense of identifying these parameters also grows, often exponentially. One way to alleviate this work is to determine which parameters in the model are most important to the system's dynamics and outputs, and then to identify only those parameters. This helps to improve the accuracy and efficiency of the identification problem for both linear and nonlinear models.

It is helpful to devise ways to facilitate the synthesis of models optimized for repetitive study of specific missions or maneuvers. Because subsystem models may have inherently different bandwidth characteristics, complex system simulations that incorporate such models may be numerically stiff. Furthermore, complexity generally makes it difficult to interpret results and identify key parameters that affect dominant dynamics.

A technique that uses Activity — an energy-based model reduction metric — can be used for selecting the most important parameters to identify.

Activity was first introduced as a concept by Louca et al. It was developed as a tool for model reduction. Activity is defined as the total power flow through a dynamic element during a time period of interest.

• High activity index: the element has an important contribution in the overall dynamics of the system.
• Low activity index: the element has a small contribution in the overall dynamics of the system. Therefore the associated component can be eliminated.

Because of its established use for model reduction, element activity is tested as a metric to measure and vary model fidelity of a complete system model run for specific scenarios.

This metric calculates the relative importance of each state based on the total power flowing through that state during a time period of interest. By selecting only the parameters associated with the most active states for system identification, one may be able to significantly accelerate this system identification in an efficient, realization-preserving manner.