Energy-Based Model Reduction Methodology for Automated Modeling

摘要

In recent years, algorithms have been developed to help automate the production ofndynamic system models. Part of this effort has been the development of algorithms thatnuse modeling metrics for generating minimum complexity models with realization preservingnstructure and parameters. Existing algorithms, add or remove ideal compliantnelements from a model, and consequently do not equally emphasize the contribution ofnthe other fundamental physical phenomena, i.e., ideal inertial or resistive elements, to thenoverall system behavior. Furthermore, these algorithms have only been developed fornlinear or linearized models, leaving the automated production of models of nonlinearnsystems unresolved. Other model reduction techniques suffer from similar limitations duento linearity or the requirement that the reduced models be realization preserving. Thisnpaper presents a new modeling metric, activity, which is based on energy. This metric isnused to order the importance of all energy elements in a system model. The ranking of thenenergy elements provides the relative importance of the model parameters and this informationnis used as a basis to reduce the size of the model and as a type of parameternsensitivity information for system design. The metric is implemented in an automatednmodeling algorithm called model order reduction algorithm (MORA) that can automaticallyngenerate a hierarchical series of reduced models that are realization preservingnbased on choosing the energy threshold below which energy elements are not included innthe model. Finally, MORA is applied to a nonlinear quarter car model to illustrate thatnenergy elements with low activity can be eliminated from the model resulting in a reducednorder model, with physically meaningful parameters, which also accurately predicts thenbehavior of the full model. The activity metric appears to be a valuable metric fornautomating the reduction of nonlinear system models—providing in the process modelsnthat provide better insight and may be more numerically efficient.