An energy-based model reduction methodology for automated modeling

Commercial competition demands a reduction in the development time of new products. While it has been recognized for a number of years that the development process can be accelerated with the use of computer simulation based on mathematical models of the product, the lack of appropriate modeling tools has limited the effectiveness of this approach. It is the premise of this work that a new modeling metric able to handle nonlinear dynamic systems and all types of energy elements, will improve the effectiveness of modeling tools. A new modeling metric, activity, which is based on energy, is developed in this work. This metric is used to rank the importance of all energy elements in a system. The ranking of the energy elements provides the relative importance of the model parameters and this information can be used to reduce the size of the model. The metric is implemented in an algorithm called Model Order Reduction Algorithm (MORA). MORA is applied to a nonlinear quarter car model showing that elements with low activity can be eliminated without any significant change in model accuracy. MORA is also applied to linear systems, where the steady state activity to sinusoidal inputs is considered. It is shown that the activity varies with frequency, and thus, a series of reduced models can be generated as a function of the excitation frequency. For multibody systems, the activity metric can be applied to each DOF of the rigid bodies. The activity metric is applied to a heavy-duty tractor-semitrailer to demonstrate that a significant number of the model parameters are insignificant, and therefore, that a substantial reduction in the model size can be achieved. Finally, an interpretation algorithm based on the activity metric is developed to provide the user with physical meaning of each low activity element eliminated. In addition, the use of the activity metric to rank the energy elements augments the insight into the model, since the engineer can focus on a smaller number of elements that are identified by MORA as important to the system behavior. In conclusion, this work develops an automated modeling algorithm, MORA, which can be used to rank model parameter importance, reduce model complexity and help provide physical insight into a system. MORA extends the applicability of automated modeling to systems that can be represented by nonlinear dynamic models and it should improve the use of modeling and simulation for product development.