Realization-Preserving Simplification and Reduction of Dynamic System Models at the Graph Level.

Abstract

The literature deems a model “proper”, if it is only as complex as necessary to fulfill its purpose. Ensuring the properness of models is critical to efficient and successful design, analysis, and control of engineering systems, but it requires much time and expertise as systems become more complex. Thus, there is a growing need for proper-modeling tools for complex systems. Existing tools are inadequate in terms of applicability to nonlinear systems at the graph level, accounting for the scenarios of interest explicitly, preserving the realization, and considering the model structure. This dissertation is aimed to address this gap within the scope of lumped parameter models of nonlinear energetic deterministic systems.

Building on the “activity” concept from the literature, a structural simplification algorithm is developed. This algorithm removes from the model structure those elements that do not contribute to the energetic behavior of the system in the considered scenario, thereby simplifying the model without affecting its predictive ability for that scenario.

To complement the simplification algorithm, a coordinate frame reorientation algorithm is developed to better orient body-fixed coordinate frames in multibody systems to render the model more conducive to simplification. This Karhunen-Loève-expansion-based algorithm detects the existence of and finds the transformation into coordinate frames preferred for simplification.

To reduce models further, a new metric is proposed to evaluate the relative contributions of various system parts to the system behavior. This metric uniquely considers the correlations between the energy-flow patterns throughout the system, and allows for the assessment of system components and their interactions. Based on this metric, a reduction algorithm is proposed. This algorithm reduces not only the model order, but also the model structure for the scenario of interest.

The proper modeling of the HMMWV is presented as a case study. The multibody dynamics of the HMMWV is modeled through a modular approach first. This “full” model is then simplified and reduced for three different scenarios: a two-double-lane-change maneuver, a shaker table setup, and driving straight. Thus, three different proper models of the HMMWV are obtained for the respective scenarios, illustrating the benefits of the proposed algorithms.