Reduction of Multibody Dynamic Models in Automotive Systems Using the Proper Orthogonal Decomposition

Abstract

The proper orthogonal decomposition (POD) is employed to reduce the order of small-scale automotive multibody systems. The reduction procedure is demonstrated using three models of increasing complexity: a simplified dynamic vehicle model with a fully independent suspension, a kinematic model of a single double-wishbone suspension, and a high-fidelity dynamic vehicle model with double-wishbone and trailing-arm suspensions. These three models were chosen to evaluate the effectiveness of the POD given systems of ordinary differential equations (ODEs), algebraic equations (AEs), and differential-algebraic equations (DAEs), respectively. These models are also components of more complicated full vehicle models used for design, control, and optimization purposes, which often involve real-time simulation. The governing kinematic and dynamic equations are generated symbolically and solved numerically. Snapshot data to construct the reduced subspace are obtained from simulations of the original nonlinear systems. The performance of the reduction scheme is evaluated based on both accuracy and computational efficiency. Good agreement is observed between the simulation results from the original models and reduced-order models, but the latter simulate substantially faster. Finally, a robustness study is conducted to explore the behavior of a reduced-order system as its input signal deviates from the reference input that was used to construct the reduced subspace.