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.

Global modes for the reduction of flexible multibody systems

“…The computational load rises quickly by increasing the number of flexible bodies, or by using refined mesh to describe the finite elements, therefore the greatest efforts of the scientific community have been directed to create reduced-order models (ROMs), i.e., models in which the number of flexible coordinates is contained [15,16,35]. Most of the ROMs implemented in the FFR are component-level based and the reduction is applied to the elastic coordinates of each flexible body [1,4,8,26,29,31,45,46]. In [24,25] a component-level reduction method based on an enhanced Craig-Bampton method is described.…”

Improving model predictive controller turnaround time using restricted Lagrangians

“…It is a reduction method that stems from linear theory but has nonetheless been successfully applied to a wide variety of nonlinear models. Applications include modeling and control of in-cylinder flow [1], the heat diffusion equation [2], [3], fluid channel flow [4], distributed reactor systems [5] and vehicle dynamics [6], to list a few. POD has been applied to control problems by reducing the order of the original plant models.…”

A generalized constraint reduction method for reduced order MBS models

“…Hence, model order reduction is only meaningful in terms of repetitive simulations. In the past, both methods were applied to dynamical systems by several authors, and the interested reader is referred to [3,5,6,10,11,13,17] and references therein.…”

“…In [17], POD model order reduction was recently applied to a suspension system. Therein, the kinematics and dynamics are treated with special attention and hence, the governed equations of motion are very distinct from those treated in this work.…”