On the Construction and Use of Surrogate Models for the Dynamic Analysis of Multibody Systems

Abstract

This study outlines an approach for speeding up the simulation of the dynamic response of vehicle models that include hysteretic nonlinear tire components. The method proposed replaces the hysteretic nonlinear tire model with a surrogate model that emulates the dynamic response of the actual tire.The approach is demonstrated via a dynamic simulation of a quarter vehicle model. In the proposed methodology, training information generated with a reduced number of harmonic excitations is used to construct the tire hysteretic force emulator using a Neural Network (NN) element. The proposed approach has two stages: a learning stage, followed by an embedding of the learned model into the quarter car model. The learning related main challenge stems from the attempt to capture with the NN element the behavior of a hysteretic element whose response depends on its loading history. The methodology is demonstrated in conjunction with a simple nonlinear quarter vehicle system as well as an ADAMS based model that uses a complex tire element. The results obtained with the surrogate model prove to be accurate and are obtained at a fraction of the CPU time required to handle the original models. The approach proposed is anticipated to be useful for reducing the duration of vehicle simulations, or when a tire model is not available but experimental data can be used to generate a surrogate model.t) x sp Sprung mass displacement ) (t x tire Tire displacement ) (t y Base displacement tire m Tire mass sp m Sprung mass sus k Suspension stiffness sus c Suspension damping coefficient tire k Tire stiffness tire c Tire damping coefficient ) (t q Restoring force ) (t g Non-hysteretic component of restoring force ) (t z Hysteretic component of restoring force , ,n κ β γ Hysteretic loop shape's control parameters t A Instantaneous amplitude t ω Instantaneous frequency t ∆ Integration time step

Multibody dynamics and control using machine learning

“…Ardeh et al [37] and Han et al [40] have reported that their surrogates trained on synthetic data offered high accuracy and efficiency compared to the full, nonlinear simulation models. Ardeh et al [37] have built a surrogate of a tire using a feed-forward neural network. The surrogate model was designed Table 1 Summary of papers on data-driven modeling of multibody systems using deep learning.…”

“…Topic DL Methods SD MD SM Surrogate models Ardeh et al [37] Submodel of a tire FFNN Azzam et al [38] Virtual sensor for loads on wind turbine gearbox FFNN García Peyrano et al [39] Mechanical unbalance of the flexible rotor of a steam turbine FFNN, SVM Inverse dynamics of robotic manipulators SOUL, RNN Rane et al [46] Internal forces in musculoskeletal models during motion CNN, FFNN Ren and Ben-Tzvi [36] Inverse kinematics and dynamics of robotic manipulators GAN Nasr et al [47] Inverse muscle dynamics in musculoskeletal models…”