Surrogate modeling of waveform response using singular value decomposition and Bayesian optimization

Abstract

In the early stage of vehicle development, it is required to implement a target cascading study by solving inverse problems. However, simulation costs of vehicle dynamics to predict transient responses and frequency responses make the target cascading study difficult. The purpose of this paper is to propose a method to construct a surrogate model which can predict waveform responses and a solution of Bayesian optimization using posterior distribution of trained waveform responses. Replacement of the expensive simulation by the more economical surrogate model can enhance the target cascading study. In this paper, we construct a vectorized training data matrix from the waveform responses which can be evaluated from CAE simulations based on the Design of Experiments. In this proposed method, supervised and unsupervised learning are introduced. The singular value decomposition is used as a feature extraction method (Unsupervised learning) and applied to the training data. Obtained singular vectors are used as feature modes to represent the training data. Gaussian Process model is introduced as a regression model (Supervised learning) and applied to each weight of feature modes which can be obtained by projection of training data to feature modes. The waveform response can be predicted by the superposition of prediction feature values and feature modes. By using the posterior distribution of trained Gaussian Process, Expected Improvement function is evaluated and used in Bayesian optimization to minimize a cost function which is evaluated from the posterior mean of a predicted waveform. The feasibility of the proposed method is illustrated by an application for the suspension design problem of impact harshness phenomenon.

Keywords

• gaussian process
• design of experiments
• singular value decomposition
• bayesian optimization
• inverse problem
• vehicle dynamics
• multibody dynamics