A Polynomial-Chaos-Based Multifidelity Approach to the Efficient Uncertainty Quantification of Online Simulations of Automotive Propulsion Systems

Abstract

As a result of the increasing system complexity and more strict performance requirements, intelligent and robust decision-making and control capabilities are of great importance for future automotive propulsion systems. Due to the significant uncertainties from both unavoidable modeling errors and probabilistic environmental disturbances, the ability to quantify the effect of these uncertainties on system behaviors plays a crucial role in enabling advanced control designs in the future for propulsion systems. However, quantifying uncertainties in complex nonlinear systems can cause significant computational burdens. Given the limited computing power on-board a vehicle, developing algorithms with high enough efficiency to quantify uncertainties in automotive propulsion systems in real-time is a major challenge. Traditional uncertainty quantification methods for complicated nonlinear systems, such as Monte Carlo, often rely on sampling — a computationally prohibitive process in many applications. Previous research has shown promises in using spectral decomposition methods such as generalized polynomial chaos to reduce the online computational cost of uncertainty quantification. However, such method suffers from poor scalability and bias issues. In this article, we seek to alleviate these computational bottlenecks by using a multifidelity approach that utilizes Control Variate to combine generalized polynomial chaos with Monte Carlo. Results on the mean, variance, and skewness estimations of vehicle axle shaft torque show that the proposed method corrects the bias caused by Polynomial Chaos expansions while significantly reducing the overall estimator variance compared to that of a conventional Monte Carlo estimator.