Optimization of Gaussian Process Regression Model for Characterization of In-Vehicle Wet Clutch Behavior

The advancement of Machine-learning (ML) methods enables data-driven creation of Reduced Order Models (ROMs) for automotive components and systems. For example, Gaussian Process Regression (GPR) has emerged as a powerful tool in recent years for building a static ROM as an alternative to a conventional parametric model or a multi-dimensional look-up table. GPR provides a mathematical framework for probabilistically representing complex non-linear behavior. Today, GPR is available in various programing tools and commercial CAE packages. However, the application of GPR is system dependent and often requires careful design considerations such as selection of input features and specification of kernel functions. Hence there is a need for GPR design optimization driven by application requirements. For example, a moving window size for training must be tuned to balance performance and computational efficiency for tracking changing system behavior. In this paper, a detailed design evaluation of GPR is conducted for the characterization of an engine disconnect clutch in P2 hybrid electric vehicle. Specifically, a clutch transfer function is constructed using GPR that maps actuator pressure to clutch torque. The disconnect clutch exhibits highly non-linear behaviors with a distinct hysteresis loop. A casual application of GPR results in a misrepresentation of clutch behaviors with a risk of overfitting. This paper first describes a process to select input features based on statistical measures. Several pre-defined kernel functions and their combinations are evaluated for generalization capability and computational efficiency. A size of data from a moving window is also evaluated for its effect on training errors as well as efficiency. The optimized GPR is applied to a set of disconnect clutch engagement data obtained from a long drive sequence for enabling accurate tracking of clutch behaviors in vehicles. This paper concludes with a set of recommendations for successfully deploying powerful GPR tool for addressing real-world automotive problems.