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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.

Model-guided development of drivetrain control and calibration is a key enabler of robust and efficient vehicle design process. A number of CAE tools are available today for modeling hydro-mechanical systems. Automatic transmission behaviors are well understood to effectively tune the model parameters for targeted applications. Drivetrain models provide physical insight for understanding the effects of component interactions on system behaviors. They are also widely used in HIL/SIL environments to debug control strategies. Nonetheless, it is still a challenge to predict shift quality, especially during a sequence of multiple events, with enough accuracy to support model-guided control design and calibration. The inclusion of hydraulic circuits in simulation models often results in challenges for numerical simulation.

Innovations in mobility are built upon a management of complex interactions between sub-systems and components. A need for CAE tools that are capable of system simulations is well recognized, as evidenced by a growing number of commercial packages. However impressive they are, the predictability of such simulations still rests on the representation of the base components. Among them, a wet clutch actuator continues to play a critical role in the next generation propulsion systems. It converts hydraulic pressure to mechanical force to control torque transmitted through a clutch pack. The actuator is typically modeled as a hydraulic piston opposed by a mechanical spring. Because the piston slides over a seal, some models have a framework to account for seal friction. However, there are few contributions to the literature that describe the effects of seals on clutch actuator behaviors.

A transmission system model is developed at various complexities in order to capture the transient behaviors in drivability and fuel economy simulations. A large number of model parameters bring more degree of freedom to correlate with vehicular test data. However, in practice, it requires extensive time and effort to tune the parameters to satisfy the model performance requirements. Among the transmission model, a hydraulic clutch actuator plays a critical role in transient shift simulations. It is particularly difficult to tune the actuator model when it is over-parameterized. Therefore, it is of great importance to develop a hydraulic actuator model that is easy to adjust while retaining sufficient complexity for replicating realistic transient behaviors. This paper describes a systematic approach for reducing the hydraulic actuator model into a piecewise 1st order representation based on piston movement.

A direct trajectory optimization approach is developed to assess the capability of a GTDI-DCT Powertrain, with a Gasoline Turbocharged Direct Injection (GTDI) engine and Dual Clutch Transmission (DCT), to satisfy stringent drivability requirements during launch. The optimization is performed directly on a high fidelity black box powertrain model for which a single simulation of a launch event takes about 8 minutes. To address this challenging problem, an efficient parameterization of the control trajectory using Gaussian kernel functions and a Mesh Adaptive Direct Search optimizer are exploited. The results and observations are reported for the case of clutch torque optimization for launch at normal conditions, at high altitude conditions and at non-zero grade conditions. The results and observations are also presented for the case of simultaneous optimization of multiple actuator trajectories at normal conditions.

PET (Powertrain Engineering Tool) [1, 2] is based on an object-oriented hierarchy system and therefore each component (parent) has its own sub-component (child) systems. Developing explicit forms of objective functions and constraints is simple due to the object-oriented component system of PET. This system automatically recognizes the geometry of components and related design functions in its sub-component levels. This paper discusses computational efficiency, solution accuracy and robustness of software when using closed-form representatives of the derivatives of objective functions and constraints in sequential quadratic programming. Examples of generating closed-form representatives of the derivatives of objective functions and constraints in C/FORTRAN language syntax by using a symbolic processor, Mathematica [3], and mass reduction of the piston-pin are also presented.