In-Cylinder Pressure Estimation in a Multi-Cylinder Engine by Combining the Instantaneous Crankshaft Speed Data and a 0D Thermodynamic Model. Numerical Validation

Abstract

Modern engines require continuous and detailed monitoring in order to minimize variations in performance and emissions during their operation. To this aim, the engine thermodynamic cycle must be brought into focus, with special emphasis on the combustion process. The in-cylinder pressure is the parameter that is most directly associated with the engine thermodynamic cycle. Direct measurements by means of dynamic pressure sensors are commonly used for research and development purpose. Currently, however, the cost and intrusiveness of such sensors, together with the harsh operating conditions that limits their lifetime, make direct measurements of the in-cylinder pressure not yet suitable for mass production applications. As a consequence, there’s great interest in developing cost-effective and reliable alternative solutions to extract pressure trace and combustion indicators such as the indicated mean effective pressure (IMEP). The paper presents a technique for reconstructing the pressure cycle of each cylinder of a multi-cylinder engine by combining the instantaneous crankshaft speed information and a 0D thermodynamic model. Crankshaft position, angular velocity and angular acceleration, coupled with the engine inertia, are used to estimate the effective torque oscillation. The average indicated torque and the combustion torque contribution of each cylinder are then evaluated by coupling the information coming from engine speed and the 0D model. Eventually, through the kinematic relationship between the effective torque and the indicated pressure, the in-cylinder pressure trace is reconstructed. The methodology proposed by the authors allows to evaluate the indicated pressure of each cylinder: this is especially useful for detecting cylinder-to-cylinder variations and misfiring events. Data from a 1D calibrated numerical model of a four-cylinder engine is used for preliminary validation at different engine speeds and loads.

In-Cylinder Pressure Estimation from Rotational Speed Measurements via Extended Kalman Filter

“…To this aim, a nonlinear least squares error (NLSE) estimate of the optimal parameter pairs α * l = α * 1,l , α * 2,l for each cylinder l, has been computed. This amounts to minimize the error between the estimated pressure (24) and the reference pressure p re f ,l , hence…”

“…Nonlinear models, such as NARX, recurrent neural networks, and Chebishev polynomial expansions, have been also considered [20][21][22][23]. An approach based on the combined use of crankshaft speed measurements and a zero-dimensional (0D) thermodynamic model has been recently presented in [24].…”