A crank-kinematics based engine cylinder pressure reconstruction model

A new inverse model is proposed for reconstructing steady-state and transient engine cylinder pressure using measured crank kinematics. An adaptive nonlinear time-dependent relationship is assumed between windowed-subsections of cylinder pressure and measured crank kinematics in a time-domain format (rather than in crank-angle-domain). This relationship comprises a linear sum of four separate nonlinear functions of crank jerk, acceleration, velocity, and crank angle. Each of these four nonlinear functions is obtained at each time instant by fitting separate m-term Chebychev polynomial expansions, where the total 4m instantaneous expansion coefficients are found using a standard (over-determined) linear least-square solution method. A convergence check on the calibration accuracy shows this initially improves as more Chebychev polynomial terms are used, but with further increase, the over-determined system becomes singular. Optimal accuracy Chebychev expansions are found to be of degree m=4, using 90 or more cycles of engine data to fit the model. To confirm the model accuracy in predictive mode, a defined measure is used, namely the ‘calibration peak pressure error’. This measure allows effective a priori exclusion of occasionally unacceptable predictions. The method is tested using varying speed data taken from a 3-cylinder DISI engine fitted with cylinder pressure sensors, and a high resolution shaft encoder. Using appropriately-filtered crank kinematics (plus the ‘calibration peak pressure error’), the model produces fast and accurate predictions for previously unseen data. Peak pressure predictions are consistently within 6.5% of target, whereas locations of peak pressure are consistently within ± 2.7° CA. The computational efficiency makes it very suitable for real-time implementation.