Multicylinder engine pressure reconstruction using NARX neural networks and crank kinematics

Abstract

A NARX neural network is adapted for cylinder pressure trace reconstruction on a multicylinder engine. Following a systematic study to establish the required NARX input information (using measured pressure traces and simulated crank kinematics), two fully recurrent training algorithms are developed and applied to real engine data. These include a back-propagation-through-time algorithm (BPTT) and an extended Kalman filter (EKF). For multi-cylinder engines, two cases are examined, both assuming crank kinematics is obtained from a single shaft-encoder fitted at the forward end of the crankshaft. In one case, a NARX model is constructed to provide an inverse relationship between the kinematics at the encoder location and the pressure trace in an arbitrary cylinder. In the second case, by transforming the kinematics (to emulate a local encoder), a different NARX model is constructed to relate the kinematics at the crank location of a particular cylinder to the corresponding pressure trace. The accuracy and efficiency of both NARX models is examined for application to a three-cylinder in-line DISI engine (in which pressure traces are measured on all cylinders). The paper shows that the computational requirements of training are substantial and, although the efficiency of the EKF algorithm is better than the BPTT, the fitting accuracies are similarly good. For generalization, however (to unseen data), neither method is yet sufficiently accurate (even for steady state engine operation) unless substantially more training data are used to achieve the target accuracy of ± 4 per cent. The overall conclusion of the paper is that the NARX model has the correct architecture for multicylinder pressure reconstruction.