NARX Technique to Predict Torque in Internal Combustion Engines

To carry out increasingly sophisticated checks, which comply with international regulations and stringent constraints, on-board computational systems are called upon to manipulate a growing number of variables, provided by an ever-increasing number of real and virtual sensors. The optimization phase of an ICE passes through the control of these numerous variables, which often exhibit rapidly changing trends over time. On the one hand, the amount of data to be processed, with narrow cyclical frequencies, entails ever more powerful computational equipment. On the other hand, computational strategies and techniques are required which allow actuation times that are useful for timely and optimized control. In the automotive industry, the 'machine learning' approach is becoming one the most used approaches to perform forecasting activities with reduced computational effort, due to both its cost-effectiveness and its simple and compact structure. In the present work, the nonlinear dynamic system we address is related to the torque estimation of an ICE through a nonlinear autoregressive with exogenous inputs (NARX) approach. Preliminary activities were performed to optimize the neural network in terms of neurons, hidden layers, and the number of input parameters to be assessed. A Shapley sensitivity analysis allowed quantification of the impact of each variable on the target prediction, and therefore, a reduction in the amount of data to be processed by the architecture. In all cases analyzed, the optimized structure was able to achieve average percentage errors on the target prediction that were always lower than a critical threshold of 10%. In particular, when the dataset was augmented or the analyzed cases merged, the architecture achieved average prediction errors of about 1%, highlighting its remarkable ability to reproduce the target with fidelity.