NARX Technique to Predict Torque in Internal Combustion Engines

Abstract

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.

Investigation of a Hybrid LSTM + 1DCNN Approach to Predict In-Cylinder Pressure of Internal Combustion Engines

“…A series of tests were conducted on a 999-cc, three-cylinder engine with SMART turbocharging, 12 valves, and pent-roof combustion chambers, as indicated in Table 1 [41]. The engine uses port fuel injection (PFI) technology and is designed to run on gasoline (E5) with a RON of 95 and MON of 85, which is commonly used in the European market.…”

“…By using interpolation-based techniques, they can predict parameters and reduce the need for evaluating multiple operating points. This leads to significant improvements in memory and computational speed [36][37][38][39][40][41][42][43][44][45][46]. Based on the different ML approaches available, the LSTM + 1DCNN method appears to be a reliable way to conduct signal analysis.…”

Predicting the Torque Demand of a Battery Electric Vehicle for Real-World Driving Maneuvers Using the NARX Technique

“…Selecting a proper test maneuver to source the training or validation data should consider covering as many operating points as possible. This helps obtain sufficient information about the system's behavior with as little test effort as possible [1,7]. Based upon that, a real-world driving (RWD) scenario is implemented using a simulation model for the VUT, which was validated in a previous work [16].…”

“…Due to their reduced computational effort, cost effectiveness, and compact structure, the 'machine learning' techniques are becoming one the most popular approaches for performing prediction activities, especially in the automotive industry [7]. Among the machine learning approaches, NARX modeling is a promising method for estimating the nonlinear dynamic system of the internal combustion engine (ICE) torque [7][8][9].…”

“…Due to their reduced computational effort, cost effectiveness, and compact structure, the 'machine learning' techniques are becoming one the most popular approaches for performing prediction activities, especially in the automotive industry [7]. Among the machine learning approaches, NARX modeling is a promising method for estimating the nonlinear dynamic system of the internal combustion engine (ICE) torque [7][8][9]. For instance, the study in reference [10] investigated different intelligent modeling techniques, specifically, the NARX neural network, linear regression, and regression error with the autoregressive moving average, for modeling a diesel engine truck's fuel consumption and emissions.…”