A Dynamically Identified Algebraic NARX Air-to-Fuel Ratio Estimator

This paper proposes a system identification method to obtain a virtual in-cylinder air-to-fuel ratio (AFR) sensor using the measured engine variables of engine speed, manifold absolute pressure and fuel pulse width. An algebraic NARX model capable of estimating AFR, including transient behaviour, is identified from experimental data using ordinary least squares. A simple structure selection method is used to establish a low order algebraic model structure based on the correlation of the candidate terms with the output. The algebraic NARX structure should be more amenable to software implementation in current PCM architectures than those of alternative NN schemes.The ion current signal from the spark plug is introduced in a subsequent identification to improve the model quality. The information rich ion current signal is sampled every one degree of crank angle for 39 degrees during combustion and this window of data is then reduced to 6 inputs using principle component analysis. The two models are then critically compared with regards to the model fit.