Minimum Data Requirement for Neural Networks Based on Power Spectral Density Analysis

One of the most critical challenges ahead for diesel engines is to identify new techniques for fuel economy improvement without compromising emissions regulations. One technique is the precise control of air/fuel ratio, which requires the measurement of instantaneous fuel consumption. Measurement accuracy and repeatability for fuel rate is the key to successfully controlling the air/fuel ratio and real-time measurement of fuel consumption. The volumetric and gravimetric measurement principles are well-known methods for measurement of fuel consumption in internal combustion engines. However, the fuel flow rate measured by these methods is not suitable for either real-time control or real-time measurement purposes because of the intermittent nature of the measurements. This paper describes a technique that can be used to find the minimum data [consisting of data from just 2.5% of the non-road transient cycle (NRTC)] to solve the problem concerning discontinuous data of fuel flow rate measured using an AVL 733S fuel meter for a medium or heavy-duty diesel engine using neural networks. Only torque and speed are used as the input parameters for the fuel flow rate prediction. Power density analysis is used to find the minimum amount of the data. The results show that the nonlinear autoregressive model with exogenous inputs could predict the particulate matter successfully with
$R^{2}$
above 0.96 using 2.5% NRTC data with only torque and speed as inputs.