Prediction of Spray Vapor Tip Penetration of Diesel, Biodiesel and Synthetic Fuels Using Artificial Neural Networks with Confidence Intervals

Fuel spray and atomization processes affect the combustion and emissions characteristics of fuels in internal combustion engines. Biodiesel and synthetic fuels such as oxymethylene dimethyl ethers (OME) show great promise as alternative fuels and are complementary in terms of reproducing the fluid properties of conventional diesel fuels through blending, for instance. Averaged experimental results, empirical correlations and Computational Fluid Dynamics (CFD) have typically been used to evaluate and predict fuel spray liquid and vapor penetration values so as to better design internal combustion engines. Lately, Machine Learning (ML) is being applied to these investigations. Typically, ML spray studies use averaged experimental data and then over-trained neural networks on the limited available data. By contrast, in this study we present spray vapor tip penetration predictions using artificial neural networks with systematic treatment of uncertainties arising from experimental variability and limitations in the neural network training process. This has not been presented previously, and it allows the calculation of confidence intervals on the spray penetration predictions produced by neural networks. Using the present method, we evaluate four different diesel, biodiesel and OME fuel blends under four fuel injection conditions each and predict spray vapor tip penetration values with a correlation coefficient of 0.999. Across all fuel variants and injection conditions, one standard deviation represented less than 1.5 mm spray tip penetration (circa 2% of spray tip penetration) 1 ms from the start of injection. Despite this precision, a 95% confidence interval on neural network predictions encompassed the experimental fuel penetration data across all fuel variants, injection conditions and time steps. By calculating the confidence intervals on neural network predictions, we enable internal combustion engine designers to better quantify the applicability of neural networks in predicting spray characteristics.