Machine-learning-driven prediction of the density of waste-cooking-oil-biodiesel/1-butanol blends up to 140 MPa: a rigorously optimized artificial neural network compared with Tammann–Tait and PC-SAFT models

Abstract Accurate density data of biodiesel/alcohol blends over wide temperature and pressure ranges are needed for the design of fuel-injection systems and process equipment, and a model is needed to represent them. In this work the densities of waste cooking oil biodiesel (WCOB) + 1-butanol blends, measured at high pressure in our laboratory and reported previously, were re-analysed with an artificial neural network (ANN) built with a transparent hyperparameter search; to establish whether the ANN is a competitive model, it was compared with the modified Tammann–Tait equation and with the perturbed-chain statistical associating fluid theory (PC-SAFT). Specifically, a curated dataset comprising 866 density data points for x WCOB + (1−x) 1-butanol (x = mass fraction of WCOB), covering temperatures from 298.15 to 393.15 K, pressures from 0.1 to 140 MPa, and seven compositions, was used for model development and benchmarking. A feed-forward ANN with temperature, pressure and composition as inputs was built by a validation-based search over the number of hidden neurons (3–100), four activation functions and eight optimizers, and assessed with a held-out test subset, five-fold cross-validation (CV) and leave-one-composition-out tests. The same protocols were applied to a 36-parameter composition-dependent Tammann–Tait equation, and PC-SAFT with one binary parameter was fitted to the same data. The retained ANN (15 sigmoid hidden neurons, Adam optimizer, 76 parameters) reproduces the data with a root-mean-square error (RMSE) of 0.93 ± 0.15 kg m −3 and a coefficient of determination R 2 = 0.99942 ± 0.00018 (mean ± standard deviation over 10 random initializations); five-fold CV gives RMSE = 0.81 kg m −3 . The Tammann–Tait equation is about four times more accurate (CV RMSE = 0.19 kg m −3 ) and is the only model clearly below the expanded density uncertainty of the measurements (0.7 kg m −3 ); PC-SAFT gives RMSE = 1.70 kg m −3 . Overall, the ANN is a valid correlation of the density surface, about twice as accurate as PC-SAFT, but not the best one for these smooth data. The Tammann–Tait equation is recommended for correlating them; the ANN is of interest when no functional form is available, and any ANN should be benchmarked against a Tait-type equation on the same data. The models should be used only within the measured ranges.