Predictive model for fouling estimation in heat exchangers during oil refining operations using an explainable neural network with Levenberg–Marquardt algorithm

This paper details the process of contriving an explainable artificial intelligence model for forecasting the phenomenon of heat exchanger fouling. Unlike existing studies, the neural network approach adopted in this work follows a “white-box” paradigm, in which the model is made explainable by explicitly presenting the mathematical relationships between inputs and output, quantifying the contribution of each input variable, and elucidating how these variables influence the output. The model is developed with a large dataset of 11,626 data points with seven inputs namely: density, dissolved oxygen, time, surface temperature, fluid temperature, fluid velocity and equivalent diameter while the output is the fouling factor. Results from the model development indicate that the model demonstrates reasonable accuracy in predicting the fouling factor, as evidenced by a mean square error of 0.0021, root mean square error (RMSE) of 0.0458 and coefficient of determination of 0.9588. The relevancy factor which shows the relative contributions of each input variable and their effects on heat exchanger fouling was established to enhance the model’s explainability. In this context, it was determined that equivalent diameter, time and fluid velocity exert the most significant impacts on the fouling process, with relevancy factors of -0.46, 0.43 and 0.34 respectively, whereas fluid temperature had the least influence with a relevancy factor of – 0.029. The applicability domain of the model was established using a leverage plot, and trend analyses indicated that the model conforms to the physical trends associated with fouling phenomena. The capabilities of this model enable its integration into a software application that would facilitate real-time predictions of fouling and the optimization of input variables to maximize thermal efficiency.