Intervention of machine learning and explainable artificial intelligence based polynomial transformation approach for improved measurement of oil-water emulsion using FBG sensor

Abstract This study focuses on the application of polynomial transformations in combination with machine learning (ML) and explainable artificial intelligence (XAI) techniques to analyze tilted fiber Bragg grating (TFBG) sensor data for oil–water emulsion stability. The dataset consisting of experimental TFBG spectra (wavelength range: 1250–1650 nm) included parameters such as revolutions per minute (RPM) of the rotator, surfactant concentration (C s ), and area (indicating emulsion stability). To enhance the feature space and enable detailed analysis of parameter interactions, polynomial transformations of degree 2 were applied. This transformation provided a new dimension of study, facilitating the exploration of complex relationships in the data. Machine learning models, including linear regression and Random Forest regression, were tested on the polynomial-transformed features, with the latter achieving a high R 2 value of 99.2%. XAI techniques, particularly SHAP analysis, were used to quantify feature contribution of each individual feature (i.e., RPM and C s ), and their polynomials (i.e., RPM 2 , C s 2 , and RPM × C s ). The results revealed that C s had a significantly greater impact on emulsion stability than other parameters. Subsequently, light wavelength ( λ ) was included in the ML and XAI analyses leading to more possible combinations of polynomials (i.e., C s 2 , RPM 2 , λ 2 , C s × λ , RPM × λ , and RPM × C s ). The results re-affirmed the influence of C s on emulsion stability. Further, the combination C s × λ outperforms all other combinations. This outcome was explained in terms of spectral dependence of absorbance combined with the Beer–Lambert law. The study highlights the utility of polynomial transformations in enhancing feature representation and interpretability, offering insights for optimizing parameters and processes in crude oil emulsion stabilization.