A bias-corrected ensemble model for quantifying additive content variations in complex lubricant systems

The concentration of functional additives in lubricants is a critical parameter determining their tribological performance and service life. To achieve rapid and accurate detection of trace additive concentrations in lubricating oils, this study proposes a physics-informed Bias-Corrected Ensemble Model (BCE). By learning spectral features within complex mixtures, the method addresses the challenges in quantitative analysis caused by overlapping characteristic peaks of multiple additives and weak signals at low concentrations. Based on an extension of the Lambert-Beer law to derivative spectroscopy, an ensemble of learners was constructed to extract the intrinsic spectral features of additives. Subsequently, a meta-model was employed to systematically characterize and compensate for prediction biases induced by mixing interference. The learner ensemble and the meta-model together form the BCE, and accomplish the decomposition of overlapped spectral features in multi-component mixtures. Results demonstrate that the method enables accurate detection of specific additive content in complex simulated oil systems. The coefficient of determination (R²) for predicting the concentration of the target additive T321 reached 0.949. Furthermore, based on the model's predictions of additive concentration variations in oil samples, verification oil samples containing MoDTP were prepared according to the predicted concentrations and subjected to friction tests using a four-ball tribo-tester. The measured steady-state friction coefficient and wear scar diameter exhibited errors of less than 5.8% and 1%, respectively, compared to the results from the in-service oil samples.