Inversion algorithm of black carbon mixing state based on machine learning

Abstract. The radiative properties of black carbon (BC) are significantly influenced by its mixing state. The single-particle soot photometer (SP2) is a widely recognized instrument for quantifying BC mixing state. However, the derivation of BC mixing state from SP2 is quite challenging. Since the SP2 records individual particle signals, it requires complex data processing to convert raw signals into particle size and mixing states. Furthermore, the rapid accumulation of substantial data volumes impedes real-time analysis of BC mixing states. This study employs the Light Gradient-Boosting Machine (LightGBM), an advanced tree-based ensemble learning algorithm, to establish an inversion model that directly correlates SP2 signals with the mixing state of BC-containing particles. Our model achieves high accuracy for both particle size inversion and optical cross-section inversion of BC-containing particles, with a coefficient of determination R2 higher than 0.98. We further employ the SHapley Additive exPlanation (SHAP) method to analyze the importance of input features from SP2 signals in the inversion model of the entire particle diameter (Dp) and explore their underlying physical significance. Compared to the widely used leading-edge-only (LEO) fitting method, the machine learning (ML) method utilizes a larger coverage of signals encompassing the peak of scattering signal rather than the leading-edge data. This allows for more accurate capture of the diverse characteristics of particles. Moreover, the ML method uses signals with a high signal-to-noise ratio, providing better noise resistance. Our model is capable of accurately and efficiently acquiring the single-particle information and statistical results of the BC mixing state, which provides essential data for BC aging mechanism investigation and the assessment of further BC radiative effects.