A method for the calculation of multi-layer shielding buildup factors based on extra-trees regression and equivalent iteration

-ray attenuation in the medium has been greatly simplified with the introduction of the concept of buildup factors. However, the determination of buildup factors for multi-layer shielding structures composed of different materials remains a challenging problem. Previous studies have typically extended empirical formulas developed for double-layer shielding to multi-layer structures. In contrast, this paper proposes a method and model, termed ETMLB, for calculating buildup factors in multi-layer shielding based on single-layer and double-layer buildup factor data and the extra-trees (ETs) algorithm. In this approach, two ET regression models, ETZ and ETB, are trained using single-layer and double-layer shielding data, respectively. The ETB model first calculates the buildup factors for double-layer shielding. The double-layer system is then reduced to an equivalent single layer, whose effective atomic number is computed using ETZ. Through successive equivalent iterations, the multi-layer shielding is reduced to an equivalent double-layer system, enabling the computation of its buildup factor. The test results demonstrate that, compared with several commonly used empirical formulas, ETMLB exhibits superior computational accuracy and provides a reliable approach for the calculation of buildup factors in multi-layer shielding.