## 1 Introduction
### Previous Work  
Many scholars have done a lot of meaningful work on X-ray material identification. [PERSON] et al. (2018) of Delft University of Technology used DE-XRT combined with EMS to sort non-ferrous metals such as Alc (cast aluminum alloy), Alw (wrought aluminum alloy), Mg, Cu (copper), SS and brass. Their DE-XRT method used \(L\)-\(H\) plane measured by low-energy (75 kV) and high-energy (150 kV) for classification, while the EMS used voltage amplitude and phase shift \(U\)-\(\varphi\) polar coordinate plane measured by excitation magnetic field with frequency of 700 Hz and 5 kHz for classification. [PERSON] et al. (2018) used DE-XRT combined with the eddy current test (ECT, same as EMS in Reference (2018)) to refine aluminum alloy classification with seven kinds in the laboratory. Their DE-XRT carried out tests of the multi-energy and multi-thickness combination of copper sheets by dual-energy detector, and the results from the ECT were classified in the polar coordinate plane with amplitude values represented by radius and phase angle. Unfortunately, the experimental conditions of this method are rather strict, and there are still considerable difficulties in practical industrial application. [PERSON] et al. (2018) used dual-source DE-XRT in security inspections. They adopted the Simpson complex method to calculate the integral value of Equation (6) by subsections, solved a series of equations by MATLAB series quadratic programming (SQP), empirically selected a pair of specific low-energy and high-energy area attenuation ratios as the R_value, and simulated X-ray with MCNP (Monte Carlo N-Particle). The essence of the algorithm was to discretize the continuous spectrum by segments, and select a pair of high- and low-energy values to calculate the R_value, that is, approximately extracting the dual-energy monochromatic R_value from the continuous spectrum, so as to remove thickness effect. However, the algorithm is more sophisticated. In recent years, it has been demonstrated that Monte Carlo radiation transport tools are so useful for designing and optimizing photon (X-ray and gamma) radiation based systems ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). These tools can speed up the development or research process and save experimental costs, so they are favored by researchers. [PERSON] et al. (2018) established the relationship between energy attenuation of DE-XRT and rare element enrichment, ore size and spatial distribution in mineral processing of rare elements. [PERSON] et al. (2018) also used DE-XRT to realize coal preparation. [PERSON] et al. [13] used XRF technology to realize the recognition of a variety of plastics. X-ray is also widely used in the field of security inspection [23; 24; 25; 26]. [PERSON] et al. [24] used two-dimensional low-high energy (_L-H_) plane to identify hazardous materials. [PERSON] et al. [25] used an X-ray photon counting detector to propose an optimized material identification method suitable for a photon counting detector and energy integration detector, so as to realize the identification of hazardous materials. [PERSON] et al. [26] also used an X-ray photon counting detector to realize accurate material identification when the X-ray spectrum hardened, and simulated an X-ray spectrum with MCNP. In recent years, research on the applications of high-energy (over MeV) X-ray in the field of container security inspection has gradually increased [27; 28; 29; 30; 31; 32]. [PERSON] et al. [27] used MeV-level dual-energy X-ray so-called \(\alpha\)-curve to identify dangerous or smuggled goods in containers. Recently, in addition to X-ray research, some scholars have explored some new methods for material sorting. [PERSON] et al. [4] realized the recognition of copper and aluminum by color-sorting, and discussed and compared several intelligent optimization algorithms such as PCA-SVM (principal component analysis-support vector machines).