针对X光谱分析研究中经常遇到的谱峰重叠问题, 提出了一种基于标准差关联的高斯混合模型(GMM-SDR)和粒子群算法的重叠谱峰解析方法。 首先, 介绍了重叠峰的GMM-SDR模型, 并以GMM-SDR参数构成粒子位置, 给出了粒子目标函数及适应度值的快速算法； 然后, 利用粒子群算法的群体搜索能力, 以搜索最优GMM-SDR模型, 进而实现重叠峰的分解。 初始值采用随机设定, 将测量的所有随机数据作为一个整体, 以其对模型的概率匹配程度作为适应度值, 故该方法避免了初值设定不当带来的局部收敛问题, 克服了传统曲线拟合方法对原始有用数据的破坏, 所搜索到的模型是一个全局最优解。 通过对四个及以下重叠谱峰的分解表明, 该方法分解精度较高, 其中, 两峰重叠谱分解后的峰位、 峰面积及标准差最大相对误差分别为0.4%, 0.05%和2.07%, 三峰重叠谱分解后的峰位、 峰面积及标准差最大相对误差分别为1.2%, 0.04%和0.74%, 可适用于各种严重重叠谱峰的分解。

In X-Ray spectrum analysis, the phenomenon of overlapping often occurs among spectrum peaks. In this paper, “Gaussian Mixture Model-Standard Deviation Related”(GMM-SDR) and Particle Swarm Optimization Algorithms were used for overlapping spectrum peak analysis. First, the GMM-SDR model of overlapping peaks was introduced, and the GMM-SDR parameters constitute the particle position. The objective function and the fast algorithm for the fitness function value were proposed. Secondly, the population search technology of particle swarm optimization algorithm was used to search the optimal GMM-SDR before decomposiing the overlapping peaks. In this algorithm, the initial value was set randomly and all measured random data were regarded as a whole. Since the probability matching degree of the model was taken as the fitness value, the method avoided the local convergence problem caused by improper initial value setting, and overcame the destruction of traditional curve fitting method to the original useful data. In fact, the model built with this method is a global optimal solution. The decomposition experiments of four showed high precision of the peak position, peak area and standard deviation with fewer overlapping peaks . The maximum relative error of decomposition of the two overlapping peaks was 0.4%, 0.05%, 2.07%, and which of the three overlapping peaks was 1.2%, 0.04% and 0.74%, respectively, which can be widely used for the decomposition of other overlapping peaks.