基于统计遗传算法的X射线荧光重叠峰分解

针对X射线荧光分析中相邻谱峰之间的重叠问题，结合光谱形成过程的随机物理特性，提出了一种基于高斯混合统计模型(Gaussian mixture statistics model, GMSM)和遗传算法的重叠峰分解方法。首先，提出了重叠峰的GMSM描述方法，并分析了期望最大化法(expectation maximization, EM)的局部收敛问题;接着，将GMSM参数看作个体基因，以重叠峰随机数据序列的对数似然函数作为适应度函数，并给出了目标函数值的快速算法;然后，采用遗传算法的群体搜索技术找出全局最优解，实现重叠峰分解。该方法将所有测量的随机数据都当作“有用”来处理，其“有用”程度由其概率大小来体现，实现了原谱数据的“零损失”，搜索到的GMSM是全局最大概率意义下的“最佳匹配”模型，符合放射性测量过程的随机性。通过对四个严重重叠峰分解的实验表明，分解后的峰位、峰面积及标准偏差具有较高精度，最大误差分别为0.7道, 2.3%, 2.17%，特别适合于严重重叠的情况，并可广泛用于其他能谱重叠峰的分解。

Decomposition of X-Ray Fluorescence Overlapping Peaks Based on Statistical and Genetic Algorithms

In fluorescence analysis, the phenomenon of overlapping often occurs among adjacent peaks. In the view of the random physical properties of formation process of X fluorescence spectra, Gaussian Mixture Statistics Model (GMSM) and Genetic Algorithms were used for the decomposition of overlapping peaks. First, the GMSM was proposed to describe the overlapping peaks, and the local convergence problem of expectation maximization (EM) was analyzed. Secondly, the GMSM parameters were regarded as individual genes, and the log-likelihood function of overlapping peaks random data was set as fitness function. A fast algorithm for the objective function value was proposed. Finally, the population search technology of Genetic Algorithm was used to find the global optimal solution, and to realize the decomposition of overlapping peaks. All measured data were regarded as “useful” data. The “useful” degree was reflected by their probability. The GMSM method can achieve the “best match” effect in the maximum global probability with zero loss of original data, which can fit the random of radiation measurement process. The decomposition experiments of four serious overlapping peaks show high precision of the peak position, peak area and standard deviation. The maximum error was 0.7 channel, 2.3% and 2.17%, respectively, which is especially suitable for the condition of serious overlap and can be widely used for the decomposition of other energy spectrum.