X射线荧光分析中相邻峰重叠的分解问题是十分常见的, 谱峰重叠为谱的进一步定性分析和定量分析都带来了困难, 而通过硬件手段来减少谱峰重叠的发生往往受资金和工作条件的制约, 通常会选择通过数学手段得到重叠谱中各个子峰的相关信息来完成重叠谱的分解。 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模型(GMM)的参数独立模型和参数关联模型, 以及基于这两种模型和差分进化算法的重叠峰分解方法。 GMM模型参数构成了差分进化算法个体基因, 给出了目标函数的快速算法, 通过随机生成初始种群, 以种群中每个个体的适应度值和各个个体参数的约束条件为选择标准, 避免了初值不当带来的局部收敛问题, 并且将所有测量的随机数据参与到个体适应度值的运算当中, 避免了原谱数据的损失。 对模型参数相互独立和模型参数相关联两种情况进行了解谱分析, 首先, 对三峰重叠和四峰重叠进行仿真模拟分析, 分解结果表明, 基于GMM参数关联模型的解谱精度较GMM参数独立模型的解谱精度更高, 三峰重叠时, 参数独立模型和参数关联模型分别得到的权重最大误差为8.15%和2%, 峰位最大误差为0.30%和0.06%, 标准差的最大误差为7.5%和1.35%。 四峰重叠时, 参数独立模型和参数关联模型分别得到的权重最大误差为8.3%和4.3%, 峰位最大误差为0.12%和0.13%, 标准差的最大误差为5.04%和0.45%。 然后通过实测三峰重叠谱的解谱分析表明, 用这两种模型进行重叠谱的分解, 分解结果相对误差和待测量元素的含量有关, 随着待测元素含量的降低, 分解结果精度会降低。 仿真和实测都表明, 基于高斯混合模型和运用差分进化算法的重叠谱进行解谱时, 如果能够提前得到各个相互重叠小峰权重、 均值、 标准差之间的关系, 建立GMM参数关联模型, 减少寻优个体参数个数, 对提高复杂峰的分解精度是非常重要的。

X-ray fluorescence analysis of adjacent peaks overlapping decomposition problem is very common, spectrum peaks overlapping spectrum for further qualitative analysis and quantitative analysis are brought difficulties, and by means of hardware to reduce the spectral peaks overlapping often occurs the restriction of the capital and the working conditions, will often go on the overlapping spectrum is obtained by mathematical means of relevant information to complete the overlap of each peak spectral decomposition. This paper proposes a model GMM parameters of the independent model and GMM parameters correlation model based on the gaussian mixture (GMM), based on these two models and differential evolution algorithm of the overlapped peaks decomposition method. GMM model parameters constitute the individual genes differential evolution algorithm, presents a fast algorithm for target function, through the randomly generated initial population, In the fitness value of each individual in a population and the constraint conditions of each individual parameter as selection criteria, avoids the local convergence of the problems of the improper initial value, and all the measurement of random data involved in the operation of individual fitness value, avoid the loss of the original spectral data. Respectively for independent parameter model and the parameters associated with the model to understand the spectrum analysis, two cases through the decomposition of three kinds of overlapping spectra show that the model based on two kinds of differential evolution algorithm for the overlapping peaks decomposition is effective. First of all, the three peak simulation analysis and four peaks overlap decomposition results show that the spectral accuracy based on GMM parameters associated model spectrum GMM parameters are independent of the model solution precision is high. Three peaks overlap, parameters independent model and correlation model respectively to get the weight of maximum error is 8.15% and 2%, a maximum error of 0.30% and 0.06%, the standard deviation of the maximum error is 7.5% and 1.35%. Four overlapping peaks, parameters independent model and correlation model respectively to get the weight of maximum error is 8.3% and 4.3%, a maximum error of 0.12% and 0.13%, the standard deviation of the maximum error is 5.04% and 0.45%. Then through measured three peaks overlapping spectra of the solutions of spectrum analysis shows that with this two kinds of model of overlapping spectrum decomposition, decomposition results relative error and the measuring element content is about, with the loss of the element under test content, the decomposition results in accuracy is reduced. Simulation and measurement show that. Using differential evolution algorithm based on gaussian mixture model and overlapping spectra for solution spectrum, if you can get ahead of the small overlapping peak weight, mean, standard deviation, the relationship between the GMM parameters correlation model is set up, and decrease the number of optimization of individual parameters to improve the accuracy of the breakdown of the complex peak is very important.