Based on Differential Evolution Algorithm X Fluorescence Peak Overlapping Decomposition
LIAO Xian-li1, 2, HUANG Jin-chu1*, LAI Wan-chang1, GU Rui-qiu1, WANG Guang-xi1, TANG Lin2, ZHAI Juan1
1. College of Nuclear Technology and Automation Engineering, Chengdu University of Technology, Chengdu 610059, China
2. School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
Abstract：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.
Key words：Differential evolution algorithm; GMM parameters of the independent model; GMM parameters correlation model; Decomposition of the overlapping peaks
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