Identification of weak peaks in X-ray fluorescence spectrum analysis based on the hybrid algorithm combining genetic and Levenberg Marquardt algorithm

Accurate measurement of cadmium content in rice is of utmost importance to determine if the inspected rice product is safe to people. X-ray fluorescence analysis is frequently used for multi-element analysis because it has characteristics of fast, accurate and nondestructive. However, due to the low content of cadmium in rice, its corresponding characteristics energy peak is relatively weak and is sensitive to the background information in the X-ray energy spectrum. Thus, it is very tough to obtain the accurate values of cadmium content by utilizing traditional X-ray fluorescence analysis. In this paper, the identification of weak peaks of cadmium is much improved by proposing a hybrid algorithm combining genetic algorithm (GA) and Levenberg-Marquardt algorithm (LM). The hybrid algorithm not only takes full advantages of GA and LM respectively but also inhibits their unwanted properties: poor local search ability of GA and locally convergent of LM. The proposed hybrid algorithm is employed to identify weak peaks in X-ray spectra of six contaminated rice samples with different contents of cadmium. Two comparative experiments are conducted to compare the performance between GA, LM and the proposed hybrid algorithm. One of the comparative experiments has the relative error varying with the number of calculations, which aims to verify the accuracy and stability. The results show that the hybrid algorithm is a better option in terms of accuracy and stability. Another comparative experiment of which the average relative error varies with the number of iterations is conducted to verify the computing efficiency. The experiments show that the hybrid algorithm exhibits a faster convergence rate. Two numerical experiments demonstrate that the proposed algorithm can well resolve the identification issue of the cadmium in the X-ray spectra and significantly improve the content measurement accuracy of cadmium in the quality evaluation experiment of rice products.

精准测定稻米中的镉含量，对于判断受检稻米产品是否对人体安全至关重要。X射线荧光分析（X-ray fluorescence analysis）因具备快速、精准、无损的特性，常被用于多元素分析。然而，由于稻米中镉的含量较低，其对应的特征能峰相对微弱，且对X射线能谱中的背景信息较为敏感，因此采用传统X射线荧光分析方法难以获取精准的镉含量数值。本文提出一种结合遗传算法（Genetic Algorithm, GA）与莱文贝格-马夸特算法（Levenberg-Marquardt Algorithm, LM）的混合算法，大幅优化了镉弱峰的识别效果。该混合算法充分发挥了遗传算法与莱文贝格-马夸特算法各自的优势，同时抑制了二者的固有缺陷：遗传算法局部搜索能力不足，以及莱文贝格-马夸特算法易陷入局部收敛的问题。本文将所提混合算法应用于6份不同镉污染程度稻米样品的X射线能谱弱峰识别。为对比遗传算法、莱文贝格-马夸特算法与本文所提混合算法的性能，开展了两组对照实验：第一组实验以相对误差随计算次数的变化为评价指标，旨在验证算法的准确性与稳定性，结果表明混合算法在准确性与稳定性上均表现更优；第二组实验以平均相对误差随迭代次数的变化为评价指标，验证算法的计算效率，结果显示混合算法具备更快的收敛速度。两组数值实验证明，所提算法可有效解决X射线能谱中的镉峰识别难题，在稻米产品质量评价实验中，显著提升了镉含量的测定精度。