A Multi-Derivation-Spline Wavelet Analysis Method for Low Atomic Number Element EDXRF
WU Lian-hui1, 2, 3, HE Jian-feng1, 2, 3*, ZHOU Shi-rong2, 3, WANG Xue-yuan1, 2, YE Zhi-xiang2, 3
1. Fundamental Science on Radioactive Geology and Exploration Technology Laboratory, East China University of Technology, Nanchang 330013, China
2. Jiangxi Engineering Laboratory on Radioactive Geoscience and Big Data Technology, East China University of Technology, Nanchang 330013, China
3. Information Engineering College, East China University of Technology, Nanchang 330013, China
摘要： 能量色散X射线荧光（EDXRF）光谱分析待测元素的信息主要反映在能谱的特征峰峰位以及特征峰净峰面积中。对于特征峰的准确检测是EDXRF光谱分析的关键。特征X射线之间的能量在低原子序数元素中相差很小，在实际测量过程中由其他一些因素干扰会导致EDXRF光谱中特征峰产生严重重叠，以EDXRF光谱中低序列元素的重叠峰作为研究对象，提出一种四次导数结合三样条小波变换处理低序列元素重叠峰的新方法。通过数学模型模拟重叠峰检测了该方法的可行性，并仿真了实测X荧光光谱数据进行检测得到良好的效果，通过使用了CIT-3000SY X 荧光元素录井仪实测T铅黄铜数据和混合轻元素数据荧光光谱作为验证。首先，介绍导数法以及三样条小波法分解重叠的原理。导数法阶数越高信号越畸形但可以有效提高重峰分离度，而三样条小波变换对低分离度重峰处理较为无力但能有效的保持峰型。通过Tsallis峰信号模拟重叠峰，模拟出3个峰信号，第1个峰和第2个峰的分离度R=0.33，第2个峰和第3个峰的分离度R=0.67，导数处理后信号任仍具有一部分重叠，但是导数处理后不仅保留了信号的峰位值，且出现了分离度变大的现象，而三样条小波对低分离度重叠峰的分解较为无力，但是对于分离度较大的重叠峰具有较好的效果，信号通过四次导增加分离度再进行三样条小波变换，通过调节样条小波分解层次的次数，然后对分解出的高频信号采取适当的系数进行放大，最后进行信号重构。实验实现了对模拟信号的分解。验证了此方法针对重叠峰分解具有可行性。实验采用分解4层的三样条小波变换以及放大6倍的高频信号。然后，处理仿真K元素的重叠光谱，实现了重叠峰的分解，通过仿真实验表明新方法能准确的识别峰位，结果表明只有1%之内的误差，证明了新方法对X荧光光谱重叠峰分解的适用性。最后用此方法对CIT-3000SY X荧光元素录井仪实测T铅黄铜元素数据以及混合轻元素数据X荧光光谱进行处理，实现了对重叠峰的分解，且分解后的峰位误差控制在1%之内，具有较高的准确率。实验结果证明：四次导数结合三样条小波变换能有效分离重叠峰，并且在处理X荧光光谱的重叠峰分解上具有实用性。
关键词：X射线荧光光谱；四次导数；三样条小波变换；低分离度重叠峰分解
Abstract：The information of elements to be measured in the energy dispersion X-ray fluorescence(EDXRF) spectrum is included in the characteristic peak position and the characteristic peak net peak area. Accurate detection of characteristic peaks is the key to energy dispersive X-ray fluorescence spectroscopy. The energy difference between the characteristic X-rays of many low sequence elements is very small, there are many kinds of interference in the process of fluorescence spectrum generation，resulting in serious overlapping peaks of measured X-ray fluorescence data, in this paper, overlapping peaks are taken as the research object，this paper presents a method to deal with overlapping peaks by combining the fourth derivative with the three-spline wavelet transform. The effectiveness of the method was tested by simulating overlapping peaks. The data of X-ray fluorescence spectrum and measured data are verified and analyzed. Firstly, the principle of the derivative method and three-spline wavelet method to decompose overlap is introduced in detail. The higher the derivative order, the more distorted the signal, but it can effectively improve the separation degree of the overlapping peak. The three-spline wavelet transform is weak for the to deal with peak with low separation degree, but it can effectively maintain the peak shape. By simulating the data. Among the three overlapping peaks, the separation degree of peak 1 and peak 2 is R=0.33. The separation degree of peak two and peak three R=0.67, after the fourth derivative there is some overlap in the signal, but the fourth derivative not only retains the peak position of the signal, and the degree of separation increases. Combined with the characteristics of the three-spline wavelet transform, by adjusting the value of the decomposition hierarchy, and reconstructed by scaling up the high frequency signal by a factor greater than 1, the simulated overlapping peaks are decomposed. The number of decomposition layers of the three-spline wavelet is four, and the amplification factor of high frequency is six times. Then, the overlapping spectrum of element K is simulated. The decomposition of overlapping peaks is realized. The simulation results show that the new method can accurately identify the peak position, and the error is within 1%. The applicability of the new method to X -ray fluorescence spectrum overlap peak decomposition is proved. It is verified that this method is feasible to decompose overlapping peaks. The last, is the Ca element X-ray fluorescence spectrum data and Mixed light element X-ray fluorescence spectrum data detected by the CIT-3000SY X-ray fluorescence element logging instrument were processed. Now the decomposition of the overlapping peaks and the peak position error after decomposition are controlled within 1%, with high accuracy. The experimental results show that: The fourth derivative combined with three-spline wavelet transform can effectively separate overlapping peaks. And it is practical to deal with the overlapping peak decomposition of X-ray fluorescence spectrum.
Key words：X-ray fluorescence spectrum; Four times the derivative; Three spline wavelet; Low separation overlap peak decomposition
吴廉晖，何剑锋，周世融，汪雪元，叶志翔. 一种低原子序数元素EDXRF的多次导-样条小波解析方法研究[J]. 光谱学与光谱分析, 2021, 41(08): 2530-2535.
WU Lian-hui, HE Jian-feng, ZHOU Shi-rong, WANG Xue-yuan, YE Zhi-xiang. A Multi-Derivation-Spline Wavelet Analysis Method for Low Atomic Number Element EDXRF. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2021, 41(08): 2530-2535.
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