Standardized Cross-Validation and Its Optimization for Multi-Element LIBS Analysis
ZHONG Qi-xiu1, 2, 3, ZHAO Tian-zhuo1, 2, 3*, LI Xin1, 2, 3, LIAN Fu-qiang1, 3, XIAO Hong1, 3, NIE Shu-zhen1, 3, SUN Si-ning3, 4, FAN Zhong-wei1, 2, 3
1. Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China
2. School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China
3. National Engineering Research Center for DPSSL, Beijing 100094, China
4. Beijing GK Laser Technology Co., Ltd., Beijing 102211, China
Abstract：Cross-validation is a statistical analysis method used to verify the performance of the model, which avoids the over-fitting caused by the coincidence of the training set and the test set. The average of the Root Mean Square Error of Cross-Validation (RMSECV) is often used for cross-validation to characterize the analytical accuracy of multiple elements. However, for the case of Laser-Induced Breakdown Spectroscopy (LIBS) applied to multi-element analysis, it is found that the RMSECV of each element can be approximately expressed in a linear relationship with its concentration rang in the sample set. Since the concentration ranges of different elements in the sample set vary greatly, the difference in RMSECV between different elements is large. In the experiment, the difference between the concentration range of C and Cr in the sample set is 28.11 times, and the RMSECV difference is 8.96 times. It is found that during the optimization process, the average RMSECV may not reflect the trend of analysis accuracy of most elements, when it is too sensitive for individual elements. In order to reduce the sensitivity difference of the average RMSECV to different elements and to more fully characterize the analysis accuracy of multi-element, this paper proposes a multi-element RMSECV standardized method that divides the RMSECV of each element by the concentration range of the element in the sample set. The concept of Standardized Root Mean Square Error of Cross-Validation (SRMSECV) is therefore introduced. LIBS detection is affected by uncertain factors such as fluctuations in measurement conditions (such as laser pulse energy, vibration, etc.), which will generate abnormal spectra and have a negative impact on analysis accuracy. The median area of all spectra of the same sample is selected as the center and a spectral area interval is selected. The spectra whose area is outside the interval are discarded and the remaining spectra are used for quantitative analysis. In order to improve the multi-element analysis accuracy by filtering out the abnormal spectra, the spectral data is pre-processed by spectral area screening. On this basis, the quantitative analysis of the multi-line internal standard method for 14 elemental components in 10 Ni-based alloys in a 0.5 Pa vacuum environment was carried out. After standardization, the relative standard deviation (RSD) of RMSECV of each element decreased from 68.7% to 48.9%, and the maximum difference of RMSECV between elements decreased from 8.96 times to 3.93 times. It showed that the average SRMSECV can comprehensively characterize the analysis accuracy of multi-element, which is beneficial to the automatic optimization of calibration curve. Under the optimized area screening span, the average value of the coefficient of determination (R2) and the average SRMSECV of the 14 elements were improved to some extent, which proved the value of spectral area screening for improving the accuracy of multi-element analysis.
钟奇秀，赵天卓，李 欣，连富强，肖 红，聂树真，孙思宁，樊仲维. 多元素LIBS分析的标准化交叉验证及其优化[J]. 光谱学与光谱分析, 2020, 40(02): 622-627.
ZHONG Qi-xiu, ZHAO Tian-zhuo, LI Xin, LIAN Fu-qiang, XIAO Hong, NIE Shu-zhen, SUN Si-ning, FAN Zhong-wei. Standardized Cross-Validation and Its Optimization for Multi-Element LIBS Analysis. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2020, 40(02): 622-627.
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