多元素LIBS分析的标准化交叉验证及其优化

Standardized Cross-Validation and Its Optimization for Multi-Element LIBS Analysis

交叉验证是用于验证模型性能的一种统计分析方法,可避免由训练集与测试集重合引起的过拟合。进行交叉验证时通常使用交叉验证均方根误差(RMSECV)的均值来表征多元素的分析准确度。但对于激光诱导击穿光谱(LIBS)用于多元素分析的情况,发现各元素的RMSECV与其在样品中的浓度范围可近似用线性关系表述,由于不同元素在样品集中的浓度范围差异很大,不同元素之间的RMSECV差异较大,实验中C与Cr在样品集中的浓度范围差异为28.11倍,其RMSECV差异达到8.96倍。发现RMSECV均值对于个别元素过于灵敏,在数据优化过程中,可能导致其不能反映大多数元素的分析准确度变化趋势。为减小RMSECV均值对不同元素的灵敏度差异,更全面地表征多元素的分析准确度,提出了多元素的RMSECV标准化方法,即将各元素的RMSECV与该元素在样品集中的浓度范围相除,并引入标准化交叉验证均方根误差(SRMSECV)的概念。LIBS检测受测量条件波动(如激光脉冲能量、振动等)等不确定因素的影响,会引入异常光谱,并对分析准确度产生负面影响。为通过滤除异常光谱来提高多元素分析准确度,利用光谱面积筛选对光谱数据进行预处理,以同一样品下各张光谱的面积中位数为中心,选定某一光谱面积区间,舍弃该区间之外的光谱,并使用余下光谱用作定量分析。在此基础上,通过对0.5 Pa真空环境下的10块Ni基合金中的14种元素成分进行的多谱线内标法定量分析展开实验验证。标准化后各元素RMSECV的相对标准差(RSD)由68.7%减小至48.9%,元素间的RMSECV的最大差异由8.96倍降低至3.93倍,表明SRMSECV均值能够较全面表征多元素的分析准确度,从而有利于实现定标曲线的全自动优化。在优化面积筛选跨度下,各元素定标模型的决定系数(R2)均值与SRMSECV均值都得到一定程度的改善,证明光谱面积筛选对于提高多元素分析准确度的价值。

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(R 2)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.