Laser-induced Breakdown Spectroscopy Based on Pre-classification Strategy for Quantitative Analysis of Rock Samples
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摘要:
岩石样品中复杂的基质效应严重影响激光诱导击穿光谱（LIBS）定量分析的准确性，其原因是目标元素的发射特性会受到基质的影响，导致其发射强度偏离理想的规律。为提高定量分析准确性，本文提出一种基于岩性基质特性的预分类定量分析方法。该方法首先构建基于k近邻（kNN）与支持向量机（SVM）算法的多层分类模型识别样品的岩性进行分类，通过kNN算法将样品分成碳酸盐和硅酸盐两大类，再利用SVM算法将大类细分成6类，而后针对不同岩性样品分别构建元素定量模型。通过采用预分类方法，可以确保分析的样品具有相似的化学成分，更好地确定分析时的基准线和校准曲线，从而减少分析中的不确定度，提高定量准确性。kNN算法通过交叉验证选取最优的k值，同时使用网格寻优方法确定了SVM算法中关键惩罚参数C和RBF宽度参数γ，利用该分类模型对来自6类岩性的39个国标岩石样品和国标岩石混合样品中的Si、Ca、Mg和K元素进行分析，岩性识别的准确率达100%，保证了后续定量分析的准确性，并针对不同岩性中的不同元素采用了合适的预处理方式提升光谱数据的稳定性。相比于传统标准曲线定量方法，采用预分类方法可以减少不同岩性基质之间的相互影响，从而减小样品基质非均匀性带来的误差。对比两种方法进行数据分析，测试集样品的预测值与参考值相关性分析系数从0.231～0.664提高至0.994～0.999，平均相对标准偏差从38.2%降低至8.6%。与传统定量分析方法相比较，采用预分类定量分析方法所构建模型对上述4种元素定量分析结果准确性有着明显的提高，为提高岩石元素定量分析准确性提供新的思路，拓宽了LIBS技术的实际应用范围。
Abstract:BACKGROUND LIBS technology is a non-destructive, high sensitivity, high resolution spectroscopy technology that can be used to analyze the composition and structure of chemical substances and materials. It has extensive application in fields such as chemistry, materials science, life science, and geological exploration, and its emergence has provided new methods and technologies for the development of these fields. LIBS technology can be used to non-destructively analyze the chemical composition of underground rocks and minerals, helping geologists to better understand the composition and properties of underground resources, thus providing better guidance for geological exploration and development. In recent years, scholars at home and abroad have been exploring LIBS technology constantly, and through improving the detection system and optimizing laser pulse parameters, high sensitivity LIBS analysis at extremely low concentration has been achieved. By using finer spectral lines, higher sampling rate, and more precise laser pulse control, high resolution LIBS analysis at nanoscale has been achieved. The combination of LIBS technology with multi-spectral image processing technology can integrate information from multiple spectral channels to achieve a more comprehensive analysis of samples. However, the existence of matrix effects and spectral fluctuations always affects the accuracy of LIBS quantitative analysis, and poor reproducibility and high detection limits also need to be solved.
OBJECTIVES To improve the accuracy of quantitative analysis of complex matrix samples.
METHODS A multi-layer classification model based on k-nearest neighbors (kNN) and support vector machine (SVM) algorithms was constructed to identify the rock type of samples. The samples were divided into two major categories of felsic rocks and mafic rocks using the kNN algorithm, and then six categories were formed by the SVM algorithm. Different element quantitative models were constructed for each rock type. The kNN algorithm was selected using cross-validation to determine the optimal k value, and the key punishment parameter C and RBF width parameter γ of the SVM algorithm were determined using a grid search method. Then, appropriate pre-processing methods were adopted to improve the stability of spectral data for different elements in different rock types. Compared to the traditional standard curve quantitative method, using the pre-classification method can reduce the influence of different rock matrices on each other, thus reducing errors caused by the non-uniform matrix of samples.
RESULTS Due to the influence of matrix effects, a single pre-processing method is not suitable for all elements in quantitative analysis. Therefore, in order to improve the accuracy and stability of quantitative analysis, different methods are used to pre-process the data. For different pre-processing methods, the R2 values of four elements in six types of rock samples are mostly greater than 0.90, as shown in Table 2. After pre-processing, the correlation coefficients of the four elements are significantly improved, and they are all higher than 0.99. The correlation coefficients of Si, Ca, Mg, and K elements in the test set after quantitative analysis are increased from 0.664, 0.638, 0.461, and 0.231 to 0.999, 0.994, 0.999, and 0.996, respectively. In addition, it can be seen from the analysis of the data that the traditional quantitative analysis model has poor stability. The average relative standard deviation (RSD) of Si, Ca, Mg, and K elements in the test set are 3.4%, 10.7%, 48.2%, and 90.8%, respectively, while the RSD of four elements in the multi-layer model are 1.5%, 5.2%, 10.3%, and 17.4%, which shows a significant improvement in stability compared to traditional quantitative analysis models. At the same time, it can be more intuitively evaluated by comparing the average relative error between the predicted value and the target value of each element in the test set. As shown in Table 3, the prediction performance of Si element in the multi-layer model is the best, with an average relative error of only 4.65%. Although the average relative error of the other three elements is over 10%, it is significantly improved compared to the traditional standard curve model.
CONCLUSIONS By utilizing a multi-layer classification model for preliminary categorization, standard rock samples that match the matrix are obtained. Subsequently, quantitative analysis models are developed for samples with similar matrices. Employing distinct preprocessing methods for different elemental compositions within various rock types helps mitigate spectral discrepancies caused by matrix effects, reduces spectral fluctuations and data noise, and enhances the accuracy and stability of quantitative analysis. Standard curve models are then established for each element, enabling quantitative analysis of Si, Ca, Mg, and K elements in six categories of rock samples. Results demonstrate a notable improvement in the accuracy of quantitative analysis compared to traditional standard curve models. This model not only diminishes the impact of matrix effects on quantitative analysis but also corrects instabilities arising from hardware, environmental conditions, and sample variations. Furthermore, it alleviates the workload of data analysis, simplifying the analytical process and thereby boosting efficiency. However, the current multi-layer quantitative analysis model still exhibits some deviations in regard to different elements. In the future, a potential avenue is to consider integrating various algorithms to establish preliminary classification models, aiming for even better quantitative analysis outcomes.
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表 1 39个国标岩石样品和国标混合岩石样品的种类及Si、Ca、Mg、K元素含量
Table 1. Types and elemental contents of Si，Ca，Mg and K for 39 national standard rock samples and national standard mixed rock samples.
企业编号 国标GBW编号 岩石类型 Si 元素含量（% ） Ca元素含量（% ） Mg元素含量（% ） K元素含量（% ） ALB1 GBW03101a 泥页岩 23.32 0.09 0.28 0.66 ALB2* GBWE070146 泥页岩 21.13 6.99 1.04 3.57 ALB3 GBW07109 火成岩 25.42 0.99 0.39 6.21 ALB4 GBW07110 火成岩 29.43 1.76 0.50 4.29 ALB5* GBW07111 火成岩 27.85 3.37 1.69 2.90 ALB6* GBW07121 火成岩 30.93 1.90 0.98 2.16 ALB7 GBW070157 白云岩 3.93 20.52 11.86 0.03 ALB8* GBW070158 白云岩 0.87 21.59 12.51 0.01 ALB9 GBW070159 白云岩 1.01 21.54 12.55 0.02 ALB10* GBW070160 白云岩 2.44 21.07 12.26 0.03 ALB11 GBW07114 白云岩 0.29 21.44 13.08 0.03 ALB12* GBW07136 白云岩 3.85 23.62 10.80 0.01 ALB13 GBW03107a 石灰岩 1.89 35.78 1.07 0.35 ALB14* GBW03108a 石灰岩 1.05 33.62 3.49 0.17 ALB15* GBW07108 石灰岩 7.28 25.48 3.11 0.65 ALB16 GBW07120 石灰岩 3.10 36.50 0.43 0.12 ALB17 GBW07127 石灰岩 0.26 34.21 4.06 0.04 ALB18* GBW07128 石灰岩 0.34 29.96 6.97 0.04 ALB19 GBW07130 石灰岩 0.50 38.63 0.85 0.04 ALB20 GBWE070149 石灰岩 1.41 36.15 1.73 0.14 ALB21* GBWE070150 石灰岩 2.15 32.92 3.59 0.03 ALB22* GBWE070151 石灰岩 1.55 36.59 1.46 0.08 ALB23 GBWE070152 石灰岩 0.62 38.42 0.70 0.05 ALB24* GBWE070153 石灰岩 1.86 34.69 2.59 0.15 ALB25* GBWE070154 石灰岩 1.10 37.11 0.74 0.14 ALB26 GBWE070155 石灰岩 0.45 38.71 0.49 0.07 ALB27* GBW03109 石膏岩 0.78 28.03 1.04 0.08 ALB28* GBW03109+GBW03111a （1+1） 石膏岩 0.54 25.55 1.26 0.05 ALB29* GBW03109+GBW03111a （2+1） 石膏岩 0.62 26.38 1.19 0.06 ALB30 GBW03109+GBW03111a （3+1） 石膏岩 0.66 26.79 1.15 0.06 ALB31 GBW03111a 石膏岩 0.29 23.07 1.48 0.02 ALB32* GBW03113 砂岩 44.68 0.12 0.06 0.56 ALB33 GBW03113+GBW03104 （4+1） 砂岩 42.24 0.13 0.13 1.07 ALB34 GBW03113+GBW03104 （9+1） 砂岩 43.46 0.13 0.09 0.81 ALB35 GBW03113+GBW03111a （4+1） 砂岩 35.80 4.71 0.34 0.45 ALB36 GBW03113+GBW03111a （9+1） 砂岩 40.24 2.42 0.20 0.50 ALB37 GBW03113+GBW070156 （4+1） 砂岩 35.82 7.78 0.23 0.45 ALB38 GBW03113+GBW07108 （4+1） 砂岩 37.20 5.19 0.67 0.57 ALB39* GBW03114 砂岩 41.81 0.24 0.10 1.72 注：“*”代表测试集样品。国标混合样品编号后“（）”中的数字代表混合比例。 
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表 2 六种不同岩性岩石中不同元素的预处理方式结果对比
Table 2. Comparison of results of pretreatment methods for different elements in six different lithologies of rocks.
岩石岩性 Si （I） 250.69nm Ca （I） 585.745nm Mg （I） 516.732nm K （I） 766.489nm 数据预处理
方式$ {R}^{2} $ 数据预处理
方式$ {R}^{2} $ 数据预
处理方式$ {R}^{2} $ 数据预处理
方式$ {R}^{2} $ 白云岩 分通道归一化 0.998 无数据预处理 0.929 全谱归一化 0.999 全谱归一化 0.970 火成岩 分通道归一化 0.985 无数据预处理 0.658 无数据预处理 0.813 无数据预处理 0.860 泥页岩 分通道归一化 0.778 全谱归一化 0.962 分通道归一化 0.998 MinMax归一化 0.778 石膏岩 无数据预处理 0.981 MinMax归一化 0.780 分通道归一化 0.998 无数据预处理 0.981 石灰岩 全谱归一化 0.977 无数据预处理 0.929 全谱归一化 0.984 全谱归一化 0.985 砂岩 全谱归一化 0.977 全谱归一化 0.750 全谱归一化 0.925 全谱归一化 0.934
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表 3 传统标准曲线模型和多层模型两种方法在测试集上的定量分析结果的平均相对误差对比
Table 3. Comparison of the mean value of relative errors of the quantitative analysis results on the test set between the two methods of traditional standard curve model and multi-layer model.
元素 传统标准曲线模型
（%）多层模型
（%）Si 367.41 4.65 Ca 212.66 12.40 Mg 66.60 19.90 K 953.85 26.95
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