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实验中用来激发等离子体和接收等离子体光谱的仪器为美国TSI公司的ChemReveal台式激光诱导击穿光谱仪。此仪器采用一体化设计,集成激光器、光谱仪和样品仓于一体。一体机的激光器为Nd: YAG激光器,波长为1064nm,脉冲宽度为5ns~10ns;Echelle中阶梯ICCD高分辨率光谱仪,分辨率小于0.01nm,延迟时间为0ms~10ms,调整分辨率100ns。LIBS系统简图如图 1所示。
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实验中所用煤样品为泉东标准物质研究所提供的煤质分析国家标准物质,将9个标样用20MPa液压机压制成直径为30mm、厚度为3mm的圆饼,这9个煤样品的主要工业指标和元素组成如表 1所示。
Table 1. Mass fraction of C, H and S in 9 kinds of coal national standard samples
sample C H S GBW(E)110026 0.6498 0.0432 0.0404 GBW(E)110028 0.7565 0.0403 0.0028 GBW(E)110030 0.7518 0.049 0.0182 GBW(E)110031 0.8132 0.0351 0.0281 GBW(E)110032 0.6015 0.0389 0.0219 GBW(E)110033 0.5708 0.0388 0.0167 GBW(E)110034 0.7355 0.048 0.0143 GBW(E)110035 0.7709 0.0415 0.005 GBW(E)110038 0.6475 0.0204 0.0177 -
实验中,为了避免样品污染,首先对压成的饼状煤样品表面用激光进行表面清洗,为了减少LIBS系统实验参量的影响,在每个煤样品表面取9个点,每个点重复激发11次,即每个煤样品获取99个光谱数据,最后取光谱数据的平均值作为每个样品的光谱数据。同时,为了得到高信噪比的特征谱峰,对实验参量进行优化,主要实验参量如下:脉冲激光能量为80mJ,脉冲频率为10Hz,光谱采集延迟时间为5μs,激光光斑直径为100μm。样品在空气环境下激发,用激光激发煤样品得到谱线信息后,用光谱仪采集光谱信号,得到188.885nm~980.391nm波长范围激光诱导击穿光谱。
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实验中所用9个煤样品, 基质组成相似,188.885nm~980.391nm范围内光谱特征谱线位置大致相同。图 3a为GBW(E)110026的LIBS光谱。
由图可知,光谱在350nm~980.391nm波长范围内谱线十分拥挤,且有变化复杂的背景信号;由于光谱范围较大,且部分波段谱线密集,为了降低运算量,选取188.885nm~308.008nm波长范围LIBS光谱如图 3b所示,对比美国NIST原子光谱数据库,该波段包含常用的C、S谱线,还识别出N, Fe, Mn, Al等元素的特征谱线,且谱线信号质量较好,因此选择该波段分析;由美国NIST原子光谱数据库可知,H元素较为常用的分析谱线为H Ⅰ 656.279nm,为了分析H元素,增加655nm~660nm波长范围的光谱信号用于分析。为了减少背景噪声和实验参量的影响,首先用迭代形态学不对称重加权最小二乘法[37]对光谱数据进行基线校正处理,基线校正后的光谱图如图 4所示。以表 1中前6个样品的光谱数据用于训练PLS模型,后3个样品用于模型预测以验证模型的性能。
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为了验证PLSR模型的预测精度,用以下几个指标来判断模型的预测能力。
(1) 决定系数R2:
$ R^{2}=1-\left(S_{\mathrm{SSR}} / S_{\mathrm{SSD}}\right) $
(1) 式中,SSSR为残差平方和(sum of squares of residuals, SSR),SSSD为总偏差平方和(sum of squares of total deviation, SSD)。
$ {S_{{\rm{SSR}}}} = \sum\limits_{i = 1}^n {{{\left( {{y_i} - {{\hat y}_i}} \right)}^2}} $
(2) $ {S_{{\rm{SSD}}}} = \sum\limits_{i = 1}^n {{{\left( {{y_i} - \bar y} \right)}^2}} $
(3) 式中,n为样本个数,yi是观测值,${{\hat y}_i} $为预测值,${\bar y} $为观测值的均值。
R2越接近于1,表示光谱信号与元素含量之间相关度越好,回归效果越显著;R2>0.7,表示数据得到可信的表示;R2>0.9,说明拟合效果很好。
(2) 校正均方根误差(root mean square error of ca-libration, RMSEC):
$ {E_{{\rm{RMSEC }}}} = {\left[ {\sum\limits_{i = 1}^{{n_{\rm{c}}}} {\frac{{{{\left( {{y_i} - {{\hat y}_i}} \right)}^2}}}{{{n_{\rm{c}}} - 1}}} } \right]^{1/2}} $
(4) 式中,nc为建模样本数。
(3) 预测均方根误差(root mean square error of prediction, RMSEP):
$ {E_{{\rm{RMSEP }}}} = {\left[ {\sum\limits_{i = 1}^{{n_{\rm{p}}}} {\frac{{{{\left( {{y_i} - {{\hat y}_i}} \right)}^2}}}{{{n_{\rm{p}}} - 1}}} } \right]^{1/2}} $
(5) 式中,np为预测样本数。
(4) 平均相对误差(average relative error, ARE):
$ {E_{{\rm{ARE}}}} = \frac{1}{n}\sum\limits_{i = 1}^n {\frac{{\left| {{y_i} - {{\hat y}_i}} \right|}}{{{y_i}}}} $
(6) -
PLSR建模过程如第2节中所述,将表 1中前6个样品基线校正后的188.885nm~308.008nm和655nm~ 660nm波长范围谱线强度值构成的光谱矩阵X和元素质量分数矩阵Y作为模型的输入量,建立这几种元素的定标模型, 并将表 1中后3种样品用于含量预测。模型的预测质量分数与观测质量分数的PLSR校正模型如图 5所示。由图可知,C, H, S 3种元素校正模型的决定系数R2分别为0.9917,0.9908, 0.9916,校正均方根误差ERMSEC分别为0.8294, 0.0416, 0.1049,平均相对误差EARE分别为1.0037%, 0.8609%, 6.6930%。数据表明, 定标样本的真实质量分数与LIBS预测质量分数具有良好的拟合关系,建立的模型质量较好。
Figure 5. PLSR calibration model for the actual and predicted element concentration of samples with different R2, ERMSEC, EARE
为了判断模型的可靠性,用模型进行后3种样品元素含量预测,预测模型及结果如图 6所示。C, H, S决定系数R2分别为0.9421, 0.9894, 0.9840,预测均方根误差ERMSEP分别为2.2772, 0.2356, 0.1678,平均相对误差EARE分别为2.6348%, 7.1185%, 8.8600%。
Figure 6. PLSR prediction model for the actual and predicted element concentrations of samples with different R2, ERMSEP, EARE
结果表明,模型的预测值与真实值平均相对误差在9%以内,模型具有可信的预测精度。
激光诱导击穿光谱用于煤中多元素同步检测
Simultaneous detection of multi-elements in coal based on laser-induced breakdown spectroscopy
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摘要: 为了实现煤中碳、氢、硫3种非金属元素的快速同步定量检测, 采用激光诱导击穿光谱技术, 以波长1064nm的Nd:YAG固体激光器作为激发源, 在空气环境下烧蚀9种煤国家标准样品, 选取188.885nm~308.008nm和655nm~660nm波长范围光谱, 结合偏最小二乘回归, 同步检测煤中C, H, S 3种非金属元素, 取得了偏最小二乘回归的校正模型和预测模型数据, 并进行了理论分析和实验验证。结果表明, C, H, S元素的预测质量分数与真实质量分数的决定系数为0.9421, 0.9894, 0.9840, 预测均方根误差分别为2.2772, 0.2356, 0.1678, 平均相对误差分别为2.6348%, 7.1185%, 8.8600%。该研究证明了激光诱导击穿光谱技术结合偏最小二乘回归定量可用于煤中非金属元素的多元素检测。
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关键词:
- 光谱学 /
- 多元素同步检测 /
- 激光诱导击穿光谱技术 /
- 偏最小二乘回归 /
- 煤中非金属
Abstract: In order to achieve rapid and simultaneous quantitative detection of C, H, S in coal, laser-induced breakdown spectroscopy(LIBS) was used. A Nd:YAG solid-state laser with wavelength of 1064nm was used as excitation source. Nine kinds of national standard coal samples were ablated in air environment. Combined with partial least squares regression, the spectrum with wavelength ranges of 188.885nm~308.008nm and 655nm~660nm were selected to detect C, H and S non-metallic elements in coal simultaneously. The correction model and prediction model data of partial least squares regression were obtained. The theoretical analysis and experimental verification were carried out. The results show that, determination coefficients R2 of the predicted and real concentrations of C, H and S are 0.9421, 0.9894 and 0.9840. Root mean square error of calibration is 2.2772, 0.2356 and 0.1678. Average relative error is 2.6348%, 7.1185% and 8.8600%. LIBS combined with partial least squares regression can be used to quantitatively detect non-metallic elements in coal. -
Table 1. Mass fraction of C, H and S in 9 kinds of coal national standard samples
sample C H S GBW(E)110026 0.6498 0.0432 0.0404 GBW(E)110028 0.7565 0.0403 0.0028 GBW(E)110030 0.7518 0.049 0.0182 GBW(E)110031 0.8132 0.0351 0.0281 GBW(E)110032 0.6015 0.0389 0.0219 GBW(E)110033 0.5708 0.0388 0.0167 GBW(E)110034 0.7355 0.048 0.0143 GBW(E)110035 0.7709 0.0415 0.005 GBW(E)110038 0.6475 0.0204 0.0177 -
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