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Sep.  2019
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Quantitative analysis of phosphorus in compound fertilizer by laser induced breakdown spectroscopy

  • Corresponding author: SHA Wen, ahu001@163.com
  • Received Date: 2018-12-28
    Accepted Date: 2019-03-07
  • In order to detect its components rapidly in the production of compound fertilizer and guide the production, laser-induced breakdown spectroscopy (LIBS) and support vector machine (SVM) were used to quantitatively analyze phosphorus (P) in compound fertilizer. In the experiment, 58 compound fertilizer samples were analyzed by three characteristic spectra of PⅠ 213.5nm, PⅠ 214.9nm and PⅠ 215.4nm. 58 samples were divided into training set (43 samples) and test set (15 samples) by random selection method. The grid search method was used to optimize the parameters of the quantitative analysis model of P element in compound fertilizer. The SVM analysis model was constructed. The results show that, the correlation coefficient R2 of the calibration model of training set is 0.981. It shows that the correlation between the reference value and the predicted value of the training set is high. The correlation coefficient R2 between the reference value and the predicted value of phosphorus (P) in the samples is 0.992. The mean square error is 4.95×10-5. SVM model has strong applicability. The average absolute error and relative error of the training set are 5.9×10-4 and 3.99×10-3, respectively. The average absolute error and relative error of the test set are 5.6×10-4 and 3.28×10-3, respectively. The combination of SVM algorithm and LIBS technology can realize the rapid detection of phosphorus in compound fertilizer. This study provides a reference for rapid determination of element content in compound fertilizer.
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Quantitative analysis of phosphorus in compound fertilizer by laser induced breakdown spectroscopy

    Corresponding author: SHA Wen, ahu001@163.com
  • 1. School of Electrical Engineering and Automation, Anhui University, Hefei 230061, China
  • 2. Laboratory of Advanced Sensing and Intelligent Systems, Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei 230031, China

Abstract: In order to detect its components rapidly in the production of compound fertilizer and guide the production, laser-induced breakdown spectroscopy (LIBS) and support vector machine (SVM) were used to quantitatively analyze phosphorus (P) in compound fertilizer. In the experiment, 58 compound fertilizer samples were analyzed by three characteristic spectra of PⅠ 213.5nm, PⅠ 214.9nm and PⅠ 215.4nm. 58 samples were divided into training set (43 samples) and test set (15 samples) by random selection method. The grid search method was used to optimize the parameters of the quantitative analysis model of P element in compound fertilizer. The SVM analysis model was constructed. The results show that, the correlation coefficient R2 of the calibration model of training set is 0.981. It shows that the correlation between the reference value and the predicted value of the training set is high. The correlation coefficient R2 between the reference value and the predicted value of phosphorus (P) in the samples is 0.992. The mean square error is 4.95×10-5. SVM model has strong applicability. The average absolute error and relative error of the training set are 5.9×10-4 and 3.99×10-3, respectively. The average absolute error and relative error of the test set are 5.6×10-4 and 3.28×10-3, respectively. The combination of SVM algorithm and LIBS technology can realize the rapid detection of phosphorus in compound fertilizer. This study provides a reference for rapid determination of element content in compound fertilizer.

引言
  • 在复合肥生产中如何快速检测成分,对于复合肥企业的过程控制和产品质量控制尤为重要。当前情况下对复合肥成分的检测仍以实验室检测分析为主,常用的检测方法主要有电感耦合等离子体-质谱法[1]、石墨炉原子吸收光谱法[2]、电感耦合等离子体原子发射光谱法[3]和电化学分析方法[4]等。这些检测方法需从化肥生产线上采集样品,在实验室进行复杂的预处理。同时,由于复合肥成分含量高,需进行多次稀释,导致检测结果偏差较大。因此,急需一种能对复合肥成分进行准确、快速的检测技术。

    激光诱导击穿光谱(laser induced breakdown spectroscopy,LIBS)技术最早在1962年由BRECH在第10届国际光谱学会议中提出。此技术是基于原子发射光谱学对物质组成及浓度进行分析。它利用具有高能量的脉冲激光聚焦在样品表面,产生高温高密度等离子体,原子、离子由高能级向低能级跃迁产生的特征谱线是进行LIBS分析的基础。由于该技术对样品前期处理少,检测分析速度快,近些年已被大量运用于各领域,在化肥复领域也开展了相关研究。MA,XIE等人基于改进的偏最小二乘对钢液成分和大气痕量气体浓度定量分析[5-6];YU等人使用LIBS对污泥中Pb元素含量反演研究[7];LIAO等人使用LIBS结合多元非线性定量法分析复合肥中磷(P)元素含量[8];LI等人运用LIBS特性分析了不同物理形态的复合肥[9];LU等人使用LIBS对复合肥中氮磷钾元素含量的同步测量[10]; NICOLODELLI等人采用神经网络与激光诱导击穿光谱技术分析了有机矿物和无机肥料中的主要和次要元素[11]; WANG等人采用LIBS定量分析原油中金属元素[12], 与传统检测方法相比,LIBS技术在检测过程中易受到基体效应、激光能量波动、系统参量等的影响,使得检测结果精确度不高。在检测中为了提高测量的稳定性、精确度和灵敏度,需将LIBS技术与数据处理相结合,寻求合适的定量分析模型。

    本实验中采集的复合肥数量较少,采用传统分析方法难以获得准确结果,需寻找一种适用于小样本的统计分析方法[13]。支持向量机(support vector machines, SVM)方法理论上利用间隔最大化原理进行建模训练,该方法的最大优点在于利用核函数将原本空间中难以处理的问题映射到高维空间[14],根据理论上间隔最大化在高维空间中计算最优线性超平面,以此建立相应的线性决策函数,进而在原样本空间中难以处理的问题得到解决。在相关研究中,WANG等人将LIBS技术结合SVM模型分析了水体中重金属含量[15]; LIN利用SVM法对泥蚶中重金属污染物进行快速检测[16]; CHEN等人将LIBS技术和SVM法测定了岩屑中8种元素[17]; YU等人在塑料识别应用研究中采用SVM模型进行分析[18]; ZHANG等人采用LIBS技术对钢铁中铬和镍元素采用SVM算法进行了定量分析[19]。国外研究者将SVM法成功应用于柑橘叶[20]和蛋白质[21]的LIBS检测中,识别率分别达到了97.5%和98%。

    目前国内外多采用化学方法对复合肥中元素进行检测,耗时长(大于0.5h)、误差大(实验干预较多)、成本大、不具有泛化能力,而SVM-LIBS无需制样、直接快速、样本损失量小、具有较好的泛化能力等特点已成为研究的热点。国内外关于将SVM与LIBS技术结合对复合肥进行快速检测的分析较少,而此研究对于复合肥领域具有较强的现实意义。

    本文中以复合肥中P元素为研究对象,获得复合肥的LIBS光谱,选取P元素的3条特征波长213.5nm, 214.9nm和215.4nm为分析线。采用网格搜索法进行参量寻优建立支持向量机模型并对复合肥中磷元素进行定量分析。

1.   SVM算法模型建立
  • 对处于局部热平衡且不考虑自吸收效应的激发态离子,激光击穿光谱谱线强度可表示为:

    式中, k, i分别为跃迁谱线的上下能级;F为与光收集装置效率有关,与波长无关,同次实验测量中保持不变的实验参量;Cs为特征谱线对应的原子、离子浓度;Ak, i为特征谱线的跃迁几率;gk为上能级的简并度;Us(T)为发射元素s的配分函数;Ek为跃迁能级的上能级能量,kB为玻尔兹曼常数, 当等离子体满足局部热平衡时,温度T为常数。

    将(2)式代入(1)式得:

    根据(3)式可计算出样品中待测元素的浓度。但由于受到基体效应等影响,A在实验中很难确定,当不考虑自吸收效应时, 和Ik, i的关系可表达为:

    式中, a为比例系数。结合(1)式~(4)式,并令I=Ik, i, 得:

    式中, v为支持向量集;$\partial $ i为拉格朗日乘子;klibs(Ii, I)为核函数;b为常数。

    结合(4)式和(5)式得到激光诱导击穿光谱混合核函数:

    式中, 混合核函数由两部分组成,前者为线性核函数cIIi,后者为径向核函数(radial kernel function, RBF)。支持向量机核函数常用来解决数据的非线性映射问题,大量的实验和数据表明,RBF径向核函数具有较高的拟合和预测精度,通常被选作为核函数进行研究。

    支持向量机中对参量的调整在很大程度上决定着回归效果,所选择的径向核函数为内核函数,从而在复合肥中P元素定量分析回归模型中对参量的调整主要是惩罚系数c和核参量g[22-23]。由于本研究中复合肥样本较少,所以选取网格搜索法作为寻优方式,可能获得较好的预测结果。

2.   实验测量
  • 所搭建的一整套LIBS实验检测装置如图 1所示。实验装置由激光器、计算机、光束聚焦器、旋转平台、光谱接收器,光谱仪等组成。激光器采用Nd:YAG激光器(激发波长1064nm,单脉冲能量100mJ,脉冲宽度8ns,重复频率1Hz),型号为BigSky,ICE450。激光器发出沿水平方向上的高能量激光光束经45°反射镜转折成竖直向下,光束由焦距为40mm的聚焦镜聚焦并作用在复合肥样本表面。复合肥样本表面的作用点由于高温烧蚀而产生高温等离子体,这些高能量的等离子体在冷却过程中跃迁产生的特征光谱信号,经过焦距为35mm的石英透镜耦合至光纤探头上并传送到光谱仪进行分光检测, 使用爱万提斯的四通道光纤光谱仪(型号:Avaspec-2048-USB2)收集光谱,其波长范围为195nm~550nm和700nm~900nm,分辨率为0.1nm。在实验过程中为减少样品测量的不稳定性,防止样品内部成分不均匀导致结果误差,将样品放置在可手动调节的匀速旋转的步进电机旋转台上,将每个复合肥样品旋转一周平均20个激光脉冲作为一次测量。根据特征谱线形成机理可知使用不同的线型函数可描述相同的展宽类型,在本实验中用洛伦兹线型函数对特征谱线进行拟合,将经过拟合后的峰值作为复合肥中P元素的特征谱线强度。

    Figure 1.  LIBS system diagram

    本实验中所采用的复合肥样本由安徽徽隆集团提供,复合肥中P元素质量分数已知且元素含量范围为0.149~0.167。实验中为了保证复合肥样本的均匀性,将复合肥样本研磨粉碎过60目筛子,每个样本取3g, 在压强为8MPa的作用下制成直径为30mm的圆饼状。

    如何使信背比达到最大值是确定延迟时间和激光脉冲能量的关键,当光谱仪接收到激光器的调Q信号时,开始采集等离子体信号。通过设置不同的延迟时间得到不同的等离子体光谱,设置延迟时间为光谱仪最短起点时间1.28μs,探测器门宽1.05ms(光谱仪最小采集时间), 重复频率为1Hz, 时间步长200ns, 激光脉冲能量100mJ, 每次测试增加20个激光脉冲,将P Ⅰ214.9nm特征谱线作为分析线。由图 2可知, 谱线强度和信背比在延迟时间td=1.28μs时达到最大,此时采集时间为1.05ms。

    Figure 2.  a—relationship between intensity of phosphorus line and time b—relationship between signal-to-back ratio of phosphorus lines and time

    设置延迟时间为1.28μs, 采集时间为1.05ms, 重复频率为1Hz, 激光器能量范围55mJ~180mJ,平均每20个激光脉冲作为一组实验数据对样品进行测量。图 3a图 3b分别为P Ⅰ214.9nm特征谱线强度和信背比随激光能量的变化关系。当激光脉冲能量小于110mJ时,特征谱线信背比随激光脉冲能量的增加而增大,当超过110mJ时开始趋于稳定,综合测定选择激光器参量:波长1064nm, 激光脉冲能量100mJ, 重复频率1Hz。

    Figure 3.  a—line intensity of phosphorus as a function of laser energy b—signal-to-back ratio of phosphorus spectrum as a function of laser energy

3.   实验结果与分析
  • 实验中记录了复合肥样本在波长为200nm~500nm和700nm~900nm范围内的激光等离子体发射光谱。经查美国国家标准与技术研究院谱线库,磷元素的特征谱线较多,但强度较大的特征谱线有213.5nm, 214.9nm, 215.4nm, 253.4nm, 253.6nm, 255.3nm, 255.5nm等。图 4中给出了复合肥样本在210nm~258nm波段内的光谱图。253.4nm和253.6nm两根特征谱线虽较强但易受到复合肥中铁(Fe)元素特征谱线(252.3nm)的干扰,255.3nm和255.5nm两根谱线靠的太近,不利于分析。波长213.5nm,214.9nm和215.4nm处的特征发射谱线较清晰,受到复合肥样本的基体效应干扰较小,无重叠和自吸收现象故选择具有较好灵敏度的213.5nm, 214.9nm和215.4nm的3条特征谱线对磷元素进行特征分析。

    Figure 4.  Phosphorus spectrum in compound fertilizer

  • 正确划分训练集和测试集不仅能有助于SVM算法模型准确建立且对模型是否具有泛化能力做出更加充分判断。在SVM算法参量寻优之前需对采集的复合肥样本中划分出训练样本和测试样本。复合肥中P元素质量分数要在整个样本中均匀分布且划分的训练集样本质量分数覆盖全部样本,据此划分的训练集和测试集具有较好的代表性。徽隆集团提供的58个复合肥样本P元素质量分数分布如图 5所示。

    Figure 5.  Actual mass fraction of 58 phosphorus samples

    因为本实验中样本数量较少,根据58个磷元素质量分数分布图,采用随机选择法将样本分为训练集(43个)和测试集(15个),划分结果如图 6所示。由图 6可以看出, 训练集样本和测试集样本P元素质量分数分布均匀且训练集样本覆盖整个样本空间。

    Figure 6.  Classification results of 58 phosphorus samples

  • 采用基于台湾大学LIN等人开发的libsvm3.1软件包进行二次开发的MATLAB程序,对选取的训练集和测试集数据通过网格搜索法进行回归训练和参量寻优。首先对训练集和测试集样本特征进行降维和归一化处理,使特征按同一比例系数缩放到一个比较小的范围。在本实验中,将P元素样本的特征谱线强度归一化到[-1, 1]之间。

    SVM模型效果依赖于参量的寻优选择,本实验中采用网格搜索法对惩罚系数c和核参量g进行寻优。网格搜索法是将cg根据一定步长划分为网格[21],采取逐步逼近方法筛选得到最优的cg,即先划分较大区间和较大步长大致搜索回归效果及相应的参量并评估,然后以此参量值为中心采用较小区间和较小步长再次进行搜索,反复如此最终确定最优模型和最优的参量。若在参量寻优过程中有多组参量cg对应最优效果,则选择最小的一组为最佳参量,因为过高的c会使测试集均方误差很高而训练集均方误差很小,出现过学习状态。

    采用网格搜索法对复合肥中磷元素的参量寻优和预测效果如图 7所示。图 7a为网格搜索法参量寻优3-D图; 图 7b为训练集和测试集预测结果图,其中横坐标为样本号,纵坐标为复合肥中磷元素质量分数拟合走势图。

    Figure 7.  Phosphorus search results

    图 7a可知, 磷元素的最优参量为c=128,g=0.015625,均方误差eMSE=4.95×10-5,训练集相关系数R2=0.981,测试集相关系数R2=0.992。

4.   实验结果分析
  • 在实验中引入相对误差er和绝对误差ea来衡量模型的预测结果的准确性。相对误差描叙模型预测含量值γ与实际值μ之间的一致程度,相对误差越小表明两者一致程度越高,绝对误差表示模型预测值γ与实际值μ之间具体差值,表示二者离散程度大小。公式如下:

    基于LIBS结合SVM对复合肥中P元素质量分数定量分析,采用网格搜索法寻优参量的相对误差和绝对误差。图 8表 1为样本1号~43号训练集结果,图 9表 2为样本44号~58号测试集结果。

    Figure 8.  Prediction renderings of support vector machine modelof training set

    number
    category
    actual mass
    fraction/10-2
    SVM predictive
    mass fraction/10-2
    ea/10-2 er/10-2
    1 15.400 14.782 0.618 4.013
    2 14.900 14.837 0.063 0.423
    3 15.000 14.880 0.120 0.800
    4 15.100 15.158 0.058 0.384
    5 15.200 15.310 0.110 0.724
    6 15.300 15.363 0.063 0.412
    7 15.300 15.375 0.075 0.490
    8 15.300 15.394 0.094 0.614
    9 15.300 15.404 0.104 0.680
    10 15.300 15.354 0.054 0.353
    11 15.400 15.492 0.092 0.597
    12 15.500 15.510 0.010 0.645
    13 15.500 15.527 0.027 0.174
    14 15.500 15.552 0.052 0.335
    15 15.600 15.591 0.009 0.058
    16 15.700 15.671 0.029 0.185
    17 15.700 15.680 0.020 0.127
    18 15.700 15.684 0.016 0.102
    19 15.700 15.647 0.053 0.338
    20 15.800 15.713 0.087 0.551
    21 15.800 15.730 0.070 0.443
    22 15.900 15.836 0.064 0.403
    23 15.900 15.845 0.055 0.346
    24 15.900 15.868 0.032 0.201
    25 15.900 15.892 0.008 0.447
    26 15.900 15.883 0.017 0.107
    27 16.000 16.014 0.014 0.088
    28 16.000 16.045 0.045 0.281
    29 16.000 16.017 0.017 0.106
    30 16.000 16.051 0.051 0.319
    31 16.100 16.084 0.016 0.099
    32 16.100 16.081 0.019 0.118
    33 16.100 16.114 0.014 0.087
    34 16.200 16.167 0.033 0.204
    35 16.200 16.174 0.026 0.160
    36 16.200 16.186 0.014 0.086
    37 16.300 16.310 0.010 0.061
    38 16.300 16.340 0.040 0.245
    39 16.300 16.364 0.064 0.393
    40 16.400 16.454 0.054 0.329
    41 16.500 16.558 0.058 0.352
    42 16.600 16.582 0.018 0.108
    43 16.700 16.670 0.030 0.180

    Table 1.  Prediction effect table of support vector machine model of training set

    Figure 9.  Prediction renderings of support vector machine model of test set

    number
    category
    actual mass
    fraction/10-2
    SVM predictive
    mass fraction/10-2
    ea/10-2 er/10-2
    44 15.100 15.193 0.093 0.616
    45 15.200 15.272 0.072 0.047
    46 15.300 15.386 0.086 0.562
    47 15.400 15.645 0.245 1.591
    48 15.500 15.542 0.042 0.271
    49 15.600 15.611 0.011 0.071
    50 15.700 15.678 0.022 0.140
    51 15.800 15.719 0.081 0.513
    52 15.900 15.880 0.020 0.126
    53 16.000 16.027 0.027 0.169
    54 16.100 16.104 0.004 0.025
    55 16.200 16.180 0.020 0.123
    56 16.300 16.327 0.027 0.166
    57 16.400 16.396 0.004 0.024
    58 16.500 16.524 0.024 0.145

    Table 2.  Prediction effect table of support vector machine model of test set

    图 8中的训练集效果显示,除第1组误差较大外, SVM预测质量分数和实际值具有很好的拟合性,这证明了此模型可以用来快速检测复合肥中P元素质量分数。由图 9中的测试集效果再次显示,SVM预测值和实际值之间具有较好的一致性,较好地检测出P元素质量分数。由表 1表 2经计算可得, 复合肥中P元素的支持向量机的训练集平均绝对误差5.9×10-4,最大绝对误差为6.18×10-3,平均相对误差为3.99×10-3,最大相对误差为4×10-2;测试集平均绝对误差5.6×10-4,最大绝对误差为2.45×10-3,平均相对误差为3.28×10-3,最大相对误差为1.59×10-2

5.   结论
  • 对徽隆集团提供的58个复合肥样品采用LIBS技术进行测量,从光谱图中选取强度较大的3条谱线PⅠ213.5nm,PⅠ214.9nm和PⅠ215.4nm进行分析。采用随机选取法选取43个样本建立训练集模型,剩下15个样本为测试集。复合肥中P元素含量采用网格搜索法对参量进行寻优并建模,训练集相关系数为0.981,测试集相关系数为0.992,训练集平均绝对误差和平均相对误差分别为5.9×10-4, 3.99×10-3,测试集平均绝对误差和平均相对误差分别为5.6×10-4, 3.28×10-3,均方误差eMSE=4.95×10-5。训练集和测试集的平均绝对误差和平均相对误差都在可接受范围内,且与传统测量方法相比误差更小、预测效果更好,这说明支持向量机具有良好的回归效果。实验结果表明:复合肥中磷元素的支持向量机定量分析整体效果较优,学习和泛化能力良好,可用于复合肥中磷元素含量的快速检测。

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