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白酒年份酒是指有着一定贮存时间的白酒，白酒年份酒因其相对于其它白酒更加醇厚的口感而得到广大消费者的青睐，但同时由于白酒年份酒行业标准的不完善，使得市场上年份酒质量参差不齐。因此，亟需运用新兴技术对白酒年份酒中的物质进行检测。
白酒是一种成分比较复杂的混合物[1]，其中水和乙醇为主要物质，体积分数约为0.98，另有上千种微量物质的体积分数约为0.02，但正是这0.02的微量物质对白酒的品质有着较大的影响[2-3]。乙酸对于浓香型白酒香型的形成的贡献很大，它在一定程度上影响浓香型白酒的质量与风格[4]。它具有窖泥臭气，醇、甜，并带有底窖香味。随着白酒的贮存，白酒里也同时发生着水解、氧化、酯化等反应[5]，有些白酒中单体物质的体积分数随着白酒年份有着一定的变化，所以检测白酒年份酒中单体体积分数可以有助于白酒的质量鉴定以及白酒年份的鉴别[6-7]。
目前，常见的检测白酒年份酒中物质体积分数的技术有很多，主要包括气相色谱法[8]、超高效液相色谱法[9]、顶空固相微萃取法和气相色谱-质谱联用法[10]、固相萃取-高效液相色谱[11]等，上述几种方法在测量之前需对待测样本进行预处理，而且过程较为复杂繁琐。荧光分析法是一种新型的灵敏度较高的检测手段，其具有检测速度快、检测成本低廉、需要样品少、对样品损伤小等优势，使得3维荧光光谱在食品技术检测方面有着广泛的应用[12-16]。作者已经应用3维荧光光谱研究白酒中的主要微量物质对白酒光谱的影响，但是尚未进一步在白酒荧光光谱上进一步细化研究，比如应用荧光分析法来检测白酒中单体物质的体积分数。
本文中通过将白酒年份酒的3维荧光光谱结合三线性交替拟合残差算法来直接检测白酒年份酒中乙酸的体积分数，实现快速准确定量白酒中单体物质的目的。
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在荧光分析时，扫描k个样品的3维荧光光谱可构成一个大小为I×J×K的3维荧光矩阵，三线性模型如下[17]：
$ \mathit{\boldsymbol{X}} = \sum\limits_{n = 1}^N {{\mathit{\boldsymbol{a}}_k} \otimes {\mathit{\boldsymbol{b}}_k} \otimes {\mathit{\boldsymbol{c}}_k} + \mathit{\boldsymbol{E}}} $
(1) 式中, N代表组分数，即有荧光贡献的成分数；⊗为张量积；ak代表组分k的激发光谱矩阵；bk代表组分k的发射光谱矩阵；ck代表组分k的体积分数矩阵；E代表测量误差的大小为I×J×K的3维残差矩阵。
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交替拟合残差算法(alternating fitting residue algorithm, AFR)基于三线性模型的循环对称性来获得新的残差，并在此基础上得到3个目标函数[18]：
$ \begin{array}{c} S(\mathit{\boldsymbol{C}}) = \sum\limits_{i = 1}^I {\left\| {\mathit{\boldsymbol{B}}{^ + }{\mathit{\boldsymbol{X}}_{i \ldots }} - {\mathit{\boldsymbol{B}}^ + }\;\mathit{\boldsymbol{B}}{\rm{diag}}\left( {{\mathit{\boldsymbol{a}}_i}} \right){\mathit{\boldsymbol{C}}^{\rm{T}}}} \right\|_F^2 + } \\ p\sum\limits_{j = 1}^J {\left\| {{\mathit{\boldsymbol{X}}_{ \ldots j \ldots }}{{({\mathit{\boldsymbol{A}}^{\rm{T}}})}^ + } - {\rm{ }}\mathit{\boldsymbol{C}}{\rm{diag}}({\mathit{\boldsymbol{b}}_j}){\mathit{\boldsymbol{A}}^{\rm{T}}}{{({\mathit{\boldsymbol{A}}^{\rm{T}}})}^ + }} \right\|_F^2} \end{array} $
(2) $ \begin{array}{c} S\left( \mathit{\boldsymbol{A}} \right) = \sum\limits_{j = 1}^J {\left\| {{\rm{ }}\mathit{\boldsymbol{C}}{^ + }\mathit{\boldsymbol{X}}{_{ \ldots j \ldots }} - \mathit{\boldsymbol{C}}{^ + }\;\mathit{\boldsymbol{C}}{\rm{diag}}({\mathit{\boldsymbol{b}}_j}){\mathit{\boldsymbol{A}}^{\rm{T}}}} \right\|_F^2 + } \\ q\sum\limits_{k = 1}^K {\left\| {{\mathit{\boldsymbol{X}}_{ \ldots k}}{{({\mathit{\boldsymbol{B}}^{\rm{T}}})}^ + }{\rm{ }} - \mathit{\boldsymbol{A}}{\rm{diag}}({\mathit{\boldsymbol{c}}_k}){\mathit{\boldsymbol{B}}^{\rm{T}}}{{({\mathit{\boldsymbol{B}}^{\rm{T}}})}^ + }} \right\|_F^2} \end{array} $
(3) $ \begin{array}{c} S\left( \mathit{\boldsymbol{B}} \right) = \sum\limits_{k = 1}^K {\left\| {{\mathit{\boldsymbol{A}}^ + }\;{\mathit{\boldsymbol{X}}_{ \ldots k}} - {\mathit{\boldsymbol{A}}^ + }\;\mathit{\boldsymbol{A}}{\rm{diag}}({\mathit{\boldsymbol{c}}_k}){\mathit{\boldsymbol{B}}^{\rm{T}}}} \right\|_F^2 + } \\ r\sum\limits_{i = 1}^I {\left\| {{\mathit{\boldsymbol{X}}_{i \ldots }}{{({\mathit{\boldsymbol{C}}^{\rm{T}}})}^ + } - \mathit{\boldsymbol{B}}{\rm{diag}}({\mathit{\boldsymbol{a}}_i}){\mathit{\boldsymbol{C}}^{\rm{T}}}{{({\mathit{\boldsymbol{C}}^{\rm{T}}})}^ + }} \right\|_F^2} \end{array} $
(4) 式中, p, q, r为拟合因子，一般情况下选p=q=r=1;上标T表示转置，+表示共轭转置，F表示矩阵范数; A, B, C为因子载荷矩阵。再使用交替最小化上述目标函数来进行分解，即据(1)式通过初始值A, B求C；同理通过B, C求A；通过A, C求B，最终使得残差矩阵可以收敛。
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实验仪器：英国Edinburgh FLS920P型稳态和时间分辨荧光光谱仪、移液器、酒精计。
实验样品：某酒厂提供的某浓香型年份白酒样品，分别为1999年、2004年、2009年、2011年、2012年生产。乙酸由国家标准物质研究中心提供的分析纯，乙醇为SIGEMA公司购买的分析纯，水为超纯水。
参量设置：激发波长的测量范围为460nm~500nm，步长2nm。发射波长的测量范围为514nm~550nm，步长为2nm，激发和发射狭缝宽度分别设置为5nm，积分时间设置为0.1s。
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使用酒精计测得白酒年份酒样品酒精度为68°，使用乙酸和体积分数为0.68的乙醇水溶液配制成乙酸乙醇水溶液，乙酸的体积分数范围为0.0000~0.005，体积分数间隔为0.0005，共计11个样本作为校正集，编号为1~11，如表 1所示。扫描其3维荧光光谱，使用AFR算法结合留一交互验证法预测乙酸体积分数来检验算法的有效性与校正集的可靠性。
Table 1. The concentration of calibration
calibration sample volume fraction of acetic acid 1 0.0050 2 0.0045 3 0.0040 4 0.0035 5 0.0030 6 0.0025 7 0.0020 8 0.0015 9 0.0010 10 0.0005 11 0.0000 将5个年份的酒样作为预测集，不做任何预处理, 按照年份由高到低编号为1~5。使用FLS920P荧光光谱仪测定上述样本的3维荧光光谱并使用AFR算法预测其乙酸的体积分数。
最后使用标准添加法来验证预测结果的准确性。
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使用AFR算法分解得到乙酸在乙醇水溶液中的激发光谱与发射光谱，如图 1所示。对校正集进行留一交互验证的结果如表 2所示。表中，RMSEP为预测均方根误差(root mean square erroor of prediction)。
Figure 1. The spectra of acetic acid in ethanol aqueous solution obtained by AFR algorithm and experiment
Table 2. Analysis of calibration set by using AFR algorithm and leave-one-out cross-validation method
samplenumber the realvolume fraction the predicted volume fraction recoverypercentage/% 1 0.00500 0.00496 99.20 2 0.00450 0.00467 103.78 3 0.00400 0.00405 101.25 4 0.00350 0.00334 95.43 5 0.00300 0.00278 92.67 6 0.00250 0.00254 101.60 7 0.00200 0.00212 106.00 8 0.00150 0.00155 103.33 9 0.00100 0.00099 99.00 10 0.00050 0.00059 118.00 11 0.00000 -0.00009 — RMSEP 0.00162 average recovery percentage 102.03% correlation coefficient 0.9974 可以看出, 通过AFR算法分解出的乙酸在乙醇水溶液中的荧光激发与发射光谱与实验得到的乙酸在乙醇水溶液中的荧光光谱基本吻合，如图 1所示；同时使用AFR算法对校正集样本进行留一交互验证，预测体积分数与真实体积分数的相关系数为0.9974，预测均方根误差值为0.00162，平均回收率为102.03%，说明AFR算法可以有效地预测乙醇水溶液中乙酸的体积分数，并且配制的校正集是可靠且稳定的。
从上述结果可以看出，使用3维荧光光谱结合AFR算法可以对乙醇水溶液中乙酸的体积分数得到较好的预测结果，也对下一步预测白酒年份酒中乙酸的体积分数提供了技术帮助。
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测定5个不同年份的白酒的3维荧光光谱，样品编号为1~5，将它们做为预测集，11个不同体积分数的乙酸乙醇水溶液作为校正集，再使用AFR算法进行解析，解析出的荧光激发与发射光谱如图 2所示。预测的白酒年份酒中己酸体积分数如表 3所示。
Figure 2. The spectra of acetic acid in Chinese aged liquor obtained by AFR algorithm and in ethanol aqueous solution obtained by experiment
Table 3. The predicted concentration of acetic acid in Chinese aged liquor by using AFR
sample number the predicted volume fraction 1 0.00089 2 0.00119 3 0.00186 4 0.00276 5 0.00383 由图 2可以看出，AFR算法分解出的白酒中乙酸的荧光激发与发射光谱与实验得到的乙酸在乙醇水溶液中的激发与发射光谱基本吻合，AFR算法预测白酒中乙酸的体积分数是可靠的，由表 3中得到预测的体积分数从编号1~5分别为0.00089，0.00119，0.00186，0.00276，0.00383。
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以2009年的样品白酒为例，向其中添加不同体积分数的乙酸，使用FLS920光谱仪测量其3维荧光光谱，将其作为预测集并结合AFR算法进行光谱分解，预测体积分数及回收率见表 4。
Table 4. Analysis of the predicted set by using AFR
sample number the real volume fraction the predictedvolume fraction recovery percentage/% Ⅰ 0.00165 0.00155 93.94 Ⅱ 0.00184 0.00182 98.91 Ⅲ 0.00205 0.00217 105.85 Ⅳ 0.00246 0.00252 102.44 Ⅴ 0.00264 0.00287 108.71 RMSEP 0.00045 average recovery percentage 101.97% correlation coefficient 0.9926 根据表 3得知, 2009年白酒样品中乙酸体积分数为0.00119。向Ⅰ~Ⅴ号样品分别加入不同体积分数的乙酸, 使酒中乙酸体积分数变为0.00165，0.00184，0.00205，0.00246，0.00264，将1~5号样品作为预测集，使用AFR算法进行解析，得到预测体积分数为0.00155，0.00182，0.00217，0.00252，0.00287，得到预测体积分数与真实体积分数的相关系数为0.9926，平均回收率为101.97%，RMSEP为0.00045。同时对其它4个年份酒样本进行标准添加法并使用AFR算法预测体积分数，得到1号、3号、4号、5号年份酒样本的平均回收率分别为103.82%, 103.72%, 102.59%, 102.08%，预测体积分数与真实体积分数的相关系数分别为0.9891, 0.9971, 0.9964, 0.9978。以上结果表明：使用AFR算法预测的白酒年份酒中乙酸体积分数是准确有效的。
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提供了一个简单快速的方法来检测白酒年份酒中乙酸的体积分数，在有干扰物存在的情况下，不需要经过任何对样品预处理的过程。使用乙酸乙醇水溶液作为校正集，待测酒样为预测集，使用AFR算法进行解析并测定，待测酒样中乙酸的体积分数分别为0.00089, 0.00119, 0.00186, 0.00276, 0.00383，再通过使用标准添加法验证得到上述测定结果是比较准确的。由此可以说明本方法测量的结果准确可靠，可为检测白酒年份酒中单体的体积分数测量提供一个新的思路。
3维荧光光谱测定白酒年份酒中乙酸的体积分数
Determination of volume fraction of acetic acid in Chinese aged liquor by 3-D fluorescence spectrometry
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摘要: 为了快速测定白酒年份酒中乙酸的体积分数，采用3维荧光光谱结合交替拟合残差算法，首先将不同体积分数的乙酸乙醇水溶液的3维荧光光谱作为校正集，然后将白酒的3维荧光光谱作为预测集，利用交替拟合残差算法进行解析分辨，采用标准添加法来验证结果的准确性。结果表明，预测体积分数与真实体积分数的相关系数为0.9926，平均回收率为101.97%；3维荧光光谱结合交替拟合残差算法可以快速有效地测定白酒年份酒中乙酸的体积分数。这一结果对白酒年份酒中单体体积分数的检测是有帮助的。Abstract: In order to quickly determine the volume fraction of acetic acid in Chinese aged liquor, 3-D fluorescence spectroscopy and alternate fitting residual algorithm were used. Firstly, 3-D fluorescence spectra of different volume fraction of acetic acid of ethanol aqueous solution was used as the calibration set. 3-D fluorescence spectrum of liquor was used as the predicted set. Alternate fitting residual algorithm was used to analyze. Standard addition method was used to verify the accuracy of the results. Through theoretical analysis and experimental verification, the results show that, correlation coefficient between the predicted volume fraction and the experimental volume fraction is 0.9926. Average recovery percentage is 101.97%. 3-D fluorescence spectrometry combined with alternate fitting residual algorithm can quickly and effectively determine the volume fraction of acetic acid in Chinese aged liquor. This result is helpful for the detection of monomer volume fraction in Chinese aged liquor.
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a—excitation spectra b—emission spectra
Figure 1. The spectra of acetic acid in ethanol aqueous solution obtained by AFR algorithm and experiment
a—excitation spectra b—emission spectra
Figure 2. The spectra of acetic acid in Chinese aged liquor obtained by AFR algorithm and in ethanol aqueous solution obtained by experiment
Table 1. The concentration of calibration
calibration sample volume fraction of acetic acid 1 0.0050 2 0.0045 3 0.0040 4 0.0035 5 0.0030 6 0.0025 7 0.0020 8 0.0015 9 0.0010 10 0.0005 11 0.0000 
下载: 导出CSV
Table 2. Analysis of calibration set by using AFR algorithm and leave-one-out cross-validation method
samplenumber the realvolume fraction the predicted volume fraction recoverypercentage/% 1 0.00500 0.00496 99.20 2 0.00450 0.00467 103.78 3 0.00400 0.00405 101.25 4 0.00350 0.00334 95.43 5 0.00300 0.00278 92.67 6 0.00250 0.00254 101.60 7 0.00200 0.00212 106.00 8 0.00150 0.00155 103.33 9 0.00100 0.00099 99.00 10 0.00050 0.00059 118.00 11 0.00000 -0.00009 — RMSEP 0.00162 average recovery percentage 102.03% correlation coefficient 0.9974
下载: 导出CSV
Table 3. The predicted concentration of acetic acid in Chinese aged liquor by using AFR
sample number the predicted volume fraction 1 0.00089 2 0.00119 3 0.00186 4 0.00276 5 0.00383
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Table 4. Analysis of the predicted set by using AFR
sample number the real volume fraction the predictedvolume fraction recovery percentage/% Ⅰ 0.00165 0.00155 93.94 Ⅱ 0.00184 0.00182 98.91 Ⅲ 0.00205 0.00217 105.85 Ⅳ 0.00246 0.00252 102.44 Ⅴ 0.00264 0.00287 108.71 RMSEP 0.00045 average recovery percentage 101.97% correlation coefficient 0.9926
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