多维校正方法及在植物激素与农药定量分析中的应用研究
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摘要
随着现代科学技术的飞速发展,人们对自然现象的研究逐步深入,化学家所面临的研究体系日益复杂,促使物理、电子学家研制大量新型多通道高阶分析仪器。高阶分析仪器所产生的数据,不再是简单的标量或矢量响应数据,而是成千上万个数据点组成的基于阵列基础之上的三维或四维的数据阵。这些庞大的数据阵在含有丰富的有用的化学信息的同时,也含有一些仪器噪音、干扰物质响应和背景响应等,促使化学计量学多维校正理论与方法不断地发展。多维校正方法利用“数学分离”去除背景基质和干扰信号,从而代替或增强了“化学或物理分离”效果；即使在目标分析物与背景干扰物质的响应信号相互重叠的情况下,仍能实现目标分析物的直接快速定量分析。为直接解决农业化学、环境化学、生物医药等学科中的实际分析难题提供了强有力的武器。本文作者在跟踪化学计量学发展前沿与动态及当前分析化学界亟需解决的难题的基础上,对多维校正方法进行了深入的理论研究及其在植物激素、除草剂定量分析中的应用研究。本论文的主要内容如下：
1.三维校正方法用于农业体系中植物激素的定量分析(第2-4章)
吲哚乙酸(IAA)是一种植物激素,它在很低的浓度下就可以调节植物生长与发育的全过程：从发芽到果实成熟。因此,在复杂体系中吲哚乙酸的定量分析是十分重要的工作。本文提出了一种新的直接测定土壤样中吲哚乙酸含量的荧光分析方法(第2章)。它运用激发-发射矩阵荧光(EEMs)并结合以交替三线性分解(ATLD)算法和自加权交替三线性分解(SWATLD)算法为基础的二阶校正方法。本方法充分体现了三维荧光二阶校正方法的“二阶优势”,即使在土壤样品中有未知荧光干扰物共存也能够定量测定吲哚乙酸的浓度,避免了繁琐的前处理工作。另外,实际应用证明,这两种算法对预估计的过大组分数不敏感。
提出了较灵敏的激发发射荧光光谱与二阶校正相结合,同时测定银杏叶和芽样品中脱落酸(ABA)和赤霉素(GA)含量的方法(第3章)。该方法基于交替归一加权残差(ANWE)算法和平行因子分析(PARAFAC)算法,能够在提取液中存在未知干扰物的情况下同时测定脱落酸和赤霉素的含量。尽管这两种分析物的激发和发射光谱与植物提取液中的内源荧光物质光谱严重重叠,但该方法仍然获得满意的结果。在银杏叶样品中,脱落酸和赤霉素的检测下限分别是6.9ng mL-1和9.6ng mL-1,满足了银杏叶样在不同时期时脱落酸和赤霉素的浓度范围(从几百到几ng g-1)。另外,为了进一步考察该方法的准确性,评价了ANWE和PARAFAC算法的一些统计参数和品质因子。该方法为植物提取液中植物激素的定量测定提供了新的途径,进而在植物生长过程研究中可能有更多的应用。
激动素(kinetin,简称KT)是一种非天然的细胞分裂素,具有促进细胞分裂、延缓离体叶片和切花衰老的作用。6-苄氨基嘌呤(6-Benzylaminopurine,简称6-BAP)是第一个人工合成的细胞分裂素,具有延缓叶片衰老、保绿作用。秋水仙素(colchicine,简称COL),一种生物碱,能抑制有丝分裂,广泛应用于细胞学、遗传学的研究和植物育种。运用高效液相色谱-二极管阵列(HPLC-DAD)结合自加权交替三线性分解(SWALTD)算法同时测定黄豆芽、黄豆提取液和土壤中的三种植物生长调节剂激动素、6-苄氨基嘌呤和秋水仙素(第4章)。在相同的简单色谱条件下,该方法成功快速地定量分析了三种不同背景体系黄豆芽、黄豆提取液和土壤样品中激动素、6-苄氨基嘌呤和秋水仙素的含量,充分体现了二阶校正方法的“二阶优势”。
2.三维校正方法用于环境体系中除草剂的定量分析(第5-6章)
提出了一种快速、非分离的荧光分析方法,该方法基于激发-发射矩阵荧光和二阶校正方法,成功地检测了土壤、淤泥、污水和河水等环境样品中除草剂敌草胺(NAP)的含量(第5章)。在pH为2.2的0.1mol L-1柠檬酸钠-盐酸缓冲溶液介质中,敌草胺体系的荧光强度得到了极大地增强。为了处理环境样品中内源的荧光物质干扰,采用有效的二阶校正方法,在复杂的环境样品中准确测定了敌草胺的含量。另外,我们利用交替惩罚三线性分解(APTLD)算法与多个环境基质样品数据集,实施不同的校正步骤包括单基质模型、同天的多基质模型和总模型,进一步考察了二阶校正方法的性能。结果表明二阶校正方法能够在多种不同基质的样品中同时测定一种或多种感兴趣组分,进一步丰富了二阶校正方法的“二阶优势”的内涵。
给出了基于APTLD算法的二阶校正方法用于解析高效液相色谱-二极管阵列检测(HPLC-DAD)数据的新的应用实例(第6章)。该方法准确可靠地分析了土壤、淤泥和污水中莠去津、莠灭净和扑草净的含量。尽管三种三嗪类除草剂的色谱保留时间和光谱图与环境样品中背景干扰物的色谱流出时间和光谱图严重重叠,仍然获得了满意的结果。另外,运用椭圆置信区间(EJCR)测试评价了该方法的准确度和精密度。该方法为复杂环境样品中多种有害物质的同时定量分析开辟了新的道路,并且通过对污水-土壤-淤泥整体系统的了解,为环境的改善和管理提供了可靠的科学依据。
3.开发了一种新的方法用于解析非四线性的四维数据(第7章)
在四维数据产生过程中,由于实验条件的不可控制性,经常出现其中一维是非线性的情况,面对这样的非四线性的四维数据,而经典的解析四维数据阵的算法,如四线性平行因子算法(4-PARAFAC),则无能为力。因此,提出了非四线性四维数据分解方法(第7章)。该方法将非四线性的四维数据,沿着非线性的一维展开,形成一个扩展的三维数据阵,然后可以选择合适的三线性分解算法进行分解,对获得的扩展矩阵,按照单个样本进行逐列归一化,得到样本的相对浓度,从而实现对非四线性四维数据的解析。我们利用模拟的和真实的四维数据对该方法进行了测试,并与四线性平行因子分析算法进行了比较。研究结果显示,该方法可以实现对非四线性的四维数据的解析,获得了满意的定性定量结果。而当非线性比较严重时,四线性平行因子分析算法不能进行正确的分辨与校正。在实际复杂化学体系和过程量测数据分析中,该新方法将有可能成为一种普适性算法。
With the rapid development of modern science and technology, the natural phenomena have been studied in depth. The application systems that chemistry researchers are faced become more and more complicated, which makes physical scientist manufacture a large number of multi-channel and high-order analytical instruments. The data produced by the instruments are three-dimensional or four-dimensional data arrays, rather than just simple scaler or vector response data. The data arrays contain useful chemical information, at the same time, including background and interference response, it boosts the development of chemometric multi-way calibration methods. Multi-way calibration can extract useful chemical information from these complex data arrays; they can replace the "physical or chemical separation" with "mathematical separation" strategy through separating the signals of target analytes away from those of uncalibrated background or interferences. The benefit of the method, known as "second-order advantage", is capable to determine the content of analytes of interest even in the presence of unknown interferents. Such methods have shown positive effects on various subjects, especially agricultural chemistry, environmental chemistry, biochemistry and pharmaceutical chemistry, and can provide a variety of powerful techniques to resolve practical difficult problems occurred in these subjects. The research work in this dissertation focuses on the methodologies of multi-way calibration and applying it to quantitation of phytohormones and herbicides.
1. Quantitative analysis of phytohormones in agricultural system by using second-order calibration method (Chapter2to Chapter4)
Indole-3-acetic acid (IAA) is one phytohormone of the auxin group and is capable of coordinating the overall process of plant growth and development. IAA is active in the very low concentration range. Therefore, it is important to quantify IAA in the low concentration range in complex system. A new spectrofluorimetric method for the direct determination of IAA in soil is proposed and discussed (Chapter2). It combines the fluorescence excitation-emission matrices (EEMs) with second-order calibration methods based on the alternating trilinear decomposition (ATLD) algorithm and the self-weighed alternating trilinear decomposition (SWATLD) algorithm. These methodologies fully exploit the second-order advantage of second-order calibration method, allowing the concentrations of indole-3-acetic acid to be quantified even in the presence of unknown fluorescent interferents in soil samples. Moreover, it has been demonstrated that both algorithms are insensitive to the number of components in complex system.
A sensitive excitation-emission fluorescence method with second-order calibration strategy is proposed to simultaneously determine of abscisic acid (ABA) and gibberellin (GA) contents in extracts of leaves and buds of ginkgo (Chapter3). The methodology is based on the alternating normalization-weighed error (ANWE) and the parallel factor analysis (PARAFAC) algorithms, which make it possible that gibberellin and abscisic acid concentration can be attained in extract of plants even in the presence of unknown interference from potential interfering matrix contaminants introduced during simple pretreatment procedure. Satisfactory recoveries were obtained although the excitation and emission profiles of the abscisic acid and gibberellin were heavily overlapped with each other and with background in the plant extracts. The limits of detection obtained for gibberellin and abscisic acid in leaf samples were9.6and6.9ng mL-1, respectively, which were in the concentration range (from hundreds to several ng g-1) for gibberellin and abscisic acid in leaves in different periods. Furthermore, in order to investigate the performance of the developed method, some statistical parameters and figures of merit of ANWE and PARAFAC are evaluated. The method proposed lights a new avenue to determine quantitatively phytohormones in extracts of plants with a simple pretreatment procedure, and may hold potential to be extended as a promising alternative for more practical applications in plant growth process.
Kinetin (KT) is a synthetic substance belonging to the cytokinines family.6-Benzylaminopurine (6-BAP) is a common model compound as one of the most important classes of plant hormones—cytokinins. Colchicine is an alkaloid prepared from the dried corns and seeds of colchicum autumnale. A novel method based on high performance liquid chromatography-diode array detection (HPLC-DAD) coupled with SWATLD algorithm is decribed for the determination of kinetin,6-benzylaminopurine and colchicine in extracts of bean and buds of bean and soil samples (Chapter4). Satisfactory results have been achieved for kinetin,6-benzylaminopurine and colchicine in three different complex samples at simple chromatographic condition, fully exploiting the "second-order advantage" of second-order calibration method.2. Second-order calibration method for quantitative analysis of herbicides in environmental system (Chapter5to Chapter6)
A rapid non-separative spectrofluorometric method based on the second-order calibration of excitation-emission matrix (EEM) fluorescence is proposed for the determination of napropamide (NAP) in soil, river sediment, and wastewater as well as river water samples (Chapter5). With0.10mol L-1sodium citrate-hydrochloric acid (HC1) buffer solution of pH=2.2, the system of NAP has a large increase in fluorescence intensity. To handle the intrinsic fluorescence interferences of environmental samples, the alternating penalty trilinear decomposition (APTLD) algorithm as an efficient second-order calibration method is employed. Satisfactory results have been achieved for napropamide in complex environmental samples. Furthermore, in order to fully investigate the performance of second-order calibration method, we test the second-order calibration method using different calibration approaches including the single matrix model, the intra-day various matrices model and the global model based on the APTLD algorithm with nature environmental datasets. The results showed the second-order calibration methods also enable one or more analyte(s) of interest to be determined simultaneously in the samples with various types of matrices. The maintenance of second-order advantage has been demonstrated in simultaneous determination of the analyte of interest in the environmental samples of various matrices.
A novel application of second-order calibration method based on an APTLD algorithm is presented to treat with the data from high performance liquid chromatography-diode array detection (HPLC-DAD)(Chapter6). The method makes it possible to accurately and reliably analyze atrazine (ATR), ametryn (AME) and prometryne (PRO) contents in soil, river sediment and wastewater samples. Satisfactory results are obtained although the elution time and spectral profiles of atrazine, ametryn and prometryne are heavily overlapped with the background in environmental samples. Furthermore, the accuracy and precision of the proposed method are evaluated with the elliptical joint confidence region (EJCR) test. It lights a new avenue to determine quantitatively herbicides in environmental samples with a simple pretreatment procedure and provides the scientific basis for an improved environment management through a better understanding of the wastewater-soil-river sediment system as a whole.
3. Developing a new method for decomposition non-quadrilinear four-way data (Chapter7)
A four-way data array deviates from the quadrilinear condition, because of non-linear relationship between signal and analyte concentration, non-multilinear signal for a single sample and non-constant component profiles. The classic algorithms for decomposition four-way data, such as quadrilinear parrel factor analysis (4-PARAFAC), can not treat with these data array. The new method produced in the dissertation can model for non-quadrilinear four-way data (Chapter7). The four-way data array is rearranged into an expanded three-way data array following the non-linear way, then it is decomposed by three-way calibration algorithms, finally the relative spectra and concentration have been attained. Based on these attracted merits, such a novel method may hold great potential to be extended as a promising alternative for the non-quadrilinear four-way data array analysis and high-order calibration.
1.三维校正方法用于农业体系中植物激素的定量分析(第2-4章)
吲哚乙酸(IAA)是一种植物激素,它在很低的浓度下就可以调节植物生长与发育的全过程：从发芽到果实成熟。因此,在复杂体系中吲哚乙酸的定量分析是十分重要的工作。本文提出了一种新的直接测定土壤样中吲哚乙酸含量的荧光分析方法(第2章)。它运用激发-发射矩阵荧光(EEMs)并结合以交替三线性分解(ATLD)算法和自加权交替三线性分解(SWATLD)算法为基础的二阶校正方法。本方法充分体现了三维荧光二阶校正方法的“二阶优势”,即使在土壤样品中有未知荧光干扰物共存也能够定量测定吲哚乙酸的浓度,避免了繁琐的前处理工作。另外,实际应用证明,这两种算法对预估计的过大组分数不敏感。
提出了较灵敏的激发发射荧光光谱与二阶校正相结合,同时测定银杏叶和芽样品中脱落酸(ABA)和赤霉素(GA)含量的方法(第3章)。该方法基于交替归一加权残差(ANWE)算法和平行因子分析(PARAFAC)算法,能够在提取液中存在未知干扰物的情况下同时测定脱落酸和赤霉素的含量。尽管这两种分析物的激发和发射光谱与植物提取液中的内源荧光物质光谱严重重叠,但该方法仍然获得满意的结果。在银杏叶样品中,脱落酸和赤霉素的检测下限分别是6.9ng mL-1和9.6ng mL-1,满足了银杏叶样在不同时期时脱落酸和赤霉素的浓度范围(从几百到几ng g-1)。另外,为了进一步考察该方法的准确性,评价了ANWE和PARAFAC算法的一些统计参数和品质因子。该方法为植物提取液中植物激素的定量测定提供了新的途径,进而在植物生长过程研究中可能有更多的应用。
激动素(kinetin,简称KT)是一种非天然的细胞分裂素,具有促进细胞分裂、延缓离体叶片和切花衰老的作用。6-苄氨基嘌呤(6-Benzylaminopurine,简称6-BAP)是第一个人工合成的细胞分裂素,具有延缓叶片衰老、保绿作用。秋水仙素(colchicine,简称COL),一种生物碱,能抑制有丝分裂,广泛应用于细胞学、遗传学的研究和植物育种。运用高效液相色谱-二极管阵列(HPLC-DAD)结合自加权交替三线性分解(SWALTD)算法同时测定黄豆芽、黄豆提取液和土壤中的三种植物生长调节剂激动素、6-苄氨基嘌呤和秋水仙素(第4章)。在相同的简单色谱条件下,该方法成功快速地定量分析了三种不同背景体系黄豆芽、黄豆提取液和土壤样品中激动素、6-苄氨基嘌呤和秋水仙素的含量,充分体现了二阶校正方法的“二阶优势”。
2.三维校正方法用于环境体系中除草剂的定量分析(第5-6章)
提出了一种快速、非分离的荧光分析方法,该方法基于激发-发射矩阵荧光和二阶校正方法,成功地检测了土壤、淤泥、污水和河水等环境样品中除草剂敌草胺(NAP)的含量(第5章)。在pH为2.2的0.1mol L-1柠檬酸钠-盐酸缓冲溶液介质中,敌草胺体系的荧光强度得到了极大地增强。为了处理环境样品中内源的荧光物质干扰,采用有效的二阶校正方法,在复杂的环境样品中准确测定了敌草胺的含量。另外,我们利用交替惩罚三线性分解(APTLD)算法与多个环境基质样品数据集,实施不同的校正步骤包括单基质模型、同天的多基质模型和总模型,进一步考察了二阶校正方法的性能。结果表明二阶校正方法能够在多种不同基质的样品中同时测定一种或多种感兴趣组分,进一步丰富了二阶校正方法的“二阶优势”的内涵。
给出了基于APTLD算法的二阶校正方法用于解析高效液相色谱-二极管阵列检测(HPLC-DAD)数据的新的应用实例(第6章)。该方法准确可靠地分析了土壤、淤泥和污水中莠去津、莠灭净和扑草净的含量。尽管三种三嗪类除草剂的色谱保留时间和光谱图与环境样品中背景干扰物的色谱流出时间和光谱图严重重叠,仍然获得了满意的结果。另外,运用椭圆置信区间(EJCR)测试评价了该方法的准确度和精密度。该方法为复杂环境样品中多种有害物质的同时定量分析开辟了新的道路,并且通过对污水-土壤-淤泥整体系统的了解,为环境的改善和管理提供了可靠的科学依据。
3.开发了一种新的方法用于解析非四线性的四维数据(第7章)
在四维数据产生过程中,由于实验条件的不可控制性,经常出现其中一维是非线性的情况,面对这样的非四线性的四维数据,而经典的解析四维数据阵的算法,如四线性平行因子算法(4-PARAFAC),则无能为力。因此,提出了非四线性四维数据分解方法(第7章)。该方法将非四线性的四维数据,沿着非线性的一维展开,形成一个扩展的三维数据阵,然后可以选择合适的三线性分解算法进行分解,对获得的扩展矩阵,按照单个样本进行逐列归一化,得到样本的相对浓度,从而实现对非四线性四维数据的解析。我们利用模拟的和真实的四维数据对该方法进行了测试,并与四线性平行因子分析算法进行了比较。研究结果显示,该方法可以实现对非四线性的四维数据的解析,获得了满意的定性定量结果。而当非线性比较严重时,四线性平行因子分析算法不能进行正确的分辨与校正。在实际复杂化学体系和过程量测数据分析中,该新方法将有可能成为一种普适性算法。
With the rapid development of modern science and technology, the natural phenomena have been studied in depth. The application systems that chemistry researchers are faced become more and more complicated, which makes physical scientist manufacture a large number of multi-channel and high-order analytical instruments. The data produced by the instruments are three-dimensional or four-dimensional data arrays, rather than just simple scaler or vector response data. The data arrays contain useful chemical information, at the same time, including background and interference response, it boosts the development of chemometric multi-way calibration methods. Multi-way calibration can extract useful chemical information from these complex data arrays; they can replace the "physical or chemical separation" with "mathematical separation" strategy through separating the signals of target analytes away from those of uncalibrated background or interferences. The benefit of the method, known as "second-order advantage", is capable to determine the content of analytes of interest even in the presence of unknown interferents. Such methods have shown positive effects on various subjects, especially agricultural chemistry, environmental chemistry, biochemistry and pharmaceutical chemistry, and can provide a variety of powerful techniques to resolve practical difficult problems occurred in these subjects. The research work in this dissertation focuses on the methodologies of multi-way calibration and applying it to quantitation of phytohormones and herbicides.
1. Quantitative analysis of phytohormones in agricultural system by using second-order calibration method (Chapter2to Chapter4)
Indole-3-acetic acid (IAA) is one phytohormone of the auxin group and is capable of coordinating the overall process of plant growth and development. IAA is active in the very low concentration range. Therefore, it is important to quantify IAA in the low concentration range in complex system. A new spectrofluorimetric method for the direct determination of IAA in soil is proposed and discussed (Chapter2). It combines the fluorescence excitation-emission matrices (EEMs) with second-order calibration methods based on the alternating trilinear decomposition (ATLD) algorithm and the self-weighed alternating trilinear decomposition (SWATLD) algorithm. These methodologies fully exploit the second-order advantage of second-order calibration method, allowing the concentrations of indole-3-acetic acid to be quantified even in the presence of unknown fluorescent interferents in soil samples. Moreover, it has been demonstrated that both algorithms are insensitive to the number of components in complex system.
A sensitive excitation-emission fluorescence method with second-order calibration strategy is proposed to simultaneously determine of abscisic acid (ABA) and gibberellin (GA) contents in extracts of leaves and buds of ginkgo (Chapter3). The methodology is based on the alternating normalization-weighed error (ANWE) and the parallel factor analysis (PARAFAC) algorithms, which make it possible that gibberellin and abscisic acid concentration can be attained in extract of plants even in the presence of unknown interference from potential interfering matrix contaminants introduced during simple pretreatment procedure. Satisfactory recoveries were obtained although the excitation and emission profiles of the abscisic acid and gibberellin were heavily overlapped with each other and with background in the plant extracts. The limits of detection obtained for gibberellin and abscisic acid in leaf samples were9.6and6.9ng mL-1, respectively, which were in the concentration range (from hundreds to several ng g-1) for gibberellin and abscisic acid in leaves in different periods. Furthermore, in order to investigate the performance of the developed method, some statistical parameters and figures of merit of ANWE and PARAFAC are evaluated. The method proposed lights a new avenue to determine quantitatively phytohormones in extracts of plants with a simple pretreatment procedure, and may hold potential to be extended as a promising alternative for more practical applications in plant growth process.
Kinetin (KT) is a synthetic substance belonging to the cytokinines family.6-Benzylaminopurine (6-BAP) is a common model compound as one of the most important classes of plant hormones—cytokinins. Colchicine is an alkaloid prepared from the dried corns and seeds of colchicum autumnale. A novel method based on high performance liquid chromatography-diode array detection (HPLC-DAD) coupled with SWATLD algorithm is decribed for the determination of kinetin,6-benzylaminopurine and colchicine in extracts of bean and buds of bean and soil samples (Chapter4). Satisfactory results have been achieved for kinetin,6-benzylaminopurine and colchicine in three different complex samples at simple chromatographic condition, fully exploiting the "second-order advantage" of second-order calibration method.2. Second-order calibration method for quantitative analysis of herbicides in environmental system (Chapter5to Chapter6)
A rapid non-separative spectrofluorometric method based on the second-order calibration of excitation-emission matrix (EEM) fluorescence is proposed for the determination of napropamide (NAP) in soil, river sediment, and wastewater as well as river water samples (Chapter5). With0.10mol L-1sodium citrate-hydrochloric acid (HC1) buffer solution of pH=2.2, the system of NAP has a large increase in fluorescence intensity. To handle the intrinsic fluorescence interferences of environmental samples, the alternating penalty trilinear decomposition (APTLD) algorithm as an efficient second-order calibration method is employed. Satisfactory results have been achieved for napropamide in complex environmental samples. Furthermore, in order to fully investigate the performance of second-order calibration method, we test the second-order calibration method using different calibration approaches including the single matrix model, the intra-day various matrices model and the global model based on the APTLD algorithm with nature environmental datasets. The results showed the second-order calibration methods also enable one or more analyte(s) of interest to be determined simultaneously in the samples with various types of matrices. The maintenance of second-order advantage has been demonstrated in simultaneous determination of the analyte of interest in the environmental samples of various matrices.
A novel application of second-order calibration method based on an APTLD algorithm is presented to treat with the data from high performance liquid chromatography-diode array detection (HPLC-DAD)(Chapter6). The method makes it possible to accurately and reliably analyze atrazine (ATR), ametryn (AME) and prometryne (PRO) contents in soil, river sediment and wastewater samples. Satisfactory results are obtained although the elution time and spectral profiles of atrazine, ametryn and prometryne are heavily overlapped with the background in environmental samples. Furthermore, the accuracy and precision of the proposed method are evaluated with the elliptical joint confidence region (EJCR) test. It lights a new avenue to determine quantitatively herbicides in environmental samples with a simple pretreatment procedure and provides the scientific basis for an improved environment management through a better understanding of the wastewater-soil-river sediment system as a whole.
3. Developing a new method for decomposition non-quadrilinear four-way data (Chapter7)
A four-way data array deviates from the quadrilinear condition, because of non-linear relationship between signal and analyte concentration, non-multilinear signal for a single sample and non-constant component profiles. The classic algorithms for decomposition four-way data, such as quadrilinear parrel factor analysis (4-PARAFAC), can not treat with these data array. The new method produced in the dissertation can model for non-quadrilinear four-way data (Chapter7). The four-way data array is rearranged into an expanded three-way data array following the non-linear way, then it is decomposed by three-way calibration algorithms, finally the relative spectra and concentration have been attained. Based on these attracted merits, such a novel method may hold great potential to be extended as a promising alternative for the non-quadrilinear four-way data array analysis and high-order calibration.
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