# The Application of Classical Least Square Algorithm in the Quantitative Analysis of Lime in Wheat Flour by ATR-MIR Spectroscopy

Dong Wang, Donghai Han, Zhihong Ma, Ligang Pan, Liu Zhao, Ping Han, Jihua Wang

► To cite this version:

Dong Wang, Donghai Han, Zhihong Ma, Ligang Pan, Liu Zhao, et al.. The Application of Classical Least Square Algorithm in the Quantitative Analysis of Lime in Wheat Flour by ATR-MIR Spectroscopy. 5th Computer and Computing Technologies in Agriculture (CCTA), Oct 2011, Beijing, China. pp.8-16, 10.1007/978-3-642-27278-3_2. hal-01360958

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
The Application of Classical Least Square Algorithm in
the Quantitative Analysis of Lime in Wheat Flour by
ATR-MIR Spectroscopy

Dong Wang<sup>1,2,3</sup>, Donghai Han<sup>1</sup>, Zhihong Ma<sup>3</sup>, Ligang Pan<sup>3</sup>, Liu Zhao<sup>3</sup>, Ping Han<sup>3</sup>, Jihua Wang<sup>2,3*</sup>

¹ College of Food Science and Nutritional Engineering, China Agricultural University, Beijing
100083, P. R. China

² Beijing Research Center for Information Technology in Agriculture, Beijing 100097, P. R. China

³ Beijing Research Center for Agri-food Testing and Farmland Monitoring, Beijing 100097, P. R. China

{wangd@nercita.org.cn wangjh@nercita.org.cn}

**Abstract.** In this thesis, classical least square (CLS) regression was applied in the attenuate total reflection mid-infrared (ATR-MIR) spectra data processing of lime in wheat flour to develop the corrected peak height model of the raw spectra, the corrected peak area model of the raw spectra, the corrected peak

Supported by Beijing Postdoctoral Research Foundation; China Postdoctoral Science Foundation (49th) (No. 20110490318); Postdoctoral Science Foundation of Beijing Academy of Agriculture and Forestry Science; Special Research of Public Welfare Industry, the Ministry of Agriculture of People's Republic of China (No. 201203046) and National High Technology Research and Development Program 863 (2010AA10Z201).

Author: Dong WANG, Ph.D., major: NIR spectroscopy analysis and NIR micro-imaging analysis, College of Food Science & Nutritional Engineering, China Agricultural University, Beijing 100083, P. R. China, Email: wangd@nercita.org.cn;

* Corresponding Author: Jihua WANG, Researcher, Ph.D., major: Agricultural information technology, Beijing Research Center for Information Technology in Agriculture, Beijing 100097, P. R. China, Email: wangjh@nercita.org.cn.

Address: Beijing 2449-26 mailbox, City of Beijing, P. R. China, Postcode: 100097 (Beijing Research Center for Information Technology in Agriculture).
height model of the 2nd derivative spectra and the corrected peak area model of
the 2nd derivative spectra respectively. The result indicated that the correlation
coefficients of the four models mentioned above are 0.9648, 0.9696, -0.9646
and -0.9599 respectively. F-test result indicated that a very remarkable
correlation exists between the estimated and specified values of the calibration
set and external validation set. The detection limits of the four models
mentioned above are 3.51 %, 3.21 %, 3.51 % and 3.69 % respectively, which
can fulfill the demand for the rapid quality safe screening of wheat flour in the
market. This method, to some extent, can provide some references for not only
the design and manufacturing of the special MIR instrument for the quality safe
control of wheat flour in the market but also the quantitative determination of
banned additives in wheat flour.

**Key words:** Classical Least Square, Attenuate Total Reflection, Mid-Infrared Spectroscopy, Wheat Flour, Lime

# 1 Introduction

Wheat flour is one of the important food sources for human beings, of which the quality safety is highly focused by all quarters of society. However, the quality safety incidents about wheat flour have been reported frequently in recent years, such as lime added in it, which results in not only negative influence but also being harmful to the customers' health. Therefore, the development of rapid, simple, practical and low-cost determination method for detecting lime in wheat flour becomes particularly urgent and very important.

Among the common instrument analytical methods, mid-infrared (MIR)
spectroscopy analysis is widely applied in the fields of the identification and
characterization of microbes[1], detection and identification of bacteria[2], quality
analysis of edible oil[3, 4], quantitative determination of anthocyanins in cherry[5]
with the advantages of distinguishable peaks, strong characteristics, high sensitivity,
rapid analysis and non-invasive analysis.

However, the traditional MIR analysis involves the sample preparation such as
tabletting with KBr, which is difficult for the operators. Attenuated total reflection
(ATR) technology can acquire the information of samples according to the reflective
signals of the sample surface, which is free of sample preparation. ATR technology
has the advantages of high sensitivity, distinguishable peaks, user-friendly control and
non-interference by humidity. Based upon the advantages mentioned above, ATR
technology is now being widely applied in the fields of analysis of juice sweetness[6],
biology structure studies[7], material study[8] and so forth. Therefore, it is convenient
to collect the MIR spectra of powder samples, such as wheat flour, by ATR
technology.

It is known by the experiment data that lime, such as calcium oxide, calcium
hydroxide, has the characteristic absorption peaks in the MIR range, which is the
theoretical foundation of the qualitative and quantitative analysis to it. The
characteristic absorption peak in MIR range of wheat flour is far away from that of
lime, i.e. the interference from wheat flour is not very obvious. Based on the MIR
spectral characteristics of wheat flour and lime, CLS algorithm has a certain potential
application in the quantitative analysis of lime in wheat flour by MIR spectra data.

Classical least square (CLS) regression is a data processing method applied in the
data regression of analytical chemistry commonly[9, 10]. The basic principle of CLS
is that to calculate the evaluated values of the regression coefficients between the
independents and dependents according to a group of obvious values in order to
decrease the errors between the specified values and the predicted values furthest. The
obvious errors of CLS obey three hypotheses, i.e. the obvious values are independent
each other with the same precision, the obvious errors are non-systematical, the
obvious errors are as the law of normal distribution[11]. Compared to partial least
square regression and principal component regression, CLS regression is easy to
understand relatively. Meanwhile, it is easier to achieve CLS algorithm on the special
MIR detection instruments, which is in favor of the promotion of this technology.

In this research, ATR-MIR spectra of the wheat samples mixed with lime were
collected. The quantitative determination of lime in wheat flour by ATR-MIR
combined with CLS algorithm was studied. The corrected peak height / area models
of the raw spectra and the corrected peak height / area models of the 2nd derivative
spectra were developed respectively. The external validation set was employed to
evaluate the prediction performance of the models. This method is of great
importance to the rapid quantitative screening of lime in wheat flour. This research, to
some extent, will provide some references to not only the design and manufacturing
the special MIR spectrometer for the quality safety screening of wheat flour, but also
the quantitative determination of other banned additives in wheat flour.
# 2 Experiment

## 2.1 Instrument and Materials

Instrument: FT-MIR spectrometer, type: Spectrum 400, Perkin Elmer, U.S.

The ATR-MIR spectra are collected by FT-MIR spectrometer combined with ATR accessory, of which, the reference spectrum is collected by air, the wavenumber range is 4000 cm⁻¹ - 540 cm⁻¹, the wavenumber resolution is 4 cm⁻¹, the time of accumulation is 240. The reference spectrum is collected once every 30 minutes.

Materials: wheat flour milled by the winter wheat from Changping experimental base of Beijing, without any additives. Calcium oxide and calcium hydroxide: A.R.

## 2.2 Method

The quantitative calibration models of lime are developed by the corrected peak height and corrected peak area of lime in ATR-MIR spectra combined with the algorithm of classical least square. The external validation set, of which the average and standard deviation are similar to the calibration set, is employed to evaluate the prediction performances of the models. The contents of lime in both the calibration set and external validation set are distributed in the range of 0.6 % - 16.0 % uniformly. The mass of each sample is about 50 grams. The mass data of wheat flour and lime in each sample are recorded according to analytical balance accurately. The information of the content of lime in the samples is showed in table 1.

<table><caption>**Tab. 1.** The information of the content of lime in the wheat flour samples (%)</caption><thead><tr><td>Items</td><td>Calibration set</td><td>External validation set</td></tr></thead><tbody><tr><td>Sample size</td><td>30</td><td>10</td></tr><tr><td>Minimum</td><td>0.6831</td><td>0.9643</td></tr><tr><td>Maximum</td><td>15.8145</td><td>14.1465</td></tr><tr><td>Average</td><td>5.2319</td><td>5.3556</td></tr><tr><td>Standard deviation</td><td>4.36</td><td>4.49</td></tr></tbody></table>

In order to decrease the error of peak height and peak area measurement, the
corrected peak height / area models of the 2^nd^ derivative spectra are discussed despite the corrected peak height / area models of the raw spectra. The 2^nd^ derivative [12] is one of the data preprocessing method that is applied in the data preprocessing in MIR data commonly, which can eliminate the baseline drifting and baseline translation.

The corrected height is the distance between the peak top of the target peak and the connecting line of the two base points around the target peak, while the corrected area is the integral value between the spectrum curve and the connecting line of the two base points around the target peak. The sketch maps of the measurement of corrected peak height and corrected peak area of the raw and the 2^nd^ derivative spectra are showed as figure 1.

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** the sketch maps of the measurement of the corrected peak height (A1) and the corrected peak area (A2) of the raw spectra and the corrected peak height (B1) and the corrected peak area (B2) of the 2^nd^ derivative spectra</figcaption></figure>

Correlation coefficient (r) and root mean square error of calibration (RMSEC) are regarded as the parameters to evaluate the models' performance; while standard error of prediction (SEP) and ratio performance deviation (RPD) are regarded as the parameters to evaluate the models' prediction performance; the statistic F-test value is regarded as the parameter to evaluate the regression significant of regression equation.

Looking up in the *F-test* value table according to the sample size of the calibration set and external validation set, *F*_{(1,28)} = 7.64, *F*_{(1,8)} = 11.26 when the significance level *α* = 0.01.
# 3 Result and Discussion

## 3.1 Development of Calibration Models

Some of the ATR-MIR spectra of the samples from calibration set are showed as figure 2, from which, it can be seen clearly that the characteristic peak of lime exists at 3642 cm⁻¹.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Some of the ATR-MIR spectra of calibration set</figcaption></figure>

The calibration models of lime in wheat flour are developed by the content of lime, i.e. the specified values, in wheat flour and the corrected peak height of the raw spectra data, the corrected peak area of the raw spectra data, the corrected peak height of the 2^nd^ derivative spectra data and the corrected peak area of the 2^nd^ derivative spectra data respectively. The sample size of the calibration set is 30. The correlations between the specified values and the corrected peak height of the raw spectra, the corrected peak area of the raw spectra, the corrected peak height of the 2^nd^ derivative spectra and the corrected peak area of the 2^nd^ derivative spectra are showed as figure 3, while the regression equations, correlation coefficients (r) and F-test values (F) of the four calibration models are showed in table 2.

<figure><img src="image_4.png" /></figure>

A1

<figure><img src="image_5.png" /></figure>

A2

<figure><img src="image_6.png" /></figure>

B1

<figure><img src="image_7.png" /></figure>

B2
<caption>**Fig. 3.** The correlations between the specified values and the corrected peak height of the raw spectra (A1), the corrected peak area of the raw spectra (A2), the corrected peak height of the 2nd derivative spectra (B1) and the corrected peak area of the 2nd derivative spectra (B2)</caption>

<table><caption>**Tab. 2.** The regression equations, correlation coefficients (r) and F-test values (F) of the calibration models</caption><thead><tr><th>Models</th><th>Regression equation</th><th>r</th><th>F</th></tr></thead><tbody><tr><td>Corrected peak height of raw spectra</td><td>y = 0.0029x + 0.0034</td><td>0.9648</td><td>377</td></tr><tr><td>Corrected peak area of raw spectra</td><td>y = 0.0426x + 0.0183</td><td>0.9696</td><td>440</td></tr><tr><td>Corrected peak height of 2nd derivative spectra</td><td>y = -1.6070x - 2.1049</td><td>-0.9646</td><td>375</td></tr><tr><td>Corrected peak area of 2nd derivative spectra</td><td>y = -13.6530x - 25.6610</td><td>-0.9599</td><td>328</td></tr></tbody></table>

It can be seen from table 2 that the absolute values of the correlation coefficients of the models are no less than 0.95; the *F*-test values of the models are all much larger than that looked up in *F*-test value table ($F_{(1,28)}$ = 7.64 when the significance level $\alpha$ = 0.01), which indicated that a very remarkable correlation exists between the specified values and the corrected peak heights / areas of the raw spectra or the corrected peak heights / areas of the 2nd derivative spectra, which indicates that CLS regression has a certain potential application in the quantitative analysis of lime in wheat flour by ATR-MIR spectra data.

The correlations between the specified values and estimated values by self-prediction of the models are showed as figure 4.

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** The correlations between the estimated and specified values of the calibration set</figcaption></figure>
A1: the corrected peak height model of the raw spectra, A2: the corrected peak area model of the raw spectra, B1: the corrected peak height model of the 2nd derivative spectra, B2: the corrected peak area model of the 2nd derivative spectra

It can be seen from figure 4 that, for each model, a good correlation exists between the specified values and estimated values by self-prediction of the model. The regression equations, correlation coefficients ($r_c$), root mean square errors of calibration (RMSEC), F-test values ($F_c$) of the four groups of data by self-prediction are showed as figure 3.

<table><caption>**Tab. 3.** The regression equations, correlation coefficients ($r_c$), RMSEC and F-test values ($F_c$) of the calibration set by self-prediction</caption><thead><tr><th>Models</th><th>Regression equation</th><th>r<sub>c</sub></th><th>RMSEC</th><th>F<sub>c</sub></th></tr></thead><tbody><tr><td>Corrected peak height of raw spectra</td><td>y = 1.0020x + 0.0061</td><td>0.9649</td><td>1.17</td><td>378</td></tr><tr><td>Corrected peak area of raw spectra</td><td>y = 0.9981x + 0.0198</td><td>0.9699</td><td>1.07</td><td>444</td></tr><tr><td>Corrected peak height of 2<sup>nd</sup> derivative spectra</td><td>y = 0.9988x + 0.0106</td><td>0.9647</td><td>1.17</td><td>376</td></tr><tr><td>Corrected peak area of 2<sup>nd</sup> derivative spectra</td><td>y = 0.9947x + 0.0497</td><td>0.9606</td><td>1.23</td><td>334</td></tr></tbody></table>

It can be seen from figure 3 that for all of the regression equations by self-prediction, the slopes are all close to 1, the intercepts are close to 0, the correlation coefficients are no less than 0.96, the F-test values are much larger than that looked up in F-test value table ($F_{(1,28)}$ = 7.64 when the significance level $\alpha$ = 0.01), which indicates that, for each model, a very remarkable correlation exists between the specified values and estimated values by the self-prediction of the calibration model, i.e. CLS regression has a certain potential application in the quantitative analysis of lime in wheat flour by ATR-MIR spectra data.

## 3.2 External Validation

The external validation set is employed to evaluate the prediction performance of the
calibration models. The sample size of the external validation set is 10. The correlation between the specified values and estimated values by the corrected peak height model of the raw spectra, the corrected peak area model of the raw spectra, the corrected peak height model of the 2nd derivative spectra, the corrected peak area model of the 2nd derivative spectra are showed as figure 5.

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** The correlations between the estimated and specified values of the external validation set</figcaption></figure>

A1: the corrected peak height model of the raw spectra, A2: the corrected peak area model of the raw spectra, B1: the corrected peak height model of the 2nd derivative spectra, B2: the corrected peak area model of the 2nd derivative spectra

It can be seen from figure 5 that a good correlation exists between the estimated and specified values of the external validation set for each model. The regression equations, correlation coefficients ($r_p$), standard errors of prediction (SEP), ratio performance deviations (RPD) and the F-test values ($F_p$) of the external validation set are showed in table 4.

<table><caption>**Tab. 4.** The regression equations, correlation coefficients ($r_p$), SEP, RPD and F-test values ($F_p$) of the external validation set</caption><thead><tr><th>Models</th><th>Regression equation</th><th>r<sub>p</sub></th><th>SEP</th><th>RPD</th><th>F<sub>p</sub></th></tr></thead><tbody><tr><td>Corrected peak height of raw spectra</td><td>y = 1.4658x - 1.1709</td><td>0.9954</td><td>2.59</td><td>1.73</td><td>862</td></tr><tr><td>Corrected peak area of raw spectra</td><td>y = 1.4471x - 1.1580</td><td>0.9954</td><td>2.47</td><td>1.81</td><td>862</td></tr><tr><td>Corrected peak height of 2<sup>nd</sup> derivative spectra</td><td>y = 1.4425x - 1.0632</td><td>0.9964</td><td>2.48</td><td>1.81</td><td>1119</td></tr><tr><td>Corrected peak area of spectra</td><td>y = 1.4224x - 1.0096</td><td>0.9935</td><td>2.42</td><td>1.85</td><td>607</td></tr></tbody></table>
2<sup>nd</sup> derivative spectra

It can be seen from table 4 that for all the regression equations of external validation set, the correlation coefficients between the estimated and specified values are no less than 0.99, standard errors of prediction are no more than 2.6, ratio performance deviation are no less than 1.7, *F*-test values are much larger than that looked up in *F*-test value table ($F_{(1,8)}$ = 11.26 when the significance level $\alpha$ = 0.01), which indicates that a very remarkable correlation exists between the estimated and specified values of the external validation set for each model, i.e. the CLS regression has a certain potential application in the quantitative prediction of lime in wheat flour by ATR-MIR spectra data.

Comparing the four models, it can be seen that the differences among the four models are not significant in regression equations, correlation coefficients and the prediction results of the external validation set, the reason of which is that the characteristic peak of lime in ATR-MIR spectrum (3642 cm⁻¹) is far away from the absorption peak of wheat flour in ATR-MIR spectrum (3300 cm⁻¹), therefore, the interference from the spectral background becomes weak. According to that the detection limit is three times the RMSEC[11], the detection limits of the corrected peak height / area models of the raw spectra and the corrected peak height / area models of the 2<sup>nd</sup> derivative spectra are 3.51 %, 3.21 %, 3.51 % and 3.69 % respectively, which are much less than that added in wheat flour for the purpose of weight increment. This method can fulfill the demand of rapid quality screening of wheat flour in the market.

4 Conclusion

Classical least square algorithm was applied in the development of the quantitative
calibration models of lime in the wheat flour samples. The result indicated that the
CLS regression has a certain potential application in the quantitative determination of
lime in wheat flour by ATR-MIR spectra data. The detection limits of the corrected
peak height / area models of the raw spectra and the corrected peak height / area
models of the 2<sup>nd</sup> derivative spectra are 3.51 %, 3.21 %, 3.51 % and 3.69 %
respectively, which are much less than that added in wheat flour for the purpose of
weight increment. This method can fulfill the demand of rapid quality screening of
wheat flour in the market, which is of great and positive meaning to the monitoring of
wheat flour in the market and the guarantee of the customers' health. This research, to
some extent, will also provide some references to the quantitative determination of
other banned additives and the design and manufacturing of the special MIR
spectrometer for the quality screening of wheat flour in the market. The method to
decrease the detection limit is still being researched.

**Acknowledgment.** This thesis is supported by Beijing Postdoctoral Research Foundation; China Postdoctoral Science Foundation (49th) (No. 20110490318); Postdoctoral Science Foundation of Beijing Academy of Agriculture and Forestry Science; Special Research of Public Welfare Industry, the Ministry of Agriculture of People's Republic of China (No. 201203046) and National High Technology Research and Development Program 863 (2010AA10Z201).

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