In order to collect the actual PM samples for THz measurement in air, a standard air sampler (Minivol Tactical Air Sampler) was employed. In the process of PM collection, the air would pass through a 10-μ m cut-off and a 2.5-μ m cut-off successively, and then the PM_2.5 were collected on a quartz filter membrane, which had a diameter of 47 mm). A total of 28 PM_2.5 were collected in air. The collection of PM_2.5 was finished in the campus of China University of Petroleum, Beijing, China, from March 25 to June 5, 2014. THz spectra of PM_2.5 were obtained by using a Bruker Fourier-transform infrared (FTIR) spectrometer. Co-adding 64 scans at a resolution of 4 cm^-1 with strong apodization were set in the measurement process. Silicon carbide was the optical source, emitting steady emissions with continuous wavelengths in THz range. A Michelson interferometer was used to obtain interference pulses, which would then focus on the sample location. Finally, the spectral data of PM_2.5 would be collected by the detector and recorded in computer.

All the blank filters were weighed before collecting and the reweighed after PM_2.5 were collected. The flow rate of air equaled 7 L· min^-1. Thus, the PM_2.5 concentration ρ was obtained by using the expression ρ =mN^-1t^-1, where m, N and t were the mass of PM_2.5, flow rate and sampling time, respectively. In terms of THz spectra, the filters without and with PM_2.5 were employed as reference and samples. The spectra were recorded as frequency-domain spectra (FDS) in computer. The frequency dependence of absorbance (A) spectra can be obtained by log(E_ref./E_sam.), where E_ref. and E_sam. were the amplitudes of the reference and sample in FDSs which were obtained directly in FTIR measurement, respectively^[18].

The quantitative monitoring of PM_2.5 concentration is a continuously wide-concerned topic to not only ordinary citizens, but also the environmental departments. Initially, we performed a basic characterization of the transmitted THz absorption parameters of a series of PM_2.5 based on the FTIR measurement. An FTIR spectrometer had a higher signal-to-noise ratio (SNR) in high frequency range. Herein the SNRs were not rather high in the 1~3 THz range and 8~10 THz range. Thus the frequency between 3~8 THz was selected for the analysis in this research. The inset of Fig.1 shows the frequency dependent amplitude spectra of filter without (Ref.) and with (Sam.) PM_2.5 in the frequency range from 3 to 8 THz. It is observed that the amplitude of sample is smaller than that of reference over the entire range, proving the absorption effect of PM_2.5 to THz radiation. Thus, it can be concluded that molecular vibration modes of PM_2.5 components have corresponding characteristics in THz range, which is the basis for THz wave to be employed to monitor PM_2.5 in air.

Fig.1

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	Fig.1 Frequency dependent absorbance spectra of PM2.5 in the frequency range from 3 to 8 THz. PM2.5 mass vary from 0.50 to 2.50 mg. The absorbance spectra have an absorption band with a 6.6-THz central frequency. The inset represents the frequency-domain spectra (FDS) of reference (Ref.) and a PM2.5 (Sam.), which are used to obtain absorbance spectra

According to the FDS, the frequency dependent absorbance spectra can be obtained by log(E_Ref./E_Sam.). Here, a Savitzky-Golay filter was used to pre-process the absorbance values. The filter would reduce the instrument noise and smooth curve, but not distort the spectral wave forms and absorption features. Fig.1 plots the smoothed frequency dependent values of absorbance of all the PM_2.5 along it depth with the mass of 0.50~2.50 mg, from 3 to 8 THz. As a THz pulse propagates through an absorptive medium, such as PM_2.5, the pulse width broadens due to the dispersion^[19]. It is noted that there exists a broad absorption band whose central frequency is located at ~6.6 THz. In the range smaller and larger than 6.6 THz, the absorbance values gradually increase and decrease with increasing frequency for most PM_2.5 collected in air, respectively. There are deviations among several PM_2.5, whose absorbance increases in the whole range. This phenomenon may be caused by sudden change of pollution sources when the PM_2.5 was collected. A strong absorption effect was observed, and the larger the PM_2.5 mass was, the stronger the PM_2.5 absorption showed.

For quantitatively monitoring PM_2.5 in air with THz radiation, we extracted the absorbance values at several frequencies around 6.6 THz and related them to the respective mass, shown in Fig.2. The x- and y-axis represent PM_2.5 mass and absorbance respectively. With the augment of mass absorbance basically increased at 6.0, 6.3, 6.6 and 7.0 THz. Based on the collected tendency, we fitted the linear models and calculated the correlation coefficient R between them. All the points were located at two sides of the fitted lines. In the four linear models at selected frequencies, R_s equaled 0.851, 0.858, 0.869 and 0.878. The results indicated that there existed quantitative relationship between THz absorbance and PM_2.5 with high correlation.

Fig.2

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	Fig.2 Linear relations between PM2.5 mass and absorbance at four frequencies around the central frequency of 6.6 THz The selected frequencies were 6.0 (a), 6.3 (b), 6.6 (c) and 7.0 THz (d)

For the extraction of full-spectrum information between PM_2.5 concentration and THz absorption as no obvious and sharp absorption peaks are found in Fig.1, we employed PCA algorithm based absorbance spectra where the absorption effect of PM_2.5 components over the whole frequency range were taken into account. PCA reduced the number of dimensions within the frequency-dependent data while retaining as much of the overall variations as possible based on uncorrelated projections. It can be used for both qualitative and quantitative analysis. The calculation of PCA results in several variables defined as principal components (PCs), which contained information of samples and spectral variables that were called as scores and loadings. The eigenvector corresponding to the maximum eigenvalue for PC 1 is the direction of the maximum variance distribution of absorbance spectra, so PC 1 has the highest contribution rate in all, followed by PC 2, PC 3 and so on^[10].

Fig.3

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	Fig.3 Principal component analysis (PCA) model of PM2.5 based on the absorbance spectra over the entire frequency range (a): PC 1 versus PC 2 of all PM2.5 with the contribution rate of 90.5% and 8.6%, respectively; (b): PM2.5 mass dependent PC 1 score extracted from (a) and the linear model between mass and PC 1

According to the PCA calculation results, PC 1 and PC 2 are found to describe 90.5% and 8.6% of the variance within the absorbance data, with the total contribution rate of 99.1% in all deviations. Thus, a two-dimensional score system containing PC 1 as well as PC 2 were built and plotted in Fig.3(a). The points in the system represent PC 1 and PC 2 scores of respective PM_2.5 based on absorbance over the entire range. In order to discuss the quantitative relationship of PCs and PM_2.5, only PC1 was extracted and related to PM_2.5 because of its largest contribution rate (90.5%). Fig.3(b) shows PM_2.5 mass dependence of PC 1 score, which reflect the most information of absorption effect in the entire range. With the augment of PM_2.5 mass, PC 1 scores increase basically, validating the absorption regulation of PM_2.5 in Fig.1. Based on the collected trend, a linear model can be built between PC 1 and PM_2.5 mass. R of the model is found as 0.862, which is close to Rs at selected frequencies in Fig.2. Due to the multiple linear regression algorithm in PCA calculation, the results represent similar absorption trend over the entire range from 3 to 8 THz.

In order to monitor PM_2.5 concentration more precisely for the public, the THz absorbance spectra should be further treated to improve the correlation and minimize the error. Linear models in Figs.2 and 3 depend on the Beer’ s law, which is, however, based on one frequency or one PC and is therefore, more fragile to environmental and instrumental noises. To build more robust and precise multiple models, chemometrics methods, including PLS, SVM and BPANN were employed respectively. PLS was one of the most used ways for quantitative analysis, which related two data matrices by a linear multivariate model. PLS has the advantage of analyzing strongly collinear and noisy data. The extracted features can eliminate the uncorrelated information and noise which have great influence in single linear models in the absorbance spectra. The underlying model with PLS is described as X=TP^T+E and y=Tq+f, where X and y are the input and output data, T is the matrix of the extracted features, P and q are the loading matrices, and E as well as f are the relative error terms^{[20, 21]}. SVM is a computing learning algorithm and has been applied in regression analysis, classification, forecasting and pattern recognition. SVM depends on structural risk minimization and statistical machine learning process. The algorithm will generate as a sparse prediction function which needs a selected number of training points called support vectors. In the SVM calculation, the equations are based on the theory of Vanik. The SVM estimates the function as f(x)=ω ϕ (x)+b, where ϕ (x) is the high-dimensional space feature, and ω as well as b are a normal vector and the bias term^{[22, 23]}. BPANN is a mathematical nonlinear dynamics system simulating structure and function of biological neural networks in the human brain. No priori model was required for ANN even when noise was present. Based on searching an error surface using gradient descent for point with minimum error, BP learning algorithm can store a lot of input-output mapping relationships without prior revealing the mathematical equation. Generally, BPANN includes input, hidden and output layers^{[24, 25]}.

All the samples were divided into two subsets: the calibration or training set and validation or prediction set. The calibration or training set was used for calculating an analytical model and the validation or prediction set for testing and verify the accuracy of the model. Here, in order to identify all the subsequently given spectra correctly in prediction set, the number of calibration or training set should exceed that of validation or prediction set in PLS, SVM and BPANN calculation. To evaluate the reliability and precision of the model, the correlation coefficient R and root-mean square error (RMSE) were calculated. R is related to the covariance cov(x, y) and variance matrix v(x) by R=cov(x, y)/(v(x)v(y))1/2, and RMSE can be calculated by RMSE=(∑(x-y)2/n)1/2,where n is the sum of samples in a set, and x as well as y represent actual and predicted mass, respectively. A R value close to 1 and a small RMSE indicate the model has high precision. Especially, the prediction error of the PM_2.5 in validation or prediction set was introduced to finally assess the model predictive ability. A model with better prediction ability was to have a smaller prediction error^[14].

Figs. 4— 6 show the predicted PM_2.5 mass versus actual PM_2.5 mass in PLS, SVM and BPANN, respectively, with the absorbance spectra in Fig.1 over the entire range from 3 to 8 THz as the input. Eight groups of PM_2.5 are randomly selected as the validation or prediction set and the left twenty PM_2.5 as the calibration or training set. In the two-dimensional systems of PLS, SVM and BPANN, all the points are located near the reference (Ref.) lines, which represent zero residuals between the predicted and actual PM_2.5 mass. Thus, the predicted values are close to the actual data in the quantitative models. In order to precisely evaluate the models, we calculated R and RMSE of calibration or training and validation or prediction set, which were listed in Table 1. According to the values in Table 1, we can find that R_s of calibration and prediction sets exceed 0.93 and 0.89, and RMSEs are less than 0.23 and 0.37, respectively. Further comparing the results of three methods, it can be concluded that BPANN method shows lowest prediction error of 0.207 mg and presents the highest correlation, indicating that it has the best antinoise ability among the three methods in this PM_2.5 monitoring system. SVM also presents a high correlation and a low prediction error similar to BPANN. PLS showed a relatively lower precision compared with BPANN and SVM, but still had a high correlation and a low error. Therefore, the results in Figs.4— 6 and Table 1 proved that the combination of THz spectroscopy and statistical methods can really improve the precision and be used to monitor PM_2.5 in air.

Fig.4

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	Fig.4 Actual versus predicted mass of PM2.5 in PLS model with the absorbance spectra over the entire frequency range as the input

Fig.5

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	Fig.5 Actual versus predicted mass of PM2.5 in SVM model

Fig.6

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	Fig.6 Actual versus predicted mass of PM2.5 in BPANN model

Table 1

Table 1

Table 1 Relative errors R and RMSE of both calibration or training and validation or prediction set in PLS, SVM and BPANN models Method Calibration or Training Validation or Prediction R RMSE/mg R RMSE/mg PLS 0.931 0.225 0.899 0.361 SVM 0.954 0.164 0.910 0.217 BPANN 0.999 0.016 0.912 0.207

Table 1 Relative errors R and RMSE of both calibration or training and validation or prediction set in PLS, SVM and BPANN models

This research performed an investigation for THz spectroscopy to quantitatively monitor PM_2.5 in air. To determine PM_2.5 concentration or mass, a linear model was initially built between PM_2.5 mass and absorbance values at selected frequencies. The measurement accuracy was closely related to the model performance. The uncertainties of PM_2.5 prediction depended on instrumental and background noises, even the variation of the reference spectra due to changes in system performance to some extent. Such uncertainties or noises cannot be avoided actually in single linear models, which was the most used method in quantitative analysis. In terms of the sample whose absorption was much strong in THz range, single linear model can be a good selection for quantitative analysis because the sample spectrum was not sensitive to the instrumental noises. For most samples such as PM_2.5, it was quite worth investigating more data analysis methods to realize more accurate PM_2.5 monitoring. The statistical algorithm was an effective selection according to this research. Statistical analysis has been applied in other fields such as agriculture. Our results together relative researches about quantitative analysis indicated that the general noise effect in the spectral data can be reduced or eliminated in the statistical analysis based on full-range-spectra calculation^{[10, 14, 15, 26]}. In terms of PM_2.5, its monitoring has been attracted broad attention in many countries. Utilizing THz spectroscopy combined with chemometrics method is useful for environmental departments. In the further study, the selection of statistical methods and parameters in calculation should be considered by selecting a larger number of PM_2.5 samples.

In conclusion, we have shown that THz radiation was capable of monitoring PM_2.5 in air quantitatively. Linear models between absorbance and PM_2.5 were initially discussed. PCA proved the similar augment tendency of absorbance with the increasing PM_2.5 mass. In addition, we found that the use of statistical methods including PLS, SVM and BPANN can improve the prediction accuracy of PM_2.5 based on the full-range-spectra analysis. Especially for BPANN and SVM, they had larger correlation and lower prediction error. Therefore, the research would be a further step for THz technique to become a valuable tool for the rapid and precise monitoring and gradually be as a normal way to monitor environmental pollution.