It becomes a key technology to measure the concentration of the vehicle exhaust components with the absorption spectra. But because of the overlap of gas absorption bands, how to separate the absorption information of each component gas from the mixed absorption spectra has become the key point to restrict the precision of the optical detection method. In this paper, the ex-perimental platform for the absorption spectrum of vehicle exhaust components has been established. Based on the ultraviolet absorption spectra measured with the platform of exhaust gas NO & NO2, the concentration regression model for the two components has been established with weighted partial least squares regression (WPLS). Finally the each spectral characteristic information of NO & NO2 gas has been separated and the concentration of each corresponding component has been reversed successfully.
Nowadays the vehicle exhaust emissions have become one of the most important factors that affect the environmental air quality in our country. Therefore, it is urgent to strengthen the monitoring of vehicle exhaust emissions [
It becomes a key technology to measure the concentration of the vehicle exhaust components with the absorption spectra. But because of the overlap of gas absorption bands, how to separate the absorption information of each component gas from the mixed absorption spectra has become the key point to restrict the precision of the optical detection method [
The partial least squares regression is multivariate statistical analysis method which is widely used. It focuses on multivariate regression modeling of multiple variables. The technology for synthesis and screening of information is used in PLS modeling process, combined with the functions of multivariate linear regression analysis, typical correlation analysis and principal component analysis [
The spectral response matrix Y and its corresponding gas concentration matrix X are simultaneously decomposed into principal components, and new synthetic variables are obtained as follows:
where T & U are load matrixes of X & Y respectively, and P & Q are scoring matrixes of X & Y respectively. E & F are the errors introduced by using PLS method to fit X & Y respectively.
The regression model is built with PLS, which uses the characteristic spectral response matrix T and the characteristic concentration matrix U of which the vectors are orthogonal to each other.
The regression coefficient matrix B is as follows, which is also called the correlation matrix.
Therefore, the main steps of PLS include the principal component decomposition for the variable matrix Y and the corresponding independent variable matrix X, and the calculation of the correlation matrix B.
Although the PLS method has more advantages than the traditional multivariate regression method, there is still low efficiency when analyzing the absorption spectra of multi-component gas, and the accuracy of the regression results is affected by the noise and sample distribution [
Assume that Yc Є RM*K is the concentration matrix of the calibration set calculated by the PLS method, then the error of the recovery rate can be obtained as the following
where“./”represents the division between the corresponding elements of matrices. Ec Є RM*K represents the recovery rate errors of K organic matters in M calibration samples. If {r1, r2, …, rM} is composed of the maximum error of the recovery rate of every row in Ec, the Gauss weight corresponding to the maximum error of the recovery rate is set as follows.
where α is the step adjustment parameter and
where β is the step adjustment parameter and
where
1) Set initial vector u, calculate the weight w of Xcr,
2) calculate the weight c of Ycr,
3) If the convergence
4) Remove the calculated components from Xcr, Ycr, then
5) Return to Step 1, until all the components are extracted.
6) According to Equation (4), calculate the regression factor
7) If the convergence
8) calculate
The UV absorption cross-sections of NO and NO2 gas within the 180 nm - 400 nm band are shown in
As shown in
In order to avoid multicollinearity, the orthogonal principle is followed in the sample concentration design for NO & NO2. Samples of different concentration are designed as shown in
Then a series of designed NO or NO2 UV absorption spectra (200 nm - 440 nm) of different concentrations have been obtained with the platform, also with their mixture absorption spectra. The NO absorption spectra of different concentrations are shown in
Single NO2 | Single NO | Single NO | Mixed NO & NO2 | |
---|---|---|---|---|
608 | 308 | 2549 | 1022 | 0 |
547.2 | 277.2 | 2294.1 | 919.8 | 254.9 |
516.8 | 261.8 | 2166.65 | 868.7 | 382.35 |
486.4 | 246.4 | 2039.2 | 817.6 | 509.8 |
456 | 231 | 1911.75 | 766.5 | 637.25 |
425.6 | 215.6 | 1784.3 | 715.4 | 764.7 |
395.2 | 200.2 | 1656.85 | 664.3 | 892.15 |
364.8 | 184.8 | 1529.4 | 613.2 | 1019.6 |
334.4 | 169.4 | 1401.95 | 562.1 | 1147.05 |
304 | 154 | 1274.5 | 511 | 1274.5 |
273.6 | 138.6 | 1147.05 | 459.9 | 1401.95 |
243.2 | 123.2 | 1019.6 | 408.8 | 1529.4 |
212.8 | 107.8 | 892.15 | 357.7 | 1656.85 |
182.4 | 92.4 | 764.7 | 306.6 | 1784.3 |
152 | 77 | 637.25 | 255.5 | 1911.75 |
121.6 | 61.6 | 509.8 | 204.4 | 2039.2 |
91.2 | 46.2 | 382.35 | 153.3 | 2166.65 |
60.8 | 30.8 | 254.9 | 102.2 | 2294.1 |
Here, the concentration inversion of NO and NO2 components from the vehicle exhaust with ultraviolet absorption spectrum based on WPLS is actually a partial least squares regression problem with three independent variables and two dependent variables, as shown in
According to Steps 1-8 in 2.2, a data processing program has been compiled with MATLAB, and then the regression models have been established with the obtained spectral sample data from which one spectral data has been selected and taken out, then the concentration have been inversed by put the selected spectral data into the model. That’s the same with every concentration. Finally the experimental results are shown in Figures 4-9.
WPLS independent variable | X1-NO2 absorbance | X2-NO absorbance | X3-NO, NO2 Mixed absorbance | |
---|---|---|---|---|
WPLS dependent variable | Y1-NO concentration | Y2-NO2 concentration | ||
As seen from the above experimental results, using either the spectra of the individual components of NO or NO2 or mixed spectra of the two components or even all the individual and mixed spectra for the regression modeling and concentration inversion based on WPLS, the experimental results are all excellent.
The approximation between the inversion results and real sample concentration are all above 99.4%, of which the highest can reach 99.97%. So it can be concluded that with WPLS algorithm the components’ characteristics of the mixed spectral in which there’re overlapped absorption with NO & NO2 can be separated, and then each concentration of the samples can be inversed accurately.
In this experiment, It’s not considered that the modeling optimization [
Be aimed at the interference caused by spectral overlap absorption in the vehicle exhaust gas concentration detection with spectra method, the experimental platform for absorption spectrum detection of exhaust gas has been built. On the basis of measuring the ultraviolet absorption spectra of exhaust components NO and NO2, the weighted partial least squares regression (WPLS) algorithm has been used and then regression models of the components’ concentration have been established, finally each NO or NO2 concentration of the mixed gas samples has been inverted successfully. From the experimental results, under the condition without the original spectral denoising and WPLS modeling band optimization, the approximation of the concentration inversion results and the real samples can reach more than 99.4%.
The work is supported by the National Key Research and Development Program of China (2016YFC0201003) & the 863 National High Technology Research and Development Program of China (No. 2014AA06A503).
Zhang, K., Zhang, Y.J., You, K., Lu, Y.B., Tang, Q.X., He, Y., Liu, G.H., Fan, B.Q., Yu, D.Q. and Liu, W.Q. (2017) Study on the Concentration Inversion of NO & NO2 Gas from the Vehicle Exhaust Based on Weighted PLS. Optics and Photonics Journal, 7, 106-115. https://doi.org/10.4236/opj.2017.78B015