Abstract
It becomes a key technology to measure the concentration of the vehicle exhaust components with the transmission spectra. But in the conventional methods for noise reduction and baseline correction, such as wavelet transform, derivative, interpolation, polynomial fitting, and so forth, the basic functions of these algorithms, the number of decomposition layers, and the way to reconstruct the signal have to be adjusted according to the characteristics of different components in the transmission spectra. The parameter settings of the algorithms above are not transcendental, so with them, it is difficult to achieve the best noise reduction effect for the vehicle exhaust spectra which are sharp and drastic in the waveform. In this paper, an adaptive ensemble empirical mode decomposition (EEMD) denoising model based on a special normalized index optimization is proposed and used in the spectral noise reduction of vehicle exhaust NOX. It is shown with the experimental results that the method can effectively improve the accuracy of the spectral noise reduction and simplify the denoising process and its operation difficulty.
1. Introduction
With the increase of the motor vehicle quantity in China, the vehicle exhaust pollution becomes more and more serious. The continuous haze weather and exceeding of PM2.5 standard are all related to the vehicle emissions. So it is urgent to monitor and control the vehicle exhaust emissions [1]. At present, the method of using spectral information to retrieve the exhaust component concentration has become the mainstream technology for the vehicle exhaust detection, so it is very important to reduce noise of the vehicle exhaust transmission spectra.
The ultraviolet transmission spectra within 200–400 nm band are commonly used to analyze the concentration of the exhaust NOX components. However, there are mainly three kinds of noises in the ultraviolet spectra, which are the electronic thermal noise, the light source fluctuation, and the interference of external communication systems. The location, amplitude, energy and width information, and so forth of NOX spectral peaks are seriously affected by these noises. So it is necessary to denoise the NOX ultraviolet transmission spectra in order to obtain clear and reliable spectral data, which is of great importance for the further analysis and concentration inversion. There are many absorption peaks of small amplitude and low energy in the exhaust NOX spectra, of which the waveforms are sharp and drastic and their effective information frequency is high. When the traditional methods are used to reduce the spectral noise, the high frequency parts with the effective information often get lost, which result in the spectral peak shifting or its intensity changing. Therefore, it is necessary to study the noise reduction method suitable for the cross-mixed condition of the high frequency signal and noise.
2. Adaptive EEMD Denoising Algorithm
2.1. Normal EEMD Denoising Algorithm and Its Deficiency
Empirical mode decomposition (EMD) is a signal processing method proposed by Huang et al. in 1998 [2–4], with which one signal can be decomposed into a finite number of intrinsic mode functions (IMF). IMF can meet the global narrowband requirement and local zero-mean condition, but there exists mode mixing problems when it is used to decompose the signal [5, 6]. Therefore, the ensemble empirical mode decomposition (EEMD) method is proposed by Huang et al. [7], in which the Gauss white noise is added into the signal to be processed so as to provide enough extreme points for smoothing abnormal events, and then the IMF components obtained by multiple decompositions are overall averaged to overcome the mode mixing. At last, the Gauss white noise can be eliminated with the ensemble average process above.
There are two main steps in the EEMD decomposition. Step 1: Gauss white noises of equal length and random amplitudes are added into the signal to be processed, then the mixed signal is decomposed with EMD, after the above process is repeated K times; finally, the IMF component cik and the remainder rik are obtained. It is pointed out that the amplitude of white noises should follow the rule below: where e is the standard deviation of the original signal, which is the deviation between the signal and the reconstruction result with EMD a is the white noise amplitude. It can be drawn that when the amplitude of the white noise increases, the repeat number K of EMD decomposition should be increased to reduce the effect of noise on the decomposition results. When the signal to be processed is mainly consisting of high frequency components, the amplitude a should be smaller and vice versa [8]. And the noise amplitude will not affect the decomposition results, unless it is very small or large. Therefore, the EEMD processing results will not change too much with the different settings of one or several parameters, which means the EEMD method is adaptive and does not rely on the subjective intervention of human beings.
Step 2: IMF components are overall averaged as the following: where n is the number of EMD decomposition. In this paper, the vehicle exhaust NOX transmission spectra after EEMD decomposition have been reconstructed, and its error probability less than 10−9 is 99.2317%, which means that using EEMD to decompose the NOX transmission spectra is approximately complete. In the process of EMD or EEMD decomposition in which there exists no mode mixing, each IMF has different frequency components and the IMFs of high frequency are always the first to be screened. So the decomposition process is considered as multiple band-pass filtering, and then by constructing a low-pass filter, the noise reduction can be realized [6–8].
In the construction process of EMD or EEMD low-pass filter, the order of the reconstructed signal is an important parameter of the filter and the selection of which is crucial to the denoising accuracy. Usually, a posterior denoising performance index is used to determine the parameters, which requires the index to evaluate the denoising effect from respects of the spectral deformation degree and SNR, and so forth. However, when the signal and noise exist in the same IMF component simultaneously, it will be all reserved or filtered by the low-pass filter in EMD or EEMD process, which will lead to low noise reduction accuracy [9, 10]. In order to solve the problem mentioned above, a normalized evaluation index is designed in the paper, with which the method of cyclic decomposition and reconstruction is used to improve denoising accuracy of EEMD.
2.2. Design of the Normalized Optimization Index for EEMD Denoising
A new EEMD method based on a special normalized index optimization is proposed here, of which the global optimum of the normalized denoising index is used as the stopping condition of the reduction process, so the process does not need any parameter setting and can be completed automatically. The signal to noise ratio (SNR), standard error (SE), and correlation coefficient (R) are used for the index to evaluate the noise reduction effect. In order to express the comprehensive change of energy, shape, and position of the spectra after the noise reduction, the normalized index r is designed as follows: where SNR′ stands for the signal to noise ratio after the spectral noise reduction. The index r combines two aspects of spectral details and approximation information to evaluate the effect of noise reduction, and it can make sure that the indexes of the two aspects are negatively correlated, so the greater the value of r, the better [9].
3. Denoising Experiment and Analysis
3.1. Acquisition of NOX Transmission Spectra from the Vehicle Exhaust
As shown in Figure 1, the experimental platform with a gas mixing equipment for acquisition of NOX transmission spectra from the vehicle exhaust has been built, with its photo being shown in Figure 2(a). UV absorption cross-sections of NO and NO2 are shown in Figure 2(b). Then NO and NO2 UV transmission spectra (200 nm–440 nm) of different concentrations and absorption path have been obtained with the platform, also with their mixture transmission spectra. The transmission spectra of 16 ppm NO is shown in Figure 2(c), and the spectra of 25 ppm NO2 is shown in Figure 2(d).
(a) Photo of the experimental system with 100 cm gas chamber
(b) Absorption cross-sections of NO and NO2 in the near UV band
(c) NO-40 cm-16 ppm
(d) NO2-100 cm-25 ppm
With the obtained spectra, it can be drawn that the noise is obvious and it affects SNR seriously in the lower concentration measurement, which will be the accurate concentration inversion of NO and NO2 gas. So it is necessary to carry on the noise reduction before the concentration inversion.
3.2. Denoising Experiment Based on EEMD and Data Analysis
The noise reduction algorithm is designed with EEMD method being combined with the normalized index r, of which the denoising flow chart is shown in Figure 3.
Step 1: the spectral signal xi is decomposed with EEMD, and then n IMF components have been obtained (there is no special operation for the residual during denoising process, and the residual is recorded as IMFn).
Step 2: the low order component IMF1 with high frequency is removed, and then the spectral signals are reconstructed to form a new spectrum, which is recorded as xi+1.
Step 3: to calculate the indeces ri+1, xi, and xi+1 are put into the following formulas: where , , n is the amount of data in each spectrum. And then, SNR, SE, and R can be put into (4) to calculate the index ri+1.
Step 4: after the index ri+1 is calculated, if ri+1 > ri, it means that the normalized index has been optimized with the (i + 1)th denoising, so there is a possibility of decomposition, filtering, and reconstruction for the spectral signals once more; then, i = i + 1 is set and the whole denoising procedure returns to step 1. If ri+1 < ri, it means that the best EEMD optimal normalized index has been obtained with the ith denoising, the EEMD noise reduction process ends, and xi is the best result with NIO EEMD denoising, at last the signal xi is assigned to x′ ().
According to the algorithm and flow chart above, the EEMD Matlab procedure has been programmed, and then it is used for denoising of three NOX UV transmission spectra. The results are shown in Figure 4. SNR of the three spectra before and after denoising is compared in Table 1, and the NOX absorbance and inverted concentrations at their respective peaks are listed in Table 2. It can be drawn from the experimental results in the two tables that SNR of the transmission spectra have been improved after denoising, and the absorbance and inverted concentrations are closer to the theoretical value calculated with the experimental system parameters.
(a) NO2-100 cm-25 ppm
(b) NO2-100 cm-25 ppm
(c) NO2-300 ppm-NO-786 ppm-100 cm
Then EMD low-pass filter [5, 6], db3 wavelet decomposition [10], and NIO EEMD are used, respectively, for noise reduction of one NOX mixed transmission spectrum (NO2-300 ppm/NO-786 ppm/100 cm) to further verify the denoising effect of NIO EEMD method. As shown in Figure 5(b), EMD low-pass filtering method has been used for one decomposition, and then the first order IMF component has been removed, finally there still exists a lot of noise in the denoised spectrum, and the three NO absorption peaks in 200–230 nm band have a large deformation. The reason is that the EMD decomposition produces a mode mixing which has been filtered with the useful signals from the original spectrum. As shown in Figure 5(c), db3 wavelet basis with 5-layer decompositions and soft threshold method has been used to construct the wavelet model for filtering and denoising, finally a certain amount of noise is still left in the spectrum. At last, the noise reduction effect of adaptive NIO EEMD method is shown in Figure 5(d).
(a) Original
(b) EMD LPF
(c) Wavelet
(d) EEMD NIO
Denoising indexes of the three algorithms are shown in Table 3, where LPF stands for the low-pass filter and NIO indicates that the noise reduction method bases on normalized index optimization mentioned above. There are absorbance values and inverted concentrations of the same spectral with three denoising algorithms listed in Table 4. Compared with the original spectrum data, better denoising effect can be obtained adaptively with NIO EEMD method, due to which the calculation accuracy of the absorbance can be improved also with the retrieval precision of NOX gas concentrations. Meanwhile, the other two algorithms have strong dependence on parameter settings, and once the parameters are not set properly, the denoising effect will be affected obviously.
4. Conclusion
In this paper, the EEMD method is used to decompose the UV transmission spectra of NOX from vehicle exhaust; then, a normalized noise performance index has been constructed, according to the global extremum of which the cycle order of the EEMD decomposition on the transmission spectra can be determined adaptively. The parameters such as basis function, threshold value, and decomposition layer do not have to be set with this method, so that the noise reduction effect of NOX spectrum does not rely on whether the setting of parameters is appropriate. With the experimental results, it can be concluded that when using in the denoising of the NOX transmission spectra, the EEMD algorithm based on normalized index optimization is better than the EMD low-pass filter and the db3 wavelet decomposition algorithm in the same situation.
Conflicts of Interest
The authors declare that there are no conflicts of interest.
Acknowledgments
The work is supported by the National Key Research and Development Program of China (2016YFC0201003) and the 863 National High Technology Research and Development Program of China (no. 2014AA06A503).