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Abstract
Particulate matter has adverse effects on the environment and human health, thus emission monitoring of particulate matter is essential for environment and human health protection. Optical methods are popular for on-line particulate matter emission monitoring due to their low cost, high sensitivity and easy maintainability. However, the measurement accuracy is susceptible to the particle size distribution of the particulate matter. To resolve this problem, a new optical method using multi-channel scattering signals and a proof-of-concept prototype sensor are proposed in this paper. According to multi-channel scattering signals, which reflect the change of particle size distribution, the prototype sensor adaptively sets the mass scattering coefficient to improve the mass concentration measurement accuracy. Compared with the state-of-the-art optical technologies, simulation results show that the relative standard deviation was reduced from 242% to 4% by our method. In the tests of our prototype sensor, the maximum relative measurement errors are 10% for di-ethylhexyl-sebacat (DEHS) monodisperse aerosols and 11% for coal smoke. Given that it is low cost, highly sensitive and easy to maintain, the new method has significant potential for precise measurement of particulate matter in mobile or stationary pollution monitoring applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Particulate matter (PM) has drawn extensive attention due to its adverse effects on environment and human health. Recent reports from Harvard University and Germany indicate that the loss of life as a result of atmospheric pollutants is approximately 8 million people per year. Thus, methods for reliably monitoring these PM are of critical importance [1–5]. Large-scale air pollution studies have revealed that the mass concentration of PM was positively related to the mortality [6–8]. It is essential to monitor the mass concentration of PM emitted from the stationary sources, such as thermal power plants, utility boilers, and fluidized beds for semi-dry desulfurization and so on. The manual gravimetric method is the standard method for aerosol mass concentration measurement. It needs several days for sampling and analysis procedure, which is labor-consuming and expensive [9]. Therefore, several technologies are developed for automatic particulate monitoring. The commercial instruments are mainly designed based on tapered element oscillating microbalances (TEOM) or Beta-attenuation technologies [10,11]. These automatic monitoring instruments are very expensive and need hours to collect the particles for each measurement [12]. Furthermore, these instruments require periodic replacement of the particle collection filters every 2-3 weeks, which significantly shortens the maintenance period [13]. Recently, several new methods are developed for particle analysis. Thermal optical methods provide nearly real time measurements of filter sample data [14]. Light absorption methods, photoacoustic methods, and laser-induced incandescence methods provide fast measurements of soot volume fraction with high resolution and accuracy down to low concentrations [15,16]. However, these methods are not suitable for commercial application due to high cost and poor maintainability.
Compared with the monitoring technologies mentioned above, light scattering methods provide highly-sensitive and rapid measurement of PM mass concentration. Meanwhile, as a non-contact measurement, the light scattering methods do not need particle collection filters, and can effectively extend the maintenance cycle to several months. However, the usage of light scattering methods is limited by the measurement accuracy. Existing optical light scattering methods adopt a linear model to calculate the PM mass concentration from the light signal, but the conversion coefficient is susceptible to the physical properties of the PM, especially the particle size distribution [17–19]. Due to the variation of combustion condition and collection efficiency of the dust removing equipment, the particle size distribution of the PM eventually released into the atmosphere will be different. Our simulation results in Section 3.1 show that the expected measurement error of light scattering based technology reaches to 454% owing to the change of particle size distribution. As a compromise, Thermo Fisher corporation develops a hybrid particulate matter continuous emission monitoring system (PM-CEMS) Model 3880i combining light scattering technology for on-line monitoring and TEOM technology for periodical calibration [20]. Comparing with the instruments using single measurement technology, this kind of hybrid instrument is even more expensive and also requires frequent maintenance.
According to Mie theory, the light scattering signals contain the information of mass concentration and particle size distribution. Several methods have been developed to improve the mass concentration measurement accuracy only using optical signals. Meng Jiang et.al established a correction model of PM mass concentration measurement according to the mass media diameter, which is derived from the light extinction and scattering signals [21]. Li Wang et.al demonstrated a spectral light extinction method to measure the concentration and particle size distribution [22]. However, the light extinction method usually needs a long light path to ensure adequate sensitivity. Ring-down is an effective approach to reduce the size of the instruments and improves the measurement sensitivity by folding the optical path. To further simplify the structure and reduce the size of the sensor, the light scattering method is adopted. In our previous work, multi-wavelength technology with empirically selected wavelengths is proposed to measure the aerosol mass concentration and estimate the particle size distribution [23]. Dong Chen proposed a laboratory analysis method using a fixed detector and a rotating detector to obtain mass concentration and particle size respectively [24]. It implies that the light scattering signals at different observing angles also contain the information of mass concentration and particle size distribution.
In this work, a new method is proposed to improve the PM mass concentration measurement accuracy. Particle size distribution tracking technology is developed using multi-channel scattering signals with optimized wavelengths and observing angles. Instead of a preset constant value, the mass scattering coefficient is adaptively set to reduce the measurement errors caused by the change of particle size distribution. A proof-of-concept prototype sensor with 3 optimized light scattering channels is designed to verify the method proposed in this paper, which has a simple optical structure and only a few optical components. The experimental results of the prototype sensor show that our sensor is very sensitive and can precisely measure the mass concentration of DEHS aerosols and coal smoke.
The contribution of this study are as follows:
- • We proposed a non-linear model to measure the aerosol mass concentration via optical signals, where the mass scattering coefficient is adaptively set with the change of particle size distribution.
- • We developed a particle size distribution tracking technology using multi-channel scattering signals, where the optical parameters (number of measurement channel, wavelengths and observing angles) are comprehensively optimized to minimize the tracking error.
- • We designed a proof-of-concept sensor, which is highly-sensitive, low-cost and easy to maintain. The simulation and experimental results show that our sensor can precisely measure the mass concentration of PM with different particle size distributions.
The following paper is organized into four sections: Section 2 describes the sensing method of PM mass concentration with adaptively adjusted mass scattering coefficient using multi-channel scattering signals. Section 3 shows experimental results of simulation, DEHS monodisperse aerosols and coal smoke. Section 4 concludes the whole paper.
2. Methods
2.1 Existing linear model for particulate matter mass concentration measurement
The PM mass concentration CM is proportional to the volume concentration CV, where the mass density ρ is a constant value obtained by laboratory calibration. Thus CM can be described by the particle size distribution f(x):
where CN is the PM number concentration, x is the particle diameter. The mass concentration can be obtained by light scattering technologies. As illustrated by Van de Hulst et. al. [25–27], the scattering light can be described by Mie scattering theory, where the particles are considered as sphere or optical equivalent sphere. The scattering light intensity P is also related to the particle size distribution: where q(x, m, λ, θ) describes the light intensity scattered by a single particle with diameter x based on Mie theory, m is the refractive index, λ is the wavelength of incident light, θ is the observing angle. The channel coefficient K is used to describe the systematic factors that would affect the measurement of scattering light intensity P, such as the incident light intensity, the volume of sampling cross section, the amplification coefficient of the amplifier, the response sensitivity of the photodiode, and so on.To measure the PM mass concentration, existing PM-CEMS adopts a linear conversion mode with a preset empirical mass scattering coefficient T:
As discussed above, Eq. (3) holds only if q(x, m, λ, θ) = πx3/6 T. However, as shown in Fig. 1(a), the scattering light intensity per volume concentration πx3/6q(x, m, λ, θ) is not constant with the change of the particle size. Thus, the simplified linear model Eq. (3) will cause mass concentration measurement errors. As an example shown in Fig. 1(b), when the scattering light intensities are consistent, the mass concentration of the aerosol sample B with bigger particle size reaches up to 3.56 times that of the aerosol sample A with smaller particle size. Since the mass scattering coefficient is a constant value in the linear model, existing PM-CEMS may fail to measure the mass concentration correctly when the PM size distribution changes. Specifically, the mass concentration of the small particle size aerosol will be overestimated, while that of the big particle size aerosol will be underestimated.
Fig. 1. The mass concentration measurement using the existing linear model will cause errors due to the variation of mass scattering coefficient. (a) The relative volume concentration per unit scattering intensity of a single particle with the change of the particle size. (b) The mass concentration of aerosols with different particle size distribution when the scattering light intensities are consistent.
2.2 Non-linear model with adaptively adjusted mass scattering coefficient
As discussed above, the mass scattering coefficient T is related to the particle size distribution f(x) rather than a constant value, thus Eq. (3) is rewritten as:
As to PM emitted from stationary sources, the particle size distribution can be described by the lognormal distribution model [28,29]:
On the other hand, as illustrated by Eq. (2), the scattering light intensity P is also affected by the particle size distribution f[μ, σ](x). With only one measurement channel, existing PM-CEMS can only estimate the concentration via the linear model, while no information of particle size distribution can be obtained. To eliminate the effect of concentration, we use the ratio vector R(μ, σ) to track the change of particle size distribution, where the ith element Ri(μ, σ) is defined as the ratio of the scattering signals Pi with optical parameter set [λi, θi] to the basic scattering signal PB with [λB, θB]:
Thus, the non-linear model from scattering signals to PM mass concentration CM is proposed as:
As discussed above, the flow chart of mass concentration sensing method with multi-channel scattering signals is shown in Fig. 2. By measuring the scattering signals set P = {PB, P1, …, Pi}, our method calculates the ratio vector R = {R1, R2 …, Ri} to track the change of particle size distribution, and then adaptively set the mass scattering coefficient T by Eq. (7). Thus, the mass concentration of aerosol samples with different particle size distributions can be precisely measured according to Eq. (8).
Fig. 2. The flow chart of dynamically adjusted particle mass concentration sensing method using the non-linear model.
2.3 Optical parameters optimization for particle size distribution tracking technology
The scattering ratio vector R(μ, σ) needs sufficient information to track the change of particle size distribution. Otherwise, measurement error will be introduced when R(μ, σ) of different particle size distributions are too similar to be differentiated. Specifically, the aerosol samples [μj, σj] and [μk, σk] are considered to be differentiable if
As described by Eq. (9), if the ith PM sample is distinguishable from all of the other PM samples, our non-linear model uses the practical mass scattering coefficient of ith PM sample TGTi as the mass scattering coefficient of the prototype sensor. Otherwise, the PM samples which cannot be distinguished from the ith PM sample make up an undistinguishable group [μS, σS] (including the ith PM sample). The mass scattering coefficients of all undistinguishable PM samples TS are the potential output of G(R(μi, σi)). As a compromise, Tavg is defined as the average values of all mass scattering coefficient of PM samples in [μS, σS] according to Eq. (10).
In order to minimize the measurement error, the optical parameter set [λ, $\boldsymbol{\theta}$] of the optical system are optimized according to Eq. (12).
3. Typographical results and discussion
3.1 Optimum optical parameters of the particulate matter mass concentration monitoring system
The optical parameter set [λ, θ] is optimized by Eq. (12) according to the properties of PM. As a typical aerosol pollutant, the coal smoke emitted from the thermoelectricity power plants are investigated. With the help of dust removal equipment, particles eventually emitted from the stationary air pollution sources usually are smaller than 10 μm [30–32], thus the particle size range is set to 100 nm to 10000 nm with an increment of 10 nm in simulation. Previous studies [21,33–35] indicate that the typical range of μ and σ is 200 nm - 2500 nm and 1.5 - 2.0, respectively. Since the wavelengths of 450 nm, 650 nm and 950 nm are very close, the corresponding refractive indices are considered as the same. The particles are supposed to be uniformly mixed or consist of single substance, thus the refractive index of coal smoke is set to 1.7 + 0.1i. The parameters of the coal smoke are summarized in Table 1.
Table 1. Parameters of the particulate matter emitted from the stationary sources
On the other hand, the design of PM monitoring system is limited by the availability of the optical components and mechanical structure. The wavelengths of the incident light are selected from 450 nm, 650 nm, and 950 nm in consideration of cost. Due to the limitation of mechanical design and the interference caused by the stray light, the observing angle is restricted from 40° to 140° with an increment of 5°. Meanwhile, the discrimination threshold Dt is selected to be 5% in the simulation, which is fair enough to cover the systematic measurement errors of the scattering light.
According to the ranges of optical parameters discussed above and PM samples listed in Table 1, [λ, $\boldsymbol{\theta}$] is optimized by Eq. (12) with traversal algorithm. As the optimum simulation results shown in Table 2, RSDm is reduced with increasing number of measurement channels.
Table 2. Expected accuracy of the PM mass concentration by multi-channel scattering signals.
For further illustrating the mechanism of the non-linear conversion model, the adaptive mass scattering coefficient and relative error of each aerosol sample are shown in Fig. 3, where TGT and Tavg are normalized by the maximum value of TGT and the relative error REM is defined as:
Fig. 3. The reconstructed conversion factor T and expected measurement error of mass concentration with different measurement channels in simulation experiment. (a) Normalized TGT verses Tavg with 1 measurement channel. (b) REM with 1 measurement channel. (c) Normalized TGT verses Tavg with 2 measurement channels. (d) REM with 2 measurement channels. (e) Normalized TGT verses Tavg with 3 measurement channels. (f) REM with 3 measurement channels.
As illustrated by Eq (13), REM is defined as the relative error of the mass concentration and can be simplified as the function of TGT and Tavg.
As the linear model in existing PM-CEMS (n=1) illustrated by Fig. 3(a) the particle size distribution cannot be tracked. Therefore, the mass scattering coefficient of each aerosol sample is the average mass scattering coefficient of all aerosol samples according to Eq. (10), where the relative measurement error ranges from −85% to 454%. With an additional measurement channel (n = 2) in Fig. 3(b), the scattering ratio vector is calculated to estimate the particle size distribution and adaptively set the mass scattering coefficient according to Eq. (7). The expected measurement error is significantly reduced by non-linear model with relative measurement error from −37% to 71%. It is worth noting that the measurement accuracy changes with the standard deviation σ, since 2 channels cannot provide sufficient information to estimate μ and σ simultaneously. Therefore, 3 measurement channels in Fig. 3(c) further reduce the measurement error, where the relative error ranges from −12% to 19%. As illustrated in Table 2, more scattering light channels (n>3) further reduce the measurement error slightly, but also increase the system complexity. In consideration of measurement accuracy and structural complexity, the mass concentration monitoring device with 3 measurement channels reaches a proper balance between performances and costs, where the optimum parameter sets are [950 nm - 40°, 950 nm 140°, 450 nm - 135°].
According to the simulation optimization results, we design the proof-of-concept prototype sensor as shown in Fig. 4. Compared with a light extinction method, the optical path of light scattering method is very short. Hence, the structure of the prototype sensor is simple and small with a height 70 mm and a diameter 80 mm. A 450 nm laser and a 950 nm laser are adopted as the light sources, where the polarization angle of each laser is 45° and the power is 5 mW, (More details of polarization angle are discussed in Section 2 of Supplement 1). The collimated incident lights travel through the aerosol sample and then are absorbed by the light traps with absorptive filters. The particles are considered to be evenly distributed in the sampling cross section. Thus, the intensities of the scattering lights are affected by the total light intensity and unaffected by the light intensity distributions of the incident lights. Two photodiodes are used to receive the scattering light signals at the specific observing angles. With limited light collecting aperture and small half-power angle of the PD, the view scopes of scattering light receivers are considered to be collimated as well (More design details of the prototype sensor can be found in Section 3 and 4 of Supplement 1). The integral amplify circuits and 16-bit Analog-Digital converters are adopted to provide highly sensitive measurement. In order to keep the sample flow rate constant, isokinetic sampling structures are adopted in the design of inlet pipe and outlet pipe. Our sensor provides real-time, on-line and non-contact measurement of PM and extends the maintenance period without using particle collection filter.
Fig. 4. The overall structure of the proof-of-concept prototype sensor. (a) and (b) are the 3D mechanical design of the prototype sensor. (c) and (d) are the pictures of the prototype sensor. 1. 450 nm laser, 2. PD1, 3. 950 nm laser, 4. 450 nm light trap, 5. 950 nm light trap, 6. PD2, 7. Flue, 8. Inlet, 9. Outlet.
3.2 Simulation experiments of particulate matter with random particle size distribution
A simulation experiment using 1000 random-generated particle size distributions are carried out to evaluate the performance of our prototype sensor. The ranges of the simulation parameters are consistent with those listed in Table 1, while the increment strides are not limited. Specifically, the count median diameter μ is random generated from 200 nm to 2500 nm and the geometric standard deviation σ is random generated from 1.5 to 2.0. The scattering ratio vectors of these simulation sample are calculated according to Mie theory, and thus the mass scattering coefficients are obtained.
As the simulation results shown in Fig. 5, the mass scattering coefficient is adaptively set with the change of particle size distribution. The relative deviation of the mass concentration ranges from –14% to 21% and corresponding relative standard error is 4%. It implies that the parameter intervals in Table 1 are appropriate and the non-linear model is suitable for any aerosol sample within the parameter range.
Fig. 5. The reconstructed conversion factor T and expected mass concentration measurement error of our prototype sensor to 1000 simulation aerosol pollutants with random particle size distributions. (a) Normalized TGT verses Tavg of our prototype sensor. (b) REM of our prototype sensor.
3.3 Laboratory experiments of monodisperse DEHS aerosol samples and coal smoke
A laboratory validation measurements were conducted to measure the monodisperse DEHS aerosol samples with different particle sizes. As the experimental platform shown in Fig. 6, the aerosols samples are generated by the monodisperse aerosol generator (MAG, TSI MAG-3475), and then pumped into the dilution chamber for testing. Meanwhile, as the reference instruments, scanning mobility particle sizer (SMPS, TSI SMPS-3938) and the aerodynamic particle sizer (APS, TSI APS-3321) are used to measure the particle size distributions. With the knowledge of particle size given by the reference instruments and the refractive index of DEHS 1.45, the channel coefficients K are calibrated according to the measurement results and simulation results.
Fig. 6. The aerosol testing and particle sizing platform. (a)The block diagram of aerosols testing platform. (b) The picture of aerosols testing platform.
As the experimental results shown in Fig. 7(a) and (b), the output of existing linear model is 328% higher than the mass concentration given by the SMPS. Meanwhile, our prototype sensor can significantly improve the mass concentration measurement accuracy by adaptively set the mass scattering coefficient with the change of particle size distribution, where the results are in agreement to the SMPS within 10%.
Fig. 7. Experimental results of single channel system, our prototype sensor and the reference instruments. The mass concentrations (a) and measurement deviation (b) of DEHS aerosol samples. The measurement results of mass concentrations (c) and measurement deviation (d) of coal smoke.
As one of the major air pollutants, coal smoke are also tested by our prototype sensor. The experiments are repeated multiple times with different fuel quantities and aging times to obtain the coal smoke with different particle size distributions. As shown in Fig. 7(c) and (d), the deviation of the linear model to coal smoke ranges from 81% to 131%, while that of our prototype sensor is constrained within −9% to 11%. Correspondingly, the sensitivity of our sensor varies from 0.003 mg/m3 to 0.082 mg/m3 with the change of the mass scattering coefficient. Thus, our sensor can provide highly sensitive and precise measurement of coal smoke mass concentration.
4. Conclusion
In this paper, we propose a new optical method to precisely measure the mass concentration of PM. Compared with the state of art PM-CEMS using the linear model, our method adopts a non-linear model to adaptively set the mass scattering coefficient with the change of particle size distribution using the multi-channel scattering technology. A proof-of-concept prototype sensor with optimized parameter sets [950 nm - 40°, 950 nm - 140°, 450 nm - 135°] was designed, which is simple-structure, low-cost and easy to maintain. According to the tests of the monodisperse DEHS aerosol samples and the coal smoke, our prototype sensor has significantly improved the mass concentration measurement accuracy in comparison with existing PM-CEMS using linear model. This new optical method can provide highly-sensitive, on-line and precise measurement of the PM mass concentration for both stationary and mobile aerosol pollution monitoring applications.
Funding
National Natural Science Foundation of China (61873322, 6210011211); Science Technology Foundation of Ministry of Emergency Management of China (2020XFZD13); Fundamental Research Funds for the Central Universities of Huazhong University of Science and Technology (2020kfyXJJS102).
Acknowledgments
We thank Dr. Zheng Dou for the help in the design of mechanical structure and electronic system.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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