Study on neural network algorithm for detecting respirable dust in photoacoustic cavity

With the rapid development of industrialization and urbanization in China, the problem of environmental pollution has become increasingly prominent. As one of the important pollutants, dust has seriously threatened people’s physical and mental health. In terms of prevention and treatment of occupational diseases, dust is the main inducing factor of pneumoconiosis, with an annual incidence of nearly 27 000 cases.¹ In the aspect of production safety, high concentration dust will cause dust explosion accidents under certain field conditions. Therefore, the problem of high-precision dust concentration detection needs to be solved.

In terms of dust concentration detection, the main methods for dust concentration detection at home and abroad include the weighing method,² β-ray method,³ charge induction method,⁴ light scattering method,⁵ light transmission method,⁶ ultrasonic method,⁷ etc. At present, the achievements are mainly focused on the detection accuracy, principles and methods, and practical applications. Yu et al.⁸ studied the influence of the incident laser wavelength, dust particle diameter, and dust particle refractive index on the scattered light intensity distribution and obtained the scattered light intensity curve of a single suspended dust particle under different characteristic parameters. Zhang et al.⁹ conducted a study on dust dynamic concentration distribution based on the “ultrasound-electricity” hybrid detection system and fusion model, providing a fast and accurate method for detecting dynamic and complex dust concentration. She et al.¹⁰ developed the dust detector and its concentration estimation method by using an advanced imager, and the measured data were in good agreement with the high-precision measuring instrument. Based on an LED array light source, Li and Sang¹¹ analyzed the performance of dust concentration-related photoelectric detection, which improved the reliability of dust concentration measurement results. The above measurement methods and research play an important role in the detection of dust. Compared with the above technologies, the photoacoustic spectroscopy technology has the advantages of continuous, reliable, low-cost, and real-time detection. Photoacoustic spectroscopy technology has been widely used in environmental atmospheric trace gas detection,¹² medical respiratory gas analysis,¹³ optical absorption characteristics of agricultural grains,¹⁴ and molecular spectroscopy.¹⁵ 

In the study of the neural network algorithm, Cheng et al.¹⁶ established a three-layer back propagation (BP) neural network model with multiple input factors to predict the ignition characteristics of hybrid coal, and the relative average error of the predicted ignition temperature was only 1.22%. Yu et al.¹⁷ applied the three-layer BP neural network model to the prediction of auto claim amount, providing a reference for the pricing and claim amount estimation of the insurance industry. Du et al.¹⁸ established a hospital drug management system model based on a genetic algorithm and BP neural network and applied it to the practice of the hospital drug inventory management to improve the efficiency of the hospital drug inventory management.

As a new dust detection technology, photoacoustic spectroscopy has the advantages of high sensitivity, high dynamic range, no wavelength selectivity, and it can directly measure particles in the natural suspension state. This paper focuses on the neural network algorithm to improve the detection accuracy of atmospheric respirable dust by the photoacoustic spectroscopy system. The structure of the traditional photoacoustic cavity was designed, the influence factors of the photoacoustic spectroscopy detection system for respirable dust were obtained, and the neural network algorithm was used for correction.

Photoacoustic spectroscopy technology is a detection method based on the photoacoustic effect. When the molecules or atoms of the measured object absorb a certain power of optical P₀ and form a heat source with periodic changes, the gas pressure in the measured cavity changes periodically and the sound signal is stimulated. Among them, the microphone used to detect the photoacoustic signal S_PA and the pool constant C_cell is regarded as the inherent property of the photoacoustic cavity, and its value can be systematically calibrated by an object with a known absorption cross section. Therefore, the absorption coefficient α_abs of a specific substance can be obtained by detecting the sound source,^19,20

The basic structure of the traditional photoacoustic cavity designed in this paper is shown in Fig. 1. As the core component, the resonator cavity adopts the longitudinal resonance mode of the first order. Under the excitation of its resonant frequency, better photoacoustic signals can be obtained.

In order to improve the photoacoustic response signal, the resonator cavity in the photoacoustic cavity was taken as the research object, and the gas medium in the resonator cavity was taken as the solution domain. A three-dimensional simulation model was established to simulate the acoustic visualization of the resonator cavity. In order to suppress the low frequency noise in the photoacoustic cavity, the length of the resonator cavity should not be too long in order to obtain a higher working frequency as far as possible, usually not less than 1 kHz. At the same time, in order to match the modulation of the laser in the photoacoustic system, the resonant frequency of the resonator cavity should be between 1 and 2 kHz. Therefore, the length of the resonator cavity is set between 85 and 120 mm. Several parameters of the length and radius of the resonator cavity were selected, respectively, for simulation analysis. Through numerical simulation technology, the acoustic visualization simulation cloud map of the resonator cavity with different structural parameters was obtained, as shown in Fig. 2. From the figure, it can be intuitively concluded that the acoustic characteristics of all kinds of resonator cavity were the same, with the middle of the resonator cavity as the maximum acoustic position, and the sound pressure gradually decreases along the axis toward both ends.

With other parameters unchanged and only the radius of the resonator cavity changed, the variation of the resonance frequency of the photoacoustic cell was simulated and analyzed, as shown in Fig. 3(a). As can be seen from the figure, the resonance frequency of the photoacoustic cell decreases first and then increases with the increase in the resonator cavity radius. The effect of the resonator cavity radius on the resonance frequency of the photoacoustic cell was weak. Furthermore, other parameters were kept unchanged and only the length of the resonator cavity was changed to simulate the variation of the resonance frequency of the photoacoustic cell, as shown in Fig. 3(b). It can be seen from the figure that the resonance frequency of the resonator cavity decreases with the increase in the length of the resonator cavity, and the length of the resonator cavity has a great influence on the resonance frequency of the photoacoustic cell. Through the simulation calculation of the acoustic resonance frequency, the first order acoustic resonance frequency of the resonator cavity can meet the requirements of 1–2 kHz. From the simulation effect of structural parameters, the length of the resonator cavity has a greater effect on the resonant frequency than the radius of the resonator cavity. The design of the resonator cavity should consider the volume factor, anti-interference ability, and processing conditions. If the length was too long, it was not easy to drill and polish at one time, and if the length was too short, it was not conducive to the acoustic performance of the photoacoustic cell. The radius of the resonator cavity should be slightly larger than the spot size of the beam, so considering the actual situation, the length parameter of the resonator cavity was designed as 120 mm and the inner diameter parameter was 8 mm. In order to reduce the noise caused by air flow and window absorption, the buffer cavity with the length half of the resonator cavity and the radius greater than three times of the resonator cavity was mostly used. Therefore, the length of the buffer cavity was 60 mm and the inner diameter was 25 mm.

In order to control noise and minimize the influence of background interference noise, buffer partition was designed in the buffer cavity to form a two-stage buffer air intake mode, as shown in Fig. 4. Figure 5 shows the acoustic simulation cloud image of the two-stage buffering mode (the fluid material in the cavity was set as nitrogen). According to the simulation results, the middle part of the resonator cavity was the maximum acoustic position, and the sound pressure value decreases along the axis toward both ends. The sound pressure values in the three cavities formed between the partitions or window segments are equal, and the closer to the two ends of the system, the lower the sound pressure values in the cavities. The simulation results showed that the buffer partition in the buffer cavity has little effect on the acoustic field distribution in the system, and the position and mode of acoustic acquisition need not be changed during the experimental measurement.

Based on the size of the traditional photoacoustic cavity obtained from simulation analysis, the photoacoustic spectroscopy measurement system for respirable dust was established, as shown in Fig. 6. The system mainly includes a 405 nm blue diode laser (Shanghai xi long, China, DL-405), photoacoustic cell, and signal acquisition system. The ambient atmosphere was controlled by a mass flow meter (Seven star Huachuang, China, CS200) and enters the photoacoustic cell (internal polished, aluminum cylindrical cavity) at a rate of 200 ml/min. The disturbance signal was collected by the microphone (Beijing prestige, China, MP201) and then sent to the lock-in amplifier through the preamplifier (MA221), which was collected and processed by the LabVIEW control program. At the same time, it was equipped with a sample gas system for calibration research. The time constant of the lock-in amplifier was 3 s, the sensitivity was 200 µV, the attenuation rate was 12 dB, and the service time was 1000 ms. Since dust has no obvious absorption peak, NO₂ gas with a known absorption coefficient was often used to calibrate the system. The effective absorption cross section of NO₂ can be obtained from the MPI Mainz database (Bogumil, 2003, 293 K). The central wavelength of the laser spectrum was 403.56 nm, and the corresponding NO₂ effective absorption cross section was 5.9485 × 10⁻¹⁹ cm²/mol.

Cavity ring-down spectroscopy is mainly based on the Lambert–Beer law. An optical resonator cavity (sealed with a high reflector at both ends) was used to increase its effective absorption path. When the incident light was coupled to the cavity, multiple reflections occur in the cavity and the light intensity signal after passing through the optical resonator cavity decays exponentially. According to the length of the optical resonator cavity d, the sample length Ls, the ring-down time τ, the background ring-down time τ₀, and the speed of light c, the relationship between the ring-down time and the extinction coefficient to be measured can be established. Extinction coefficient α_ext of a specific measured substance based on the cavity ring-down spectrum can be expressed as²¹ 

Figure 7 shows the cavity ring-down spectroscopy system developed by the research group. The cavity ring-down spectroscopy system mainly includes a 405 nm blue light diode laser (Shanghai xi long, China, DL-405), optical resonator (an inner diameter of 8 mm and a length of 780 mm), and signal processing system. A 5 µm filter membrane was used to filter the interference of large particles on the sampling line. The temperature and humidity meter (AZ8808) was connected in parallel through a tee pipe to collect the ambient temperature and humidity parameters. A small air extraction pump (N83KNE) was used for rear air extraction to make the ambient air enter the cavity ring-down system after passing through the buffer pipeline.

From September 18, 2019 to September 22, 2019, the photoacoustic spectroscopy respirable dust measurement system was used to measure the ambient atmospheric dust in Dongpu reservoir (Google: latitude 31°89′, longitude 117°20′) of Hefei City, Anhui Province. The object of the measurement was the respirable dust in urban air, and the particle size was less than 5 μm. The diode laser cavity ring-down spectroscopy system developed by the research group was selected as the reference instrument. The diode laser band was 405 nm, and the detection limit of the system was 6.6 × 10⁻¹¹. The system synchronously measures the concentration of respirable dust in urban air with the respirable dust measurement system by photoacoustic spectroscopy, and the measurement results are shown in Fig. 8(a). After the respirable dust measurement system by photoacoustic spectroscopy passes the preliminary measurement background, the system automatically records the photoacoustic signal every 1 s (the time resolution was 1 s), and the measurement results after averaging 60 s are shown as the red line in Fig. 8(a). The measured results of the diode laser cavity ring-down spectroscopy system are shown in Fig. 8(a), black line. Figure 8(b) shows the measurement correlation between the photoacoustic spectroscopy measurement respirable dust system and the cavity ring-down spectroscopy system.

As can be seen from the figure, the correlation coefficient R² between the respirable dust system measured by photoacoustic spectroscopy and the cavity ring-down spectroscopy system was 0.681, the slope after linear fitting was about 0.767 ± 0.007, and the intercept was about 1.527 ± 0.043. Generally speaking, the measured values of the two systems change in the same trend, but the value difference was large, and the correlation was poor. Because the experimental site was located next to the reservoir, the temperature and humidity factors have a certain impact on the photoacoustic spectroscopy respirable dust measurement system, while the cavity ring-down spectroscopy system itself has a temperature and humidity compensation system. The above reasons are the main reasons for the poor correlation between the two systems, so the neural network algorithm correction analysis was carried out for the photoacoustic spectroscopy respirable dust measurement system.

The neural network model correction method is mainly based on the neuron model, which completes the data correction through the self-learning of the model. The three-layer BP neural network algorithm was selected in this paper. In the parameters of the three-layer BP neural network, the number of hidden layer nodes will play a decisive role in the algorithm performance. The commonly used design methods were based on empirical formulas,

In the above formula, l is the number of nodes in the hidden layer, n is the number of input nodes, m is the number of output nodes, and a is a constant between 1 and 10. In this paper, n = 3 and m = 1, and the empirical value range of l can be obtained from 3 to 12. Due to the differences among the influencing factors, the optimal number of nodes was often near the empirical value, so it needs to be determined comprehensively by combining the empirical formula and multiple tests. Based on this, the average absolute error between the reference value and the output value of the model was adopted in this paper as the assessment index for the node selection of the hidden layer. The specific analysis is shown in Table I, and the detailed trend is shown in Fig. 9. As can be seen from the chart, there was no optimal value of nodes 3–12 set according to the empirical formula. Therefore, the average absolute error obtained from the extended analysis of the number of nodes in the hidden layer as shown in the red box in the figure. It can be seen from the analysis that when the number of hidden layers was between 13 and 17, the model has a better effect and the average absolute error was about 0.800.

In order to select the best number of hidden layer nodes, the model performance was analyzed in the range of hidden layer nodes between 13 and 17, as shown in Fig. 10. Specific performance indices are shown in Table II.

According to the above analysis, when the number of hidden layer nodes was 13 and 17, the performance of the model was better. When selecting the number of hidden layer nodes, we need to consider the number of iterations, mean square error, and mean absolute error. Compared with 17, 15 has a smaller number of iterations. Although the mean square error has a little loss, the average absolute error was smaller than 17. Therefore, the number of hidden layer nodes was set to 15.

In order to make the program run repeatable, the same random seed should be used each time for weight and threshold initialization. At the same time, during the simulation of the BP neural network model, the input sample data were divided into three parts: training sample, determined sample, and test sample, accounting for 60%, 20%, and 20%, respectively. The comparison and correlation of the corresponding neural network model simulation results are shown in Fig. 11.

The abscissa of Fig. 11 was the normalized output, the ordinate was the sample output, and the abscissa and ordinate were all relative quantities without unit. By comparing the simulation results, it can be seen that the linearity between the output value of the model and the reference measurement value was very high, with a slope of 0.96. The training sample was the first 60% of the sample, and the training output results are shown in Fig. 11(a). The correlation R was 0.980, R² was 0.961, and the intercept was 0.011. The determined sample was the middle 20% of the sample, and the determined output results are shown in Fig. 11(b). The correlation R was 0.980, R² was 0.961, and the intercept was 0.011. The test sample was the last 20% of the sample, and the test output results are shown in Fig. 11(c). The correlation R was 0.982, R² was 0.964, and the intercept was 0.009. Finally, the whole sample was taken as the object for testing, and the test results are shown in Fig. 11(d). The correlation R was 0.981, R² was 0.962, and the intercept was 0.011.

This paper aims to improve the measurement accuracy of respirable dust by a photoacoustic spectroscopy system. A photoacoustic spectroscopy measurement system for respirable dust based on the traditional photoacoustic cavity was designed, and the system accuracy research based on neural network algorithm was carried out. The specific conclusions are as follows:

1. A system for measuring respirable dust by photoacoustic spectroscopy was designed. When the photoacoustic response value was affected by temperature and humidity, the photoacoustic response value correction of the three-layer BP neural network algorithm was carried out. The correction results showed that the output value of the neural network model was consistent with the reference true value: the slope was more than 0.96. It can be seen that the neural network algorithm has high precision and good adaptability.

2. The photoacoustic response value of the photoacoustic spectroscopy system was easily affected by temperature and humidity, so the accuracy of the system should be corrected before field test. The research of this paper shows that the neural network algorithm can effectively improve the detection accuracy of respirable dust by the photoacoustic spectroscopy system, reduce the detection error, and meet the high-precision detection of respirable dust by the system.

This work was supported by the Open Foundation of State Key Laboratory of Coal Resources in Western China of Xi’an University of Science and Technology (Grant No. SKLCRKF20-14) and the Research and Development Project of Wuhu Research Institute of Anhui University of Science and Technology (Grant No. ALW2020YF17) and theMajor Scientific Research Project of Anhui Universities [No. KJ2021ZD (Huawei Jin)].

The authors have no conflicts to disclose.

The data that support the findings of this study are available within the article.