PMT Fluorescence Signal Denoising Processing Based on Wavelet Transform and BP Neural Network

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This study is aimed at the detection of sulfur dioxide concentration in the real environment. Due to the vast territory of China and the large temperature difference span between the north and the south, the current sulfur dioxide detection devices find it difficult to meet the requirements of portability, low-cost delivery, and temperature adaptability. A reliable real-time monitoring device and detection algorithm for sulfur dioxide concentration using PMT are proposed.

Abstract

Air is the environmental foundation for human life and production, and its composition changes are closely related to human activities. Sulfur dioxide (SO₂) is one of the main atmospheric pollutants, mainly derived from the combustion of fossil fuels. But SO₂ is a trace gas in the atmosphere, and its concentration may be less than one part per billion (ppb). This paper is based on the principle of photoluminescence and uses a photomultiplier tube (PMT) as a photoelectric converter to develop a device for real-time detection of SO₂ concentration in the atmosphere. This paper focuses on the impact of noise interference on weak electrical signals and uses wavelet transform to denoise the signals. At the same time, considering that the photoelectric system is susceptible to temperature changes, a multi parameter fitting model is constructed, and a BP neural network is used to further process the signal, separating the real data from the original data. Finally, a high-precision and wide-range trace level sulfur dioxide concentration detection device and algorithm were obtained.

1. Introduction

With the rapid development of modern industry, the harmful gases produced in chemical industry production have attracted people’s attention. Among them, sulfur dioxide is the main component that causes sulfuric acid rain. Usually, based on different detection principles and implementation methods, gas detection techniques can be divided into two categories: optical detection methods and non-optical detection methods. The development and application of non-optical detection methods occurred earlier; they directly detect and quantitatively analyze the measured gas by detecting the physical and chemical reactions between substances. There exist electrochemical methods, chemical fluorescence methods, gas chromatography, and mass spectrometry methods. However, the above-mentioned detection methods often fail to meet the requirements of real-time monitoring of air pollution and harsh environmental conditions in some application scenarios due to poor sensitivity, selectivity, and linearity, as well as long measurement times and the need for offline detection.

In recent years, optical-based trace gas detection methods have made significant progress. According to different detection principles, absorption spectroscopy is mainly divided into direct absorption spectroscopy technology and indirect absorption spectroscopy technology. There are various types of direct absorption spectroscopy techniques, and there are many mature ones that have been studied and applied, such as tunable diode laser absorption spectroscopy (TDLAS) [1,2], cavity ring down absorption spectroscopy (CRDS) [3,4], and cavity enhancement technology [5,6]. Typical indirect absorption spectroscopy techniques include fluorescence spectroscopy [7], photothermal spectroscopy (PTS) [8,9,10], and photoacoustic spectroscopy (PAS).

The ultraviolet fluorescence method based on the principle of photoluminescence has become the mainstream solution due to its advantages of high accuracy, high reliability, and no other pollution. Regarding UV fluorescence detection technology for sulfur dioxide gas concentration, Hideo Okabe analyzed and studied the relationship between excitation wavelength and fluorescence intensity in the spectral range of 200 nm–230 nm. The experiment showed that under appropriate excitation wavelength, the fluorescence intensity detected by the detector can be used to measure the content of sulfur dioxide in the gas. This experiment also became the basic experiment for sulfur dioxide ultraviolet fluorescence detection, and it was later verified through experimental methods that 213.8 nm is the optimal excitation wavelength for detecting sulfur dioxide fluorescence [11]. Afterwards, Bradshaw first used an Nd: YAG laser to induce fluorescence in sulfur dioxide [12]. G. Somesfalean et al. achieved a detection sensitivity of 20 ppm for SO₂ gas using a UV diode laser [13]. Yutaka Matsumi used a broadband optical parametric oscillator to generate double frequency light in a laser-induced fluorophore, achieving a detection limit of 5 ppt for SO₂ in the instrument [14]. However, due to the extremely low content of sulfur dioxide gas in the air, the excited fluorescence signal was very weak. Meanwhile, the process of photoelectric signal detection is inevitably affected by temperature drift [15,16] and electronic noise, which poses high requirements for the acquisition circuit and subsequent data processing. Therefore, it is of great significance to develop new gas detection technologies and methods with high sensitivity, good selectivity, high detection efficiency, and real-time online monitoring. This paper achieves the effective capture and amplification of weak fluorescence signals by combining appropriate optical paths and acquisition circuits. At the same time, wavelet transform [17] is used to denoise the PMT signal, and a BP neural network [18] is used to process the temperature drift of PMT. After verification, it is found the detection device [19] has a high accuracy and strong anti-interference ability.

2. Detection System Section

2.1. Optical Path Section

Firstly, based on the principle of photoluminescence, sulfur dioxide molecules are irradiated by ultraviolet light with a wavelength of 200 nm–220 nm to produce excited sulfur dioxide molecules, which emit fluorescence with a wavelength of 240 nm–420 nm during their return to the ground state. Within a certain concentration range, the fluorescence intensity is directly proportional to the concentration of sulfur dioxide in the sample air. The optical path and assembly diagram of the detection equipment are shown in Figure 1.

The excitation light source selected is the L12745-01 pulse xenon lamp [20] from Hamamatsu Photonics Co., Ltd. in Iwata City, Japan. It has a rated power of 20 W and can provide spectra in the 185 nm–2500 nm wavelength range. The duration of a single excitation signal is about 5 microseconds.

In order to obtain the required wavelength range of ultraviolet light for the experiment and reduce the interference of impurity light, four reflective bandpass filters are placed on the excitation light path, with a wavelength range of 209 nm–219 nm [21], the incident angle is 45°. Reflective filters have a stronger retention effect on the required spectral intensity than transmissive filters, which can increase the proportion of spectral intensity required and reduce interference from impurity light. Afterwards, through the combination of multiple positive lens, the light entering the reaction chamber is concentrated directly below the PMT, which can obtain the strongest fluorescence signal. In addition, a conical structure needs to be designed at the rear end of the chamber, with the inner side sprayed with absorbing material. The purpose of doing so is to absorb the light entering the chamber as much as possible, avoid diffuse reflection in the chamber, and be received by PMT again, which will reduce the proportion of fluorescence signal.

The photoelectric converter selected is the R11558 photomultiplier tube from Hamamatsu Photonics Co., Ltd. in Japan, equipped with a magnetic shielding shell, with a response band of 300 nm–650 nm. The PMT power supply module adopts the original C12597-01 high-voltage base. Due to the introduction of power supply, it will bring more electromagnetic crosstalk, which will add impurities to the output of PMT. Therefore, resistor programming has been chosen for high-voltage base power supply. The high-voltage base provides a reference power line that can provide gain voltage to the PMT through resistive voltage division, thereby avoiding the introduction of more electromagnetic crosstalk. A bandpass filter with a wavelength range of 280 nm–400 nm is placed directly below the PMT, which can effectively detect the fluorescence emitted by sulfur dioxide molecules during their return to the ground state and reduce the interference of some impurity light. Of course, it is also necessary to place a combination of plano-convex lenses to integrate the optical path, ensuring that the generated fluorescence signal is focused on the effective detection part of PMT, in order to obtain the strongest fluorescence signal.

2.2. Circuit Section

The acquisition circuit is composed of the STM32 platform and the FPGA platform [22,23]. The STM32 part selects STM32F407ZGT6 (STMicroelectronics, Plan-les-Ouates, Switzerland) as the main control chip, responsible for communicating with the FPGA platform and upper computer. The FPGA platform chooses EP4CE6E22C8N (Intel, Santa Clara, CA, USA) as the main control chip, which can drive high-performance ADCs with its bandwidth and slew rate. It is also responsible for joint communication with the STM32 main control chip. LTC2387-18FA (Analog Devices, Wilmington, MA, USA) is chosen as the analog-to-digital converter, which is a high-performance ADC with 18-bit depth and 10 M speed.

Due to the fact that the original signal output by PMT is a reverse signal, the signal first enters an inverted operational amplifier circuit and, then, outputs a signal with adjustable size and positive direction. Then, the subtractor circuit is entered. This process is shown in Figure 2, where the red part represents the fluorescence signal of sulfur dioxide. After passing through this part of the circuit, the proportion of sulfur dioxide fluorescence signal significantly increases, which helps to improve the sensitivity and resolution of the detection device.

Then, the signal enters the differential amplification circuit, which divides the signal into two paths with different DC biases, opposite directions, and no phase deviation. The difference between the two signals is used as an analog signal to enter the ADC for analog-to-digital conversion. The two signals are transmitted by two signal lines with extremely short physical distances, and it can be considered that they are subjected to the same external interference, which can effectively reduce the impact of external interference and common mode noise on the electrical signal [24]. In addition, a four-layer circuit board is used in the experiment, with the power supply and grounding parts located in separate board layers. Compared to common double-layer circuit boards, it has better electrical performance. The physical image of the collection circuit is shown in Figure 3.

3. Wavelet Transform

Due to sulfur dioxide being a trace gas in the atmosphere, the number of fluorescent photons generated by excitation is very small, making it susceptible to interference from electronic noise. Therefore, noise reduction processing is the key to improving the accuracy of equipment detection.

Wavelet transform [25,26] is a powerful signal processing tool and a mathematical method widely used in various fields such as signal processing and seismic exploration. It decomposes and analyzes signals at different scales and positions using wavelet functions.

Before reaching the optimal decomposition level of the signal, the relationship between signal-to-noise ratio and decomposition level is expressed as an approximate positive correlation. After reaching the optimal decomposition level, the signal-to-noise ratio of the signal will not increase again but will instead decrease. Applying threshold denoising techniques to each sub band [27] can effectively remove noise and preserve the true signal.

The MATLAB multi-resolution analysis is an important tool for wavelet transform analysis. In order to distinguish effective signals from noisy signals, a series of detail signals with different resolutions can be used for hierarchical representation. The process of wavelet decomposition is shown in Figure 4.

In this fluorescence detection system, the effective signal is usually a low-frequency signal, while electronic noise is usually a high-frequency signal. Therefore, the original signal can be decomposed a certain number of times through wavelet transform to isolate the effective signal from noise, thereby removing the interference of high-frequency electronic noise and improving the signal-to-noise ratio. The wavelet transform denoising used in this article can be divided into the following three steps:

(1) Original signal decomposition. Firstly, select multiple original signals, perform N-layer wavelet decomposition on the signals, identify common trends in the signals, and modify and compare the parameters.

(2) Noise signal removal. Adjust and optimize the high-frequency noise threshold coefficients for each layer from layer 1 to layer N, and select the optimal noise reduction coefficient to reduce the impact of electronic noise.

(3) Effective signal reconstruction. Perform wavelet reconstruction of fluorescence signals based on the low-frequency coefficients of the Nth layer of wavelet decomposition and the high-frequency coefficients of the 1st to Nth layers after quantization processing.

The most crucial step in these three steps is the determination of the threshold, which aims to remove electronic noise as much as possible while ensuring that the effective signal is not distorted. Due to the discontinuity of the hard threshold function at the selected threshold, it can cause system oscillations and cause distortion. A soft threshold will cause some singularities to disappear [28,29], resulting in the loss of key details of the signal, so this paper proposes an improved threshold wavelet decomposition algorithm for this experimental environment.

The collection of fluorescent signals faces noise problems, mainly due to the following reasons:

(1) The signal itself is weak. Due to the concentration of sulfur dioxide in this experiment being at the ppb level, the excited fluorescence signal is very weak. If not properly processed, such a signal is easily masked by other noise.

(2) Device noise. Electronic components usually introduce a certain degree of noise, such as operational amplifiers, filters, voltage stabilizing chips, etc. These noises may come from the internal circuits of the device or from the interaction between the device and the external electromagnetic environment.

(3) Environmental noise. There may be various sources of interference in the experimental environment, such as power crosstalk, electromagnetic radiation, thermal noise, etc. These interference sources will introduce additional noise, affecting the accuracy of the signal and the analysis of the data.

In the experiment, due to the inability to achieve complete darkness, the photomultiplier tube will still output small electrical signals when not exposed to pulsed xenon lamps. After passing through the operational amplifier circuit, it will output static noise as shown in Figure 5. After calculation, the standard deviation of static noise is 4404.932, and the average absolute deviation is 3533.375. This will have a significant impact on the accuracy of subsequent experiments.

Six wavelet algorithms were selected for denoising, and the results are shown in

Table 1. Performance comparison of wavelet algorithms.

Wavelet Algorithm	Decomposition Level	Evaluation Index	Hard Threshold	Soft Threshold	Improvement Threshold
db10	4	SNR	37.68	39.58	40.29
		Mean standard deviation	3451	3102	2993
sym8	5	SNR	36.65	42.68	44.26
		Mean standard deviation	2864	2685	2697
coif5	4	SNR	38.61	39.31	39.98
		Mean standard deviation	3504	3220	3302
bior5.5	5	SNR	39.41	40.24	41.11
		Mean standard deviation	2845	2811	2774
ribo6.8	5	SNR	34.43	36.68	37.40
		Mean standard deviation	3102	2992	2864
fk22	5	SNR	38.86	40.24	40.82
		Mean standard deviation	3305	3105	3102

below. Finally, the sym8 wavelet was selected for 5-layer decomposition.

After repeated experiments and multiple adjustments to the threshold, the thresholds for the first to fifth layers were determined to be 2233.843, 3237.675, 5129.732, 8748.381, and 9686.040, respectively. Figure 6 shows the process of wavelet denoising, and Figure 7 shows the comparison before and after denoising.

The denoising effect and signal fidelity can be determined by performing fast Fourier transform (FFT) analysis on the processed signal. The FFT image after denoising is shown in Figure 8. The results indicate that noise reduction processing effectively reduces noise interference without causing serious signal distortion.

The advantages of wavelet transform in time-frequency localization and frequency band segmentation can effectively distinguish between effective signals and noisy signals. Its excellent zoom performance enables the method based on multi-resolution analysis and wavelet transform to have fine scale division ability, which can effectively improve the detection accuracy [30] of this experiment. Embedding the above MATLAB code in Quartus and Keil can achieve real-time data processing without the need to import it into a PC for analysis, thus simplifying the experimental process.

4. Temperature Drift of PMT

4.1. Data Collection

Firstly, verify the feasibility of the detection device. Use the square wave signal generated by flipping the pin level of the STM32 main control chip (STMicroelectronics) to drive the excitation light source. Set the working frequency of the pulse xenon lamp to 10 Hz, the number of data acquisition points to 600, and the gas flow rate to be measured to 6 L/min. Compared with ordinary electronic devices such as resistors and capacitors, photomultiplier tubes are more susceptible to the influence of environmental temperature, mainly manifested as nonlinear changes in the gain rate with temperature. Record the peak value of the fluorescence waveform as PMT Output Value, the static reference value when not irradiated as PMT Base Value, and the difference between the two as valid data, denoted as AD Value [31], as shown in Figure 9. This can, to some extent, reduce the impact of temperature changes on the detection results.

The temperature sensor is selected as MLX90614 (Melexis, Shenzhen, China) with a resolution of 0.02 °C. Use it to monitor the temperature of PMT. Inject pure nitrogen gas into the reaction chamber, and after a period of experimentation, obtain the temperature data as shown in Figure 10.

It can be observed that as the ambient temperature gradually increased during the detection process, the gain rate of PMT changed [32,33,34], manifested as a decrease in both the optical PMT Output Value and PMT Base Value, and their change rates were different. In order to mitigate the impact of temperature changes, different weights were assigned to the PMT Output Value and PMT Base Value by calculating their respective proportions of change. Finally, the following weighted comparison Figure 11 was obtained. Due to the fact that the gain rate of PMT increased as the temperature decreased, the AD Value should also increase as the temperature decreases, which is consistent with the test results. Before processing, the standard deviation of AD Value was 5843.183, and the average absolute error was 5030.428.

4.2. Data Processing

In the selection of algorithms, the commonly used Empirical Mode Decomposition (EMD) algorithm is first considered. However, the EMD algorithm still has many shortcomings in practical calculation and application, including mode mixing, endpoint effects, and screening iteration stopping standards. Among them, when there are intermittent phenomena caused by abnormal events (such as intermittent signals, pulse interference, and noise) in the signal, the decomposition results of EMD will exhibit mode aliasing. The occurrence of mode aliasing not only leads to false time-frequency distribution but also causes IMF to lose its physical meaning.

The widely used Kalman Filter (KF) [35] is an earlier time-domain denoising algorithm, mainly applied in fields such as communication, navigation, sensor networks, etc., but it can only be applied to linear systems. The later proposed Extended Kalman Filter (EKF) has theoretical limitations that cannot be overcome by themselves, such as low first-order linearization approximation accuracy, the need to calculate Jacobian matrices, and the requirement for continuous differentiability of nonlinear functions. Secondly, EKF is sensitive to the selection of initial estimation and process noise. When there are complex situations such as model mismatch, measurement interference, measurement loss, measurement delay, or state mutation in the system, EKF filtering accuracy is poor, and numerical stability is poor.

Although Particle Filters (PFs) are also suitable for nonlinear and non-Gaussian systems, their computational cost is high and increases with the increase in state dimensions. At the same time, a large number of particles are required to calculate the posterior distribution, and in high-dimensional state spaces, PF are more susceptible to problems such as insufficient sample size and particle degradation, leading to unstable estimation results. The limitation of its high computational complexity is also not suitable for long-term operation on platforms with limited computing and storage performance, such as embedded systems.

The characteristic of an ELMAN neural network [36] is that the output of the hidden layer is delayed and stored by the receiving layer, which makes it sensitive to historical state data. The addition of internal feedback network enhances the network’s ability to process dynamic information, thereby achieving the goal of dynamic modeling. In addition, ELMAN neural networks can approximate any nonlinear mapping with arbitrary accuracy, without considering the specific form of external noise on the system. If the input and output data of the system are correct, the system can be modeled. However, due to the fact that the learning process of ELMAN neural networks is based on gradient descent, this may result in the network only being able to find local optimal solutions and unable to find global optimal solutions.

BP neural networks [37,38] are suitable for solving problems that traditional algorithms or computational methods find difficult to solve. A BP neural network is a mature nonlinear mapping method for solving real-world problems. In addition, it has the ability to classify any complex pattern and can solve XOR problems that simple sensors cannot solve. A BP neural network does not require mathematical relationships to determine the mapping relationship between input and output. It only imports input and output data into the training set, trains itself, finds exercises between the input and output, establishes a model, and finally imports input values into the model to obtain the latest expected output values.

The transmission process of the BP neural network consists of two parts, namely forward transmission and backward transmission. In the forward transmission process, data are processed layer by layer from the entry layer to the hidden layer and, then, transferred to the output layer. The condition of each level of neuron directly affects the condition of the next level of neuron. Assuming that the expected output value cannot be obtained at the output layer, it enters the opposite direction of transmission, regresses the bias information along the original interface channel, and adjusts the weights of each neuron to minimize the bias information.

This paper utilizes the principle of the BP neural network algorithm and uses MATLAB R2021b to train the neural network for AD value and temperature. The comparison results of the algorithms are shown in

Table 2. Comparison of training algorithms.

Training Algorithm	Layers	MSE	R
Levenberg–Marquardt	12	1.4808 × 106	0.9775
Bayesian regularization	14	1.4032 × 106	0.9767
Quantify conjugate gradient	4	1.1334 × 106	0.9821

. In this experiment, the quantify conjugate gradient algorithm is selected as the fitting algorithm [39].

A total of 350 sets of data were randomly selected from the 500 sets of data collected above for training. The training/testing/validation ratio was 7:1.5:1.5, and a BP neural network was used to train the data. The hidden layer was set to 4, and 41 repeated training sessions were conducted. The training situation is shown in Figure 12 and Figure 13. The best performance was obtained in the 35th round of training.

The training, validation, and testing of the neural network are shown in Figure 14.

The comparison after neural network training is shown in Figure 15. After calculation, the standard deviation of static noise is 5686.011, and the average absolute deviation is 4850.8.

5. Experimental Verification

According to the National Environmental Protection Standard HJ 1044-2019 [40] of the People’s Republic of China, when the concentrations of methane, nitric oxide, and hydrogen sulfide in the sample air are 2155 ppb, 123 ppb, and 6939 ppb, respectively, the determination results of sulfur dioxide will be affected by 3 ppb, 3 ppb, and no more than 1 ppb. When aromatic hydrocarbons are present in the sample air, it can affect the measurement results and can be removed through a hydrocarbon remover. Under normal circumstances, the interference of the aforementioned gases in the ambient air can be ignored. In terms of gas configuration, the TR1BKD dynamic calibration instrument from Zhongke Tianrong (Beijing) Technology Co., Ltd. (Beijing, China) was used, which can configure standard gases mixed with nitrogen and sulfur dioxide with a resolution of 0.01 ppb. Different concentrations of sulfur dioxide gas were gradually introduced, and data were obtained. In Figure 16, two fitted data represent the detection accuracy before and after processing, respectively. This indicates that the detection device proposed in this article has good linear detection accuracy.

It is also necessary to consider the working conditions in the actual environment. Select five sets of standard gases with different concentrations; feed them into the detector for multiple sampling, and observe their stability. The results are shown in Figure 17. The coefficient of variation is a commonly used statistical indicator in statistics. It is a relative statistical measure of data dispersion, mainly used to compare the dispersion of sample data, using the ratio of standard deviation to mean for comparison. After calculation, the dispersion coefficients of 0 ppb, 100 ppb, 200 ppb, 300 ppb, 400 ppb, and 500 ppb after treatment are 0.2656%, 0.2468%, 0.2895%, 0.3334%, 0.3715%, and 0.3156%, respectively, proving the good reliability of the detector.

6. Conclusions

This paper develops a sulfur dioxide concentration detection device based on PMT. Using wavelet transform to denoise PMT signals and using a BP neural network algorithm to denoise the temperature drift phenomenon of PMT, the signal-to-noise ratio is improved. After verification, the detection results are close to the actual values, with good resolution and reliability. In the future, it may be possible to apply Unscented Kalman Filters (UKFs) for multi-sensor data fusion to further improve the performance of detection device.