Method for predicting concentration of nitrogen dioxide in coal-fired flue gas through combination of photoacoustic spectrometry and PINN

Abstract

The invention discloses a method for predicting the concentration of nitrogen dioxide in coal-fired flue gas based on a physical information neural network. The method comprises the following steps: (1) acquiring one-dimensional photoacoustic spectrum data of nitrogen dioxide in coal-fired flue gas; (2) denoising the one-dimensional photoacoustic spectroscopic data of the nitrogen dioxide in the coal-fired flue gas; (3) carrying out data set division on the photoacoustic spectrum data of the nitrogen dioxide in the coal-fired flue gas according to the sample; (4) establishing a coal-fired flue gas nitrogen dioxide concentration prediction model of the physical information neural network; (5) integrating a weight distribution strategy based on uncertainty evaluation into the neural network; and (6) checking the model effect. According to the coal-fired flue gas nitrogen dioxide concentration prediction model based on the physical information neural network, the defects existing in an existing coal-fired flue gas nitrogen dioxide concentration prediction method are overcome, the new physical information neural network model is provided, prediction precision can be improved, calculation efficiency can be optimized, and the model is quite suitable for prediction of the coal-fired flue gas nitrogen dioxide concentration.

Description

Technical Field

[0001] This invention relates to the field of predicting nitrogen dioxide concentration in coal-fired flue gas, and in particular to a method for predicting nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network. Background Technology

[0002] With increasingly stringent global environmental policies, harmful gases emitted from industrial facilities such as coal-fired power plants, especially nitrogen dioxide (NO2), have become a serious hazard. NO2 is a highly oxidizing gaseous pollutant that significantly harms human health and the ecological environment. It reacts with moisture in the respiratory mucosa, causing symptoms such as coughing and difficulty breathing. Long-term exposure increases the risk of respiratory and cardiovascular diseases, weakens lung immunity, and affects lung development in children. At the ecological level, NO2 is a major precursor to acid rain, can acidify soil and water, corrode buildings, and participate in the formation of photochemical smog, harming humans and plants. High concentrations can directly damage plant leaves and hinder photosynthesis. Therefore, accurately predicting the concentration of NO2 in coal-fired flue gas is crucial for effective emission control and optimized treatment measures. Common gas concentration measurement technologies include electrochemical sensor technology, infrared absorption spectroscopy, and gas chromatography. However, the application of these traditional methods in complex industrial environments is limited in many ways. For example, while electrochemical sensor technology is convenient, its stability and long-term reliability are poor; infrared absorption spectroscopy, although highly accurate, has high equipment costs and is significantly affected by environmental factors.

[0003] In recent years, photoacoustic spectroscopy has shown great potential in the field of gas monitoring due to its advantages such as non-contact operation, high sensitivity, and fast response speed. Based on the photoacoustic effect, when gas molecules absorb light of a specific wavelength, they release energy through non-radiative transitions, generating thermal expansion and forming sound waves. Measuring the intensity of these sound waves allows for the inference of gas concentration. Its advantages include: ultra-high sensitivity and detection limits, reaching ppb levels or even lower with no baseline drift; high selectivity and anti-interference capabilities, achieved by matching the characteristic absorption peaks of the target gas with a customized wavelength light source, and resistance to optical interference from dust, water vapor, etc.; fast response speed, enabling real-time online monitoring without gas pretreatment; wide measurement range and linear response range, maintaining good linearity from ppb levels to percentage concentrations; high system integration, portability, and low power consumption, suitable for portable devices and battery-powered scenarios; broad applicability to a wide range of gases, covering almost all infrared-active gases and enabling simultaneous multi-component analysis; low maintenance costs, with no consumable components and long calibration cycles, making it widely used in environmental monitoring, industrial process control, medical diagnostics, aerospace, and other fields. Although photoacoustic spectroscopy has significant advantages in gas detection, in practical applications, the complex composition of coal-fired flue gas and changes in environmental factors (such as temperature, humidity, and airflow) can interfere with the photoacoustic spectral signals. Therefore, accurately extracting effective information on nitrogen dioxide concentration from these photoacoustic signals has become a key challenge in the application of this technology.

[0004] Currently, traditional neural networks are primarily based on data-driven machine learning models, which fit the mapping relationship between input and output through the connection and weight adjustment of multiple layers of neurons. Their design does not consider specific physical laws or equations, relying solely on patterns and statistical features in the training data for learning. This method requires a large amount of labeled data, and the quality of the data directly affects the model's performance. If the data conflicts with physical laws, the model will still fit incorrect patterns.

[0005] To overcome this problem, this invention proposes a method for predicting nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network. This method transforms physical equations (such as the Navier-Stokes equation and the Schrödinger equation) into mathematical constraints and embeds them into the loss function. During training, the model not only needs to match the data but also ensures that the residuals of the physical equations are sufficiently small. Therefore, this network has lower data requirements and is particularly suitable for scenarios where physical experiments are costly and data is difficult to obtain. Even with only a small amount of observational data, the reliability of predictions can be improved through physical constraints. Summary of the Invention

[0006] This invention provides a method for predicting nitrogen dioxide concentration in coal-fired flue gas based on physical information neural networks, which can improve the prediction accuracy of nitrogen dioxide concentration.

[0007] This invention provides a method for predicting nitrogen dioxide concentration in coal-fired flue gas based on physical information neural networks, comprising the following steps:

[0008] S1. Acquisition of one-dimensional photoacoustic spectral data of nitrogen dioxide in coal-fired flue gas;

[0009] S2. Denoise the one-dimensional photoacoustic spectrum data of nitrogen dioxide in coal-fired flue gas;

[0010] S3, the photoacoustic spectral data samples of nitrogen dioxide from coal-fired flue gas were divided into datasets;

[0011] S4. Establish a prediction model for nitrogen dioxide concentration in coal-fired flue gas based on physical information neural networks;

[0012] S5. Incorporate a weight allocation strategy based on uncertainty assessment into the prediction model;

[0013] S6. Verify the model's effectiveness.

[0014] Furthermore, in S1, photoacoustic spectroscopy is used to collect spectral data from multiple experimental samples, obtain photoacoustic spectral characteristic information of each sample, and obtain photoacoustic spectral data of different concentrations of nitrogen dioxide.

[0015] Furthermore, in S2, SG smoothing is used to denoise the one-dimensional photoacoustic spectral data of nitrogen dioxide in coal-fired flue gas, as detailed below:

[0016] S21. Let the width of the filter window be n = 2m + 1. Let the set of n points with equal wavelength intervals in a spectral range be X, and let the measurement points be x = (-m, -m + 1, 0, ..., 0, 1, ..., m - 1, m):

[0017] S22. Fit the data points within the window using a k-1 polynomial:

[0018] y = a0 + a1x + a2x 2 +...+a k-1 x k-1 (1)

[0019] S23. There are n measurement points in the filter window, so there are n fitting equations. These are combined into a system of linear equations:

[0020] However, for the equation to have a solution, n should be greater than or equal to k; generally, n > k is chosen. This can be represented in matrix form as follows:

[0021] Y (2m+1)×1 =X (2m+1)×k ·A k×1 +E (2m+1)×1 (3)

[0022] S24. Determine the fitting parameters A using the least squares method:

[0023]

[0024] S25. Calculate the filter value using the fitted parameter A.

[0025]

[0026] Furthermore, in S3, the k-fold cross-validation method is used to partition the dataset, randomly dividing it into k disjoint subsets. k-fold cross-validation requires k iterations. In the i-th iteration (i = 1, 2, 3, ..., k), the i-th fold (subset) is used as the test set, and the remaining k-1 folds (subsets) are used as the training set, requiring a total of k iterations.

[0027] Furthermore, in S4, a prediction model is defined: a physics-information neural network-based prediction model for nitrogen dioxide concentration in coal-fired gas. This model consists of one input layer, five hidden layers, and one output layer. The input layer includes location information *x* and time information *t*, providing the spatiotemporal constraints of the physical field. Each of the five hidden layers has 50 neurons, used to fit the nonlinear mapping of concentration *c*(x, t) using the tanh activation function. The output layer outputs the concentration *c*, and then physical constraint terms are added to establish the prediction model for nitrogen dioxide concentration in coal-fired gas based on the physics-information neural network. A simplified diagram of the model structure is shown below. Figure 2 As shown, the specific explanation is as follows:

[0028] S41. An input layer contains position information x and time information t. The initial conditions and boundary conditions of the physical field are obtained through these two quantities.

[0029] S42. Concentration prediction using the principle of photoacoustic spectroscopy requires the calculation of complex spatiotemporal functions. Therefore, the network consists of five hidden layers, each containing 50 neurons, used to fit the nonlinear mapping of concentration c(x,t). The tanh activation function is used.

[0030] S43. The output is concentration c, which is embedded with the physical calculation formula to form the physical loss function. This physical loss function is then weighted and summed with the original data loss function to form the current network's loss function. The physical loss function is as follows:

[0031]

[0032] The data loss function is as follows:

[0033]

[0034] Together they constitute the network loss function:

[0035] L=λ PDE LPDE +λ date L date (8)

[0036] In the formula: N is the gas molecule density; α is the absorption coefficient of the gas to be measured; c is the concentration of the gas to be measured; P laser γ is the effective optical power; g is the normalized light intensity distribution; p is the sound pressure; γ is the specific heat capacity; υ0 is the sound velocity of the gas being measured; t is time; c i For the true value, These are predicted values.

[0038] Furthermore, in S5, the physical information neural network model established in step S4 is integrated with a weight allocation strategy based on uncertainty assessment to obtain the test model, as detailed below:

[0039] S51. Calculate the absolute error under data-driven conditions:

[0040]

[0041] S52. Calculate the mean absolute error of all samples under the data-driven prediction model:

[0042]

[0043] S53. Determine the stability redistribution weights by calculating the error value:

[0044]

[0045] S54. Calculate the predicted values ​​of the physical model using the physical model.

[0046]

[0047] S55. Repeat the above operations similar to those for data-driven approaches, and reallocate the weights of the physical loss term:

[0048]

[0049] Furthermore, in S6, a test set is used to test the model's prediction performance.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0051] This invention significantly improves the prediction accuracy and stability of nitrogen dioxide concentration in coal-fired flue gas by integrating photoacoustic spectroscopy detection technology and physical information neural networks, utilizing deep learning methods incorporating physical information. Simultaneously, it optimizes computational efficiency by combining a weight allocation strategy for uncertainty assessment. Attached Figure Description

[0052] Figure 1 The flowchart illustrates a method for predicting nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network, as provided by this invention.

[0053] Figure 2 This is a simplified structural diagram of the network provided by the present invention for predicting nitrogen dioxide concentration in coal-fired flue gas. Detailed Implementation

[0054] The following is in conjunction with the appendix Figure 1-2 The present invention will be described in detail with respect to a specific embodiment, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiment.

[0055] The experimental environment was Windows 10, Python 2024, and the development framework was PyTorch. During training, an Nvidia RTX 3060 Ti GPU was used to accelerate the training process.

[0056] like Figure 1 As shown, this invention provides a method for predicting nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network, comprising the following steps:

[0057] S1. Acquisition of one-dimensional photoacoustic spectral data of nitrogen dioxide in coal-fired flue gas;

[0058] S2. Denoise the one-dimensional photoacoustic spectrum data of nitrogen dioxide in coal-fired flue gas;

[0059] S3, the photoacoustic spectral data samples of nitrogen dioxide from coal-fired flue gas were divided into datasets;

[0060] S4. Establish a prediction model for nitrogen dioxide concentration in coal-fired flue gas based on physical information neural networks;

[0061] S5. Incorporate a weight allocation strategy based on uncertainty assessment into the prediction model;

[0062] S6. Verify the model's effectiveness.

[0063] Preferably, in step S1, photoacoustic spectroscopy is used to collect spectral data from multiple groups of experimental samples, obtain photoacoustic spectral characteristic information of each sample, and obtain photoacoustic spectral data of different concentrations of nitrogen dioxide.

[0064] Preferably, in step S2, SG smoothing is used to denoise the one-dimensional photoacoustic spectral data of nitrogen dioxide in coal-fired flue gas.

[0065] Preferably, in step S3, the k-fold cross-validation method is used to partition the dataset, randomly dividing the dataset into k disjoint subsets. k-fold cross-validation requires k iterations. In the i-th iteration (i = 1, 2, 3, ..., k), the i-th fold (subset) is used as the test set, and the remaining k-1 folds (subsets) are used as the training set, requiring a total of k iterations.

[0066] Preferably, in step S4, a prediction model is defined: a physical information neural network-based prediction model for nitrogen dioxide concentration in coal-fired gas. This model consists of one input layer, five hidden layers, and one output layer. The input layer includes location information x and time information t, providing the spatiotemporal constraints of the physical field. Each of the five hidden layers contains 50 neurons, used to fit the nonlinear mapping of concentration c(x,t) using the tanh activation function. The output layer outputs the concentration c, and then physical constraint terms are added to establish the prediction model for nitrogen dioxide concentration in coal-fired gas based on the physical information neural network.

[0067] Preferably, in step S5, an uncertainty-based weight allocation strategy is incorporated into the model, and the model is trained to obtain a test model.

[0068] Preferably, in step S6, the trained model is tested using a test set.

[0069] Example 1:

[0070] In step S1, the present invention uses the quantum cascade laser developed by Chengdu Multispectral Optics Technology Co., Ltd. as the core light source of the photoacoustic spectroscopy experimental module to collect spectral data of multiple coal-fired flue gas samples in the wavelength range of 300-575nm, and successfully obtains high-resolution photoacoustic spectral data of each sample.

[0071] Example 2:

[0072] In step S2, the nitrogen dioxide photoacoustic spectral data obtained in step S1 is used to denoise the one-dimensional photoacoustic spectral data of nitrogen dioxide in coal-fired flue gas using SG smoothing. The specific method is as follows:

[0073] SG smoothing was used to denoise the one-dimensional photoacoustic spectral data of nitrogen dioxide from coal-fired gas, as detailed below:

[0074] S21. Let the width of the filter window be n = 2m + 1. Let the set of n points with equal wavelength intervals in a spectral range be X, and let the measurement points be x = (-m, -m + 1, 0, ..., 0, 1, ..., m - 1, m):

[0075] S22. Fit the data points within the window using a k-1 polynomial:

[0076] y = a0 + a1x + a2x2 +...+a k-1 x k-1 (18)

[0077] S23. There are n measurement points in the filter window, so there are n fitting equations. These are combined into a system of linear equations:

[0078] However, for the equation to have a solution, n should be greater than or equal to k; generally, n > k is chosen. This can be represented in matrix form as follows:

[0079] Y (2m+1)×1 =X (2m+1)×k ·A k×1 +E (2m+1)×1 (20)

[0080] S24. Determine the fitting parameters A using the least squares method:

[0081]

[0082] S25. Calculate the filter value using the fitted parameter A.

[0083]

[0084] Example 3:

[0085] In step 3, the k-fold cross-validation method is used to partition the dataset, randomly dividing it into k disjoint subsets. k-fold cross-validation requires k iterations. In the i-th iteration (i = 1, 2, 3, ..., k), the i-th fold (subset) is used as the test set, and the remaining k-1 folds (subsets) are used as the training set, requiring a total of k iterations.

[0086] Example 4:

[0087] In step 4, a prediction model is defined: a physical information neural network-based prediction model for nitrogen dioxide concentration in coal-fired gas. This model consists of one input layer, five hidden layers, and one output layer. The input layer includes location information *x* and time information *t*, providing the spatiotemporal constraints of the physical field. Each of the five hidden layers has 50 neurons, used to fit the nonlinear mapping of concentration *c*(x, t) using the tanh activation function. The output layer outputs the concentration *c*. Then, physical constraint terms are added to establish the prediction model for nitrogen dioxide concentration in coal-fired gas based on the physical information neural network. The specific method is as follows:

[0088] S41. An input layer contains position information x and time information t. The initial conditions and boundary conditions of the physical field are obtained through these two quantities.

[0089] S42. Concentration prediction using the principle of photoacoustic spectroscopy requires the calculation of complex spatiotemporal functions. Therefore, the network consists of five hidden layers, each containing 50 neurons, used to fit the nonlinear mapping of concentration c(x,t). The tanh activation function is used.

[0090] S43. The output is concentration c, which is embedded with the physical calculation formula to form the physical loss function. This physical loss function is then weighted and summed with the original data loss function to form the current network's loss function. The physical loss function is as follows:

[0091]

[0092] The data loss function is as follows:

[0093]

[0094] Together they constitute the network loss function:

[0095] L=λ PDE L PDE +λ date L date (25)

[0096] In the formula: N is the gas molecule density; α is the absorption coefficient of the gas to be measured; c is the concentration of the gas to be measured; P laser γ is the effective optical power; g is the normalized light intensity distribution; p is the sound pressure; γ is the specific heat capacity; υ0 is the sound velocity of the gas being measured; t is time; c i For the true value, These are predicted values.

[0097] Example 5:

[0098] In step 5, a weight allocation strategy is incorporated into PINN. The test model is obtained by integrating the weight allocation strategy based on uncertainty assessment into the physical information neural network model established in step S4, as detailed below:

[0099] S51. Calculate the absolute error under data-driven conditions:

[0100]

[0101] S52. Calculate the mean absolute error of all samples under the data-driven prediction model:

[0102]

[0103] S53. Determine the stability redistribution weights by calculating the error value:

[0104]

[0105] S54. Calculate the predicted values ​​of the physical model using the physical model.

[0106]

[0107] S55. Repeat the above operations similar to those for data-driven approaches, and reallocate the weights of the physical loss term:

[0108]

[0109] This invention presents a prediction model for nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network, which addresses the shortcomings of existing methods for predicting nitrogen dioxide concentration in coal-fired flue gas. The proposed physical information neural network model can improve prediction accuracy and optimize computational efficiency, making it highly suitable for predicting nitrogen dioxide concentration in coal-fired flue gas.

[0110] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0111] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for predicting nitrogen dioxide concentration in coal-fired flue gas based on physical information neural networks, characterized in that, Includes the following steps: S1. Acquisition of one-dimensional photoacoustic spectral data of nitrogen dioxide in coal-fired flue gas; S2. Denoise the one-dimensional photoacoustic spectrum data of nitrogen dioxide in coal-fired flue gas; S3, the photoacoustic spectral data samples of nitrogen dioxide from coal-fired flue gas were divided into datasets; S4. Establish a prediction model for nitrogen dioxide concentration in coal-fired flue gas based on physical information neural networks; and the specific process; S5. Incorporating a weight allocation strategy based on uncertainty assessment into the prediction model; and the specific process; S6. Verify the model's effectiveness.

2. The method for predicting nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network according to claim 1, characterized in that, In step S1, photoacoustic spectroscopy is used to collect spectral data from multiple experimental samples, obtain photoacoustic spectral characteristic information of each sample, and obtain photoacoustic spectral data of different concentrations of nitrogen dioxide.

3. The method for predicting nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network according to claim 1, characterized in that, In step S2, SG smoothing is used to denoise the one-dimensional photoacoustic spectral data of nitrogen dioxide in coal-fired flue gas.

4. The method for predicting nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network according to claim 1, characterized in that, In step S3, the k-fold cross-validation method is used to partition the dataset, randomly dividing it into k disjoint subsets. k-fold cross-validation requires k iterations. In the i-th iteration (i = 1, 2, 3, ..., k), the i-th fold (subset) is used as the test set, and the remaining k-1 folds (subsets) are used as the training set, requiring a total of k iterations.

5. The method for predicting nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network according to claim 1, characterized in that, In step S4, a prediction model is defined: a physical information neural network-based prediction model for nitrogen dioxide concentration in coal-fired gas. This model consists of one input layer, five hidden layers, and one output layer. The input layer includes location information x and time information t, providing the spatiotemporal constraints of the physical field. Each of the five hidden layers has 50 neurons, used to fit the nonlinear mapping of concentration c(x,t) using the tanh activation function. The output layer outputs the concentration c. Then, physical constraint terms are added to establish the prediction model for nitrogen dioxide concentration in coal-fired gas based on the physical information neural network. The specific method is as follows: S41. An input layer contains position information x and time information t. The initial conditions and boundary conditions of the physical field are obtained through these two quantities. S42. Concentration prediction using the principle of photoacoustic spectroscopy requires the calculation of complex spatiotemporal functions. Therefore, the network consists of five hidden layers, each containing 50 neurons, used to fit the nonlinear mapping of concentration c(x,t). The tanh activation function is used. S43. The output is the concentration c, which is embedded in the physical calculation formula to form the physical loss function. This physical loss function is then weighted together with the original data loss function to form the current network's loss function.

6. The method of integrating weight allocation strategy into physical information neural network according to claim 1, characterized in that, In step S5, the established physical information neural network model is used to incorporate a weight allocation strategy based on uncertainty assessment to obtain the test model, as explained below: S51. Calculate the absolute error under data-driven conditions: S52. Calculate the mean absolute error of all samples under the data-driven prediction model: S53. Determine the stability redistribution weights by calculating the error value: S54. Calculate the predicted values ​​of the physical model using the physical model. S55. Repeat the above operations similar to those for data-driven approaches, and reallocate the weights of the physical loss term: S56. Incorporate the reallocated weights into the loss function: S57. Train a physical information neural network that integrates weight allocation using the training set.

7. The method for predicting nitrogen dioxide concentration in coal-fired flue gas based on a physical information neural network according to claim 1, characterized in that, In step S6, the test set is used to test the effectiveness of the model's predictions.

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