Reconstruction method of furnace temperature field based on radiation transfer equation and multi-layer feedforward neural network fusion

Abstract

The furnace temperature field reconstruction method based on the radiation transfer equation and the multi-layer feedforward neural network fusion comprises the following steps: calibrating the radiation detector by using a blackbody furnace to establish the relationship between the image intensity and the radiation intensity; establishing a detailed radiation transfer equation RTE considering the medium absorption, scattering and wall effect by using a DOM algorithm; generating a data set as a learning set of the neural network by smoothing the temperature field and the fluent simulation; constructing a multi-layer feedforward neural network; predicting the temperature of each grid by the learned model to obtain the furnace cross-section temperature field. The method couples the physical constraint of the radiation transfer equation with the feedforward neural network, avoids the shortcomings of the large amount of calculation of the pure physical constraint and the lack of physical theory support of the pure data driving, has small workload for replacing the fluent model simulation learning set for different sites, and can quickly obtain the temperature measurement result by calling the pre-learned model, and occupies less computing resources.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of coal-fired power generation, and particularly relates to a furnace temperature field reconstruction method based on fusion of a radiation transfer equation and a multilayer feedforward neural network. BACKGROUND

[0002] Accurate monitoring of the temperature field of a boiler cross section is crucial for combustion efficiency optimization, pollutant control and safe operation of equipment, and especially under deep peak shaving conditions, the temperature field distribution directly affects the stability and economy of the boiler. At present, the temperature field of a pulverized coal boiler cross section can be monitored by shooting flame images of a certain cross section by four or more cameras, establishing a radiation transfer equation by using a DRESOR method, inversely solving the radiation transfer equation based on a Tikhonov regularization algorithm, and realizing reconstruction of the furnace cross section temperature field. This method has a large amount of calculation, occupies a large amount of computing resources, and takes about 3 seconds for each calculation. Under the background of double carbon, power station pulverized coal boilers need to participate in frequent fast load regulation and peak shaving, and under this background, this method cannot quickly realize temperature field reconstruction, so as to provide limited signals for the control system. Although a machine learning method based on pure data driving can quickly respond to predict the furnace cross section temperature field, the combustion information in the furnace obtained by using existing measuring points of the unit is limited, such as coal quality, wind and powder parameters, and the present stage is difficult to accurately measure and obtain online, and the accuracy of the model driving needs to be verified. SUMMARY

[0003] The method proposed in the application combines the physical constraints of the radiation transfer equation with the data set generated by FLUENT simulation to construct a multilayer feedforward neural network model with theoretical reliability and calculation real-time performance. Compared with the method of solving the radiation transfer equation by using the traditional DRESOR method, the present method has the following obvious advantages: first, the neural network model obtained by pre-training only needs to be simply loaded when applied, which greatly reduces the configuration requirements of the industrial computer; second, the calculation time of the method is shortened from the 3-second level of the traditional method to the millisecond level, which can meet the real-time control requirements of fast load variation under deep peak shaving conditions; finally, by fusing the theoretical constraints of the physical model and the efficient characteristics of data driving, the calculation efficiency is significantly improved while ensuring the reconstruction accuracy, effectively solving the dual contradiction of large calculation amount of pure physical model and insufficient accuracy of pure data driving.

[0004] The furnace temperature field reconstruction method based on fusion of a radiation transfer equation and a multilayer feedforward neural network comprises the following steps:

[0005] Step 1, blackbody furnace calibration: calibrate the radiation detector by using a blackbody furnace to establish the relationship between image intensity and radiation intensity;

[0006] Step 2, establish a detailed radiation transfer equation RTE considering the medium absorption, scattering and wall effect by using a DOM algorithm;

[0007] Step 3, generate a dataset as a learning set of the neural network by smoothing the temperature field and fluent simulation;

[0008] Step 4, build a multi-layer feedforward neural network, including the following steps:

[0009] Step 4-1, data preparation, including setting the model output scalar and data preprocessing;

[0010] Step 4-2, build a neural network, including a multi-layer feedforward structure of an input layer, 3 hidden layers, and an output layer, and define a composite loss function including a mean square error term and a temperature gradient penalty term;

[0011] Step 4-3, determine the training strategy;

[0012] Step 5, the learned model predicts the temperature of each grid to obtain the furnace cross-section temperature field.

[0013] The present application has the following beneficial effects:

[0014] (1) Cross-domain technology fusion: coupling the physical constraints of the radiation transfer equation with the feedforward neural network avoids the shortcomings of large computational load of pure physical constraints and no physical theory support of pure data-driven;

[0015] (2) Wide model applicability: only the fluent model simulation learning set needs to be replaced for different sites, the workload is small, and different power plants use different boiler styles and geometric sizes, so only the boiler modeling needs to be replaced in different sites, and the simulation calculation idea remains unchanged;

[0016] (3) Easy to deploy: calling the pre-learned model can quickly obtain the temperature measurement result, and occupies less computing resources. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 It is a blackbody furnace calibration experiment schematic diagram in the specific embodiment of the present application.

[0018] Figure 2 It is a multi-layer feedforward neural network schematic diagram in the specific embodiment of the present application.

[0019] Figure 3 It is a furnace radiation schematic diagram in the specific embodiment of the present application.

[0020] Figure 4 It is a furnace cross-section grid division schematic diagram in the specific embodiment of the present application.

[0021] Figure 5 It is a model cross-section temperature field reconstruction result in the specific embodiment of the present application. DETAILED DESCRIPTION

[0022] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0023] Step 1, Blackbody Furnace Calibration: The calibration system is as follows Figure 1 As shown, the system consists of a blackbody furnace, detector, detector bracket, computer, network cable, and power cord. The detector comprises a CCD camera, a high-temperature resistant lens, and a stainless steel casing. A CCD is a photoelectric sensor that converts light signals into electrical signals. Each pixel in the image outputs three signals: R, G, and B, all of which are relative intensities. Therefore, absolute intensity calibration of the CCD camera output is necessary. The calibration process is performed on the blackbody furnace. During calibration, the blackbody furnace temperature is set between 800℃ and 1440℃. At the same temperature, the exposure time is adjusted to gradually increase the maximum value of the R channel from a lower value to 250. Ten images are acquired at each temperature. Each temperature corresponds to the blackbody radiation intensity at two wavelengths. After image acquisition, the obtained image data is processed, and calibration curves for the R and G channels are plotted. Thus, the calibration curve establishes the relationship between monochromatic radiation intensity, image intensity, and camera exposure time. The calibration curve can be expressed by the following formula:

[0024] (1)

[0025] (2)

[0026] In the formula, These represent image intensity, specifically the r and g values ​​of the image. This represents the exposure time when the camera captures the image in this frame. A dual bandpass filter is placed in front of the CCD, with response wavelengths of 550nm and 650nm respectively, and a half-bandwidth of 10nm. Therefore, in the formula... Pick ; Pick In subsequent calculations, only the radiation intensity at wavelengths of 550nm and 650nm will be considered.

[0027] Step 2, Establishment of the Radiative Transfer Equation (RTE): The Radiative Transfer Equation is established along the line of sight. The steady-state form is:

[0028] (3)

[0029] In the formula, For in position ,direction Radiation energy on the surface; Indicates temperature the blackbody intensity at the location is the scattering phase function, representing the distribution of scattered energy from direction to direction ; is the absorption coefficient of the solid medium in the furnace, is the scattering coefficient of the solid medium in the furnace, the extinction coefficient and the scattering rate of the solid medium are:

[0030] (4)

[0031] (5)

[0032] As shown by Figure 3 , the radiation detector (camera) receives the radiation intensity in the furnace at position along the line-of-sight direction, which can be represented by the following formula:

[0033] (6)

[0034] In the formula, is the emissivity of the furnace wall; is the starting point of the line-of-sight path; is the optical thickness, indicating the cumulative attenuation from position to , which can be represented by the following formula:

[0035] (7)

[0036] is the wall contribution term, which is represented by the following formula:

[0037] (8)

[0038] In the formula, is used to determine the incident direction, and less than 0 indicates incidence, is the unit normal vector; I b ( r 0) represents the blackbody radiation intensity at position , represents the radiation intensity at position in the incident direction .

[0039] The radiation intensity received by the radiation detector is related to temperature, wall emissivity, absorption coefficient, and scattering coefficient, and the radiation intensity is a function of these four quantities, which can be represented by the following formula:

[0040] (9) ​

[0041] The furnace cross section is divided into grids, as shown in Figure 4 each grid corresponds to a temperature, and solving the temperature value of each grid can calculate the temperature field of the furnace cross section. As can be seen from equation (11), in each grid, an I value corresponds to a set of temperature, wall emissivity, absorption coefficient, and scattering coefficient.

[0042] Matrix the equation (9):

[0043] (10)

[0044] wherein, , , , respectively represent the radiation intensity, temperature, absorption coefficient, and scattering coefficient corresponding to each grid; is the wall emissivity.

[0045] Step 3, obtain the simulation data set.

[0046] fluent simulation: use fluent software to build a numerical model of combustion and radiation in the boiler furnace. The solver uses a pressure-based steady-state solver. The Realizable k-ε model is used for the turbulence model, which uses mathematical constraints to improve model performance, is suitable for predicting moderate to strong swirl, and has better performance in strong streamline bending, vortex, and rotation. Radiation model: Discrete Ordinates (DO) model; number of radiation iterations: 20 times per flow iteration; angle discretization: θxφ=3x3 (according to the accuracy requirement, θ and φ are the zenith angle and azimuth angle used to discretize the spatial solid angle, θxφ=3x3 means that along the zenith angle θ direction, it is divided into 3 intervals from 0 to π, and along the azimuth angle φ direction, it is divided into 3 intervals from 0 to 2π). Set the particle size distribution of the coal powder used in the boiler to follow the Rosin-Rammler distribution, with a particle size distribution of 10-200um, an average particle size of 50um, and a distribution parameter of 1.1. Simulate the boiler load of 30%-100%, simulate once every 1%, a total of 71 temperature fields.

[0047] Smooth physical field: radiation parameter generation setting conditions: absorption coefficient in the range of [0.1, 0.8], step size 0.01, a total of 71; scattering coefficient in the range of [0.1, 0.8], step size 0.01, a total of 71; wall is a diffuse reflection surface, emissivity in the range of [0.6, 0.9], step size 0.01, a total of 31. Three different combinations have a total of 71*71*31=156271. The grid setting of the temperature field is as shown in Figure 4The grid cell temperature range is 700-1700°C, the temperature difference between adjacent grids is less than 10°C, and a total of 20*101=2020 temperatures are generated. Smooth physical field generation temperature The process is shown in the following formula.

[0048] For each grid There are:

[0049] (11)

[0050] For any adjacent grid And Satisfy:

[0051] (12)

[0052] The constraint violation function is set as follows:

[0053] (13)

[0054] Where, The total violation is used to judge whether the temperature field constraint meets the conditions. When and only when All constraints are met.

[0055] The temperature range violation can be represented by the following formula:

[0056] (14)

[0057] When , .

[0058] The adjacent grid temperature difference violation can be represented by the following formula:

[0059] (15)

[0060] When , .

[0061] Combination of temperature and radiation parameters There are 2091*156271=326,762,661 different combinations. All combinations are substituted into equation (9) to calculate the boundary radiation intensity at wavelengths of 550nm and 650nm , the data processing is shown in the following formula, and 326,762,661 pairs of Data as neural network training data set.

[0062] (16)

[0063] (17)

[0064] Step 4, Constructing the multi-layer feedforward neural network.

[0065] Constructing the multi-layer feedforward neural network, the schematic diagram of the neural network is shown in Figure 2 .

[0066] Step 4-1, Data preparation.

[0067] Suppose the simulation generates a training dataset containing samples, then the vector contained in each sample can be represented by the following formula:

[0068] (18)

[0069] Model output scalar:

[0070] (19)

[0071] Data preprocessing is performed.

[0072] Input feature standardization:

[0073] Z-score standardization is used, and the calculation of each feature dimension is as follows:

[0074] (20)

[0075] Where are the mean and standard deviation of the th feature, respectively.

[0076] Output temperature normalization:

[0077] The temperature is mapped to the interval [0, 1], where T max and T min represent the maximum and minimum values of all T in equation (17), respectively:

[0078] (21)

[0079] Step 4-2, Constructing the neural network.

[0080] Constructing a multi-layer feedforward neural network containing 3 hidden layers , which can be represented by the following formula:

[0081] (22)

[0082] Where, the input layer, where R represents the real number field, Rm×n represents a space composed of m rows and n columns of real number matrices:

[0083] (23)

[0084] Hidden layer 1, containing 256 nodes:

[0085] (24)

[0086] Hidden layer 2 (128 nodes):

[0087] (25)

[0088] Hidden layer 3 (64 nodes):

[0089] (26)

[0090] Output layer (1 node):

[0091] (27)

[0092] wherein, is a weight matrix, representing the full connection weight from the upper layer to the next layer, and the definition is:

[0093]

[0094]

[0095]

[0096]

[0097] , , , are respectively the bias parameters of the first, second, third and fourth layers of the neural network, and the definitions are:

[0098]

[0099]

[0100]

[0101]

[0102] LeakyReLU, is an activation function, and the expressions are respectively:

[0103] (28)

[0104] (29)

[0105] is the input value of the neuron; is the leakage coefficient, usually taken as 0.01-0.3.

[0106] Define a composite loss function with physical constraints.

[0107] Mean square error term:

[0108] (30)

[0109] where, is the number of samples in the training batch; is the true value.

[0110] Temperature gradient penalty term:

[0111] (31)

[0112] where, is the number of rows and columns of the temperature field grid division; is the horizontal and vertical difference operator, respectively; is the Frobenius norm.

[0113] Define a composite loss function with physical constraints:

[0114] (32)

[0115] where, is a user-defined coefficient.

[0116] Step 4-3, determine the training strategy.

[0117] The model training uses the following optimization algorithm: Levenberg-Marquardt (LM algorithm), for the th iteration:

[0118] (33)

[0119] where, is the grid parameter set; is the Jacobian matrix of the residual with respect to the parameters; is the residual vector; is the damping factor.

[0120] Terminate training when the validation set loss does not decrease for 20 consecutive rounds.

[0121] is the Figure 4As shown, the calibrated four cameras are used to collect images at the 25.5m level of a boiler of a power plant, and the radiation signal collection is completed. The measured radiation intensity under the working condition is obtained, the pre-trained multi-layer feedforward neural network is called, the input of the measured data and the loading of the model are completed. The model outputs the predicted temperature values of all the grids of the section, and each temperature value is rearranged according to the pre-set furnace direction and converted into a.dat file. The temperature.dat files under different working conditions are drawn into the form of temperature cloud maps, as shown in Figure 5 As shown, the visualization of the temperature of the furnace section is completed. The whole process from data collection to output takes less than 100 milliseconds, which meets the real-time monitoring requirements of industrial processes and overcomes the shortcomings of long time consumption and large occupation of computing resources in pure physical model calculation.

[0122] The above is only the preferred embodiment of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiment. Any equivalent modification or change made by those skilled in the art according to the disclosed content of the present application shall be included in the protection scope recited in the claims.

Claims

1. A furnace temperature field reconstruction method based on the fusion of the radiation transfer equation and a multilayer feedforward neural network, characterized in that: The method includes the following steps: Step 1, Blackbody furnace calibration: Use a blackbody furnace to calibrate the radiation detector and establish the relationship between image intensity and radiation intensity; In step 1, the blackbody furnace calibration system consists of a blackbody furnace, a detector, a detector bracket, a computer, network cables, and power cords. Absolute intensity calibration is performed on the CCD camera output. The calibration process is carried out on the blackbody furnace, and the calibration curve is expressed by the following formula: I 650nm =I R =f(r,τ) (1) I 550nm =I G =f(g,τ) (2) In the formula, r and g represent the image intensity, i.e., the r and g values ​​of the image; τ represents the exposure time when the camera captures the image; a dual bandpass filter is set at the front end of the CCD, with response wavelengths of 550nm and 650nm respectively, and a half-bandwidth of 10nm; therefore, λ in the formula... r Take 650×10 -9 m; λ g Take 550×10 -9 m; In subsequent calculations, only the radiation intensity at wavelengths of 550nm and 650nm will be considered; Step 2: Use the DOM algorithm to establish the detailed radiative transfer equation (RTE) that takes into account medium absorption, scattering, and wall effects; In step 2, the radiation transfer equation RTE is applied along the line of sight. The steady-state form is: In the formula, For position r, direction Radiated energy on; I b (T) represents the blackbody radiation intensity at temperature T; Let be the scattering phase function, representing the scattering phase from the direction. To the direction Scattered energy distribution; κ s σ is the absorption coefficient of the solid medium inside the furnace. s The scattering coefficient, extinction coefficient β, and scattering rate ω of the solid medium inside the furnace are: β=κ s +s s (4) The radiation detector at position r along The intensity of radiation received from within the furnace in the direction of the line of sight is expressed by the following formula: In the formula, ε is the furnace wall emissivity; r0 is the starting point of the line-of-sight path; τ(r',r) is the optical thickness, which refers to the cumulative attenuation from position r' to r, and is expressed by the following formula: I w The wall contribution term is represented by the following formula: In the formula, Used to determine the incident direction; a value less than 0 indicates incident radiation, and n is the normal unit vector; I b (r0) represents the blackbody radiation intensity at position r0. Indicates the incident direction at position r0 The radiation intensity; The intensity of radiation received by the radiation detector is related to temperature, wall emissivity, absorption coefficient, and scattering coefficient. Since the radiation intensity is a function of these four quantities, it can be expressed by the following formula: I=F(T,ε,κ,σ) (9) The furnace cross-section is divided into N grids, each grid corresponding to a temperature. By solving for the temperature value of each grid, the temperature field of the furnace cross-section can be calculated. Transform equation (9) into a matrix: I=f(T,ε,κ,σ)(10) Where I = (I1, I2, ..., I N ) T T = (T1, T2, ..., T N ) T , κ=(κ1,κ2,...,κ N ) T , σ=(σ1,σ2,...,σ N ) T These represent the radiation intensity, temperature, absorption coefficient, and scattering coefficient corresponding to each grid, respectively; ε is the furnace wall emissivity. Step 3: Generate a dataset as the learning set for the neural network by smoothing the temperature field and using fluent simulation; Step 4, construct a multi-layer feedforward neural network, including the following steps: Step 4-1, Data preparation, including setting the model output scalar and data preprocessing; Step 4-2: Construct a neural network, including a multi-layer feedforward structure with an input layer, three hidden layers, and an output layer, and define a composite loss function that includes a mean squared error term and a temperature gradient penalty term. Step 4-3: Determine the training strategy; Step 5: Learn a good model to predict the temperature of each grid and obtain the temperature field of the furnace cross section.

2. The furnace temperature field reconstruction method based on the fusion of the radiation transfer equation and a multilayer feedforward neural network as described in claim 1, characterized in that: In step 3, for the Fluent simulation, a numerical model of combustion and radiation in the boiler furnace is constructed using Fluent software; a pressure-based steady-state solver is used; the turbulence model adopts the Realizable k-ε model, which uses mathematical constraints to improve model performance; the radiation model is the Discrete Ordinates (DO) model; the number of radiation iterations is 20 per flow iteration; angle discretization is: θ and These are the zenith angle and azimuth angle used for discrete spatial solid angles. This means dividing the zenith angle θ into three intervals from 0 to π, along the azimuth angle. The direction is divided into 3 intervals from 0 to 2π; the particle size distribution of the pulverized coal used in the boiler is set to follow the Rosin-Rammler distribution, with a particle size distribution of 10-200um, an average particle size of 50um, and a distribution parameter of 1.1; the boiler load is simulated from 30% to 100%, and the simulation is repeated every 1%, with a total of 71 temperature fields.

3. The furnace temperature field reconstruction method based on the fusion of the radiation transfer equation and a multilayer feedforward neural network as described in claim 2, characterized in that: In step 3, for the smooth physical field, the radiation parameter generation settings are: absorption coefficient in the range of [0.1, 0.8], step size 0.01, for a total of 71 parameters; The scattering coefficient is in the range of [0.1, 0.8], with a step size of 0.01, for a total of 71 values; the wall surface is a diffuse reflective surface, with an emissivity in the range of [0.6, 0.9], with a step size of 0.01, for a total of 31 values; the three different combinations generate a total of 71*71*31=156271 values; the grid cell temperature range is 700-1700℃, and the temperature difference between adjacent grid cells is less than 10℃, generating a total of 20*101=2020 temperatures; the process of smoothing the physical field to generate temperature T is shown in the following formula: For each grid i, we have: 700≤T i ≤1700 (11) For any adjacent grids i and i+1, the following holds: |T i -T i+1 |≤10 (12) The constraint violation function is expressed by the following formula: Γ(T)=Ψ(T i )+Φ(T i ,T i+1 ) (13) Where Γ represents the total violation, used to judge whether the temperature field constraints are satisfied; all constraints are satisfied if and only if Γ=0; Ψ(T i The ) represents the violation of the temperature range, expressed by the following formula: Ψ(T i )=max(700-T i ,0)+max(T i -1700,0) (14) When T i When ∈[700,1700], Ψ(T) i ) = 0; Φ(T i ,T i+1 The ) represents the temperature difference violation between adjacent grids, expressed by the following formula: Φ(T i ,T i+1 )=max(|T i -T i+1 |-10,0) (15) When |T i -T i+1 When |≤10, Φ(T) i ,T i+1 ) = 0; There are 2091*156271=326,762,661 different combinations of temperature and radiation parameters (T,ε,κ,σ); substituting all combinations into equation (9), the boundary radiation intensity I at wavelengths of 550nm and 650nm is calculated respectively. R ,I G The data processing is shown in the following formula, resulting in 326,762,661 pairs (I N ,T N The data serves as a training dataset for the neural network. T N =(T1,T2,...,T N ) T (17)。 4. The furnace temperature field reconstruction method based on the fusion of the radiation transfer equation and a multilayer feedforward neural network according to claim 3, characterized in that: In step 4-1, data preparation includes the following steps: Suppose the simulated training dataset contains N = 326,762,661 samples, then the vector contained in each sample is represented by the following formula: x i =[I R / I G (i) ](18) Model output scalar: y i =T (i) (19) Perform data preprocessing; Input feature standardization: Z-score standardization is used, and the following is calculated for each feature dimension j: Where μ j ,θ j are the mean and standard deviation of the j-th feature, respectively; Output temperature normalization: Maps the temperature to the [0,1] interval, where T max and T min Let these represent the maximum and minimum values ​​of T in equation (17):

5. The furnace temperature field reconstruction method based on the fusion of the radiation transfer equation and a multilayer feedforward neural network according to claim 4, characterized in that: In step 4-2, a multi-layer feedforward neural network N containing 3 hidden layers is constructed, represented by the following formula: in, Represents neural network operations; Input layer, where R represents the real number field, R m×n Represents the space formed by m rows and n columns of real numbers: x∈R(23) Hidden layer 1 contains 256 nodes: f1(x)=LeakyReLU(W1x+b1),W1∈R 256×1 ,b1∈R 256×1 (24) Hidden layer 2 contains 128 nodes: f2(x)=LeakyReLU(W2x+b2),W2∈R 128×256 b2∈R 128×1 (25) Hidden layer 3 contains 64 nodes: f3(x)=tanh(W3x+b3),W3∈R 64×128 ,b3∈R 64×1 (26) Output layer, containing 1 node: Where W is the weight matrix, representing the fully connected weights from the upper layer to the lower layer, defined as: Where w represents an element in the matrix, the superscript number indicates the matrix number, the subscript number indicates the row and column number of the element, and b1, b2, b3, and b4 are the bias parameters of the first, second, third, and fourth layers of the neural network, respectively, and are defined as follows: b4∈R Where b represents an element in the matrix, the superscript number indicates the matrix number, and the subscript number indicates the row and column number of the element; LeakyReLU and tanh are activation functions, with the following expressions: z is the neuron input value; α is the leakage coefficient, usually taken as 0.01-0.3; Calculate the mean square error term: Where M represents the number of samples in the training batch; y i Represents the actual value; Calculate the temperature gradient penalty term: Where H and W represent the number of rows and columns of the temperature field mesh; These represent the horizontal and vertical difference operators, respectively; || || F Denotes the Frobenius norm; Define a composite loss function that includes physical constraints: in, δ is a user-defined coefficient.

6. The furnace temperature field reconstruction method based on the fusion of the radiation transfer equation and a multilayer feedforward neural network according to claim 5, characterized in that: Step 4-3: Determine the training strategy; The model training uses the Levenberg-Marquardt optimization algorithm. For the (k+1)th iteration: i k+1 =θ k -(J T J+λI) -1 J T r (33) Where θ represents the set of mesh parameters; J is the Jacobian matrix of the residuals with respect to the parameters; r is the residual vector; and λ is the damping factor. Training is terminated when the validation set loss does not decrease for 20 consecutive rounds.

7. The furnace temperature field reconstruction method based on the fusion of the radiation transfer equation and a multilayer feedforward neural network according to claim 6, characterized in that: Four calibrated radiation detectors are used to acquire images of the boiler, completing the radiation signal acquisition work; the measured radiation intensity under the current operating conditions is obtained, and a pre-trained multilayer feedforward neural network is called to complete the input of the measured data and model loading; the model outputs the predicted temperature values ​​of all grids in the cross section, and each temperature value is rearranged according to the pre-set furnace direction and converted into a .dat file; The temperature data files under different operating conditions are plotted as temperature cloud maps to complete the visualization output of furnace cross-sectional temperature.

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