A method for reconstructing a three-dimensional temperature field of a furnace based on a double-branch residual network

Abstract

The application discloses a kind of based on double branch residual network's furnace three-dimensional temperature field reconstruction method, including obtaining the furnace three-dimensional temperature field data under multiple working conditions, discrete as point level supervised learning sample;Double branch residual neural network model is constructed, and working condition condition branch extracts global working condition characteristics with working condition variable and physical prior feature as input, and local space feature is extracted after Fourier feature mapping is carried out to coordinate coding branch on space position information;High-level feature is fused after the output of two branches and is input into fusion prediction head, and output temperature prediction value;After training model, the working condition parameters to be predicted and space position are input into model, and the furnace three-dimensional temperature field is obtained.The application realizes working condition-space information decoupling by double branch structure, enhances high-frequency detail capture ability in combination with Fourier feature mapping, solves the problem that existing method feature aliasing and local high gradient area prediction precision is low, realizes the high-precision rapid reconstruction of furnace three-dimensional temperature field.

Description

Technical Field

[0001] This invention relates to the field of boiler furnace temperature field reconstruction technology, specifically a method for reconstructing a three-dimensional furnace temperature field based on a bi-branch residual network. Background Technology

[0002] Furnace temperature is a core physical quantity characterizing boiler combustion organization, heat transfer intensity, and pollutant generation. Its spatial distribution directly affects combustion stability within the furnace and the heat absorption deviation of the water-cooled walls, and is closely related to boiler safe operation, efficiency optimization, and low-pollution combustion control. In recent years, with the development of large-scale coal-fired power units towards deep and flexible peak shaving and refined combustion, operating conditions have exhibited stronger nonlinearity, coupling, and fluctuation. Relying solely on a few measuring points or empirical judgment is insufficient to accurately characterize the complex three-dimensional temperature distribution inside the furnace. Therefore, constructing a three-dimensional furnace temperature field prediction model that balances accuracy, speed, and generalization ability has become a key issue in boiler intelligent sensing and operation optimization.

[0003] Currently, the main technical approaches for obtaining the internal temperature field of a furnace include the following two categories:

[0004] (1) Numerical simulation method based on computational fluid dynamics (CFD). The CFD method can reveal the thermal evolution law in the furnace under different boundary conditions, air distribution mode and load level by establishing a three-dimensional coupled model of combustion, flow, heat transfer and radiation. It is an important tool for boiler design optimization, combustion adjustment and offline mechanism analysis. However, the CFD method has prominent problems such as long calculation cycle, high modeling and convergence cost and difficulty in supporting online rapid decision making, and it is difficult to be directly applied to real-time temperature field sensing.

[0005] (2) Data-driven machine learning methods. In recent years, training machine learning surrogate models based on CFD data has gradually become an important research direction for temperature field reconstruction. Existing methods such as MLP (Multilayer Perceptron), DNN (Deep Neural Network), and GDNN (Guided Deep Neural Network) have verified the feasibility of rapid reconstruction of the three-dimensional temperature field inside the furnace to a certain extent. However, existing methods still have the following shortcomings:

[0006] First, most methods directly concatenate operating parameters and spatial coordinates before inputting them into a single network. This causes the two types of features with different physical meanings to overlap at the input layer, making it difficult for the network to effectively distinguish between global thermal driving information and local spatial location information. This limits the network's ability to generalize across operating conditions and capture local details.

[0007] Secondly, when ordinary multilayer perceptrons process low-dimensional spatial coordinates, they are more likely to learn global smooth low-frequency changes, but they are insufficient in representing complex high-frequency spatial patterns in local high-gradient regions such as near the burner nozzle and flame boundary, resulting in large temperature prediction errors in key areas such as the high-temperature core region and the nozzle neighborhood.

[0008] Third, existing methods generally do not fully utilize prior engineering knowledge such as the spatial arrangement of the burner. The models have a weak ability to perceive the location of heat sources and the structure of the flame, making it difficult to accurately describe the local temperature changes in key areas such as the nozzle proximal region and the flame core region.

[0009] Therefore, in view of the above situation, there is an urgent need to develop a furnace three-dimensional temperature field reconstruction method based on a bi-branch residual network to overcome the shortcomings in current practical applications. Summary of the Invention

[0010] The purpose of this invention is to provide a method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network, so as to solve the problems mentioned in the background art.

[0011] To achieve the above objectives, the present invention provides the following technical solution:

[0012] A method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network includes the following steps:

[0013] S1. Acquire three-dimensional temperature field data of the furnace under various operating conditions; Discretize each set of operating condition data into point-level supervised learning samples. Each supervised learning sample includes the spatial location information of the sampling point, boiler operating condition parameters, physical prior features, and the temperature value of the sampling point.

[0014] S2. Construct a dual-branch residual neural network model, which includes a working condition branch, a coordinate encoding branch, and a fusion prediction head;

[0015] The operating condition branch takes operating condition variables and physical prior features as input, projects them to the latent space through linear mapping, and extracts high-level operating condition features through a multi-layer residual MLP module.

[0016] The coordinate encoding branch takes spatial location information as input, performs Fourier feature mapping on the spatial location information, and then extracts high-level spatial features through a multi-layer residual MLP module.

[0017] S3. The working condition high-rise features and the spatial high-rise features are fused together, and the fused features are input into the fusion prediction head to output the temperature prediction value.

[0018] S4. Using the dataset constructed in step S1, train the dual-branch residual neural network model constructed in step S2 with the loss function. Input the working condition parameters of the working condition to be predicted and the spatial location information inside the furnace into the trained model to obtain the three-dimensional temperature field of the furnace under the working condition.

[0019] As a further aspect of the present invention: the residual MLP module in step S2 specifically comprises: for any input latent vector The residual block is represented as:

[0020] ;

[0021] in, For the residual function, A two-layer MLP structure is adopted, consisting of a first linear layer, an activation function, layer normalization, Dropout, and a second linear layer connected sequentially. Its form is as follows:

[0022] ;

[0023] In the formula, To act on the input The first linear layer weight matrix, The weight matrix of the second linear layer, b 1 and b 2 For the bias term, LN(·) represents layer normalization.

[0024] As a further aspect of the present invention: the Fourier feature mapping in step S2 specifically involves performing multi-band sine and cosine expansions on the three coordinate components of the spatial location information, while retaining the original three coordinate components. For coordinate component x, the Fourier feature mapping result is as follows:

[0025] ;

[0026] Where B is the Fourier band number, and the value of B ranges from 4 to 10.

[0027] As a further aspect of the present invention: the physical prior features include at least one of the following three categories of features:

[0028] The first category is spatial geometric features, which include the normalized coordinates of the sampling point, the radial distance of the sampling point in the horizontal section of the furnace, the planar distance from the sampling point to the central axis of the furnace, coordinate intersection terms, and higher-order terms in the height direction.

[0029] The second category is operating condition coupling characteristics, including the air-fuel ratio, the ratio of primary air volume to secondary air volume, the coupling terms of load and fuel heat input, and the interaction terms of air volume and space height.

[0030] The third category is prior features of the burner neighborhood: including the Euclidean distance from the sampling point to each burner nozzle, the distance from the sampling point to the nearest burner nozzle, the distance from the sampling point to the second nearest burner nozzle, the number of the nearest burner nozzle, and the local coordinate difference of the sampling point relative to the nearest burner nozzle.

[0031] As a further aspect of the present invention: in step S4, a region-weighted loss function is used as the loss function, and the near-field samples of the nozzle are assigned a higher weight than the far-field samples.

[0032] As a further aspect of the present invention: the boiler operating condition parameters mentioned in step S1 include at least one of the following: unit load, total air volume, primary air volume, secondary air volume, separate burnout air volume, coal feed rate, lower heating value of coal type, and dry ash-free volatile matter content.

[0033] As a further aspect of the present invention: the acquisition of three-dimensional temperature field data of the furnace under multiple operating conditions in step S1 specifically involves: using CFD software to conduct multi-condition three-dimensional combustion numerical simulation of the target coal-fired boiler, wherein the changing dimensions of the operating conditions include at least one of coal type, unit load, and air distribution mode; the CFD numerical simulation uses a Realizable k-ε turbulence model to simulate turbulent flow in the furnace, a P1 radiation model to simulate radiative heat transfer, a gray-weighted gas radiation model to calculate flue gas emissivity, a component transport model to define the reaction mechanism to achieve multi-component coupled calculation, and a discrete phase model to describe the movement and combustion process of pulverized coal particles.

[0034] As a further aspect of the present invention: the dataset in step S1 is divided according to the working condition file, and all working condition data are divided into training set, validation set and test set according to the proportion.

[0035] As a further aspect of the present invention: the fusion of the working condition high-rise features and the spatial high-rise features in step S3 specifically involves: splicing the working condition high-rise features and the spatial high-rise features in the feature dimension; the fusion prediction head consists of a fully connected layer, an activation function, layer normalization, and residual mapping, and outputs a scalar temperature value after compressing the feature dimension layer by layer.

[0036] As a further aspect of the present invention: before executing step S2, a preprocessing step for the input data is included: standardizing or normalizing the operating condition variables, physical prior features, and spatial location information; standardizing the temperature values ​​in the same way as the input features; and obtaining the physical temperature value by inverse standardizing the temperature prediction value output by the model; the standardization process is as follows:

[0037] ;

[0038] in, , , and All values ​​are calculated solely from the training set and are fixed for use on the validation and test sets.

[0039] Compared with the prior art, the beneficial effects of the present invention are:

[0040] 1. Decoupling of operating conditions and spatial information enhances cross-operating condition generalization ability. Existing methods directly concatenate operating condition parameters and spatial coordinates into a single network, resulting in aliasing of features with different physical properties at the input layer. This invention employs a dual-branch network architecture: the operating condition branch independently extracts global thermal information, while the coordinate branch independently extracts local spatial features, achieving fusion in a high-dimensional latent space. This avoids interference between heterogeneous features, enabling the model to have stronger generalization ability for new operating conditions such as unseen coal types and unseen loads.

[0041] 2. Enhanced Fourier Feature Mapping for Improved High-Frequency Detail Capture: Ordinary networks, when processing low-dimensional coordinates, naturally tend to learn low-frequency smooth variations, failing to adequately represent complex spatial patterns in high-gradient regions such as the nozzle near-zone and flame boundary. This invention introduces Fourier feature mapping into the coordinate branch, expanding the low-dimensional coordinates into a multi-frequency periodic feature space. This allows the network to simultaneously capture low-frequency attenuation trends along the furnace height and high-frequency variation details in local high-gradient regions, significantly improving the prediction accuracy for key areas such as the main combustion zone and burner near-zone.

[0042] 3. Introducing burner spatial priors to improve reconstruction accuracy in key areas. Existing methods do not fully utilize engineering prior knowledge such as burner spatial layout. This invention constructs neighborhood prior features such as the distance from the sampling point to the burner nozzle and the relative coordinates of the nearest nozzle, enabling the model to explicitly perceive the location of the heat source; at the same time, a region-weighted loss is used to assign higher weights to samples near the nozzle, guiding the model to prioritize optimization of engineering-sensitive areas, effectively reducing prediction errors in high-gradient regions.

[0043] 4. Residual structure ensures stable training of deep networks. This invention introduces residual MLP modules in the working condition branch, coordinate branch, and fusion prediction head, transforming the learning objective from directly fitting the complete mapping to learning incremental correction. From a physical perspective, the temperature field can be understood as the superposition of the global thermal background and local spatial perturbations. The residual blocks learn the temperature distribution correction based on existing features layer by layer, alleviating the gradient decay and degradation problems of deep networks.

[0044] 5. Rapid reconstruction to meet real-time engineering needs. Traditional CFD solutions for single operating conditions take hours to days. This invention, after offline training, only requires inputting operating condition parameters and spatial location into the model during the online phase to obtain the temperature field, achieving millisecond-level response and supporting real-time application scenarios such as boiler digital twins, online monitoring, and combustion optimization. Attached Figure Description

[0045] Figure 1 This is a flowchart of the furnace three-dimensional temperature field reconstruction method based on a dual-branch residual network according to the present invention;

[0046] Figure 2 This is a schematic diagram of the boiler geometry and mesh division in an embodiment of the present invention;

[0047] Figure 3 This is a diagram of the model's physical prior feature structure in an embodiment of the present invention;

[0048] Figure 4 This is a comparison chart of prediction results for different partitions in an embodiment of the present invention. Detailed Implementation

[0049] The technical solution of this application will be further described in detail below with reference to specific embodiments.

[0050] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0051] Example 1

[0052] This embodiment takes a 660MW ultra-supercritical coal-fired boiler as the research object and describes in detail the specific implementation process of the furnace three-dimensional temperature field reconstruction method based on a dual-branch residual network described in this invention.

[0053] I. Construction of CFD Numerical Simulation Dataset

[0054] In this embodiment, the boiler adopts a single furnace, a П-shaped arrangement, and a suspended structure. For example... Figure 2 As shown. The furnace height is 67,800 mm, and the cross-sectional area is 19,230 mm × 19,264 mm. The burners are arranged on the four walls, using a tangential combustion method. There are five burners (AE) and 14 layers of secondary air and separate burnout air on the four walls.

[0055] The geometric model was built using SpaceClaim, and the mesh was generated using Gambit. The main furnace body used a structured hexahedral mesh, while complex parts such as the burner nozzles and SOFA openings used unstructured tetrahedral meshes. After mesh independence verification, a final mesh size of 2.9 million was used for numerical combustion simulation.

[0056] In the CFD simulation, a Realizable k-ε turbulence model was used, the P1 model was used for radiative heat transfer, the gray-weighted WSGGM model was used to calculate the flue gas emissivity, the combustion reaction was described by a component transport model, and pulverized coal combustion was described by a discrete phase model. The model was verified by field measurement data, and the error remained within 4.9%.

[0057] This embodiment uses three types of coal, and for each type, 20 sets of calculations are performed under different loads (30%-100%) and different air distribution methods, resulting in a total of 60 sets of temperature field data. The boundary conditions are as follows:

[0058] Table 1. Boundary Condition Range for Boiler Pulverized Coal Combustion Simulation

[0059]

[0060] Each set of working condition data is discretized into a large number of point-level supervised learning samples. For the i-th spatial sampling point in the k-th working condition, its supervised learning sample can be written as:

[0061] ;

[0062] in, Here are the three-dimensional coordinates of the sampling point. This refers to the physical prior features corresponding to this point. This is a label for the actual temperature obtained from CFD calculations. Through this point-level sample organization, the model can fully utilize the spatial distribution information in each three-dimensional temperature field with a limited number of operating conditions, thereby learning the mapping relationship between the operating condition boundary conditions and the local temperature response.

[0063] The operating parameter vector c includes: load L, total air volume m. air Primary air volume (m) pa Secondary air volume (m) sa SOFA air volume (m) sofa Coal feed rate (m) coal Low heating value Q net Dry, ash-free, volatile matter-free V daf .

[0064] The physical prior features include the following three categories: Figure 3 As shown:

[0065] The first category is spatial geometric features, which include the normalized coordinates of the sampling point, the radial distance of the sampling point in the horizontal section of the furnace, the planar distance from the sampling point to the central axis of the furnace, coordinate intersection terms, and higher-order terms in the height direction.

[0066] The second category is operating condition coupling characteristics, including the air-fuel ratio, the ratio of primary air volume to secondary air volume, the coupling terms of load and fuel heat input, and the interaction terms of air volume and space height.

[0067] The third category is prior features of the burner neighborhood: including the Euclidean distance from the sampling point to each burner nozzle, the distance from the sampling point to the nearest burner nozzle, the distance from the sampling point to the second nearest burner nozzle, the number of the nearest burner nozzle, and the local coordinate difference of the sampling point relative to the nearest burner nozzle.

[0068] Before performing model training, a preprocessing step is also included for the input data.

[0069] Since the dimensions and numerical ranges of different input variables vary considerably, the data preprocessing section employs a standardization method based on training set statistics to normalize the input features and output temperature. For any input feature X and temperature value T, the standardized form is as follows:

[0070] ;

[0071] in, , , and All values ​​are calculated solely from the training set and are fixed for use on the validation and test sets. This process avoids data leakage while ensuring the numerical comparability of samples from different operating conditions and spatial regions during network training.

[0072] The dataset was partitioned according to operating condition files, randomly divided into training, validation, and test sets in a ratio of 40:8:12. This partitioning by operating condition allows for a more rigorous test of the model's predictive ability for temperature fields under conditions where no coal type, load, or air distribution combination is known, and it better meets the needs of practical engineering applications for rapidly reconstructing the furnace temperature field based on new operating boundary conditions.

[0073] II. Construction of a Two-Branch Residual Neural Network Model

[0074] like Figure 1 As shown, the dual-branch residual neural network model constructed in this embodiment includes three parts: the working condition branch, the coordinate encoding branch, and the fusion prediction head.

[0075] (1) Operating Condition Branch

[0076] The input to the operating condition branch consists of operating condition variables and related physical prior features. This input includes raw operating condition parameters such as load, total air volume, primary air volume, secondary air volume, SOFA air volume, coal feed rate, lower heating value, and volatile matter content, as well as derived features such as the air-to-coal ratio, the ratio of primary to secondary air, heat input intensity, burner neighborhood distance, and local relative coordinates. The operating condition branch projects the input to a unified latent space through a linear mapping:

[0077] ;

[0078] In the formula, and For linear layer weights and biases, Representation layer normalization, This represents a nonlinear activation function. In this embodiment, GELU is used as the activation function to improve the network's ability to smoothly fit complex nonlinear relationships. After initial mapping, the operating condition features are further input into a multi-layer residual MLP module for deeper characterization:

[0079] ;

[0080] in, Let l be the input feature of the l-th residual block. For the l-th residual mapping in the working condition branch, This represents the number of residual blocks in the load case branch. Inputting these variables into independent load case branches avoids direct mixing with the original spatial coordinates at the input layer, thereby enhancing the model's ability to extract global load case driving information.

[0081] (2) Coordinate encoding branch

[0082] The coordinate encoding branch takes spatial location information as input, performs Fourier feature mapping on the spatial location information, and then extracts high-level spatial features through a multi-layer residual MLP module.

[0083] For ordinary MLPs that take low-dimensional coordinates as input, the network is usually better at learning global smooth changes, but lacks the ability to fit local high-frequency details. Therefore, this invention introduces Fourier feature mapping into the coordinate branch, projecting low-dimensional spatial coordinates onto a high-dimensional periodic feature space to enhance the network's ability to express complex spatial details.

[0084] Let the normalized spatial coordinates be:

[0085] ;

[0086] Where x, y, and z represent the scale-normalized coordinates of the furnace in the transverse, longitudinal, and height directions, respectively. For each coordinate component, B frequency bands are introduced for sine and cosine expansion, and the Fourier feature map can be defined as:

[0087] ;

[0088] In the formula, B represents the number of Fourier frequency bands. In this embodiment, B=6, meaning that each coordinate direction is mapped to the sine and cosine basis functions corresponding to the 6 frequency bands. Since the original 3D coordinates are also preserved in the mapping result, the input dimension of the coordinate branch is: When B=6, the input dimension of the coordinate branch is 39. This structure allows the network to simultaneously retain the low-frequency spatial location information expressed by the original coordinates and enhances its ability to distinguish local high-frequency spatial changes through multi-frequency sine and cosine basis functions. For the furnace temperature field, the low-frequency part mainly corresponds to the overall temperature decay along the height direction and the layered structure of the main combustion zone and the burnout zone; the high-frequency part mainly corresponds to the near-burner zone, flame boundary, local mixing layer, and temperature gradient changes near the wall. Fourier coordinate encoding enables these spatial information at different scales to be explicitly expanded in the input layer, thereby reducing the difficulty for the subsequent MLP hidden layer to learn complex spatial frequency components.

[0089] The feature input coordinate branch encoder after coordinate encoding is calculated as follows:

[0090] [ ];

[0091] High-level spatial features are extracted using a multi-layer residual MLP module.

[0092] ;

[0093] in, This is the input for the l-th residual block of the coordinate branch. For coordinate branch residual mapping, This refers to the number of residual blocks in the coordinate branch. In this embodiment, both the working condition branch and the coordinate branch adopt a symmetrical three-layer residual tower structure, i.e. = =3, so that the two types of features have similar representation depth and latent space scale before entering the fusion layer, which is beneficial to subsequent fusion.

[0094] (3) Residual MLP module

[0095] This embodiment introduces residual MLP modules in the load condition branch, coordinate branch, and fusion prediction head to improve the network's ability to express complex nonlinear mappings and maintain training stability. For any input latent vector h, the residual block is represented as:

[0096] ;

[0097] in, For the residual function, A two-layer MLP structure is adopted, consisting of a first linear layer, an activation function, layer normalization, Dropout, and a second linear layer connected sequentially. Its form is as follows:

[0098] ;

[0099] In the formula, To act on the input The first linear layer weight matrix, The weight matrix of the second linear layer, b 1 and b 2LN(·) represents layer normalization, acting as a bias term. The role of residual connections is to transform the learning objective of deep networks from directly fitting complex functions to learning incremental corrections relative to input features, thereby alleviating gradient decay and degradation problems during deep MLP training. For the furnace temperature field reconstruction task, the residual structure also has a clear physical interpretation: the temperature field can be understood as being composed of a global thermal background and local spatial perturbations. The residual blocks learn the temperature distribution correction based on existing features layer by layer, rather than refitting the complete mapping at each layer.

[0100] (4) Feature fusion and temperature prediction

[0101] After the conditional branch and the coordinate encoding branch, the model obtains the global condition latent features. and local spatial latent features :

[0102] ;

[0103] The two are then concatenated along the feature dimension:

[0104] ;

[0105] Features after fusion It simultaneously includes global temperature field background information determined by operating conditions and local temperature structure information determined by spatial coordinates. This feature is further input into the fusion prediction head:

[0106] ;

[0107] in, This is to predict the temperature in the normalized space. The fusion prediction head consists of several fully connected layers, GELU activation, Layer Norm, and residual mapping, compressing the feature dimensions layer by layer, and finally outputting a scalar temperature value. In practical applications, the normalized temperature output by the model needs to be denormalized to the physical temperature using the temperature statistics of the training set.

[0108] ;

[0109] in, and These are the mean and standard deviation of the temperature in the training set, respectively.

[0110] From a physical perspective, the fusion prediction head undertakes the task of modeling the coupled relationship between conditional thermal state and spatial response. For the same spatial coordinates, different loads, air volumes, and coal quality conditions will lead to significant changes in temperature values; for the same operating condition, different spatial locations correspond to different combustion stages, heat transfer intensities, and local jet effects. Therefore, only by fusing the operating condition branch and the coordinate branch in the high-level implicit space can the model simultaneously express the temperature field differences across operating conditions and the spatial distribution details under the same operating condition.

[0111] In this embodiment, the hidden layer dimension of the working condition branch and the coordinate branch is set to 128, and the scalar temperature value is output after the feature dimension is compressed layer by layer by the fusion prediction head.

[0112] III. Model Training

[0113] This embodiment trains the constructed bi-branch residual neural network model using a loss function. This embodiment employs a region-weighted loss function, assigning higher weights to near-field samples than to far-field samples.

[0114] The model was trained using the Adam optimizer with a learning rate of 1.32 × 10⁻⁶. −4 The weight decay is 6.84 × 10. −4 The batch size is 360, the epoch is 100, and the early stopping strategy patience is 30.

[0115] IV. Temperature Field Reconstruction and Effect Verification

[0116] By inputting the operating parameters of the operating condition to be predicted and the spatial location information inside the furnace into the trained model, the three-dimensional temperature field of the furnace under that operating condition is obtained.

[0117] To comprehensively evaluate the model's performance in reconstructing the three-dimensional temperature field of the furnace, this embodiment assesses it from three levels: overall error, error per operating condition, and regional error. The overall indicators used are root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and coefficient of determination (R²). 2 ), respectively defined as:

[0118] ;

[0119] ;

[0120] ;

[0121] ;

[0122] in, This represents the true average temperature. RMSE is more sensitive to large errors and is suitable for characterizing the overall reconstruction accuracy; MAE provides a more intuitive reflection of the mean absolute deviation; MAPE helps in analyzing the relative error level; R... 2 This is used to measure the model's ability to explain trends in temperature change.

[0123] The overall performance metrics of this embodiment on the test set are: RMSE 81.897K, MAE 49.667K, MAPE 3.785%, R 2 It is 0.9204.

[0124] The prediction results by coal type are shown in the table below:

[0125] Table 2 Evaluation Table of Prediction Results by Coal Type

[0126]

[0127] The average MAPE for the three coal types were 3.23%, 4.22%, and 3.78%, respectively, and the model maintained high prediction accuracy for all three coal types.

[0128] Regional prediction results are as follows Figure 4 As shown in the table below (divided by distance from the sampling point to the nearest burner nozzle), the results are as follows:

[0129] Table 3 Nozzle Zone Prediction and Evaluation Table

[0130]

[0131] The MAPE in the near-nozzle region was 3.32%, in the transition region it was 3.58%, and in the far-nozzle region it was 3.82%, verifying the effectiveness of burner neighborhood prior features and regional weighted loss in improving the prediction accuracy of key areas.

[0132] To verify the effectiveness of each key module of this invention, an ablation experiment was also conducted in this embodiment. The ablation experiment was set up as follows: Fourier coordinate encoding was removed (the Fourier feature mapping in the coordinate branch was replaced with the direct input of the original coordinates), the dual-branch structure was removed (the operating condition variables and spatial coordinates were directly concatenated and then input into a single MLP network), the residual module was removed (the residual connections in each branch were removed), the burner spatial features were removed (the burner neighborhood prior features were removed from the input), and the nozzle region weighted training was canceled (uniform sample weights were used). Each ablation model used the same data partitioning, number of training epochs, optimizer, learning rate, batch size, and early stopping strategy as the complete model.

[0133] Ablation experiments showed that the complete model outperformed all the aforementioned ablation models in all metrics:

[0134] Table 4 Evaluation Table for Different Modules of Ablation Experiment

[0135]

[0136] Ablation experiments verified that Fourier feature mapping, bi-branch structure, residual connection, burner spatial prior features, and region weighted training in this invention all contribute to the model's predictive performance.

[0137] Compared with traditional methods, the method of this invention outperforms benchmark models such as XGBoost, MLP, DeepONet, and FNO in terms of RMSE, MAE, MAPE, and R² metrics.

[0138] Table 5 Performance Comparison of Different Model Algorithms

[0139]

[0140] The above comparison verifies the superiority of the method of the present invention in the task of rapid reconstruction of the three-dimensional temperature field of the furnace.

[0141] This method for reconstructing the three-dimensional temperature field of the furnace based on a bi-branch residual network can be widely applied to the rapid reconstruction of the three-dimensional temperature field inside the furnace of coal-fired boilers. Compared with traditional CFD case-by-case solutions, the model trained by this invention can achieve real-time prediction of the temperature field, improving computational efficiency by several orders of magnitude. It can support real-time application scenarios such as boiler digital twins, online monitoring, and combustion optimization, and has significant industrial practical value and broad application prospects.

[0142] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention, and these should also be considered within the scope of protection of the present invention. These will not affect the effectiveness of the implementation of the present invention or the practicality of the patent.

Claims

1. A method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network, characterized in that, Includes the following steps: S1. Acquire three-dimensional temperature field data of the furnace under various operating conditions; Discretize each set of operating condition data into point-level supervised learning samples. Each supervised learning sample includes the spatial location information of the sampling point, boiler operating condition parameters, physical prior features, and the temperature value of the sampling point. S2. Construct a dual-branch residual neural network model, which includes a working condition branch, a coordinate encoding branch, and a fusion prediction head; The operating condition branch takes operating condition variables and physical prior features as input, projects them to the latent space through linear mapping, and extracts high-level operating condition features through a multi-layer residual MLP module. The coordinate encoding branch takes spatial location information as input, performs Fourier feature mapping on the spatial location information, and then extracts high-level spatial features through a multi-layer residual MLP module. S3. The working condition high-rise features and the spatial high-rise features are fused together, and the fused features are input into the fusion prediction head to output the temperature prediction value. S4. Using the dataset constructed in step S1, train the dual-branch residual neural network model constructed in step S2 with the loss function. Input the working condition parameters of the working condition to be predicted and the spatial location information inside the furnace into the trained model to obtain the three-dimensional temperature field of the furnace under the working condition.

2. The method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network according to claim 1, characterized in that, The residual MLP module mentioned in step S2 specifically refers to: for any input latent vector The residual block is represented as: ； in, For the residual function, A two-layer MLP structure is adopted, consisting of a first linear layer, an activation function, layer normalization, Dropout, and a second linear layer connected sequentially. Its form is as follows: ； In the formula, To act on the input The first linear layer weight matrix, The weight matrix of the second linear layer, b 1 and b 2 For the bias term, LN(·) represents layer normalization.

3. The method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network according to claim 1, characterized in that, The Fourier feature mapping in step S2 specifically involves performing multi-band sine and cosine expansions on the three coordinate components of the spatial location information, while retaining the original three coordinate components. For coordinate component x, the Fourier feature mapping result is as follows: ； Where B is the Fourier band number, and the value of B ranges from 4 to 10.

4. The method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network according to claim 3, characterized in that, The physical prior features include at least one of the following three categories: The first category is spatial geometric features, which include the normalized coordinates of the sampling point, the radial distance of the sampling point in the horizontal section of the furnace, the planar distance from the sampling point to the central axis of the furnace, coordinate intersection terms, and higher-order terms in the height direction. The second category is operating condition coupling characteristics, including the air-fuel ratio, the ratio of primary air volume to secondary air volume, the coupling terms of load and fuel heat input, and the interaction terms of air volume and space height. The third category is prior features of the burner neighborhood: including the Euclidean distance from the sampling point to each burner nozzle, the distance from the sampling point to the nearest burner nozzle, the distance from the sampling point to the second nearest burner nozzle, the number of the nearest burner nozzle, and the local coordinate difference of the sampling point relative to the nearest burner nozzle.

5. The method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network according to claim 1, characterized in that, In step S4, a region-weighted loss function is used as the loss function, and samples in the near region of the nozzle are assigned a higher weight than those in the far region.

6. The method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network according to claim 1, characterized in that, The boiler operating parameters mentioned in step S1 include at least one of the following: unit load, total air volume, primary air volume, secondary air volume, separate burnout air volume, coal feed rate, lower heating value of coal type, and dry ash-free volatile matter content.

7. The method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network according to claim 1, characterized in that, The step S1, which involves acquiring three-dimensional furnace temperature field data under various operating conditions, specifically involves: using CFD software to conduct multi-condition three-dimensional combustion numerical simulations of the target coal-fired boiler. The variation dimensions of the operating conditions include at least one of coal type, unit load, and air distribution method. The CFD numerical simulation uses a Realizable k-ε turbulence model to simulate turbulent flow inside the furnace, a P1 radiation model to simulate radiative heat transfer, a gray-weighted gas radiation model to calculate flue gas emissivity, a component transport model to define the reaction mechanism to achieve multi-component coupled calculation, and a discrete phase model to describe the movement and combustion process of pulverized coal particles.

8. The method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network according to claim 1, characterized in that, The dataset partitioning in step S1 is done by dividing it according to the working condition files, and all working condition data are divided into training set, validation set and test set according to the proportion.

9. The method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network according to claim 1, characterized in that, The step S3, which involves fusing the high-level features of the working conditions and the high-level features of the space, specifically involves concatenating the high-level features of the working conditions and the high-level features of the space along the feature dimension. The fusion prediction head consists of a fully connected layer, an activation function, layer normalization, and residual mapping. After compressing the feature dimension layer by layer, a scalar temperature value is output.

10. The method for reconstructing the three-dimensional temperature field of a furnace based on a bi-branch residual network according to claim 1, characterized in that, Before executing step S2, a preprocessing step for the input data is also included: standardizing or normalizing the operating condition variables, physical prior features, and spatial location information; standardizing the temperature values ​​in the same way as the input features; and obtaining the physical temperature value after inverse standardization of the model's output temperature prediction value. The standardization process is as follows: ； in, , , and All values ​​are calculated solely from the training set and are fixed for use on the validation and test sets.

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