Air cooling island finned tube temperature field prediction method based on physical information neural network

Abstract

The invention belongs to the field of thermal power generating unit cold end optimization, particularly relates to an air cooling island finned tube temperature field prediction method based on a physical information neural network, and aims to realize accurate, efficient and robust prediction of an air cooling island finned tube temperature field. The method comprises the steps that operation data are collected and preprocessed based on a direct air cooling unit condenser sensor, and a data set is obtained; according to a heat conduction and fluid flow control equation, a loss function is constructed in combination with initial and boundary conditions, and a physical information neural network containing a forward flow region and reverse flow region full-connection neural network and embedded with physical prior constraints is established; then training the network by using a data set, calculating the required heat exchange area and the actual heat exchange area of the downstream region through a heat balance equation during training, and selecting to start the downstream region network or combine the two-region network according to the sizes of the required heat exchange area and the actual heat exchange area; and finally, deducing the temperature distribution of a single-row air cooling unit by using the trained network, finely adjusting model parameters if the prediction deviation exceeds a threshold value, and expanding to a multi-row structure to obtain the temperature field distribution of the whole finned tube of the air cooling island.

Description

Technical Field

[0001] This invention relates to the field of cold-end optimization of thermal power units, and in particular to a method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks. Background Technology

[0002] The flexible operation capability of thermal power units has become a key factor in mitigating fluctuations in renewable energy generation and ensuring stable grid operation. As the component with the greatest energy loss in a thermal power unit, the cold-end system's performance directly determines the overall efficiency and economy of the unit. Therefore, optimizing the cold-end system is crucial for improving the unit's overall performance.

[0003] Under winter operating conditions, direct air-cooled condensers (air-cooled islands) are highly susceptible to freezing of their finned tube bundles due to sudden drops in ambient temperature, caused by their structural characteristics. Once freezing occurs, it not only severely impacts the safe and stable operation of the unit and increases equipment maintenance costs, but may also trigger unplanned shutdowns, resulting in significant economic losses for the power plant. Therefore, accurately predicting the temperature field distribution inside the condenser's finned tubes and promptly identifying abnormal low-temperature areas is of great significance for preventing freezing accidents and ensuring unit reliability. However, due to the large size of direct air-cooled condensers, it is difficult to densely arrange temperature sensors, resulting in very limited data acquisition from existing monitoring methods. This data cannot comprehensively and accurately reflect the true distribution of the entire temperature field, leading to a serious deficiency in operational status assessment and fault early warning capabilities.

[0004] Currently, solutions to this problem mainly fall into two categories: one is a modeling method based on physical mechanisms, but it requires extensive simplification of the complex heat-fluid coupling process, which is computationally complex, inefficient, and difficult to meet the needs of online prediction; the other is a purely data-driven modeling method, which can learn mapping relationships from historical data, but it is highly dependent on a large amount of high-quality labeled data. In actual sensor-sparse working conditions, it has poor generalization ability, limited prediction accuracy, and the prediction results often violate physical laws. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks, aiming to achieve accurate, efficient and robust prediction of the temperature field of air-cooled island finned tubes.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a method for predicting the temperature field of finned tubes in air-cooled islands based on a physical information neural network, comprising: S1: collecting condenser operating data based on sensors arranged on the condenser of a direct air-cooled unit and preprocessing it to obtain a dataset; S2: constructing a loss function based on the heat conduction and fluid flow control equations, combined with initial and boundary conditions, and establishing a physical information neural network with embedded physical prior constraints, including a fully connected neural network in the downstream region and a fully connected neural network in the upstream region. The physical information neural network refers to a neural network that integrates physical laws and data modeling, embedding physical constraints into the neural network training process. S3: Train the physical information neural network using the dataset. During training, calculate the required heat transfer area and the actual heat transfer area in the co-current zone using the heat balance equation. Based on the relationship between the required heat transfer area and the actual heat transfer area in the co-current zone, select to enable the fully connected neural network in the co-current zone or jointly enable the fully connected neural networks in the co-current and counter-current zones, and update the network parameters. S4: Use the trained physical information neural network to deduce the temperature distribution of the finned tubes in a single-column air-cooled unit. After fine-tuning the parameters of the model whose prediction deviation exceeds the set threshold, expand it to a multi-column structure to obtain the overall finned tube temperature field distribution of the air-cooled island.

[0007] In step S1, the exhaust steam flow rate, back pressure, fan speed, condenser inlet and outlet air temperature, and the corresponding temperature values ​​in time and space coordinates are collected by sensors; abnormal data in the collected data are removed by using the three-times standard deviation principle to construct a dataset.

[0008] A fully connected neural network in the co-current region refers to a fully connected neural network used to simulate the heat exchange and fluid flow characteristics in the co-current region of a condenser. The inputs of the fully connected neural network in the co-current region include time information, spatial coordinates, exhaust steam flow rate, back pressure, fan speed, and condenser inlet and outlet air temperatures. The outputs of the fully connected neural network in the co-current region include finned tube temperature, fluid velocity in three directions in three-dimensional space, and fluid pressure.

[0009] The counter-flow fully connected neural network refers to a fully connected neural network used to simulate the heat exchange and fluid flow characteristics in the counter-flow zone of a condenser. The inputs of the counter-flow fully connected neural network include the residual steam flow rate and fluid pressure, time information, spatial coordinates, back pressure, fan speed, condenser inlet air temperature, and condenser outlet air temperature calculated from the outputs of the co-flow fully connected neural network. The network structure of the counter-flow fully connected neural network is the same as that of the co-flow fully connected neural network. The outputs of the counter-flow fully connected neural network include the finned tube temperature, the fluid velocity in three directions in three-dimensional space, and the fluid pressure.

[0010] The construction of the loss function in step S2 includes: using the residual terms corresponding to the condenser finned tube heat conduction equation, steam flow field equation, initial conditions, and boundary conditions as physical constraints; combining the numerical fitting residuals of the measurement data and model calculation results, and combining them according to preset weights to form the total loss function; wherein, the measurement data refers to the finned tube temperature measurement value corresponding to the spatiotemporal coordinates collected by the sensor and preprocessed in step S1, and the model calculation result refers to the finned tube temperature calculation value corresponding to the spatiotemporal coordinates of the downstream region output by the fully connected neural network when only the downstream region is enabled, or the finned tube temperature calculation value corresponding to the spatiotemporal coordinates of the downstream region output by the fully connected neural network when both the downstream and countercurrent regions are enabled, and the finned tube temperature calculation value corresponding to the spatiotemporal coordinates of the countercurrent region output by the fully connected neural network.

[0011] In step S3, based on the dataset and boundary conditions, the required heat transfer area and the actual heat transfer area in the co-current region are calculated using the heat balance equation. The actual heat transfer area in the co-current region refers to the total heat transfer area of ​​the finned tubes in the co-current region of the condenser after considering the fin surface rib efficiency correction. If the required heat transfer area is less than or equal to the actual heat transfer area in the co-current region, only the fully connected neural network in the co-current region is used for training. If the required heat transfer area is greater than the actual heat transfer area in the co-current region, both the fully connected neural networks in the co-current and counter-current regions are used for training.

[0012] In step S3, the AdamW optimizer is used to iteratively update the network parameters during backpropagation until the total loss function is lower than a set threshold or the maximum number of training rounds is reached.

[0013] The parameter fine-tuning in step S4 includes: determining whether the relative error of the predicted temperature distribution of the single-row air-cooled unit finned tube obtained by the physical information neural network exceeds a set threshold; if the relative error of the predicted temperature distribution of the single-row air-cooled unit finned tube exceeds the set threshold, freezing the parameters of the first two layers of the physical information neural network, and fine-tuning the parameters of the last two layers of the physical information neural network using the updated learning rate; wherein the updated learning rate is lower than the learning rate before the update.

[0014] The model extension in step S4 includes: using the temperature field prediction model verified by a single-row air-cooled unit as the basic model; and extending the basic model to a multi-row structure based on the structural layout and flow field coupling characteristics of the multi-row air-cooled unit to achieve overall finned tube temperature field prediction for the air-cooled island.

[0015] The heat conduction equation is the heat conduction-diffusion equation, and the steam flow field equation is the three-dimensional Navier-Stokes equation. The residual terms include the residuals of the heat conduction-diffusion equation, the three-dimensional Navier-Stokes equation, the initial condition residuals, and the boundary condition residuals.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The embodiment of this application provides a method for predicting the temperature field of finned tubes in air-cooled islands based on physical information neural networks. By constructing a physical information neural network (PINN) with embedded physical prior constraints, the method uses the heat conduction and diffusion equation of the condenser finned tube (describing the temperature transfer law) and the three-dimensional Navier-Stokes equation (describing the steam flow field characteristics) as the core constraints of the loss function. At the same time, it combines sensor measured data (after removing anomalies by the three-times standard deviation principle) to optimize the model parameters. This method avoids the simplification error and computational redundancy of pure mechanism modeling, and also makes up for the excessive dependence on sample size of pure data-driven models. It achieves the dual advantages of physical laws ensuring generalization and measured data improving accuracy, and can still maintain stable prediction performance under varying operating conditions.

[0017] 2. The method provided in this application innovatively designs a partitioned architecture of a fully connected neural network in the co-current region and a fully connected neural network in the counter-current region. It calculates the relationship between the required heat transfer area and the actual heat transfer area in the co-current region using the heat balance equation, and dynamically determines whether to activate the counter-current region model. Only a limited number of sensors are needed to collect data such as exhaust steam flow rate, back pressure, fan speed, condenser inlet and outlet air temperature, and the corresponding finned tube temperature in time and space coordinates to achieve full-domain temperature field reconstruction. This method uses physical laws to replace the traditional approach of using numerous sensors to fill blind spots. While ensuring prediction accuracy, it significantly reduces the number of sensors deployed, substantially lowering the hardware procurement costs and long-term operation and maintenance costs of power plants, making it particularly suitable for the retrofitting and upgrading of older units.

[0018] 3. This invention, through high-precision temperature field prediction, can identify abnormal low-temperature areas within the condenser in real time, such as the corners of finned tubes and the ends of the counterflow zone, providing power plants with accurate anti-freezing control data and preventing freezing accidents from the source. Simultaneously, it eliminates the need for conservative operating strategies due to inaccurate predictions, ensuring stable and full-capacity unit operation and significantly improving the economic efficiency and equipment reliability of the power plant. Attached Figure Description

[0019] Figure 1 This is a flowchart of a method for predicting the temperature field of air-cooled island finned tubes based on a physical information neural network, provided in an embodiment of this application. Figure 2 This is a physical information neural network structure diagram provided in an embodiment of this application. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0021] For example, refer to Figure 1 and Figure 2 This application provides a method for predicting the temperature field of air-cooled island finned tubes based on a physical information neural network, including: S1: Based on sensors arranged on the condenser of the direct air-cooled unit, collect condenser operation data and preprocess it to obtain a dataset.

[0022] As one possible implementation, in step S1, exhaust steam flow rate, back pressure, fan speed, condenser inlet and outlet air temperature, and corresponding spatiotemporal temperature values ​​are collected by sensors. Outliers in the collected data are removed using a three-standard-deviation principle to construct a dataset.

[0023] The core logic of the three-standard-deviation principle is: based on the normal distribution characteristics of the data, data exceeding the mean ± three standard deviations are identified as outliers. By eliminating outliers through this principle, it is ensured that the final dataset conforms to the physical mechanism logic of normal condenser operation, thereby avoiding the contamination of the dataset by physically invalid data and laying a reliable data foundation for the subsequent PINN model to integrate physical constraints.

[0024] S2: Based on the heat conduction and fluid flow control equations, a loss function is constructed by combining initial and boundary conditions. A physical information neural network with embedded physical prior constraints is established, which includes a fully connected neural network in the downstream region and a fully connected neural network in the upstream region. The physical information neural network refers to a neural network that integrates physical laws and data modeling and embeds physical constraints into the neural network training process.

[0025] A fully connected neural network in the co-current region refers to a fully connected neural network used to simulate the heat exchange and fluid flow characteristics in the co-current region of a condenser. The inputs of the fully connected neural network in the co-current region include time information, spatial coordinates, exhaust steam flow rate, back pressure, fan speed, and condenser inlet and outlet air temperatures. The outputs of the fully connected neural network in the co-current region include finned tube temperature, fluid velocity in three directions in three-dimensional space, and fluid pressure.

[0026] For example, a fully connected neural network in the downstream region can be represented in the following form: in, This serves as the input layer for a fully connected neural network in the downstream region. For time information; Represents spatial coordinates; This indicates the exhaust steam flow rate, expressed in kg / s. Indicates back pressure, unit is ; This indicates the fan speed, expressed in m / s. This indicates the inlet air temperature of the finned tube, in units of... ; This indicates the outlet air temperature of the finned tube, in °C. For the fully connected neural network in the downstream region, the first layer; and These represent the weights and biases of the fully connected neural network in the downstream region, respectively. For the fully connected neural network in the downstream region, the first layer; H is the activation function; H is the number of hidden layers in the fully connected neural network in the downstream region. For output layer; and These represent the output layer weights and biases, respectively. This is the H-1 layer of a fully connected neural network in the downstream region; This indicates the temperature of the finned tube, in units of... ; , , They represent axis, axis, Fluid velocity in the axial direction, in m / s; Represents fluid pressure, in units of The ReLU activation function is selected in this embodiment.

[0027] A counter-flow fully connected neural network is a fully connected neural network used to simulate the heat exchange and fluid flow characteristics in the counter-flow region of a condenser. The input of the counter-flow fully connected neural network includes the residual steam flow rate calculated from the output of the co-flow fully connected neural network. and fluid pressure Information includes time, spatial coordinates, back pressure, fan speed, condenser inlet air temperature, and condenser outlet air temperature; the network structure of the fully connected neural network in the counter-flow region is the same as that in the co-flow region; the output of the fully connected neural network in the counter-flow region includes finned tube temperature, fluid velocity in three directions in three-dimensional space, and fluid pressure.

[0028] For example, a fully connected neural network in the reverse flow region can be represented as: In the process of constructing fully connected neural networks in the downstream region and fully connected neural networks in the upstream region, the network is equipped with a high-precision approximation capability for complex nonlinear partial differential equation systems by setting the number of network layers, initial conditions, boundary conditions and hyperparameters.

[0029] As one possible implementation, the construction of the loss function in step S2 includes: using the residual terms corresponding to the condenser finned tube heat conduction equation, steam flow field equation, initial conditions, and boundary conditions as physical constraints; combining the numerical fitting residuals of the measurement data and model calculation results, and combining them according to preset weights to form the total loss function. Here, the measurement data refers to the finned tube temperature measurement values ​​corresponding to the spatiotemporal coordinates collected by sensors and preprocessed in step S1; the model calculation results refer to the calculated finned tube temperature values ​​corresponding to the spatiotemporal coordinates of the downstream region output by the fully connected neural network when only the downstream region is used, or the calculated finned tube temperature values ​​corresponding to the spatiotemporal coordinates of the downstream region output by the fully connected neural network when both the downstream and counter-current regions are used, and the calculated finned tube temperature values ​​corresponding to the spatiotemporal coordinates of the counter-current region output by the fully connected neural network.

[0030] As one possible implementation, the heat conduction equation is the heat conduction-diffusion equation, the steam flow field equation is the three-dimensional Navier-Stokes equation, and the residual terms include the residuals of the heat conduction-diffusion equation, the three-dimensional Navier-Stokes equation, the initial condition residuals, and the boundary condition residuals.

[0031] For example, the heat conduction equation for condenser finned tubes, i.e., the diffusion equation for the heat conduction problem, is as follows: in, For time; , , Represents the three-dimensional spatial coordinates of the sampling point; This represents the temperature of the condenser finned tubes in a direct air-cooled unit at a specific time-space coordinate, in units of... ; , and These are the thermal conductivity, density, and specific heat of the material, respectively, with units of: , and Its value can be obtained from a table of condenser materials and is considered a constant. This refers to the heat source of the condenser in a direct air-cooled unit. Since direct air-cooled units operate under varying conditions most of the time, the heat source... The value of is time-varying, therefore, in this embodiment of the application, it is used as an optimization term of the loss function for optimization. Its initial value is the heat source under rated operating conditions. .

[0032] For example, the initial condition satisfied by the condenser finned tube is: the initial condition is selected as the temperature at the start of sampling. ,Right now .

[0033] The temperature boundary conditions satisfied by the temperature field of the condenser finned tube are: in, and satisfy , , Represents the computational domain The boundary; and Temperature and heat flux at a specified boundary are respectively, in units of and ; The outward normal direction vector indicating the boundary.

[0034] For example, the steam flow field equation satisfied by the condenser finned tubes is the three-dimensional Navier-Stokes equation, in the following form: in, It is a dimensionless Reynolds number. ; This refers to the density of steam, in units of... ; Vapor viscosity, in units of ; l is the reference length, in meters; o is the reference velocity, in meters. u represents the flow velocity along the x-axis, in units of... v represents the flow velocity along the y-axis, in units of... w represents the flow velocity along the z-axis, in units of... ; Fluid pressure, unit: .

[0035] The residual terms corresponding to the heat conduction equation, the Navier-Stokes equation, initial conditions, and boundary conditions are used as physical constraints to introduce and construct the loss function of a physical information neural network. The loss function of the temperature field of the air-cooled island finned tube includes the following five parts: heat conduction equation loss, Navier-Stokes equation loss, initial condition loss, boundary condition loss, and data fitting loss. For example, the total loss function is: in, As shown below: In the formula, The temperature field loss function represents the physical information of the neural network. The residual between the measured temperature and the calculated temperature, i.e., numerical loss; The weights for numerical loss; This represents the loss in the heat conduction equation; The weights for the losses in the heat conduction equation; The loss of the Navier-Stokes equations; The weights for the Navier-Stokes equation loss; Loss due to initial conditions; The weights for the initial conditional loss; Loss due to initial conditions; The weights for the initial conditional loss; N is the number of measurement points; and Number of points to be configured for condenser finned tubes; This indicates the number of initial training data points; This indicates the number of initial training data points; These are the measured temperature and calculated temperature at the j-th measuring point, respectively, in °C. This represents the initial temperature of the j-th data point, in °C. This represents the residual of the diffusion equation for the heat conduction problem; , and These are the thermal conductivity, density, and specific heat of the material, respectively, with units of: , and ; This indicates the heat source of the condenser in a direct air-cooled unit; This represents the boundary temperature of the j-th data point, in units of... ; For heat flow at a specified boundary, The values ​​corresponding to the known boundary conditions; , , and These are the four residuals of the Navier-Stokes equations; It is a dimensionless Reynolds number; for axial velocity, in units of ; for axial velocity, in units of ; for axial velocity, in units of ; This represents the steam pressure inside the pipe, expressed in kPa.

[0036] S3: Use the dataset to train the physical information neural network. During the training process, calculate the required heat exchange area and the actual heat exchange area in the downstream zone through the heat balance equation. Based on the relationship between the required heat exchange area and the actual heat exchange area in the downstream zone, select to enable the fully connected neural network in the downstream zone or jointly enable the fully connected neural networks in the downstream and counter-current zones, and update the network parameters.

[0037] As one possible implementation, in step S3, the required heat transfer area is calculated using the heat balance equation based on the dataset and boundary conditions. Actual heat exchange area with the downstream zone The actual heat exchange area in the co-current zone refers to the total heat exchange area of ​​the finned tubes in the co-current zone of the condenser after considering the correction for the efficiency of the fin surface ribs.

[0038] For example, the total heat transfer area of ​​the finned tube after considering the fin surface rib efficiency correction. The calculation formula is: in, The surface area of ​​the air-side fins is given in units of... ; The surface area of ​​the air-side base tube is given in units of... ; The rib efficiency is considered as if the serpentine fins were straight ribs with a constant cross section.

[0039] The heat load of the air-cooled condenser is equal to the heat released by the exhaust steam from the internal turbine, and also equal to the heat absorbed by the external air. The heat balance equation can be expressed as: in, Condenser heat load, in units of ; This refers to the steam turbine exhaust volume, expressed in kg / s. This is the exhaust vapor specific enthalpy, expressed in kJ / kg; Specific enthalpy of condensate, expressed in kJ / kg; The windward area is expressed in units of... ; Air density, unit: kg / m³ 3 ; The wind speed is the face speed, expressed in m / s. Specific heat of air at constant pressure, unit: ; The temperature difference between the air inlet and outlet is expressed in °C. The main physical properties of water and water vapor involved in the formula can be calculated according to the IAPWS-IF97 international standard.

[0040] If the required heat exchange area is less than or equal to the actual heat exchange area of ​​the co-current zone, it is determined that the steam can be completely condensed in the co-current zone. Only the fully connected neural network for the co-current zone is used for training. The output of the fully connected neural network for the co-current zone includes the pipe wall temperature and the fluid velocity and pressure in three dimensions. If the required heat exchange area is greater than the actual heat exchange area of ​​the co-current zone, it is determined that the steam in the co-current zone is not completely condensed, and the remaining steam enters the counter-current zone to continue condensing. In this case, both the co-current and counter-current zone fully connected neural networks are used for training. Based on the output of the co-current zone neural network and combined with the heat balance equation, the amount of steam condensed in the co-current zone is calculated, thereby determining the amount of remaining steam entering the counter-current zone and the corresponding heat load. These parameters are then input into the counter-current zone neural network to further calculate the pipe wall temperature in that region.

[0041] For example, in step S3, the AdamW optimizer is used to iteratively update the network parameters during backpropagation until the total loss function is lower than a set threshold or the maximum number of training rounds is reached.

[0042] S4: The temperature distribution of a single-row air-cooled unit finned tube is deduced by the trained physical information neural network. After fine-tuning the parameters of the model whose prediction deviation exceeds the set threshold, it is extended to a multi-row structure to obtain the overall finned tube temperature field distribution of the air-cooled island.

[0043] As one possible implementation, the parameter fine-tuning in step S4 includes: determining whether the relative prediction error of the temperature distribution of the single-row air-cooled unit finned tube obtained by the physical information neural network exceeds a set threshold; if the relative prediction error of the temperature distribution of the single-row air-cooled unit finned tube exceeds the set threshold, freezing the parameters of the first two layers of the physical information neural network, and fine-tuning the parameters of the last two layers of the physical information neural network using the updated learning rate; wherein the updated learning rate is lower than the learning rate before the update.

[0044] As one possible implementation, the model extension in step S4 includes: using the temperature field prediction model verified by a single-row air-cooled unit as the basic model; and extending the basic model to a multi-row structure based on the structural layout and flow field coupling characteristics of the multi-row air-cooled unit to achieve overall finned tube temperature field prediction for the air-cooled island.

[0045] In the description of this specification, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0046] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks, characterized in that, include: S1: Based on the sensors arranged on the condenser of the direct air-cooled unit, collect condenser operation data and preprocess it to obtain a dataset; S2: Based on the heat conduction and fluid flow control equations, a loss function is constructed by combining initial and boundary conditions. A physical information neural network (PEN) with embedded physical prior constraints is established, which includes a fully connected neural network in the downstream region and a fully connected neural network in the upstream region. The PSN refers to a neural network that integrates physical laws and data modeling and embeds physical constraints into the neural network training process. S3: The PSN is trained using a dataset. During the training process, the required heat transfer area and the actual heat transfer area in the downstream region are calculated using the heat balance equation. Based on the relationship between the required heat transfer area and the actual heat transfer area in the downstream region, the fully connected neural network in the downstream region or the fully connected neural networks in the downstream and upstream regions are selected to be enabled, and the network parameters are updated. S4: The temperature distribution of the finned tubes of a single-column air-cooled unit is deduced through the trained PSN. After fine-tuning the parameters of the model whose prediction deviation exceeds the set threshold, the model is expanded to a multi-column structure to obtain the overall finned tube temperature field distribution of the air-cooled island.

2. The method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks according to claim 1, characterized in that, In step S1, the exhaust steam flow rate, back pressure, fan speed, condenser inlet and outlet air temperature, and the corresponding temperature values ​​in time and space coordinates are collected by sensors; abnormal data in the collected data are removed by using the three-times standard deviation principle to construct a dataset.

3. The method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks according to claim 1, characterized in that, A fully connected neural network in the co-current region refers to a fully connected neural network used to simulate the heat exchange and fluid flow characteristics in the co-current region of a condenser. The inputs of the fully connected neural network in the co-current region include time information, spatial coordinates, exhaust steam flow rate, back pressure, fan speed, and condenser inlet and outlet air temperatures. The outputs of the fully connected neural network in the co-current region include finned tube temperature, fluid velocity in three directions in three-dimensional space, and fluid pressure.

4. The method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks according to claim 3, characterized in that, The counter-flow fully connected neural network refers to a fully connected neural network used to simulate the heat exchange and fluid flow characteristics in the counter-flow zone of a condenser. The inputs of the counter-flow fully connected neural network include the residual steam flow rate and fluid pressure, time information, spatial coordinates, back pressure, fan speed, condenser inlet air temperature, and condenser outlet air temperature calculated from the outputs of the co-flow fully connected neural network. The network structure of the counter-flow fully connected neural network is the same as that of the co-flow fully connected neural network. The outputs of the counter-flow fully connected neural network include the finned tube temperature, the fluid velocity in three directions in three-dimensional space, and the fluid pressure.

5. The method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks according to claim 1, characterized in that, The construction of the loss function in step S2 includes: using the residual terms corresponding to the condenser finned tube heat conduction equation, steam flow field equation, initial conditions, and boundary conditions as physical constraints; combining the numerical fitting residuals of the measurement data and model calculation results, and combining them with preset weights to form the total loss function; wherein, the measurement data refers to the finned tube temperature measurement value corresponding to the spatiotemporal coordinates collected by the sensor and preprocessed in step S1, and the model calculation result refers to the finned tube temperature calculation value corresponding to the spatiotemporal coordinates of the downstream region output by the fully connected neural network when only the downstream region is enabled, or the finned tube temperature calculation value corresponding to the spatiotemporal coordinates of the downstream region output by the fully connected neural network when both the downstream and countercurrent regions are enabled, and the finned tube temperature calculation value corresponding to the spatiotemporal coordinates of the countercurrent region output by the fully connected neural network.

6. The method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks according to claim 1, characterized in that, In step S3, based on the dataset and boundary conditions, the required heat transfer area and the actual heat transfer area of ​​the co-current zone are calculated using the heat balance equation. The actual heat transfer area of ​​the co-current zone refers to the total heat transfer area of ​​the finned tubes in the co-current zone of the condenser after considering the fin surface rib efficiency correction. If the required heat transfer area is less than or equal to the actual heat transfer area of ​​the co-current zone, only the fully connected neural network of the co-current zone is used for training. If the required heat transfer area is greater than the actual heat transfer area of ​​the co-current zone, both the fully connected neural networks of the co-current and counter-current zones are used for training.

7. The method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks according to claim 1, characterized in that, In step S3, the AdamW optimizer is used to iteratively update the network parameters during backpropagation until the total loss function is lower than a set threshold or the maximum number of training rounds is reached.

8. The method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks according to claim 1, characterized in that, The parameter fine-tuning in step S4 includes: determining whether the relative error of the predicted temperature distribution of the single-row air-cooled unit finned tube obtained by the physical information neural network exceeds a set threshold; if the relative error of the predicted temperature distribution of the single-row air-cooled unit finned tube exceeds the set threshold, freezing the parameters of the first two layers of the physical information neural network, and fine-tuning the parameters of the last two layers of the physical information neural network using the updated learning rate; wherein the updated learning rate is lower than the learning rate before the update.

9. The method for predicting the temperature field of air-cooled island finned tubes based on physical information neural networks according to claim 1, characterized in that, The model extension in step S4 includes: using the temperature field prediction model verified by a single-row air-cooled unit as the basic model; and extending the basic model to a multi-row structure based on the structural layout and flow field coupling characteristics of the multi-row air-cooled unit to achieve overall finned tube temperature field prediction for the air-cooled island.

10. The method for predicting the temperature field of air-cooled island finned tubes based on a physical information neural network according to claim 5, characterized in that, The heat conduction equation is the heat conduction-diffusion equation, the steam flow field equation is the three-dimensional Navier-Stokes equation, and the residual terms include the residuals of the heat conduction-diffusion equation, the three-dimensional Navier-Stokes equation, the initial condition residuals, and the boundary condition residuals.

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