Temperature monitoring method of core area of friction stir welding based on digital twin

Abstract

The present invention discloses a method for monitoring the temperature of the core area of stir friction welding based on digital twins. A stir friction welding temperature monitoring system based on digital twins is constructed using the Unity3D engine. A synchronous motion simulation model of the stir friction welding process is established in the monitoring system, and a temperature prediction model is established using a randomized dual coordinate ascent (SDCA) prediction algorithm and a radial basis function neural network (RBF) interpolation algorithm. During the welding process, the temperature data of the characteristic points on the weld surface collected by the infrared thermal imager is transmitted to the monitoring system in real time via Socket communication. By calling the synchronous motion simulation model and the temperature prediction model, real-time three-dimensional visualization of the weld temperature field during the welding process can be achieved. When the predicted core area peak temperature and minimum temperature exceed the solid-liquid phase temperature threshold of the weld material, an over-limit alarm prompt is issued, providing a basis for predictive control. The present invention realizes the monitoring of the core area of the stir friction welding process and ensures the welding quality.

Description

Technical Field

[0001] The present invention belongs to the field of friction stir welding temperature monitoring and relates to a method for monitoring the temperature of a friction stir welding core area based on digital twins. Background Art

[0002] Friction stir welding (FSW) is a solid-state welding technique in which a high-speed rotating stirrer is inserted into the weldment. The stirrer moves and rubs against the weldment's end faces, generating heat that softens the weldment material and creates a squeeze effect. FSW offers advantages such as low residual stress, safety, pollution-free operation, and the production of high-quality joints. Initially applied to welding low-melting-point alloys such as aluminum and magnesium alloys, FSW has also seen significant development with higher-melting-point materials.

[0003] The temperature field distribution during FSW welding affects the plastic flow of the weld material and the weld microstructure, which in turn influences the tensile strength of the weld joint and weld quality. The temperature field in the core zone, consisting of the weld nugget zone, thermomechanically affected zone, and heat-affected zone, has a direct impact on weld quality. Previous studies have shown that when the maximum temperature in the core zone is approximately 80% of the weld material's liquefaction temperature, the weld joint achieves maximum tensile strength; when the minimum temperature in the core zone is below 80% of the weld material's solidus temperature, the joint tensile strength decreases significantly. The core zone temperature field is also the foundation for other related research, including studies on plastic material flow in the weld, joint microstructure transformation, welding parameter optimization, and welding mechanism analysis. However, due to factors such as the mechanical effects of the shoulder and stirring head, severe plastic deformation of the weld material, and complex thermomechanical coupling, the temperature field, including that in the core zone, is difficult to measure during the welding process. Current temperature measurement instruments can only measure the surface temperature of the weld. Currently, the commonly used methods for measuring the welding temperature field, including the core area, are thermocouple measurement and finite element simulation. Thermocouple measurement can damage the weldment or the stirring head structure and is not suitable for actual processing. Finite element simulation, on the other hand, suffers from long simulation times and poor real-time performance. Both methods struggle to ensure real-time temperature monitoring during welding. Furthermore, welding temperature is affected by process parameters such as FSW rotation speed, welding speed, and downward pressure. This results in operators relying solely on experience to adjust process parameters, making it difficult to ensure weld quality. Summary of the Invention

[0004] In view of the problem that some temperature fields including the core area are difficult to monitor in real time during the welding process, the present invention provides a FSW core area temperature monitoring method based on digital twin, including: using SolidWorks software to build an FSW three-dimensional model, and performing kinematic analysis on the FSW welding process, and then establishing a synchronous motion simulation model of the welding process by driving the three-dimensional model through a motion control program; establishing a weldment temperature field prediction model based on a radial basis function neural network (RBF) interpolation algorithm, and using a random double coordinate ascent (SDCA) regression algorithm to establish a core area peak temperature and minimum temperature prediction model; using an infrared thermal imager to collect real-time data during the welding process. The surface peak and minimum temperatures in the sampling area are synchronously transmitted to the FSW temperature field monitoring system built using Unity3D through Socket communication, realizing real-time monitoring of the weld surface temperature; the monitored surface temperature data are input into the synchronous motion simulation model and the RBF temperature field interpolation prediction model in real time, and computer graphics are used to realize three-dimensional visualization of the real-time temperature field of the entire weld; the real-time monitored surface temperature data are combined with the SDCA prediction model to realize real-time monitoring of the peak temperature and minimum temperature of the welding core area, and an over-limit alarm function is developed, combining the correlation between welding process parameters and welding temperature to realize early warning and regulation of the peak temperature and minimum temperature of the core area.

[0005] The temperature monitoring method of the core area of friction stir welding based on digital twin is as follows:

[0006] Step 1: Use SolidWorks software to create a FSW 3D model, and import the 3D model into 3DMax software for lightweight processing and rendering, and then import it into Unity3D software;

[0007] Step 2: Analyze the kinematic relationship of the FSW welding process and establish the parent-child relationship between the components of the 3D model. Then, establish a synchronous motion simulation model of the welding process in a program-driven manner.

[0008] Step 3: Use Deform software to simulate the temperature field of the weldment, extract the coordinates of the feature points in the temperature field simulation model and the corresponding temperature data to construct a radial basis function (RBF) temperature field interpolation prediction model, and use the generalized Multi-Quadic function as the radial basis function. The RBF temperature field interpolation prediction model is encapsulated into a C# script. At the same time, the vertex rendering method is used to generate the weldment model and convert it into a weldment automatic generation script. Then, according to the temperature data color conversion rule corresponding to the red, green, and blue gradient from high to low temperature, a script for color rendering of real-time data points is written. This script can present the core area temperature field data in the form of a three-dimensional cloud map. The established RBF interpolation script, weldment automatic generation script, color rendering script and surface temperature data reading script are combined to realize real-time temperature monitoring and three-dimensional visualization of any position in the core area of the weldment during welding.

[0009] Step 4: Use Deform software to simulate the FSW temperature field and obtain a large number of surface temperature and core temperature datasets. Use the ML.NET tool library in Visual Studio to train this dataset and establish a correlation between surface feature point temperatures and core temperature. This allows the SDCA core temperature prediction model to be established, and the peak temperature or minimum temperature threshold for the core temperature prediction model to be set in real time.

[0010] Step 5: Integrate the established synchronous motion simulation model, RBF temperature field interpolation prediction model, and SDCA core area temperature prediction model into Unity3D software to form a digital twin model;

[0011] Step 6: During the welding process, the peak and minimum surface temperature data within the sampling area collected by the infrared thermal imager in real time are synchronously transmitted via Socket communication based on the TCP protocol to achieve real-time monitoring of the surface temperature. At the same time, the peak and minimum surface temperature data within the sampling area collected by the infrared thermal imager are combined with the digital twin model to perform dynamic, realistic, and multi-dimensional mapping of the actual welding process, realizing real-time 3D visualization of the weldment temperature and core area temperature monitoring.

[0012] Step 7: When the core area peak temperature and the minimum temperature exceed the solid-liquid phase temperature threshold of the weldment material, the over-limit alarm function is triggered, providing a reference for welding process control.

[0013] The beneficial effects of the present invention are as follows: the digital twin technology is used to realize real-time monitoring of the core zone temperature during stir friction welding, realize functions such as synchronous mapping of the welding process, three-dimensional visualization of the weld temperature field, and early warning and control of the core zone temperature. The monitoring system has also been verified on-site, which can provide a reference for welding process control. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is the overall technical solution of the monitoring system established according to the temperature monitoring method of the core area of stir friction welding based on digital twin of the present invention;

[0015] Figure 2 It is the validation of the prediction results of the SDCA model;

[0016] Figure 3 It is a three-dimensional cloud diagram of weldment temperature during motion simulation. DETAILED DESCRIPTION

[0017] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0018] The temperature monitoring system according to the present invention has strong real-time performance, high visualization and good intuitiveness. Figure 1 As shown in the figure, in the temperature monitoring system, the three-dimensional model is dynamically driven through synchronous motion simulation to visualize the welding process. This not only realizes the synchronous mapping between the virtual model and the physical entity, but also helps to enhance the authenticity and real-time performance of temperature monitoring. The details are as follows:

[0019] The FSW 3D model was constructed using SolidWorks software, which was then imported into 3DMax software to set the material and color, and lightweighted. The processed 3D model was then imported into Unity3D software. In addition to the 3D model, a kinematic analysis of the FSW welding process was also required. The motion of the heavy-load friction stir welding machine consists of five moving axes and one adjustable fixed axis. The motion analysis of each axis of the heavy-duty stir friction welding machine is carried out, among which: the X-axis is the horizontal feed axis, which is driven by a servo motor, and the worktable drives the weldment to move through the screw nut, and moves horizontally at the X-axis guide rail of the machine bed, which is responsible for the horizontal feed motion of the weldment on the worktable and the stirring head; the Y-axis is the longitudinal feed axis, and the motor drives the machine head to move longitudinally on the guide rail, so that the stirring head and the weldment produce longitudinal feed; the Z-axis is mainly responsible for controlling the downward pressure, stay and exit stages of the stirring head along the vertical part surface, and the stirring head device is driven by the screw nut to realize the movement perpendicular to the processing plane; the A-axis is responsible for adjusting the stirring head, which can change the process inclination angle (the angle formed by the axis of the stirring needle and the normal of the processing plane), affecting the welding performance; the C-axis needs to move in coordination with the X- and Y-axes to avoid errors caused by small arcs; the main function of the spindle is to rotate the stirring head, transmit torque, and generate relative motion with the workpiece. The size of the spindle speed directly affects the temperature change at the weld during welding;

[0020] Combining the established three-dimensional model with kinematic analysis, the kinematic relationship between models is established. The motion relationship between FSW models is described by the parent-child construction relationship, and a tree structure of the FSW machine tool motion model is established based on Unity3D. After the parent-child construction relationship between model components is established, the control of its child objects is obtained step by step through the script on the parent object. In Unity3D software, the Transform component is used to control the movement and rotation of each part model. Based on the kinematic analysis, a C# program is written to control the motion of each model. The program is dragged to the corresponding model in the virtual scene, and the Box Collider and RigidBody components are added to simulate the collision and gravity effects in the real world. With the help of the engine operation, the synchronous mapping of the FSW welding process is achieved. At the same time, the model motion is controlled by adjusting the welding process parameters on the Inspector component. Different instructions are used to control the changes in motion as needed to keep synchronized with the objects in motion in the real physical scene.

[0021] The temperature of each point on the weld shows a certain correlation with the distance from the weld. The interpolation function of the radial basis function (RBF) interpolation is determined by the distance between the interpolation point and the given point. It has the advantages of simple interpolation and no grid division. Therefore, in order to make full use of the relationship between the temperatures of some existing feature points, the present invention uses the RBF interpolation algorithm to quickly and batch estimate the temperature value of any position on the weld. Interpolation function The point to be estimated l and the given point l i The Euclidean distance r of the coordinates i =||ll i ||Decision, namely:

[0022]

[0023] Based on the radial basis interpolation model and the interpolation points, the weight coefficient is solved to obtain ω i (i=1,2,…,m), get the temperature value T of the point to be estimated:

[0024]

[0025] The present invention adopts the generalized Multi-Quadic function as the radial basis function. Since the welding process is complicated and the temperature is affected by environmental factors, it is necessary to introduce the adjustment parameter β to adjust the basis function in the actual interpolation approximation problem. The basis function is Substituting into formula (2) we get:

[0026]

[0027] It is known from the radial basis neural network interpolation model that the temperature is the product of the basis function and the weight coefficient, so it can be calculated based on the known point li Inversely solve the weight coefficient ω for the temperature value of (i=1,2,…,m) i (i=1,2,…,m), and solve the temperature T of any point l accordingly.

[0028] The core zone peak temperature and minimum temperature have a particularly significant impact on welding quality during the welding process. Since the RBF interpolation algorithm mainly considers the spatial position correlation of each point on the weldment, it fails to fully consider the relationship between other factors and temperature. Regression analysis can accurately measure the degree of correlation between various factors and the degree of regression fit, improving the effect of the prediction equation. Therefore, the present invention selects the stochastic dual coordinate ascent (SDCA) algorithm with strong regression ability to predict the core zone peak temperature and minimum temperature in real time. The SDCA algorithm is a convex objective function optimization algorithm that combines the best characteristics and functions of the logistic regression and SVM algorithms. It can accurately predict the target value through regression. The process of establishing the SDCA core zone temperature prediction model is as follows:

[0029] Given data (x1,x2,y)1,…,(x1,x2,y) n The training set is constructed. In each sample (x1, x2, y), x1 and x2 are input values, which are the peak surface temperature and the minimum surface temperature in the sampling area, respectively. y is the target value, which is the core area temperature value, including the peak temperature and the minimum temperature in the core area. The predicted value of y can be expressed as follows:

[0030]

[0031] Where w1 and w2 are the weights of the two input quantities, b is the bias, and the weights and bias are first initialized to random values; then the weights and bias are updated using the samples in the training set to minimize the predicted value The average error with the true value y. In order to avoid overfitting, a regularization term needs to be added in the form of:

[0032]

[0033] Where n is the number of samples in the dataset and λ is the regularization coefficient. The SDCA algorithm is then used to solve the dual problem of the above minimization problem. The dual problem has the following form:

[0034]

[0035] where α i The SDCA algorithm is an iterative algorithm that randomly selects a sample and updates the dual variable in each iteration; specifically, it calculates the weight update Δw corresponding to the sample. i and Δb i , and then update the weights and bias terms:

[0036] w1=w1+Δw i x i1 (7)

[0037] w2=w2+Δw i x i2 (8)

[0038] b=b+Δb i (9)

[0039] Where x i1 and x i2 are the two input quantities of the i-th sample, and then recalculate the predicted value of each sample The loss function of the model is calculated, and the square loss function is used as the loss function of the model. If the loss function of the model has converged, then the training can be stopped to obtain the final model parameters. At this time, the peak temperature and the minimum temperature of the core area can be predicted in real time according to formula (4). Finally, the samples on the test set are used to calculate the average relative percentage error, maximum relative percentage error and mean square error of the model to evaluate the performance of the model.

[0040] The present invention uses Deform software to simulate the temperature field under five different welding process parameters. During the welding feed stage, one set of temperature data is extracted every 5 mm of feed. Each simulation model extracts eight sets of temperatures at corresponding moments. In post-processing, a total of 40 sets of surface temperature and core area temperature data are extracted, as shown in the table below. The surface feature point is located 5 mm in front of the stirring head, symmetrical along the weld seam, and within the upper surface range of the weldment with a size of 5 mm × 10 mm. The sampling area collected by the infrared thermal imager in real time also falls within this range.

[0041] Table 1 Surface characteristic point temperature and core area temperature of weldment (℃)

[0042]

[0043] 31 groups of data were randomly selected as training sets and 9 groups as test sets. The training sets were trained with the help of the ML.NET tool library in Visual Studio software to obtain the SDCA core area peak temperature and minimum temperature prediction models. The test set was used to verify the model, and the model prediction results were compared with the actual results. The comparison results are shown in the figure. Figure 2 Table 2 shows the average relative percentage error, maximum relative percentage error, and mean square error of the core area peak temperature and minimum temperature predictions, which confirms the accuracy of the SCDA algorithm in predicting the core area temperature.

[0044] Table 2 Comparison of prediction accuracy of peak temperature and minimum temperature in the core area of weldment

[0045]

[0046] Develop the data communication function between the infrared thermal imager FLIR A615 temperature measurement software and the monitoring system, and transmit the measured temperature data to the monitoring system developed by Unity3D in real time. The specific implementation method is as follows:

[0047] First, the FLIR A615 side creates a network service using the Socket socket handle, then uses the bind() function to bind the IP address of the host and allocate a port number for this service, and establishes a real-time listening to the monitoring system side through the listen() function; in addition, the monitoring system side also uses the Socket socket handle to start a network service, and uses the connect() function to send a connection request to the FLIR A615 side. After the FLIR A615 side normally listens to this connection request, it uses the accept() function to accept the connection request and establish a network connection. At this time, data interaction between the temperature field monitoring system and the FLIRA 615 software can be achieved;

[0048] During the welding process, the surface feature point temperature data collected by the FLIR A615 is saved in string type, and then the encode("utf-8") method is called to convert the string type to bytes type. After that, the send(msg) function of the Socket object can be used to send the temperature data in bytes type to the data buffer; when there is enough buffer in the send buffer, that is, Len(buff)>Len(msg), msg can be sent out at one time; when there is not enough buffer in the send buffer, that is, Len(buff)<Len(msg), only a part of the data of msg is sent out in one call, and the send(msg) interface needs to be called repeatedly many times to send out the data; the temperature field monitoring system, as the receiving end, calls the recv(msg) function to receive the buffer data. When there is enough data in the buffer, that is, Len(buff)>Len(msg), more than one complete data is received when the recv(msg) interface returns; when the data in the receive buffer is insufficient, that is, Len(buff)<Len(msg), incomplete data is received when the recv(msg) returns, and the recv(msg) interface needs to be called repeatedly many times to receive the complete data; through the above transmission method, the surface peak and minimum temperature data in the sampling area collected by the infrared thermal imager in real time are synchronously transmitted to the temperature monitoring system to realize the real-time monitoring of the surface temperature.

[0049] After the temperature monitoring system receives the real-time transmitted surface feature point temperature data, it uses the GUI to display the surface feature point temperature during the welding process in real time in the temperature field monitoring system, and at the same time calls the established RBF and temperature field interpolation prediction model to quickly and batch predict the temperature value of any point on the weldment; write a weldment automatic generation script based on the vertex rendering method, which can automatically generate weldments and divide the grid according to a large number of point coordinates; then, according to the temperature data conversion color rule corresponding to the red, green and blue gradient from high to low temperature, write a script for color rendering for real-time data points, which can automatically generate a temperature cloud map of the entire weldment according to the coordinates and temperature values of a large number of points; combining the above-mentioned established RBF interpolation script, weldment automatic generation script, color rendering script and surface temperature data reading script, it can realize real-time monitoring of the temperature of any position of the weldment during the welding process, and intuitively present it in the form of a three-dimensional cloud map in the synchronous motion simulation model, such as Figure 3 shown.

[0050] After receiving real-time surface feature point temperature data, the temperature monitoring system invokes the SDCA core zone temperature prediction model. The predicted core zone peak and minimum temperatures are presented as line graphs within the temperature monitoring system using the XCharts component. An over-temperature threshold alarm function is developed within the temperature field monitoring system. This function is triggered when the SDCA model-predicted core zone peak temperature exceeds 80% of the weld material's liquefaction temperature or the minimum temperature falls below 80% of the weld material's solidus temperature. When the predicted core zone temperature exceeds the threshold, predictive control of welding process parameters is proposed based on the correlation between welding process parameters and core zone temperature.

[0051] The digital twin-based FSW temperature monitoring system is built with the Unity3D engine. Its functions such as synchronous mapping of the welding process, three-dimensional visualization of the weldment temperature field, and core area temperature warning and control can help workers issue control instructions and emergency instructions to the physical entity in a timely manner during the welding process, so as to keep the welding temperature within a reasonable range and improve the welding quality.

[0052] This invention can be used to validate a temperature monitoring system using a heavy-duty friction stir welding machine. The FSW temperature monitoring system, based on digital twins, uses socket communication to continuously transmit welding temperature data from the temperature measurement software to the monitoring system for display. The temperature data is collected at a frequency of 10Hz, enabling three-dimensional visualization of the real-time temperature field of the weldment and early warning and control of the core temperature.

Claims

1. A method for monitoring the temperature of the core area of friction stir welding based on digital twin, characterized in that: The steps include: Step 1: Use SolidWorks software to create a FSW 3D model, and import the 3D model into 3DMax software for lightweight processing and rendering, and then import it into Unity3D software; Step 2: Analyze the kinematic relationship of the FSW welding process and establish the parent-child relationship between the components of the 3D model. Then, establish a synchronous motion simulation model of the welding process in a program-driven manner. Step 3: Use Deform software to simulate the temperature field of the weldment, extract the coordinates of the feature points in the temperature field simulation model and the corresponding temperature data to construct a radial basis function neural network (RBF) temperature field interpolation prediction model, use the generalized Multi-Quadic function as the radial basis function, and encapsulate the RBF temperature field interpolation prediction model into a C# script; at the same time, use the vertex rendering method to generate the weldment model and convert it into a weldment automatic generation script; then, according to the temperature data color conversion rule corresponding to the red, green, and blue gradient from high to low temperature, write a script for color rendering of real-time data points. This script realizes the presentation of the core area temperature field data in the form of a three-dimensional cloud map; combine the established RBF interpolation script, weldment automatic generation script, color rendering script and surface temperature data reading script to realize real-time temperature monitoring and three-dimensional visualization of any position in the core area of the weldment during welding; Step 4: Use Deform software to simulate the FSW temperature field and obtain surface and core temperature datasets. Use the ML.NET tool library in Visual Studio to train this dataset and establish a correlation between surface feature point temperatures and core temperature. This allows the SDCA core temperature prediction model to be established, and the peak or minimum temperature threshold for the core temperature prediction model to be set in real time. Step 5: Integrate the established synchronous motion simulation model, RBF temperature field interpolation prediction model, and SDCA core area temperature prediction model into Unity3D software to form a digital twin model; Step 6: During the welding process, the peak and minimum surface temperature data within the sampling area collected by the infrared thermal imager in real time are synchronously transmitted via Socket communication based on the TCP protocol to achieve real-time monitoring of the surface temperature. At the same time, the peak and minimum surface temperature data within the sampling area collected by the infrared thermal imager are combined with the digital twin model to perform dynamic, realistic, and multi-dimensional mapping of the actual welding process, realizing real-time 3D visualization of the weldment temperature and core area temperature monitoring. Step 7: When the core area peak temperature and the minimum temperature exceed the solid-liquid phase temperature threshold of the weldment material, the over-limit alarm function is triggered, providing a reference for welding process control.

2. The method for monitoring the temperature of the core area of friction stir welding based on digital twinning according to claim 1, characterized in that: The process of establishing the synchronous motion simulation model is as follows: Combining the established FSW three-dimensional model with kinematic analysis, a kinematic relationship between models is established. The motion relationship between FSW models is described by the parent-child construction relationship, and a tree structure of the FSW machine tool motion model is established based on Unity3D. After the parent-child construction relationship between model components is established, the control of its child objects is obtained step by step through the script on the parent object. In Unity3D software, the Transform component is used to control the movement and rotation of each part model. Based on the kinematic analysis, a C# program is written to control the motion of each model. The program is dragged to the corresponding model in the virtual scene, and Box Collider and RigidBody components are added to simulate the collision and gravity effects in the real world. With the help of the engine operation, the synchronous mapping of the FSW welding process is achieved. At the same time, the model motion is controlled by adjusting the welding process parameters on the Inspector component. Different instructions are used to control the changes in motion as needed to keep synchronized with the objects in motion in the real physical scene.

3. The method for monitoring the temperature of the core area of friction stir welding based on digital twinning according to claim 1, characterized in that: The establishment process of the RBF temperature field interpolation prediction model is as follows: Interpolation function The point to be estimated l and the given point l i The Euclidean distance r of the coordinates i =||ll i ||Decision, namely: Based on the radial basis interpolation model and the interpolation points, the weight coefficient is solved to obtain ω i , i=1,2,…,m, and get the temperature value T of the point to be estimated: The generalized Multi-Quadic function is used as the radial basis function, and the adjustment parameter β is introduced to adjust the basis function. The basis function is Substituting into formula (2) we get: It is known from the radial basis neural network interpolation model that temperature is the product of basis function and weight coefficient, so according to the known point l i The temperature value is inversely solved to obtain the weight coefficient ω i , and solve the temperature T at any point l accordingly.

4. The method for monitoring the temperature of the core area of friction stir welding based on digital twinning according to claim 1, characterized in that: The process of establishing the SDCA core area temperature prediction model is as follows: Given data (x1,x2,y)1,…,(x1,x2,y) n The training set is constructed. In each sample (x1, x2, y), x1 and x2 are input values, which are the peak surface temperature and the minimum surface temperature in the sampling area, respectively. y is the target value, which is the core area temperature value, including the peak temperature and the minimum temperature in the core area. The relationship between x and y is expressed by the following formula: Where w1 and w2 are the weights of the two input quantities, b is the bias, and the weights and bias are first initialized to random values; The weights and biases are then updated using samples from the training set to minimize the predicted value. and the true value The average error; in order to avoid overfitting, a regularization term is added in the form of: Where n is the number of samples in the dataset and λ is the regularization coefficient. The SDCA algorithm is then used to solve the dual problem of the above minimization problem. The dual problem has the following form: where α i The SDCA algorithm is an iterative algorithm that randomly selects a sample and updates the dual variable in each iteration; specifically, it calculates the weight update Δw corresponding to the sample. i and Δb i , and then update the weights and bias terms: w1=w1+Δw i x i1 (7) w2=w2+Δw i x i2 (8) b=b+Δb i (9) Where x i1 and x i2 The two input quantities for the i-th sample are then recalculated for each sample. The loss function of the model is calculated, and the square loss function is used as the loss function of the model. If the loss function of the model has converged, the training is stopped and the final model parameters are obtained. At this time, the peak temperature and the minimum temperature of the core area are predicted in real time according to formula (4). Finally, the samples on the test set are used to calculate the average relative percentage error, maximum relative percentage error and mean square error of the model to evaluate the performance of the model.

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