A circuit board temperature field modeling method based on an unsupervised physical constraint neural network

Abstract

This invention relates to a method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network. First, a two-dimensional matrix is ​​encoded based on sensor location and acquired data. Then, the partial differential equation of heat conduction is solved using the finite difference method. Third-order von Neumann boundary conditions are embedded. A U-Net network model is constructed. A joint physical-network output loss function based on root mean square error is established. Finally, the optimal model is used to reconstruct the entire transient and steady-state temperature field from single-point temperature data. This invention utilizes discrete temperature input from temperature sensors to achieve high-precision modeling of the transient temperature evolution and steady-state temperature field distribution of the entire circuit board. It eliminates the dependence of data-driven models on high-cost, high-precision full-temperature field labeled data, and solves the problem of traditional temperature monitoring technology being constrained by the size of infrared thermal imagers and the number of distributed sensors. This provides a theoretically complete and low-cost innovative solution for the thermal health management of complex electronic devices.

Description

Technical Field

[0001] This invention belongs to the field of comprehensive electronic technology, specifically relating to a method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network. Background Technology

[0002] As the core of electronic devices, circuit boards integrate two or more chip units through a substrate, providing fast data processing speeds and enhancing the module's computing efficiency and functional versatility. However, factors such as power supply and operating environment during operation can reduce circuit reliability, causing localized overheating and ultimately leading to module failure. Traditional temperature monitoring methods have significant limitations in addressing these issues: infrared thermal imaging is constrained by installation volume and cannot track dynamic temperature fields in real time; distributed thermal sensors are limited by installation density and cannot cover the entire area; and numerical simulation is limited by computational resources and can only be used for offline analysis.

[0003] Traditional temperature field modeling primarily employs the finite element method (FEM), whose core principle is to discretize the continuous temperature field into a set of temperature values ​​at finite element nodes and obtain discrete solutions by solving the partial differential equations of heat conduction. However, as circuit boards evolve towards high-density integrated architectures, their heat conduction control equations exhibit significant nonlinear characteristics. Numerically solving these strongly nonlinear equations requires substantial computational resources, making it difficult to meet the timeliness requirements of thermal monitoring in modern electronic devices. With the development of machine learning technology, neural networks, with their powerful high-dimensional nonlinear representation capabilities, are gradually becoming a core technology replacing traditional numerical simulation. In the field of partial differential equation solving, neural networks, as general-purpose function approximators, can construct surrogate models that efficiently handle complex heat transfer problems, reducing computation time by 2-3 orders of magnitude compared to numerical methods. Current research methods have limitations in solving the problem of rapid temperature field calculation. First, traditional thermal management solutions cannot simultaneously meet the requirements of efficient computation, low cost, and online real-time modeling. Secondly, while neural network methods demonstrate good prediction results for simple two-dimensional steady-state temperature field problems, research on transient temperature field problems is scarce. Furthermore, transient temperature field prediction primarily extracts information from historical moments to predict future temperatures, emphasizing the continuity of prediction but lacking real-time prediction of temperature fields under different parameters and time periods. In addition, deep learning methods require large amounts of training data to achieve reliable modeling, and preparing simulation data is very costly. Summary of the Invention

[0004] This invention provides a circuit board temperature field modeling method based on unsupervised physical constraint neural networks. It utilizes a neural network architecture to achieve transient and steady-state temperature field modeling tasks for circuit boards, abandoning the dependence of traditional data-driven methods on large-scale labeled datasets, and solving the problem that traditional temperature monitoring technology is constrained by the size of infrared thermal imagers and the number of distributed sensors installed.

[0005] To address the above technical problems, this invention provides a method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network, characterized by the following steps: Step 1, Sensor Data Encoding: The layout information of the obtained circuit board surface temperature sensors is encoded into a sparse matrix, where the sensor position corresponds to the temperature measurement value, and the non-measurement area is assigned a zero value, constructing an input tensor with dimension n×m; Step 2: Solving the partial differential equation: The partial differential equation for heat conduction of the circuit board is discretized and solved using the finite difference method. The two-dimensional central difference formula is substituted into the partial differential equation for heat conduction, and the resulting finite difference operator is reconstructed into the product transformation form of the parameter matrix to obtain the numerical solution of the temperature field. Step 3: Embedding boundary conditions: Embed third-order von Neumann boundary conditions at the boundary of the solution domain. Use a mirror-symmetric filling strategy to construct virtual grid points outside the boundary so that the physical equation constraints are satisfied at the boundary of the solution domain. Step 4, U-Net encoding and decoding modeling: Build a U-Net network model, using the input tensor described in S1 as input, and extract and fuse multi-scale spatial features through an encoder-decoder and a skip link mechanism to achieve end-to-end reconstruction of the sparse matrix into an n×m full temperature field; Step 5: Construction of physical loss function: Construct a physical constraint loss function based on root mean square error. The physical constraint loss function includes a physical constraint term composed of the numerical solutions of the temperature field obtained from S2 and S3 and a network output term composed of the output of the U-Net network model obtained from S4. This guides the training process of the U-Net network model to output accurate temperature field modeling results. Step 6: Transient temperature field prediction: Use the U-Net network model with the corresponding time step to model the transient temperature field of the circuit board on the collected test set; Step 7: Steady-state temperature field prediction: Use a U-Net network model that reaches the steady-state time step to model the steady-state temperature field of the circuit board based on the collected test set.

[0006] Beneficial Effects: This invention effectively addresses the limitations of traditional thermal management solutions, enabling the creation of a real-time cloud map of the entire plate's temperature field using single-point temperature data from sensors. Furthermore, it achieves modeling results approaching those of supervised learning even without temperature field labels, while doubling the computational efficiency compared to numerical simulation. The physical constraint mechanism proposed in this paper eliminates the reliance of traditional data-driven models on high-cost, high-precision full-temperature field labeled data, providing a theoretically sound and low-cost innovative solution for the thermal health management of complex electronic devices. Attached Figure Description

[0007] Figure 1 This invention provides a schematic diagram of a temperature sensor collecting data on a circuit board. Figure 2 A flowchart illustrating a specific method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network, provided by this invention; Figure 3 This invention provides a U-Net network model architecture diagram; Figure 4 A diagram illustrating the construction process of a physical constraint loss function provided by this invention. Detailed Implementation

[0008] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below.

[0009] This invention proposes a method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network, comprising the following steps: Step 1, Sensor Data Encoding: Encode the layout information of the temperature sensors on the circuit board surface into a sparse matrix, where the sensor position corresponds to the temperature measurement value, and the non-measurement area is assigned a zero value, constructing an input tensor with dimension n×m; Step 2: Solving the partial differential equation: Solve the partial differential equation of heat conduction based on the finite difference method, and optimize the solution steps of the partial differential operator; Step 3: Boundary condition embedding: Design a filling strategy applicable to third-order von Neumann boundary conditions to ensure that the physical equation constraints are satisfied at the boundary of the solution domain and improve the modeling accuracy at the boundary. Step 4: U-Net Encoding and Decoding Modeling: Build the U-Net network model, optimize the network architecture, extract and fuse multi-scale spatial features through the encoder-decoder and skip link mechanism, and set network training parameters to achieve end-to-end reconstruction of the sparse matrix into an n×m full temperature field. The input to the model is the sparse matrix from Step 1.

[0010] Step 5: Construction of Physical Loss Function: Establish a physical-network output joint loss function based on root mean square error to guide network training; Step 6: Transient temperature field prediction: Use a deep neural network model with the corresponding time step to model the transient temperature field of the circuit board based on the collected test set.

[0011] Step 7: Steady-state temperature field prediction: Use the corresponding deep neural network model to model the steady-state temperature field of the circuit board based on the collected test set.

[0012] Further, the specific process of step one involves abstracting the circuit board into a rectangular solution domain of size a×b, and discretizing it into a uniform grid of n×m nodes. The horizontal spatial step size is then h=a / n, and the vertical spatial step size is k=b / m. The spatial arrangement of the temperature sensors and the captured temperature constitute key design variables. It is an intensity distribution function related to the temperature sensor. Temperature sensor i Location Let be the temperature at the sampling point, and the initial temperature field distribution be... .

[0013] Furthermore, the specific process of step two involves applying the two-dimensional central difference formula, as shown below, to approximate the solution of the second-order derivative terms in the partial differential equation, transforming the continuous differential equation into a system of algebraic equations. To simplify the calculation, the subsequent derivation assumes h=k.

[0014] Where u is the solution of the temperature field, and n is a number of time steps, i.e., the time when the temperature field needs to be output. (21) The transient temperature field satisfies the two-dimensional heat conduction equation, and its expression is as follows.

[0015] Where, constant It is thermal conductivity. It represents all points within the heat-conducting plate, where u is the solution to the transient temperature field, and new parameters are introduced. Let n represent the time step. Then the two-dimensional heat conduction equation at time n can be expressed as: Substituting the two-dimensional central difference formula into the heat conduction equation and simplifying it, we get... in This represents the temperature at each location point in the transient temperature field at the current moment.

[0016] (22) The steady-state temperature field satisfies the Poisson equation, which is expressed as follows.

[0017] Where U is the solution of the steady-state temperature field, substituting the two-dimensional central difference formula into the Poisson equation and simplifying, we can obtain... in This represents the steady-state temperature at each location point in the steady-state temperature field.

[0018] (23) Vectorize the temperature field of the discrete mesh of the two-dimensional heat-conducting plate and reconstruct the finite difference operator into a product transformation form of the parameter matrix. Given , and , can make , The corresponding parameter matrices are respectively .

[0019] Furthermore, the specific process of step three involves the diffusion and transfer of energy generated by the heat source within the plate, ultimately reaching thermal equilibrium under adiabatic boundary conditions. This invention uses the finite difference method to solve the third-order Neumann boundary conditions.

[0020] The third-order Neumann boundary condition in the horizontal direction can be expressed as: The finite difference method can be used to obtain The formula can be simplified to This invention constructs virtual grid points outside the boundary based on the central difference formula to achieve derivative approximation, that is, it uses the mirror symmetry method to fill the boundary external value with the adjacent internal node. After extending the internal domain nodes to the surrounding domain through the Neumann boundary condition, the boundary filling value is automatically corrected by utilizing the continuity of the derivative of the heat conduction equation, without the need to calculate the boundary value separately. After the calculation is completed, the filling value is removed to obtain a highly accurate boundary value.

[0021] Furthermore, step four involves using the tensor from step one as input to design a deep convolutional neural network architecture, realizing an end-to-end mapping model from initial parameters to the temperature field distribution, serving as a substitute model for numerical solutions. This invention selects the U-Net model, where consecutive convolutional layers in the encoder path progressively generate high-level semantic codes through local feature extraction, achieving global information capture of the input matrix. The corresponding decoder path uses single-linear interpolation instead of traditional transposed convolutional layers to reconstruct the temperature field. Additionally, skip connections between the encoder and decoder at the same level enable multi-scale feature fusion, allowing U-Net to demonstrate significant application potential in the task.

[0022] Further, the specific process of step five involves constructing a physical loss function using the root mean square error (RMSE) and calculating the deviation between the modeling result of the network in step four and the numerical solution. The numerical solution of the temperature field generated by the finite difference method provides physical constraints for the neural network. The network output and the physical constraint terms are combined to form the final physical constraint loss function. The physical terms force the network output to satisfy the heat conduction equation and its boundary conditions. The loss functions for the transient and steady-state temperature fields can be expressed as follows: in and The results are the calculations for the transient and steady-state temperature fields, respectively. To model the output of a neural network trained at different times for transient temperature fields, The output of the neural network used to model the steady-state temperature field.

[0023] Example: Reference Figure 1 , Figure 2 As shown, the present invention provides a method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network, comprising the following steps: (1) Data acquisition: Assume that the circuit board is a 0.1×0.1 rectangle and is divided into 200×200 discrete points. Arrange 64 temperature sensors to collect single-point temperature data, record the coordinates and temperature of the sensors at each sampling point, and set the non-sensor area to 0 to obtain the sparse matrix of the initial intensity distribution.

[0024] (2) Data preprocessing: First, a single-channel dimension is added to the 200×200 input matrix to convert it into a 200×200×1 three-dimensional tensor structure to meet the multi-channel feature extraction requirements of the convolutional neural network; second, the temperature values ​​are subjected to mean-variance standardization to eliminate dimensional differences and accelerate model convergence.

[0025] (3) Divide the dataset: During the experiment, the dataset with a sample size of 10,000 was divided into training set, validation set and test set in a ratio of 8:2:1.

[0026] (4) Build the U-Net network model, such as Figure 3 The diagram shows the architecture of the U-Net network model.

[0027] (41) Convolutional layer: Use a 3×3 convolutional kernel with a stride of 1 and padding of 1 to ensure that the feature map size is constant and only the number of channels is changed; (42) Downsampling layer: Four downsampling operations are performed between the five convolutional layers, and a 2×2 average pooling layer is used to compress the feature map size and increase the number of channels. The number of channels output after the four downsampling operations are 64, 128, 256, and 512, respectively; (43) Upsampling layer: Four upsampling operations are performed between the five convolutional layers. 2×2 single linear interpolation is used to restore the resolution of the feature map and reduce the number of channels. The number of channels output after the four upsampling operations corresponds to 512, 256, 128, and 64 for the downsampling layer, respectively. Combined with the skip connection mechanism, multi-scale feature fusion can be achieved. (44) Output layer: Using a 1×1 convolution kernel with zero padding, the number of output channels of the network is adjusted from 64 to 1, and the results are visualized in two dimensions.

[0028] (5) Construct the physical constraint loss function, such as Figure 4 The diagram illustrates the construction process of the loss function. The specific procedure is as follows: (51) Boundary treatment: Third-order Neumann boundary condition constraints are applied by mirror filling to ensure the accuracy and precision of the equation solution; (52) Substitute the two-dimensional central difference formula into the two-dimensional heat conduction formula and the Poisson equation, and obtain the partial differential operator by merging simplified formulas of the same type; (53) Reconstruct the simplified formula into a product transformation form of the parameter matrix to optimize the solution steps of the partial differential operator; (54) Combining the output of the deep neural network, the error between the network output and the numerical calculation is fitted by the root mean square error to obtain the physical constraint loss function to guide the network training.

[0029] (6) Train the model. The training steps are as follows: (61) Initialize the parameters of each network layer in the U-Net network model; (62) Training parameter settings: The Adam optimizer is used to update parameters during network training, and the initial learning rate is set to 1×10. -4 Each training batch using the mini-batch strategy contains 2 samples, and the number of training iterations is 400 rounds.

[0030] (63) Training and validation sets are input into the model for training: During the training process, hyperparameter optimization and network weight updates are used to gradually improve the model's ability to generalize and predict unknown samples. Finally, based on the principle of minimizing the validation set loss function, the optimal model weights are selected for performance evaluation on the test set.

[0031] (7) Real-time construction: Input the test set into the optimal network model with the minimum loss saved on the validation set as described in step (6) to realize the construction of transient and steady-state temperature fields in real time.

[0032] (71) Construction of transient temperature field: Assuming the thermal conductivity of the circuit board The time step is 0.00002. If the value is 0.01, then the key parameter value for calculating the optimization matrix is: Under various initial heat source intensity distributions, the model outputs results every 100 time steps to simulate the transient temperature field evolution process.

[0033] (72) Construction of steady-state temperature field: Assuming the thermal conductivity of the circuit board With a value of 0.00002, the model outputs the temperature field distribution after the circuit board and the environment complete heat exchange, reaching a steady state under various initial heat source intensity distribution conditions.

[0034] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network, characterized in that, Includes the following steps: Step 1, Sensor Data Encoding: The layout information of the obtained circuit board surface temperature sensors is encoded into a sparse matrix, where the sensor position corresponds to the temperature measurement value, and the non-measurement area is assigned a zero value, constructing an input tensor with dimension n×m; Step 2: Solving the partial differential equation: The partial differential equation for heat conduction of the circuit board is discretized and solved using the finite difference method. The two-dimensional central difference formula is substituted into the partial differential equation for heat conduction, and the resulting finite difference operator is reconstructed into the product transformation form of the parameter matrix to obtain the numerical solution of the temperature field. Step 3: Embedding boundary conditions: Embed third-order von Neumann boundary conditions at the boundary of the solution domain. Use a mirror-symmetric filling strategy to construct virtual grid points outside the boundary so that the physical equation constraints are satisfied at the boundary of the solution domain. Step 4, U-Net encoding and decoding modeling: Build a U-Net network model, using the input tensor described in S1 as input, and extract and fuse multi-scale spatial features through an encoder-decoder and a skip link mechanism to achieve end-to-end reconstruction of the sparse matrix into an n×m full temperature field; Step 5: Construction of physical loss function: Construct a physical constraint loss function based on root mean square error. The physical constraint loss function includes a physical constraint term composed of the numerical solutions of the temperature field obtained from S2 and S3 and a network output term composed of the output of the U-Net network model obtained from S4. This guides the training process of the U-Net network model to output accurate temperature field modeling results. Step 6: Transient temperature field prediction: Use the U-Net network model with the corresponding time step to model the transient temperature field of the circuit board on the collected test set; Step 7: Steady-state temperature field prediction: Use a U-Net network model that reaches the steady-state time step to model the steady-state temperature field of the circuit board based on the collected test set.

2. The method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network according to claim 1, characterized in that, The specific process of step one is to abstract the circuit board into a rectangular solution domain of size a×b, and discretize it into a uniform grid of n×m nodes. Then the spatial step size in the horizontal direction is h=a / n, and the spatial step size in the vertical direction is k=b / m; let It is an intensity distribution function related to the temperature sensor. Temperature sensor i Location The temperature at the collection points is based on the location of each temperature sensor. and temperature at the collection point Construct the sparse matrix.

3. The method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network according to claim 2, characterized in that: 。 4. The method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network according to claim 2, characterized in that, In step two, the partial differential equations of heat conduction include the two-dimensional heat conduction equation satisfied by the transient temperature field and the Poisson equation satisfied by the steady-state temperature field. The second derivative terms are approximated using the two-dimensional central difference formula, transforming the continuous differential equation into a system of algebraic equations, and h=k is set. A time step Δt is introduced to obtain the two-dimensional heat conduction equation at time n, which is substituted into the two-dimensional central difference formula for simplification to obtain the iterative relationship of the transient temperature field. The two-dimensional central difference formula is substituted into the Poisson equation for simplification to obtain the steady-state temperature field relationship. The temperature field of the discrete mesh is vectorized, and the finite difference operator is reconstructed into a product transformation form of the parameter matrix. Given the thermal conductivity λ, the time step Δt, and the spatial step h, let... , This yields the corresponding parameter matrix.

5. The method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network according to claim 1, characterized in that, In S3, the third-order Neumann boundary condition in the horizontal direction is expressed as: Approximated by the finite difference method: ； Virtual grid points are constructed outside the boundary based on the central difference formula. The external boundary value is filled with the mirror symmetry method, which is equal to the adjacent internal node. After expanding the internal domain nodes to the surrounding domain through the Neumann boundary condition, the boundary filling value is automatically corrected by the continuity of the derivative of the heat conduction equation. After the calculation is completed, the filling value is removed to obtain the boundary value.

6. The method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network according to claim 1, characterized in that, In S4, the U-Net network model extracts local features and gradually generates high-level semantic codes through continuous convolutional layers in the encoder path to achieve global information capture of the input matrix; the decoder path uses single linear interpolation to replace the transposed convolutional layer to reconstruct the temperature field; and the encoder and decoder at the same level achieve multi-scale feature fusion through skip connections.

7. The method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network according to claim 6, characterized in that, The U-Net network model includes 5 convolutional layers, with 4 downsampling operations and 4 upsampling operations performed between these 5 convolutional layers. The downsampling operation uses a 2×2 average pooling layer to compress the feature map size and increase the number of channels. After the 4 downsampling operations, the number of output channels is 64, 128, 256, and 512, respectively. The upsampling operation uses 2×2 single linear interpolation to restore the feature map resolution and reduce the number of channels. After the 4 upsampling operations, the number of output channels is 512, 256, 128, and 64, respectively, corresponding to the downsampling layer. The output layer uses a 1×1 convolutional kernel with zero padding to adjust the number of output channels from 64 to 1.

8. The method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network according to claim 1, characterized in that, In S5, the deviation between the modeling results and the numerical solution of the neural network model is calculated using the root mean square error to construct the physical loss function. The physical constraint loss function Loss1 for the transient temperature field and the physical constraint loss function Loss2 for the steady-state temperature field are expressed as follows: in and The results are the calculations for the transient and steady-state temperature fields, respectively. The output of the U-Net network model is used to model the transient temperature field trained at different times. The output of the U-Net network model is used to model the steady-state temperature field. The network output, combined with the physical constraint terms, constitutes the final physical constraint loss function, guiding the U-Net network model to output more accurate temperature field modeling results.

9. The method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network according to claim 1, characterized in that, In S4, the U-Net network model is trained using the Adam optimizer, with an initial learning rate set to 1×10⁻⁶. -4 Each training batch contains 2 samples, and the number of training iterations is 400 rounds. Furthermore, the dataset with a sample size of 10,000 is divided into a training set, a validation set, and a test set in a ratio of 8:2:1, and the optimal model weights are selected based on the principle of minimizing the loss function of the validation set.

10. The method for modeling the temperature field of a circuit board based on an unsupervised physical constraint neural network according to claim 1, characterized in that, In S6, when modeling the transient temperature field... The time step is 0.00002. If the value is 0.01, then the key parameter value for calculating the optimization matrix is: Under various initial heat source intensity distribution conditions, the model outputs results every 100 time steps to simulate the transient temperature field evolution process; when modeling the steady-state temperature field, the thermal conductivity of the circuit board is set to λ=0.00002, and under various initial heat source intensity distribution conditions, the model outputs the temperature field distribution after the circuit board completes heat exchange with the environment and reaches a steady state.

Images