A method for predicting performance of a heat sink based on a Lévy distribution random configuration network

Abstract

The application discloses a heat sink performance prediction method based on a Lévy distribution random configuration network, and belongs to the technical field of thermal management and artificial intelligence, and the prediction method comprises the following steps: acquiring data set composed of heat sink structure parameters and performance index data; standardizing the data and dividing the data into a training set and a test set; constructing a Lévy-SCN prediction model, generating random numbers subject to Lévy distribution by using a Mantegna algorithm to construct candidate input weights and biases, screening the best candidate nodes through a supervised inequality constraint, and using random weights as an alternative solution to continue training when there is no effective node; and performing performance prediction by using the trained model. The application can accurately predict thermal resistance, maximum temperature, convective heat transfer coefficient and pressure drop at the same time, significantly improves prediction accuracy and training robustness, and provides reliable and efficient evaluation for multi-objective optimization design of a heat sink.

Description

Technical Field

[0001] This invention relates to the fields of thermal management and artificial intelligence, specifically to a method for predicting heat sink performance based on Lévy distributed augmented stochastic configuration network (SCN), used for optimizing the structural parameters and rapidly evaluating the performance of heat sinks in electronic devices. Background Technology

[0002] With the continuous increase in power density of electronic devices, heat dissipation has become a key bottleneck restricting their performance and reliability. Forced air-cooled heat sinks are widely used in aerospace, power electronics, and new energy fields due to their compact structure and high heat dissipation efficiency. Traditional heat sink performance evaluation mainly relies on computational fluid dynamics (CFD) simulation. Although this method has high accuracy, it is computationally time-consuming and has a long iterative design cycle, making it difficult to meet the rapid optimization needs in the early design stage. Therefore, constructing a data-driven prediction model that can quickly and accurately map the complex nonlinear relationship between heat sink structural parameters and thermal performance indicators has significant engineering application value.

[0003] Randomized Networks (SCNs) are incremental single-hidden-layer feedforward neural networks proposed in recent years. Unlike traditional randomized weighted networks such as Randomized Vector Function Chain Networks (RVFLs) or Extreme Learning Machines (ELMs), SCNs use a supervision mechanism to constrain the random generation of hidden layer node parameters, ensuring that newly added nodes effectively reduce network residuals. This theoretically guarantees universal approximation and exhibits good generalization and fast learning capabilities.

[0004] Existing technologies, such as the paper "Optimal Randomness for Stochastic Configuration Network (SCN) with Heavy-Tailed Distributions" (Entropy, 2021), explore the use of heavy-tailed distributions (such as Lévy, Cauchy, and Weibull distributions) to initialize the input weights and biases of SCN in order to improve model performance. This research shows that on standard regression and classification datasets, SCNs using heavy-tailed distributions can achieve performance similar to the original SCN with fewer hidden layer nodes, or achieve higher test accuracy in classification tasks. However, the research background of this technology is general machine learning regression and classification problems, and does not involve complex engineering thermodynamics problems. In particular, when facing the task of predicting radiator performance with strong nonlinearity and multivariate coupling characteristics, existing technologies do not provide effective solutions for how to design targeted SCN parameter generation strategies based on Lévy distributions, and how to solve the problem of SCN premature termination due to search failures during training, leading to substandard model performance. Summary of the Invention

[0005] The purpose of this invention is to solve the above-mentioned problems by providing a radiator performance prediction method based on Lévy distributed random configuration network that can simultaneously and accurately predict thermal resistance, maximum temperature, convective heat transfer coefficient and pressure drop, significantly improve prediction accuracy and training robustness, and provide a reliable and efficient evaluation method for multi-objective optimization design of radiators.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] The present invention provides a method for predicting heat sink performance based on a Lévy distributed random configuration network, comprising the following steps:

[0008] Step 1: Prepare the dataset: Obtain the structural parameters and corresponding performance index data of the heat sink to form the original dataset; the structural parameters include substrate thickness, fin thickness, number of fins, external dimensions and airflow, and the performance indexes include thermal resistance, maximum temperature, convective heat transfer coefficient and pressure drop;

[0009] Step 2, Data Preprocessing: Standardize the original dataset and divide it into training and test sets;

[0010] Step 3: Construct the Lévy-SCN prediction model:

[0011] The heat sink performance prediction model is constructed based on a Lévy distribution randomized network, specifically including the following sub-steps:

[0012] (1) Initialize model hyperparameters: Set the maximum number of hidden layer nodes, the maximum number of random configurations, the tolerance error, the candidate set of regularization parameters, the candidate set of constraint relaxation parameters, and the stability index of the Lévy distribution, and initialize the network residuals and the current number of hidden layer nodes;

[0013] (2) Start incrementally building the loop. When the loop condition is met, execute the following sub-steps:

[0014] (2a) Generate candidate node pool: Use the Mantegna algorithm to generate random numbers that follow the Lévy distribution, construct candidate input weights and candidate biases, and calculate candidate hidden layer outputs;

[0015] (2b) Evaluate and select the best candidate node: Calculate the supervision value of each candidate node according to the supervision inequality constraint, and select the candidate node with the largest supervision value and that satisfies the constraint as the best candidate node;

[0016] (2c) Adding nodes: If there are valid nodes, the best candidate node is added to the network; if there are no valid nodes, randomly generated weights and biases are used as candidate nodes to be added to the network.

[0017] (2d) Update network parameters: Update the number of hidden layer nodes, calculate the current hidden layer output matrix, calculate the output weights using the least squares method, calculate the current network prediction value and update the residuals;

[0018] (3) Judgment of loop termination condition: When the maximum number of hidden layer nodes is reached or the current error is less than the tolerance error, the training is terminated and the trained Lévy-SCN heat sink performance prediction model is output.

[0019] Step 4: Use the model to make predictions:

[0020] The heat sink structural parameters to be predicted are input into the trained Lévy-SCN model, which outputs the predicted results of the heat sink performance indicators.

[0021] The above-mentioned method for predicting radiator performance based on a Lévy distribution random configuration network uses the z-score standardization method in step two.

[0022] In the above-mentioned method for predicting radiator performance based on a Lévy distribution random configuration network, the stability index β of the Lévy distribution in step three is preferably 1.5.

[0023] The above-mentioned method for predicting radiator performance based on a Lévy distribution random configuration network requires that at least 60% of the output dimensions satisfy the constraint conditions in the supervised inequality constraint described in step three.

[0024] The above-mentioned method for predicting radiator performance based on a Lévy distribution random configuration network is used to predict the performance of a Y-shaped radiator.

[0025] Compared with the prior art, the present invention has significant advantages, as can be seen from the above technical solution:

[0026] 1. Significantly Improved Prediction Accuracy: This invention introduces a Lévy distribution with heavy-tailed characteristics to generate the hidden layer parameters of the SCN, enhancing the model's ability to explore and fit complex patterns and nonlinear relationships in radiator performance data. Experimental results show that the model constructed in this invention achieves an average coefficient of determination (R²) of 0.965 on the test set, an improvement of 8.7% compared to the standard SCN and 11.9% compared to the three-layer Deep-SCN.

[0027] 2. Enhanced Training Robustness: This invention effectively avoids the problem of the model prematurely stopping training due to the inability to find nodes that meet the conditions by using random weights as an alternative when the SCN search fails. This ensures that the model can continue to optimize until it reaches the expected performance, thereby improving the stability of the training process and the upper limit of the model's final performance.

[0028] 3. Multi-objective integrated prediction: This invention can simultaneously and accurately predict four key performance indicators: thermal resistance, maximum temperature, convective heat transfer coefficient and pressure drop. It provides a reliable and efficient evaluation tool for the multi-objective optimization design of heat sinks, and significantly reduces the time cost of relying on CFD simulation. Attached Figure Description

[0029] Figure 1 This is a flowchart of the present invention.

[0030] Figure 2 This is a scatter plot of the prediction results of the standard SCN model for four performance metrics on the radiator test set.

[0031] Figure 3 This is a scatter plot of the prediction results of the three-layer Deep-SCN model for four performance metrics on the heat sink test set.

[0032] Figure 4 This is a scatter plot showing the prediction results of the Lévy-SCN model of this invention on the heat sink test set for four performance indicators.

[0033] Figure 5-1 A scatter plot showing the prediction results of the FCNN model for four performance metrics on the heat sink test set.

[0034] Figure 5-2 A scatter plot showing the prediction results of the RVFL model for four performance metrics on the radiator test set.

[0035] Figure 5-3 A scatter plot showing the prediction results of the SVM model for four performance metrics on the heat sink test set.

[0036] Figure 5-4 Scatter plots showing the prediction results of the UAP-DSCN model for four performance metrics on the radiator test set. Detailed Implementation

[0037] The following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a heat sink performance prediction method based on a Lévy distributed random configuration network proposed in accordance with the present invention.

[0038] Example 1:

[0039] A radiator performance prediction method based on a Lévy distribution randomized network is proposed to simultaneously predict four performance indicators of a Y-fin radiator: thermal resistance, maximum temperature, convective heat transfer coefficient, and pressure drop. The method includes the following steps:

[0040] Step 1: Prepare the dataset:

[0041] (1) A parametric model of the Y-shaped heat sink was constructed using computational fluid dynamics (CFD) simulation software. Eight structural and operating parameters were set as input variables: substrate thickness B (mm), first fin thickness C1 (mm), second fin thickness C2 (mm), number of row fins N1, number of column fins N2, external length L1 (mm), external width W1 (mm), and airflow (CFM). Four performance indicators were set as output variables: thermal resistance R. th (Unit: K / W), Maximum device temperature T max (Unit: °C), surface average convective heat transfer coefficient h (unit: W / (m²·K)) and pressure drop ΔP (unit: Pa);

[0042] (2) The Latin hypercube sampling method was used to generate 150 different combinations of input parameters in the design space. CFD simulations were performed on each combination, and the four output values ​​corresponding to each input were recorded to form the original dataset.

[0043] Step 2, Data Preprocessing:

[0044] (1) The z-score method is used to standardize the eight input features and four output features in the original dataset. For any feature x, the formula for calculating its standardized value x' is: x' = (x-μ) / σ, where μ is the mean of the feature in all 150 samples and σ is the standard deviation of the feature;

[0045] (2) Using a random number generator with seed 42, the 150 standardized data sets are randomly divided into training and test sets. 70% (105 sets) are used as the training set for model building; the remaining 30% (45 sets) are used as the test set for evaluating model performance.

[0046] Step 3: Construct the Lévy-SCN prediction model:

[0047] (1) Initialize model hyperparameters: Set the maximum number of hidden layer nodes L max =50, maximum number of random configurations T max =50, tolerance error tol=0.05; set the candidate set of regularization parameters r = [0.1, 0.5, 1, 2, 5, 10, 20], and the candidate set of constraint relaxation parameters ε = [0.7, 0.8, 0.9, 0.95, 0.99]; set the stability index of the Lévy distribution β=1.5; initialize the network residual e to equal the output matrix Y of the training set. train The current number of hidden layer nodes L=0;

[0048] (2) Start the incremental construction loop: When L < 50 and the current error e > 0.05, execute the following sub-steps:

[0049] (2a) Generate candidate node pool: Repeat T max = Less than 50 operations — Use the Mantegna algorithm to generate a random number following a Lévy distribution. Specifically, generate two independent, standard normally distributed random numbers u and v, and calculate the step size s = u / |v| (1 / β) Then let the candidate input weights w g = 2 × rand(8, 1)-1 + s, candidate bias b g = 2 × rand(1, 1)-1 + s; For the current candidate node, calculate its hidden layer output vector h for all training samples. g =sigmoid(X train × w g + b g ), where the activation function is the sigmoid function, which has the form g(z)=1 / (1+exp(-z));

[0050] (2b) Evaluate and select the best candidate node: For each of the 50 candidate nodes generated so far, iterate through all combinations of r and ε, and calculate its supervision value ξ. The calculation formula is: ξ = (h g T × e) 2 / (h g T × h g )- (1-r-ε)× e T × e; Among all candidates satisfying ξ > 0, select the candidate node with the largest ξ value and record its w. best b best and the corresponding r best and ε best Check if there are any valid nodes, i.e., whether candidate nodes with ξ > 0 have been found;

[0051] (2c) Add a node: If a valid node (ξ) exists best If > 0), then w best and b best Add it to the network as a parameter of the (L+1)th hidden layer node; if there is no valid node (i.e., ξ) best If the weights are 0, then discard all candidate nodes generated in the 50 searches of this round, and randomly generate a set of alternative weights w. rand and bias b rand Its generation method is: w rand= 2 × rand(8,1)-1,b rand = 2 × rand(1, 1)-1, where w rand and b rand It is added to the network as a parameter of the (L+1)th hidden layer node;

[0052] (2d) Update network parameters: Update the current number of hidden layer nodes L = L + 1; calculate the hidden layer output matrix H of the current network for all training samples. L = [h1, h2, ..., h L The output weight β is calculated using the least squares method. L = (H L T ×H L + (r best Or the default value is r=1)×I). -1 × H L T × Y train , where I is the identity matrix; calculate the current network prediction value. Update the current error ;

[0053] (3) Loop termination condition judgment: When L reaches 50 or the F norm of the current error e is less than tol=0.05, exit the loop and output the trained Lévy-SCN radiator performance prediction model.

[0054] Step 4: Use the model to make predictions:

[0055] The radiator structural parameters to be predicted (i.e., the 8 input features) are standardized using z-scores according to the mean and standard deviation in step two, and then input into the Lévy-SCN model trained in step three. The model output is the predicted value of the 4 standardized performance indicators. Finally, the predicted values ​​are inversely standardized according to the mean and standard deviation of the output features in step two to obtain the predicted results of thermal resistance, maximum temperature, convective heat transfer coefficient and pressure drop in real physical space.

[0056] Test Example: Performance Verification and Comparative Test

[0057] The Lévy-SCN model constructed in Embodiment 1 of this invention is compared with the performance of existing technologies such as standard SCN, three-layer Deep-SCN, SCN variants using uniform distribution (USCN), normal distribution (NSCN), Laplace distribution (LSCN), and Weibull distribution (WSCN), as well as models such as FCNN, RVFL, SVM, and UAP-DSCN, on the same test set.

[0058] (a) Evaluation Indicators

[0059] The coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are used as evaluation indicators. The formulas for each indicator are as follows:

[0060]

[0061]

[0062]

[0063]

[0064] (II) Test Results

[0065] The average R² performance of each model on the test set is shown in Table 1, and the detailed error statistics of each model on the four performance metrics are shown in Tables 2 to 5.

[0066] Table 1. Comparison of average R² performance of different models on the heatsink test set

[0067]

[0068] Table 2 Statistical results of thermal resistance prediction performance of different models

[0069]

[0070] Table 3 Statistical results of the highest temperature prediction performance of different models

[0071]

[0072] Table 4. Statistical results of the predicted performance of surface-average convective heat transfer coefficient for different models

[0073]

[0074] Table 5 Statistical results of voltage drop prediction performance of different models

[0075]

[0076] (III) Results Analysis

[0077] As can be seen from Table 1, the Lévy-SCN model proposed in this invention achieves an average R² of 0.9650 on the test set, which is significantly higher than that of the standard SCN (0.8588), Deep-SCN (0.8400), and all other comparative models, indicating that this invention has the strongest overall explanatory and predictive ability for radiator performance.

[0078] As can be seen from the detailed comparisons in Tables 2 to 5, for the four individual performance indicators of thermal resistance, maximum temperature, convective heat transfer coefficient, and pressure drop, the Lévy-SCN model has the highest R² in the test set, and the lowest or near-lowest RMSE, MAE, and MAPE. For example, in pressure drop prediction, the model of this invention has an R² as high as 0.9951 and a MAPE of only 3.63%, which is far superior to the standard SCN's 0.9678 and 9.81%.

[0079] Combination Figure 2 , Figure 3 and Figure 4 By comparing the scatter plots, we can see that... Figure 2 The standard SCN model shown deviates significantly from the actual values ​​in some groups. Figure 3 The fluctuations and deviations between the predicted points and the actual values ​​of the three-layer Deep-SCN model shown are more significant, while Figure 4 The predicted values ​​of the Lévy-SCN model of this invention, as shown, highly overlap with the actual values ​​across all four performance metrics, with minimal deviation. This indicates that a single-layer SCN combined with Lévy distribution enhancement is sufficient to effectively describe the mapping relationship between independent and dependent variables, while deeper networks and more nodes may lead to model overfitting, affecting prediction performance and stability. Furthermore, Figure 5-1 , 5-2 In the comparison models of FCNN, RVFL, SVM and UAP-DSCN shown in 5-3 and 5-4, although FCNN and SVM can roughly follow the changing trend of the actual values, their overall prediction accuracy and stability are still inferior to the model of this invention.

[0080] In summary, the experimental results of this invention fully demonstrate the high accuracy, high stability, and excellent generalization ability of the proposed method in predicting heat sink performance, achieving significantly better technical results than existing technologies, and providing a reliable technical means for rapid performance evaluation and structural optimization of heat sinks for electronic devices.

[0081] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments without departing from the technical essence of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting radiator performance based on a Lévy distributed randomized network, characterized in that, Includes the following steps: Step 1: Prepare the dataset: Obtain the structural parameters and corresponding performance index data of the heat sink to form the original dataset; Step 2, Data Preprocessing: Standardize the original dataset and divide it into training and test sets; Step 3: Constructing the Lévy-SCN prediction model: A radiator performance prediction model is constructed based on a Lévy-distributed stochastic network, specifically including the following sub-steps: (1) Initialize model hyperparameters: Set the maximum number of hidden layer nodes, the maximum number of random configurations, the tolerance error, the candidate set of regularization parameters, the candidate set of constraint relaxation parameters, and the stability index of the Lévy distribution, and initialize the network residuals and the current number of hidden layer nodes; (2) Start incrementally building the loop. When the loop condition is met, execute the following sub-steps: (2a) Generate candidate node pool: Use the Mantegna algorithm to generate random numbers that follow the Lévy distribution, construct candidate input weights and candidate biases, and calculate candidate hidden layer outputs; (2b) Evaluate and select the best candidate node: calculate the supervision value of each candidate node for the supervision inequality constraint, and select the candidate node with the largest supervision value and that satisfies the constraint as the best candidate node; (2c) Adding nodes: If there are valid nodes, the best candidate node is added to the network; if there are no valid nodes, randomly generated weights and biases are used as candidate nodes to be added to the network. (2d) Update network parameters: Update the number of hidden layer nodes, calculate the current hidden layer output matrix, calculate the output weights using the least squares method, calculate the current network prediction value and update the residuals; (3) Judgment of loop termination condition: When the maximum number of hidden layer nodes is reached or the current error is less than the tolerance error, the training is terminated and the trained Lévy-SCN heat sink performance prediction model is output. Step 4: Use the model for prediction: Input the heat sink structural parameters to be predicted into the trained Lévy-SCN model, and output the predicted results of the heat sink performance indicators.

2. The radiator performance prediction method based on Lévy distributed randomized network as described in claim 1, characterized in that, The structural parameters mentioned in step one include substrate thickness, fin thickness, number of fins, external dimensions, and airflow. The performance indicators include thermal resistance, maximum temperature, convective heat transfer coefficient, and pressure drop.

3. The radiator performance prediction method based on Lévy distributed randomized network as described in claim 1, characterized in that, The standardization process described in step two uses the z-score standardization method.

4. The radiator performance prediction method based on Lévy distributed randomized network as described in claim 1, characterized in that, The stability index β of the Lévy distribution described in step three is 1.

5.

5. The radiator performance prediction method based on Lévy distributed randomized network as described in claim 1, characterized in that, In the supervised inequality constraints described in step three, at least 60% of the output dimensions are required to satisfy the constraints.

6. The radiator performance prediction method based on Lévy distributed randomized network as described in claim 1, characterized in that, The method described is used to predict the performance of Y-shaped heat sinks.

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