Variable cross-section thermoelectric power generation system optimization model based on deep neural network
The optimization model of the temperature difference power generation system constructed by deep neural network solves the problem of poor repetitive modeling and generalization capabilities in traditional methods, and realizes efficient prediction and optimization of the performance parameters of the variable cross-section temperature difference power generation system under different boundary conditions, improving the calculation speed and accuracy.
Patent Information
- Application Number
- CN202510618434.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-14
- Publication Date
- 2025-08-19
AI Technical Summary
The optimization methods of existing temperature-differential power generation systems have problems with poor repeat modeling, overfitting and generalization capabilities, and it is difficult to effectively optimize and predict their performance under different boundary conditions.
The variable cross-section temperature difference power generation system optimization model is adopted based on deep neural networks. By building a matrix of input layer and output layer, the appropriate number of neural network layers and activation functions are selected, and data standardization and k-fold cross-validation are carried out to establish a database containing 2398 samples, and L1/L2 regularization is used to ensure the generalization ability and prediction accuracy of the model.
Accurate and fast prediction of the performance parameters of variable cross-section temperature difference power generation system under different boundary conditions is achieved, the calculation speed is 10 times higher, the prediction accuracy reaches 0.96, which is significantly better than the traditional ANN model, the loss is reduced to 0.00058, and there is no significant difference in prediction accuracy.
Smart Images
Figure CN120509307A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of thermoelectric power generation, and in particular relates to an optimization model of a variable-section thermoelectric power generation system based on a deep neural network. Background Art
[0002] The conversion efficiency of the thermoelectric power generation system is affected by its geometric structure and boundary conditions. In the optimization process of the thermoelectric power generation system, if traditional finite element methods such as the ANN model are used, there are the following defects: repeated modeling is required, overfitting is prone to occur due to insufficient training data, and the constructed model has poor generalization ability on new data. In addition, the ANN model has weak interpretability and it is difficult to clearly reveal the causal relationship between input and output, and it cannot meet the optimization target requirements under different boundary conditions. Summary of the Invention
[0003] In order to address the shortcomings of the existing technology, the present invention proposes a variable-section thermoelectric power generation system optimization model based on deep neural network (Genetic Algorithms-Deep Neural Network, GA-DNN). The constructed model can accurately and quickly predict the efficiency, output power and thermal stress under different boundary conditions by inputting data such as the particle shape, geometric dimensions and boundary conditions of the thermoelectric power generation system.
[0004] The specific technical solution adopted is: an optimization model of a variable-section temperature difference power generation system based on a deep neural network, which is constructed through the following steps:
[0005] Step 1. Construct the input and output layers: The input layer is a 2400×11 matrix, and the output layer is a 2400×6 matrix. The 11 variables in the input layer include particle shape, boundary conditions, particle length in the x-direction, particle length in the y-direction, particle length in the z-direction, bottom copper sheet thickness, cold surface temperature, hot surface temperature, convection heat transfer coefficient, heat flux, and resistivity. The output layer contains the six performance parameters of the variable-section thermoelectric power generation system, including heat generation, conversion efficiency, output power, current, voltage, and cold surface equivalent thermal stress.
[0006] Step 2. Selection of neural network hyperparameters: The number of neural network layers includes the input layer, the first hidden layer, the second hidden layer, the third hidden layer and the output layer. The activation function of the input layer is Relu and the number of neurons is 11. The activation function of the first hidden layer is Sigmoid and the number of neurons is 30. The activation function of the second hidden layer is Sigmoid and the number of neurons is 64. The activation function of the third hidden layer is Tanh and the number of neurons is 24. The activation function of the output layer is Tanh and the number of neurons is 6. The learning rate of the neural network is set to 0.01, and the regularization term is L1=1×e -7, L2=1×e -7 ;
[0007] Step 3. Determine the number of iterations: The data of the variable cross-section temperature difference power generation system were standardized, and a database containing 2398 samples and 17 characteristic parameters was constructed; the data set was divided into training set and test set in a ratio of 7:3, and the model evaluation adopted the k-fold cross-validation method, with the k value set to 10; the original data in the training set was randomly divided into 10 mutually exclusive subsets, and 9 subsets were used for model training in each iteration, and the remaining subset was used for validation. The process was repeated 10 times to ensure that each subset was used as a validation set once; by performing 10-fold cross-validation and calculating the R of each validation 2 Score, all R 2 The average value of the scores will be used as the final evaluation indicator, and the judgment standard is that the value is greater than 0.95, and the number of iterations is determined to be 1000.
[0008] Moreover, the boundary conditions in the variables of step 1 include at least three types: constant temperature, constant heat flux density and constant convective heat transfer coefficient.
[0009] Moreover, the particle shapes in the variables of step 1 include at least four types: conical, cylindrical, rectangular and trapezoidal.
[0010] Moreover, the standardization process in step 3 is to process the data using the deviation standardization method, perform Min-Max standardization on all input parameters, and convert data of different scales or dimensions into a unified scale.
[0011] Moreover, the model takes as input at least the particle shape, boundary conditions, particle length in the x-direction, particle length in the y-direction, particle length in the z-direction and thickness of the bottom copper sheet of the variable-section temperature difference power generation system, and outputs at least the predicted conversion efficiency, output power and equivalent thermal stress under the corresponding boundary conditions.
[0012] Compared with the existing technology, the beneficial effects of this technical solution are:
[0013] 1. The optimization model constructed using deep neural network technology in this invention can optimize and predict the performance parameters of at least four variable-section thermoelectric power generation systems: conical, cylindrical, rectangular, and trapezoidal, under the three boundary conditions of constant temperature, constant heat flux, and constant convective heat transfer coefficient. By inputting the thermoelectric power generation system's geometric dimensions, leg shape, and various boundary conditions, it can accurately and rapidly predict its efficiency, power, and thermal stress under these various boundary conditions. A unified neural network prediction model is established for these three boundary conditions and four variable-section shapes, avoiding the repeated modeling required by traditional finite element methods.
[0014] 2. We constructed a database containing 2,398 samples and 17 characteristic parameters and standardized the data using deviation normalization to eliminate the effects of dimension and value range. The dataset was divided into training and test sets in a 7:3 ratio. Model evaluation employed k-fold cross-validation with a k value of 10 to ensure model robustness. L1 / L2 regularization was used to ensure model generalization and prediction accuracy.
[0015] 3. The final model input layer is a 2400×11 matrix, and the output layer is a 2400×6 matrix. The calculation speed is increased by more than 10 times, and the accuracy prediction R 2 It reached 0.96, the lowest loss dropped to 0.00058, and the prediction accuracy reached above 0.96, which was significantly better than the traditional ANN model error <4%. At this time, there was no significant difference in the accuracy of the model prediction after 1000 iterations. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] Figure 1 Schematic diagrams of single-pair PN junctions with four different leg shapes: (a) conical; (b) cylindrical; (c) rectangular; and (d) trapezoidal.
[0017] Figure 2 Schematic diagram of heat transfer boundary conditions for four different leg shape cross sections, (a) is conical; (b) is cylindrical; (c) is rectangular; (d) is trapezoidal;
[0018] Figure 3 The thermal stress distribution of different particle types. (a) shows the comparison of different leg shapes under different boundary conditions; (b) shows the comparison of legs and legs + copper sheets under heat flux boundary conditions.
[0019] Figure 4 Graph showing the neural network training results for the variable-section temperature difference power generation system optimization model constructed for the embodiment: (a) is the loss; (b) is the accuracy. DETAILED DESCRIPTION
[0020] The present invention will be described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.
[0021] In order to demonstrate the advantages of the variable cross-section design of the leg shape and the different performance parameters of different variable cross-sections, the following experiments were conducted:
[0022] In the experiment, models of four variable-section temperature difference power generation systems under three boundary conditions were established and simulation calculations were carried out. Figure 1 It is a schematic diagram of a single pair of variable cross-section PN junctions. Figure 1 and Figure 2It can be seen that the variable cross-section design can effectively adjust the heat flow distribution and current density distribution inside the thermoelectric power generation legs, thereby reducing thermal stress while improving the thermoelectric conversion efficiency. Therefore, by optimizing the geometric shape of the legs, the thermal stress concentration problem caused by the temperature gradient can be alleviated to a certain extent, while improving the overall performance of the thermoelectric power generation system. It can also extend the service life of the thermoelectric power generation system and improve its reliability while ensuring the output power.
[0023] Depend on Figure 3 (a) It can be seen that different boundary conditions will have an impact on the thermal stress of the variable cross-section. Under the boundary conditions of equal heat flux density, the thermal stress of the variable cross-section thermoelectric power generation system will show obvious differences, while the thermal stress under the constant temperature boundary conditions will not differ too much. When the same heat flux density is applied or the same convection heat transfer coefficient is set, the maximum temperature of the hot end of the different thermoelectric power generation leg cross-sections is different, which leads to an increase in thermal stress. This is due to the different thermal conductivity of different variable cross-sections, resulting in a higher temperature gradient. Figure 3 (b) It can be seen that when the thermoelectric power generation leg and the thermoelectric power generation leg + copper sheet are selected as the analysis objects of the static structure respectively, the thermal stress of the thermoelectric power generation leg alone is lower, and the overall thermal stress of the thermoelectric power generation leg + copper sheet will increase, which indicates that the thermal stress is concentrated at the connection between the thermoelectric power generation leg and the copper sheet.
[0024] Based on the above experiments, the variable cross-section thermoelectric power generation system must have the need for performance parameter prediction and optimization under different boundary conditions. The present invention constructs an optimization model for the variable cross-section thermoelectric power generation system based on a deep neural network:
[0025] Step 1. Construct the input and output layers: The input layer is a 2400×11 matrix, and the output layer is a 2400×6 matrix. The 11 variables in the input layer include particle shape, boundary conditions, particle length in the x-direction, particle length in the y-direction, particle length in the z-direction, bottom copper sheet thickness, cold surface temperature, hot surface temperature, convection heat transfer coefficient, heat flux, and resistivity. Particle shape, particle length in the x-direction, particle length in the y-direction, and particle length in the z-direction together constitute the data of the leg shape. The output layer contains the six performance parameters of the variable-section thermoelectric power generation system, including heat generation, conversion efficiency, output power, current, voltage, and cold surface equivalent thermal stress.
[0026] Step 2. Selection of neural network hyperparameters: The number of neural network layers includes the input layer, the first hidden layer, the second hidden layer, the third hidden layer and the output layer. The activation function of the input layer is Relu and the number of neurons is 11. The activation function of the first hidden layer is Sigmoid and the number of neurons is 30. The activation function of the second hidden layer is Sigmoid and the number of neurons is 64. The activation function of the third hidden layer is Tanh and the number of neurons is 24. The activation function of the output layer is Tanh and the number of neurons is 6. The learning rate of the neural network is set to 0.01, and the regularization term is L1=1×e -7 , L2=1×e -7 ;
[0027] The optimal neural network hyperparameters are shown in the following table:
[0028]
[0029] Step 3. Determine the number of iterations: Standardize the data of the variable-section temperature difference power generation system, perform Min-Max standardization on all input parameters, convert data of different scales or dimensions into a unified scale, and construct a database containing 2398 samples and 17 characteristic parameters; divide the data set into training set and test set in a ratio of 7:3, and use the k-fold cross-validation method for model evaluation, with the k value set to 10; randomly divide the original data in the training set into 10 mutually exclusive subsets, use 9 subsets for model training in each iteration, and the remaining 1 subset is used for verification. The process is repeated 10 times to ensure that each subset is used as a verification set once; by repeating this process 10 times and calculating the evaluation index of each verification, the performance of the model on different verification sets can be obtained. By performing 10-fold cross-validation and calculating the R of each verification 2 Score, all R 2 The average of the scores will be used as the final evaluation indicator, so as to provide a more comprehensive and reliable evaluation of the model's performance. When the model was trained for 1000 times, the loss dropped to a minimum of 0.00058, and the prediction accuracy reached above 0.96. At this time, there was no significant difference in the accuracy of the model's prediction after 1000 iterations, so 1000 was selected as the number of iterations for the model to perform prediction analysis. The prediction loss graph is shown below: Figure 4 As shown in (a), the prediction accuracy is shown in Figure 4 (b) shown.
[0030] In addition, the constructed model also uses the following formula to calculate the final output results.
[0031] 1. Thermoelectric conversion efficiency. When there is a temperature difference between the two ends of the PN junction of the thermoelectric power generation module, the heat absorbed by the PN junction from the hot end is composed of three parts: heat generated by the Peltier effect, Joule heat, and conduction heat, namely:
[0032]
[0033] Where Q H and Q C are the heat flows at the hot and cold ends of the thermoelectric power generation device, respectively, in W. Where K is the total thermal conductivity of the thermoelectric power generation module, in W / mK. Where T H and T C They represent the high-temperature end temperature and the low-temperature end temperature of the thermoelectric material respectively, and the unit is K.
[0034] The Seebeck electromotive force in the circuit is:
[0035] V PN =α(T H -T C ) Formula 3
[0036] If the internal resistance of the thermoelectric power generation device is r, the output power of the device is:
[0037]
[0038] Thermoelectric power generation device hot end absorbs heat Q H After that, part of the heat is absorbed by the device and converted into electrical energy P, and the rest of the heat flows out of the device to the cold end. From this, the conversion efficiency η of the device can be obtained as:
[0039]
[0040] Let m = R L / r (called matching coefficient), the above formula can be simplified to:
[0041]
[0042] For a specific thermoelectric power generation device, its power generation efficiency will change with the change of the matching coefficient m. Let dη / dm=0, the maximum power generation efficiency η of the device can be solved max for:
[0043]
[0044] in, is the average temperature of the hot and cold ends of the device.
[0045] 2. Maximum output power: According to the circuit principle and Seebeck's law, the output power of the thermoelectric power generation device is:
[0046]
[0047] It can be seen from this that when the load resistance R LWhen the internal resistance r of the thermoelectric power generation device is matched, that is, m = 1, the maximum output power can be obtained, and its value is:
[0048]
[0049] When the hot end of the thermoelectric power generation device absorbs heat Q H After that, part of the heat is absorbed by the device and converted into electrical energy P, and the rest of the heat flows out of the device to the cold end. From this, the conversion efficiency η of the device can be obtained as:
[0050]
[0051] 3. During the thermoelectric power generation process, due to the temperature gradient between the high-temperature end and the low-temperature end, thermal stress will be generated inside the leg. The thermal stress equation can be described by the dimensionless displacement-deformation relationship equation:
[0052]
[0053] The relationship between these strain components and thermal stress can be further described by generalized Hooke's Law, where thermal stress is not only related to the elastic modulus and Poisson's ratio of the material, but also closely related to the thermal expansion coefficient caused by temperature gradient.
[0054] 4. The three-dimensional model established to simulate the thermoelectric effect needs to consider the interaction between heat and electricity. The coupled equation of temperature T and electric potential is expressed as:
[0055]
[0056] Where σ is the conductivity; J is the current density; α is the Seebeck coefficient; and A is the area of the contact surface (m2).
[0057] The charge and heat flux conservation equations are:
[0058]
[0059] Where V is the potential scalar.
[0060] In addition, the calculation formula of the internal heat source q can be expressed as:
[0061]
[0062] Where k is the thermal conductivity, unit (W / m·K)
[0063] The calculation formula for the output power of the thermoelectric power generation system is:
[0064]
[0065] Where Rin Represents the internal resistance of the thermoelectric power generation system; R L represents the load resistance; α P , α N Represents the Seebeck coefficient of P and N particles.
[0066] From this formula, we can get that when R L =R in The maximum output power exists when . Therefore, it is necessary to keep the value of the load resistance the same as the value of the internal resistance. The thermoelectric conversion efficiency of the thermoelectric power generation system can be calculated from the input current and output power:
[0067]
[0068] Where Q in is the heat flux on the surface of the thermoelectric power generation system.
[0069] From Formula 9 and Formula 10, the thermal stress and thermal strain can be expressed as follows under the asymmetric Jacobi matrix:
[0070]
[0071] High temperature leads to high thermal stress, and thermal stress is expressed as compressive stress. In the thermoelectric power generation system, the three principal stresses are expressed as σ1, σ2, and σ3. At this time, the Von Mises stress σ VON It can be expressed in terms of three principal stresses:
[0072]
[0073] In summary, the beneficial effects of this technical solution are:
[0074] 1. The optimization model constructed using deep neural network technology in this invention can optimize and predict the performance parameters of at least four variable-section thermoelectric power generation systems: conical, cylindrical, rectangular, and trapezoidal, under the three boundary conditions of constant temperature, constant heat flux, and constant convective heat transfer coefficient. By inputting the thermoelectric power generation system's geometric dimensions, leg shape, and various boundary conditions, it can accurately and rapidly predict its efficiency, power, and thermal stress under these various boundary conditions. A unified neural network prediction model is established for these three boundary conditions and four variable-section shapes, avoiding the repeated modeling required by traditional finite element methods.
[0075] 2. We constructed a database containing 2,398 samples and 17 characteristic parameters and standardized the data using deviation normalization to eliminate the effects of dimension and value range. The dataset was divided into training and test sets in a 7:3 ratio. Model evaluation employed k-fold cross-validation with a k value of 10 to ensure model robustness. L1 / L2 regularization was used to ensure model generalization and prediction accuracy.
[0076] 3. The final model input layer is a 2400×11 matrix, and the output layer is a 2400×6 matrix. The calculation speed is increased by more than 10 times, and the accuracy prediction R 2 It reached 0.96, the lowest loss dropped to 0.00058, and the prediction accuracy reached above 0.96, which was significantly better than the traditional ANN model error <4%. At this time, there was no significant difference in the accuracy of the model prediction after 1000 iterations.
Claims
1. A variable cross-section temperature difference power generation system optimization model based on deep neural network, characterized in that: The model is constructed through the following steps: Step 1. Construct the input and output layers: The input layer is a 2400×11 matrix, and the output layer is a 2400×6 matrix. The 11 variables in the input layer include particle shape, boundary conditions, particle length in the x-direction, particle length in the y-direction, particle length in the z-direction, bottom copper sheet thickness, cold surface temperature, hot surface temperature, convection heat transfer coefficient, heat flux, and resistivity. The output layer contains the six performance parameters of the variable-section thermoelectric power generation system, including heat generation, conversion efficiency, output power, current, voltage, and cold surface equivalent thermal stress. Step 2. Selection of neural network hyperparameters: The number of neural network layers includes the input layer, the first hidden layer, the second hidden layer, the third hidden layer and the output layer. The activation function of the input layer is Relu and the number of neurons is 11. The activation function of the first hidden layer is Sigmoid and the number of neurons is 30. The activation function of the second hidden layer is Sigmoid and the number of neurons is 64. The activation function of the third hidden layer is Tanh and the number of neurons is 24. The activation function of the output layer is Tanh and the number of neurons is 6. The learning rate of the neural network is set to 0.01, and the regularization term is L1=1×e -7 , L2=1×e -7 ; Step 3. Determine the number of iterations: The data of the variable cross-section temperature difference power generation system were standardized, and a database containing 2398 samples and 17 characteristic parameters was constructed; the data set was divided into training set and test set in a ratio of 7:3, and the model evaluation adopted the k-fold cross-validation method, with the k value set to 10; the original data in the training set was randomly divided into 10 mutually exclusive subsets, and 9 subsets were used for model training in each iteration, and the remaining subset was used for validation. The process was repeated 10 times to ensure that each subset was used as a validation set once; by performing 10-fold cross-validation and calculating the R of each validation 2 Score, all R 2 The average value of the scores will be used as the final evaluation indicator, and the judgment standard is that the value is greater than 0.95, and the number of iterations is determined to be 1000.
2. The variable cross-section temperature difference power generation system optimization model based on a deep neural network according to claim 1 is characterized by: The boundary conditions in the variables of step 1 include at least three types: constant temperature, constant heat flux density and constant convective heat transfer coefficient.
3. The variable cross-section temperature difference power generation system optimization model based on a deep neural network according to claim 1 is characterized by: The particle shapes in the variables of step 1 include at least four types: conical, cylindrical, rectangular and trapezoidal.
4. The variable cross-section temperature difference power generation system optimization model based on a deep neural network according to claim 1 is characterized by: In step 3, the standardization process is to process the data using the deviation standardization method, perform Min-Max standardization on all input parameters, and convert data of different scales or dimensions into a unified scale.
5. The variable cross-section temperature difference power generation system optimization model based on a deep neural network according to claim 1 is characterized by: The model takes as input at least the particle shape, boundary conditions, particle length in the x-direction, particle length in the y-direction, particle length in the z-direction and thickness of the bottom copper sheet of the variable-section temperature difference power generation system, and outputs at least the predicted conversion efficiency, output power and equivalent thermal stress under the corresponding boundary conditions.