A radiator structure optimization design method based on non-dominated sorting genetic algorithm

Abstract

This invention discloses a heat sink structure optimization design method based on a non-dominated sorting genetic algorithm, belonging to the field of heat sink optimization design technology. The method first determines the structural parameters to be optimized (heat sink length, width, height, fin thickness, fin spacing, substrate thickness) and the optimization objective function (maximum junction temperature of power devices, heat sink mass, heat sink entropy productivity). Then, Latin hypercube sampling is used to sample parameters and establish a geometric model. Sample data is constructed through thermal simulation, and a surrogate model is established using response surface methodology. Finally, multi-objective optimization is performed based on the non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set, and the best solution is selected through comprehensive performance evaluation indicators. This invention effectively reduces heat sink mass and cost while ensuring heat dissipation performance, shortens the R&D cycle, and is applicable to the heat dissipation optimization design of power devices in power electronic systems.

Description

Technical Field

[0001] This invention relates to the field of radiator optimization design technology, specifically to a multi-objective optimization method for radiators based on a non-dominated sorting genetic algorithm. Background Technology

[0002] Power devices (such as IGBTs, MOSFETs, and CPUs) generate a large amount of heat during operation. If heat dissipation is not timely, the junction temperature of the devices will become too high, affecting their performance and lifespan. As the core component of the thermal management system of power devices, the heat sink dissipates the heat generated by the devices into the surrounding environment by increasing the heat dissipation area and enhancing convection heat transfer.

[0003] Traditional methods for optimizing radiator structures mainly include experimental and empirical methods. Experimental methods involve building physical prototypes for testing, which has drawbacks such as long development cycles and high costs. Furthermore, they often focus only on heat dissipation performance while neglecting other factors like mass and size, frequently resulting in overly bulky and costly radiators. Empirical methods rely on simplifying assumptions and empirical formulas for estimation, but their computational accuracy is limited, making it difficult to accurately predict the performance of complex radiator structures.

[0004] In recent years, the development of numerical simulation technology and intelligent optimization algorithms has provided new approaches for heat sink optimization design. However, in existing technologies, directly combining simulation models with optimization algorithms suffers from high computational costs and low optimization efficiency; while single-objective optimization struggles to balance the conflicting demands of heat dissipation performance, quality, and cost.

[0005] Therefore, there is an urgent need for a method that can quickly and accurately perform multi-objective optimization design of radiators, so as to achieve lightweight and low-cost design of radiators while ensuring heat dissipation performance. Summary of the Invention

[0006] To address the problems of high computational cost and low optimization efficiency associated with directly combining simulation models with optimization algorithms in existing technologies, and the difficulty of balancing conflicting requirements such as heat dissipation performance, quality, and cost in single-objective optimization, this invention provides a heat sink structure optimization design method based on a non-dominated sorting genetic algorithm. By constructing a surrogate model to reduce computational cost, a multi-objective optimization algorithm is used to balance the contradiction between heat dissipation performance and quality, obtaining the Pareto optimal solution set, and selecting the best design scheme through comprehensive evaluation indicators, this invention solves the technical problems of long heat sink optimization design cycle, high cost, and difficulty in balancing multiple performance indicators in existing technologies.

[0007] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: A heat sink structure optimization design method based on a non-dominated sorting genetic algorithm includes the following steps: S1: Steps for determining parameters and objectives; A structural analysis of the radiator is performed to determine the structural parameters to be optimized and the objective function for optimization.

[0008] The structural parameters to be optimized include: heat sink length. x 1 Radiator width x 2 Radiator height x 3 fin thickness x 4 Fin spacing x 5 and substrate thickness x 6 .

[0009] The optimization objective function includes: the objective function for the highest junction temperature of the power device. f 1 (x) Radiator quality objective function f 2 (x) and the objective function of heat sink entropy productivity f 3 (x) .

[0010] The highest junction temperature of the power device refers to the highest temperature of the PN junction inside the power device, which is a key indicator for measuring heat dissipation performance; the quality of the heat sink directly affects material costs and installation requirements; the entropy yield of the heat sink reflects the irreversible loss in the heat transfer process and is an indicator for evaluating heat transfer efficiency.

[0011] S2: Sampling and modeling steps; The structural parameters of the radiator are sampled using Latin hypercube sampling, and a geometric model is established based on the sampling results. Different combinations of radiator parameters sampled by Latin hypercube sampling are used to establish the geometric model required for thermal simulation using three-dimensional modeling software. Latin hypercube sampling is a stratified random sampling technique that can fully cover the design space with a smaller sample size, thereby improving the representativeness of the sample.

[0012] S3: Simulation and Sample Construction Steps; Perform thermal simulation analysis on the geometric models established by all sampling results in step S2, obtain the optimization target response value corresponding to each sample, and construct a sample dataset.

[0013] The thermal simulation analysis employs computational fluid dynamics (CFD) to set the power consumption, ambient temperature, material properties, and boundary conditions of the power device, solve for the temperature field and flow field distribution, and extract the highest junction temperature of the power device and the mass data of the heat sink.

[0014] S4: Steps for building the proxy model; Using the sample dataset obtained in step S3, a surrogate model between the optimization objective function and the structural parameters to be optimized is established using the response surface methodology.

[0015] The proxy model for the highest junction temperature of the power device is a second-order polynomial regression equation: (1) In the formula: T chip This indicates the highest junction temperature of the power device, expressed in °C. x i Indicates the first i The design variable, i.e. the first design variable. i One structural parameter to be optimized; N Indicates the number of variables. N =6; g 0 Represents a constant term. b i Denotes the coefficient of the linear term. c ii Denotes the coefficient of the quadratic term. c ij Represents the coefficient of the mixed term. e This indicates the error term.

[0016] The coefficient g 0 , b i , c ii , c ij The fit was obtained using the least squares method, and the fitting accuracy was measured by the coefficient of determination R0. 2 The root mean square error (RMSE) is used for evaluation, and R is required to be... 2 > 0.95 and RMSE < 5%.

[0017] S5: Optimize the model building steps; Based on the surrogate model established in step S4, constraints are set for the structural parameters to be optimized as determined in step S1, and a multi-objective optimization model for the radiator is established.

[0018] The objective function for the quality of the heat sink is: (2) In the formula: MIndicates the mass of the radiator, in units of g ; n Indicates the number of cooling channels in the radiator; r This indicates the density of the radiator material, in units of... g / mm 3 ; n fin Indicates the number of fins. n fin = x 2 / (x 4 +x 5 ) ; x 1 Indicates the length of the heatsink, in units of mm ; x 2 Indicates the width of the heatsink, in units of mm ; x 3 Indicates the height of the radiator, in units of mm ; x 4 Indicates fin thickness, in units of mm ; x 5 Indicates the fin spacing, in units of mm ; x 6 Indicates substrate thickness, in units of mm .

[0019] The constraints on the structural parameters to be optimized are determined based on the installation space, processing technology, and strength requirements of the power devices: (3) The units of all parameters in the formula are... mm .

[0020] S6: Multi-objective optimization solution steps; The multi-objective optimization model of the radiator established in step S5 is solved using a non-dominated sorting genetic algorithm to obtain the optimal combination of structural parameters.

[0021] The specific implementation steps of step S6 are as follows: S61: Steps for setting the objective function; Based on the surrogate model established in step S4, set the objective function vector for the multi-objective optimization problem: (4) In the formula: F(x) Represent the objective function vector; f 1 (x)The objective function representing the maximum junction temperature of the power device is determined by formula (1), with units of . ℃ ; f 2 (x) The objective function representing the radiator quality is determined by formula (2), and the unit is . g ; f 3 (x) The objective function representing the entropy productivity of the radiator is expressed in W / K. x Represents a vector of design variables. x =[ x 1 , x 2 , x 3 , x 4 , x 5 , x 6 ] T ; S62: Constraint setting steps; The constraints of the heat sink structure parameters are set according to the installation space size requirements of the power devices and formula (3); S63: Algorithm parameter setting and initialization steps; Set the population size for the non-dominated sorting genetic algorithm. M =50, Maximum number of iterations G max =800, crossover probability c p =0.9, Probability of Mutation m p =0.2, within the constraint range, randomly generate the initial population as the parent population. t p ; S64: Genetic manipulation steps; Based on the probability of mutation m p Perform mutation operations on the parent population, and then determine the crossover probability. c p Simulated binary crossover and recombination are performed to generate offspring populations. t q ; S65: Environmental selection steps; offspring population t q and parental population t p Merging to form a hybrid species t R = tp ∪ t q The objective function value of all individuals in the mixed population is calculated according to formula (4), and non-dominated ranking and crowding degree are calculated. The optimal population is selected based on the ranking results and crowding degree. Q Each individual as a new paternal population t p+1 ; The non-dominated ordination divides the population into different levels of non-dominated frontiers based on Pareto dominance, with individuals at lower levels being more superior.

[0022] The formula for calculating the congestion level is: (5) In the formula: Indicates the first i The individual in the first m Crowding degree under a single objective function; Indicates the first i The individual in the first m Function values ​​under each objective function; and They represent the first and second digits in the current population, respectively. m The maximum and minimum values ​​of the objective function; The crowding level is used to assess the distribution density of individuals within the same non-dominant class. A higher crowding level indicates that the individual is more sparsely populated, which is beneficial for maintaining population diversity.

[0023] S66: Iterative judgment steps; If the current iteration number t Less than the maximum number of iterations G max Then let t = t + 1 If not, return to step S64; otherwise, proceed to step S67. S67: Steps for selecting the optimal solution; The Pareto optimal solution set of the radiator structural parameters is obtained. The Pareto optimal solution set is comprehensively evaluated, and the best optimization scheme of the radiator is selected.

[0024] The method for comprehensively evaluating the Pareto optimal solution set includes: First, the feasibility index of all solutions in the Pareto optimal solution set is calculated, and solutions with a feasibility index greater than a preset threshold (e.g., 7) are selected to form a feasible solution set. The feasibility index is set based on engineering experience, taking into account factors such as heat dissipation performance, structural strength, and processing technology.

[0025] Then, calculate the Nusselt number of all solutions in the feasible solution set. No Average heat transfer coefficient of radiator havg The HCP value is a comprehensive evaluation index for thermal performance.

[0026] The Nusel No The calculation formula is: (6) In the formula: No Nusselt numbers are dimensionless. C and n This represents the empirical coefficient, which is generally taken as... C =0.59、 n =0.25; Gr This represents the Grashof number, which is dimensionless. Pr The Prandtl number is dimensionless and is typically taken as 0.7 for air. g Represents gravitational acceleration. g =9.8 m / s 2 The unit is m / s 2 ; β The coefficient of volumetric expansion of air is expressed in units of 1000 ppm. K -1 ; β = 1 / T m , T m For membrane temperature, the unit is... K ; L The characteristic length is represented by the fin height for rectangular fins. L = x 3 The unit is m ; T S This indicates the surface temperature of the radiator, in units of... ℃ ; T ∞ Indicates ambient temperature, in units of ℃ ; n The kinematic viscosity of air is expressed in units of 1000 kJ / m². m 2 / s .

[0027] The average heat transfer coefficient of the radiator h avg The calculation formula is: (7) (8) (9) (9a) In the formula: h avg This represents the average heat transfer coefficient of the radiator, expressed in units of... W / (m 2 ·K) ; l air The thermal conductivity of air is expressed in units of 1000 m / s. W / (m·K) ; L c Indicates the feature length, in units of m ; Re L Represents the Reynolds number based on the characteristic length, which is dimensionless; V 0 This indicates the operating point airflow velocity of the radiator, in units of... m / s ; x 3 Indicates the height of the radiator, in units of mm ; x 4 Indicates fin thickness, in units of mm ; x 5 Indicates the fin spacing, in units of mm .

[0028] Finally, the thermal performance comprehensive evaluation index HCP value is calculated, and the solution with the smallest HCP value is selected as the optimal optimization scheme.

[0029] The formula for calculating the comprehensive thermal performance evaluation index HCP is as follows: (10) In the formula: HCP This represents a comprehensive evaluation index of thermal performance, in units of... ℃·g / W ; T chip This indicates the highest junction temperature of the power device, in units of 1. ℃ ; M Indicates the mass of the radiator, in units of g ; h avg This represents the average heat transfer coefficient of the radiator, expressed in units of... W / (m 2 ·K) ; A This represents the total surface area of ​​the radiator, in units of... m 2 ; A lower HCP value indicates that the radiator has a higher heat transfer coefficient at a lower junction temperature and with a smaller mass, which means it has better overall thermal performance.

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The present invention uses Latin hypercube sampling and response surface methodology to construct a surrogate model, which greatly reduces the number of computational fluid dynamics simulations, shortens the optimization cycle from several weeks to several days, significantly improves optimization efficiency, and reduces computational costs.

[0031] (2) The present invention uses a non-dominated sorting genetic algorithm for multi-objective optimization, which can simultaneously consider multiple conflicting objectives such as heat dissipation performance, quality, and entropy production rate, and obtain a uniformly distributed Pareto optimal solution set, providing designers with multiple alternative schemes and avoiding the limitations of single-objective optimization.

[0032] (3) This invention proposes a solution evaluation method based on the Nusselt number, average heat transfer coefficient and thermal performance comprehensive evaluation index HCP, which can select the design scheme with the best comprehensive performance from the Pareto optimal solution set and solve the problem of difficulty in selecting multi-objective optimization results.

[0033] (4) Under the premise of ensuring the heat dissipation requirements of power devices, the present invention can effectively reduce the mass and volume of the heat sink, reduce costs, improve the reliability and service life of the device, and meet the multiple performance requirements of power electronic systems for forced air cooling heat sinks with low thermal resistance, small size and light weight, and has good engineering application value. Attached Figure Description

[0034] Figure 1 This is a flowchart of the heat sink structure optimization design method of the present invention.

[0035] Figure 2 This is a schematic diagram of the heat sink structure of the present invention.

[0036] Figure 3 This is a cross-validation diagram of the junction temperature surrogate model for power devices.

[0037] Figure 4 The flowchart shows the implementation of the non-dominated sorting genetic algorithm.

[0038] Figure 5 This is a feasibility assessment diagram for the design scheme.

[0039] Figure 6A comparison chart of HCP values ​​for the optimal solution set. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0041] This invention provides a heat sink structure optimization design method based on a non-dominated sorting genetic algorithm, comprising the following steps: S1: Steps for determining parameters and objectives; A structural analysis of the radiator is performed to determine the structural parameters to be optimized and the objective function for optimization.

[0042] The structural parameters to be optimized include: heat sink length. x 1 Radiator width x 2 Radiator height x 3 fin thickness x 4 Fin spacing x 5 and substrate thickness x 6 .

[0043] The optimization objective function includes: the objective function for the highest junction temperature of the power device. f 1 (x) Radiator quality objective function f 2 (x) and the objective function of heat sink entropy productivity f 3 (x) .

[0044] The highest junction temperature of the power device refers to the highest temperature of the PN junction inside the power device, which is a key indicator for measuring heat dissipation performance; the quality of the heat sink directly affects material costs and installation requirements; the entropy yield of the heat sink reflects the irreversible loss in the heat transfer process and is an indicator for evaluating heat transfer efficiency.

[0045] S2: Sampling and modeling steps; The structural parameters of the radiator are sampled using Latin hypercube sampling, and a geometric model is established based on the sampling results. Different combinations of radiator parameters sampled by Latin hypercube sampling are used to establish the geometric model required for thermal simulation using three-dimensional modeling software. Latin hypercube sampling is a stratified random sampling technique that can fully cover the design space with a smaller sample size, thereby improving the representativeness of the sample.

[0046] S3: Simulation and Sample Construction Steps; Perform thermal simulation analysis on the geometric models established by all sampling results in step S2, obtain the optimization target response value corresponding to each sample, and construct a sample dataset.

[0047] The thermal simulation analysis employs computational fluid dynamics (CFD) to set the power consumption, ambient temperature, material properties, and boundary conditions of the power device, solve for the temperature field and flow field distribution, and extract the highest junction temperature of the power device and the mass data of the heat sink.

[0048] S4: Steps for building the proxy model; Using the sample dataset obtained in step S3, a surrogate model between the optimization objective function and the structural parameters to be optimized is established using the response surface methodology.

[0049] The proxy model for the highest junction temperature of the power device is a second-order polynomial regression equation: (1) In the formula: T chip This indicates the highest junction temperature of the power device, expressed in °C. x i Indicates the first i The design variable, i.e. the first design variable. i One structural parameter to be optimized; N Indicates the number of variables. N =6; g 0 Represents a constant term. b i Denotes the coefficient of the linear term. c ii Denotes the coefficient of the quadratic term. c ij Represents the coefficient of the mixed term. e This indicates the error term.

[0050] The coefficient g 0 , b i , c ii , c ij The fit was obtained using the least squares method, and the fitting accuracy was measured by the coefficient of determination R0. 2 The root mean square error (RMSE) is used for evaluation, and R is required to be... 2 > 0.95 and RMSE < 5%.

[0051] S5: Optimize the model building steps; Based on the surrogate model established in step S4, constraints are set for the structural parameters to be optimized as determined in step S1, and a multi-objective optimization model for the radiator is established.

[0052] The objective function for the quality of the heat sink is: (2) In the formula: M Indicates the mass of the radiator, in units of g ; n Indicates the number of cooling channels in the radiator; r This indicates the density of the radiator material, in units of... g / mm 3 ; n fin Indicates the number of fins. n fin = x 2 / (x 4 +x 5 ) ; x 1 Indicates the length of the heatsink, in units of mm ; x 2 Indicates the width of the heatsink, in units of mm ; x 3 Indicates the height of the radiator, in units of mm ; x 4 Indicates fin thickness, in units of mm ; x 5 Indicates the fin spacing, in units of mm ; x 6 Indicates substrate thickness, in units of mm .

[0053] The constraints on the structural parameters to be optimized are determined based on the installation space, processing technology, and strength requirements of the power devices: (3) The units of all parameters in the formula are... mm .

[0054] S6: Multi-objective optimization solution steps; The multi-objective optimization model of the radiator established in step S5 is solved using a non-dominated sorting genetic algorithm to obtain the optimal combination of structural parameters.

[0055] The specific implementation steps of step S6 are as follows: S61: Steps for setting the objective function; Based on the surrogate model established in step S4, set the objective function vector for the multi-objective optimization problem: (4) In the formula: F(x) Represent the objective function vector; f 1 (x) The objective function representing the maximum junction temperature of the power device is determined by formula (1), with units of . ℃ ; f 2 (x) The objective function representing the radiator quality is determined by formula (2), and the unit is . g ; f 3 (x) The objective function representing the entropy productivity of the radiator is expressed in W / K. x Represents a vector of design variables. x =[ x 1 , x 2 , x 3 , x 4 , x 5 , x 6 ] T ; S62: Constraint setting steps; The constraints of the heat sink structure parameters are set according to the installation space size requirements of the power devices and formula (3); S63: Algorithm parameter setting and initialization steps; Set the population size for the non-dominated sorting genetic algorithm. M =50, Maximum number of iterations G max =800, crossover probability c p =0.9, Probability of Mutation m p =0.2, within the constraint range, randomly generate the initial population as the parent population. t p ; S64: Genetic manipulation steps; Based on the probability of mutation m p Perform mutation operations on the parent population, and then determine the crossover probability. c pSimulated binary crossover and recombination are performed to generate offspring populations. t q ; S65: Environmental selection steps; offspring population t q and parental population t p Merging to form a hybrid species t R = t p ∪ t q The objective function value of all individuals in the mixed population is calculated according to formula (4), and non-dominated ranking and crowding degree are calculated. The optimal population is selected based on the ranking results and crowding degree. Q Each individual as a new paternal population t p+1 ; The non-dominated ordination divides the population into different levels of non-dominated frontiers based on Pareto dominance, with individuals at lower levels being more superior.

[0056] The formula for calculating the congestion level is: (5) In the formula: Indicates the first i The individual in the first m Crowding degree under a single objective function; Indicates the first i The individual in the first m Function values ​​under each objective function; and They represent the first and second digits in the current population, respectively. m The maximum and minimum values ​​of the objective function; The crowding level is used to assess the distribution density of individuals within the same non-dominant class. A higher crowding level indicates that the individual is more sparsely populated, which is beneficial for maintaining population diversity.

[0057] S66: Iterative judgment steps; If the current iteration number t Less than the maximum number of iterations G max Then let t = t + 1 If not, return to step S64; otherwise, proceed to step S67. S67: Steps for selecting the optimal solution; The Pareto optimal solution set of the radiator structural parameters is obtained. The Pareto optimal solution set is comprehensively evaluated, and the best optimization scheme of the radiator is selected.

[0058] The method for comprehensively evaluating the Pareto optimal solution set includes: First, the feasibility index of all solutions in the Pareto optimal solution set is calculated, and solutions with a feasibility index greater than a preset threshold (e.g., 7) are selected to form a feasible solution set. The feasibility index is set based on engineering experience, taking into account factors such as heat dissipation performance, structural strength, and processing technology.

[0059] Then, calculate the Nusselt number of all solutions in the feasible solution set. No Average heat transfer coefficient of radiator h avg The HCP value is a comprehensive evaluation index for thermal performance.

[0060] The Nusel No The calculation formula is: (6) In the formula: No Nusselt numbers are dimensionless. C and n This represents the empirical coefficient, which is generally taken as... C =0.59、 n =0.25; Gr This represents the Grashof number, which is dimensionless. Pr The Prandtl number is dimensionless and is typically taken as 0.7 for air. g Represents gravitational acceleration. g =9.8 m / s 2 The unit is m / s 2 ; β The coefficient of volumetric expansion of air is expressed in units of 1000 ppm. K -1 ; β = 1 / T m , T m For membrane temperature, the unit is... K ; L The characteristic length is represented by the fin height for rectangular fins. L = x 3 The unit is m ; T S This indicates the surface temperature of the radiator, in units of... ℃ ; T ∞Indicates ambient temperature, in units of ℃ ; n The kinematic viscosity of air is expressed in units of 1000 kJ / m². m 2 / s .

[0061] The average heat transfer coefficient of the radiator h avg The calculation formula is: (7) (8) (9) (9a) In the formula: h avg This represents the average heat transfer coefficient of the radiator, expressed in units of... W / (m 2 ·K) ; l air The thermal conductivity of air is expressed in units of 1000 m / s. W / (m·K) ; L c Indicates the feature length, in units of m ; Re L Represents the Reynolds number based on the characteristic length, which is dimensionless; V 0 This indicates the operating point airflow velocity of the radiator, in units of... m / s ; x 3 Indicates the height of the radiator, in units of mm ; x 4 Indicates fin thickness, in units of mm ; x 5 Indicates the fin spacing, in units of mm .

[0062] Finally, the thermal performance comprehensive evaluation index HCP value is calculated, and the solution with the smallest HCP value is selected as the optimal optimization scheme.

[0063] The formula for calculating the comprehensive thermal performance evaluation index HCP is as follows: (10) In the formula: HCPThis represents a comprehensive evaluation index of thermal performance, in units of... ℃·g / W ; T chip This indicates the highest junction temperature of the power device, in units of 1. ℃ ; M Indicates the mass of the radiator, in units of g ; h avg This represents the average heat transfer coefficient of the radiator, expressed in units of... W / (m 2 ·K) ; A This represents the total surface area of ​​the radiator, in units of... m 2 ; A lower HCP value indicates that the radiator has a higher heat transfer coefficient at a lower junction temperature and with a smaller mass, which means it has better overall thermal performance.

[0064] Example: Optimized design of Raspberry Pi CPU heatsink; This embodiment uses the CPU heatsink of a Raspberry Pi microcomputer as the optimization target to verify the effectiveness of the method of the present invention. The verification process is as follows: Figure 1 .

[0065] Step S1: Determine the structural parameters to be optimized and the optimization objective. The power device on the heatsink is a Broadcom BCM2835 CPU chip, with a maximum power consumption of 1.4W and a maximum allowable junction temperature of 85℃ during normal operation. The heatsink material is 6061 aluminum alloy with a density of... r = 2.7 × 10 -3 g / mm 3 .

[0066] The structure of the radiator is as follows Figure 2 As shown, the structural parameters to be optimized include: heat sink length x1, heat sink width x2, heat sink height x3, fin thickness x4, fin spacing x5, and substrate thickness x6.

[0067] Based on the installation space limitations and manufacturing process requirements of the Raspberry Pi, the constraint ranges of each parameter are shown in Table 1: Table 1. Range of values ​​for parameters to be optimized The optimization objective is to minimize the highest junction temperature of the power devices. T chip Minimize the mass of the heat sink M .

[0068] Step S2: Latin hypercube sampling and geometric modeling; Based on the value range in Table 1, 70 combinations of structural parameters were generated using Latin hypercube sampling. During sampling, it was ensured that the samples were evenly distributed across all dimensions to avoid clustering.

[0069] Using Creo Parametric 3D modeling software, a geometric model of the heat sink was created based on each set of structural parameters. During modeling, care was taken to maintain the correct number of fins. n fin = x 2 / (x 4 +x 5 ) The value is an integer, and the integrity of the connection between the fins and the substrate is ensured.

[0070] Step S3: Thermal simulation and sample construction; Import the 70 sets of geometric models into the FLOEFD thermal simulation software and set the following boundary conditions: CPU power consumption: 1.4W; Ambient temperature: 25℃; Material properties: Aluminum alloy 6061, thermal conductivity 167 W / (m·K); Convection conditions: coupling of natural convection and radiative heat transfer; Mesh settings: Adaptive mesh is used with a minimum mesh size of 0.1 mm to ensure fine mesh densification in the fin boundary layer; The simulation yielded the highest CPU junction temperature and heatsink mass corresponding to each set of structural parameters, and a dataset containing 70 samples was constructed, as shown in Table 2: Table 2 Test Design Scheme for Radiator Structural Parameters Step S4: Establish the agent model; Import the sample data from Table 2 into Design-Expert software, and use a second-order polynomial model from the response surface methodology to fit the highest junction temperature of the power device. T chip and radiator quality M Relationship with various structural parameters.

[0071] After analysis of variance and regression analysis, the regression equation for the highest junction temperature of the power device was obtained (specific coefficient values ​​omitted), and the model's coefficient of determination R0 was determined. 2 = 0.978, adjust R 2 = 0.965, predicted R2 = 0.942, indicating that the model has good fitting accuracy and predictive ability. Figure 3 The cross-validation results of the surrogate model are shown. The predicted values ​​and simulated values ​​are basically located near the diagonal, which verifies the reliability of the surrogate model.

[0072] The radiator mass is calculated using formula (2), which is a deterministic model and does not require fitting.

[0073] Steps S5-S6: Multi-objective optimization solution; Based on the established agent model, a multi-objective optimization problem is set up: The objective function is: (11) The constraints are: (12) Based on the objective function and constraints, the multi-objective optimization model for the heat sink can be expressed as: (13) refer to Figure 4 The maximum number of iterations was set to 800, the population size to 50, the crossover probability to 0.9, the mutation probability to 0.2, the crossover distribution index to 20, and the mutation distribution index to 20. After 800 generations of evolution, a uniformly distributed Pareto optimal front was obtained, containing 50 non-dominated solutions.

[0074] Step S67: Optimal solution selection; The 50 Pareto optimal solutions were evaluated for feasibility, and the feasibility index of each solution was calculated (considering junction temperature <70℃, mass <25g, and structural machinability). Twelve solutions with a feasibility index greater than 7 were selected and formed into a feasible solution set.

[0075] Calculate the Nusselt number Nu (Formula 6), the average heat transfer coefficient h_avg (Formulas 7-9), and the comprehensive thermal performance evaluation index HCP (Formula 10) for each solution in the feasible solution set.

[0076] Figure 5 The feasibility assessment results of all proposed solutions are presented. Figure 6 The HCP values ​​of the 10 most feasible solutions are compared. The solution with the lowest HCP value is selected as the optimal optimization solution.

[0077] The comparison of results before and after optimization is shown in Table 3.

[0078] Table 3 Comparison of results before and after optimization As can be seen from Table 3, the optimized scheme reduces the heat sink mass by 3.33% while ensuring heat dissipation performance (junction temperature reduced by 10.6%), and all structural parameters meet the constraints, thus verifying the effectiveness of the method of the present invention.

[0079] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A heat sink structure optimization design method based on a non-dominated sorting genetic algorithm, characterized in that, Includes the following steps: S1: Perform structural analysis on the radiator to determine the structural parameters to be optimized and the objective function for optimization; wherein, the structural parameters to be optimized include: radiator length. x 1 Radiator width x 2 Radiator height x 3 fin thickness x 4 Fin spacing x 5 and substrate thickness x 6 The optimization objective function includes: the objective function for the highest junction temperature of the power device. f 1 (x) Radiator quality objective function f 2 (x) and the objective function of heat sink entropy productivity f 3 (x) ; S2: The structural parameters of the radiator are sampled using Latin hypercube sampling, and a geometric model is established based on the sampling results; S3: Perform thermal simulation analysis on the geometric model established by all sampling results in step S2, obtain the optimization target response value corresponding to each sample, and construct the sample dataset; S4: Using the sample dataset obtained in step S3, a proxy model between the objective function for optimizing the heat sink quality and the structural parameters to be optimized is established using the response surface methodology. S5: Based on the surrogate model established in step S4, optimize the structural parameters (heat sink length) determined in step S1. x 1 Radiator width x 2 Radiator height x 3 fin thickness x 4 Fin spacing x 5 and substrate thickness x 6 Establish constraints and build a multi-objective optimization model for the radiator; S6: Solve the multi-objective optimization model of the radiator established in step S5 based on the non-dominated sorting genetic algorithm to obtain the optimal combination of structural parameters.

2. The heat sink structure optimization design method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that, In step S4, The proxy model for the highest junction temperature of the power device is a second-order polynomial regression equation: (1) In the formula: T chip This indicates the highest junction temperature of the power device, expressed in °C. x i Indicates the first i The design variable, i.e. the first design variable. i One structural parameter to be optimized; N Indicates the number of variables. N =6; ζ 0 Represents a constant term. b i Denotes the coefficient of the linear term. c ii Denotes the coefficient of the quadratic term. c ij Represents the coefficient of the mixed term. ε This indicates the error term.

3. The heat sink structure optimization design method based on non-dominated sorting genetic algorithm according to claim 2, characterized in that, In step S5, The objective function for the quality of the heat sink is: (2) In the formula: M Indicates the mass of the radiator, in units of g ; n Indicates the number of cooling channels in the radiator; ρ This indicates the density of the radiator material, in units of... g / mm 3 ; n fin Indicates the number of fins. n fin = x 2 / (x 4 +x 5 ) ; x 1 Indicates the length of the heatsink, in units of mm ; x 2 Indicates the width of the heatsink, in units of mm ; x 3 Indicates the height of the radiator, in units of mm ; x 4 Indicates fin thickness, in units of mm ; x 5 Indicates fin spacing, in units of mm ; x 6 Indicates substrate thickness, in units of mm .

4. The constraints on the structural parameters to be optimized are as follows: (3) In the formula: x i,min and x i,max They represent the first i The lower and upper limits of each structural parameter.

5. The heat sink structure optimization design method based on non-dominated sorting genetic algorithm according to claim 3, characterized in that, The specific implementation steps of step S6 are as follows: S61: Based on the surrogate model established in step S4, set the objective function vector for the multi-objective optimization problem: (4) In the formula: F(x) Represent the objective function vector; f 1 (x) The objective function representing the highest junction temperature of the power device is determined by formula (1); f 2 (x) The objective function for radiator quality is represented by formula (2); f 3 (x) The objective function representing the entropy productivity of the radiator; x Represents a vector of design variables. x =[ x 1 , x 2 , x 3 , x 4 , x 5 , x 6 ] T ; S62: Set the constraints on the heat sink structural parameters according to the installation space size requirements of the power devices and formula (3); S63: Set the population size for the non-dominated sorting genetic algorithm M Maximum number of iterations G max Crossover probability c p Probability of mutation m p Within the constraints, an initial population is randomly generated as the parent population. t p ; S64: Based on mutation probability m p Perform mutation operations on the parent population, and then determine the crossover probability. c p Crossover and recombination are performed to generate offspring populations. t q ; S65: Offspring population t q and parental population t p Merging to form a hybrid species t R = t p ∪ t q The objective function value of all individuals in the mixed population is calculated according to formula (4), and non-dominated ranking and crowding degree are calculated. The optimal population is selected based on the ranking results and crowding degree. Q Each individual as a new paternal population t p+1 ; The formula for calculating the congestion level is: (5) In the formula: Indicates the first i The individual in the first m Crowding degree under a single objective function; Indicates the first i The individual in the first m Function values ​​under each objective function; and They represent the first and second digits in the current population, respectively. m The maximum and minimum values ​​of the objective function; S66: If the current iteration number is... t Less than the maximum number of iterations G max Then let t = t + 1 Return to step S64; Otherwise, proceed to step S67; S67: Obtain the Pareto optimal solution set of the radiator structural parameters, comprehensively evaluate the Pareto optimal solution set, and select the best optimization scheme for the radiator.

6. The heat sink structure optimization design method based on non-dominated sorting genetic algorithm according to claim 4, characterized in that, In step S67, the method for comprehensively evaluating the Pareto optimal solution set includes: Calculate the feasibility index of all solutions in the Pareto optimal solution set, and select solutions with feasibility indices greater than a preset threshold to form a feasible solution set; Calculate the Nusselt number of all solutions in the feasible solution set. Nu Average heat transfer coefficient of radiator h avg Comprehensive evaluation index of thermal performance HCP Value; Choice HCP The solution with the smallest value is taken as the optimal optimization scheme.

7. The heat sink structure optimization design method based on non-dominated sorting genetic algorithm according to claim 5, characterized in that, The Nusel Nu The calculation formula is: (6) In the formula: Nu Nusselt numbers are dimensionless. C and n Represents the empirical coefficient; Gr Represent Grashof numbers; Pr Represent the Prandtl number; g Represents gravitational acceleration, with units of . m / s 2 ; β The coefficient of volumetric expansion of air is expressed in units of 1000 ppm. K -1 ; L Indicates the feature length, in units of m ; T S This indicates the surface temperature of the radiator, in units of... ℃ ; T ∞ Indicates ambient temperature, in units of ℃ ; ν The kinematic viscosity of air is expressed in units of 1000 kJ / m². m 2 / s .

8. The heat sink structure optimization design method based on non-dominated sorting genetic algorithm according to claim 5, characterized in that, The average heat transfer coefficient of the radiator h avg The calculation formula is: (7) (8) (9) In the formula: h avg This represents the average heat transfer coefficient of the radiator, expressed in units of... W / (m 2 ·K) ; λ air The thermal conductivity of air is expressed in units of 1000 m / s. W / (m·K) ; L c Indicates the feature length, in units of m ; Re L Represents the Reynolds number based on the feature length; x 3 Indicates the height of the radiator, in units of mm ; x 4 Indicates fin thickness, in units of mm ; x 5 Indicates the fin spacing, in units of mm .

9. The heat sink structure optimization design method based on non-dominated sorting genetic algorithm according to claim 5, characterized in that, The comprehensive evaluation index of thermal performance HCP The calculation formula is: (10) In the formula: HCP This represents a comprehensive evaluation index of thermal performance, in units of... ℃·g / W ; T chip This indicates the highest junction temperature of the power device, in units of... ℃ ; M Indicates the mass of the radiator, in units of g ; h avg This represents the average heat transfer coefficient of the radiator, expressed in units of... W / (m 2 ·K) ; A This represents the total surface area of ​​the heat sink (including the bottom surface of the base plate and the surface area of ​​all fins), in m². 2 Lower HCP The value indicates that the radiator has better overall thermal performance.

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