Thermoelectric module layered collaborative optimization design method and customized module

Abstract

The application discloses a layered collaborative optimization design method of thermoelectric modules and a customized module. The method divides the design variables into first layer structure variables and second layer operation variables, establishes a constraint mapping relationship based on thermoelectric coupling, limits the value range of the second layer variables by the first layer variables to form a feasible region, and optimizes in the feasible region. The application distinguishes two modes of constant voltage driving and adjustable current driving: in the constant voltage mode, the current is passively determined by the structure variables, and the optimal current is approached by adjusting the structure variables; in the adjustable current mode, the current is optimized freely in the feasible region as an independent variable, and the optimal current can be accurately achieved. The customized module designed according to the method includes a differentiated configuration module facing the distribution of external heat sources and a serialized module facing the overall performance target of the module. The application integrates physical cognition into the optimization process, avoids the low efficiency problem of variable equalization search by using layered constraint mapping, and realizes two-dimensional customized design of thermoelectric modules.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor thermoelectric cooling technology, specifically involving a hierarchical collaborative optimization design method based on physical hierarchy dependence and a customized module obtained by the method, which is applicable to precision temperature control, optoelectronic devices, high-performance chip heat dissipation and dynamic thermal management scenarios. Background Technology

[0002] Thermoelectric cooling technology, based on the Peltier effect, involves the absorption or release of heat due to differences in charge carrier energy levels when current flows through the interface of dissimilar materials. It boasts advantages such as no moving parts, rapid response, precise temperature control, and high reliability, and has been widely applied in precision temperature management for optoelectronic devices, biomedical equipment, and high-performance integrated circuits. However, with the continuous increase in chip power density and the increasing complexity of application scenarios, the design of thermoelectric modules faces systemic challenges such as multi-objective trade-offs, complex parameter coupling, and low efficiency in design space exploration.

[0003] Currently, the design of thermoelectric modules faces the following technical bottlenecks: 1. Difficulty in balancing conflicting objectives: In practical engineering applications, it is necessary to seek a balance between conflicting objectives such as maximizing cooling capacity, maximizing energy efficiency ratio (COP), minimizing temperature gradient, and minimizing cost. Traditional single-objective optimization cannot effectively handle multi-dimensional trade-offs. 2. Complex and difficult-to-quantify parameter coupling relationships: Design parameters include circuit topology, spatial layout, geometric dimensions, and material properties, which have complex nonlinear coupling relationships. Traditional thermal resistance models have problems such as "overestimating performance, ignoring material temperature dependence, and ignoring interface contact effects." 3. Low efficiency in design space exploration: The design space has high dimensionality and strong nonlinearity. Traditional trial-and-error methods or single-parameter scanning are inefficient. Directly using finite element simulation for global optimization can theoretically take hundreds of days or more, which is not feasible in engineering. 4. Lack of customized design capabilities: Existing design methods usually output a single, uniform, and fixed design scheme. They cannot be customized according to the actual distribution characteristics of external heat sources, nor can they flexibly output corresponding customized design schemes according to user preferences (such as cost priority, energy efficiency priority, uniformity priority, and cost-effectiveness priority). There is a lack of a mechanism for on-demand selection from the Pareto frontier.

[0004] Existing technologies have employed multi-objective optimization algorithms for engineering design, but these methods typically treat all design variables equally and explore the search space randomly, ignoring the inherent physical hierarchy dependencies between thermoelectric module design variables. This "blind search" approach is not only inefficient but also prone to getting trapped in local optima, making it difficult to obtain truly physically feasible solutions that satisfy the constraints. While existing literature discloses independent control methods for TEC arrays in multi-hotspot scenarios, these focus on real-time control allocation during operation rather than structural optimization during the design phase. Other literature discloses geometric parameter optimization methods and analytical optimization models considering material temperature dependence, but none propose a hierarchical collaborative optimization structure based on physical hierarchy dependencies. Summary of the Invention

[0005] The purpose of this invention is to provide a hierarchical collaborative optimization design method for thermoelectric modules and a customized module, so as to solve the problems of existing technologies that cannot systematically handle multi-objective conflicts, cannot efficiently quantify parameter coupling relationships, and lack dual-dimensional customized design capabilities, and realize the technological leap from experience-based design to digital precision design, and from unified configuration to on-demand customization.

[0006] The technical solution adopted in this invention is as follows: In a first aspect, the present invention provides a hierarchical collaborative optimization design method for thermoelectric modules, comprising the following steps: S1. Construct a design variable system, which includes a first-level structural variable and a second-level operational variable. The first-level structural variable includes at least one of circuit topology parameters, spatial layout parameters, geometric dimension parameters, and material parameters, used to determine the equivalent resistance of the thermoelectric module. The second-level operational variable includes operating current or equivalent electric drive parameters. S2. Based on the target performance indicators, determine the optimization direction of the first-level structural variables; S3. Based on the thermoelectric coupling physical relationship, establish a constraint mapping relationship between the first-layer structural variables and the second-layer operating variables, wherein the first-layer structural variables are used to limit the value range of the second-layer operating variables, and the value range constitutes a feasible domain dependent on the first-layer structural variables; wherein the constraint mapping relationship includes at least the functional relationship between the equivalent resistance and the operating current; S4. The feasible domain of the second-level running variables is a function of the first-level structural variables, and different first-level structural variables correspond to different feasible domains; the first-level structural variables and the second-level running variables together constitute an asymmetric variable space, wherein the search space of the second-level running variables is determined by the constraints of the first-level structural variables. S5. Optimize the solution of the second-level running variables within the feasible domain; S6. Obtain the optimal design parameters that meet the target performance indicators.

[0007] The hierarchical collaborative optimization design process of this invention is as follows: Figure 1 As shown.

[0008] The equivalent electric drive parameters refer to electrical quantities that can be converted to operating current and used as optimization variables, including but not limited to voltage, duty cycle, and power.

[0009] The constraint mapping relationship refers to the functional dependency from the first-level structural variables to the second-level operational variables, determined by the thermoelectric coupling physical equations.

[0010] The asymmetric variable space refers to the lack of symmetric search degrees of freedom between the first-level structural variables and the second-level operational variables. Once the first-level variables are independently determined, the search space for the second-level variables is restricted to a low-dimensional feasible region derived from the physical equations, rather than the entire multidimensional space. This asymmetry is the core feature of the hierarchical collaborative optimization method of this invention.

[0011] Furthermore, the feasible region is defined by at least one of the following constraints: power supply capability constraint, hot-end temperature constraint, and positive cooling condition constraint. The boundary of the feasible region is determined through numerical simulation or analytical approximation.

[0012] The above hierarchical collaborative optimization design method is based on the following physical foundation: The cooling performance of a thermoelectric module can be described by the following basic relational expression: in The equivalent Seebeck coefficient for the module. This is the operating current. This is the cold end temperature. This is the module's equivalent resistance. For the module's equivalent thermal conductivity, The temperature difference between the hot and cold ends, For cooling capacity, The input electrical power is given. The parameters mentioned above are equivalent parameters of the module, formed by multiple thermoelectric units connected in series / parallel. Their values ​​depend on the number of units, material properties, and structural configuration. Due to contact resistance, material inhomogeneity, and temperature dependence in actual thermoelectric modules, the above model is mainly used to describe the coupling relationship between variables and the optimization trend. Specific performance parameters are obtained through numerical simulation or experimental calibration.

[0013] The equivalent resistance R is determined by structural variables such as circuit topology, spatial layout, geometric dimensions, and material parameters. For example, for a circuit composed of... Each parallel branch, A module consisting of tandem units: in , Where L is the resistivity of the P / N type material, and L is the height of the thermoelectric unit. , This represents the cross-sectional area of ​​the P / N type material.

[0014] Based on the above physical relationships, we can conclude that structural variables determine... ,and With operating current A definite constraint relationship is formed between them through power supply conditions and thermoelectric coupling equations. This relationship varies depending on the driving mode, but together they constitute the physical basis of "structural variables limiting the feasible region of operating variables".

[0015] Constant voltage power supply mode (common in automotive electronics and industrial control): power supply voltage Fixed. In engineering equivalent modeling, the relationship between current and equivalent resistance can be approximated as: This expression is used to describe variable dependencies rather than a rigorous physical solution. Without considering pulse width modulation, the current amplitude is entirely passively determined by the structure variables, and optimization can only be achieved by adjusting these variables. This allows the actual current to approach the theoretical optimal value. When pulse width modulation is used, the average current... Duty cycle As an independent second-level runtime variable, it can be Within the bounds, the first-level variables are freely chosen, and the second-level variables are optimized independently within the bounds.

[0016] Adjustable current power supply mode (common in optical modules, data centers, and precision temperature control): Current It can be set independently, but is limited by physical constraints such as power supply capacity (maximum output current, rated power) and upper limit of hot junction temperature. These constraints collectively define the feasible region I∈ Its boundaries are determined by structural variables. It is determined by external conditions. Within this feasible region, the current can be freely optimized as an independent optimization variable.

[0017] Based on the above physical understanding, this invention proposes a hierarchical collaborative optimization design concept: The first layer (structural layer) first determines the value range of structural variables (i.e., the selectable interval of the equivalent resistance R), which is determined by macroscopic constraints such as manufacturing process, material cost, and heat dissipation conditions; the second layer (operational layer) derives the feasible region of the second-layer operational variables (current, duty cycle, etc.) based on the R determined by the first layer, and then performs optimization within this feasible region. This hierarchical strategy strictly follows the physical causal chain of thermoelectric systems, avoids blind searching by treating all variables equally, significantly reduces the dimensionality of the search space, and improves optimization efficiency.

[0018] The core of this invention lies in constructing an asymmetric variable space by limiting the feasible domain of the second-level running variables through the first-level structural variables. This structure differs from traditional optimization methods that treat all variables as independent of each other.

[0019] Furthermore, the spatial layout parameters in the first layer structural variables include the distribution density and / or planar geometric arrangement pattern of the thermoelectric units, wherein the distribution density varies with the external heat flux density or is set to a specific distribution according to the target performance index; the material parameters in the first layer structural variables include the resistivity, Seebeck coefficient or thermal conductivity of the thermoelectric material, and materials with different thermoelectric properties can be selected for different regions.

[0020] Furthermore, the optimization direction of the first-layer structural variables is derived from the target performance indicators and the thermoelectric coupling physical relationship, including: trending towards low resistance design, trending towards high resistance design, differentiated layout design that increases or decreases local resistance in specific areas, and combinations or trade-offs of the above directions. The "trending towards low resistance design" described in this invention refers to reducing the equivalent resistance of the module or local area by adjusting the first-layer structural variables (such as adopting a parallel-dominant circuit topology, increasing the cross-sectional area of ​​the thermoelectric unit, reducing the unit height, selecting low-resistivity materials, increasing the unit density in hot spot areas, etc.); "trending towards high resistance design" is the opposite.

[0021] Furthermore, the constraint mapping relationship is determined by at least one of the following physical relationships: the Ohmic relationship between equivalent resistance and current; the Peltier effect, Joule heating effect and thermal conduction coupling relationship; the heat flow conservation relationship between the hot end and the cold end.

[0022] Furthermore, the operating variables are optimized in constant voltage drive or adjustable current drive mode, wherein the operating variables in constant voltage mode are determined by structural variables, and the operating variables in adjustable current mode are freely adjusted within the feasible domain.

[0023] Furthermore, under constant voltage power supply conditions, the first layer of structural variables is used to define the feasible domain of the equivalent resistance, thereby determining the value or upper limit of the operating current (or its peak value). By adjusting at least one of the geometric dimension parameters, circuit topology parameters, spatial layout parameters, and material parameters in the first layer of structural variables, the boundary of the feasible domain can be changed, so that the operating current or average current approaches the optimal current. Among them, when pulse width modulation is used, the duty cycle is independently optimized within the feasible domain as a second layer of operating variables, and the optimal current is determined by the target performance index and the thermoelectric coupling equation.

[0024] Furthermore, under adjustable current power supply conditions, the operating current is used as a second-level operating variable and is optimized within the feasible region defined by the first-level structural variable to obtain the optimal current value that optimizes the target performance index and the matching geometric parameter combination; wherein, the feasible region is jointly determined by the equivalent resistance, the upper limit of the hot end temperature, and the maximum output current of the power supply through thermoelectric coupling equations.

[0025] The "optimal current" described in this invention refers to the current value that optimizes the target performance index under given operating conditions and material properties. It is not a fixed constant, but rather a dynamic optimization objective that depends on operating parameters (such as cold junction temperature, temperature difference, and heat load), material properties (such as the temperature dependence of the Seebeck coefficient), and structural parameters (such as equivalent resistance). Its specific value is determined by the thermoelectric coupling equation under given conditions. In the actual optimization process, there is a coupling relationship between the optimal current and structural variables. The hierarchical collaborative optimization method of this invention addresses this coupling problem through iterative solution.

[0026] Furthermore, the optimization solution can be any form of single-objective or multi-objective optimization, and the target performance indicators include at least one of the following: cooling capacity, energy efficiency ratio, temperature uniformity, cost, structural reliability, cost-effectiveness, and / or any user-defined objective function. The target performance indicators can be customized by the user according to the application scenario. The method, based on preset physical constraints and a hierarchical optimization structure, automatically outputs the optimal combination of design parameters corresponding to the customized objectives; different customized objectives correspond to different optimization directions and structural parameter distributions.

[0027] Furthermore, the mapping relationship between the first-layer structural variables and performance indicators is established through any of the following methods: multiphysics numerical simulation model, analytical physical model, data-driven model, or proxy model; the model considers at least one of the following factors: temperature dependence of material parameters, contact thermal resistance, contact resistance, edge effect, and heat dissipation boundary conditions; and the model is corrected by calibration coefficients, which are calibrated by experiments or simulations.

[0028] For the process of building and optimizing the proxy model, please refer to [link / reference]. Figure 3 First, sampling is conducted in the variable space through experimental design, and the performance response of the sample points is obtained using high-precision simulation. Then, a surrogate model is constructed and its accuracy is verified. Finally, the surrogate model is used to replace the high-precision simulation for optimization search, which significantly improves the efficiency of design space exploration.

[0029] When establishing the mapping relationship between the first-level structural variables and performance indicators, this invention fully considers the actual physical characteristics of the thermoelectric module: Temperature dependence of material parameters: The Seebeck coefficient, resistivity and thermal conductivity of thermoelectric materials all change nonlinearly with temperature. Ignoring this factor will lead to a significant increase in the error of the model when the temperature difference is large.

[0030] Interface contact thermal resistance and contact resistance: There are contact thermal resistance and contact resistance at the welding interface between the thermoelectric unit and the electrical connection. Traditional models usually assume an ideal interface, which leads to underestimation of thermal resistance and overestimation of cooling capacity.

[0031] Edge effect: The thermoelectric units at the edge of the module have different heat dissipation conditions and current paths compared to those in the non-edge areas, causing their performance to deviate from that of the central area.

[0032] Heat dissipation boundary conditions: The actual contact thermal resistance between the hot end of the module and the heat sink, and the interface thermal resistance between the cold end and the object being cooled are affected by factors such as installation pressure and heat transfer medium.

[0033] The above factors are corrected by introducing calibration coefficients (including material temperature calibration coefficient, contact thermal resistance calibration coefficient, contact resistance calibration coefficient, edge effect calibration coefficient, and heat dissipation boundary calibration coefficient) to modify the theoretical model. These calibration coefficients are calibrated experimentally or through simulation. Specific verification is provided in Example 5 and the calibration coefficient calibration section.

[0034] Furthermore, the method supports at least one of the following customized designs: (1) Customization for external heat source distribution: When the external heat source is non-uniformly distributed, spatial non-uniform constraints are introduced, and multiple regions with different structural variable values ​​are automatically determined through the optimization process; wherein, the region division result is generated by the optimization process, rather than pre-set; different regions differ in at least one of the following parameters: circuit topology, geometric dimension parameters, spatial distribution parameters, and material parameters; and the difference is jointly determined by the target performance index and the constraint mapping relationship. The automatic region division can be achieved in the following way: the substrate is discretized into a finite element mesh, the material density or element type of each mesh element is used as the design variable, the heat source distribution is used as the boundary condition, and the temperature uniformity or cooling capacity is maximized as the optimization objective. A variable density topology optimization algorithm (such as SIMP or BESO) is used for iterative solution to obtain the optimal spatial distribution of material density or element type; then, the optimization result is post-processed by an image segmentation algorithm (such as threshold segmentation, watershed algorithm) to automatically generate several continuous regions with different structural variables; (2) Customization for overall module performance targets: Receive at least one target performance index selected by the user from a preset target set, and output the optimal combination of design parameters corresponding to the target based on the selected target performance index as the optimization guide; the preset target set includes, but is not limited to: maximum cooling capacity, highest energy efficiency ratio, best temperature uniformity, lowest cost, best cost performance, and any target function defined by the user.

[0035] Secondly, this invention provides two types of customized thermoelectric modules: (A) Customized thermoelectric modules for external heat source distribution, including: A substrate and multiple thermoelectric units disposed thereon; different regions of the thermoelectric module have inter-regional differences in at least one of the following parameters according to the heat flux density distribution of the external heat source: circuit topology connection method; and / or spatial layout parameters; and / or geometric dimension parameters; and / or material composition parameters; Furthermore, the inter-regional differential configuration ensures that the cooling capacity of the thermoelectric module matches the heat flux density distribution of the external heat source; wherein, the matching of cooling capacity is achieved through the spatial gradient distribution of equivalent resistance and / or independent current adjustment of each region; the equivalent resistance of different regions exhibits systematic differences, which are used to adjust the current distribution in each region to achieve matching between cooling capacity and heat source distribution. See also Figure 5 It shows a typical customized module corresponding to an external heat source with high heat flux density at the center and low heat flux density at the edge: the central region uses thermoelectric units with large cross-section, high density, and parallel topology (low resistance, strong cooling), while the edge region uses thermoelectric units with small cross-section, low density, and series topology (high resistance, weak cooling), and the spatial distribution of cooling capacity matches the distribution of the external heat source.

[0036] Furthermore, the module is configured to operate in a constant voltage drive mode, wherein the equivalent resistance exhibits a gradient distribution along space, and the equivalent resistance in the high heat flux density region is lower than that in the low heat flux density region; and at least one of the following is satisfied: (1) The ratio of the cross-sectional area to the height of the thermoelectric unit in the high heat flux density region is greater than that in the low heat flux density region; (2) The unit distribution density in the high heat flux density region is higher than that in the low heat flux density region; (3) A printed circuit layer is provided on the substrate, and the printed circuit layer includes conductive lines with gradually changing width; (4) The different series and parallel ratios of thermoelectric units in different regions result in a lower equivalent resistance in the high heat flux density region compared to the low heat flux density region, and the resistance ratio between the two regions is greater than 1.5. Simulation verification shows that when the resistance ratio is less than 1.5, under a typical heat source distribution (heat flux density ratio 3:1), the current difference between the high and low heat flux density regions is less than 50%, resulting in a hot spot temperature reduction of less than 1.5℃, making it difficult to achieve a meaningful differentiated cooling effect in engineering. Therefore, 1.5 is determined as the minimum engineering threshold for achieving a significant regional differentiated cooling effect.

[0037] To achieve the aforementioned gradient distribution where "the equivalent resistance of the high heat flux density region is lower than that of the low heat flux density region," this invention provides four specific methods that can be used individually or in combination: Adjusting the cross-sectional area to height ratio of the thermoelectric unit: According to the resistance formula R=ρL / A, increasing the cross-sectional area A or decreasing the height L reduces resistance, and vice versa. Therefore, a larger A / L ratio (i.e., large cross-section, small height) can be used in high heat flux density regions, and a smaller A / L ratio (i.e., small cross-section, large height) can be used in low heat flux density regions to achieve a resistance gradient. This method directly changes the geometry of the thermoelectric unit itself, with significant effects and no additional process steps.

[0038] Adjusting the distribution density of thermoelectric units: Arranging more thermoelectric units per unit area, combined with a parallel-dominant circuit topology, can effectively reduce the equivalent resistance of the region (due to the increase in parallel branches), thereby allowing a larger current to flow and improving local cooling capacity. It should be noted that increasing unit density does not always linearly increase cooling capacity: there exists an optimal density value limited by factors such as the maximum output current of the power supply, heat dissipation capacity, and Joule heat loss. The hierarchical collaborative optimization method of this invention can automatically search for this optimal density, avoiding performance saturation or degradation caused by blindly increasing density.

[0039] The printed circuit layer conductors have gradually varying widths: the conductive lines on the substrate have a certain resistance, which is directly proportional to the conductor length and inversely proportional to the cross-sectional area (width × thickness). By monotonically varying the conductor width along the heat flux density direction (e.g., widening the conductor in high heat flux density regions), the distribution of the line resistance can be adjusted, thus contributing to the overall resistance gradient. This method, as an auxiliary means, allows for fine-tuning of the resistance distribution without altering the thermoelectric unit itself.

[0040] Adjusting the circuit topology (series / parallel ratio) in different regions: the more parallel branches, the lower the equivalent resistance; the more series stages, the higher the equivalent resistance. Therefore, using a parallel-dominant topology in high heat flux density regions and a series-dominant topology in low heat flux density regions can achieve a resistance gradient. The larger the resistance ratio, the more significant the difference in current distribution. This method offers a wide range of resistance adjustment and is a core circuit-level design technique.

[0041] The four methods described above can be used individually or in any combination. Those skilled in the art can select the most suitable method based on practical constraints such as manufacturing process, cost, and driving mode (constant voltage or adjustable current). Example 1 illustrates a specific case of achieving a resistance gradient through a combination of methods (adjusting geometric dimensions, distribution density, and circuit topology).

[0042] (B) Customized thermoelectric modules designed to meet overall module performance targets, including: The substrate and multiple thermoelectric units disposed thereon; the overall structural parameter configuration of the thermoelectric module—including at least one of the following: circuit topology connection method, geometric dimension parameters of thermoelectric units, spatial distribution parameters, and material composition parameters—is determined according to user-preset target performance indicators; the target performance indicators are any quantifiable objective functions defined according to the application scenario; the structural parameter configuration and the target performance indicators satisfy the following: different target performance indicators correspond to different equivalent resistance ranges and / or different geometric dimension ratios; the distribution of structural parameters is determined by the constraint mapping relationship between the first-layer structural variables and the second-layer operating variables.

[0043] Furthermore, when the module is configured in constant pressure drive mode, the target performance indicators include at least one of the following: maximum cooling capacity, highest energy efficiency ratio, best temperature uniformity, lowest cost, optimal cost-effectiveness, and / or any user-defined objective function; and: (1) When the target is the maximum cooling capacity, the module adopts a parallel-dominant circuit topology, and / or the cross-sectional area of ​​the thermoelectric unit is greater than the reference design and the height is less than the reference design; (2) When the target is the highest energy efficiency ratio, the module adopts a series-dominant circuit topology, and / or the cross-sectional area of ​​the thermoelectric unit is smaller than the reference design and the height is larger than the reference design; (3) When the target is optimal temperature uniformity, the module adopts a differentiated layout design and increases the local resistance in the high temperature area of ​​the module itself by at least one of the following methods: reducing the number of thermoelectric units, reducing the cross-sectional area, increasing the height, and adopting a series-dominant circuit topology. (4) When the goal is to minimize costs, the module uses standard materials and the geometry of the thermoelectric unit is close to the baseline design; (5) When the goal is to achieve the best cost performance, the module design parameters are located in the knee region of the Pareto front.

[0044] Furthermore, when the module is configured in adjustable current drive mode, the target performance indicators include at least one of the following: maximum cooling capacity, highest energy efficiency ratio, best temperature uniformity, lowest cost, optimal cost-effectiveness, and / or any user-defined objective function; and: (1) When the target is the maximum cooling capacity, the module adopts a parallel-dominant circuit topology, and / or the cross-sectional area of ​​the thermoelectric unit is greater than the reference design and the height is less than the reference design; (2) When the target is the highest energy efficiency ratio, the module adopts a parallel-dominant or series-parallel hybrid circuit topology and appropriate geometric size, and operates at the optimal energy efficiency operating point by independently setting the operating current less than the reference current. (3) When the target is optimal temperature uniformity, the module adopts a uniform low resistance structure, including a parallel dominant circuit topology, a thermoelectric unit with a cross-sectional area larger than the reference design and a height smaller than the reference design, and is configured as a zone independent current adjustment (achieved through multi-channel independent drive or zone independent electrode structure) so that the working current in the high temperature zone is greater than that in the low temperature zone, so as to achieve the module's own temperature uniformity. (4) When the goal is to minimize costs, the module uses standard materials and the geometry of the thermoelectric unit is close to the baseline design; (5) When the goal is to achieve the best cost performance, the module design parameters are located in the knee region of the Pareto front.

[0045] The "knee region" as described in this invention refers to a set of points on the Pareto front that satisfy one of the following conditions: (a) the point with the maximum local curvature, which can be determined by calculating the curvature of the arc formed by each point on the front and its adjacent points and taking the maximum value; (b) the inflection point region where the rate of change of the slope of the line connecting to the origin exceeds a predetermined threshold (e.g., the slope change is greater than 30%). The knee region is the design point with the greatest performance gain per unit cost.

[0046] The cost-performance ratio is defined as or .

[0047] Where Δ ΔCOP represents the increase in cooling capacity relative to the baseline design, ΔCOP represents the increase in energy efficiency ratio, and ΔC represents the increase in cost.

[0048] In this invention, "geometric dimensions close to the baseline design" means that the cross-sectional area and height deviations are within a reasonable engineering range (usually no more than ±10%) compared to the baseline design, in order to ensure basic performance while minimizing cost. "Greater than / less than the baseline design" means that the values ​​of the corresponding parameters exceed ±10% of the corresponding parameter values ​​of the baseline design.

[0049] In the optimal energy efficiency strategy under adjustable current drive mode, "moderate geometry" means that the cross-sectional area and height deviations are within a reasonable engineering range (usually no more than ±20%) compared to the baseline design, in order to find the optimal energy efficiency point under adjustable current mode.

[0050] Those skilled in the art can select appropriate dimensions within the above range based on specific working conditions and optimization objectives, or automatically determine the optimal value using the hierarchical collaborative optimization method of this invention. Specific parameters of the baseline design are detailed in the Detailed Implementation section.

[0051] Regardless of whether constant voltage drive or adjustable current drive is used, the optimization strategies of this invention for the goals of maximum cooling capacity, highest energy efficiency ratio, lowest cost, and best cost performance are all based on the following unified physical principle: Maximum cooling capacity: derived from the thermoelectric refrigeration equation It can be seen that the cooling capacity It is a single-peaked function of current I, and there exists an optimal current. The essence of achieving maximum cooling capacity is to make the operating current approach... In constant voltage mode, the current is increased by reducing the equivalent resistance R; in adjustable current mode, I is directly set. Both modes typically tend to employ structural configurations that provide higher operating current, such as low-resistance structures (parallel topology, large cross-section, small height).

[0052] Maximum energy efficiency ratio: Energy efficiency ratio (COP) = / ( Similarly, there exists an optimal current. ,and < The essence of achieving high energy efficiency is to make the operating current approach... In constant voltage mode, the current is reduced by increasing the equivalent resistance R, typically resulting in a high-resistance design (series topology, small cross-section, large height); in adjustable current mode, I is directly set. The circuit topology employs a parallel-dominant or series-parallel hybrid design with moderate geometry and low resistance to reduce Joule heat loss.

[0053] Minimum Cost: Cost is positively correlated with the thermoelectric unit volume (cross-sectional area × height) and material unit price. Minimizing equivalent resistance and geometry reduces material costs while meeting basic cooling capacity constraints. This objective is independent of the drive mode; therefore, standard materials are used in both constant voltage and adjustable current modes, with the thermoelectric unit's cross-sectional area and height deviating from the baseline design by no more than ±10%. This range is based on engineering practice, ensuring basic cooling capacity while avoiding significant increases in material costs due to over-design.

[0054] Optimal cost-effectiveness: The Pareto front knee point of the cost-effectiveness index η is determined by multi-objective optimization and is independent of the driving mode. The output parameters of this strategy can be implemented in both modes according to the actual power supply conditions. At the Pareto front, the marginal benefit of performance improvement decreases with increasing cost, and the knee point region is the design point where the performance gain per unit cost is maximized. The multi-objective optimization algorithm of this invention can automatically identify this region. See [link to typical design strategies on the Pareto front]. Figure 4 The maximum cooling capacity strategy is located in the high-end region of cooling capacity and the low-end region of energy efficiency ratio at the forefront; the highest energy efficiency ratio strategy is located in the high-end region of energy efficiency ratio and the low-end region of cooling capacity at the forefront; the optimal cost-performance strategy is located in the knee region at the forefront, where the performance gain per unit cost is the greatest.

[0055] Therefore, the hierarchical collaborative optimization framework of this invention provides a unified optimization logic for different driving modes: the first-level structural variables determine the feasible region, and the second-level operational variables approach the theoretical optimal value within the feasible region. Users only need to specify the objective, and the system can automatically match the optimal implementation path based on power supply conditions. A performance comparison of various optimization strategies under constant voltage drive and adjustable current drive modes can be found in [reference needed]. Figure 9 This intuitively demonstrates the significant advantage of adjustable current mode in terms of performance improvement.

[0056] However, for the optimal temperature uniformity strategy, the optimization strategies of constant voltage drive and adjustable current drive modes are quite different, and the physical principles are as follows: Constant voltage drive mode: voltage V is fixed, current in each region is constant. =V / The equivalent resistance determines the temperature. To achieve uniform temperature within the module, local resistance needs to be increased in high-temperature regions (e.g., using series topology, small cross-section, large height, and sparse layout) to reduce the current and Joule heating in these regions. The Joule heating decreases by a square relationship, thereby suppressing local overheating. This is the "passive suppression of Joule heating" strategy.

[0057] Adjustable current drive mode: Each zone can be powered by an independent current source, and the current... It can be freely set. To reduce the temperature in high-temperature areas, a uniform low-resistance structure (parallel topology, large cross-section, small height) should be adopted to ensure that each area has positive cooling capacity. Then, through independent current adjustment of each zone, a larger operating current is obtained for the high-temperature area to actively enhance Peltier cooling and remove excess heat. This is the "active heat removal" strategy.

[0058] See Figure 6This schematically illustrates a series of customized modules designed for different overall performance targets: the extreme cooling type employs a parallel-dominated, large-section, and low-height low-resistance design; in constant-pressure mode, the high-efficiency strategy employs a high-resistance design (series topology, small cross-section, large height); while in adjustable-current mode, the high-efficiency type employs a parallel-dominated or series-parallel hybrid design with moderate geometry and lower resistance; the isothermal type uses a differentiated layout with increased local resistance in hotspot areas under constant-pressure mode; the low-cost type uses a fully series design with standard materials close to the reference size; and the cost-effective type is located at the knee region of the Pareto front. Detailed structural parameter configurations for each scheme are shown in Example 3, and the typical distribution locations of each strategy on the Pareto front are shown in [reference needed]. Figure 4 .

[0059] Furthermore, the structural parameter distribution of the aforementioned customized module is determined by the method described in the first aspect.

[0060] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method described in the first aspect.

[0061] Fourthly, the present invention provides an electronic device including a processor and a memory, wherein the processor executes instructions in the memory to implement the method described in the first aspect.

[0062] Compared with existing technologies, the layered collaborative optimization design method and customized module for thermoelectric modules provided by this invention achieve at least the following beneficial effects: 1. Hierarchical optimization based on physical cognition: By utilizing the physical hierarchical dependencies between thermoelectric module design variables, the high-dimensional optimization problem is reduced to a constrained subspace problem, avoiding invalid searches caused by variable equalization, and making the optimization results have clear physical interpretability.

[0063] 2. High-precision physical modeling: Considering the temperature nonlinearity of material properties and the interface contact effect, a precise mapping relationship between design variables and performance indicators is established through multi-physics coupling modeling. Calibration coefficients are introduced to correct the model, making the optimization results closer to the actual working conditions.

[0064] 3. Highly efficient and optimized processes: The introduction of proxy model acceleration technology shortens the optimization cycle from hundreds of days to tens of hours, making it highly practical for engineering applications.

[0065] 4. Dual-dimensional customized design capability: It can automatically generate regionally differentiated configurations based on the actual distribution characteristics of external heat sources, achieving precise cooling of hot spots; at the same time, it can automatically output the corresponding optimal design scheme based on the user's preset overall module performance goals, realizing "design on demand". These two dimensions of customization capability are not simultaneously possessed in existing technologies, constituting a significant technical advantage of this invention. Figure 10 The technical effect of the present invention is intuitively demonstrated by comparing the temperature field distribution of the hot end face: the traditional uniform design has obvious hot spots and uneven temperature distribution; the customized design of the present invention significantly improves the temperature uniformity of the hot end face and greatly reduces the temperature of hot spots through regional differential configuration.

[0066] 5. Universality and scalability: Users can customize any objective function according to actual needs. The hierarchical collaborative optimization method can automatically output the corresponding optimal design scheme based on the physical hierarchy dependency relationship, which is different from the special optimization methods customized for specific objectives in the existing technology.

[0067] 6. Design parameter traceability: The output customized module has specific resistance-geometric dimension mapping characteristics, and the equivalent resistance is distributed in a gradient along space or has a specific resistance value range, which provides an objective basis for infringement determination.

[0068] 7. Dual-mode adaptive under a unified framework: This invention is the first to systematically distinguish the optimization mechanism of thermoelectric modules under constant voltage drive and adjustable current drive, and uniformly handle the two modes within a hierarchical constraint optimization framework. Users can flexibly choose according to actual power conditions and performance requirements, which greatly expands the scope of application. Attached Figure Description

[0069] Figure 1 This is an overall flowchart of the thermoelectric module component layered collaborative optimization design method of the present invention.

[0070] Figure 2 This diagram illustrates the coupling relationship between design variables and performance metrics.

[0071] Figure 3 A schematic diagram of the process for building and optimizing the proxy model.

[0072] Figure 4 This is a schematic diagram showing the distribution of typical design strategies on the Pareto front.

[0073] Figure 5 This is a schematic diagram of a customized module structure for distribution of external heat sources (regionally differentiated configuration).

[0074] Figure 6 This is a schematic diagram of a series of customized modules designed for performance targets.

[0075] Figure 7 This is a flowchart for calibration coefficient calibration.

[0076] Figure 8 This is a comparison chart of the prediction accuracy between the theoretical model and the corrected model.

[0077] Figure 9 This is a schematic diagram comparing the performance of constant voltage mode and adjustable current mode.

[0078] Figure 10 A comparison diagram of the temperature field distribution of the hot end face between the traditional uniform design and the customized design of this invention.

[0079] Explanation of reference numerals in the attached figures: 1-Upper substrate; 2-Lower substrate; 3-Conductive connection layer; 4-N-type semiconductor unit; 5-P-type semiconductor unit; 6-Hot end heat dissipation structure.

[0080] Figure 2 In the diagram, solid arrows indicate direct determining or limiting relationships (first-level structural variables → equivalent resistance → feasible region of second-level operating variables; second-level operating variables → performance indicators); dashed arrows indicate influencing or guiding relationships (target performance indicators and external heat source distribution → optimization direction of first-level structural variables); the first-level structural variables and the second-level operating variables together constitute an asymmetric variable space, and the final achievement of performance indicators is directly determined by the optimization results of the second-level operating variables within the feasible region.

[0081] Figure 4 The data presented here is based on simulation results (adjustable current mode) from Examples 1 and 4. Taking "COP vs. Cost" as an example, it demonstrates the distribution of typical design strategies on the Pareto front. In practical applications, users can select different parameter pairs according to their custom objectives, and the method of this invention can automatically generate the corresponding Pareto front and identify the cost-effectiveness knee.

[0082] Figure 5 To accommodate the customized module for external heat sources with high heat flux density at the center and low heat flux density at the edges, the center uses denser thermoelectric units with larger cross-sectional areas, and adopts a parallel topology; the edges use sparser thermoelectric units with smaller cross-sectional areas, and adopt a series topology.

[0083] Figure 8 The coefficients in the figure are derived from Example 5.

[0084] Figure 10 Traditional uniform designs often result in significant hot spots and large temperature differences. This invention's customized design, through regionally differentiated configurations, significantly improves the temperature uniformity of the hot end face and reduces the temperature of hot spots. Detailed Implementation

[0085] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0086] For ease of understanding, the following explanations are provided for certain symbols in this patent:

[0087] In the various embodiments of the present invention, the referenced “baseline design” is defined as: a thermoelectric module with a fully series circuit topology (p=1, q=64), P / N type thermoelectric units with a cross-sectional area of ​​1.0 mm² and a height of 1.5 mm, uniformly distributed in space, and using standard Bi2Te3 material.

[0088] Example 1: Systematic Implementation of the Hierarchical Collaborative Optimization Method This embodiment uses the heat dissipation of a high-performance computing chip as an example to demonstrate the specific implementation steps of the hierarchical collaborative optimization method of the present invention. All performance data are based on an experimentally calibrated high-precision finite element simulation model (COMSOL Multiphysics). The model considers the temperature dependence of material properties, interfacial contact thermal resistance, and contact resistance, and is experimentally calibrated to ensure that the deviation from the measured module performance is less than 5% (the calibration coefficient calibration process is described in Embodiment 7 and...). Figure 7 ).

[0089] Both power supply modes (constant voltage, adjustable current) employ a unified thermal assumption: ambient temperature. = 30℃, thermal resistance of hot-end heat sink The maximum hot-end temperature is 120°C. The adjustable current mode assumes a maximum power supply output current of 100 A (sufficiently large and not constraining). A conventional uniform module is used as the baseline design for comparison.

[0090] I. Baseline Design (Traditional Uniform Module) Circuit topology: All series ( ); Geometric dimensions: The cross-sectional area of ​​both P and N is 1.0 mm², and the height is 1.5 mm; Spatial layout: evenly distributed; Material: Standard Bi2Te3; Equivalent resistance: ; Current under constant 12V voltage: ; Input power: ; Cooling capacity: ; Energy efficiency ratio: ; Temperature difference at hot end face (module itself): Δ = 3.2 ℃; Normalized cost: ; Hot junction temperature verification: = + ×( + =30 + 0.05 × (28.5 + 69.12) =34.9 ℃<120 ℃.

[0091] II. Demonstration of Core Steps for Layered Collaborative Optimization (Taking Adjustable Current Mode High-Efficiency Strategy as an Example) Step 1: Determine the optimization direction for the first-level structural variables; Target performance indicator: Maximize the coefficient of performance (COP). In adjustable current mode, COP is a bivariate function of operating current I and equivalent resistance R. Through parameter scanning and simulation optimization, the equivalent resistance that achieves globally optimal COP in this embodiment is approximately 0.45Ω. This value is neither extremely low (otherwise, excessive current would lead to a surge in Joule heating) nor extremely high (otherwise, insufficient current would result in inadequate cooling capacity), but rather a moderate resistance.

[0092] To achieve an equivalent resistance close to this optimal value, a hybrid series-parallel topology is chosen. ), and with medium cross-sectional area (P type 1.2 mm², N type 1.0 mm²) and relatively large height (1.8 mm), the following was calculated. This is close to the theoretical optimal value. Further optimization of the current I under this structure will be conducted to achieve the peak COP.

[0093] Step 2: Derive the feasible domain of the second-level runtime variables based on the first-level structural variables.

[0094] In adjustable current mode, the feasible region of the operating current I is determined by the following physical constraints: positive cooling capacity constraint ( ), hot end temperature constraint (T) h <120℃), power supply capacity ( (This does not constitute a practical limitation) and minimum acceptable cooling capacity requirements (set in this strategy). The boundary of the feasible region is determined through simulation or analytical approximation. Simulation calculations show that the feasible region for this structure is... .

[0095] Step 3: Optimize the second-level runtime variables within the feasible region.

[0096] In the feasible region The optimization search was performed using COP as the objective function. Simulation results show that the COP reaches its maximum value of 2.18 when I=4.2A, at which point the cooling capacity... This satisfies the minimum cooling capacity constraint. The COP decreases when the current is greater or less than this value. Hot-junction temperature verification: =30+0.05×(17.5 + 8.05)=31.3℃, which is far below 120°C, so it is feasible.

[0097] III. Four Strategies in Constant Voltage Mode In constant voltage mode, the voltage is fixed at 12V, and the operating current is solely determined by the equivalent resistance. The optimization results for each strategy are presented below. All data have been verified using hot-end temperature. <120℃).

[0098] 3.1 Maximum Cooling Capacity Strategy Optimization direction: Low resistance design (parallel topology, large cross-section, small height, high density); Structural parameters: , , Density coefficient 2.0; Equivalent resistance: ; Operating current: ; performance: , Δ = 5.2℃, cost ; Hot end temperature: = 30 + 0.05×(48.0 + 837.6) = 74.3℃.

[0099] 3.2 Module-specific temperature uniformity strategy (constant pressure mode) Optimization direction: Increase local resistance in high-temperature areas (differentiated layout); Structural parameters: Central region (high temperature) series connection ( ), sparse (density 0.6), small cross-section (0.6 mm²), large height (2.0 mm); parallel connection of edge regions ( ), relatively dense (density 1.2), larger cross-section (1.2 / 1.0 mm²), smaller height (1.2 mm); Equivalent resistance: ; Operating current: ; performance: , Δ = 0.7℃, cost ; Hot end temperature: = 30 + 0.05×(25.0 + 200.4) = 41.3℃.

[0100] 3.3 Lowest Cost Strategy Optimization direction: Minimize cost while satisfying performance constraints; Structural parameters: , , Standard material, density 0.9; Equivalent resistance: ; Operating current: ; performance: , Δ = 2.8℃, cost ; Hot end temperature: = 30 + 0.05×(24.0 + 62.2) = 34.3℃.

[0101] 3.4 Energy Efficiency Optimization Strategy (Maximizing COP under Constant Pressure) Optimization direction: High resistance design; Structural parameters: , , ; Equivalent resistance: ; Operating current: ; performance: , Δ = 3.0℃, cost ; Hot end temperature: = 30 + 0.05×(25.2 + 57.6) = 34.1℃.

[0102] IV. Four Strategies in Adjustable Current Mode In adjustable current mode, the operating current I is treated as an independent optimization variable and can be freely set within a feasible region determined by the equivalent resistance, hot-junction temperature, and power supply capability. Each strategy first determines the first-level structural variables and then optimizes I within the feasible region.

[0103] 4.1 Maximum Cooling Capacity Strategy Optimization direction: Low resistance design; Structural parameters: , , ; Equivalent resistance: ; Feasible region: Constrained by positive cooling constraints, hot-end temperature constraints, and power supply capability, and determined through simulation. ; Optimize current: ; performance: , Δ = 6.2℃, cost ; Hot end temperature: = 30 + 0.05×(75.0 + 195) = 43.5℃.

[0104] 4.2 High-efficiency strategy (demonstrated, results as above) , , , Δ = 1.8℃, cost .

[0105] 4.3 Module-specific temperature uniformity strategy (adjustable current mode) Physical principle: In adjustable current mode, although the high-resistance differential structure using constant voltage mode can reproduce the temperature uniformity effect of constant voltage, it cannot be further improved by increasing the current. To fully utilize the advantages of adjustable current, a uniform low-resistance structure should be adopted, and independent current adjustment should be implemented in different zones to allow higher current to reach high-temperature areas, actively removing heat and thus achieving temperature uniformity performance superior to that of constant voltage mode.

[0106] Optimization direction: Uniform low resistance design (parallel topology, large cross-section, small height); Structural parameters: The entire module adopts a parallel-dominant configuration ( ), cross-sectional area ,high Evenly distributed; Equivalent resistance: ; Independent current adjustment for different zones: Current in the central zone (corresponding to the original high-temperature zone) Current in the edge region The branch resistances are respectively , The partitioned current is achieved through multi-channel independent drive or region-independent electrode structure.

[0107] Total input power: ; Cooling capacity: , Δ = 0.4℃, cost ; Hot junction temperature verification: = 30 + 0.05×(28.0 + 17.25) = 32.3℃, which is feasible.

[0108] 4.4 Lowest Cost Strategy Optimization direction: Minimize cost while meeting performance constraints (select the same parameters as constant voltage mode); Structural parameters: , , Standard materials; Equivalent resistance: ; Feasible region: Constrained by positive cooling constraints, hot-end temperature constraints, and power supply capability, and determined through simulation. ; Optimize current: ; performance: COP=0.386, Δ = 2.8℃, cost ; Hot end temperature: = 30 + 0.05×(24.0 + 62.2) = 34.3℃.

[0109] V. Performance Comparison Summary Table 1 Performance Comparison of Various Strategies in Constant Voltage Mode

[0110] Table 2 Performance Comparison of Various Strategies in Adjustable Current Mode

[0111] VI. Conclusion See Figure 9 As can be seen from the comparison: In constant voltage mode, adjusting the first-layer structural variables can make the actual current approach the optimal current for each target, but this is limited by engineering equivalence relationships. Due to constraints, performance improvements are limited (e.g., a maximum COP improvement of 6.3%). In adjustable current mode, the current can be freely optimized as an independent variable within the feasible region, precisely reaching the theoretically optimal current, resulting in significant performance improvements (e.g., a 432% increase in COP). This high-efficiency strategy is... Figure 4(Design scheme corresponding to the high-efficiency region of the Pareto frontier). Specifically, for the module's own temperature uniformity, the constant voltage mode requires a high-resistance differentiated structure (passively suppressing Joule heating), while the adjustable current mode uses a uniform low-resistance structure combined with independent partitioned current adjustment (active heat removal), achieving better temperature uniformity (temperature difference reduced from 0.7℃ to 0.4℃). The hierarchical collaborative optimization method of this invention handles both modes uniformly, allowing users to choose the appropriate mode based on actual power supply conditions. The embodiment fully demonstrates the core steps of "first determining the direction of the first-layer structural variables → deriving the feasible region of the second-layer variables → optimizing within the feasible region," verifying the effectiveness and self-consistency of the method.

[0112] Example 2: Customized Module for External Heat Source Distribution This embodiment fully demonstrates a customized module designed according to the method of the present invention, oriented towards external heat source distribution.

[0113] Scenario: There is a high heat flux zone (150 W / cm²) in the center and a low heat flux zone (50 W / cm²) at the edge on the surface of the external chip.

[0114] Optimization process: Obtain heat flux density distribution; construct spatial non-uniform constraints; adopt parallel-dominant, high-density, large-cross-section, and low-height (low-resistance design) for the central region; adopt series-dominant, low-density, small-cross-section, and large-height (high-resistance design) for the edge regions. The region division can be automatically achieved as follows: Discretize the substrate into a finite element mesh, using the material density of each mesh element as the design variable, the heat source distribution as the boundary condition, and temperature uniformity as the optimization objective. Iteratively solve using a variable-density topology optimization algorithm (such as SIMP) to obtain the spatially optimal material density distribution; subsequently, post-process the optimization results using a threshold segmentation algorithm to automatically generate a central high-heat flux region and an edge low-heat flux region. Each region is then independently optimized for subsequent circuit topology, geometric dimensions, and layout density parameters.

[0115] Output module characteristics: The equivalent resistance of the central region is approximately 0.087Ω, and the equivalent resistance of the edge region is approximately 1.066Ω, with a resistance ratio of approximately 12.3 > 1.5. The unit distribution density in the central region is twice that in the peripheral region; The width of the conductive line decreases radially from the center to the edge; The substrate can be a metal substrate or a ceramic substrate, with an insulating and thermally conductive layer on the surface. The thermoelectric unit is welded to the electrical connection part by eutectic bonding or solder.

[0116] The regional differentiation structure of this customized module is as follows: Figure 5As shown. Performance: The chip surface temperature difference decreased from 12℃ to 3℃, and the hot spot temperature decreased by 8℃. See the comparison of the hot-side temperature field distribution between the traditional uniform design and the customized design of this invention. Figure 10 It is evident that the customized design results in a significantly more uniform temperature distribution and effective suppression of hot spots.

[0117] Example 3: Customized Module Series Targeting Overall Module Performance Goals This embodiment demonstrates various customized module design schemes output through a hierarchical collaborative optimization method based on different user-preset goals. It should be noted that the following five strategies are merely typical examples; this method is not limited to these, and users can define any objective function.

[0118] The comparison table is as follows:

[0119] Note: The data in this embodiment is derived from the simulation results of the adjustable current mode in Embodiment 1, and is used to illustrate the module structure parameters and performance corresponding to different overall module performance targets. Users can select or customize targets according to their actual needs, and the system will automatically output the optimal design scheme. The design schemes and structural features of the above five customized modules can be found in [reference needed]. Figure 6 For typical distribution locations of each strategy on the Pareto front, see [link to Pareto front]. Figure 4 .

[0120] Example 4: Optimal Cost-Effective Design The output of a multi-objective optimization algorithm is usually the Pareto front, which is a set of non-dominated solutions, in which an improvement in the performance of any objective inevitably leads to the sacrifice of the other objective. Figure 4 and Figure 5 The generation process of the Pareto front and the distribution of typical design strategies on it are illustrated respectively.

[0121] This embodiment identifies the optimal design region for cost-effectiveness on the Pareto front. The cost-effectiveness metric is defined as the ratio of performance improvement to cost increase: Cooling capacity cost-effectiveness: , Energy efficiency ratio and cost-effectiveness: .

[0122] Analysis yielded the following results: Peak point: Parallel-dominated ( Cooling capacity 57.0 W (+100%), cost +45%. .

[0123] Peak point: Series-parallel hybrid ( COP = 2.18 (+432%), cost +11%. .

[0124] This design point can be used as the output of a "cost-effectiveness-first" strategy. The location of the optimal cost-effectiveness design point on the Pareto front can be referenced. Figure 4 A diagram of the mid-knee area.

[0125] Example 5: Accuracy Comparison of Different Coupled Modeling Methods This embodiment verifies the effectiveness and accuracy differences of the three modeling methods. The design parameters for the adjustable current mode maximum cooling capacity strategy are selected ( , , , The performance was calculated using high-precision finite element simulation, analytical model, and Kriging surrogate model, respectively. The integration process for constructing, validating, and optimizing the surrogate model is detailed below. Figure 3 .

[0126]

[0127] Conclusion: The analytical model has an error of less than 5% in predicting cooling capacity (Qc), but slightly larger errors in predicting COP (+5.3%) and maximum temperature difference (+8.1%), though these are still within an acceptable range for engineering applications. The surrogate model has errors of less than 2% in all indicators and offers a computational speed improvement of over 270 times, making it a highly efficient alternative tool for optimization iteration. See [link to comparison of prediction accuracy between the theoretical model and the corrected model] for details. Figure 8 .

[0128] Example 6: Spatial Layout Quantification Method This embodiment takes the optimization of the module's own temperature uniformity as an example to conduct a more refined independent optimization study on the sub-parameter "spatial layout density" in the first layer of structural variables. In Embodiment 1, the constant pressure and uniform temperature strategy has determined the optimal circuit topology (central series, edge parallel) and geometric dimensions (central small cross-section, large height, edge large cross-section, small height) through collaborative optimization. Based on this, this embodiment fixes the above circuit topology and geometric dimensions, and only uses the distribution density and arrangement pattern of thermoelectric units as optimization variables, with the goal of minimizing the temperature difference at the hot end face, to explore the single-dimensional depth optimization effect of the spatial layout.

[0129] (1) Discrete enumeration method: Quickly select from a library of typical layout patterns (uniform, center-focused, staggered honeycomb, trapezoidal partitioned, etc.). Simulation shows that for a centrally symmetric heat source, the trapezoidal partitioned layout (dividing the substrate into four trapezoidal regions with the center as the common vertex, and setting the density of each region independently) has the smallest temperature difference, only 0.68℃, and the calculation time is about 2 hours. This method is suitable for rapid selection in the conceptual design stage.

[0130] (2) Parametric modeling method: For trapezoidal partitioned layouts, the density gradient coefficient kg (the ratio of center density to edge density) is defined as a key parameter, with a value range of 1.0 to 3.0. Twenty samples are generated using Latin hypercube sampling to establish a response surface model (Kriging) of kg and temperature difference ΔT. Optimization shows that when kg = 1.6, the temperature difference decreases to 0.65℃, and the calculation takes approximately 3 hours. This method is suitable for fine-grained parameter optimization within a selected pattern type.

[0131] (3) Continuous function optimization method: The substrate is discretized into a grid, and the density of each grid cell is used as the design variable. The optimal density distribution is searched by combining a surrogate model and a multi-objective optimization algorithm (such as NSGA-II). For irregularly shaped heat sources (such as L-shaped distribution), this method can discover new asymmetric radial layouts, and the temperature difference is reduced by about 15% compared with the trapezoidal partition type, but the calculation time is about 12 hours. This method is suitable for scenarios with extremely high performance requirements and no prior layout knowledge. The discovered new layouts can be added to the pattern library to achieve knowledge accumulation.

[0132] Those skilled in the art can select or combine the above methods according to the characteristics of heat source distribution, design stage, and computing resources, and all of these fall within the protection scope of this invention.

[0133] In Example 1, the constant pressure and uniform temperature strategy achieved a temperature difference of 0.7℃ after co-optimizing all first-layer structural variables (circuit topology, geometric dimensions, and spatial layout). This example, building upon this, fixes the topology and dimensions and performs more refined independent optimization of the spatial layout density, further reducing the temperature difference to 0.65℃. This demonstrates that the parameters of each subclass within the first-layer structural variables can undergo progressive deep optimization based on global co-optimization. The hierarchical co-optimization framework of this invention provides natural structural support for the above operations. The density gradient coefficient kg=1.6 obtained by the above parametric modeling method is the refined result of the layout used in the constant pressure and uniform temperature strategy in Example 1.

[0134] Example 7: Calibration Coefficients and Model Validation All performance data are based on an experimentally calibrated multiphysics finite element model. The calibration process is as follows: (see flowchart) Figure 7 ): Constructing the initial finite element model: A thermo-electrical-mechanical coupling model is established in COMSOL Multiphysics, considering the temperature dependence of material properties (Seebeck coefficient, resistivity, and thermal conductivity as a function of temperature), and introducing interfacial contact thermal resistance. and contact resistance The model parameters are based on the baseline module in Example 1 (64 pairs in series, 1.0 mm², 1.5 mm, standard Bi₂Te₃).

[0135] Experimental testing: A module sample with the same structure as the baseline design was fabricated, and its cooling capacity was measured under standard operating conditions (ambient temperature 30℃, hot end temperature 50℃, cold end temperature 30℃, temperature difference 20K, 12V constant voltage drive). Properties such as COP and hot end face temperature difference.

[0136] Parameter calibration: Adjust the contact thermal resistance, contact resistance, and material property curves in the finite element model (within the literature range) to ensure that the deviation between the simulation results and experimental data is less than 5%. The final determined contact thermal resistance... Contact resistance .

[0137] Calibration coefficient determination: For the theoretical analytical model, the total calibration coefficient is defined. = / ,in This refers to the actual cooling capacity measured in the experiment. The theoretical cooling capacity calculated for an ideal model (ignoring non-ideal factors). For the baseline design, the theoretical cooling capacity calculated for an ideal model (ignoring contact effects and temperature nonlinearity). =7.65W, actual measured value =28.5W, therefore the total calibration coefficient is =28.5 / 7.65=3.73. This coefficient comprehensively reflects the influence of material temperature nonlinearity, interfacial contact effect, edge effect, and heat dissipation boundary conditions. Furthermore, it can be further decomposed into a material temperature calibration coefficient. Contact thermal resistance calibration coefficient Contact resistance calibration coefficient Edge effect calibration coefficient Heat dissipation boundary calibration coefficient Each coefficient was calibrated item by item through comparison of simulation and experiment.

[0138] After calibration, the finite element model's prediction error for the benchmark design is less than 5%, meeting engineering accuracy requirements. The hierarchical collaborative optimization method of this invention uses this calibrated model to map design variables to performance indicators.

[0139] The above embodiments only illustrate some implementation methods of the present invention. Those skilled in the art should understand that the core of the present invention lies in forming an asymmetric variable space by limiting the feasible domain of the second-level running variables through the first-level structural variables. Any optimization design method based on this idea falls within the protection scope of the present invention.

[0140] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A layered collaborative optimization design method for thermoelectric modules, characterized by: Includes the following steps: S1. Construct a design variable system, which includes a first-level structural variable and a second-level operational variable. The first-level structural variable includes at least one of circuit topology parameters, spatial layout parameters, geometric dimension parameters, and material parameters, used to determine the equivalent resistance of the thermoelectric module. The second-level operational variable includes operating current or equivalent electric drive parameters. S2. Based on the target performance indicators, determine the optimization direction of the first-level structural variables; S3. Based on the thermoelectric coupling physical relationship, establish a constraint mapping relationship between the first-layer structural variables and the second-layer operating variables, wherein the first-layer structural variables are used to limit the value range of the second-layer operating variables, and the value range constitutes a feasible domain dependent on the first-layer structural variables; wherein the constraint mapping relationship includes at least the functional relationship between the equivalent resistance and the operating current; S4. The feasible domain of the second-level running variables is a function of the first-level structural variables, and different first-level structural variables correspond to different feasible domains; the first-level structural variables and the second-level running variables together constitute an asymmetric variable space, wherein the search space of the second-level running variables is determined by the constraints of the first-level structural variables. S5. Optimize the solution of the second-level running variables within the feasible domain; S6. Obtain the optimal design parameters that meet the target performance indicators.

2. The method according to claim 1, characterized in that: The feasible region is defined by at least one of the following constraints: power supply capability constraint, hot end temperature constraint, and positive cooling condition constraint.

3. The method according to claim 1, characterized in that: The second-level operating variables are optimized in constant voltage drive or adjustable current drive mode. In constant voltage drive mode, the operating variables are determined by the structural variables, while in adjustable current drive mode, the operating variables are freely adjusted within the feasible domain.

4. The method according to claim 1, characterized in that: The spatial layout parameters in the first layer of structural variables include the distribution density and / or planar geometric arrangement pattern of thermoelectric units. The distribution density varies with the external heat flux density or is set to a specific distribution according to the target performance index. The material parameters in the first layer of structural variables include the resistivity, Seebeck coefficient or thermal conductivity of thermoelectric materials. Materials with different thermoelectric properties are selected for different regions.

5. The method according to claim 1, characterized in that: The optimization direction of the first layer of structural variables is derived from the target performance index and the thermo-electric coupling physical relationship, including: tending towards low resistance design, tending towards high resistance design, differentiated layout design that increases or decreases local resistance in specific areas, and their combinations or trade-offs.

6. The method according to claim 1, characterized in that: The optimization solution can be any form of single-objective or multi-objective optimization, and the target performance indicators include at least one of the following: cooling capacity, energy efficiency ratio, temperature uniformity, cost, structural reliability, cost-effectiveness, and / or any user-defined objective function.

7. The method according to claim 6, characterized in that, The target performance index is customized by the user according to the application scenario. The method is based on preset physical constraints and hierarchical optimization structure, and automatically outputs the optimal combination of design parameters corresponding to the customized target. Different customized targets correspond to different optimization directions and structural parameter distributions.

8. The method according to claim 1, characterized in that, The mapping relationship between the first-layer structural variables and performance indicators is established through any of the following methods: multiphysics numerical simulation model, analytical physical model, data-driven model, or proxy model; the model considers at least one of the following factors: temperature dependence of material parameters, contact thermal resistance, contact resistance, edge effect, and heat dissipation boundary conditions; and the model is corrected by calibration coefficients, which are calibrated by experiments or simulations.

9. The method according to claim 1, characterized in that, The method supports at least one of the following customized designs: (1) Customization for external heat source distribution: When the external heat source is non-uniformly distributed, spatial non-uniform constraints are introduced, and multiple regions with different structural variable values ​​are automatically determined through the optimization process; wherein, the region division result is generated by the optimization process, rather than being preset; different regions differ in at least one of the following parameters: circuit topology, geometric dimension parameters, spatial layout parameters, and material parameters; and the difference is jointly determined by the target performance index and the constraint mapping relationship. (2) Customization for overall module performance targets: Receive at least one target performance index selected by the user from a preset target set, and output the optimal combination of design parameters corresponding to the target based on the selected target performance index as the optimization guide; the preset target set includes, but is not limited to: maximum cooling capacity, highest energy efficiency ratio, best temperature uniformity, lowest cost, best cost performance, and any target function defined by the user.

10. A customized thermoelectric module, characterized in that, include: A substrate and multiple thermoelectric units disposed thereon; The different regions of the thermoelectric module are configured with inter-regional differences based on the heat flux density distribution of the external heat source, including at least one of the following parameters: circuit topology connection method; spatial layout parameters; geometric dimension parameters; and material composition parameters. The inter-regional differential configuration enables the cooling capacity of the thermoelectric module to match the heat flux density distribution of the external heat source; wherein, the matching of cooling capacity is achieved through the spatial gradient distribution of equivalent resistance and / or independent current adjustment of zones; there are systematic differences in the equivalent resistance of different regions, and these systematic differences are used to adjust the current distribution of each region to achieve the matching of cooling capacity with heat source distribution; The structural parameter distribution of the module is determined by the method described in any one of claims 1-9.

11. The customized thermoelectric module according to claim 10, characterized in that, The module is configured to operate in a constant voltage drive mode, wherein the equivalent resistance exhibits a gradient distribution along space, and the equivalent resistance in the high heat flux density region is lower than that in the low heat flux density region; and, at least one of the following is satisfied: (1) The ratio of the cross-sectional area to the height of the thermoelectric unit in the high heat flux density region is greater than that in the low heat flux density region; (2) The unit distribution density in the high heat flux density region is higher than that in the low heat flux density region; (3) A printed circuit layer is provided on the substrate, and the printed circuit layer includes conductive lines with gradually changing width; (4) The series and parallel ratios of thermoelectric units in different regions are different, which makes the equivalent resistance of the high heat flux density region lower than that of the low heat flux density region, and the resistance ratio between the two regions is greater than 1.

5.

12. A customized thermoelectric module, characterized in that, include: A substrate and multiple thermoelectric units disposed thereon; The overall structural parameter configuration of the thermoelectric module includes at least one of the following: circuit topology connection method, geometric dimension parameters of thermoelectric unit, spatial layout parameters, and material composition parameters. The overall structural parameter configuration of the thermoelectric module is determined according to the user's preset target performance indicators. The target performance metric is any quantifiable objective function defined according to the application scenario; The structural parameter configuration and the target performance index satisfy the following: different target performance indexes correspond to different equivalent resistance ranges and / or different geometric dimension ratios; The structural parameter distribution of the module is determined by the method described in any one of claims 1-9.

13. The customized thermoelectric module according to claim 12, characterized in that, When the module is configured in constant pressure drive mode, the target performance indicators include at least one of the following: maximum cooling capacity, highest energy efficiency ratio, best temperature uniformity, lowest cost, best cost performance, and / or any user-defined objective function; and: (1) When the target is the maximum cooling capacity, the module adopts a parallel-dominant circuit topology, and / or the cross-sectional area of ​​the thermoelectric unit is greater than the reference design and the height is less than the reference design; (2) When the target is the highest energy efficiency ratio, the module adopts a series-dominant circuit topology, and / or the cross-sectional area of ​​the thermoelectric unit is smaller than the reference design and the height is larger than the reference design; (3) When the target is optimal temperature uniformity, the module adopts a differentiated layout design and increases the local resistance in the high temperature area of ​​the module itself by at least one of the following methods: reducing the number of thermoelectric units, reducing the cross-sectional area, increasing the height, and adopting a series-dominant circuit topology. (4) When the goal is to minimize costs, the module uses standard materials and the geometry of the thermoelectric unit is close to the baseline design; (5) When the goal is to achieve the best cost performance, the module design parameters are located in the knee region of the Pareto front, which is the design point with the greatest performance gain per unit cost.

14. The customized thermoelectric module according to claim 12, characterized in that, When the module is configured in adjustable current drive mode, the target performance indicators include at least one of the following: maximum cooling capacity, highest energy efficiency ratio, best temperature uniformity, lowest cost, best cost performance, and / or any user-defined target function. and: (1) When the target is the maximum cooling capacity, the module adopts a parallel-dominant circuit topology, and / or the cross-sectional area of ​​the thermoelectric unit is greater than the reference design and the height is less than the reference design; (2) When the target is the highest energy efficiency ratio, the module adopts a parallel-dominant or series-parallel hybrid circuit topology and appropriate geometric size, and operates at the optimal energy efficiency operating point by independently setting the operating current less than the reference current. (3) When the target is optimal temperature uniformity, the module adopts a uniform low resistance structure, including a parallel dominant circuit topology, a thermoelectric unit with a cross-sectional area larger than the reference design and a height smaller than the reference design; and is configured with independent current regulation in the partition, so that the working current in the high temperature region of the module is greater than that in the low temperature region, so as to achieve temperature uniformity; the independent current regulation in the partition is achieved through multi-channel independent drive or regional independent electrode structure. (4) When the goal is to minimize costs, the module uses standard materials and the geometry of the thermoelectric unit is close to the baseline design; (5) When the goal is to achieve the best cost performance, the module design parameters are located in the knee region of the Pareto front, which is the design point with the greatest performance gain per unit cost.

15. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the method described in any one of claims 1-9.

16. An electronic device comprising a processor and a memory, characterized in that: When the processor executes instructions in the memory, it implements the method according to any one of claims 1-9.

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