A manifolded microchannel pin fin topology robust optimization design method and system

Abstract

This invention discloses a robust optimization design method and system for manifold microchannels with needle-rib topology preservation. The method includes obtaining a structure-performance sample containing the needle-rib feature size ratio β, manifold layer height ratio γ, and the number of needle-rib rows N; establishing a needle-rib-free topology branch Ω0 and a needle-rib-containing topology branch Ω1, along with performance prediction paths; generating non-dominated candidates within Ω0∪Ω1; calculating the weighted ideal point distance for multiple sets of target weights to obtain the preference selection frequency; performing topology preservation perturbation on the preference candidates, keeping N constant while perturbing β and γ within the branch boundaries, and calculating the response variation coefficient; determining the target structure jointly by the preference selection frequency and the response variation coefficient; and writing the dimensions and fluctuations into a parametric CAD / CAE model. This invention avoids physically corresponding β-N combinations, isolates the contamination of continuous parameter fluctuation evaluation by discrete topology switching, and outputs a directly verifiable geometric model.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design technology for thermal management structures of electronic devices, and specifically to a robust optimization design method and system for maintaining the topology of manifold-type microchannel pin ribs. Background Technology

[0002] Manifold microchannels distribute the cooling medium to multiple short microchannels through an upper manifold, shortening the flow path. While fins enhance local turbulence and heat transfer, the size and number of fins, as well as the height relationship between the manifold and microchannel layers, simultaneously alter thermal resistance, local pressure drop, and temperature non-uniformity. Therefore, trade-offs must be struck between multiple thermal performance objectives when designing manifold microchannel finned structures.

[0003] Existing technologies disclose manifold-type microchannels, topology-optimized fins, finite element evaluation, multi-objective optimization, and geometric output. For example, US20210180880A1 relates to manifold-type microchannels and topology-optimized fins; WO2025223311A1 / CN118551603B relates to multi-objective topology optimization, finite element evaluation, and structural output of microchannel heat sinks; CN119864329A discloses a radial microchannel heat sink with a manifold structure, wherein the central region of the cold plate layer is provided with a pin fin array. However, the above-mentioned existing technologies still have the following shortcomings when dealing with the pin fin topology:

[0004] When the needle-rib feature size ratio β and the number of needle-rib rows N are enumerated as mutually independent variables, combinations with no physical correspondence will be generated, such as β=0 and N>0 or β>0 and N=0.

[0005] When ribbed and non-ribbed samples are forced into the same continuous design domain, candidate generation and perturbation propagation may span discrete topological states.

[0006] A fixed set of target weights can only yield one preference point and cannot quantify the stability of the candidate's selection in the complete target preference domain;

[0007] Selecting a solution solely based on the preferred frequency cannot reflect the performance fluctuations caused by continuous changes in β and γ;

[0008] Outputting only the scale and number of rows cannot directly form a solid structure input that can be used for geometric modeling and simulation verification. Summary of the Invention

[0009] The technical problem to be solved by this invention is to address the shortcomings of existing technologies by proposing a robust optimization design method and system for manifold microchannel needle-rib topology preservation. This method establishes a closed design chain from "β-N needle-rib topology branch constraints - generation of non-dominated candidates within the branch - target weight domain preference statistics - topology preservation continuous parameter perturbation - joint determination of nominal preference and performance fluctuation - parameterized CAD / CAE geometric output". This avoids mixing β-N combinations or discrete topology switching without physical correspondence into the evaluation of continuous parameter fluctuations, and enables the determination rules of the target structure to be repeatedly executed by the written optimization program code.

[0010] To solve the above problems, the present invention adopts the following technical solution:

[0011] First, this invention proposes a robust optimization design method for maintaining the topology of manifold-type microchannel needle ribs, comprising the following steps:

[0012] Obtain a representative manifold-short microchannel unit structure-performance sample set. Each sample set contains a structural parameter vector and a performance response vector. The structural parameter vector includes the needle-rib feature size ratio β, the manifold layer height ratio γ, and the number of needle-rib rows N.

[0013] Based on the topological states of the needle ribs represented by β and N, establish a topological branch Ω0 without needle ribs and a topological branch Ω1 with needle ribs. Ω0 satisfies β=0 and N=0, and Ω1 satisfies β>0 and N belongs to a preset set of positive integer discrete states. Then, establish the corresponding performance prediction path.

[0014] Candidates are generated within Ω0∪Ω1. The performance prediction path of the corresponding branch is called to obtain the nominal performance prediction value. The non-dominated candidate set is formed by minimizing the dominance relationship.

[0015] Normalize the nominal performance predictions of each item in the non-dominated candidate set, generate multiple sets of target weights, and calculate the preference selection frequency of each candidate being selected as the minimum weighted ideal point distance candidate.

[0016] For candidates with a preference selection frequency greater than zero, generate perturbation samples, keep N unchanged, keep β of the non-ribbed topology branch at 0, and perturb γ of the two topology branches and β of the ribbed topology branch within the corresponding branch boundaries. Obtain the perturbation prediction value through the performance prediction path of the branch and calculate the response variation coefficient.

[0017] Calculate the target selection score, which increases with the frequency of preference selection and decreases with the arithmetic mean of the coefficients of variation of each response, and determine the target structure parameter vector;

[0018] The transverse feature dimensions of the needle rib and the height of the manifold layer are calculated based on the target structural parameter vector and the preset net width and height of the microchannel. The position of the needle rib is determined by N. The transverse feature dimensions of the needle rib, the height of the manifold layer, N, the position of the needle rib and the response variation coefficient are written into the parametric CAD / CAE geometric model to generate representative manifold-short microchannel unit geometric model data.

[0019] Preferably, the needle-free rib topological branch Ω0 is further defined as β=0, N=0, γ∈[3.0,4.5]; the needle-rib topological branch Ω1 is further defined as β∈[0.1,0.3], γ∈[3.0,4.5], N∈{2,4,6,8,10}.

[0020] Preferably, the performance prediction path of the needle-free rib topology branch is a one-dimensional piecewise cubic Hermite interpolation model with γ as the independent variable; the performance prediction path of the needle-rib topology branch is a regression model of three Gaussian processes corresponding to thermal resistance, pressure drop and temperature nonuniformity, respectively.

[0021] Preferably, β, γ, and N with needle-ribbed topological branches are standardized; the Gaussian process regression model uses a product kernel of a constant kernel and a Matern-5 / 2 kernel, superimposed with a white noise kernel, solves the kernel function hyperparameters by maximizing the logarithmic marginal likelihood, and uses K-fold cross-validation to determine the prediction error.

[0022] Preferably, 2000 perturbed samples are generated for each perturbed candidate; β in the needle-ribbed topological branch follows a normal distribution with mean β of the candidate, standard deviation 0.05β, and truncated to [0.1, 0.3], and γ follows a normal distribution with mean γ of the candidate, standard deviation 0.03γ, and truncated to [3.0, 4.5]; the response variation coefficient Calculate using the following formula:

[0023] ;

[0024] in, Let be the coefficient of variation of the performance response of candidate i. and These are the sample mean and sample standard deviation of the perturbation prediction sequence, respectively.

[0025] Preferably, the multiple sets of target weight vectors are generated according to a Dirichlet(1,1,1) distribution, with the number of sets M=10000; for the minimization target, according to... Normalize the range of the j-th nominal performance prediction value of candidate i, and the j-th component of the positive ideal point is z. j + =min i z ij ;

[0026] Among them, y j,min and y j,max Let be the minimum and maximum values ​​of the j-th item in the non-dominated candidate set, respectively; if y j,max =y j,min Then let all z of the project target ij =0; a positive ideal point is defined as z = 0; + =(z1 + z2 + z3 + )ᵀ, where z j + =min i z ij Under the range normalization of the above minimization objective, z + =(0,0,0)ᵀ;

[0027] For satisfying w j A weight vector w whose weights are ≥0 and whose sum of the weights of the three objectives is 1, according to Calculate the weighted ideal point distance of candidate i, based on the number of times candidate i is selected as the minimum distance candidate, n. i ,according to Calculate the frequency of preference selection .

[0028] Where M is the total number of target weight vector groups; k is the group number of the target weight vector, k=1,2,…,M; i is the non-dominated candidate number; j is the performance target number, j∈{1,2,3}; w is any group of target weight vectors, and the weight vector of the kth group is denoted as w_k when calculating group by group. (k) ;w j The j-th component of this weight vector is denoted as w when calculated group by group. j (k) ;y ij z is the nominal performance prediction value of the j-th candidate i; ij z is the corresponding range normalized value; j + D is the j-th component of the positive ideal point; i (w) represents the weighted ideal point distance of candidate i relative to the set of weight vectors; n i P represents the number of times candidate i is identified as the minimum distance candidate under the weights of M groups; opt,i Choose the frequency of preference for candidate i.

[0029] Preferably, the target selection score is calculated according to the following formula. :

[0030] ;

[0031] λ is a positive disturbance risk penalty coefficient.

[0032] Preferably, the net width of the microchannel Wch = 400 μm, the height of the microchannel Hmc = 200 μm, the target structural parameter vector is β = 0.222, γ = 4.5, N = 4, the lateral feature size of the cylindrical needle rib dpin = 88.8 μm, the manifold layer height Hmf = 900 μm, and the center of each row of needle ribs relative to the short microchannel inlet are 0.2 mm, 0.6 mm, 1.0 mm, and 1.4 mm, respectively.

[0033] Meanwhile, this invention proposes a manifold-type microchannel needle rib topology-preserving robust optimization design system, comprising:

[0034] The sample acquisition module is used to acquire a structure-performance sample set of the manifold microchannel thermal management structure;

[0035] The topology branching module is used to establish a ribless topology branch Ω0 and a ribbed topology branch Ω1 according to the ribbed topology states characterized by β and N.

[0036] The performance prediction module is used to establish performance prediction paths corresponding to each topology branch;

[0037] The candidate generation module is used to generate candidate structure parameter vectors within Ω0∪Ω1, call the corresponding performance prediction path to obtain nominal performance prediction values, and form a non-dominated candidate set.

[0038] The preference statistics module is used to normalize the nominal performance prediction values ​​of each item in the non-dominated candidate set, generate multiple sets of target weight vectors, calculate the weighted ideal point distance of each non-dominated candidate relative to the positive ideal point, and determine the preference selection frequency of each candidate.

[0039] The topology-preserving perturbation module is used to generate continuous structural parameter perturbation samples for candidates with a preference selection frequency greater than zero, keeping the number of needle rib rows N unchanged and perturbing β and γ within the corresponding branch boundaries, obtaining the perturbation prediction sequence and calculating the response variation coefficient;

[0040] The target structure determination module is used to calculate the target selection score, which increases with the frequency of preference selection and decreases with the arithmetic mean of the coefficients of variation of each response, and to determine at least one target structure parameter vector.

[0041] The parametric geometry output module is used to calculate the lateral feature dimensions of the needle ribs and the height of the manifold layer based on the target structure parameter vector and the preset microchannel net width and microchannel height. It determines the arrangement position of each row of needle ribs according to the number of needle rib rows N, and writes the lateral feature dimensions of the needle ribs, the height of the manifold layer, the number of needle rib rows, the arrangement position of each row, and the response variation coefficient into the parametric CAD / CAE geometric model to generate representative manifold-short microchannel unit geometric model data.

[0042] Meanwhile, the present invention proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the present invention.

[0043] The present invention, by adopting the above technical solution, has the following beneficial effects:

[0044] 1. This invention divides the needle-rib topology state into a needle-rib-free topology branch Ω0 and a needle-rib-containing topology branch Ω1 according to the relationship between β and N. It also restricts candidate generation, model calling and perturbation propagation to Ω0∪Ω1, thereby avoiding the entry of combinations with no physical correspondence, such as β=0 and N>0 or β>0 and N=0, into the optimization process, thus improving the effectiveness of the candidate set.

[0045] 2. This invention maintains the number of rib rows N unchanged when continuously perturbing the structural parameters of the preferred candidates. Furthermore, β in the ribless topology branch is always 0, and β in the ribbed topology branch is always within its branch boundary. This ensures that the calculated response variation coefficient corresponds to the continuous changes of β and γ under the same entity topology state, isolating the contamination of continuous parameter fluctuations caused by discrete topology switching. Numerical ablation results show that cross-topology independent resampling of the baseline generates an average of 16.65% invalid samples with β>0 and N=0, and an average of 83.28% of the samples change the original number of rib rows; while topology preservation perturbation does not generate the aforementioned invalid samples.

[0046] 3. This invention generates multiple sets of weight vectors within the target weight simplex and statistically analyzes the preference selection frequency, rather than using only fixed weights. Therefore, it can quantify the stability of candidate selection in the complete target preference domain.

[0047] 4. The target selection score of this invention takes into account both the preference selection frequency and the response variation coefficient, thus enabling the priority selection of candidates that are both stable in the target weight domain and insensitive to fluctuations in the continuous parameters β and γ.

[0048] 5. This invention calculates the absolute dimensions based on the target structure parameter vector and writes them into the parametric CAD / CAE geometric model. Therefore, it can directly output the solid structure input that can be used for geometric modeling and simulation verification, instead of just outputting the scale and number of rows. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the structural parameters of the manifold-type microchannel involved in the present invention.

[0050] Figure 2 This is a flowchart illustrating the overall process of the method involved in this invention.

[0051] Figure 3 This is a schematic diagram of the feasible region encoding of the β-N pin-rib topology branch involved in the present invention, wherein the pinless topology branch Ω0 and the pin-rib topology branch Ω1 are separated from each other.

[0052] Figure 4 This is a schematic diagram of the branch performance response prediction path involved in the present invention.

[0053] Figure 5 This is a schematic diagram of the weighted ideal point distance and preference selection frequency as a preferred embodiment of the present invention.

[0054] Figure 6 This is a schematic diagram of the topology-preserving parameter perturbation and optional joint robust sorting involved in the present invention.

[0055] Figure 7 This is a schematic diagram of a representative manifold-short microchannel unit structure involved in the present invention.

[0056] Figure 8 This invention relates to a COMSOL numerical temperature field with a common structure.

[0057] Figure 9 This invention relates to an improved COMSOL numerical temperature field.

[0058] Figure 10 This invention relates to an improved COMSOL numerical velocity field structure. Detailed Implementation

[0059] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0060] Example 1: This example is a specific implementation of a robust optimization design method for maintaining the topology of manifold-type microchannel needle ribs. (Refer to...) Figure 2 Specifically, it includes the following steps:

[0061] S101, Obtain the sample set. Each sample set includes a structural parameter vector x=[β,γ,N]ᵀ and a corresponding performance response vector y=[y1,y2,y3]ᵀ. Here, x is the structural parameter vector, y is the performance response vector, the superscript T indicates transpose, and β is the lateral feature size d of the needle rib. pin With microchannel net width W ch The ratio, where γ is the manifold height H mf With microchannel height H mc The ratio is given by N, where N is the number of needle rib rows set along the flow direction; y1, y2, and y3 are the performance responses of the first to third items, respectively, in this embodiment using the dimensionless thermal resistance R*, dimensionless pressure drop f*, and dimensionless temperature nonuniformity T* given in Appendix 2 of Problem B of the 2026 APMCM Competition. Table 1 shows a partial selection of source data. The 12 groups in the table are representative selections of the 84 groups of source data, covering the needle-ribless branches and the needle-ribbed branches with N=2, 4, 6, 8, and 10, and covering the boundary combinations of β and γ; all 84 groups of data have the same 7-column field structure.

[0062] Table 1

[0063]

[0064] S102, establish the needle-rib topology branches. The branch Ω0 without needle ribs satisfies β=0 and N=0; the branch Ω1 with needle ribs satisfies β>0 and N∈{2,4,6,8,10}. Candidate generation, model invocation, and perturbation propagation are all restricted to Ω0∪Ω1.

[0065] S103, Establish the performance prediction path. Ω0 establishes a one-dimensional interpolation path with γ as a continuous variable; Ω1 establishes prediction models for thermal resistance, pressure drop, and temperature non-uniformity for standardized β, γ, and N, respectively. Ω0 has only 4 samples; branching is used to characterize the response relationship under ribless and ribbed topologies, respectively, and to prevent candidate and perturbation samples from crossing the β-N topological relationship.

[0066] Specifically, for the ribless topological branch Ω0, four groups of nodes are first arranged in ascending order of γ. A one-dimensional piecewise cubic Hermite interpolation curve is established for thermal resistance, pressure drop, and temperature nonuniformity, respectively. The function value at each node is taken as the corresponding source sample response value, and the node slope is determined according to the rule of maintaining the monotonicity of adjacent intervals and the curve shape. When querying, γ is input and the three predicted response values ​​are output respectively. This path is only used within γ∈[3.0,4.5], does not cross to the ribbed topological branch, and does not extend beyond the said interval.

[0067] For the ribbed topological branch Ω1, β, γ, and N are first standardized according to the mean and standard deviation of the training folds, respectively. Then, a Gaussian process regression model is trained for thermal resistance, pressure drop, and temperature nonuniformity. Each model uses a product kernel of a constant kernel and a Matérn-5 / 2 kernel, superimposed with a white noise kernel. The initial length scale is [1,1,1], the constraint range is [10⁻²,10²], the constant kernel constraint range is [10⁻³,10³], and the initial white noise value is 10⁻. 5 The constraint range is [10⁻ 9 [10⁻²]; Hyperparameters are solved by maximizing the logarithmic marginal likelihood, and R², RMSE and MAE are calculated using 5-fold cross-validation. After full-sample fitting, three nominal performance predictions are output from the input (β,γ,N).

[0068] S104, generating valid candidates. Ω0 takes γ∈[3.0,4.5] with a step size of 0.01; Ω1 takes β∈[0.1,0.3] with a step size of 0.002, γ∈[3.0,4.5] with a step size of 0.01, and N∈{2,4,6,8,10}. This generates 76,406 valid candidates, and minimizing the dominance relation according to the three objectives yields 1,864 non-dominated candidates.

[0069] S105, Statistical objective preference. Let yij Let be the nominal performance prediction value of the j-th non-dominated candidate i. All three objectives are minimization objectives. Range normalization is performed on each objective separately:

[0070]

[0071] Among them, y j,min and y j,max Let be the minimum and maximum values ​​of the j-th item in the non-dominated candidate set, respectively; if y j,max =y j,min Then let all z of the project target ij =0. A positive ideal point is defined as z = 0. + =(z1 + z2 + z3 + )ᵀ, where z j + =min i z ij Under the range normalization of the above minimization objective, z + =(0,0,0)ᵀ.

[0072] Generate M sets of weight vectors w=(w1,w2,w3)ᵀ within the target weight simplex, satisfying w j ≥0 and w1+w2+w3=1. For each set of weight vectors, calculate the weighted ideal point distance of candidate i relative to the positive ideal point according to the following formula:

[0073]

[0074] Select D i (w) The smallest candidate; when distances are the same, a unique candidate is determined by ascending order of the normalized values ​​of R*, f*, and T*, and the candidate number. The candidate i is determined by the number of times it has been selected, n. i The ratio of M to the frequency of preference selection is calculated.

[0075]

[0076] The optimized program code written to implement this invention is only applicable to P. opt,i Candidates with a value greater than 0 continue to undergo local perturbation evaluation. In this invention, P... opt,i All of these represent the frequency of choosing the same preference.

[0077] S106, propagation topology preservation perturbation. For the candidate samples selected in S105, generate perturbation samples, with 2,000 groups generated for each candidate. When N=0, β is fixed at 0; when N>0, N remains the original discrete number of rows, and β follows a normal distribution with a mean of candidate β, a standard deviation of 0.05β, and truncated to [0.1, 0.3]; γ follows a normal distribution with a mean of candidate γ, a standard deviation of 0.03γ, and truncated to [3.0, 4.5]. The above standard deviations are for numerical perturbation scenarios, not for measured manufacturing tolerances.

[0078] S107, input the perturbation sample into the performance prediction path of its respective topology branch to obtain the perturbation prediction sequence of thermal resistance, voltage drop, and temperature nonuniformity. For the j-th performance response of candidate i, calculate:

[0079]

[0080] Where, μ ij and s ij These are the sample mean and sample standard deviation of the perturbation prediction sequence, respectively. The response coefficient of variation, as a fluctuation associated with the candidate structural parameter vector, does not represent the continuity of different rib row numbers or the presence or absence of ribs.

[0081] S108, determine the target structure. Calculate one term for each candidate structure as a function of P. opt,i The target selection score, which increases with the increase of the arithmetic mean of the three response coefficients of variation, and decreases with the increase of the target selection score, is used to sort the targets from high to low and determine at least one target structure parameter vector. The optimization program code written to implement this invention adopts the following approach:

[0082]

[0083] In this embodiment, λ = 2.0 is used. This formula is a specific implementation of S108. In the current data, the Spearman correlation coefficient between preference frequency ranking and joint robust ranking is 0.998265. The top 20 candidates are the same, and when λ = 0, 1, 2, 3, and 5, candidate 24764 is the preferred candidate.

[0084] S109 generates parametric geometry. W ch H is the net width of the microchannel. mc d represents the height of the microchannel. pin H represents the transverse characteristic dimension of the needle rib and, in the cylindrical needle rib embodiment, the diameter. mf L is the height of the manifold layer. ch The representative short microchannel is defined along its flow direction length. Based on the target candidate β, γ, N, and the fundamental scale W... ch H mc ,according to Calculate the transverse feature size of the needle rib, according to Calculate the manifold height; based on N, Lch The position of each pin row rib is determined by the end spacing, and d is used to determine the position of each pin row rib. pin H mf The number of needle rib rows, the position of each row, and their response variation coefficients are written into the parametric CAD or CAE geometric model to generate representative manifold-short microchannel unit geometric model data.

[0085] The terms and symbols used in this embodiment are explained as follows:

[0086] I. Standardized Terminology:

[0087] 1. "Representative manifold-short microchannel unit" refers to a periodic or local computational unit comprising a manifold cavity, a short microchannel segment communicating with the manifold cavity, and an optional pin array. This term is used consistently throughout this invention.

[0088] 2. β is the ratio of the needle-rib feature size, defined as the transverse feature size d of the needle-rib. pin With microchannel net width W ch The ratio, that is ; d in the cylindrical needle rib embodiment pin That is, the diameter of the needle rib.

[0089] 3. γ is the manifold height ratio, defined as the manifold height H. mf With microchannel height H mc The ratio, that is .

[0090] 4. N is the number of needle rib rows arranged along the flow direction in a representative manifold-short microchannel unit, and N is a non-negative integer discrete variable.

[0091] 5. Ω0 is a ribless topological branch that satisfies β=0 and N=0; Ω1 is a ribbed topological branch that satisfies β>0 and N belongs to a preset set of positive integer discrete sets.

[0092] II. Symbol Explanation:

[0093] β; the ratio of the transverse characteristic dimension of the needle rib to the net width of the microchannel; dimensionless;

[0094] γ; the ratio of manifold height to microchannel height; dimensionless;

[0095] N; the number of needle rib rows arranged along the flow direction; a non-negative integer;

[0096] d pin ; Transverse characteristic dimension of the needle rib; Diameter for cylindrical needle ribs; Length;

[0097] W ch Microchannel net width; length;

[0098] H mc Microchannel height; length;

[0099] H mf manifold height; length;

[0100] L ch Representative short microchannel length; length;

[0101] R*; dimensionless thermal resistance response; dimensionless;

[0102] f*; Dimensionless pressure drop response; Dimensionless;

[0103] T*; Dimensionless temperature nonuniformity response; Dimensionless;

[0104] P opt,i ; The preference selection frequency of candidate i under the target weights of M groups; [0,1];

[0105] CV ij The coefficient of variation of the performance response of candidate i; non-negative and dimensionless.

[0106] RI i Joint robustness index of candidate i; non-negative, dimensionless;

[0107] λ; Disturbance risk penalty coefficient; positive number.

[0108] M; Total number of target weight vector groups; Positive integer;

[0109] k; the index of the target weight vector group; a positive integer from 1 to M;

[0110] i; non-dominant candidate number; positive integer;

[0111] j; performance target or performance response number; take 1, 2 or 3;

[0112] y ij The nominal performance prediction value of candidate i for the j-th term;

[0113] z ij ; Normalized range of the j-th target of candidate i; [0,1];

[0114] z j + The j-th component of the ideal point; dimensionless;

[0115] w (k) The target weight vector for the kth group; all three components are non-negative and their sum is 1;

[0116] w j (k) The j-th component of the k-th target weight vector; [0,1];

[0117] D i(w (k) ); the weighted ideal point distance of candidate i relative to the k-th group of target weight vectors; non-negative;

[0118] n i The number of times candidate i is identified as the minimum distance candidate under the weights of M groups; a non-negative integer;

[0119] μ ij The sample mean of the j-th perturbation prediction sequence of candidate i;

[0120] s ij ; the sample standard deviation of the j-th perturbation prediction sequence of candidate i; non-negative.

[0121] The structural parameters and their geometric meanings in this embodiment are as follows: Figure 1 As shown, the overall optimization steps are as follows: Figure 2 As shown. According to Figure 2 In S101, the source data used in this embodiment comes from Appendix 2 of Problem B of the 2026 APMCM Competition, which contains 84 sets of structure-performance samples, including 4 sets of branches without ribs and 80 sets of branches with ribs. β takes values ​​of 0, 0.1, 0.15, 0.2, and 0.3, γ takes values ​​of 3.0, 3.5, 4.0, and 4.5, and N takes values ​​of 0, 2, 4, 6, 8, and 10; all source samples satisfy β=0 if and only if N=0.

[0122] For the needle-rib branch, StandardScaler is first used to standardize β, γ, and N according to the mean and standard deviation of the training folds. Each performance response model adopts a "constant kernel × Matern-5 / 2 kernel + white noise kernel". The initial value of the Matern kernel length scale is [1,1,1], with a constraint range of [10^-2,10^2]; the constant kernel range is [10^-3,10^3]; the white noise initial value is 10^-5, with a range of [10^-9,10^-2]. Hyperparameters are solved by maximizing the logarithmic marginal likelihood; 5-fold cross-validation is performed with 3 optimizer restarts per fold, and the final full-sample fitting is performed with 8 restarts. The random seed is fixed at 20260726, and normalize_y is performed on the output.

[0123] The results of the 5-fold cross-validation of the needle-rib branch are as follows: R*: R²=0.998941, RMSE=0.000353, MAE=0.000254; f*: R²=0.998966, RMSE=0.000892, MAE=0.000496; T*: R²=0.994550, RMSE=0.001324, MAE=0.000925.

[0124] The needle-free branch has only 4 γ nodes and uses piecewise cubic Hermite interpolation for deterministic queries within the complete model. This branch does not extrapolate beyond [3.0, 4.5], nor does it replace independent validation with the fitting error of the 4 nodes.

[0125] Example 2: Ablation control:

[0126] like Figure 3 As shown, the candidate codes are first encoded into a ribless topological branch Ω0 and a ribbed topological branch Ω1 according to the β-N relationship; as... Figure 4 As shown, each candidate only invokes the performance response prediction path of its own branch. Independent enumeration of β∈{0}∪[0.1,0.3], γ∈[3.0,4.5], and N∈{0,2,4,6,8,10} yields 92,412 combinations; among which, 16,006 combinations have β=0 and N>0 or β>0 and N=0. After executing the Ω0∪Ω1 condition, there are 76,406 valid candidates and 0 invalid candidates.

[0127] The same 4-fold partitioning was used to recalculate the single cross-topology GPR and topology branching models, and the results are as follows:

[0128] Dimensionless thermal resistance: Overall RMSE of single cross-topology GPR = 0.000543, overall RMSE of topological branch model = 0.001459; RMSE of ribbed branch is 0.000397 and 0.000399 respectively.

[0129] Dimensionless pressure drop: Overall RMSE of single cross-topology GPR = 0.000767, overall RMSE of topology branch model = 0.001095; RMSE of needle-rib branch is 0.000681 and 0.000681 respectively.

[0130] Dimensionless temperature nonuniformity: The overall RMSE of the single cross-topological GPR model is 0.001961, and the overall RMSE of the topological branch model is 0.003726; the RMSEs of the ribbed branch model are 0.001091 and 0.001103, respectively.

[0131] Example 3: Topology Preservation Perturbation and Cross-Topology Baseline Comparison:

[0132] Topology preservation parameter perturbations and their relationship with target selection are as follows: Figure 6As shown. To isolate the effect of the fixed discrete topological state, a cross-topological numerical baseline is constructed while maintaining the distribution of β and γ perturbations, the candidate set, the surrogate model, and the 2,000 samples per candidate. N is independently and uniformly resampled from {0,2,4,6,8,10}. For all 397 needle-rib candidates in this embodiment, samples with β>0 and N=0 do not satisfy the β-N physical relationship and are marked as invalid samples and excluded from the response CV calculation. This cross-topological numerical baseline is used as the ablation control in this embodiment.

[0133] After recalculation with a fixed random seed of 20260730, the average proportion of invalid samples across topological baselines was 16.65%, and the average proportion of topological changes was 83.28%. Compared with topological preservation perturbation, the mean absolute shift of the average CV of the three responses was 0.035149, and the median was 0.035264. When ranked by the same preference frequency and λ=2, the Spearman correlation coefficient between the two rankings was 0.990761, the intersection of the top 20 candidates was 20 / 20, the mean absolute ranking shift of the candidates was 8.65, the median was 3, and the maximum was 80, with the first choice being candidate 24764.

[0134] This comparison shows that cross-topology baselines introduce non-physically corresponding β-N combinations and pin row number switching into the evaluation of continuous parameter fluctuations; topology-preserving perturbations cause CV to describe only the continuous changes of β and γ under fixed pin topology conditions.

[0135] Example 4: Weight Region and Joint Robust Sorting

[0136] The relationship between weighted ideal point distance and preference selection frequency is as follows: Figure 5 As shown. 10,000 sets of Dirichlet (1,1,1) weighted sampling were performed on 1,864 non-dominated candidates, and 397 candidates were selected at least once. The equal-weighted w=(1 / 3,1 / 3,1 / 3) yielded candidate #24764; this candidate also had the highest selection frequency, 0.0894. The Spearman correlation coefficient between the ranking by preference frequency alone and the joint robust ranking with λ=2 was 0.998265, the intersection of the top 20 candidates was 20 / 20, and the first candidate in both rankings was #24764.

[0137] Candidate #24764 corresponds to β=0.222, γ=4.5, N=4; prediction R*=0.741229, f*=0.085009, T*=0.772161; average CV=0.008460, joint robustness index RI=0.087900. Verification for λ=0, 1, 2, 3, and 5 shows that the preferred candidate remains #24764, indicating that the preferred candidate in this embodiment has stability against the listed penalty coefficients.

[0138] Example 5: Absolute dimensions of the target structure and CAD output:

[0139] like Figure 7 As shown, this embodiment converts the target structural parameters into a representative manifold-short microchannel unit geometric model. Let W... ch =400 μm, H mc =200 μm. Based on β=0.222, the diameter d of the cylindrical needle rib is... pin =88.8 μm; Based on γ=4.5, the manifold layer height H mf =900 μm. Representative short microchannel length L ch =1.6 mm, N=4, the center of each row relative to the short microchannel inlet is 0.2, 0.6, 1.0 and 1.4 mm respectively, and the center distance between adjacent rows is 400 μm. The transverse period width is 800 μm and the substrate thickness is 520 μm.

[0140] The representative unit has a total flow length of 2.4 mm, consisting of a 0.4 mm inlet manifold section, a 1.6 mm short microchannel, and a 0.4 mm outlet manifold section. In the original attached drawing, 0.52 mm represents the vertical base thickness; 1.6 mm represents the horizontal clear width of the outlet opening; and 2.4 mm represents the horizontal clear distance between adjacent outlet openings, therefore the outlet center distance is 4.0 mm. The complete length and width of the top inlet are not explicitly marked in the original drawing and are not included in the necessary dimensions.

[0141] The AutoCAD 2026 model contains 10 3D entities: base, sidewalls, channel core, four cylindrical pin ribs, cover plate, and equivalent chip. The second AutoCAD test did not report any repaired objects, deleted objects, or errors. This CAD test only confirms that this embodiment can form a closed local 3D structure.

[0142] Example 6: Comparison of COMSOL values ​​between ordinary and improved structures under the same working conditions:

[0143] Figure 8 The numerical temperature field of a representative element of a common structure is shown. Figure 9 The numerical temperature field of a representative element of the improved structure is shown. Figure 10Numerical velocity fields of representative elements of the improved structure are shown. A three-dimensional fluid-solid conjugate heat transfer model was established using COMSOL Multiphysics 6.3. The cooling medium is water: density 998.2 kg / m³, specific heat capacity at constant pressure 4182 J / (kg·K), thermal conductivity 0.6 W / (m·K), and dynamic viscosity 0.001003 Pa·s. The heat sink material is aluminum nitride: density 3260 kg / m³, specific heat capacity at constant pressure 700 J / (kg·K), and thermal conductivity 200 W / (m·K). The equivalent material of the chip has a density of 19320 kg / m³, a specific heat capacity at constant pressure of 130 J / (kg·K), and a thermal conductivity of 298 W / (m·K).

[0144] The chip domain dimensions are 2.4 mm × 0.8 mm × 0.2 mm, with a volumetric heat source of 5 × 10^9 W / m³, corresponding to a calculated domain heating power of 1.92 W. The inlet temperature is 293 K, and the nominal total mass flow rate is 1 g / s. Based on 55 equivalent flow paths, the representative unit inlet mass flow rate is 1 / 55 g / s. The outlet gauge pressure is 0 Pa; the external surface ambient temperature is 293 K, and the convective heat transfer coefficient is 10 W / (m²·K). The standard and improved structures operate under the same conditions.

[0145] Three-level meshes with maximum element sizes of 50 μm, 35 μm, and 25 μm were used for the two structures, respectively. The results for the 25 μm mesh are as follows:

[0146] Indicators; Standard structure; Improved structure; Relative changes in improved structure:

[0147] Representative unit local pressure drop / Pa; 247.403; 429.479; +73.59%;

[0148] Chip domain highest temperature / K; 310.014; 309.221; -0.793 K;

[0149] Maximum temperature rise / K; 17.014; 16.221; -4.66%;

[0150] Chip domain volume average temperature / K; 307.404; 306.668; -0.736 K;

[0151] Average temperature rise / K; 14.404; 13.668; -5.11%;

[0152] Chip domain temperature difference / K; 7.152; 6.849; -4.24%;

[0153] Representative unit thermal resistance / (K·W^-1); 8.862; 8.448; -4.66%;

[0154] Representative unit pump work / W; 4.506×10^-6; 7.823×10^-6; +73.59%;

[0155] Maximum flow velocity (m·s^-1); 0.456; 0.563; +23.49%;

[0156] When the mesh size is refined from 35 μm to 25 μm, the maximum temperature changes for the ordinary structure and the improved structure are 0.279% and 0.298%, respectively, and the local pressure drop changes are 2.390% and 4.157%, respectively. The relative errors of mass conservation under the 25 μm mesh are 0.105% and 0.128%, respectively, and the relative residuals of heat balance are 0.338% and 0.624%, respectively.

[0157] The above results indicate that a trade-off exists between thermal performance and flow resistance within this computational domain. The pressure difference is calculated using the average pressure of the inlet and outlet areas of a representative unit, and does not include the total pressure drop of the entire system, including losses from joints, main manifolds, branch junctions, and outlet joints.

[0158] Example 7: 55 / 60 flow path sensitivity:

[0159] With a 35 μm grid, after changing the total mass flow rate of 1 g / s from 55 to 60 flow paths, the local pressure drop of representative elements in the ordinary and improved structures changed by -10.55% and -10.74%, respectively, and the maximum temperature changed by +0.179 K and +0.233 K, respectively. Both 55 and 60 represent flow distribution scenarios.

[0160] Example 8: This example proposes a manifold-type microchannel needle rib topology-preserving robust optimization design system, including:

[0161] The sample acquisition module is used to acquire a structure-performance sample set of the manifold microchannel thermal management structure;

[0162] The topology branching module is used to establish a ribless topology branch Ω0 and a ribbed topology branch Ω1 according to the ribbed topology states characterized by β and N.

[0163] The performance prediction module is used to establish performance prediction paths corresponding to each topology branch;

[0164] The candidate generation module is used to generate candidate structure parameter vectors within Ω0∪Ω1, call the corresponding performance prediction path to obtain nominal performance prediction values, and form a non-dominated candidate set.

[0165] The preference statistics module is used to normalize the nominal performance prediction values ​​of each item in the non-dominated candidate set, generate multiple sets of target weight vectors, calculate the weighted ideal point distance of each non-dominated candidate relative to the positive ideal point, and determine the preference selection frequency of each candidate.

[0166] The topology-preserving perturbation module is used to generate continuous structural parameter perturbation samples for candidates with a preference selection frequency greater than zero, keeping the number of needle rib rows N unchanged and perturbing β and γ within the corresponding branch boundaries, obtaining the perturbation prediction sequence and calculating the response variation coefficient;

[0167] The target structure determination module is used to calculate the target selection score, which increases with the frequency of preference selection and decreases with the arithmetic mean of the coefficients of variation of each response, and to determine at least one target structure parameter vector.

[0168] The parametric geometry output module is used to calculate the lateral feature dimensions of the needle ribs and the height of the manifold layer based on the target structure parameter vector and the preset microchannel net width and microchannel height. It determines the arrangement position of each row of needle ribs according to the number of needle rib rows N, and writes the lateral feature dimensions of the needle ribs, the height of the manifold layer, the number of needle rib rows, the arrangement position of each row, and the response variation coefficient into the parametric CAD / CAE geometric model to generate representative manifold-short microchannel unit geometric model data.

[0169] Example 9: This example proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method described in this invention.

[0170] It should be noted that the processing flow of embodiments 2-9 corresponds to the specific steps of the method provided in embodiment 1 of the present invention, and has the corresponding functional modules and beneficial effects of the method. Technical details not described in detail in this embodiment can be found in the method provided in embodiment 1 of the present invention.

[0171] The program code used to implement the methods of this application may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0172] The specific implementation schemes described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific implementation schemes of the present invention and are not intended to limit the scope of the present invention. Any equivalent changes and modifications made by those skilled in the art without departing from the concept and principles of the present invention should fall within the scope of protection of the present invention.

Claims

1. A robust optimization design method for maintaining the topology of manifold-type microchannel needle ribs, characterized in that, Includes the following steps: Obtain a representative manifold-short microchannel unit structure-performance sample set. Each sample set contains a structural parameter vector and a performance response vector. The structural parameter vector includes the needle-rib feature size ratio β, the manifold layer height ratio γ, and the number of needle-rib rows N. Based on the topological states of the needle ribs represented by β and N, establish a topological branch Ω0 without needle ribs and a topological branch Ω1 with needle ribs. Ω0 satisfies β=0 and N=0, and Ω1 satisfies β>0 and N belongs to a preset set of positive integer discrete states. Then, establish the corresponding performance prediction path. Candidates are generated within Ω0∪Ω1. The performance prediction path of the corresponding branch is called to obtain the nominal performance prediction value. The non-dominated candidate set is formed by minimizing the dominance relationship. Normalize the nominal performance predictions of each item in the non-dominated candidate set, generate multiple sets of target weights, and calculate the preference selection frequency of each candidate being selected as the minimum weighted ideal point distance candidate. For candidates with a preference selection frequency greater than zero, generate perturbation samples, keep N unchanged, keep β of the non-ribbed topology branch at 0, and perturb γ of the two topology branches and β of the ribbed topology branch within the corresponding branch boundaries. Obtain the perturbation prediction value through the performance prediction path of the branch and calculate the response variation coefficient. Calculate the target selection score, which increases with the frequency of preference selection and decreases with the arithmetic mean of the coefficients of variation of each response, and determine the target structure parameter vector; The transverse feature dimensions of the needle rib and the height of the manifold layer are calculated based on the target structural parameter vector and the preset net width and height of the microchannel. The position of the needle rib is determined by N. The transverse feature dimensions of the needle rib, the height of the manifold layer, N, the position of the needle rib and the response variation coefficient are written into the parametric CAD / CAE geometric model to generate representative manifold-short microchannel unit geometric model data.

2. The method according to claim 1, characterized in that, The needle-free rib topological branch Ω0 is further defined as β=0, N=0, γ∈[3.0,4.5]; the needle-rib topological branch Ω1 is further defined as β∈[0.1,0.3], γ∈[3.0,4.5], N∈{2,4,6,8,10}.

3. The method according to claim 1, characterized in that, The performance prediction path of the needle-free topology branch is a one-dimensional piecewise cubic Hermite interpolation model with γ as the independent variable; the performance prediction path of the needle-ribbed topology branch is a regression model of three Gaussian processes corresponding to thermal resistance, pressure drop and temperature nonuniformity, respectively.

4. The method according to claim 3, characterized in that, β, γ, and N with needle-ribbed topological branches are standardized; the Gaussian process regression model uses a product kernel of a constant kernel and a Matern-5 / 2 kernel, superimposed with a white noise kernel, solves the kernel function hyperparameters by maximizing the logarithmic marginal likelihood, and uses K-fold cross-validation to determine the prediction error.

5. The method according to claim 1, characterized in that, Each perturbed candidate generates 2000 perturbed samples; β in the needle-ribbed topological branch follows a normal distribution with mean β of the candidate, standard deviation 0.05β, and truncated to [0.1, 0.3], and γ follows a normal distribution with mean γ of the candidate, standard deviation 0.03γ, and truncated to [3.0, 4.5]; the response variation coefficient Calculate using the following formula: ； in, Let be the coefficient of variation of the performance response of candidate i. and These are the sample mean and sample standard deviation of the perturbation prediction sequence, respectively.

6. The method according to claim 1, characterized in that, The multiple sets of target weight vectors are generated according to the Dirichlet(1,1,1) distribution, with the number of sets M=10000; for the minimization target, according to... Normalize the range of the j-th nominal performance prediction value of candidate i, and the j-th component of the positive ideal point is z. j + =min i z ij ; Among them, y j,min and y j,max Let be the minimum and maximum values ​​of the j-th item in the non-dominated candidate set, respectively; if y j,max =y j,min Then let all z of the project target ij =0; a positive ideal point is defined as z = 0; + =(z1 + z2 + z3 + )ᵀ, where z j + =min i z ij Under the range normalization of the above minimization objective, z + =(0,0,0)ᵀ; For satisfying w j A weight vector w whose weights are ≥0 and whose sum of the weights of the three objectives is 1, according to Calculate the weighted ideal point distance of candidate i, based on the number of times candidate i is selected as the minimum distance candidate, n. i ,according to Calculate the frequency of preference selection; Where M is the total number of target weight vector groups; k is the group number of the target weight vector, k=1,2,…,M; i is the non-dominated candidate number; j is the performance target number, j∈{1,2,3}; w is any group of target weight vectors, and the weight vector of the kth group is denoted as w_k when calculating group by group. (k) ;w j The j-th component of this weight vector is denoted as w when calculated group by group. j (k) ;y ij z is the nominal performance prediction value of the j-th candidate i; ij z is the corresponding range normalized value; j + D is the j-th component of the positive ideal point; i (w) represents the weighted ideal point distance of candidate i relative to the set of weight vectors; n i P represents the number of times candidate i is identified as the minimum distance candidate under the weights of M groups; opt,i Choose the frequency of preference for candidate i.

7. The method according to claim 1, characterized in that, The target selection score is calculated using the following formula. : ； λ is a positive disturbance risk penalty coefficient.

8. The method according to claim 1, characterized in that, The microchannel net width Wch = 400 μm, the microchannel height Hmc = 200 μm, the target structural parameter vector is β = 0.222, γ = 4.5, N = 4, the lateral feature size of the cylindrical needle rib is dpin = 88.8 μm, the manifold layer height is Hmf = 900 μm, and the center of each row of needle ribs relative to the short microchannel inlet is 0.2 mm, 0.6 mm, 1.0 mm and 1.4 mm respectively.

9. A manifold-type microchannel needle rib topology-preserving robust optimization design system, characterized in that, include: The sample acquisition module is used to acquire a structure-performance sample set of the manifold microchannel thermal management structure; The topology branching module is used to establish a ribless topology branch Ω0 and a ribbed topology branch Ω1 according to the ribbed topology states characterized by β and N. The performance prediction module is used to establish performance prediction paths corresponding to each topology branch; The candidate generation module is used to generate candidate structure parameter vectors within Ω0∪Ω1, call the corresponding performance prediction path to obtain nominal performance prediction values, and form a non-dominated candidate set. The preference statistics module is used to normalize the nominal performance prediction values ​​of each item in the non-dominated candidate set, generate multiple sets of target weight vectors, calculate the weighted ideal point distance of each non-dominated candidate relative to the positive ideal point, and determine the preference selection frequency of each candidate. The topology-preserving perturbation module is used to generate continuous structural parameter perturbation samples for candidates with a preference selection frequency greater than zero, keeping the number of needle rib rows N unchanged and perturbing β and γ within the corresponding branch boundaries, obtaining the perturbation prediction sequence and calculating the response variation coefficient; The target structure determination module is used to calculate the target selection score, which increases with the frequency of preference selection and decreases with the arithmetic mean of the coefficients of variation of each response, and to determine at least one target structure parameter vector. The parametric geometry output module is used to calculate the lateral feature dimensions of the needle ribs and the height of the manifold layer based on the target structure parameter vector and the preset microchannel net width and microchannel height. It determines the arrangement position of each row of needle ribs according to the number of needle rib rows N, and writes the lateral feature dimensions of the needle ribs, the height of the manifold layer, the number of needle rib rows, the arrangement position of each row, and the response variation coefficient into the parametric CAD / CAE geometric model to generate representative manifold-short microchannel unit geometric model data.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-8.

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