A method and system for synergistic design of performance and reliability of a thermally conductive composite material

Abstract

The application discloses a kind of heat-conducting composite material performance and reliability collaborative design method and system, comprising: the multi-dimensional index system with service reliability as core is constructed;Formula parameter is vectorized as design variable x, and multi-source heterogeneous database is constructed;Established by the hierarchical probability hybrid model of Gaussian process regression and bayesian network cascade, initial prediction model is obtained using database initialization training;With initial model as starting point, carry out multi-round iteration training, each round is based on current model recommendation candidate point, experimental verification, data update, retrain model, until convergence;After iteration is completed, the trained prediction model is obtained, and the pareto optimal solution set satisfying optimization target is output.The application embeds failure physical mechanism into data-driven model, realizes the integration of performance and reliability through active learning iterative training Collaborative optimization, with least experimental cost, obtain the preferred formula with high thermal conductivity and high reliability, solve the technical problem that design and service are disconnected in traditional method.

Description

Technical Field

[0001] This invention relates to the field of thermally conductive composite material development technology, specifically to a collaborative design method and system for the performance and reliability of thermally conductive composite materials. Background Technology

[0002] Thermally conductive composite materials are widely used in electronic packaging, thermal management, and other fields. Their research and development has long relied on the traditional "trial and error" method or expert experience, which involves a sequential approach of repeatedly adjusting formulations, testing performance, and verifying reliability. This approach has inherent drawbacks such as long development cycles, high costs, and blind pursuit of optimization.

[0003] To improve efficiency, data-driven methods, such as Bayesian optimization, have been introduced to intelligently recommend experimental formulations using surrogate models. However, these methods are susceptible to the "data desert" in the early stages of research and development, resulting in low model prediction accuracy and a tendency to get trapped in local optima. More importantly, existing methods have a singular and outdated design objective, typically focusing solely on maximizing initial thermal conductivity while completely ignoring the failure risk of materials under long-term service conditions. This leads to "optimal" formulations that, while exhibiting excellent initial performance, often fail to guarantee long-term reliability, essentially remaining a model that separates "performance design" from "reliability verification."

[0004] On the other hand, traditional reliability design based on failure physics, due to the complexity of its mechanistic model calculations, is usually only used as a passive verification tool after the formulation is determined, and it is difficult to actively and efficiently integrate it into the optimization process across a broad composition space. In summary, existing technologies cannot synergistically optimize the two core and mutually restrictive goals of "high thermal conductivity" and "high service reliability" in the early stages of R&D, resulting in a fundamental technical contradiction of "design and service disconnect, optimization and reliability conflict." Therefore, there is an urgent need for an intelligent design method that can integrate reliability goals at the design stage to achieve integrated optimization of performance and reliability. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a collaborative design method and system for the performance and reliability of thermally conductive composite materials, realizing integrated collaborative optimization of performance design and reliability assurance, and fundamentally solving the technical contradictions of design and service disconnect and optimization and reliability conflict in traditional methods.

[0006] This invention is achieved through the following technical solution: A method for co-designing the performance and reliability of thermally conductive composite materials includes the following steps: Step 1: Construct an indicator system with the service reliability of thermally conductive composite materials as the core objective. The system shall include at least the service performance dimension, the macroscopic characterization dimension, and the microscopic mechanism dimension. Step 2: Vectorize the thermally conductive composite material formulation parameters into design variables x, and construct a multi-source heterogeneous database containing the correspondence between design variables x and at least some of the dimensional index values ​​in Step 1; Step 3: Establish a hierarchical probabilistic hybrid model consisting of a first-layer Gaussian process regression model and a second-layer Bayesian network. Use the database to initialize and train the model to obtain an initial prediction model with the design variable x as input and the predicted values ​​of each dimension index as output. Step 4: Starting with the obtained initial prediction model, continuously train the model through multiple rounds of iteration. Each round of iteration includes recommending candidate points based on the current model, conducting experimental verification of the candidate points, adding new data to the database, and retraining the model with the updated database to obtain an updated version, until the convergence condition is met. Step 5: After the iteration is completed, the trained prediction model is obtained, and the Pareto solution set of the optimal composition scheme of the thermally conductive composite material that meets the preset optimization objective is output.

[0007] Preferably, the service performance dimension mentioned in step 1 includes service life or service performance retention rate, which serves as the final optimization target of the collaborative design; The macroscopic characterization dimensions include laboratory-measurable thermal conductivity, coefficient of thermal expansion, and accelerated aging test indicators, which serve as the basis for experimental verification and model calibration. The microscopic mechanism dimension includes simulable computational parameters that connect material formulation and macroscopic properties, serving as the physical core for revealing failure mechanisms and achieving reliable design.

[0008] Preferably, the construction of the multi-source heterogeneous database includes: Collect historical experimental data to obtain data pairs {xj, yj}, where yj contains at least the initial thermal conductivity and one data point on performance degradation after accelerated aging or fatigue. Physical simulations are run at representative points in the design space to obtain their micro-stress field, heat flow field, and micro-mechanism dimension indicators. Failure modes, empirical values ​​of interface strength, and aging kinetic parameters of similar material systems are extracted from publicly available literature and used as constraints for the prior distribution of the model.

[0009] Preferably, the first-layer Gaussian process regression model uses the Matern 5 / 2 kernel function, and its mean function is embedded with the calculation results of the improved Maxwell-Garnett model as the physical prior. The second-layer Bayesian network is constructed based on the physical relationship of failure. It includes Weibull distribution nodes describing crack initiation and Paris law nodes describing crack propagation. The key physical parameters in the network are assigned prior distributions based on literature or experience, and their posterior distributions can be updated by Bayesian inference using experimental data.

[0010] Preferably, the step 4 of recommending candidate points based on the current model includes: Based on the current version of the prediction model, a risk perception acquisition function is constructed that is defined over the entire design space. The acquisition function integrates the expected improvement of the candidate point relative to the multi-objective optimization function, the joint feasibility probability of satisfying hard constraints, and the uncertainty of the model prediction. By optimizing the acquisition function within the design space, one or more candidate component points that maximize the acquisition function value are recommended.

[0011] Preferably, when constructing the risk perception acquisition function based on the current version of the prediction model, the multi-objective optimization function and hard constraints are determined: The multi-objective optimization function includes at least the objective of maximizing thermal conductivity f1(x) and the objective of maximizing service reliability proxy index f2(x), so as to guide the search process toward the direction of synergistic optimization of thermal conductivity and service reliability; The hard constraints include at least one or more of the following: process feasibility constraints, instantaneous physical failure constraints, and regulatory and cost constraints, used to calculate the joint feasibility probability of a candidate point satisfying all hard constraints. By fusing the expected improvement of candidate points relative to the multi-objective optimization function and the joint feasibility probability of satisfying the hard constraints through the acquisition function, candidate component points with both high optimization potential and high feasibility are recommended, and finally, a Pareto optimal solution set that cannot be surpassed by other schemes on both objectives f1(x) and f2(x) is obtained.

[0012] Preferably, in step 4, the convergence condition includes one or more of the following: The improvement rate of the hypervolume metric at the Pareto front is less than the first threshold in consecutive iterations. The maximum constraint violation probability of all non-dominated solutions on the current Pareto front is below the second threshold; The average relative standard deviation of the predictions for each solution on the Pareto front is below the third threshold.

[0013] A co-design system for the performance and reliability of thermally conductive composite materials, comprising: The indicator system construction module is used to construct an indicator system with the service reliability of thermally conductive composite materials as the core objective. The system includes at least the service performance dimension, the macroscopic characterization dimension, and the microscopic mechanism dimension. The database construction module is used to vectorize the thermally conductive composite material formulation parameters into design variables x, and construct a multi-source heterogeneous database containing the correspondence between design variables x and at least some of the dimension index values ​​in step 1. The model building and initialization training module is used to build a hierarchical probabilistic hybrid model consisting of a first-layer Gaussian process regression model and a second-layer Bayesian network. The model is initialized and trained using a database to obtain an initial prediction model with the design variable x as input and the predicted values ​​of each dimension index as output. The iterative optimization module is used as a starting point to continuously train the model through multiple rounds of iteration. Each round of iteration includes recommending candidate points based on the current model, conducting experimental verification of the candidate points, adding new data to the database, and retraining the model with the updated database to obtain an updated version, until the convergence condition is met. The output module is used to obtain the trained prediction model after iteration and output the Pareto solution set of the optimal composition scheme of thermally conductive composite material that meets the preset optimization objective.

[0014] A computer device includes: a processor and a computer-readable storage medium; The processor is adapted to execute computer programs; The computer-readable storage medium stores a computer program, which, when executed by the processor, implements the co-design method for the performance and reliability of the thermally conductive composite material.

[0015] A computer-readable storage medium storing a computer program adapted to be loaded by a processor and executed by the co-design method for the performance and reliability of the thermally conductive composite material.

[0016] Compared with the prior art, the present invention has the following beneficial technical effects: This application provides a collaborative design method for the performance and reliability of thermally conductive composite materials. By constructing a multi-dimensional index system, a multi-source heterogeneous database, a cascaded probabilistic model, and iterative optimization training, a complete closed loop for the collaborative design of thermally conductive composite material performance and reliability is formed. The scheme first establishes a multi-dimensional index system with service reliability as the core, progressively linking the final goal such as service life with measurable macroscopic performance and simulable microscopic mechanisms, providing a unified evaluation standard for design. Then, the formulation parameters are vectorized into design variables, and a multi-source heterogeneous database is constructed by integrating historical experimental, physical simulation, and literature data, laying the data foundation for model training. Based on this, a hierarchical probabilistic hybrid model consisting of Gaussian process regression and Bayesian network cascades is constructed, and an initial prediction model is obtained through database initialization training. Subsequently, multiple rounds of iterative training are conducted starting from this model. Each round recommends candidate points based on the current model, performs experimental verification, updates data, and retrains the model until convergence. Finally, a well-trained prediction model and a Pareto optimal solution set are obtained. This method incorporates the failure physical mechanism as a priori into the data-driven model, overcoming the problem of data scarcity in the early stages of research and development. Through active learning and iterative training, it obtains a high-precision prediction model with minimal experimental cost. Simultaneously, it achieves performance optimization and reliability assurance, outputting an optimal formula that combines high thermal conductivity and high reliability, fundamentally resolving the technical contradiction of the disconnect between performance design and reliability verification in traditional methods.

[0017] This application also proposes a co-design system for the performance and reliability of thermally conductive composite materials, an electronic device, and a computer storage medium, which possess all the advantages of the aforementioned co-design method for the performance and reliability of thermally conductive composite materials. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of the co-design method for the performance and reliability of thermally conductive composite materials according to the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0021] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0022] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0023] See Figure 1 A method for co-designing the performance and reliability of thermally conductive composite materials includes the following steps: Step 1: Construct an indicator system with the service reliability of thermally conductive composite materials as the core objective. The system shall include at least the service performance dimension, the macroscopic characterization dimension, and the microscopic mechanism dimension. A multi-dimensional index system with the service reliability of thermally conductive composite materials as the core objective is established. This system includes at least service performance, macroscopic characterization, and microscopic mechanism dimensions. By mapping end-service requirements (such as service life and performance retention rate) step by step to laboratory-measurable macroscopic performance indicators (such as thermal conductivity, coefficient of thermal expansion, and accelerated aging indicators) and simulateable microscopic mechanism parameters (such as thermal stress concentration factor and interface defect density), a complete mapping chain from final application effect to designable physical quantities is established. This anchors material design to service reliability from the outset, avoiding the drawback of the disconnect between performance design and reliability verification in traditional methods, and achieving quantifiable, traceable, and optimizable design objectives.

[0024] Step 2: Vectorize the thermally conductive composite material formulation parameters into design variables x, and construct a multi-source heterogeneous database containing the correspondence between design variables x and at least some of the dimensional index values ​​in Step 1; The formulation parameters of thermally conductive composite materials are vectorized into design variables x, and a multi-source heterogeneous database containing the correspondence between design variables x and at least some of the dimensional index values ​​in step 1 is constructed. By encoding formulation parameters (such as filler volume fraction, flake diameter, surface oxidation degree, etc.) into high-dimensional vectors x, the composition space range to be explored is clarified. At the same time, historical experimental data, physical simulation data, and literature knowledge data are integrated to construct a "formulation-performance" correspondence dataset covering multiple sample points within the design space. This provides a data foundation with both physical priors and experimental realism for model training, solving the cold start problem of data scarcity in the early stages of research and development, while ensuring that the data items in the database strictly correspond to the index system in step 1, forming a computable material design foundation.

[0025] Step 3: Establish a hierarchical probabilistic hybrid model consisting of a first-layer Gaussian process regression model and a second-layer Bayesian network. Use the database to initialize and train the model to obtain an initial prediction model with the design variable x as input and the predicted values ​​of each dimension index as output. A hierarchical probabilistic hybrid model, consisting of a first-layer Gaussian process regression model and a second-layer Bayesian network, was constructed. The model was initialized and trained using a database to obtain an initial prediction model that takes the design variable x as input and outputs predicted values ​​for various dimensions of indicators. The first-layer Gaussian process regression model learns the mapping from the formulation x to macroscopic performance and microscopic mechanism parameters, with its mean function embedded in the physical model as prior knowledge. The second-layer Bayesian network, based on failure physics, uses the microscopic mechanism parameters output from the first layer as input and predicts service life and failure probability through physical equations such as the Weibull distribution and Paris law. The two cascaded models form an end-to-end prediction tool. This yielded a hybrid prediction model that combines physical guidance and data-driven approaches. This model leverages physical mechanisms to ensure the rationality of predictions while continuously improving accuracy through data training. Furthermore, the model output includes prediction uncertainty and failure probability, providing a foundation for subsequent optimization based on risk perception.

[0026] Step 4: Starting with the obtained initial prediction model, continuously train the model through multiple rounds of iteration. Each round of iteration includes recommending candidate points based on the current model, conducting experimental verification of the candidate points, adding new data to the database, and retraining the model with the updated database to obtain an updated version, until the convergence condition is met. Starting with the initial prediction model, the model is continuously trained through multiple iterations. Each iteration includes recommending candidate points based on the current model, experimentally validating the candidate points, adding new data to the database, and retraining the model with the updated database to obtain an updated version, until convergence is met. A Bayesian optimization framework is employed, where each iteration constructs a data acquisition function that integrates the expected improvement, feasible probability, and uncertainty based on the current model, searching for the most valuable candidate points throughout the design space. Real data is obtained through customized experiments, and the model parameters are updated with the new data, continuously improving the model's prediction accuracy in key areas. The result is that the model with the highest prediction accuracy is obtained with the fewest number of experiments, while simultaneously searching for the optimal formulation solution in terms of both performance and reliability during the iteration process.

[0027] Step 5: After the iteration is completed, the trained prediction model is obtained, and the Pareto solution set of the optimal composition scheme of the thermally conductive composite material that meets the preset optimization objective is output.

[0028] By utilizing all experimental data accumulated during the iteration process and the continuously optimized model, a Pareto optimal solution set that cannot be simultaneously surpassed by other schemes in both thermal conductivity and service reliability was selected through a multi-objective optimization method. Simultaneously, a trained predictive model capable of rapidly and accurately predicting the performance and reliability of any new composition was obtained. The results are: the final output is an optimal formulation scheme that combines high thermal conductivity and high service reliability, providing designers with a clear performance-reliability trade-off chart; furthermore, the trained model can serve as a materials design tool, supporting rapid prediction and failure mechanism analysis of future new formulations, forming an accumulative and reusable materials design knowledge asset.

[0029] Example 1 A method for co-designing the performance and reliability of thermally conductive composite materials includes the following steps: Step 1: Construct a multi-dimensional indicator system: Establish an indicator system with service reliability as the core objective. This system characterizes the material's performance from different dimensions and includes at least: 1) Service performance dimension, including service life Ls or service performance retention rate Rp, as the ultimate optimization target of collaborative design; The service life refers to the time or number of cycles that Ls takes for the key properties of the material to degrade to the failure threshold under a defined service environment profile (such as temperature cycling profile T(t), humid heat environment RH(t), load spectrum σ(t)). Service life refers to Ls, which is the core reliability indicator that needs to be predicted and guaranteed in this invention. Service life means Ls≥Lreq (specified required life).

[0030] The service performance retention rate refers to the ratio of the material's thermal conductivity to its initial value after a specific service time or accelerated testing, expressed as follows:

[0031] Target: (For example, requiring a retention rate of at least 80% at the end of the service life). This directly links long-term reliability to instantaneous performance.

[0032] 2) Macroscopic characterization dimensions, including laboratory-measurable thermal correlation coefficients and accelerated aging test indicators, serve as the basis for experimental verification and model calibration; 1. Thermal correlation coefficients include: thermal conductivity λ and coefficient of thermal expansion; The thermal conductivity λ is measured using the steady-state method or the laser flash method, and is used as the main optimization objective to maximize it under reliability constraints.

[0033] Coefficient of Thermal Expansion (CTE, α): Its compatibility with the matrix directly affects thermal stress and is a key design and constraint parameter.

[0034] 2. Accelerated aging test indicators include: thermal cycling fatigue life, high temperature aging life, interfacial bonding strength, and performance degradation slope after long-term aging. Thermal cycling fatigue life: the number of cycles performed within a specific temperature range (e.g., -40°C ~ 150°C) until cracking occurs or the thermal conductivity decreases by more than a set value (e.g., 20%), with the optimization goal being to maximize this number; High-temperature aging life: The time it takes for performance retention to drop to a threshold at a constant high temperature (e.g., 200°C). The optimization objective is to maximize this retention.

[0035] Interfacial bond strength: The interfacial strength between the filler and the matrix was measured through tests such as micro-debonding and tensile shear. The optimization target was to exceed the critical threshold.

[0036] Performance degradation slope after long-term aging: The rate constant obtained by fitting the performance degradation curve through aging tests at multiple time points. The optimization objective is to minimize it.

[0037] 3) Microscopic mechanism dimension, including simulable computational parameters that connect material formulation and macroscopic properties, serving as the physical core for revealing failure mechanisms and achieving reliable design; The microscopic mechanism dimension indicators include microstructural integrity indicators and failure physical driving indicators; The microstructure integrity indicators include effective heat conduction pathway density, interface defect density, and thermal stress concentration factor. Effective heat conduction path density: The number of effective heat flow paths per unit area calculated using a microstructure model (such as a percolation network model).

[0038] Interface defect density: The density of weak bonds or pre-existing defects at the interface as predicted or characterized.

[0039] Thermal stress concentration factor: The ratio of the maximum local thermal stress to the average stress calculated through finite element micromechanical analysis.

[0040] The failure physical driving indicators include crack initiation driving force parameters, interface debonding energy release rate, and oxidation or hydrolysis reaction front rate. Crack initiation driving force parameter: fatigue crack initiation parameters calculated based on local stress-strain field.

[0041] Interfacial debonding energy release rate: To predict the energy release rate of the interface under thermal stress, it is necessary to compare it with the interfacial fracture toughness.

[0042] Oxidation / hydrolysis reaction front rate: Environmental erosion rate predicted based on chemical kinetic model.

[0043] Step 2: Vectorize the thermally conductive composite material formulation and process parameters to be designed into design variables x to define the design space for component search; collect or generate experimental data, physical simulation data and literature knowledge data of multiple sample points in the design space, and construct a multi-source heterogeneous database containing the correspondence between the design variables x and at least some of the dimensional index values ​​in step (1); The vectorization representation of the design variable x includes: for continuous process parameters, direct encoding as numerical variables, and for categorical variables, embedding representation using unique thermal encoding or materials descriptor vectors; Vectorized representation of design variables: Encoding components and key process parameters as high-dimensional vectors x. For example: x = [filler type code, volume fraction φf, particle size distribution D50, distribution width PDI, surface functionalization degree fs, matrix crosslinking degree Xc, ...] T .

[0044] The construction of the multi-source heterogeneous database includes: 1) Historical experimental data: Collect or conduct preliminary experiments to obtain data pairs {xj, yj}; Among them, yj includes at least the initial thermal conductivity and a performance degradation data after accelerated aging or fatigue; 2) Physical simulation data: For a representative point xk in the design space, run a high-fidelity simulation based on first principles or known physical laws to obtain its micro-stress field, heat flow field and micro-mechanical dimension indicators such as theoretical thermal conductivity and thermal stress concentration factor. 3) Literature and knowledge data: Extract failure modes, empirical values ​​of interface strength, and aging kinetic parameters of similar material systems from publicly available literature as constraints for the prior distribution of the model; Step 3: Establish a hierarchical probabilistic mixture model consisting of a first-layer model and a second-layer model cascaded together, where: The first-layer model is a fast prediction model for performance and field quantities. It uses Gaussian process regression to learn the mapping law from the design variable x to macroscopic representation dimension indicators and microscopic mechanism dimension parameters. Its mean function can be embedded into the physical model as a prior. The second-layer model is a failure mechanism and life prediction probability model. A Bayesian network is constructed based on the physical relationships of failure, using the predicted distribution of the microscopic mechanism index S(x) output from the first-layer model as input. Given the design variable x, the Bayesian network propagates uncertainty according to the causal chain of failure physics: the crack initiation probability is calculated using the Weibull distribution based on the ratio of local thermal stress to interface bonding strength; the crack propagation rate is described using the Paris law; the predicted distribution of fatigue life is obtained by integrating the initial defect size and the critical crack size; and the constraint violation probability of interface debonding failure is calculated based on the comparison between the interface energy release rate and fracture toughness. Through the probabilistic dependencies between nodes in the network, the predicted distribution of service performance dimension indicators and the probability of each hard constraint being violated are finally output. The first-layer model and the second-layer model are connected in series to form an end-to-end prediction tool. The design variable x is taken as input, and the output is the joint probability prediction of each dimension index described in step 1 and its uncertainty. Using the multi-source heterogeneous initial database constructed in step 2, training samples containing design variable x and its corresponding index values ​​are collected from the database to initialize and train the hierarchical probabilistic mixture model, thereby obtaining an initial version of the prediction model.

[0045] The first layer model is a Gaussian process regression model, which is used to learn the mapping law from the design variable x to the indicators of the macroscopic representation dimension and the parameters of the microscopic mechanism dimension. Its mean function can be embedded in the physical model as a prior. In this embodiment, Gaussian process regression is used to learn the mapping law from the design variable x to indicators of the macroscopic representation dimension and parameters of the microscopic mechanism dimension. Its mean function can be embedded in the physical model as a priori. The Gaussian process regression uses the Matern 5 / 2 kernel function, and its formula is as follows: ,

[0046] In this context, σ_f² represents the signal variance. Let be the characteristic length scale, and Λ be the diagonalized length scale matrix. This kernel function can better handle the non-extremely smooth characteristics of material properties varying with composition.

[0047] The mean function can be embedded with the results of the improved Maxwell-Garnett model as a physical prior:

[0048] Where λm and λf are the thermal conductivity of the matrix and the filler, respectively, and φf is the volume fraction of the filler.

[0049] The second-layer model is a failure mechanism and lifetime prediction probability model. A Bayesian network is constructed based on the physical relationship of failure. The output of the first-layer model is used as input to predict the distribution of indicators in the service performance dimension. The key physical parameters in the Bayesian network are assigned a prior distribution based on literature or experience. Given a design variable x, the predicted distribution (including mean and uncertainty) of the micromechanical index S(x) output by the first-layer model is input into the Bayesian network, and the calculation is performed layer by layer along the failure physical relationship chain: The crack initiation probability is calculated using the Weibull distribution based on the ratio of local stress to interfacial bonding strength. The crack propagation rate is calculated using the Paris law based on the stress intensity factor amplitude after crack initiation. By combining the initial defect size and the critical crack size, the predicted distribution of fatigue life is obtained by integration; Meanwhile, based on the comparison between the interface energy release rate and the interface fracture toughness, the constraint violation probability of interface debonding failure is calculated. By leveraging the probabilistic dependencies between nodes in the network, the predicted distribution of service life (such as a log-normal distribution) and the distribution of each hard constraint function value are ultimately calculated, thereby quantifying the probability of hard constraints being violated. The key physical parameters in the Bayesian network (such as Paris law parameters C and m, interface strength distribution parameters, etc.) are assigned prior distributions based on literature or experience, and their posterior distributions can be updated by Bayesian inference using experimental data.

[0050] The third-layer model connects the first-layer model and the second-layer model to form an end-to-end prediction tool, which is used to output the joint probability prediction and uncertainty of the indicators of each dimension.

[0051] Step 4: Iteratively train the prediction model using active learning and Bayesian optimization methods, and simultaneously search for the optimal formula during the iteration process: Starting with the prediction model obtained from the initial training in Step 3, continuously train and optimize the model through multiple rounds of iteration. Each round of iteration includes the following sub-steps: (a) Based on the current version of the prediction model, calculate the risk perception acquisition function defined over the entire design space, which integrates the expected improvement of the candidate point relative to the multi-objective optimization function determined in step 1, the joint feasibility probability of satisfying all hard constraints, and the uncertainty of the model prediction. The acquisition function adopts a multi-objective expectation improvement function in the probabilistic feasible region, and its expression is:

[0052] In this equation, the first term on the right is the joint feasible probability term, which calculates the probability that x satisfies all hard constraints based on the model; the second term is the multi-objective improvement expectation term, which uses the ParEGO method to convert the multi-objective vector into a scalar through a scalarization function and calculates its expected improvement relative to the current observed Pareto front. The multi-objective optimization function uses a penalty function to handle soft constraints. For indicators that are allowed to fluctuate within a certain range but affect long-term reliability, a penalty term is introduced and incorporated into the optimization objective. The soft constraints include at least the service performance retention rate constraint.

[0053] Among them, R p,min It represents the minimum performance retention rate requirement after accelerated aging, and ρ is the penalty coefficient. If the predicted performance retention rate fails to meet the target, the thermal conductivity target value will be penalized, ensuring that the optimization process pursues high thermal conductivity while also considering long-term reliability.

[0054] The multi-objective optimization function includes at least: Objective 1: Maximize thermal conductivity ; Objective 2: Maximize service reliability metrics or

[0055] in s(x) and f(x) The service life is predicted based on the failure physics model. _f(x) represents the predicted fatigue life; The optimization objective is to find the set of all possible component solutions x that cannot be surpassed by any other solution at the same time in terms of both objectives f1(x) and f2(x), i.e., the Pareto optimal solution set; Hard constraints include at least one or more of the following categories: Process feasibility constraints, immediate physical failure constraints, and regulatory and cost constraints Process feasibility constraints:

[0056] Instantaneous physical failure constraints (calculated based on the physical model):

[0057] (The interfacial energy release rate must not exceed its fracture toughness across all possible operating temperature rise ranges.)

[0058] 3. Regulatory and cost constraints:

[0059] (b) By optimizing the acquisition function within the design space, recommend one or more candidate component points x that maximize the acquisition function value. The candidate points are new component points obtained by searching the continuous design space; By optimizing the acquisition function within the design space, a numerical optimization algorithm is used to search for one or more candidate component points x that maximize the acquisition function value. The candidate points are new component points searched from the continuous design space; for batch recommendation, a penalized logarithmic determinant point process is used to select multiple points from regions with high acquisition function values ​​to ensure that the candidate points have diversity in the design space and the predicted target space. (c) For the recommended candidate component point x Conduct physical experiments, design differentiated test schemes based on the predicted characteristics of each candidate point, and obtain experimental data corresponding to the indicators of at least the macroscopic characterization dimension in step 1. For the recommended candidate component point x Conduct experiments and design differentiated test schemes based on the prediction characteristics of each candidate point to obtain experimental data corresponding to at least the macroscopic representation dimension in step 1. For points with high prediction feasibility probability but large uncertainty, focus on testing their long-term lifetime or performance degradation curves. For points predicted to be at the boundary of the feasible domain, focus on testing to verify key constraints. (d) Add the newly acquired experimental data to the database of step 2, and retrain the hierarchical probabilistic mixture model using the updated database to update the model parameters and obtain an updated version of the prediction model; wherein, the retraining includes updating the posterior distribution of key physical parameters in the second-layer model through Bayesian inference. (e) Repeat steps (a) to (d) until the preset convergence condition is met; The hierarchical probabilistic mixture model is retrained using the updated database to update the model parameters and obtain an updated version of the prediction model. The retraining includes: refitting the first-layer Gaussian process regression model with new data and optimizing the kernel function hyperparameters using maximum marginal likelihood estimation; and updating the posterior distribution of key physical parameters in the second-layer Bayesian network through Bayesian inference (such as the Markov chain Monte Carlo method). Determine whether the preset convergence condition is met. If it is met, terminate the iteration and proceed to step 5; otherwise, return to sub-step (a) for the next iteration. The convergence condition includes one or more of the following: The improvement rate of the hypervolume metric at the Pareto front is less than the first threshold in consecutive iterations. The maximum constraint violation probability of all non-dominated solutions on the current Pareto front is below the second threshold; The average relative standard deviation of the predictions for each solution on the Pareto front is below the third threshold; Step 5: After iteration, a trained hierarchical probabilistic mixture model is obtained, which can quickly and accurately predict the values ​​of each dimension index of any component x corresponding to Step 1. At the same time, using the data accumulated during the iteration process and the model prediction results, the Pareto solution set of the optimal component scheme of the thermally conductive composite material that satisfies all hard constraints and achieves the optimal trade-off on the multi-objective optimization function is output, as well as the design map reflecting the distribution law of performance and reliability in the design space. The trained model can be used as a material design tool to receive new component x input by the user and output its performance and reliability prediction results in real time.

[0060] Example 2 A co-design system for the performance and reliability of thermally conductive composite materials, comprising: The indicator system construction module is used to construct an indicator system with the service reliability of thermally conductive composite materials as the core objective. The system includes at least the service performance dimension, the macroscopic characterization dimension, and the microscopic mechanism dimension. The database construction module is used to vectorize the thermally conductive composite material formulation parameters into design variables x, and construct a multi-source heterogeneous database containing the correspondence between design variables x and at least some of the dimension index values ​​in step 1. The model building and initialization training module is used to build a hierarchical probabilistic hybrid model consisting of a first-layer Gaussian process regression model and a second-layer Bayesian network. The model is initialized and trained using a database to obtain an initial prediction model with the design variable x as input and the predicted values ​​of each dimension index as output. The iterative optimization module is used as a starting point to continuously train the model through multiple rounds of iteration. Each round of iteration includes recommending candidate points based on the current model, conducting experimental verification of the candidate points, adding new data to the database, and retraining the model with the updated database to obtain an updated version, until the convergence condition is met. The output module is used to obtain the trained prediction model after iteration and output the Pareto solution set of the optimal composition scheme of thermally conductive composite material that meets the preset optimization objective.

[0061] It should be noted that, in the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another device, or some features may be ignored or not executed. The modules described as separate components may or may not be physically separated. The components shown as modules may be one or more physical units, that is, they may be located in one place or distributed in multiple different places. Some or all of the modules can be selected to achieve the purpose of the solution in this embodiment according to actual needs.

[0062] Furthermore, in the various embodiments of the present invention, the modules can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The integrated unit described above can be implemented in hardware or as a software functional unit.

[0063] An electronic device provided in this application includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the co-design method for the performance and reliability of thermally conductive composite materials as described in any of the above embodiments.

[0064] Another electronic device provided in this application embodiment may further include: an input port connected to a processor for transmitting multimodal data collected by an external acquisition device to the processor; a display unit connected to the processor for displaying the processor's processing results to the outside world; and a communication module connected to the processor for enabling communication between the electronic device and the outside world. The display unit may be a display panel, a laser scanning display, etc.; the communication method adopted by the communication module includes, but is not limited to, Mobile High Definition Link (HML), Universal Serial Bus (USB), High Definition Multimedia Interface (HDMI), and wireless connection (including Wi-Fi, Bluetooth, Bluetooth Low Energy, and IEEE 802.11s-based communication technology).

[0065] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the steps of the co-design method for the performance and reliability of thermally conductive composite materials as described in any of the above embodiments.

[0066] For descriptions of relevant parts in the co-design system, electronic device, and computer-readable storage medium for the performance and reliability of thermally conductive composite materials provided in this application, please refer to the detailed descriptions of the corresponding parts in the co-design method for the performance and reliability of thermally conductive composite materials provided in this application, which will not be repeated here. Furthermore, parts of the technical solutions provided in this application that are consistent with the implementation principles of corresponding technical solutions in the prior art have not been described in detail to avoid excessive elaboration.

[0067] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for the co-design of performance and reliability of thermally conductive composite materials, characterized in that, Includes the following steps: Step 1: Construct an indicator system with the service reliability of thermally conductive composite materials as the core objective. The system shall include at least the service performance dimension, the macroscopic characterization dimension, and the microscopic mechanism dimension. Step 2: Vectorize the thermally conductive composite material formulation parameters into design variables x, and construct a multi-source heterogeneous database containing the correspondence between design variables x and at least some of the dimensional index values ​​in Step 1; Step 3: Establish a hierarchical probabilistic hybrid model consisting of a first-layer Gaussian process regression model and a second-layer Bayesian network. Use the database to initialize and train the model to obtain an initial prediction model with the design variable x as input and the predicted values ​​of each dimension index as output. Step 4: Starting with the obtained initial prediction model, continuously train the model through multiple rounds of iteration. Each round of iteration includes recommending candidate points based on the current model, conducting experimental verification of the candidate points, adding new data to the database, and retraining the model with the updated database to obtain an updated version, until the convergence condition is met. Step 5: After the iteration is completed, the trained prediction model is obtained, and the Pareto solution set of the optimal composition scheme of the thermally conductive composite material that meets the preset optimization objective is output.

2. The method for co-designing the performance and reliability of thermally conductive composite materials according to claim 1, characterized in that, The service performance dimension mentioned in step 1 includes service life or service performance retention rate, which serves as the final optimization target of the collaborative design; The macroscopic characterization dimensions include laboratory-measurable thermal conductivity, coefficient of thermal expansion, and accelerated aging test indicators, which serve as the basis for experimental verification and model calibration. The microscopic mechanism dimension includes simulable computational parameters that connect material formulation and macroscopic properties, serving as the physical core for revealing failure mechanisms and achieving reliable design.

3. The method for co-designing the performance and reliability of thermally conductive composite materials according to claim 1, characterized in that, The construction of the multi-source heterogeneous database includes: Collect historical experimental data to obtain data pairs {xj, yj}, where yj contains at least the initial thermal conductivity and one data point on performance degradation after accelerated aging or fatigue. Physical simulations are run at representative points in the design space to obtain their micro-stress field, heat flow field, and micro-mechanism dimension indicators. Failure modes, empirical values ​​of interface strength, and aging kinetic parameters of similar material systems are extracted from publicly available literature and used as constraints for the prior distribution of the model.

4. The method for co-designing the performance and reliability of thermally conductive composite materials according to claim 1, characterized in that, The first-layer Gaussian process regression model uses the Matern 5 / 2 kernel function, and its mean function is embedded with the calculation results of the improved Maxwell-Garnett model as the physical prior. The second-layer Bayesian network is constructed based on the physical relationship of failure. It includes Weibull distribution nodes describing crack initiation and Paris law nodes describing crack propagation. The key physical parameters in the network are assigned prior distributions based on literature or experience, and their posterior distributions can be updated by Bayesian inference using experimental data.

5. The method for co-designing the performance and reliability of thermally conductive composite materials according to claim 1, characterized in that, Step 4, which involves recommending candidate points based on the current model, includes: Based on the current version of the prediction model, a risk perception acquisition function is constructed that is defined over the entire design space. The acquisition function integrates the expected improvement of the candidate point relative to the multi-objective optimization function, the joint feasibility probability of satisfying hard constraints, and the uncertainty of the model prediction. By optimizing the acquisition function within the design space, one or more candidate component points that maximize the acquisition function value are recommended.

6. The method for co-designing the performance and reliability of thermally conductive composite materials according to claim 1, characterized in that, When constructing the risk perception acquisition function based on the current version of the prediction model, determine the multi-objective optimization function and hard constraints: The multi-objective optimization function includes at least the objective of maximizing thermal conductivity f1(x) and the objective of maximizing service reliability proxy index f2(x), so as to guide the search process toward the direction of synergistic optimization of thermal conductivity and service reliability; The hard constraints include at least one or more of the following: process feasibility constraints, instantaneous physical failure constraints, and regulatory and cost constraints, used to calculate the joint feasibility probability of a candidate point satisfying all hard constraints. By fusing the expected improvement of candidate points relative to the multi-objective optimization function and the joint feasibility probability of satisfying the hard constraints through the acquisition function, candidate component points with both high optimization potential and high feasibility are recommended, and finally, a Pareto optimal solution set that cannot be surpassed by other schemes on both objectives f1(x) and f2(x) is obtained.

7. The method for co-designing the performance and reliability of thermally conductive composite materials according to claim 1, characterized in that, In step 4, the convergence condition includes one or more of the following: The improvement rate of the hypervolume metric at the Pareto front is less than the first threshold in consecutive iterations. The maximum constraint violation probability of all non-dominated solutions on the current Pareto front is below the second threshold; The average relative standard deviation of the predictions for each solution on the Pareto front is below the third threshold.

8. A co-design system for the performance and reliability of thermally conductive composite materials, characterized in that, include: The indicator system construction module is used to construct an indicator system with the service reliability of thermally conductive composite materials as the core objective. The system includes at least the service performance dimension, the macroscopic characterization dimension, and the microscopic mechanism dimension. The database construction module is used to vectorize the thermally conductive composite material formulation parameters into design variables x, and construct a multi-source heterogeneous database containing the correspondence between design variables x and at least some of the dimension index values ​​in step 1. The model building and initialization training module is used to build a hierarchical probabilistic hybrid model consisting of a first-layer Gaussian process regression model and a second-layer Bayesian network. The model is initialized and trained using a database to obtain an initial prediction model with the design variable x as input and the predicted values ​​of each dimension index as output. The iterative optimization module is used as a starting point to continuously train the model through multiple rounds of iteration. Each round of iteration includes recommending candidate points based on the current model, conducting experimental verification of the candidate points, adding new data to the database, and retraining the model with the updated database to obtain an updated version, until the convergence condition is met. The output module is used to obtain the trained prediction model after iteration and output the Pareto solution set of the optimal composition scheme of thermally conductive composite material that meets the preset optimization objective.

9. A computer device, characterized in that, include: Processor and computer-readable storage media; The processor is adapted to execute computer programs; The computer-readable storage medium stores a computer program, which, when executed by the processor, implements the co-design method for the performance and reliability of thermally conductive composite materials as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and executed by the co-design method for the performance and reliability of thermally conductive composite materials as described in any one of claims 1-7.

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