Bayesian optimization method and system based on elite guidance and storage medium

Abstract

The application discloses an elite guide-based Bayesian optimization method, comprising the following steps: step 1, problem definition and initialization: defining input features: element composition, grain size and loading conditions, and defining an initial search range; defining optimization objectives: maximizing average fatigue life, minimizing life coefficient of variation and maximizing reliability; loading a pre-trained static weighted integrated model; step 2, Bayesian optimizer initialization: creating a Bayesian optimizer instance: selecting a Gaussian process GPmodel kernel function; setting boundaries: the initial range of the search space. The application has significant advantages in complex alloy material composition optimization through systematic integration of multi-dimensional performance evaluation, dynamic search strategy and intelligent optimization mechanism. Firstly, for the problem of multi-working condition performance robustness evaluation, all loading condition combinations are covered through full factorial experiment design, and the average fatigue life, life coefficient of variation and reliability index are innovatively defined.

Description

Technical Field

[0001] This invention relates to the field of interdisciplinary technology of intelligent optimization and materials design, specifically to an elite-guided Bayesian optimization method, system, and storage medium. Background Technology

[0002] In the design of advanced alloy materials, it is necessary to simultaneously optimize the material's multi-dimensional performance, including fatigue life, life fluctuation, and reliability under various operating conditions. Since the alloy's composition, average grain size, and loading conditions together constitute an extremely high-dimensional search space, its solution domain is not only vast but may also contain numerous local optima. This leads to challenges for optimization algorithms in finding the global optimum or near-global optimum, including difficulties in convergence or excessively slow convergence speed. The root cause of this problem lies in the complex nonlinear mapping relationship between material properties and multi-dimensional variables. Although our current predictive model has high accuracy, when it is embedded as the optimization objective function in the optimization process, each performance evaluation implies a time-consuming model inference. While a traditional global optimization algorithm might offer a chance of finding an optimal solution through a "blind" global search, the sheer number of times the prediction model needs to be invoked results in an prohibitively high computational cost, leading to inefficient convergence. Conversely, using gradient-based algorithms for faster convergence can easily trap the algorithm in local optima due to the complexities of the search space, prematurely terminating the search and compromising the optimality of the final solution—a risk to convergence. The challenge in resolving this dilemma lies in finding a delicate balance between "exploration" and "utilization": ensuring the algorithm has the capacity to escape local optima and broadly explore different regions of the solution space, while simultaneously focusing precisely on promising neighborhoods for a rapid approach to the global optimum.

[0003] Existing technologies face systemic challenges in optimizing alloy material composition under complex working conditions. These challenges stem from inherent limitations of traditional methods and data-driven models, as well as the imperfections in optimization strategies and hybrid mechanisms, which fail to meet the demands for high efficiency and accuracy. Traditional experimental methods, such as trial-and-error and orthogonal experiments, are extremely inefficient due to their reliance on experience. Trial-and-error methods require massive numbers of experiments and are prone to getting trapped in local optima, while orthogonal experiments, although scaled down, still cannot cover high-dimensional sparse regions. Theoretical calculations, such as CALPHAD and first-principles calculations, are limited by mechanistic assumptions and computational resources. CALPHAD lacks accuracy in predicting non-equilibrium phase transitions, and DFT is only applicable to nanoscale systems with few variables, making it difficult to support engineering design. While data-driven machine learning surrogate models can replace expensive experiments, they suffer from a contradiction between interpretability and generalization: traditional models such as random forests and SVMs have limited ability to capture high-dimensional nonlinear coupling relationships, and deep neural networks rely on massive amounts of labeled data and have poor interpretability. Furthermore, existing models are mostly trained for single working conditions and cannot directly integrate multi-dimensional performance indicators such as average lifetime, coefficient of variation, and reliability under multiple loading conditions, making it difficult to support robust optimization.

[0004] The shortcomings of optimization algorithms and hybrid methods further exacerbate the complexity of the problem. While Bayesian optimization can balance exploration and development, its fixed contraction strategy (such as static contraction coefficient) leads to the early omission of potential regions and inefficient convergence in later stages, and it fails to fully utilize the information of elite individuals generated during iteration to correct model biases. Evolutionary algorithms tend to converge prematurely in high-dimensional spaces due to the loss of population diversity, while gradient optimization heavily relies on the selection of initial points and is prone to getting trapped in local optima. Hybrid methods attempt to integrate experimentation, computation, and machine learning, but they face challenges such as broken data loops and difficulties in multi-scale coordination: the distribution of theoretical calculations and real experimental data deviates significantly, and high experimental costs limit high-frequency iteration; multi-scale optimization needs to solve the scale bridging problem from atomic scale to macroscopic performance, and existing methods lack a unified feature fusion framework, resulting in insufficient utilization of multi-scale information. These limitations collectively restrict the efficient and accurate optimization of the composition of complex alloy materials, urgently requiring breakthrough methods to address them. Summary of the Invention

[0005] The purpose of this invention is to provide an elite-guided Bayesian optimization method, system, and storage medium to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: an elite-guided Bayesian optimization method, comprising the following steps:

[0007] Step 1, Problem Definition and Initialization:

[0008] Define the input features: elemental composition, grain size, and loading conditions, and define the initial search range;

[0009] Define the optimization objectives as follows: maximize mean fatigue life, minimize the coefficient of variation of life, and maximize reliability;

[0010] Load the pre-trained static weighted ensemble model;

[0011] Step 2, Bayesian optimizer initialization:

[0012] Create a Bayesian optimizer instance: Select the Gaussian process GPmodel kernel function;

[0013] Set boundaries: the initial range of the search space;

[0014] Step 3: Initial sample evaluation performed only in the first 3 rounds:

[0015] Generate the input matrix, i.e., generate the input feature matrix: elemental composition, grain size, and loading conditions;

[0016] Use the ensemble model to predict fatigue life;

[0017] Calculate performance metrics: mean fatigue life, coefficient of variation of life, and reliability;

[0018] Calculate the overall score;

[0019] Record the comprehensive score evaluation results as the initial training set for GP;

[0020] Step 4, Iterative optimization loop: (The following operations must be performed in each round)

[0021] 401. Generate candidate sample points:

[0022] For the first 3 iterations: take points from the initial sample pool (generated by Latin hypercube) of the Bayesian optimizer;

[0023] Otherwise: start optimization from random points, avoid local optima, maximize the acquisition function (EI), and obtain the next candidate point;

[0024] 402. Parallel evaluation of candidate samples:

[0025] Repeat step 3 for each candidate point;

[0026] Filter out invalid results, such as model prediction errors, and retain valid samples;

[0027] 403. Update the Gaussian process model:

[0028] Add the x (elemental composition and grain size) and y (overall score) of the valid samples to the GP training set;

[0029] Retrain the GP;

[0030] 404. Selecting Elite Teams:

[0031] Grouping by loading conditions: All candidate samples are divided into n_loading groups according to loading conditions. If there are three loading conditions, then n_loading is the product of the number of cases under each loading condition, n1*n2*n3.

[0032] The top 100 high-life samples from each group are selected, sorted in descending order of fatigue life, and the Top 100 are selected.

[0033] Summarize the Top 100 of all groups: the top 2 combinations with the highest statistical frequency are used as elite combinations to update the search scope in the future;

[0034] 405. Dynamically shrink the search range:

[0035] Calculate the shrinkage coefficient, which can be a fixed coefficient or an exponential cooling type variation coefficient;

[0036] Update element range: For each feature in the two elite combinations, multiply the larger value by the shrinkage coefficient and divide the smaller value by the shrinkage coefficient to form new upper and lower bounds for optimization;

[0037] 406. Convergence Check and Termination:

[0038] Check the original convergence conditions: whether the differences in each parameter of the elite combination, namely elemental composition and grain size, are less than the preset threshold;

[0039] Check the Bayesian convergence criteria: the prediction variance of the optimal points for three consecutive rounds is less than 1% of the original range average, and the parameter change of the optimal points for three consecutive rounds is less than 5%;

[0040] The iteration terminates when any convergence condition is met or the maximum number of iterations is reached.

[0041] Step 5: Saving and Outputting Results

[0042] Save the best combination for each round: elemental composition, grain size, overall score, average lifetime, coefficient of variation, and reliability;

[0043] Save the globally optimal combination: the combination with the highest overall score during the iteration process;

[0044] The final output includes elemental composition, grain size, performance indicators, and optimization history.

[0045] Within the dynamic shrinkage search range, the fixed shrinkage coefficient method employs a constant shrinkage ratio throughout the entire process. =1.2, converges quickly and requires no additional parameter tuning. In contrast, the simulated annealing variable coefficient method borrows the exponential cooling mechanism of simulated annealing, where the shrinkage coefficient dynamically decays with the number of iterations. The specific formula is as follows:

[0046]

[0047] Indicates the number of iterations. Indicates the initial shrinkage coefficient. Indicates the final shrinkage coefficient. Indicates the cooling rate. This indicates the exponential cooling term.

[0048] In the first three iterations, the initial samples are taken from the initial sample pool of the Bayesian optimizer, and the pre-trained static weighted ensemble model is called to make predictions based on the exponential lifetime prediction results. Based on these prediction results, for any candidate material, its three core performance indicators under various loading conditions are calculated: average fatigue life, lifetime variation coefficient, and reliability index.

[0049] In the fourth iteration, sample points are generated by a Bayesian optimizer. This optimizer learns the mapping relationship between historical sample points and comprehensive scores based on Gaussian process regression. It finds the next evaluation point by maximizing the expectation to improve the acquisition function, balancing the exploration of unknown regions with the utilization of high-scoring regions. The evaluation process for new sample points is the same as the previous three rounds: generating the input matrix, ensemble model prediction, calculating performance indicators and comprehensive scores. The standardized benchmark for the comprehensive score is still the maximum average lifetime of the current iteration, ensuring the dynamic adaptability of the score. After each iteration, elite combination screening and range narrowing are still performed, while tracking the global best combination. If the comprehensive score of the top combination in the current iteration is higher than the historical best, the best combination and the best score are updated.

[0050] An elite-guided Bayesian optimization system includes:

[0051] Memory, used to store instructions;

[0052] A processor for executing the instructions, causing the device to perform operations that implement an elite-guided Bayesian optimization method.

[0053] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements an elite-guided Bayesian optimization method.

[0054] Compared with the prior art, the beneficial effects of the present invention are:

[0055] This invention demonstrates significant advantages in optimizing the composition of complex alloy materials by systematically integrating multi-dimensional performance evaluation, dynamic search strategies, and intelligent optimization mechanisms.

[0056] Firstly, addressing the challenge of evaluating the robustness of performance under multiple operating conditions, a full-factor experimental design was used to cover all combinations of loading conditions. Furthermore, the mean fatigue life, life variation coefficient, and reliability index were innovatively defined. The material performance was quantified from three dimensions: overall performance, volatility, and quantiles. This approach overcomes the limitations of traditional methods that rely on optimizing a single index, and achieves a comprehensive characterization of the material's service robustness.

[0057] Secondly, it has outstanding multi-objective optimization integration capabilities. The comprehensive scoring function eliminates dimensional differences through normalization and dynamically integrates normalized lifetime, stability factor and reliability index in the form of product, transforming multi-objectives into single-objective optimization problems. Moreover, the normalization benchmark is dynamically updated with iteration, ensuring that the score always matches the current optimal solution and significantly improving the accuracy of the optimization direction.

[0058] Third, the search strategy achieves an efficient balance between exploration and development. Bayesian optimization relies on the Gaussian process surrogate model to accurately capture the trend and uncertainty of the component-performance mapping. It combines expected improvement and upper confidence limit acquisition function to balance the exploration of unknown regions and the utilization of high-scoring regions. At the same time, it introduces an elite-guided dynamic contraction mechanism. By selecting high-frequency elite individuals as the search benchmark, it adopts an exponentially cooled dynamic contraction coefficient to dynamically adjust the boundary of the search space. It avoids local optima in the early stage and accelerates convergence in the later stage, breaking through the efficiency bottleneck of fixed contraction strategy.

[0059] Fourth, the convergence robustness is significantly enhanced. By tracking the global optimal combination, identifying high-frequency elite groups, and implementing triple termination conditions (elite individual parameter differences, model prediction accuracy, and number of iterations), it avoids misjudging convergence due to slow score improvement, thus ensuring the global optimality and stability of the output solution.

[0060] In summary, this method significantly reduces computational costs in high-dimensional alloy composition space, while also improving fatigue life and reducing life fluctuations, successfully achieving precise optimization and efficient design of material properties under complex working conditions. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the iterative process of the present invention;

[0062] Figure 2 This is a comparison chart of the prediction performance of a single model and an ensemble model in this invention;

[0063] Figure 3 This is a schematic diagram of the prediction error distribution corresponding to the shrinkage boundary optimization results of the present invention. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] Please see Figure 1-3 This invention provides a technical solution: a Bayesian optimization method, system, and storage medium based on elite guidance, such as... Figure 1 As shown, the elite-guided Bayesian optimization system of this invention is a systematic and iterative process.

[0066] The design variables encompassed the composition percentages and average grain sizes of 12 key alloying elements. A 13-dimensional initial sample was generated using quasi-Monte Carlo Latin hypercube sampling, while the composition vector was normalized to ensure that the sum of the 12 elements was 100%. Furthermore, to comprehensively evaluate the robustness of the material properties, external loading conditions (including maximum stress, minimum stress, and temperature) were combined through a full-factor experimental design, thereby ensuring that the optimization process covered all possible operating conditions.

[0067] The optimization objective is to simultaneously maximize the average fatigue life of the material, minimize its life fluctuations, and maximize performance reliability.

[0068] Based on prior knowledge, an initial search range was set for each variable, which includes the minimum and maximum values, forming the initial design space.

[0069] In the first three iterations, the initial samples are taken from the initial sample pool (generated by Latin hypercube) of the Bayesian optimizer. A pre-trained statically weighted ensemble model is then used to make predictions based on the exponential lifetime prediction results. Based on these predictions, for any candidate material... Calculate its in Three core performance indicators under various loading conditions: the first is average fatigue life, which measures the overall performance of the material.

[0070]

[0071] in This represents the total number of load conditions. Material In loading conditions The first is fatigue life. The second is the life variation coefficient, which is used to evaluate the fluctuation of material properties under different working conditions; the lower the value, the higher the stability.

[0072]

[0073] Thirdly, reliability metrics are defined as the proportion of samples whose lifespan exceeds its first quartile, used to measure the robustness of performance:

[0074]

[0075] in, For indicator functions, Lifetime vector The first quartile. To achieve the transformation from multi-objective to single-objective, this study constructs a comprehensive scoring function that normalizes and weights the above three indicators, and fuses them using a product form, thereby assigning a unique comprehensive score to each candidate material combination. This function weights and integrates the above three indicators, first normalizing the average lifetime in the current iteration batch to eliminate dimensions:

[0076]

[0077] The normalized lifetime, stability factor (negatively correlated with the coefficient of variation), and reliability index are then combined using a product formula:

[0078]

[0079] in, , and All scores are assigned a pre-defined weight. The scoring system integrates three dimensions: average lifetime, stability, and reliability. Ultimately, each candidate material combination receives a comprehensive score, and the combination with the highest score is recorded. This record is updated in each iteration.

[0080] These initial samples with comprehensive scores constitute the training set of the Gaussian process surrogate model. Subsequently, in each iteration, the surrogate model is based on the existing dataset. Construct the objective function The posterior distribution:

[0081]

[0082] Its mean function reflects the approximate trend of the objective function, while the covariance function (such as the Matern kernel) characterizes the prediction uncertainty. The mean function and the covariance function are respectively:

[0083]

[0084]

[0085] in, For the Matern kernel function, For noise variance, , Bayesian optimization balances "exploration" and "development" through a collection function, with common strategies including Expected Improvement (EI) and Upper Confidence Bound (UCB). Maximizing the collection function is used to determine new candidate points, whose performance, evaluated by the true objective function, is added to the training set to update the parameters and posterior distribution of the Gaussian process surrogate model. Let the current optimal observation be... Then a certain point The desired improvement is:

[0086]

[0087] Its closed-form expression is:

[0088]

[0089] in:

[0090]

[0091] and These are the cumulative distribution function and probability density function of the standard normal distribution, respectively. The formula for calculating UCB is:

[0092]

[0093] in, To develop the coefficients for the trade-offs, in each iteration, maximizing the acquisition function determines new candidate points, which are then evaluated against the true objective function. The resulting new samples are added to the training set, thereby updating the parameters and posterior distribution of the Gaussian process model.

[0094] In the core part of the optimization algorithm, this study proposes an elite-guided iterative shrinkage loop. This framework uses Bayesian optimization as the guiding mechanism, gradually focusing on the search region during the iteration process. Specifically, after completing the evaluation of the current iteration, the top 100 combinations of fatigue life under each loading condition are first counted. Then, the top 100 combinations under all conditions are summarized, and the two combinations with the highest frequency are selected as the benchmark for the next round of search space shrinkage. The boundary shrinkage strategy of the search space is the core mechanism for balancing global exploration and local utilization and avoiding local optima. Its design rationality directly determines the efficiency and solution quality of the optimization algorithm. This paper systematically compares and analyzes two typical paradigms of boundary shrinkage coefficients: fixed shrinkage coefficient and simulated annealing variable coefficient. The fixed shrinkage coefficient method uses a constant shrinkage ratio DYNCOEF=1.2 throughout the process, which converges quickly and does not require additional parameter tuning. In contrast, the simulated annealing variable coefficient method borrows the exponential cooling mechanism of simulated annealing, and the shrinkage coefficient dynamically decays with the number of iterations, as shown in the following formula:

[0095]

[0096] Indicates the number of iterations. Indicates the initial shrinkage coefficient. Indicates the final shrinkage coefficient. Indicates the cooling rate. This represents the exponential cooling term. In the specific implementation, the larger value of the composition and grain size is multiplied by the dynamic shrinkage coefficient of the current iteration as a new upper bound, and the smaller value is divided by the dynamic shrinkage coefficient as a new lower bound, forming a new optimization search range. This allows for rapid convergence to the promising region in the early stages and fine-grained search in the later stages, effectively balancing the contradiction between exploration and development.

[0097] Starting from the fourth iteration, sample points are generated by a Bayesian optimizer. This optimizer learns the mapping relationship between historical sample points and comprehensive scores based on Gaussian process regression. It finds the next evaluation point by maximizing the expected value to improve the acquisition function, balancing the exploration of unknown regions with the utilization of high-scoring regions. The evaluation process for new sample points is consistent with the previous three rounds: generating the input matrix, ensemble model prediction, calculating performance metrics and comprehensive scores. The standardized benchmark for the comprehensive score remains the maximum average lifetime of the current iteration, ensuring the dynamic adaptability of the score. After each iteration, elite combination screening and range narrowing are still performed, while tracking the globally best combination. If the comprehensive score of the top combination in the current iteration is higher than the historical best, the best combination and the best score are updated. Convergence detection combines the dimensional differences of the top combinations and the identification of high-frequency combinations. Even if the improvement in the comprehensive score is not significant, the repeated appearance of high-frequency combinations reflects that the optimization has entered a stable region, enhancing the robustness of convergence judgment.

[0098] The iteration termination condition employs a triple criterion: convergence is considered achieved when the difference between elite individuals in the parameter space is below the convergence threshold; or convergence is considered achieved when the variance of the optimal point is sufficiently small and the optimal point position is stable for multiple consecutive rounds, i.e., the standard deviation of the Bayesian model's prediction of the optimal point is less than 1% of the average of the original parameter range and the parameter change of the optimal point recommended by the Bayesian model for three consecutive rounds is less than 5%; or termination is forcibly achieved when the maximum number of iterations is reached, ultimately outputting the global optimal solution. In summary, this optimization framework, through the exploration-expansion balance of Bayesian optimization and the dynamic contraction mechanism guided by elites, achieves a balance between global approximation and efficiency, enabling it to rapidly approach the optimal solution in complex multi-condition material design spaces.

[0099] In summary, this optimization framework covers the global search space through initial Latin hypercube sampling, provides reliable performance predictions through ensemble models, integrates multi-dimensional performance indicators through comprehensive scoring, guides sample points to move towards high-potential regions through Bayesian optimization, and gradually focuses the optimization direction through dynamic range shrinkage. The first three rounds complete the framework initialization and basic learning, and subsequent iterations achieve efficient convergence through Bayesian guidance and range shrinkage, ultimately obtaining the required combination of material composition and grain size. This process avoids the high computational cost of global search and overcomes the premature convergence problem of local optimization, providing an effective solution for the collaborative optimization of complex material systems.

[0100] The specific steps are as follows:

[0101] Step 1: Problem Definition and Initialization

[0102] Define the input features (composition, grain size, loading conditions, etc.) and define the initial search range;

[0103] Define the optimization objectives as follows: maximize average fatigue life, minimize the coefficient of variation of life, and maximize reliability;

[0104] Load the pre-trained static weighted ensemble model;

[0105] Step 2: Bayesian optimizer initialization

[0106] Create a Bayesian optimizer instance: Select the Gaussian process (GPmodel) kernel function;

[0107] Set boundaries: the initial range of the search space;

[0108] Step 3: Initial Sample Evaluation (Executed only in the first 3 rounds)

[0109] Generate the input matrix, that is, generate the input feature matrix (composition-grain size-loading conditions, etc.).

[0110] Use the ensemble model to predict fatigue life;

[0111] Calculate performance indicators: mean fatigue life, coefficient of variation of life, and reliability;

[0112] Calculate the overall score;

[0113] Record the comprehensive score evaluation results as the initial training set for GP;

[0114] Step 4: Iteratively optimize the loop (the following operations must be performed in each round)

[0115] 401: Generate candidate sample points

[0116] For the first 3 iterations: take points from the initial sample pool (generated by Latin hypercube) of the Bayesian optimizer;

[0117] Otherwise: start optimization from random points, avoid local optima, maximize the acquisition function (EI), and obtain the next candidate point.

[0118] 402: Parallel evaluation of candidate samples

[0119] Repeat step three for each candidate point: generate input matrix - model prediction - calculate performance metrics - comprehensive score;

[0120] Filter out invalid results (such as model prediction errors) and retain valid samples;

[0121] 403: Updating the Gaussian Process Model

[0122] Add the x (composition-grain) and y (overall score) of the valid samples to the GP training set;

[0123] Retrain the GP;

[0124] 404: Selecting Elite Teams

[0125] Grouping by loading conditions: All candidate samples are divided into n_loading groups according to loading conditions (if there are three loading conditions, then n_loading is the product of the number of cases under each loading condition, n1*n2*n3).

[0126] The top 100 high-life samples from each group are selected, sorted in descending order of fatigue life, and the Top 100 are selected.

[0127] The top 100 from all groups are summarized: the two most frequent combinations are used as elite combinations to update the search scope later.

[0128] 405: Dynamically shrink the search range

[0129] Calculate the shrinkage coefficient (which can be a fixed coefficient or an exponential cooling type variation coefficient).

[0130] Update element range: For each feature in the two elite combinations, multiply the larger value by the shrinkage coefficient and divide the smaller value by the shrinkage coefficient to form new upper and lower bounds for optimization;

[0131] 406: Convergence Check and Termination

[0132] Check the original convergence conditions: whether the differences in each parameter (elemental composition, grain size) of the elite combination are less than the preset threshold;

[0133] Check the Bayesian convergence criteria: The prediction variance σ of the optimal points for three consecutive rounds is less than 1% of the original range mean. The parameter variation of the optimal points for three consecutive rounds is less than 5%.

[0134] The iteration terminates when any convergence condition is met or the maximum number of iterations is reached.

[0135] Step 5: Saving and Outputting Results

[0136] Save the best combination for each round: composition, grain size, overall score, average lifetime, coefficient of variation, and reliability.

[0137] Save the globally optimal combination: the combination with the highest overall score during the iteration process.

[0138] The final output includes composition, grain size, performance indicators, and optimization history.

[0139] The "integrated model" of this invention is a statically weighted integration of the ET model and the GBM model, and is deployed locally. This patent only uses this model as an example. Any high-performance prediction model can be nested into this optimization method.

[0140] Figure 2 This compares the prediction performance of individual models with that of ensemble models. Figure 2 Figure 'a' shows the fitting performance of the ET model on the training set. Approximately 99% of the data points fall within the 3-fold dispersion band, and 94.8% of the data points are within the 2-fold dispersion band, indicating that the model has high prediction accuracy. Figure 2 In Figure b, the GBM model performs well on the training data. The scatter plots are closely distributed around the 45° reference line, reflecting the model's strong fitting ability to the training data, especially its potential in high-dimensional, small-sample scenarios. Even with data spanning five orders of magnitude, the ensemble model effectively controls all prediction errors within a 3x dispersion band, with GBM playing a crucial role with a 53.1% weight, effectively integrating its core advantages.

[0141] The contraction boundary in the "elite-guided strategy" of this invention has two forms: a fixed value and an exponential cooling variation type described above. Both forms are within the scope of protection. The following is an application example of the fixed-value contraction boundary:

[0142] Figure 3 The value 'a' corresponds to the prediction error distribution based on the 1.2x shrinkage boundary optimization result. In this combination, the proportion of samples with predicted values ​​higher than experimental values ​​is 60.0%. Within the red area, the average improvement in predicted lifetime still reaches 141.8%, and the average positive improvement across all data is 73.1%. This indicates that this composition-grain structure has strong fatigue life enhancement potential and exhibits good predictive performance and stability under a wide range of service conditions.

[0143] Figure 3In Figure 'b', the prediction error distribution corresponds to the result of optimization with a 1.3x shrinkage boundary. In this combination, the proportion of samples with predicted values ​​higher than experimental values ​​is 55.8%. Within the red area, the average improvement in predicted lifetime still reaches 188.1%, and the average positive improvement across all data is 91.6%. This indicates that compared to the composition-grain combination optimized with a 1.2x shrinkage boundary, this composition-grain combination offers a weaker improvement in fatigue lifetime, but still possesses a certain capacity for improvement and exhibits good stability under a wide range of service conditions.

[0144] This method can be directly applied to material composition optimization scenarios, or it can be packaged into a general program package and called by R&D personnel in different fields through standardized interfaces, thereby improving the automation and efficiency of material design under complex working conditions.

[0145] An elite-guided Bayesian optimization system includes:

[0146] Memory, used to store instructions;

[0147] A processor for executing the instructions, causing the device to perform operations that implement an elite-guided Bayesian optimization method.

[0148] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements an elite-guided Bayesian optimization method.

[0149] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

Claims

1. An elite-guided Bayesian optimization method, characterized in that, Includes the following steps: Step 1, Problem Definition and Initialization: Define the input features: elemental composition, grain size, and loading conditions, and define the initial search range; Define the optimization objectives as follows: maximize mean fatigue life, minimize the coefficient of variation of life, and maximize reliability; Load the pre-trained static weighted ensemble model; Step 2, Bayesian optimizer initialization: Create a Bayesian optimizer instance: Select the Gaussian process GPmodel kernel function; Set boundaries: the initial range of the search space; Step 3: Initial sample evaluation performed only in the first 3 rounds: Generate the input matrix, i.e., generate the input feature matrix: elemental composition, grain size, and loading conditions; Use the ensemble model to predict fatigue life; Calculate performance metrics: mean fatigue life, coefficient of variation of life, and reliability; Calculate the overall score; Record the comprehensive score evaluation results as the initial training set for GP; Step 4: Iteratively optimize the loop:

401. Generate candidate sample points: For the first 3 iterations: take points from the initial sample pool of the Bayesian optimizer; Otherwise: start optimization from random points to avoid local optima, maximize the sampling function EI, and obtain the next candidate point; 402. Parallel evaluation of candidate samples: Repeat step 3 for each candidate point; Filter out invalid results, such as model prediction errors, and retain valid samples; 403. Update the Gaussian process model: Add the x and y of the valid samples to the GP training set; Retrain the GP; 404. Selecting Elite Teams: Grouping by loading conditions: All candidate samples are divided into n_loading groups according to loading conditions. If there are three loading conditions, then n_loading is the product of the number of cases under each loading condition, n1*n2*n3. The top 100 high-life samples from each group are selected, sorted in descending order of fatigue life, and the Top 100 are selected. Summarize the Top 100 of all groups: the top 2 combinations with the highest statistical frequency are used as elite combinations to update the search scope in the future; 405. Dynamically shrink the search range: Calculate the shrinkage coefficient, which can be a fixed coefficient or an exponential cooling type variation coefficient; Update element range: For each feature in the two elite combinations, multiply the larger value by the shrinkage coefficient and divide the smaller value by the shrinkage coefficient to form new upper and lower bounds for optimization; 406. Convergence Check and Termination: Check the original convergence conditions: whether the differences in each parameter of the elite combination, namely elemental composition and grain size, are less than the preset threshold; Check the Bayesian convergence criteria: the prediction variance of the optimal points in three consecutive rounds is less than 1% of the original range average, and the parameter change of the optimal points in three consecutive rounds is less than 5%. The iteration terminates when any convergence condition is met or the maximum number of iterations is reached. Step 5: Saving and Outputting Results Save the best combination for each round: elemental composition, grain size, overall score, average lifetime, coefficient of variation, and reliability; Save the globally optimal combination: the combination with the highest overall score during the iteration process; The final output includes elemental composition, grain size, performance indicators, and optimization history.

2. The elite-guided Bayesian optimization method according to claim 1, characterized in that: Within the dynamic shrinkage search range, the fixed shrinkage coefficient method employs a constant shrinkage ratio throughout the entire process. =1.2, converges quickly and requires no additional parameter tuning. In contrast, the simulated annealing variable coefficient method borrows the exponential cooling mechanism of simulated annealing, where the shrinkage coefficient dynamically decays with the number of iterations. The specific formula is as follows: Indicates the number of iterations. Indicates the initial shrinkage coefficient. Indicates the final shrinkage coefficient. Indicates the cooling rate. This indicates the exponential cooling term.

3. The elite-guided Bayesian optimization method according to claim 1, characterized in that: In the first three iterations, the initial samples are taken from the initial sample pool of the Bayesian optimizer, and the pre-trained static weighted ensemble model is called to make predictions based on the exponential lifetime prediction results. Based on these prediction results, for any candidate material, its three core performance indicators under various loading conditions are calculated: average fatigue life, lifetime variation coefficient, and reliability index.

4. The Bayesian optimization method based on elite guidance according to claim 1, characterized in that: In the fourth iteration, sample points are generated by a Bayesian optimizer. This optimizer learns the mapping relationship between historical sample points and comprehensive scores based on Gaussian process regression. It finds the next evaluation point by maximizing the expectation to improve the acquisition function, balancing the exploration of unknown regions with the utilization of high-scoring regions. The evaluation process for new sample points is the same as the previous three rounds: generating the input matrix, ensemble model prediction, calculating performance indicators and comprehensive scores. The standardized benchmark for the comprehensive score is still the maximum average lifetime of the current iteration, ensuring the dynamic adaptability of the score. After each iteration, elite combination screening and range narrowing are still performed, while tracking the global best combination. If the comprehensive score of the top combination in the current iteration is higher than the historical best, the best combination and the best score are updated.

5. The elite-guided Bayesian optimization method according to claim 1, characterized in that: The comprehensive score normalizes and weights the three performance indicators, and then fuses them using a product form, thereby assigning a unique comprehensive score to each candidate material combination. The function is as follows: in, , and All materials are assigned a pre-defined weight. Each candidate material combination receives a comprehensive score, and the combination with the highest score is recorded. This record is updated in each iteration.

6. A Bayesian optimization system based on elite guidance, characterized in that: include: Memory, used to store instructions; A processor for executing the instructions, causing the device to perform operations implementing the elite-guided Bayesian optimization method as described in any one of claims 1-5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the elite-guided Bayesian optimization method as described in any one of claims 1-5.

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