A multi-objective safety Bayesian optimization method and device for material development, a computer device and a medium

Abstract

Embodiments of the present application provide a multi-objective safety Bayesian optimization method and device for material development, computer equipment and medium, which relates to the technical field of artificial intelligence, and the method comprises the following steps: constructing a model dataset through a material performance dataset and a safety sample dataset; training an integrated Gaussian process model, modeling a performance objective function and a constraint function, and generating a proxy model; through the proxy model and a safety domain judgment condition, evaluating whether a candidate point in a design space meets a safety constraint, saving the candidate point that meets the safety constraint to a safety domain to generate an expanded safety domain, evaluating the candidate point in the expanded safety domain, and selecting an optimal point as a test candidate point; correcting the value of the test candidate point based on the result of experimental testing, adding the corrected candidate point to the model dataset, training the proxy model through the model dataset, and iterating. The scheme realizes efficient optimization of multi-objective performance indicators through a multi-objective optimization strategy.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and in particular to a multi-objective safe Bayesian optimization method, apparatus, computer equipment, and medium for materials development. Background Technology

[0002] In fields such as high-performance materials research and development, complex manufacturing process optimization, and service reliability design, the mapping relationship between material composition, preparation process, and macroscopic properties is often highly nonlinear, strongly coupled, and difficult to analyze. Especially in high-end manufacturing systems such as high-temperature alloys, aluminum alloys, composite materials, and additive manufacturing metal materials, performance evaluation experiments are costly, time-consuming, and have a huge space of feasible parameters, making traditional experimental design and parameter optimization processes extremely inefficient.

[0003] Currently, for material performance optimization and design space search, academia and industry mainly adopt the following two technical approaches:

[0004] One approach is multi-objective optimization methods based on heuristic algorithms. Examples include genetic algorithms, particle swarm optimization (PSO), and differential evolution, which obtain approximate Pareto optimal solutions through repeated computation and simulation. However, these algorithms have significant limitations: firstly, they require repeated computation or experimentation in a large parameter space, resulting in extremely high computational and experimental costs; secondly, they cannot effectively handle experimental safety constraints (such as sample cracking, melt pool instability, and energy exceeding limits), and in the absence of knowledge of safety boundaries, they are prone to generating infeasible or dangerous design points, making them difficult to directly apply to high-cost experimental environments.

[0005] Secondly, there is the intelligent design method based on Bayesian optimization (BO). Bayesian optimization uses a surrogate model (usually a Gaussian process, GP) to model the objective function and guides the next sampling step through a sampling function, achieving global optimization with high sample efficiency. Although this method performs well in small sample optimization problems, existing research mainly focuses on single-objective or unconstrained cases. When facing common multi-objective trade-offs in materials design (such as strength versus ductility, thermal conductivity versus corrosion resistance) and safety constraints (such as process windows, equipment limits, and physical failure boundaries), traditional Bayesian optimization has the following key problems:

[0006] 1. Lack of safety modeling mechanisms. Conventional Bayesian optimization only focuses on improving performance objectives, ignoring the uncertainties of constraints, which may lead to equipment damage or sample failure in real experiments;

[0007] 2. Multi-objective optimization is inefficient. Existing multi-objective Bayesian optimization methods are mostly based on acquisition functions such as improved hypervolume (EHVI), but their computational complexity and search instability increase sharply when constraints exist;

[0008] 3. The safe region is difficult to expand adaptively. With limited early samples, the algorithm often overestimates the danger zone or gets trapped in a local safe region, leading to a shrinking search space and an inability to continuously explore new feasible solutions.

[0009] 4. Limited sampling strategies. Most methods still rely on fixed sampling functions or gridded candidate point sets, making it difficult to efficiently search for Pareto optimal points within complex, continuous, safe spaces.

[0010] In summary, existing multi-objective optimization techniques have significant shortcomings in small-sample, high-cost material design tasks under safety constraints: they either neglect safety, leading to high experimental risks, or they struggle to obtain globally effective Pareto fronts with limited samples. How to achieve efficient collaborative optimization of multi-objective performance and adaptive safety domain expansion while ensuring safety constraints has become a core scientific and engineering challenge that urgently needs to be overcome in the field of intelligent material design and optimization. Summary of the Invention

[0011] In view of this, embodiments of the present invention provide a multi-objective safety Bayesian optimization method for materials development to address the technical problems in existing technologies, such as the lack of a safety modeling mechanism, low efficiency of multi-objective optimization, difficulty in adaptively expanding the safety domain, and a single sampling strategy. The method includes:

[0012] A material performance dataset including material design parameters and performance data is constructed, a safety sample dataset including safety constraint indicators is constructed, a model dataset is constructed using the material performance dataset and the safety sample dataset, and a design space including the range of material design parameters is determined based on the optimization problem;

[0013] Using the material property dataset and the safety sample dataset, an ensemble Gaussian process model is trained to model the performance objective function and constraint function, generating a surrogate model.

[0014] Using the proxy model and security domain determination conditions, the candidate points in the design space are evaluated to see if they meet the security constraints. The candidate points that meet the security constraints are saved to the security domain to generate an expanded security domain. The candidate points in the expanded security domain are evaluated by a comprehensive multi-objective acquisition function, and the optimal point is selected as the test candidate point.

[0015] Experimental tests are conducted on the candidate test points. Based on the results of the experimental tests, the values ​​of the candidate test points are corrected to generate corrected candidate points. The corrected candidate points are then added to the model dataset. The surrogate model is trained and iterated using the model dataset until a pre-set iteration stopping condition is met, thereby generating a trained surrogate model.

[0016] This invention also provides a multi-objective safety Bayesian optimization device for materials development, addressing the technical problems of existing technologies such as lack of safety modeling mechanisms, low efficiency of multi-objective optimization, difficulty in adaptively expanding the safety domain, and limited sampling strategies. The device includes:

[0017] The dataset construction module is used to construct a material performance dataset including material design parameters and performance data, construct a safety sample dataset including safety constraint indicators, construct a model dataset using the material performance dataset and the safety sample dataset, and determine a design space including the range of material design parameters based on the optimization problem.

[0018] A proxy model construction module is used to train an ensemble Gaussian process model using the material property dataset and the safety sample dataset, model the performance objective function and constraint function, and generate a proxy model.

[0019] The module for obtaining test candidate points is used to evaluate whether the candidate points in the design space meet the safety constraints through the proxy model and the safety domain determination conditions, save the candidate points that meet the safety constraints to the safety domain, generate an extended safety domain, evaluate the candidate points in the extended safety domain through a comprehensive multi-objective acquisition function, and select the optimal point as the test candidate point.

[0020] The model iteration optimization module is used to conduct experimental tests on the test candidate points, correct the values ​​of the test candidate points based on the experimental test results, generate corrected candidate points, append the corrected candidate points to the model dataset, train and iterate the surrogate model through the model dataset until the convergence condition of the surrogate model is met, and generate the trained surrogate model.

[0021] This invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements any of the above-mentioned multi-objective safety Bayesian optimization methods for materials development, in order to solve the technical problems in the prior art, such as lack of safety modeling mechanism, low efficiency of multi-objective optimization, difficulty in adaptively expanding the safety domain, and single sampling strategy.

[0022] This invention also provides a computer-readable storage medium storing a computer program that executes any of the above-described multi-objective safe Bayesian optimization methods for materials development, in order to solve the technical problems in the prior art such as lack of a safety modeling mechanism, low efficiency of multi-objective optimization, difficulty in adaptively expanding the safety domain, and single sampling strategy.

[0023] Compared with the prior art, the beneficial effects that at least one technical solution adopted in the embodiments of this specification can achieve include at least:

[0024] By combining a safety assessment mechanism with a multi-objective optimization strategy, safe and efficient optimization of multi-objective performance indicators is achieved in high-risk or high-cost scenarios. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart of a multi-objective safe Bayesian optimization method for materials development provided in an embodiment of the present invention;

[0027] Figure 2 This is a flowchart illustrating an embodiment of the multi-objective safety Bayesian optimization method for materials development described above, provided by an embodiment of the present invention.

[0028] Figure 3 This is a structural block diagram of a computer device provided in an embodiment of the present invention;

[0029] Figure 4 This is a structural block diagram of a multi-objective safety Bayesian optimization device for materials development provided in an embodiment of the present invention. Detailed Implementation

[0030] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0031] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0032] The core idea of ​​this invention is as follows: A surrogate model framework based on an Ensemble Gaussian Process (GP) is used to jointly model the objective function and safety constraint function. A dynamic safety domain is defined using confidence lower bound (LCB) constraints and a Lipschitz continuity extension mechanism. Within this safety domain, efficient search and selection of candidate points are achieved based on multi-objective acquisition functions (such as EHVI and MOEI) and the Safe Particle Swarm Optimization (SafePSO) algorithm. In the early stage, the algorithm forms an initial safety domain through discrete candidate point evaluation. Later, based on Lipschitz continuity, it adaptively expands the continuously reachable safety domain, thereby realizing the dynamic evolution of the safety domain from local to global.

[0033] In this embodiment of the invention, a multi-objective safe Bayesian optimization method for materials development is provided, such as... Figure 1 As shown, the method includes:

[0034] Step S101: Construct a material performance dataset including material design parameters and performance data, construct a safety sample dataset including safety constraint indicators, construct a model dataset using the material performance dataset and the safety sample dataset, and determine a design space including the range of material design parameters based on the optimization problem;

[0035] Step S102: Using the material property dataset and the safety sample dataset, train an ensemble Gaussian process model to model the performance objective function and constraint function, and generate a surrogate model;

[0036] Step S103: Using the proxy model and security domain determination conditions, evaluate whether the candidate points in the design space meet the security constraints, save the candidate points that meet the security constraints to the security domain, generate the extended security domain, evaluate the candidate points in the extended security domain by integrating the multi-objective acquisition function, and select the optimal point as the test candidate point;

[0037] Step S104: Conduct experimental tests on the test candidate points, correct the values ​​of the test candidate points based on the experimental test results, generate corrected candidate points, add the corrected candidate points to the model dataset, train and iterate the surrogate model through the model dataset until the preset iteration stopping condition is met, and generate the trained surrogate model.

[0038] In specific implementation, the following steps are used to evaluate whether candidate points in the design space satisfy security constraints using the surrogate model and security domain determination conditions, and to save candidate points that satisfy the security constraints to the security domain: A sample threshold is set, and the security constraint determination process is divided into a discrete stage and a continuous stage based on the sample threshold; in the discrete stage, a security point determination method based on statistical confidence lower bound is used, and the surrogate model is used to predict the security constraint function of each candidate point in the design space to obtain the mean function of the candidate points. Sum of variance functions ,in, Candidate points; based on the lower confidence bound criterion, and the mean function and the variance function Calculate each of the candidate points security value ,in, Let be the mean of the safety constraint function. Let the standard deviation of the safety constraint function be . To control the confidence level as a constant; if the candidate point security value Greater than or equal to the safety threshold , will the current candidate point Included in security domain Where t is the iteration number; in the continuous phase, a safety point determination method based on Lipschitz continuity is used to predict the safety constraint function of each candidate point in the design space using the surrogate model, thereby obtaining the mean function of the candidate points. Sum of variance functions If the candidate point satisfy Then the candidate point The security domain is ,in, Belongs to the security domain Candidate points, for The mean, This is an estimate of the Lipschitz constant. For safety margin items, () is a mapping operator that uses the Lipschitz continuity principle to extrapolate and extend a confirmed set of discrete safe points into a continuously reachable safe region; based on the discrete stage safe region and the continuous stage security domain Build a security domain .

[0039] In specific implementation, the following steps are used to evaluate candidate points in the extended security domain using a comprehensive multi-objective acquisition function, and select the optimal point as the test candidate point: A sample threshold is set, and the sample sampling process is divided into discrete and continuous stages based on the sample threshold; an exploratory multi-objective acquisition function is constructed for the discrete stage, and a probability-weighted multi-objective security acquisition function is constructed for the continuous stage; the final comprehensive multi-objective security acquisition function is constructed using the exploratory multi-objective acquisition function and the probability-weighted multi-objective security acquisition function; in the discrete stage, a set of candidate sample points is obtained. ,in, x As candidate points, For the first i 1 candidate point i The candidate point number, This refers to the number of samples collected in the initial stage. The sample threshold for discrete patterns; through the candidate sample point set Define discrete security domains ,in, Candidate points Security value, t Candidate point number, The safety threshold is used; each candidate point is calculated using the exploratory multi-target acquisition function. The multi-target acquisition function value, and the candidate points are ranked according to the multi-target acquisition function value. The candidate points with the highest multi-objective acquisition function values ​​are sorted and selected as discrete experimental candidate points. The actual material target performance values ​​and / or safety constraint values ​​of these discrete experimental candidate points are obtained through material experiments or material calculations and saved to the training dataset of the surrogate model. In the continuous phase, a continuous reachable safety region is defined for the continuous phase. ,in, For security domains, For continuously reachable regions based on the Lipschitz extension, () is a mapping operator that uses the Lipschitz continuity principle to extrapolate and expand a confirmed discrete set of safe points into a continuously reachable safe domain. The sample threshold is used to determine whether a switch from the discrete stage to the continuous stage is needed. If so, the safe domains of the two modes are interpolated and fused using a smooth switching method to generate the expanded safe domain. ,in, To ensure a smooth transition step size, As weight, For transition rounds; a multi-objective safe particle swarm optimization algorithm is adopted in the continuously reachable safe domain. In the process, a global search is performed on the final multi-objective safety acquisition function to obtain the candidate point with the highest value of the multi-objective acquisition function as the continuous experimental candidate point. The actual material target performance value and / or safety constraint value of the continuous experimental candidate point are obtained through material experiments or material calculations and saved to the training dataset of the surrogate model.

[0040] In specific implementation, the following steps are used to determine whether it is necessary to switch from the discrete stage to the continuous stage based on the sample threshold:

[0041] Number of samples Greater than or equal to the sample threshold As a first condition; calculate the model uncertainty of the proxy model, and ensure that the model uncertainty is less than or equal to the prediction variance threshold. As a second condition; calculation t Estimate of the Lipschitz constant at time -1 and t Estimates of the Lipschitz constant at time t absolute value of the difference The absolute value is less than or equal to the Lipschitz convergence threshold. As a third condition, among which... The estimated value of the Lipschitz constant; satisfying any two of the first, second, and third conditions is used as the condition for switching from the discrete stage to the continuous stage.

[0042] In specific implementation, the following steps are used to construct an exploratory multi-target acquisition function for the discrete stage, a probability-weighted multi-target safety acquisition function for the continuous stage, and finally, a comprehensive multi-target safety acquisition function is constructed using the exploratory multi-target acquisition function and the probability-weighted multi-target safety acquisition function:

[0043] Calculate the probability of safety ,in, x As candidate points, Pr () represents the probability. g ( x ) is the input x The safety constraint function, The cumulative distribution function of the standard normal distribution. The prediction variance of the Gaussian process surrogate model. The mean of the predictions from the Gaussian process surrogate model; based on the stated security probability. Standard deviation of the prediction of the objective function Construct an exploratory multi-target acquisition function ,in, For the objective function At candidate point The predicted standard deviation at the given point; calculate the expected improvement of the multi-objective target. ,in, As a current cutting-edge hypervolume index in Pareto, For the current non-dominated solution set, The target function vector to be predicted. Candidate points The increment to the hypervolume index after being added to the current solution set, HV() is the hypervolume index calculation function; according to the aforementioned safety probability and multi-objective expectation improvement Construct a probability-weighted multi-target security acquisition function The final integrated multi-target safe acquisition function is constructed by combining the exploratory multi-target acquisition function with the probability-weighted multi-target safe acquisition function. ,in, This is an exploratory multi-target acquisition function. A probability-weighted multi-target security acquisition function. To adjust the weight of the algorithm between exploration and optimization capabilities based on user needs.

[0044] In specific implementation, the following steps are used to construct a material performance dataset including material design parameters and performance data, construct a safety sample dataset including safety constraint indicators, and construct a model dataset using the material performance dataset and the safety sample dataset:

[0045] Based on input parameters Compared with performance target value Construct a materials properties dataset, in which, For the first i A vector of design variables for an experimental or simulation sample. d For the dimensions of design parameters, For the first m One performance target value, M Dimensions for performance target values; construct a set of safety constraint parameters. ,in, As a safety constraint indicator, K The dimension of the constraint function; based on the set of security constraint parameters. Build the model dataset.

[0046] In specific implementation, the following steps are taken to achieve the goal based on the set of security constraint parameters. Build the model dataset:

[0047] Through the set of security constraint parameters Determine each sample in the material properties dataset. Safety constraint indicators Is it greater than or equal to the safety threshold? If so, save the sample to a safe sample set. ,in, , Let i be the safety classification label for the i-th sample. When the value is 1, the i-th sample satisfies the safety constraints. If the value is the actual value of the security constraint function corresponding to the i-th sample, then the sample is saved to the unsafe sample set. ,in, , Let i be the safety classification label for the i-th sample. When the value is 0, the i-th sample does not satisfy the safety constraint; the safe sample set is... and the aforementioned insecure sample set As a model dataset.

[0048] like Figure 2 As shown, in one embodiment of the present invention, the multi-objective safety Bayesian optimization method for materials development includes:

[0049] Step 1: Data collection and preparation.

[0050] 1.1 Collection of material parameters and performance data.

[0051] Acquire experimental or computational material data relevant to the target optimization task to form a material property dataset. Each sample consists of input parameters and performance indicators.

[0052]

[0053] in, This represents the design variable vector for the i-th experimental or simulation sample. For design parameter dimensions, For performance target value, This represents the m-th performance target value.

[0054] Data sources include: laboratory material performance tests (such as creep tests of single-crystal high-temperature alloys, high-temperature tensile tests of aluminum alloys, etc.); first-principles calculations, CALPHAD thermodynamic simulations, finite element numerical simulations; and historical composition-process-performance data recorded in the enterprise's production database.

[0055] 1.2 Collection of safety constraint variables and safety labels.

[0056] For different material systems and preparation processes, determine the set of constraint parameters related to experimental feasibility or process safety:

[0057]

[0058] Each of them Corresponding to a security constraint index, k Numbering of safety constraint indicators, such as: process energy density (to prevent overheating or undermelting of the molten pool); upper limits of equipment parameters (such as laser power, scanning speed, die casting temperature, etc.); sample quality indicators (such as porosity, crack rate, thermal strain concentration, etc.).

[0059] For each sample Define security thresholds If the following conditions are met:

[0060]

[0061] in, K Let be the total number of safety constraint indicators. If so, the sample is considered a safe sample; otherwise, it is considered an unsafe sample.

[0062] 1.3 Establish a secure sample dataset.

[0063] Sample points that meet the safety constraints are selected from the material property sample set:

[0064]

[0065] The remaining samples constitute the unsafe sample set:

[0066]

[0067] Security Sample Set Used for safety modeling and safety region initialization of constraint functions, unsafe sample set Used to train the boundary recognition capability of constraint functions. When the value is 1, the i-th sample satisfies the safety constraints.

[0068] 1.4 Data standardization.

[0069] To eliminate the dimensional differences between different physical quantities, all input parameters and output indices are normalized:

[0070]

[0071] in, and These are the mean and standard deviation, respectively. These are dimensionless variables after Z-Score standardization (or standard deviation standardization). The standardized data is used for training subsequent Gaussian process models to improve convergence stability and prediction accuracy.

[0072] Step 2: Data preprocessing and input / output.

[0073] Before constructing the multi-objective safety Bayesian optimization model, the original material data is cleaned and characterized. First, the categories and ranges of input parameters and output performance indicators are determined. Input parameters include component ratios, processing conditions, and microstructural characteristics, while output performance indicators include multi-objective functions such as strength, elongation, and thermal conductivity, as well as safety constraint functions. Second, missing data is filled using Gaussian interpolation or the K-nearest neighbor method, and outliers are removed using standardized residuals or Local Outlier Factor (LOF) detection to reduce noise. Then, feature engineering is performed, including correlation screening, principal component analysis (PCA) dimensionality reduction, and normalization to ensure that parameters in each dimension are distributed under the same scale. Finally, the processed data is randomly divided into training and test sets (approximately 8:2 ratio), or K-fold cross-validation is used to evaluate the model's generalization performance when the sample size is small. The preprocessed standardized dataset is used for subsequent surrogate model training and safety domain construction, providing a data foundation for the algorithm's stability and safety.

[0074] Step 3: Modeling of objectives and constraints based on integrated Gaussian processes.

[0075] After data preprocessing, to improve the model's generalization ability and computational efficiency, this embodiment of the invention employs an integrated Gaussian process (EGP) instead of a single Gaussian process model in the modeling of the performance objective function and safety constraint function. This method can effectively distribute the computational burden as the number of samples gradually increases, and improve the fitting accuracy and uncertainty estimation stability for complex material systems.

[0076] 3.1 When the sample size is small (e.g.) When the threshold is typically set to 100–200, a single Gaussian process model is used for each performance target. With safety constraints Separate modeling:

[0077]

[0078] in, It is a mean function. For the covariance kernel function, It follows a Gaussian distribution.

[0079] 3.2 When the number of samples continues to increase, the computational complexity of training a single model rises to... At that time, an ensemble modeling mechanism was adopted instead. The training data was randomly divided into L non-overlapping subsets:

[0080]

[0081] in, DThis is the original training set. L The total number of subsets. l The index (number) of the subset. For the first A set of non-overlapping subsets.

[0082] Independent Gaussian process models are trained for each subset. During the prediction phase, for any point to be evaluated... Each sub-model outputs the predicted mean. With variance The overall prediction of the ensemble model is achieved through weighted aggregation:

[0083] ,in, The overall prediction mean of the integrated model represents the final prediction result given by the system. For the first Each sub-model treats evaluation points The predicted mean.

[0084] ,in, The overall prediction variance of the integrated model measures the uncertainty of the final prediction, including the inherent uncertainty of each sub-model and the consistency among them. For the first Each sub-model treats evaluation points The prediction variance.

[0085] Among them, weight Dynamically updated based on the prediction accuracy of each sub-model on the validation set:

[0086] ,in, For the first The root mean square error of each sub-model on the validation set For the first The root mean square error of each sub-model (used to sum and calculate normalized weights).

[0087] By employing this weighted aggregation strategy, the ensemble model effectively reduces the risk of overfitting and computational overhead of a single model in high-dimensional data while preserving the prediction accuracy of local Gaussian processes.

[0088] Step 4: Safety determination based on the joint constraints of confidence lower bound and Lipschitz continuity.

[0089] 4.1 Determining safe points based on statistical confidence lower bounds.

[0090] The safety constraint function for each candidate point is predicted using a surrogate model of an integrated Gaussian process, and the mean function for that point is calculated. and variance Based on this, its security is predicted; according to the lower confidence bound (LCB) criterion, the security value of each candidate point is calculated:

[0091]

[0092] in, The lower confidence threshold, Let be the mean of the safety constraint function. Its standard deviation, To control the confidence level constant, it is usually set using the model's training data; the LCB value of each candidate point is compared with a preset safety threshold. If a comparison is made, If the point satisfies the security constraints, it can be included in the security domain. ,like If a point is not safe, it is considered unsafe and cannot be included in the safe domain.

[0093] 4.2 Spatial security extension based on Lipschitz continuity.

[0094] Assume constraint function Satisfying the Lipschitz continuity condition:

[0095]

[0096] Where L is the Lipschitz constant. When Belongs to security domain At any point If the following conditions are met:

[0097]

[0098] Then, this point is considered to be safe under the smoothness assumption of the function, denoted as the Lipschitz reachable safe region. , This is an estimate of the Lipschitz constant. This is a safety margin term used to compensate for model errors.

[0099] By combining the two mechanisms mentioned above, a comprehensive security domain is formed:

[0100]

[0101] in, This represents the set of safe points under the current statistical confidence level. This represents the reachable safe region obtained by extrapolating based on function continuity. (Comprehensive safe region) It serves as the search space in subsequent acquisition function optimization and candidate point recommendation, enabling efficient exploration and optimization while ensuring safety constraints.

[0102] Step 5: Phased security domain expansion.

[0103] 5.1 Discrete Mode Stage (Initial Exploration Stage).

[0104] When the sample size is small or the model prediction uncertainty is high, the algorithm uses a discrete candidate point set to construct the safety region and evaluate candidate points. This stage obtains a finite sample point set through grid sampling or Latin hypercube sampling.

[0105]

[0106] in, The candidate sample point set obtained by sampling, For discrete pattern sample thresholds, This represents the number of samples collected in the initial stage. For each candidate point, the multi-target acquisition function value is calculated and sorted. The safest point with the highest acquisition value is then used for experimentation or simulation.

[0107] The security domain in discrete mode is defined as follows:

[0108] ,in, constraint function At sample points The lower confidence limit at a point is used to measure a conservative estimate of whether the safety constraints are met at that point.

[0109] 5.2 Continuous mode stage (stable optimization stage).

[0110] Once the statistical uncertainty of the surrogate model converges and the Lipschitz constant estimate stabilizes, the algorithm switches to a continuous reachable safety region search mode. In this mode, the safety region is defined as:

[0111]

[0112] in, For LCB-based security point sets, The region is a continuously reachable region based on the Lipschitz extension. The optimization process for candidate points is carried out in the continuous domain, using Safe Particle Swarm Optimization (SafePSO) to search for the maximum value of the acquisition function.

[0113]

[0114] in, For multi-target acquisition functions (EHVI or MOEI). This represents the independent variable that maximizes the function within the parentheses. (i.e., the optimal candidate point) For safety probability.

[0115] 5.3 The smooth switching criterion is that the switching between discrete and continuous modes is constrained by the following conditions. Switching is triggered when any two of the conditions are met simultaneously: The number of samples reaches a threshold: Model uncertainty decreases: ,in, This represents the set of samples (or candidate points) at the t-th iteration. Representative set The number of samples in the set (i.e., the cardinality of the set). Represents safety constraint function Gaussian process model at input The standard deviation of the forecast (i.e., uncertainty) at that point. For the prediction variance threshold; the Lipschitz constant estimate is stable: ,in The Lipschitz convergence threshold is used; the algorithm transitions from discrete mode when any two of the above conditions are met. Smooth transition to continuous mode And perform global acquisition function optimization within a continuously reachable security domain.

[0116] 5.4 Smooth Transition Mechanism: To avoid sampling discontinuities during mode switching, the algorithm implements a smooth transition mechanism during transition rounds. A linear weighting smoothing strategy is introduced nearby to interpolate and fuse the safety regions of the two modes:

[0117]

[0118] in, To ensure a smooth transition step size, the algorithm achieves a smooth transition from finite discrete sampling to continuous reachable exploration while maintaining safety, through the above mechanism.

[0119] Step 6: A phased "exploration and development" two-stage dynamic data collection mechanism.

[0120] 6.1 Extension phase.

[0121] In the early stages of the algorithm, the surrogate model has significant uncertainty. To guide the model to expand into unknown areas, the acquisition function is mainly based on uncertainty measurement, combined with safety probability to form an exploratory acquisition function (the first acquisition function):

[0122]

[0123] in, The safety probability is defined as the confidence probability that the constraint function satisfies the safety conditions:

[0124]

[0125] in, The cumulative distribution function of the standard normal distribution; The prediction variance of the surrogate model for the multi-objective Gaussian process reflects the degree of uncertainty at that point. This is the safety threshold.

[0126] Based on the above definition, the acquisition function takes a higher value in regions with high security probability and high prediction uncertainty, thereby guiding the algorithm to explore unknown regions within the security domain and gradually expand the boundary of the security domain.

[0127] 6.2 Optimization phase.

[0128] In the later stages of the algorithm, when the surrogate model stabilizes and the safe region has formed a continuously reachable area, the acquisition function shifts to primarily using multi-objective improvement metrics to enhance the Pareto front of the current feasible solution set. The acquisition function at this stage is defined as a safety probability-weighted expected hypervolume improvement or a multi-objective expected improvement:

[0129]

[0130] in:

[0131]

[0132] in, This represents the current Pareto frontier hypervolume index. This is the current non-dominated solution set; The target function vector to be predicted. Candidate points The increment of the hypervolume index after being added to the current solution set; HV() is the hypervolume index calculation function.

[0133] 6.3 Overall Objectives.

[0134] The final multi-target secure acquisition function is defined as follows:

[0135]

[0136] in, Let EHVI, MOEI, or ParEGO be any multi-objective improvement metric function. This definition enables joint optimization of multi-objective performance under safety constraints, ensuring that the algorithm simultaneously possesses safety, globality, and efficient convergence in high-dimensional complex material design spaces.

[0137] Step 7: Particle swarm optimization algorithm with multi-objective acquisition function as fitness function.

[0138] The multi-objective safe particle swarm optimization algorithm uses the multi-objective acquisition function value as the particle fitness and searches only within the predicted safe continuous safety domain. Its implementation steps include:

[0139] 7.1 Search Space Constraints.

[0140] The search space for particle swarm optimization is restricted to the comprehensive safety domain:

[0141]

[0142] in, For safety probability, As a safety threshold, For a set of safe points defined based on a confidence lower bound, This is a reachable safety domain based on the Lipschitz continuum extension.

[0143] 7.2 Particle velocity and position update.

[0144] Initialize the particle swarm and set the positions of the particles. and speed ,in, The initial positions of the particles are randomly distributed within the safety region, and it is ensured that the initial position of each particle satisfies the safety constraints.

[0145] Based on the particle position and velocity update rules, the particle's velocity and position are updated in each iteration step, using the following update formula:

[0146]

[0147]

[0148] in, For particles At time step speed, For particles Location, For particles The optimal position of an individual This represents the globally optimal position for the entire particle swarm. For inertial weights, and The acceleration constant, and It is a random number;

[0149] 7.3 Fitness calculation.

[0150] By calculating the fitness value of each particle, its performance under the multi-objective acquisition function and the safety constraint function is evaluated. Fitness value The calculation formula is:

[0151]

[0152] in, For fitness value, It can be Expected Hypervolume Improvement (EHVI), Multi-Objective Expected Improvement (MOEI), or Weighted Expected Improvement (ParEGO); the optimal position of an individual particle is updated based on its fitness value. and global optimal position And ensure that the updated particle positions still satisfy the safety constraints;

[0153] In each iteration, the velocity and position of the particle swarm are dynamically adjusted to optimize the search range, ensuring that the best-performing candidate point can be found within the safe domain, while maximizing exploration efficiency and avoiding getting trapped in local optima. A safe expansion mechanism is introduced, which pushes particles away from unsafe areas by adjusting their velocity or position when their position approaches the boundary of the safe domain, ensuring that the exploration always takes place within the safe domain.

[0154] Step 8: Dynamic scheduling of hyperparameters for the Gaussian process surrogate model.

[0155] In the iterative process of multi-objective safe Bayesian optimization, this invention introduces a dynamic hyperparameter scheduling mechanism for key hyperparameters of the Gaussian process surrogate model to achieve adaptive evolution of the model from global exploration to local convergence, thereby improving optimization efficiency and convergence stability. This mechanism mainly includes the dynamic adjustment of the following three types of parameters:

[0156] 8.1 Adaptive Update of Kernel Function Length Scale Parameter. For Gaussian process kernel functions...

[0157]

[0158] in, Let i be the length scale parameter of the i-th input dimension. This is the signal variance, also known as the scaling factor of the kernel function or the output variance. During the iteration process, it is determined based on the distribution density of the sampling points. With prediction error Dynamic adjustment:

[0159]

[0160] in, For adjustment coefficients, tThe time step is defined as follows: when the samples are sparse and the error is large, the length scale parameter is larger to maintain smoothness; when the samples are dense and the model accuracy improves, the length scale parameter is gradually reduced to enhance local resolution.

[0161] 8.2 Dynamic adjustment of function norm parameters.

[0162] Variance coefficients (signal strength parameters) in kernel functions The control model is sensitive to output fluctuations. Its update rule is:

[0163]

[0164] in, This represents the average variance of the model predictions in the t-th iteration. The learning rate or update step size parameter determines how quickly the signal variance adjusts with iteration. Let be the prediction variance of the model in the t-th iteration. This represents the prediction variance of the initial iteration model. This mechanism maintains a high uncertainty estimate in the early stages to facilitate exploration, and gradually reduces the signal strength as the sample size increases to prevent overfitting.

[0165] 8.3 Confidence Parameters Gradual scaling.

[0166] In the calculation of the acquisition function (such as the lower confidence bound LCB):

[0167]

[0168] Confidence parameters To maintain a balance between exploration and exploitation, an incremental strategy should be adopted:

[0169]

[0170] in, As the initial value, The adjustment coefficients are used. A larger confidence interval in the early stages helps to conservatively explore the safe region, while the interval is gradually reduced in later stages to improve optimization efficiency. Through these three types of dynamic scheduling mechanisms, the Gaussian process model can automatically adjust its smoothness and confidence range according to the sampling density and iteration stage, enabling the model to have wide-area perception capabilities in the global exploration stage and high-precision prediction capabilities in the local convergence stage.

[0171] To verify the effectiveness of the multi-objective safe Bayesian optimization method of this invention, it was applied to the optimization design of the TC4 titanium alloy additive manufacturing process. The specific implementation is as follows:

[0172] 1. Data collection and preparation.

[0173] 1.1 Collection of process parameters and performance data.

[0174] Commonly used additive manufacturing process parameters are selected as design variables to form an input vector: ,in, The laser power ranges from 150 to 400 W. The scanning speed ranges from 400 to 1200 mm / s; The layer thickness ranges from 20 to 60 μm. The scanning spacing ranges from 50 to 150 μm; The scanning strategy angle (rotation angle) ranges from 0 to 90°.

[0175] The corresponding performance targets include:

[0176] Units are UTS (MPa) and EL (%). Data sources include: historical experimental records, finite element thermal-structural simulations, and material microstructure simulations.

[0177] 1.2 Collection of safety constraint parameters.

[0178] Define constraints related to experimental safety or printing process feasibility:

[0179] ,in, The maximum molten pool temperature (°C) is 1800°C. Porosity (%), with an upper limit of 2%; The residual stress concentration (MPa) has an upper limit of 500 MPa.

[0180] The safety threshold is set as follows:

[0181] .

[0182] 1.3 Data Standardization: Normalize the input and output data.

[0183]

[0184] 2. Proxy model training.

[0185] After data preprocessing and standardization, to accurately predict the additive manufacturing process performance and safety constraints of TC4 titanium alloy, this invention employs Gaussian processes and their ensemble form for surrogate modeling. The specific training process is as follows:

[0186] 2.1 Establish a Gaussian process model for each objective function and safety constraint function, with an initial sample size of... When the sample size To improve computational efficiency and fitting accuracy, an Integrated Gaussian Process (EGP) is employed. The RBF kernel is used as the model kernel function, with initial length scale parameters set according to the range of each dimension's parameters, and a dynamic adjustment mechanism activated in subsequent iterations. A separate Gaussian process model is established for each performance metric (e.g., tensile strength UTS, elongation EL).

[0187]

[0188] For each safety constraint index (maximum molten pool temperature, porosity, residual stress) Establish independent Gaussian processes:

[0189]

[0190] Used to predict the safety probability of candidate points Similarly, the RBF kernel function is used to apply the length scale parameter. With variance Perform initialization.

[0191] As the number of samples continues to increase, the computational complexity of training a single model rises to... At that time, an ensemble modeling mechanism was adopted instead. The training data was randomly divided into L non-overlapping subsets:

[0192]

[0193] Independent Gaussian process models are trained for each subset. During the prediction phase, for any point to be evaluated... Each sub-model outputs the predicted mean. With variance The overall prediction of the ensemble model is achieved through weighted aggregation:

[0194]

[0195]

[0196] Among them, weight Dynamically updated based on the prediction accuracy of each sub-model on the validation set:

[0197]

[0198] 3. Security Domain Determination and Extension: Confidence Lower Bound Determination:

[0199]

[0200] when If the condition is met, the point is deemed unsafe; otherwise, it is included in the safe domain. Lipschitz reachable safe region: Assuming the constraint functions satisfy Lipschitz continuity.

[0201]

[0202] estimate (Based on historical simulation data), safety margin Comprehensive security domain:

[0203]

[0204] 4. Phased Safety Domain Expansion: To ensure the safety and efficiency of material process optimization, this invention adopts a phased safety domain expansion strategy, dividing the safety domain into two phases: a discrete mode and a continuous mode, gradually realizing the dynamic expansion of the safety domain from local to global. The specific implementation method is as follows:

[0205] 4.1 Discrete Pattern (Initial Exploration): When the sample size is small or the model prediction uncertainty is high, a discrete pattern is used to construct the safety region; an initial candidate point set is generated through Latin Hypercube Sampling (LHS) or uniform grid sampling.

[0206]

[0207] Input variables include laser power Scanning speed Layer thickness Scanning Spacing Scanning angle For each candidate point, the mean and standard deviation of the safety constraints are predicted using a Gaussian process, and the lower confidence bound (LCB) is calculated:

[0208]

[0209] Select one that meets the safety threshold The points are used as the initial security domain. In the set of security points... Internal calculation acquisition function:

[0210]

[0211] Sort the collected values ​​and select the top k candidate points for experiments or simulations; update the Gaussian process model and add new sample points.

[0212] 4.2 Global Optimization Phase (Continuous Mode): The conditions for the algorithm to switch from discrete mode to continuous mode are as follows: the number of samples reaches the threshold; the model prediction variance decreases; the Lipschitz constant estimate is stable; when any two of the above conditions are met simultaneously, the mode switch is triggered.

[0213] Extrapolation of the security region using Lipschitz continuity:

[0214]

[0215] Within the continuous domain, the safety domain expands from discrete points to a continuously reachable region, covering a larger design space. In the continuous safety domain... Internal execution of SafePSO:

[0216]

[0217] The initial positions of the particles are randomly distributed in And maintain safety constraints; ensure the search process is conducted within the safety domain by iteratively updating particle velocity and position.

[0218] 5. Two-stage dynamic acquisition function.

[0219] To achieve multi-objective performance optimization while ensuring safety constraints, this invention adopts a two-stage dynamic acquisition function strategy of Explore-Exploit. The acquisition function is dynamically adjusted according to the uncertainty of the optimization iteration stage and the surrogate model, so as to achieve a smooth transition from global exploration to local fine optimization.

[0220] 5.1 Expansion Phase (Exploratory Acquisition Function).

[0221] This approach is suitable for scenarios where the number of samples is small and prediction uncertainty is high during the initial training phase of a proxy model, and where the safety domain boundary has not been fully explored, requiring the active search for unknown regions to expand the safety domain.

[0222] Data Acquisition Function Definition: The data acquisition function during the exploration phase is primarily characterized by uncertainty, while also incorporating a weighted safety probability.

[0223]

[0224] in, For safety probability; The uncertainty in the target performance prediction is output by the Gaussian process variance. This safety probability prioritizes points with high safety probabilities and large prediction uncertainties for experiments or simulations; it guides the algorithm to explore unknown regions within the safety region and expand the boundary of the safety region; and it prevents the early model from prematurely converging to local optima.

[0225] Taking TC4 additive manufacturing as an example: Assuming laser power P ∈ [200, 400] W and scanning speed v ∈ [500, 1200] mm / s, calculate on candidate point x:

[0226] ,in, denoted as the standard deviation of the Gaussian process model's prediction of tensile strength (UTS) at candidate point x, representing the uncertainty of the predicted value at that point. Experiments were conducted using the top 5 candidate points with the highest collected values ​​to update the GP model.

[0227] 5.2 Dynamic stage switching and integrated acquisition function.

[0228] Once the sample size reaches a certain level, the model's prediction accuracy tends to stabilize, and the exploration of the unknown design space also becomes more comprehensive. The potential benefits of continuing to explore areas with high uncertainty decrease, so it is necessary to change the acquisition function to a function that focuses on developing high-performance regions.

[0229] Comprehensive data acquisition function: through weights Smooth transition between exploration and development phases:

[0230]

[0231] in, The iteration count increases linearly with the number of iterations; during the transition period, both safe domain exploration and Pareto front optimization are considered.

[0232] 6. Safe Particle Swarm Optimization (SafePSO).

[0233] To efficiently search for the maximum value of a multi-objective acquisition function within a continuous safe domain, the SafePSO algorithm is introduced into multi-objective safe Bayesian optimization. By iteratively updating the particle swarm within the safe domain, global optimization and safety constraints are both achieved.

[0234] 6.1 Definition and constraints of the search space.

[0235] The particle search space is restricted to the comprehensive safety domain:

[0236]

[0237] in, A set of safe points based on the confidence lower bound (LCB); For the reachable safety region based on Lipschitz continuum extension; safety threshold. A value of 0.95 can be used to ensure high experimental reliability. Design variable ranges: laser power P = 200–400 W; scanning speed v = 500–1200 mm / s; layer thickness h = 20–60 μm; scanning spacing t = 50–150 μm; scanning angle θ = 0–90°.

[0238] 6.2 Particle velocity and position update.

[0239] Initialize the particle swarm and set the positions of the particles. and speed ,in The initial positions of the particles are randomly distributed within the safety region, and it is ensured that the initial position of each particle satisfies the safety constraints.

[0240] Based on the particle position and velocity update rules, the particle's velocity and position are updated in each iteration step, using the following update formula:

[0241]

[0242]

[0243] in, For particles At time step speed, For particles Location, For particles The optimal position of an individual This represents the globally optimal position for the entire particle swarm. For inertial weights, and The acceleration constant, and It is a random number;

[0244] 6.3: Fitness calculation.

[0245] By calculating the fitness value of each particle, its performance under the multi-objective acquisition function and the safety constraint function is evaluated. Fitness value The calculation formula is:

[0246]

[0247] in, It can be Expected Hypervolume Improvement (EHVI), Multi-Objective Expected Improvement (MOEI), or Weighted Expected Improvement (ParEGO); the optimal position of an individual particle is updated based on its fitness value. and global optimal position And ensure that the updated particle positions still satisfy the safety constraints;

[0248] 6.4 Convergence and Output.

[0249] Convergence criteria: Maximum number of iterations T_max = 50–100; or the change in the globally optimal g over n consecutive iterations < ε (e.g., ε = 1e-3); Output: Optimal combination of process parameters; corresponding multi-objective performance prediction values. Update security domain This information is used for the next round of Bayesian optimization iterations. After 50 iterations of particle swarm optimization, SafePSO searches within a continuous safe domain to obtain the Pareto front process parameters; it then outputs the optimal candidate points for experimental verification.

[0250] In this embodiment, a computer device is provided, such as... Figure 3 As shown, it includes a memory 301, a processor 302, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements any of the above-mentioned multi-objective safe Bayesian optimization methods for materials development.

[0251] Specifically, the computer device can be a computer terminal, a server, or a similar computing device.

[0252] In this embodiment, a computer-readable storage medium is provided, which stores a computer program that executes any of the above-described multi-objective safe Bayesian optimization methods for materials development.

[0253] Specifically, computer-readable storage media include both permanent and non-permanent, removable and non-removable media, which can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer-readable storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable storage media do not include transient media, such as modulated data signals and carrier waves.

[0254] Based on the same inventive concept, this invention also provides a multi-objective secure Bayesian optimization device for materials development, as described in the following embodiments. Since the problem-solving principle of the multi-objective secure Bayesian optimization device for materials development is similar to that of the multi-objective secure Bayesian optimization method for materials development, the implementation of the multi-objective secure Bayesian optimization device for materials development can refer to the implementation of the multi-objective secure Bayesian optimization method for materials development, and repeated details will not be elaborated further. As used below, the terms "unit" or "module" can refer to a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0255] Figure 4 This is a structural block diagram of a multi-objective safe Bayesian optimization device for materials development according to an embodiment of the present invention, such as... Figure 4 As shown, it includes: a dataset construction module 401, a proxy model construction module 402, a test candidate point acquisition module 403, and a model iteration optimization module 404. The structure is described below.

[0256] The dataset construction module 401 is used to construct a material performance dataset including material design parameters and performance data, construct a safety sample dataset including safety constraint indicators, construct a model dataset through the material performance dataset and the safety sample dataset, and determine a design space including the range of material design parameters based on the optimization problem.

[0257] The proxy model construction module 402 is used to train an ensemble Gaussian process model using the material property dataset and the safety sample dataset, model the performance objective function and constraint function, and generate a proxy model.

[0258] The test candidate point acquisition module 403 is used to evaluate whether the candidate points in the design space meet the safety constraints through the proxy model and the safety domain determination conditions, save the candidate points that meet the safety constraints to the safety domain, generate the extended safety domain, evaluate the candidate points in the extended safety domain through the comprehensive multi-objective acquisition function, and select the optimal point as the test candidate point.

[0259] The model iteration optimization module 404 is used to conduct experimental tests on the test candidate points, correct the values ​​of the test candidate points based on the experimental test results, generate corrected candidate points, add the corrected candidate points to the model dataset, train and iterate the surrogate model through the model dataset until the preset iteration stopping condition is met, and generate the trained surrogate model.

[0260] In one embodiment, the dataset building module includes:

[0261] Material property dataset construction unit, used for data based on input parameters Compared with performance target value Construct a materials properties dataset, in which, For the first i A vector of design variables for an experimental or simulation sample. d For the dimensions of design parameters, For the first m One performance target value, M The dimension of the performance target value;

[0262] Constructing a set of safety constraint parameters is a unit used to construct a set of safety constraint parameters. ,in, As a safety constraint indicator, K The dimension of the constraint function;

[0263] Construct model dataset units for use based on the set of security constraint parameters. Build the model dataset.

[0264] In one embodiment, the model dataset building unit is also used to construct the set of security constraint parameters. Determine each sample in the material properties dataset. Safety constraint indicators Is it greater than or equal to the safety threshold? If so, save the sample to a safe sample set. ,in, , Let i be the safety classification label for the i-th sample. When the value is 1, the i-th sample satisfies the safety constraints. If the value is the actual value of the security constraint function corresponding to the i-th sample, then the sample is saved to the unsafe sample set. ,in, , Let i be the safety classification label for the i-th sample. When the value is 0, the i-th sample does not satisfy the safety constraint; the safe sample set is... and the aforementioned insecure sample set As a model dataset.

[0265] In one embodiment, the module for obtaining test candidate points includes:

[0266] The judgment stage unit is used to set a sample threshold and divide the safety constraint judgment process into a discrete stage and a continuous stage according to the sample threshold.

[0267] The discrete-stage computational unit is used to predict the safety constraint function of each candidate point in the design space using the surrogate model in the discrete-stage process, based on a safety point determination method using statistical confidence lower bounds, and to obtain the mean function of the candidate points. Sum of variance functions ,in, Candidate points;

[0268] The safety value calculation unit is used to calculate the safety value based on the lower confidence boundary criterion and the mean function. and the variance function Calculate each of the candidate points security value ,in, Let be the mean of the safety constraint function. Let the standard deviation of the safety constraint function be . A constant used to control the confidence level;

[0269] Security domain construction unit, used if the candidate point security value Greater than or equal to the safety threshold , will the current candidate point Included in security domain ,in, t This represents the number of iterations.

[0270] The continuous stage calculation unit is used to predict the safety constraint function of each candidate point in the design space using the surrogate model in the continuous stage, based on the Lipschitz continuity-based safety point determination method, to obtain the mean function of the candidate points. Sum of variance functions ;

[0271] Construct reachable safety domain units for use if the candidate points satisfy Then the candidate point The security domain is ,in, Belongs to the security domain Candidate points, for The mean, This is an estimate of the Lipschitz constant. For safety margin items, () is a mapping operator that uses the Lipschitz continuity principle to extrapolate and extend the confirmed discrete safe point set into a continuous reachable safe domain;

[0272] Construct a comprehensive security domain unit for use based on the security domain and the reachable security domain Build a comprehensive security domain .

[0273] In one embodiment, the module for obtaining test candidate points further includes:

[0274] The processing stage segmentation unit is used to set a sample threshold and divide the sample sampling process into a discrete stage and a continuous stage according to the sample threshold.

[0275] The function construction unit is used to construct an exploratory multi-target acquisition function for the discrete stage, a probability-weighted multi-target safety acquisition function for the continuous stage, and to construct the final integrated multi-target safety acquisition function through the exploratory multi-target acquisition function and the probability-weighted multi-target safety acquisition function.

[0276] The candidate sample point set generation unit is used to obtain the candidate sample point set during the discrete stage. ,in, x As candidate points, For the first i 1 candidate point i The candidate point number, This refers to the number of samples collected in the initial stage. The sample threshold for discrete patterns;

[0277] Define a discrete security domain unit for using the candidate sample point set. Define discrete security domains ,in, Candidate points Security value, t Candidate point number, This is a safety threshold;

[0278] The first candidate point acquisition unit is used to calculate each candidate point using the exploratory multi-target acquisition function. The multi-target acquisition function value, and the candidate points are ranked according to the multi-target acquisition function value. The candidate points with the highest multi-target acquisition function values ​​are sorted and selected as discrete experimental candidate points. The actual material target performance values ​​and / or safety constraint values ​​of the discrete experimental candidate points are obtained through material experiments or material calculations and saved to the training dataset of the surrogate model.

[0279] Construct a continuous reachable security domain unit for defining the continuous reachable security domain of the continuous phase. ,in, For security domains, For continuously reachable regions based on the Lipschitz extension, () is a mapping operator that uses the Lipschitz continuity principle to extrapolate and extend the confirmed discrete safe point set into a continuous reachable safe domain;

[0280] The mode switching unit is used to determine whether it is necessary to switch from the discrete stage to the continuous stage based on the sample threshold. If so, it performs interpolation fusion on the security domains of the two modes through a smooth switching method to generate an extended security domain. ,in, To ensure a smooth transition step size, As weight, This is a transitional round;

[0281] The final objective function construction unit is used to construct the final multi-target safe acquisition function.

[0282] The second candidate point acquisition unit is used to employ a multi-objective safe particle swarm optimization algorithm to select candidate points within the continuously reachable safe domain. In the process, a global search is performed on the final multi-objective safety acquisition function to obtain the candidate point with the highest value of the multi-objective acquisition function as the continuous experimental candidate point. The actual material target performance value and / or safety constraint value of the continuous experimental candidate point are obtained through material experiments or material calculations and saved to the training dataset of the surrogate model.

[0283] In one embodiment, the mode switching unit is also used to adjust the number of samples. Greater than or equal to the sample threshold As a first condition; calculate the model uncertainty of the proxy model, and ensure that the model uncertainty is less than or equal to the prediction variance threshold. As a second condition; calculation t Estimate of the Lipschitz constant at time -1 and t Estimates of the Lipschitz constant at time t The absolute value of the value is less than or equal to the Lipschitz convergence threshold. As a third condition, among which... The estimated value of the Lipschitz constant; satisfying any two of the first, second, and third conditions is used as the condition for switching from the discrete stage to the continuous stage.

[0284] In one embodiment, the function building unit is also used to calculate the security probability. ,in, x As candidate points, Pr () represents the probability. g ( x ) is the input x The safety constraint function, The cumulative distribution function of the standard normal distribution. The prediction variance of the Gaussian process surrogate model. The mean of the predictions from the Gaussian process surrogate model; based on the stated security probability. Standard deviation of the prediction of the objective function Construct an exploratory multi-target acquisition function ,in, For the objective function At candidate point The predicted standard deviation at the given point; calculate the expected improvement of the multi-objective target. ,in, As a current cutting-edge hypervolume index in Pareto, For the current non-dominated solution set, The target function vector to be predicted. Candidate points The increment to the hypervolume index after being added to the current solution set, HV() is the hypervolume index calculation function; according to the aforementioned safety probability and multi-objective expectation improvement Construct a probability-weighted multi-target security acquisition function The final integrated multi-target safe acquisition function is constructed by combining the exploratory multi-target acquisition function with the probability-weighted multi-target safe acquisition function. ,in, This is an exploratory multi-target acquisition function. A probability-weighted multi-target security acquisition function. To adjust the weight of the algorithm between exploration and optimization capabilities based on user needs.

[0285] The multi-objective safe Bayesian optimization method for materials development proposed in this invention is fundamentally about achieving efficient and safe optimization of multi-objective performance in complex material design spaces even with extremely limited experimental samples (e.g., tens to hundreds of experimental or simulation points). One example is its application in the optimization of the TC4 titanium alloy additive manufacturing process. Using only a small amount of initial experimental data and completely unknown combinations of process parameters, this method enables rapid discovery and global optimization of the Pareto front for multiple objectives (such as tensile strength and elongation) through adaptive expansion of the safety domain and a two-stage acquisition function.

[0286] The aforementioned advantages stem from the powerful uncertainty modeling capabilities of Gaussian processes (GP) and their ensemble models. Combined with the proposed joint safety determination mechanism of confidence lower bound (LCB) and Lipschitz continuity, the phased safety domain expansion strategy, and the exploration-development two-stage dynamic acquisition function, the optimization system can adaptively balance safety constraints and multi-objective performance improvement without requiring large-scale experiments or high-risk trials. Furthermore, by incorporating the Safe Particle Swarm Optimization (SafePSO) algorithm for global search of the acquisition function, this method can achieve efficient candidate point selection and local fine-tuning while ensuring safety constraints, thereby significantly reducing experimental costs and safety risks, and improving the efficiency and reliability of material design and process parameter optimization. In summary, the multi-objective safe Bayesian optimization method proposed in this application can achieve efficient, safe, and interpretable multi-objective performance collaborative optimization in small-sample, high-risk material development scenarios, providing intelligent decision support for complex material design.

[0287] The embodiments of the present invention achieve the following technical effects:

[0288] This paper proposes a multi-objective safe optimization method based on Bayesian optimization. By introducing a surrogate model to model the constraints and updating the safety domain in real time during optimization iterations, it overcomes the shortcomings of traditional methods where constraints require prior knowledge and cannot be dynamically updated. In traditional optimization methods, the addition of constraints often relies on expert experience or pre-set prior knowledge, and these constraints are fixed during optimization iterations and cannot be adjusted according to actual conditions, which limits the flexibility and accuracy of the optimization process. This method constructs an ensemble Gaussian process model and updates the safety domain in real time based on newly acquired data in each iteration. This allows the constraints to be dynamically adjusted as the optimization process progresses, thereby more accurately guiding the optimization search and avoiding the search for infeasible solutions or dangerous regions that may occur in traditional methods. This innovation enables the optimization process to adaptively adjust safety constraints, improves the exploration efficiency of the search space, and reduces the risk of unsafe experiments. Furthermore, this invention can significantly reduce dependence on expensive experimental resources and improve the utilization efficiency of experimental resources in high-risk, high-cost experimental environments through learning and intelligent search using limited experimental data. These innovations not only improve the accuracy and stability of multi-objective optimization but also make the optimization process more flexible and intelligent, providing a novel solution for materials design and process optimization. By introducing a safety constraint mechanism, the risk and number of unsafe experiments are significantly reduced in high-risk, high-cost materials design and manufacturing scenarios, while improving the efficiency of multi-objective optimization and enhancing both experimental efficiency and safety. The adoption of a safety domain adaptive expansion mechanism dynamically adjusts the search space based on sample distribution and uncertainty, ensuring that the exploration process always occurs within the safety domain, effectively avoiding experimental failures and resource waste. Combining multi-objective acquisition functions, particle swarm optimization (PSO), and Gaussian process models, this method can intelligently search for optimal material parameters and process combinations with limited experimental data, reducing dependence on expensive experimental resources, improving the utilization efficiency of experimental resources, and making the optimization process highly efficient and intelligent. Through acquisition functions such as expected hypervolume improvement (EHVI) and multi-objective expected improvement (MOEI), this invention achieves synergistic optimization of multiple performance objectives while ensuring safety constraints, providing a balanced materials design scheme.

[0289] Obviously, those skilled in the art should understand that the modules or steps of the above-described embodiments of the present invention can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device. In some cases, the steps shown or described can be performed in a different order than those presented here, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the embodiments of the present invention are not limited to any particular hardware and software combination.

[0290] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, various modifications and variations can be made to the embodiments of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-objective safety Bayesian optimization method for materials development, characterized in that, include: A material performance dataset including material design parameters and performance data is constructed, a safety sample dataset including safety constraint indicators is constructed, a model dataset is constructed using the material performance dataset and the safety sample dataset, and a design space including the range of material design parameters is determined based on the optimization problem; Using the material property dataset and the safety sample dataset, an ensemble Gaussian process model is trained to model the performance objective function and constraint function, generating a surrogate model. Using the surrogate model and security domain determination criteria, the candidate points in the design space are evaluated to determine whether they satisfy security constraints. Candidate points satisfying the security constraints are saved to the security domain, generating an expanded security domain. The candidate points in the expanded security domain are evaluated using a comprehensive multi-objective acquisition function, and the optimal point is selected as the experimental candidate point, including: Set a sample threshold, and divide the sample sampling process into discrete and continuous stages based on the sample threshold; An exploratory multi-target acquisition function is constructed for the discrete phase, and a probability-weighted multi-target safety acquisition function is constructed for the continuous phase. The final integrated multi-target safety acquisition function is constructed by combining the exploratory multi-target acquisition function and the probability-weighted multi-target safety acquisition function. In the discrete stage, a set of candidate sample points is obtained. ,in, x As candidate points, For the first i 1 candidate point i The candidate point number, This refers to the number of samples collected in the initial stage. The sample threshold for discrete patterns; Through the candidate sample point set Define discrete security domains ,in, Candidate points Security value, t Candidate point number, This is a safety threshold; Each candidate point is calculated using the aforementioned exploratory multi-target acquisition function. The multi-target acquisition function value, and the candidate points are ranked according to the multi-target acquisition function value. The candidate points with the highest multi-target acquisition function values ​​are sorted and selected as discrete experimental candidate points. The actual material target performance values ​​and / or safety constraint values ​​of the discrete experimental candidate points are obtained through material experiments or material calculations and saved to the training dataset of the surrogate model. In the consecutive phases, a consecutive reachable security domain is defined for the consecutive phases. ,in, For security domains, For continuously reachable regions based on the Lipschitz extension, () is a mapping operator that uses the Lipschitz continuity principle to extrapolate and extend the confirmed discrete safe point set into a continuous reachable safe domain; The sample threshold is used to determine whether it is necessary to switch from the discrete stage to the continuous stage. If so, the security domains of the two modes are interpolated and fused using a smooth switching method to generate an expanded security domain. ,in, To ensure a smooth transition step size, As weight, This is a transitional round; A multi-objective safety particle swarm optimization algorithm is employed in the continuously reachable safety domain. In the process, a global search is performed on the final multi-objective safety acquisition function to obtain the candidate point with the highest value of the multi-objective acquisition function as the continuous experimental candidate point. The real material target performance value and / or safety constraint value of the continuous experimental candidate point are obtained through material experiments or material calculations and saved to the training dataset of the proxy model. Experimental tests are conducted on the candidate test points. Based on the results of the experimental tests, the values ​​of the candidate test points are corrected to generate corrected candidate points. The corrected candidate points are then added to the model dataset. The surrogate model is trained and iterated using the model dataset until a pre-set iteration stopping condition is met, thereby generating a trained surrogate model.

2. The multi-objective safe Bayesian optimization method for materials development as described in claim 1, characterized in that, Using the proxy model and security domain determination criteria, the candidate points in the design space are evaluated to determine whether they satisfy security constraints. Candidate points that satisfy the security constraints are then saved to the security domain, including: Set a sample threshold, and divide the safety constraint determination process into a discrete stage and a continuous stage based on the sample threshold; In the discrete stage, a safe point determination method based on statistical confidence lower bounds is used to predict the safety constraint function of each candidate point in the design space using the surrogate model, thereby obtaining the mean function of the candidate points. and variance function ,in, Candidate points; Based on the lower confidence bound criterion and the mean function and the variance function Calculate each of the candidate points security value ,in, Let be the mean of the safety constraint function. Let the standard deviation of the safety constraint function be . A constant used to control the confidence level; If the candidate point security value Greater than or equal to the safety threshold , will the current candidate point Included in security domain Where t is the number of iterations; In the continuity phase, a safety point determination method based on Lipschitz continuity is used to predict the safety constraint function of each candidate point in the design space using the surrogate model, thereby obtaining the mean function of the candidate points. Sum of variance functions ; If the candidate point satisfy Then the candidate point The security domain is ,in, Belongs to the security domain Candidate points, for The mean, This is an estimate of the Lipschitz constant. For safety margin items, () is a mapping operator that uses the Lipschitz continuity principle to extrapolate and extend the confirmed discrete safe point set into a continuous reachable safe domain; Based on the discrete-stage security domain and the continuous stage security domain Build a security domain .

3. The multi-objective safe Bayesian optimization method for materials development as described in claim 1, characterized in that, Determining whether to switch from the discrete stage to the continuous stage based on the sample threshold includes: Number of samples Greater than or equal to the sample threshold As the first condition; Calculate the model uncertainty of the surrogate model, and set the model uncertainty to be less than or equal to the prediction variance threshold. As a second condition; calculate t Estimate of the Lipschitz constant at time -1 and t Estimates of the Lipschitz constant at time t absolute value of the difference The absolute value is less than or equal to the Lipschitz convergence threshold. As a third condition, among which... This is an estimate of the Lipschitz constant; Satisfying any two of the first, second, and third conditions will be used as the conditions for switching from the discrete stage to the continuous stage.

4. The multi-objective safety Bayesian optimization method for materials development as described in claim 1, characterized in that, Constructing an exploratory multi-target acquisition function for the discrete phase, constructing a probability-weighted multi-target safety acquisition function for the continuous phase, and constructing a final integrated multi-target safety acquisition function using the exploratory multi-target acquisition function and the probability-weighted multi-target safety acquisition function, including: Calculate the probability of safety ,in, x As candidate points, Pr () represents the probability. g ( x ) is the input x The safety constraint function, The cumulative distribution function of the standard normal distribution. The prediction variance of the Gaussian process surrogate model. The mean of the predictions from the Gaussian process surrogate model; Based on the security probability Standard deviation of the prediction of the objective function Construct an exploratory multi-target acquisition function ,in, For the objective function At candidate point The standard deviation of the forecast at that location; Calculate the expected improvement of multiple objectives ,in, As a current cutting-edge hypervolume index in Pareto, For the current non-dominated solution set, The target function vector to be predicted. Candidate points The increment of the hypervolume index after being added to the current solution set; HV() is the hypervolume index calculation function. Based on the security probability and multi-objective expectation improvement Construct a probability-weighted multi-target security acquisition function ; By combining the exploratory multi-target acquisition function with the probability-weighted multi-target safe acquisition function, a final integrated multi-target safe acquisition function is constructed. ,in, This is an exploratory multi-target acquisition function. A probability-weighted multi-target security acquisition function. To adjust the weight of the algorithm between exploration and optimization capabilities based on user needs.

5. The multi-objective safe Bayesian optimization method for materials development as described in any one of claims 1 to 4, characterized in that, Construct a material performance dataset including material design parameters and performance data; construct a safety sample dataset including safety constraint indicators; and construct a model dataset using the material performance dataset and the safety sample dataset, including: Based on input parameters Compared with performance target value Construct a materials properties dataset, in which, For the first i A vector of design variables for an experimental or simulation sample. d For the dimensions of design parameters, For the first m One performance target value, M The dimension of the performance target value; Construct a set of safety constraint parameters ,in, As a safety constraint indicator, K The dimension of the constraint function; Based on the set of security constraint parameters Build the model dataset.

6. The multi-objective safety Bayesian optimization method for materials development as described in claim 5, characterized in that, Based on the set of security constraint parameters Build the model dataset, including: Through the set of security constraint parameters Determine each sample in the material properties dataset. Safety constraint indicators Is it greater than or equal to the safety threshold? ; If so, save the sample to a secure sample set. ,in, , Let i be the safety classification label for the i-th sample. When the value is 1, the i-th sample satisfies the safety constraints. This represents the actual value of the safety constraint function corresponding to the i-th sample; If not, save the sample to the insecure sample set. ,in, , Let i be the safety classification label for the i-th sample. When the value is 0, the i-th sample does not satisfy the safety constraints; The security sample set and the aforementioned insecure sample set As a model dataset.

7. A multi-objective safety Bayesian optimization device for materials development, characterized in that, include: The dataset construction module is used to construct a material performance dataset including material design parameters and performance data, construct a safety sample dataset including safety constraint indicators, construct a model dataset using the material performance dataset and the safety sample dataset, and determine a design space including the range of material design parameters based on the optimization problem. A proxy model construction module is used to train an ensemble Gaussian process model using the material property dataset and the safety sample dataset, model the performance objective function and constraint function, and generate a proxy model. The module for obtaining test candidate points is used to evaluate whether the candidate points in the design space meet the safety constraints through the proxy model and the safety domain determination conditions, save the candidate points that meet the safety constraints to the safety domain, generate an extended safety domain, evaluate the candidate points in the extended safety domain through a comprehensive multi-objective acquisition function, and select the optimal point as the test candidate point. The module for obtaining test candidate points includes: The processing stage segmentation unit is used to set a sample threshold and divide the sample sampling process into a discrete stage and a continuous stage according to the sample threshold. The function construction unit is used to construct an exploratory multi-target acquisition function for the discrete stage, a probability-weighted multi-target safety acquisition function for the continuous stage, and to construct the final integrated multi-target safety acquisition function through the exploratory multi-target acquisition function and the probability-weighted multi-target safety acquisition function. The candidate sample point set generation unit is used to obtain the candidate sample point set during the discrete stage. ,in, x As candidate points, For the first i 1 candidate point i The candidate point number, This refers to the number of samples collected in the initial stage. The sample threshold for discrete patterns; Define a discrete security domain unit for using the candidate sample point set. Define discrete security domains ,in, Candidate points Security value, t Candidate point number, This is a safety threshold; The first candidate point acquisition unit is used to calculate each candidate point using the exploratory multi-target acquisition function. The multi-target acquisition function value, and the candidate points are ranked according to the multi-target acquisition function value. The candidate points with the highest multi-target acquisition function values ​​are sorted and selected as discrete experimental candidate points. The actual material target performance values ​​and / or safety constraint values ​​of the discrete experimental candidate points are obtained through material experiments or material calculations and saved to the training dataset of the surrogate model. Construct a continuous reachable security domain unit for defining the continuous reachable security domain of the continuous phase. ,in, For security domains, For continuously reachable regions based on the Lipschitz extension, () is a mapping operator that uses the Lipschitz continuity principle to extrapolate and extend the confirmed discrete safe point set into a continuous reachable safe domain; The mode switching unit is used to determine whether it is necessary to switch from the discrete stage to the continuous stage based on the sample threshold. If so, it performs interpolation fusion on the security domains of the two modes through a smooth switching method to generate an extended security domain. ,in, To ensure a smooth transition step size, As weight, This is a transitional round; The second candidate point acquisition unit is used to employ a multi-objective safe particle swarm optimization algorithm to select candidate points within the continuously reachable safe domain. In the process, a global search is performed on the final multi-objective safety acquisition function to obtain the candidate point with the highest value of the multi-objective acquisition function as the continuous experimental candidate point. The real material target performance value and / or safety constraint value of the continuous experimental candidate point are obtained through material experiments or material calculations and saved to the training dataset of the proxy model. The model iteration optimization module is used to conduct experimental tests on the test candidate points, correct the values ​​of the test candidate points based on the experimental test results, generate corrected candidate points, append the corrected candidate points to the model dataset, train and iterate the surrogate model through the model dataset until the convergence condition of the surrogate model is met, and generate the trained surrogate model.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the multi-objective safe Bayesian optimization method for materials development as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that executes the multi-objective safe Bayesian optimization method for materials development as described in any one of claims 1 to 6.

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