Method for predicting output characteristics of object based on proxy model

Abstract

The invention relates to a method for predicting object output characteristics based on a proxy model. The method comprises the following steps: screening characteristic input parameters from original input parameters of an object; selecting a plurality of agent models according to the to-be-predicted output characteristics; optimizing the plurality of agent models by adopting a group search algorithm to obtain a plurality of optimized agent models; respectively inputting the characteristic input parameters into the plurality of optimization agent models to obtain a plurality of prediction results; calculating a corresponding weighted error between each prediction result and an actual result as a loss function by adopting different evaluation indexes of a plurality of weighted values; and selecting the prediction result with the minimum loss function or the optimal evaluation index and the corresponding optimization agent model as an optimal prediction result and an optimal optimization agent model respectively. According to the invention, the method effectively solves a problem that the proxy model is liable to fall into local optimum during the prediction of the output characteristics of the object, improves the robustness of the initial input parameters, and remarkably improves the generalization capability.

Description

Technical Field

[0001] This invention relates to the field of object characteristic prediction, and in particular to a method for predicting the output characteristics of an object based on a surrogate model. Background Technology

[0002] In various industries, there are frequent problems involving predicting the output characteristics of a given object. For example, in engineering design, this might involve predicting the optimal airfoil shape or the allowable values ​​for composite materials. Allowable values ​​for composite materials are limits on their mechanical properties determined through statistical methods, set based on the structural design of the composite. Furthermore, in economics, society, and finance, it is often necessary to predict economic output, population trends, and money supply. To perform such predictions, mathematical prediction models are needed to evaluate the object's output characteristics under different design input parameters. However, in practice, design input parameters are often numerous and diverse, requiring a large number of simulations, such as tens of thousands. This creates a significant computational burden, consuming considerable time and effort.

[0003] To reduce the computational burden during prediction while ensuring the required accuracy, surrogate models are frequently used. Also called approximate models, surrogate models produce results very close to the original model but with less computational cost. Several machine learning modeling methods, such as response surface methodology, Kriging, support vector machines, and artificial neural networks, have adopted surrogate models. However, these surrogate models generally suffer from high sensitivity to initial input parameters, susceptibility to local optima, inability to find the global optimum, and difficulty adapting to real-world applications with high parameter dimensionality and strong nonlinearity. Furthermore, existing research often directly uses a single surrogate model for global modeling, lacking a dynamic adaptation mechanism to the distribution characteristics of multi-source data, resulting in insufficient generalization ability in complex performance predictions. Generalization ability, based on the implicit patterns reflected in the training data, indicates the predictive model's ability to adapt to new samples. It is a core characteristic of a model maintaining effectiveness when processing new data, reflecting its ability to make effective inferences on untrained datasets. Summary of the Invention

[0004] The purpose of this invention is to propose a method for predicting the output characteristics of an object based on a proxy model, which at least partially solves the problems in the prior art.

[0005] The objective is achieved by a method for predicting the output characteristics of an object based on a surrogate model, as proposed according to the present invention. According to the present invention, the method includes the following steps: Select characteristic input parameters that are associated with the output characteristics to be predicted from the object's original input parameters; Based on the output characteristics to be predicted, multiple surrogate models based on different characteristic prediction principles are selected; A swarm search algorithm is used to optimize multiple agent models to obtain multiple optimized agent models. The characteristic input parameters are input into multiple optimized surrogate models to obtain multiple corresponding prediction results; Using different evaluation metrics with multiple weighting values, the corresponding weighted error between each predicted result and the actual result is calculated as the loss function; and The prediction result with the minimum loss function or the best evaluation index and the corresponding optimized surrogate model are selected as the best prediction result and the best optimized surrogate model, respectively.

[0006] This invention constructs a collaboratively enhanced integrated learning framework by integrating complementary mathematical principles and different fitting mechanisms of multivariate surrogate models. Combined with dynamic feature selection and adaptive weight allocation strategies, it autonomously adapts to datasets with different complexities and nonlinear features. This effectively solves the problem that surrogate models are prone to getting trapped in local optima and failing to find the global optimum when predicting the output characteristics of objects. It avoids the structural defects of single models and the risk of data-model mismatch, improves robustness to initial input parameters, and can dynamically adapt to multi-source data and high-dimensional parameters, significantly improving generalization ability and achieving high-precision prediction of the output characteristics of objects with different data characteristics.

[0007] According to one embodiment of the present invention, in the step of screening characteristic input parameters, characteristic input parameters are selected based on the building block principle, the relevance threshold principle, and the feature dimension principle. Here, these three principles ensure that the selected characteristic input parameters are sufficiently representative and important to the original input parameters, remove redundant features and eliminate noise, thereby fundamentally reducing the computational burden of the model and improving the model's prediction accuracy.

[0008] In one embodiment of the present invention, the selection of characteristic input parameters based on the building block principle includes: according to the complexity of the object, a unidirectional feature transfer mechanism from low to high complexity is adopted to form a hierarchical constraint relationship between the original input parameters of different complexities when selecting characteristic input parameters. The building block principle requires that the performance parameters of low-complexity specimens be used as input features of high-complexity specimens, and prohibits reverse modeling, thereby forming a hierarchical constraint relationship from low to high during feature selection, thus reducing the need for complex experimental data.

[0009] According to one embodiment of the present invention, screening characteristic input parameters based on the correlation threshold principle includes: using a correlation coefficient to evaluate the correlation between the original input parameters and the output characteristic to be predicted; when the correlation coefficient is greater than or equal to the correlation threshold, the corresponding original input parameter is selected as a characteristic input parameter. The correlation threshold principle ensures a strong correlation between the model's input parameters and the output characteristic to be predicted, filtering out weakly correlated or uncorrelated features, thereby reducing the computational workload of the model and improving prediction accuracy. Here, the correlation threshold can be dynamically adjusted according to the type of object and / or the output characteristic to be predicted, thus adapting the correlation threshold to different objects and / or different output characteristics to be predicted.

[0010] In one embodiment of the present invention, screening characteristic input parameters based on the feature dimension principle includes: minimizing the sample size of the characteristic input parameters. m With feature dimension n The following dynamic constraint relationships must be satisfied: ; The feature dimension principle establishes a dynamic constraint relationship between the minimum sample size of the characteristic input parameters and the feature dimension. It ensures that under finite sample conditions, the sample size is sufficient to maintain the degree of freedom of the model, while avoiding an excessive number of feature dimensions, preventing the curse of dimensionality, and minimizing the computational burden.

[0011] According to one embodiment of the present invention, the surrogate model is designed to dynamically adjust based on characteristic input parameters. In other words, when the characteristic input parameters change, such as when the object being predicted is different, or even if the object is the same but the output characteristics being examined are different, the surrogate model used to predict the relevant output characteristics also dynamically adjusts accordingly. This improves the adaptability to various different objects and expands the application range for various output characteristics to be predicted.

[0012] In one embodiment of the invention, the surrogate model is specified as one or more of the following models: response surface methodology, support vector machine, backpropagation neural network, and Kriging. Some examples of surrogate models are given here, but the invention is obviously not limited to these models; rather, various appropriate surrogate models can be flexibly selected according to the actual application and specific requirements.

[0013] According to one embodiment of the present invention, the swarm search algorithm is one of the following algorithms: particle swarm optimization algorithm, ant colony optimization algorithm, bee colony optimization algorithm, or genetic algorithm. Swarm search algorithms are swarm intelligence algorithms; similarly, the present invention is not limited to the swarm search algorithm examples given herein, but various appropriate swarm search algorithms can be selected as needed.

[0014] In one embodiment of the present invention, the method further includes: adaptively adjusting the evaluation indicators and their weighting values ​​according to the output characteristics to be predicted. Different evaluation indicators are used to evaluate different output characteristics to be predicted. Furthermore, when multiple evaluation indicators are used, corresponding weighting values ​​are assigned to each evaluation indicator according to its importance or contribution rate. In this way, the predictive ability and prediction results of the model can be accurately and comprehensively reflected, and the model's adaptability to different objects or different output characteristics can be improved.

[0015] In one embodiment of the present invention, the evaluation metric is one or more of the following: relative mean error, relative standard deviation error, relative B-benchmark error, average relative error, and mean square error. Some commonly used examples of evaluation metrics are mentioned herein. It is understood that the present invention is not limited to these listed evaluation metrics. Furthermore, the specific evaluation metrics used depend on the target prediction object and the characteristics of the model's output to be predicted.

[0016] In one embodiment of the present invention, the object is a composite material, and the output characteristic to be predicted is the allowable value of the composite material. An engineering design object is given here, but the present invention can also be applied to other objects and other output characteristics of the object to be predicted, such as predicting total economic output, population change trends, money supply, etc. The present invention does not limit this application.

[0017] This application also relates to a computer program product, including code that, when executed by a computer, causes the computer to perform the method described above. The various embodiments and advantages of the method for predicting the output characteristics of an object based on a surrogate model according to this application described above also apply to the computer program product of this application, and will not be repeated here. Attached Figure Description

[0018] To better understand the above and other objects, features, advantages, and functions of this application, reference can be made to the preferred embodiments shown in the accompanying drawings. The same reference numerals in the drawings denote the same parts. Those skilled in the art should understand that the drawings are intended to schematically illustrate the preferred embodiments of this application and do not limit the scope of this application in any way; the parts in the drawings are not drawn to scale. Figure 1 This is a general flowchart of the method for predicting the output characteristics of an object based on a proxy model according to the present invention; Figure 2 This is a flowchart illustrating an exemplary application of the method according to the present invention in predicting allowable values ​​of composite materials using a particle swarm optimization algorithm; Figure 3 This is an exemplary schematic diagram illustrating the modular principle employed in the method according to the present invention; Figure 4 This is an exemplary schematic diagram illustrating the principle of the adaptive ensemble learning strategy employed in the method according to the present invention; Figure 5 The process of screening the original input parameters using relevant principles in predicting the notched compressive strength of composite materials according to the method of the present invention is illustrated. Figure 6 Dataset information on the notchless compressive strength of composite materials is shown; Figure 7 The modeling information for the notched compressive strength of the composite material is shown; Figure 8 The ranking of indices for predicting the notched compressive strength of composite materials is shown. Figure 9 The method according to the present invention is shown to predict the properties of compressed laminates; and Figure 10 This illustrates a situation in the prior art where the surrogate model gets stuck in a local optimum during fitting and fails to find the global optimum. Detailed Implementation

[0019] The specific embodiments of this application will now be described in detail with reference to the accompanying drawings. The embodiments described herein are merely preferred embodiments based on this application; those skilled in the art can conceive of other ways to implement this application based on the preferred embodiments, and such other ways also fall within the scope of this application.

[0020] The following is combined with Figures 1 to 9 The method 100 according to the present invention will be described in detail below. First, refer to... Figure 1 This document illustrates the overall flowchart of a method 100 for predicting the output characteristics of an object based on a surrogate model according to the present invention. As described above, the method 100 according to the present invention can be used to predict different output characteristics of different objects. For example, the object can be a composite material commonly used in engineering design, and the output characteristic to be predicted is, for example, the allowable value of the mechanical properties of the composite material. However, the method 100 of the present invention can also be applied to other objects and predict other output characteristics of the objects, such as predicting economic output, population change trends, money supply, etc. Therefore, the method 100 of the present invention has broad applicability and is not limited to the few examples listed. The present invention will be described below using the prediction of the allowable mechanical properties of composite materials as an example.

[0021] The method 100 according to the present invention begins with step S1, which involves selecting characteristic input parameters from the original input parameters of the object to identify those associated with the output characteristic to be predicted. For composite materials, since the goal is to predict their allowable mechanical values, characteristic input parameters associated with the output characteristic to be predicted, i.e., the allowable mechanical value, are selected from the original input parameters of the composite material. The output characteristic to be predicted, or the prediction target, of the composite material is, for example, a mechanical parameter that reflects the performance of the composite material, such as ultimate stress and ultimate strain. The allowable value is calculated using mechanical property data combined with engineering algorithms. The original input parameters of the composite material include relevant mechanical property parameters and material parameters, which are numerous and diverse. Characteristic input parameters refer to the most representative and important parameters selected from the many original input parameters. These characteristic input parameters are retained, and redundant data and noise are removed, thereby improving the accuracy of the model.

[0022] According to a specific embodiment of the present invention, the notched compressive strength S of the composite material is determined. C As allowed values, and determine the relevant original input parameters X={X1,X2,…,X... n When determining the original input parameters, data cleaning and noise reduction are usually performed to initially remove irrelevant data, improve prediction accuracy, and reduce computational workload. The unnotched compressive strength of a composite material refers to the maximum stress that the composite material can withstand under compressive load without considering the effects of notches or defects; it reflects the inherent compressive strength of the composite material in the absence of external damage or defects.

[0023] When selecting characteristic input parameters from the original input parameters, three principles should be followed: the building block principle, the relevance threshold principle, and the feature dimension principle. Selecting characteristic input parameters based on the building block principle involves: according to the complexity of the object, employing a unidirectional feature transfer mechanism from low to high complexity, forming a hierarchical constraint relationship between original input parameters of different complexities during the selection process. For details on the building block principle, see [link to relevant documentation]. Figure 3 A unidirectional feature transfer mechanism is established based on the complexity of the specimen, for example, "material parameters → one-way sheet → laminate → typical part". Here, the underlying parameters include the mechanical properties of the one-way sheet; considering that the laminate contains multiple plies, the ply ratio is also included as an input feature. Figure 3 As shown, following a bottom-up approach, the mechanical property parameters of low-complexity specimens (such as one-way plates) are used as input features for high-complexity specimens (such as laminates), and reverse modeling is prohibited, thus forming a hierarchical constraint relationship. In this way, especially for complex objects, the number of input parameters can be significantly reduced while ensuring prediction accuracy, thereby reducing the computational burden of the model.

[0024] Specifically, such as Figure 6 As shown in Table 1, this invention obtained 85 data points of raw input parameters related to the notched compressive strength of the composite material, which consist of data from 5 different layups. See also... Figure 6 Composite materials, for example, are laminates composed of multiple plies. Taking the first type of ply (number 1 in Table 1, each ply representing a one-way sheet) as an example, the subscript " s The quotation marks "" indicate symmetrical arrangement, and the subscript "2" indicates that the content within the brackets is repeated twice, for example, [45 / 0 / -45 / 90]. 2s The ply angles starting from the first layer are 45°, 0°, -45°, 90°, 45°, 0°, -45°, 90°, 90°, -45°, 0°, 45°, 90°, -45°, 0°, and 45°. Among them, the ply ratios of 0°, ±45°, and 90° are 25 / 50 / 25, resulting in 33 data points for the first ply. This pattern continues for the second to fifth ply types.

[0025] Selecting characteristic input parameters based on the correlation threshold principle includes: using the correlation coefficient. ρ The correlation between the original input parameters and the output characteristics to be predicted is evaluated. When the correlation coefficient is greater than or equal to the correlation threshold, the corresponding original input parameter is selected as the characteristic input parameter. Specifically, the correlation coefficient is used. ρ To assess the correlation between parameters, for example, for the allowable value of composite materials, a correlation threshold of 0.4 can be set, which serves as the selection threshold for characteristic input parameters. The correlation coefficient is calculated using the following equation (1) to filter out weakly correlated and irrelevant parameters: (1) Where X and Y represent the input and output parameters, respectively. , This is the corresponding mean. In this invention, the correlation threshold can be dynamically adjusted according to the type of object and / or the output characteristics to be predicted, so that it can be adapted to different objects and / or different output characteristics to be predicted.

[0026] Specifically, in this example, the calculation results for the correlation of notched compressive strength are shown below. Figure 5 The input features for unnotched compressive strength (11 in total) are determined based on the correlation threshold principle. These include 0° tensile modulus, 0° compressive strength, 0° compressive modulus, 90° tensile strength, 90° compressive modulus, Poisson's ratio, longitudinal and transverse shear modulus, and features that must exist in this context. Figure 5 The input features not explicitly marked are the 0° layer ratio, 90° layer ratio, 45° layer ratio, and -45° layer ratio. (This is from...) Figure 5As can be seen, features such as fiber volume content were removed according to the building block principle, and features such as longitudinal and transverse shear modulus were removed according to the correlation threshold principle.

[0027] Selecting characteristic input parameters based on the feature dimension principle includes: using multinomial response surface theory to minimize the sample size of the characteristic input parameters. m With feature dimension n The dynamic constraint relationship is satisfied, as shown in equation (2). This principle ensures that the model's degrees of freedom are maintained under finite sample conditions, preventing the curse of dimensionality. During the reverse solution, given the sample size... m The corresponding maximum feature dimension is determined by equation (3). Based on the feature dimension principle, when the sample size is 85 (a total of 85 data points), the maximum number of input features is approximately 11 according to equation (3). (2) (3)

[0028] After selecting the characteristic input parameters associated with the output characteristics to be predicted from the original input parameters of the object according to the above three principles, step S2 is performed, which involves selecting multiple surrogate models based on different characteristic prediction principles according to the output characteristics to be predicted. In other words, intelligent surrogate models with different mathematical principles and fitting ideas are selected. These include, for example, Response Surface Methodology (RSM), Support Vector Machine Regression (SVMR), Back Propagation Neural Network (BPNN), and Kriging, as shown below: BPNN: y=f(w i f(w i x+b)+b) (4) (5) (6) (7) It should be noted that this invention is not limited to the aforementioned surrogate model, but can be flexibly selected according to the material properties to be predicted. For example, when predicting unnotched tensile properties, the surrogate model can be selected... BPNN And optimize it, while selecting when predicting compression characteristics. SVMR And make it optimal.

[0029] In one embodiment of the present invention, the proxy model is designed to be dynamically adjusted based on the characteristic input parameters. In other words, the characteristic input parameters may be different, but by optimizing multiple (e.g., the current four) proxy models, the optimal proxy model and corresponding parameters can always be selected. Therefore, the present invention can flexibly select different proxy models, thus being applicable to different input parameters of various objects, expanding the scope of application of the present invention.

[0030] However, the aforementioned surrogate model is prone to the problem of searching the initial space during the fitting process. That is, if the starting position of the fitting is different, the effect achieved by the iteration will also be different, making the model prone to getting trapped in local optima and unable to find the global optimum, such as... Figure 10 As shown. To address this problem, in step S3, this paper employs a swarm search algorithm to optimize multiple surrogate models, resulting in multiple optimized surrogate models. This allows for finding the optimal initial position in the global space, assigning optimal initial values ​​to the target parameters, and thus resolving the issue of the aforementioned models easily getting trapped in local optima. Swarm search algorithms are collective intelligence optimization algorithms, including Particle Swarm Optimization (PSO), ant colony optimization, bee colony optimization, genetic algorithms, etc. This invention can flexibly select the specific type of swarm search algorithm as needed. The following will use Particle Swarm Optimization (PSO) as an example to illustrate this invention in detail.

[0031] PSO is a probabilistic search algorithm based on group collaboration, developed by simulating the foraging behavior of bird flocks. Its core idea is to dynamically adjust the particle velocity (movement direction and distance) and position (solution) by sharing individual and group historical optimal information in the solution space to find the global optimal solution. The velocity update formula of PSO (see Equation (8), which includes inertia, individual cognition and social collaboration) and the position update formula (see Equation (9)) are iteratively optimized. In this formula, the inertia weight balances the global exploration and local development capabilities, the individual learning factor and the group learning factor reflect the particle's dependence on its own experience and the group's experience, respectively, and the random number enhances the search diversity, ultimately causing the particle swarm to converge to the optimal position. (8) (9) in, i For particle serial numbers, i =1,2,…, N , N For particle swarm scale, d The particle dimension number. d =1,2,…, D , D In particle dimension, kFor the number of iterations, ω For inertial weights, c 1 represents the individual learning factor. c 2 represents the group learning factor. p id,pbest It is the first i The optimal position found by each particle. p d,pbest It is the optimal position found by the group search (the optimal solution for the group). r 1 and r 2 is a random number within the interval [0, 1], used to increase the randomness of the search.

[0032] Using the Particle Swarm Optimization (PSO) algorithm, we obtained Particle Swarm Optimization-Back Propagation Neural Network (PSO-BPNN), Particle Swarm Optimization-Support Vector Machine Regression (PSO-SVMR), and Particle Swarm Optimization-Kriging (PSO-Kriging) for intelligent agent modeling under global search. (See...) Figure 2 Furthermore, for the response surface, weights are assigned to its sample points in a weighted form (e.g., functional fractional weights), and then improved using weighted least squares to obtain the Refined Response Surface Methodology (RRSM), which also helps in finding the global optimum. The role of PSO differs for different surrogate models. For example, for neural networks, PSO is used to find the optimal weights and thresholds; for Kriging, PSO is used to find the optimal nugget constant and camber; for support vector machines, PSO is used to find the optimal penalty parameters and kernel function parameters, and so on.

[0033] After obtaining the optimized surrogate model through the swarm search algorithm, step S4 of method 100 of the present invention is executed: the characteristic input parameters are input into multiple optimized surrogate models respectively to obtain multiple corresponding prediction results, such as... Figure 2 and Figure 4 As shown. Therefore, the characteristic input parameters are first classified into a training set for training the optimized agent model, a test set for practical testing of the optimized agent model, and a validation set for verifying the optimized agent model, as shown below. Figure 7As shown in Table 2, in step S4, an adaptive ensemble learning system for predicting the allowable value of composite materials is constructed, for example, using a surrogate model. Through multi-dimensional performance evaluation and dynamic weight adjustment, the optimal surrogate model is intelligently selected. Specifically, the unnotched compressive strength dataset is substituted into the adaptive ensemble learning system for training. Considering the complete engineering constraints, based on the principle of "conservative estimation of allowable values," if the predicted allowable value is higher than the actual experimental allowable value, the surrogate model is retrained until the requirements are met.

[0034] After obtaining multiple corresponding prediction results, different evaluation metrics with various weighting values ​​are used to calculate the corresponding weighted error between each prediction result and the actual result as the loss function, which is step S5 of method 100 of the present invention. Here, multiple machine learning methods, such as PSO-BPNN, PSO-SVMR, PSO-Kriging, and RRSM, are integrated, and a weighted averaging strategy is used to select the best model for datasets with different characteristics, forming a global model with more accurate predictions and stronger robustness, thereby improving the generalization ability and stability of the overall model. Figure 4 As shown. For each prediction result, the corresponding machine learning evaluation index is selected, such as relative mean error (RME, see Equation (10)), relative standard deviation error (RSDE, see Equation (11)), relative B-allowableness error (RBE, see Equation (12)), mean relative error (MRE, see Equation (14)), and mean square error (MSE, see Equation (15)). (10) (11) (12) (13) (14) (15) Here, for equations (10)-(13), E yEXP This is the average value from performance tests. E yPRE This is the performance prediction mean. σ yEXP For the standard deviation of performance testing, σyPRE The standard deviation of performance prediction B yEXP For performance testing B Benchmark value B yPRE For performance prediction B Benchmark value This is the average performance. n For the number of samples, C v The coefficient of variation is 1. Z r Let be the standard normal distribution quantiles associated with the confidence level. In equations (14)-(15), n For the sample size, y i EXP For the first i Predicted values ​​for each sample, y i PRE For the first i The true value of each sample.

[0035] Here, these evaluation indicators are assigned corresponding weight values. For example, RME, RSDE, and RBE are assigned weights of 0.25, 0.25, and 0.25, respectively, and MRE and MSE are assigned weights of 0.125 and 0.125, respectively, thereby constructing a weighted error (WE) as a loss function, as shown in equation (16). (16)

[0036] In one embodiment of the present invention, the method further includes adaptively adjusting the evaluation indicators and their weighting values ​​according to the output characteristics to be predicted. This means that, for different objects and different output characteristics to be predicted, the evaluation indicators and their weighting values ​​of each prediction result can be flexibly and dynamically adjusted as needed to conform to the actual prediction situation and meet the corresponding evaluation requirements.

[0037] Finally, in step S6, the prediction result with the minimum loss function or the best evaluation index and the corresponding optimized surrogate model are selected as the best prediction result and the best optimized surrogate model, respectively. See also Figure 8 Table 3 shows some of the model prediction results. It is evident that the minimum loss function WE is 219, thus representing the best prediction result, and its corresponding optimal surrogate model is PSO-SVMR. It should be noted that, as needed, the best prediction results and corresponding optimal surrogate models for one or more evaluation metrics (e.g., RSDE, MSE, RBE) can be selected as the best prediction result and optimal surrogate model. This is... Figure 9As can be seen from the graph, the horizontal axis represents the sample number, and the vertical axis SC_EXP (Streangth compression_experiment) represents the compression strength test value.

[0038] This application also relates to a computer program product, including code that, when executed by a computer, causes the computer to perform the method 100 described above. The various embodiments and advantages of the method 100 for predicting the output characteristics of an object based on a proxy model according to this application described above are also applicable to the computer program product of this application, and will not be repeated here.

[0039] Compared with existing technologies, this invention solves the problems of local optima of surrogate models and insufficient generalization of single models in the prediction of allowable values ​​of composite materials by using adaptive ensemble learning of surrogate models. Based on dozens to hundreds of experimental data, it can achieve a prediction accuracy of over 90%, and achieves higher accuracy in the prediction of allowable values ​​of composite materials under limited sample conditions. It increases the analytical ability and predictive conservatism of the model for input and output characteristics such as complex mechanical property relationships, and realizes efficient, robust and intelligent prediction of allowable values ​​of objects such as composite materials that meet the requirements of various engineering aspects.

[0040] Some embodiments of this application have been described for illustrative purposes, but this application is not limited to these embodiments. Many modifications and variations will also arise in those skilled in the art. Therefore, these embodiments were selected and described to better illustrate the principles and practical applications of this application and to enable those skilled in the art to understand its contents; that is, all modifications and variations made without departing from the spirit of this application will fall within the protection scope of this application as defined by the appended claims.

Claims

1. A method (100) for predicting the output characteristics of an object based on a surrogate model, comprising the following steps: S1: Select characteristic input parameters that are associated with the output characteristics to be predicted from the original input parameters of the object; S2: Based on the output characteristics to be predicted, select multiple surrogate models based on different characteristic prediction principles; S3: The multiple agent models are optimized using a group search algorithm to obtain multiple optimized agent models. S4: Input the characteristic input parameters into the multiple optimized proxy models respectively to obtain the corresponding multiple prediction results; S5: Using different evaluation indicators with multiple weighting values, calculate the corresponding weighted error between each prediction result and the actual result as a loss function; as well as S6: Select the prediction result with the minimum loss function or the best evaluation index and the corresponding optimized surrogate model as the best prediction result and the best optimized surrogate model, respectively.

2. The method (100) according to claim 1, wherein, In step S1, the characteristic input parameters are selected based on the building block principle, the relevance threshold principle, and the feature dimension principle.

3. The method (100) according to claim 2, wherein, The selection of the characteristic input parameters based on the building block principle includes: according to the complexity of the object, a one-way feature transfer mechanism with complexity from low to high is adopted to form a hierarchical constraint relationship between the original input parameters with different complexities when selecting the characteristic input parameters.

4. The method (100) according to claim 2, wherein, The selection of the characteristic input parameters based on the aforementioned relevance threshold principle includes: using the correlation coefficient ( ρ The correlation between the original input parameters and the output characteristics to be predicted is evaluated. When the correlation coefficient is greater than or equal to the correlation threshold, the corresponding original input parameters are selected as the characteristic input parameters.

5. The method (100) according to claim 4, wherein, The correlation threshold is dynamically adjusted based on the type of the object and / or the output characteristics to be predicted.

6. The method (100) according to claim 2, wherein, The selection of the characteristic input parameters based on the aforementioned feature dimension principle includes: minimizing the sample size of the characteristic input parameters ( m ) and feature dimension ( n The following dynamic constraint relationship must be satisfied: ; .

7. The method (100) according to claim 1, wherein, The proxy model is designed to dynamically adjust based on the characteristic input parameters.

8. The method (100) according to claim 7, wherein, The surrogate model is one or more of the following models: Response Surface Model (RSM), Support Vector Machine (SVMR), Backpropagation Neural Network (BPNN), and Kriging.

9. The method (100) according to claim 1, wherein, The swarm search algorithm is one of the following algorithms: Particle Swarm Optimization (PSO), Ant Colony Optimization, Bee Colony Optimization, or Genetic Algorithm.

10. The method (100) according to claim 1, wherein, It also includes: adaptively adjusting the evaluation index and its weighting value according to the output characteristics to be predicted.

11. The method (100) according to claim 10, wherein, The evaluation index is one or more of the following: relative mean error (RME), relative standard deviation error (RSDE), relative error to the B benchmark (RBE), mean relative error (MRE), and mean square error (MSE).

12. The method (100) according to claim 1, wherein, The object is a composite material, and the output characteristic to be predicted is the allowable value of the composite material.

13. A computer program product comprising code that, when executed by a computer, causes the computer to perform the method (100) according to any one of claims 1 to 12.

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