Energy field prediction test design method based on Bayesian depth active learning guidance

Abstract

The invention discloses a Bayesian deep active learning guided energy field prediction test design method, and belongs to the field of spacecraft manufacturing and application. The implementation method comprises the following steps: dividing energy field analysis models with different precisions according to grid density in finite element analysis, constructing a Bayesian multi-credibility neural network model for energy field prediction, deeply mining deep features of training data with different precisions by using the network model, constructing a deep feature explicit transfer link based on meta learning, and predicting the energy field according to the explicit transfer link. Step-by-step learning of deep features of the energy field is realized; a high-dimensional space hypersphere with mutual exclusion attributes is constructed, sample stacking is avoided, and active selection and collection of new samples are completed; constructing a multi-credibility model screening method with the maximum cost-effectiveness ratio, selecting an analysis model with the cost performance as high as possible at a newly-added sample, calling the selected analysis model to generate a result, obtaining new training data, and updating part of parameters of the Bayesian multi-credibility neural network until a termination condition is met, so as to realize energy field prediction.

Description

Technical Field

[0001] The present invention belongs to the field of spacecraft manufacturing and application, and relates to a meta-learning-based multi-credibility Bayesian convolutional neural network agent model construction and an experimental design method based on maximum cost-effectiveness active learning. Background Art

[0002] High-precision and efficient prediction of energy fields is a prerequisite and key to aircraft landing point planning. Physical experiments for energy field prediction are costly and impractical for large-scale implementation. Finite element simulation has gradually become the primary method for energy field prediction. However, finite element simulation for energy field prediction is time-consuming and cannot simulate all operating conditions, severely limiting the real-time performance of aircraft landing point planning. Proxy model technology is the most effective method for reducing the computational burden of finite element simulation, but directly constructing proxy models based on high-precision energy fields is still computationally and costly. Multi-credibility modeling approaches, guided by a small amount of high-precision test data, integrate a larger amount of computationally inefficient and low-precision data. Compared to traditional proxy model approaches based directly on high-precision finite element simulation, this approach effectively reduces the computational burden. However, the rational configuration of multi-credibility data extraction schemes, including physical experiment design, allows for targeted and more scientific physical experiments, rather than relying on traditional subjective experience. This approach, while ensuring energy field prediction accuracy, minimizes the number of physical experiments and the amount of high-precision and time-consuming finite element simulation data, and holds significant engineering value.

[0003] ① Energy field prediction projects often rely on a large number of physical experiments, and the experimental design plans are often determined by human subjective experience, resulting in a large degree of redundancy and waste, and low utilization of experimental data.

[0004] ② Finite element simulation analysis and physical experiments are currently the main means of energy field prediction. Currently, energy field prediction is basically carried out in engineering by mainly using experimental data and supplemented by finite element simulation analysis. Due to the lack of multi-source data fusion algorithms at the system level and experimental design methods for multi-source data configuration, a large number of physical experiments are still required.

[0005] ③ Energy field prediction involves high-dimensional output of the energy field. Traditional proxy model technology for single-output problems often requires the construction of multiple proxy models or the use of dimensionality reduction methods. The former greatly increases the complexity and maintenance cost of the model, and the latter may lose some important information, thereby affecting the accuracy and reliability of energy field prediction, and thus bringing great difficulties to the experimental design of multi-source data. Summary of the Invention

[0006] The purpose of the present invention is to provide an energy field prediction experiment design method guided by Bayesian deep active learning. By establishing a meta-learning-based explicit feature transfer link to achieve multi-source data fusion, an experiment design strategy based on maximum cost-effective active learning is constructed, which improves the energy field prediction accuracy while reducing the experiment and energy field optimization costs.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] The present invention discloses a Bayesian deep active learning guided energy field prediction test design method, which divides energy field analysis models of different precisions according to the grid density in finite element analysis, calls analysis models of different precisions to generate training data respectively, constructs a Bayesian multi-credibility neural network model for energy field prediction, uses the constructed network model to deeply mine the deep features of training data of different precisions, constructs an explicit transmission link of deep features based on meta-learning, realizes step-by-step learning of deep features of energy field, completes the transmission of features from low-precision samples to high-precision samples, and realizes high-precision prediction of energy field; constructs a high-dimensional space hypersphere with mutually exclusive properties to avoid sample stacking and complete the active selection and collection of new samples; constructs a multi-credibility model screening method that maximizes cost-effectiveness, selects an analysis model with the highest cost-effectiveness as possible at the newly added sample, calls the selected analysis model to generate results, obtains new training data, and updates some parameters of the Bayesian multi-credibility neural network until the energy field prediction accuracy meets the termination condition, that is, energy field prediction is achieved.

[0009] The present invention discloses a Bayesian deep active learning-guided energy field prediction experiment design method, comprising the following steps:

[0010] Step 1: Build a 3D model based on the aircraft structure design, retaining key features such as fillets, holes, and connectors. Select a material constitutive model and corresponding model parameters. Material constitutive models include Johnson-Cook, Zerilli-Arm-strong, and Steinberg-Cochran-Guinan. Model parameters corresponding to these material constitutive models include yield strength A, hardening coefficient B, strain rate sensitivity coefficient C, and temperature softening coefficient m.

[0011] High-order elements are used for meshing, with locally refined meshes applied to critical areas, to construct a high-precision finite element simulation analysis model, denoted as y3. Linear elements such as C3D4 tetrahedron elements are used for meshing, removing noncritical geometric features to create a medium-precision analysis model, denoted as y2. Shell or beam elements are used instead of solid elements to simplify the aircraft geometry, resulting in a low-precision analysis model, denoted as y1. High-order elements include hexahedron elements or quadratic tetrahedron elements. Critical areas include stress concentration areas and key load-bearing components.

[0012] Step 2: Based on the length and width of the aircraft's energy field, the energy field is divided into a number of square grids with predetermined side lengths. The energy field information contained within each grid is counted. For the fragment energy field, the number of fragments meeting the kinetic energy threshold within each grid is counted to obtain a gridded energy field. By rasterizing the energy field, the output size of analysis models of varying precision remains consistent. The resulting gridded energy field facilitates the training and output of the Bayesian multi-credibility neural network in step 3.

[0013] The specific implementation method of step 2 is:

[0014] Step 2.1: For the fragment energy field, the finite element simulation analysis model generates an energy field that includes the position, mass, and velocity of each fragment. The energy field is expressed in the form of a matrix:

[0015]

[0016] in, and They represent the horizontal and vertical coordinates, mass and velocity of the fragments respectively.

[0017] Step 2.2: Determine the maximum damage range W of the aircraft's energy field p and L p , grid the energy field and divide it into G square grids K with side length b rt (r=1,…,r p ; t=1,…,t p ), the coordinates of the center point of each square grid are In order to make the gridded energy field more regular, define W p and L p is an integer multiple of b, that is, r p =W p / b,t p =L p / b,r p ×t p =G.

[0018] Step 2.3: Combined with the grid division in step 2.2, the energy field is converted into an aggregated energy field. The aggregated fragment energy field becomes a matrix composed of the grid center point and the aggregated kinetic energy field.

[0019] Combined with the grid division, the kinetic energy in each square is statistically obtained as follows:

[0020]

[0021] The matrix representation of the energy field after aggregation of a certain precision is shown in formula (3), and this matrix is ​​used as the output data of energy field prediction.

[0022]

[0023] Through the rasterization processing in step 2, the output results of analysis models with different precision are unified in format and size, and a rasterized energy field is obtained, which facilitates the construction of a multi-credibility model.

[0024] Step three: Based on the given number of samples of the energy field finite element simulation analysis model with different precision, the input variables are sampled in the design space through Latin hypercube to obtain input samples, and the analysis models with different precision are called respectively to generate training response samples.

[0025] According to the given number of samples [n1, n2, n3] of the energy field finite element simulation analysis model with different precision, the input samples are obtained by sampling the input variables in the design space through Latin hypercube Call analysis models of different precisions respectively to generate training response samples Sample response It is the energy field aggregation matrix after the gridding process in step 2. The input variables include the material constitutive model parameters and working conditions.

[0026] A more accurate energy field finite element simulation model provides fewer samples, while a less accurate model provides more samples, i.e., n1 is the largest and n3 is the smallest. Finally, the input and output sample datasets are {D1, D2, D3} and {d1, d2, d3}, respectively.

[0027] Step 4: To predict the fragment energy field, an improved Bayesian convolutional neural network (BCNN) is constructed, taking the material constitutive model parameters and operating conditions as input (x) and outputting the energy field (y). This network primarily consists of linear layers and Bayesian convolutional layers. The input layer and multiple hidden layers employ linear mapping to extract nonlinear features from the material parameters and operating conditions and map them to a high-dimensional feature space. The output layer employs a Bayesian convolutional structure to model the local continuity of the energy field in spatial coordinates. The Bayesian inference mechanism is used to model model uncertainty, enabling a joint estimation of the mean and variance of the predicted energy value at each spatial point. The bias term in the convolutional output layer is set to 0 to ensure physical consistency and structural simplicity of the prediction results, consistent with the actual law of smooth decay or symmetrical diffusion of energy in space during energy field generation. A KL divergence regularization term is introduced during training to constrain the consistency of the prior and posterior distributions, enhancing the ability of the finite element simulation analysis model to express the spatial distribution pattern of the energy field. Analytical expressions for the predicted mean and variance of the energy field under arbitrary input conditions are constructed. This BCNN structure not only improves the prediction accuracy, but also provides reliable confidence intervals under limited samples.

[0028] The specific implementation method of step four is:

[0029] Step 4.1: Define a deep neural network with L layers:

[0030]

[0031] Among them, w L and b L are the weights and biases of the Lth layer (i.e., the output layer) of the network; is the iterative value of the input variable x after the first L-1 layer network operation; θ - Represents all network parameters of the first L-1 layer; f θ It represents a deep neural network with the final network parameter θ.

[0032] Step 4.2: In the deep neural network defined in step 4.1, w and b are both fixed values. To improve the robustness of the network, it is assumed that the weights and biases are transformed from fixed values ​​to obey a certain probability distribution. Based on the fully connected neural network, only the output layer is set to a Bayesian convolution layer, making the output layer unbiased. This is the basic structure of the Bayesian convolutional neural network, which can ensure the physical consistency and structural simplicity of the prediction results, and conforms to the actual law that energy in the energy field is smoothly attenuated or symmetrically diffused in space during generation. The corresponding BCNN is expressed as follows:

[0033]

[0034] Among them, θ -Represents the network parameters of other layers, is the output vector of the penultimate layer.

[0035] Step 4.3: Let the network parameters of the Bayesian convolutional neural network be θ, and p(θ) be the prior distribution of the parameters, which is a standard normal distribution. Given a training set {X, Y}, where X is the input data and Y is the output response data, based on the Bayesian formula, the posterior probability of θ is as follows:

[0036]

[0037] Where p(Y|X,θ) is the likelihood function and ∫p(Y|X,θ)p(θ)dθ is the marginal integral.

[0038] The variational inference method is used to calculate the integral. The basic idea is to establish a simple distribution that obeys the normal distribution to approximate the posterior distribution p(θ|X,Y). By adjusting the mean and variance of the simple distribution, the Kullback-Leibler (KL) divergence between the simple distribution and the posterior distribution is minimized to obtain the optimal parameter estimate θ. * Therefore, in Bayesian network training, variational inference methods often assume that network weights and biases are normally distributed and keep the distribution type unchanged, while their mean and variance are continuously updated during the training process.

[0039] Step 4.4: Combined with the network parameters obtained in step 4.3, based on the trained Bayesian convolutional neural network, the posterior distribution of the Bayesian convolutional neural network response prediction at the input position x is:

[0040] p(x)~N(α(x),η(x)) (7)

[0041] in:

[0042]

[0043] Where, Expressing expectation.

[0044] The above formula (8) is calculated using Gauss integral numerical integration.

[0045]

[0046] Among them, t k and g k They represent the Gaussian integral node and integral weight corresponding to the weight w of the output layer, respectively, and the distribution mean μ of w w and standard deviation σ w Decide.

[0047] By analyzing expressions (9) and (10), the predicted mean and variance of each square of the predicted aggregate energy field are obtained. The BCNN predicted mean is output as the final prediction result, and the predicted variance will serve the subsequent active learning experiment design process.

[0048] Step 5: Convert the input and output samples {D t ,d t}(t=1,2,3) perform sampling with replacement and construct multiple task subsets T i (i=1,…,K), forming a task set to support task-level meta-learning training. During the training phase, data at different confidence levels are input step by step from low to high precision. Using the model-agnostic meta-learning (MAML) method, the initial parameters of the shared model are continuously optimized through each layer of task training, allowing these parameters to quickly adapt to the energy field prediction requirements of the current training task. During training, an explicit cross-confidence feature transfer link is constructed to mine deep feature information contained in samples of different precision levels. This information is explicitly transferred to the higher-confidence model through the network structure, enhancing the physical expressiveness and prediction consistency of the features. Through a meta-learning-driven step-by-step training mechanism, knowledge transfer and rapid adaptation of the energy field from low-precision to high-precision samples are achieved. When the high-precision sample {D3,d3} is introduced, the network already has good initialization capabilities, requiring only a small amount of high-cost, high-precision simulation data to achieve rapid convergence and high-precision predictions, significantly reducing training costs and the computational resources required for high-precision modeling.

[0049] Step 6: Introduce the scarce experimental data in practice {D e ,d e The energy field grid points measured in the physical experiment are not as dense as the gridded energy field in step 2, and the output energy field data are not measured at the same grid points. Therefore, the multi-credibility neural network trained in step 5 is combined with the linear interpolation method to obtain the output data on the energy field grid points in the physical experiment, so that the finite element simulation analysis model is consistent with the experimental output data, and the experimental data {D e ,d e}Train and update parameters of multi-credibility neural networks to further improve the consistency between BCNN network predictions and experiments.

[0050] In step seven, energy field prediction is performed based on the currently constructed multi-credibility Bayesian convolutional neural network, and the accuracy of the Bayesian convolutional neural network is verified through the test set. If the accuracy meets the requirements, the construction of the multi-credibility Bayesian convolutional neural network is completed, otherwise proceed to step eight.

[0051] The specific implementation method of step seven is:

[0052] Based on the currently constructed multi-credibility Bayesian convolutional neural network, a test set is generated on a high-precision energy field finite element simulation analysis model. Experimental data can also be used as a test set to calculate the root mean square error (RMSE) of the network prediction to verify the accuracy of the Bayesian convolutional neural network. The RMSE is defined as follows:

[0053]

[0054] Among them, m represents the number of samples in the test set, y i Indicates high-precision energy field response value, Represents the energy field prediction value based on multi-credibility Bayesian convolutional neural network.

[0055] If the accuracy does not meet the requirements, that is, RMSE>Δ, new samples need to be drawn, where Δ is the set threshold.

[0056] In step eight, the prediction variance from step four is combined to establish a maximum a posteriori variance estimate. The input location with the largest a posteriori variance is identified in the global input space and designated as the most critical sampling point (i.e., the point of maximum uncertainty) for the current stage. Several candidate points with variances close to the maximum variance are simultaneously selected as multi-point supplementary samples. A screening mechanism based on a high-dimensional mutually exclusive hypersphere structure is established. A high-dimensional hypersphere region with a certain radius is constructed in the input space, centered around the selected key point, and defined as an exclusive region. Subsequent candidate points are considered only if they do not fall within the region of the existing hypersphere. During hypersphere construction, the radius of the hypersphere is determined by the scale and distribution characteristics of the input variables, ensuring clear boundaries and no overlap between regions. All selected sample points form a set of spatially exclusive, globally uniformly distributed sampling points in the input space. This screening mechanism effectively guides sampling toward regions of high model uncertainty, enhancing the information content of the samples while avoiding clustering and stacking of sampling points in the input space, thereby improving the diversity and distribution rationality of the experimental design.

[0057] The specific implementation method of step eight is:

[0058] The Bayesian convolutional neural network can provide the advantage of the posterior variance of the response prediction, and establish a multi-point sampling method based on the maximum posterior variance. Considering that for deep learning, if too few samples are drawn each time, the accuracy of the BCNN network will not be significantly improved, and the sampling process will be very lengthy. However, the number of samples drawn each time cannot be too large, otherwise the advantage of sequential sampling cannot be utilized. Therefore, based on experience, the upper limit of the number of samples drawn each time is set to n S. Establish a maximum a posteriori variance search strategy. According to the prediction variance given in step 4.4, sum the prediction methods of each square in the predicted aggregated energy field of any input position as the posterior variance of the input position, select the input position with the largest posterior variance as the key input sample, and select several points whose posterior variance is close to the maximum posterior variance as candidate input samples. In order to avoid the stacking of samples near a certain input position and limit the overall improvement of network accuracy, a distance-based sample screening principle is proposed. According to the Euclidean distance between any two points in the key sample and the candidate sample, a set of distances that are not too close to each other (d≥d t ) and the overall posterior variance is larger, then all valid input samples of this sequence sampling are obtained. By setting the distance threshold d t To avoid samples being too close together:

[0059]

[0060] Among them, d max Indicates the maximum value of all dimensional variation ranges of the current sample input space. It represents the maximum Euclidean distance between candidate samples and key samples. β is a correction parameter, generally set to 0.1. Because variables of different dimensions have different ranges, in order to avoid the impact of excessively large or small ranges in individual dimensions, the ranges of all dimensions need to be normalized before calculating the distance.

[0061] Step nine: A cost-effectiveness index is constructed that comprehensively considers the prediction gain and computational cost to guide the selection of cost-effective sample analysis models. This index integrates the simulation computing resource consumption (such as CPU time, memory usage, meshing complexity, etc.) required for the accuracy level of the analysis model and its contribution to improving the energy field prediction accuracy, thereby achieving a quantitative measurement of "cost-effectiveness". The analysis models are sorted according to the cost-effectiveness index, and analysis models with large marginal benefits in improving prediction accuracy and relatively low computational costs are given priority, thus constructing a set of experimental design inputs with high cost-effectiveness, low redundancy, and high contribution.

[0062] The specific implementation method of step nine is:

[0063] Step 9.1: Establish a cost-effectiveness index (CEI) that takes into account the maximum cost-effectiveness of the sample.

[0064]

[0065] Where, subscript t represents the tth analysis model y in the low-precision energy field analysis model t (x); C t represents yt The cost of (x) can be the modeling time cost or labor cost, the computational cost of calling the model once, or a combination thereof; Corr t Indicates the input sample position y t The closer the value is to 1, the more likely y is to be positive at this input sample. t The closer the prediction accuracy of (x) is to y3(x).

[0066] Step 9.2: Corr t (x) is represented by y t The posterior distribution p of the BCNN response predictions for (x) and y3(x) t The distance between (x) and p3(x) is calculated by introducing the Wasserstein distance criterion to quantify the distance between the two distributions. Regarding the calculation of the posterior distribution, all low-precision models y can be obtained in the process of multi-credibility model fusion. t Bayesian Convolutional Neural Network for (x) Without calling the real analysis model, it can be based on the trained Bayesian convolutional neural network Using formula (8), we can get the posterior distribution p of the response prediction at the input position x: t (x)~N(α t (x),η t (x)).

[0067] Step 9.3: Determine the analytical model (including analytical model and experiment) that should be called at the new sample input position, denote the analytical model with the largest CEI value as M*, obtain the energy field prediction response data of M* at the input sample position, and reduce the cost as much as possible while ensuring the improvement of the neural network accuracy.

[0068]

[0069] Add the samples extracted from the sequence to the old samples, and repeat steps five to eight based on the updated sample set until the energy prediction accuracy index of the multi-credibility Bayesian convolutional neural network meets the requirements, and obtain the energy field prediction experiment design results guided by Bayesian deep active learning.

[0070] It also includes step ten. After the multi-credibility Bayesian convolutional neural network prediction model is constructed, the aircraft energy field is predicted based on the energy field finite element simulation analysis model to obtain energy field prediction results that are consistent with the test data. While improving the energy field modeling speed and reducing the test cost, the accuracy of aircraft damage assessment is guaranteed, thereby improving the accuracy and efficiency of firepower allocation and firepower planning.

[0071] Beneficial effects:

[0072] 1. The present invention discloses a Bayesian deep active learning guided energy field prediction test design method, which fully utilizes the convenience and low cost of finite element simulation analysis to establish finite element simulation analysis models with different accuracies of energy field prediction, and combines experimental data to perform meta-learning-based multi-credibility data fusion modeling, thereby achieving high-precision and high-efficiency prediction of the energy field and significantly reducing experimental costs and simulation time.

[0073] 2. The present invention discloses a Bayesian deep active learning guided energy field prediction experiment design method, which constructs an improved Bayesian convolutional network with an output layer as an unbiased layer, realizes the analytical expression of the predicted mean and variance, and lays the foundation for the rapid formulation of subsequent experimental design plans.

[0074] 3. The present invention discloses a Bayesian deep active learning guided energy field prediction experiment design method, establishes a set of meta-learning based explicit feature transfer links, proposes a multi-point sampling method based on maximum posterior variance and maximized cost-effectiveness, and forms a cost-effective experiment design scheme including simulation and experiment. It specifically increases physical experiments and high-precision simulation deep data, realizes high-precision prediction of energy fields under small samples, and significantly reduces experimental costs and simulation time.

[0075] 4. The present invention discloses a Bayesian deep active learning guided energy field prediction test design method, which establishes an energy field aggregation strategy to ensure the uniformity of output responses of analysis models with different precisions. At the same time, it combines a multi-credibility Bayesian convolutional neural network architecture to achieve rapid and accurate prediction of high-dimensional field variables of the energy field, providing the necessary prerequisite for the effective formulation of subsequent experimental design plans. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 Flowchart of the energy field prediction experiment design method guided by Bayesian deep active learning of the present invention.

[0077] Figure 2 Schematic diagram of a Bayesian network.

[0078] Figure 3 Schematic diagram of multi-credibility modeling based on meta-learning.

[0079] Figure 4 Input sample selection diagram.

[0080] Figure 5 RMSE change curve during the generation of active learning experimental design schemes. DETAILED DESCRIPTION

[0081] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0082] Example 1:

[0083] like Figure 1 As shown, the present embodiment discloses a Bayesian deep active learning-guided energy field prediction experiment design method, and the specific implementation steps are as follows:

[0084] Step 1: Build a 3D model based on the aircraft structure design, retaining key features such as fillets, holes, and connectors. Select a material constitutive model and corresponding model parameters. Material constitutive models include Johnson-Cook, Zerilli-Arm-strong, and Steinberg-Cochran-Guinan. Model parameters corresponding to these material constitutive models include yield strength A, hardening coefficient B, strain rate sensitivity coefficient C, and temperature softening coefficient m.

[0085] High-order elements are used for meshing, with locally refined meshes applied to critical areas, to construct a high-precision finite element simulation analysis model, denoted as y3. Linear elements such as C3D4 tetrahedron elements are used for meshing, removing noncritical geometric features to create a medium-precision analysis model, denoted as y2. Shell or beam elements are used instead of solid elements to simplify the aircraft geometry, resulting in a low-precision analysis model, denoted as y1. High-order elements include hexahedron elements or quadratic tetrahedron elements. Critical areas include stress concentration areas and key load-bearing components.

[0086] Step 2: Based on the length and width of the aircraft's energy field, the energy field is divided into a number of square grids with predetermined side lengths. The energy field information contained within each grid is counted. For the fragment energy field, the number of fragments meeting the kinetic energy threshold within each grid is counted to obtain a gridded energy field. By rasterizing the energy field, the output size of analysis models of varying precision remains consistent. The resulting gridded energy field facilitates the training and output of the Bayesian multi-credibility neural network in step 3.

[0087] The specific implementation method of step 2 is:

[0088] Step 2.1: For the fragment energy field, the finite element simulation analysis model generates an energy field that includes the position, mass, and velocity of each fragment. The energy field is expressed in the form of a matrix:

[0089]

[0090] in, and They represent the horizontal and vertical coordinates, mass and velocity of the fragments respectively.

[0091] Step 2.2: Determine the maximum damage range W of the aircraft's energy field p and L p, grid the energy field and divide it into G square grids K with side length b rt (r=1,…,r p ; t=1,…,t p ), the coordinates of the center point of each square grid are In order to make the gridded energy field more regular, define W p and L p is an integer multiple of b, that is, r p =W p / b,t p =L p / b,r p ×t p =G.

[0092] Step 2.3: Combined with the grid division in step 2.2, the energy field is converted into an aggregated energy field. The aggregated fragment energy field becomes a matrix composed of the grid center point and the aggregated kinetic energy field.

[0093] Combined with the grid division, the kinetic energy in each square is statistically obtained as follows:

[0094]

[0095] The matrix representation of the energy field after aggregation of a certain precision is shown in formula (3), and this matrix is ​​used as the output data of energy field prediction.

[0096]

[0097] Through the rasterization processing in step 2, the output results of analysis models with different precision are unified in format and size, and a rasterized energy field is obtained, which facilitates the construction of a multi-credibility model.

[0098] Step 3: Based on the given sample size [200, 100, 20], the input variables (material constitutive model parameters and working conditions) are sampled in the design space by Latin hypercube to obtain the input samples. Call three analysis models of different precision to generate training response samples It should be noted that the response sample here is the energy field aggregation matrix that has been gridded after step 2. Finally, the input and output sample data sets are obtained, which are {D1, D2, D3} and {d1, d2, d3} respectively.

[0099] Step 4: For the prediction of fragment energy field, an improved Bayesian convolutional neural network (BCNN) is constructed with material constitutive model parameters and working conditions as input x and energy field y as output. The network mainly consists of linear layers and Bayesian convolution layers, in which the input layer and multiple hidden layers adopt linear mapping to extract nonlinear features in material parameters and working conditions and map them to high-dimensional feature space; the output layer adopts Bayesian convolution structure to model the local continuity features of the energy field in spatial coordinates; the model uncertainty modeling capability is introduced through the Bayesian reasoning mechanism to realize the joint estimation of the mean and variance of the energy prediction value of each spatial point. Figure 2 As shown, the bias term of the convolutional output layer is set to 0 to ensure the physical consistency and structural simplicity of the prediction results, and to conform to the actual law of smooth attenuation or symmetrical diffusion of energy in space during energy field generation. A KL divergence regularization term is introduced during training to constrain the consistency of the prior and posterior distributions, enhancing the ability of the energy field finite element simulation analysis model to express the spatial distribution pattern of the energy field. Analytical expressions for the predicted mean and predicted variance of the energy field under arbitrary input conditions are constructed. This BCNN structure not only improves prediction accuracy but also provides reliable confidence intervals with limited samples.

[0100] The specific implementation method of step four is:

[0101] Step 4.1: Define a deep neural network with L layers:

[0102]

[0103] Among them, w L and b L are the weights and biases of the Lth layer (i.e., the output layer) of the network; is the iterative value of the input variable x after the first L-1 layer network operation; θ - Represents all network parameters of the first L-1 layer; f θ It represents a deep neural network with the final network parameter θ.

[0104] Step 4.2: In the deep neural network defined in step 4.1, w and b are both fixed values. To improve the robustness of the network, it is assumed that the weights and biases are transformed from fixed values ​​to obey a certain probability distribution. Based on the fully connected neural network, only the output layer is set to a Bayesian convolution layer, making the output layer unbiased. This is the basic structure of the Bayesian convolutional neural network, which can ensure the physical consistency and structural simplicity of the prediction results, and conforms to the actual law that energy in the energy field is smoothly attenuated or symmetrically diffused in space during generation. The corresponding BCNN is expressed as follows:

[0105]

[0106] Among them, θ - Represents the network parameters of other layers, is the output vector of the penultimate layer.

[0107] Step 4.3: Let the network parameters of the Bayesian convolutional neural network be θ, and p(θ) be the prior distribution of the parameters, which is a standard normal distribution. Given a training set {X, Y}, where X is the input data and Y is the output response data, based on the Bayesian formula, the posterior probability of θ is as follows:

[0108]

[0109] Where p(Y|X,θ) is the likelihood function and ∫p(Y|X,θ)p(θ)dθ is the marginal integral.

[0110] The variational inference method is used to calculate the integral. The basic idea is to establish a simple distribution that obeys the normal distribution to approximate the posterior distribution p(θ|X,Y). By adjusting the mean and variance of the simple distribution, the Kullback-Leibler (KL) divergence between the simple distribution and the posterior distribution is minimized to obtain the optimal parameter estimate θ. * Therefore, in Bayesian network training, variational inference methods often assume that network weights and biases are normally distributed and keep the distribution type unchanged, while their mean and variance are continuously updated during the training process.

[0111] Step 4.4: Combined with the network parameters obtained in step 4.3, based on the trained Bayesian convolutional neural network, the posterior distribution of the Bayesian convolutional neural network response prediction at the input position x is:

[0112] p(x)~N(α(x),η(x)) (21)

[0113] in:

[0114]

[0115] Where, Expressing expectation.

[0116] The above formula (8) is calculated using Gauss integral numerical integration.

[0117]

[0118] Among them, t k and g k They represent the Gaussian integral node and integral weight corresponding to the weight w of the output layer, respectively, and the distribution mean μ of w w and standard deviation σ w Decide.

[0119] By analyzing expressions (9) and (10), the predicted mean and variance of each square of the predicted aggregate energy field are obtained. The BCNN predicted mean is output as the final prediction result, and the predicted variance will serve the subsequent active learning experiment design process.

[0120] Step 5: Convert the input and output samples {D t ,d t}(t=1,2,3) perform sampling with replacement and construct multiple task subsets T i (i=1,…,K), forming a task set to support task-level meta-learning training, such as Figure 3 As shown in the figure. During the training phase, data at different credibility levels are input step by step in the order from low precision to high precision. The model-agnostic meta-learning (MAML) method is used to continuously optimize the initial parameters of the shared model through each layer of task training, so that the parameters can quickly adapt to the energy field prediction requirements of the current training task. During the training process, an explicit cross-credibility feature transfer link is constructed to mine the deep feature information contained in samples of different precisions, and explicitly transfer it to the higher credibility model through the network structure to enhance the physical expressiveness and prediction consistency of the features. Through the meta-learning-driven step-by-step training mechanism, the knowledge transfer and rapid adaptation of the energy field from low-precision to high-precision samples are achieved. When the high-precision sample {D3, d3} is introduced, the network already has good initialization capabilities and only requires a small amount of high-cost and high-precision simulation data to achieve rapid convergence and high-precision prediction, significantly reducing the training cost and the computing resources required for high-precision modeling.

[0121] Step 6: Introduce the scarce experimental data in practice {D e ,d e The energy field grid points measured in the physical experiment are not as dense as the gridded energy field in step 2, and the output energy field data are not measured at the same grid points. Therefore, the multi-credibility neural network trained in step 5 is combined with the linear interpolation method to obtain the output data on the energy field grid points in the physical experiment, so that the finite element simulation analysis model is consistent with the experimental output data, and the experimental data {D e ,d e}Train and update parameters of multi-credibility neural networks to further improve the consistency between BCNN network predictions and experiments.

[0122] In step seven, energy field prediction is performed based on the currently constructed multi-credibility Bayesian convolutional neural network, and the accuracy of the Bayesian convolutional neural network is verified through the test set. If the accuracy meets the requirements, the construction of the multi-credibility Bayesian convolutional neural network is completed, otherwise proceed to step eight.

[0123] The specific implementation method of step seven is:

[0124] Based on the currently constructed multi-credibility Bayesian convolutional neural network, a test set is generated on a high-precision energy field finite element simulation analysis model. Experimental data can also be used as a test set to calculate the root mean square error (RMSE) of the network prediction to verify the accuracy of the Bayesian convolutional neural network. The RMSE is defined as follows:

[0125]

[0126] Among them, m represents the number of samples in the test set, y i Indicates high-precision energy field response value, Represents the energy field prediction value based on multi-credibility Bayesian convolutional neural network.

[0127] If the accuracy does not meet the requirements, that is, RMSE>Δ, new samples need to be drawn, where Δ is the set threshold, which is 0.5.

[0128] In step eight, the prediction variance from step four is combined to establish a maximum a posteriori variance estimate. The input location with the largest a posteriori variance is identified in the global input space and designated as the most critical sampling point (i.e., the point of maximum uncertainty) for the current stage. Several candidate points with variances close to the maximum variance are simultaneously selected as multi-point supplementary samples. A screening mechanism based on a high-dimensional mutually exclusive hypersphere structure is established. A high-dimensional hypersphere region with a certain radius is constructed in the input space, centered around the selected key point, and defined as an exclusive region. Subsequent candidate points are considered only if they do not fall within the region of the existing hypersphere. During hypersphere construction, the radius of the hypersphere is determined by the scale and distribution characteristics of the input variables, ensuring clear boundaries and no overlap between regions. All selected sample points form a set of spatially exclusive, globally uniformly distributed sampling points in the input space. This screening mechanism effectively guides sampling toward regions of high model uncertainty, enhancing the information content of the samples while avoiding clustering and stacking of sampling points in the input space, thereby improving the diversity and distribution rationality of the experimental design.

[0129] The specific implementation method of step eight is:

[0130] The Bayesian convolutional neural network can provide the advantage of the posterior variance of the response prediction, and establish a multi-point sampling method based on the maximum posterior variance. Considering that for deep learning, if too few samples are drawn each time, the accuracy of the BCNN network will not be significantly improved, and the sampling process will be very lengthy. However, the number of samples drawn each time cannot be too large, otherwise the advantage of sequential sampling cannot be utilized. Therefore, based on experience, the upper limit of the number of samples drawn each time is set to n S. Establish a maximum a posteriori variance search strategy. According to the prediction variance given in step 4.4, sum the prediction methods of each square in the predicted aggregated energy field of any input position as the posterior variance of the input position, select the input position with the largest posterior variance as the key input sample, and select several points whose posterior variance is close to the maximum posterior variance as candidate input samples. In order to avoid the stacking of samples near a certain input position and limit the overall improvement of network accuracy, a distance-based sample screening principle is proposed. According to the Euclidean distance between any two points in the key sample and the candidate sample, a set of distances that are not too close to each other (d≥d t ) and the overall posterior variance is larger, then all valid input samples of this sequence sampling are obtained. By setting the distance threshold d t To avoid samples being too close together:

[0131]

[0132] Among them, d max Indicates the maximum value of all dimensional variation ranges of the current sample input space. It represents the maximum Euclidean distance between candidate samples and key samples. β is a correction parameter, generally set to 0.1. Because variables of different dimensions have different ranges, in order to avoid the impact of excessively large or small ranges in individual dimensions, the ranges of all dimensions need to be normalized before calculating the distance. Figure 4 The projection of the hypersphere on a 1-dimensional plane is shown.

[0133] Step nine: A cost-effectiveness index is constructed that comprehensively considers the prediction gain and computational cost to guide the selection of cost-effective sample analysis models. This index integrates the simulation computing resource consumption (such as CPU time, memory usage, meshing complexity, etc.) required for the accuracy level of the analysis model and its contribution to improving the energy field prediction accuracy, thereby achieving a quantitative measurement of "cost-effectiveness". The analysis models are sorted according to the cost-effectiveness index, and analysis models with large marginal benefits in improving prediction accuracy and relatively low computational costs are given priority, thus constructing a set of experimental design inputs with high cost-effectiveness, low redundancy, and high contribution.

[0134] The specific implementation method of step nine is:

[0135] Step 9.1: Establish a cost-effectiveness index (CEI) that takes into account the maximum cost-effectiveness of the sample.

[0136]

[0137] Where, subscript t represents the tth analysis model y in the low-precision energy field analysis model t(x); C t represents y t The cost of (x) can be the modeling time cost or labor cost, the computational cost of calling the model once, or a combination thereof; Corr t Indicates the input sample position y t The closer the value is to 1, the more likely y is to be positive at this input sample. t The closer the prediction accuracy of (x) is to y3(x).

[0138] Step 9.2: Corr t (x) is represented by y t The posterior distribution p of the BCNN response predictions for (x) and y3(x) t The distance between (x) and p3(x) is calculated by introducing the Wasserstein distance criterion to quantify the distance between the two distributions. Regarding the calculation of the posterior distribution, all low-precision models y can be obtained in the process of multi-credibility model fusion. t Bayesian Convolutional Neural Network for (x) Without calling the real analysis model, it can be based on the trained Bayesian convolutional neural network Using formula (8), we can get the posterior distribution p of the response prediction at the input position x: t (x)~N(α t (x),η t (x)).

[0139] Step 9.3: Determine the analytical model (including analytical model and experiment) that should be called at the new sample input position, denote the analytical model with the largest CEI value as M*, obtain the energy field prediction response data of M* at the input sample position, and reduce the cost as much as possible while ensuring the improvement of the neural network accuracy.

[0140]

[0141] Add the samples extracted from the sequence to the old samples, and repeat steps five to eight based on the updated sample set until the energy prediction accuracy index of the multi-credibility Bayesian convolutional neural network meets the requirements, and obtain the energy field prediction experiment design results guided by Bayesian deep active learning.

[0142] Figure 5 The RMSE curve of the network prediction error during the generation of the active learning experimental design scheme is shown. It can be seen from the figure that with the advancement of active learning, the prediction accuracy of the network is constantly improving, which is reflected in the gradual decrease of RMSE until the accuracy requirements are met.

[0143] Table 1 shows the experimental design scheme generated by active learning. It can be found that during the active learning process, the active learning strategy neither blindly selects high-precision samples (n3) nor blindly selects low-precision samples (n1). Instead, it adaptively selects samples based on the cost-effectiveness of the samples to form the most cost-effective experimental design scheme.

[0144] To further verify the effectiveness of the patented method, we also trained the network using Latin hypercube sampling to generate training samples based on the final number of active learning samples [227, 114, 29] and tested its accuracy. The results are shown in Table 1, as RMSE*. This comparison shows that the patented method is more accurate and can achieve better resource allocation.

[0145] Table 1 Experimental design of active learning

[0146]

[0147] It also includes step ten. After the multi-credibility Bayesian convolutional neural network prediction model is constructed, the aircraft energy field is predicted based on the energy field finite element simulation analysis model to obtain energy field prediction results that are consistent with the test data. While improving the energy field modeling speed and reducing the test cost, the accuracy of aircraft damage assessment is guaranteed, thereby improving the accuracy and efficiency of firepower allocation and firepower planning.

[0148] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A Bayesian deep active learning-guided energy field prediction experiment design method, characterized by: According to the grid density in finite element analysis, energy field analysis models of different precisions are divided, and analysis models of different precisions are called respectively to generate training data. A Bayesian multi-credibility neural network model for energy field prediction is constructed. The constructed network model is used to deeply mine the deep features of training data of different precisions, and an explicit transmission link of deep features based on meta-learning is constructed to realize step-by-step learning of deep features of the energy field, complete the transmission of features from low-precision samples to high-precision samples, and realize high-precision prediction of the energy field; a high-dimensional space hypersphere with mutually exclusive properties is constructed to avoid sample stacking and complete the active selection and collection of new samples; a multi-credibility model screening method that maximizes cost-effectiveness is constructed, and the analysis model with the highest cost-effectiveness as possible is selected at the newly added sample. The selected analysis model is called to generate results, and new training data is obtained. Some parameters of the Bayesian multi-credibility neural network are updated until the energy field prediction accuracy meets the termination condition, that is, energy field prediction is achieved.

2. The Bayesian deep active learning-guided energy field prediction experiment design method according to claim 1, characterized in that: The following steps are included: Step 1: Build a 3D model based on the aircraft structure design, retain key features, and select a material constitutive model and corresponding model parameters. Material constitutive models include Johnson-Cook, Zerilli-Arm-strong, and Steinberg-Cochran-Guinan. Model parameters corresponding to the material constitutive model include yield strength A, hardening coefficient B, strain rate sensitivity coefficient C, and temperature softening coefficient m. Key features include preservation such as fillets, holes, and connectors; Step 2: Based on the length and width of the aircraft energy field, the energy field is divided into several square grids with predetermined side lengths. The energy field information contained in each grid is counted. For the fragment energy field, the number of fragments that meet the kinetic energy threshold in each grid is counted to obtain a gridded energy field. By rasterizing the energy field, the output size of analysis models with different accuracies is kept consistent, and the gridded energy field is obtained, which facilitates the training and output of the Bayesian multi-credibility neural network in step 3. Step 3: Based on the number of samples of the given energy field finite element simulation analysis model with different precision, the input variables are sampled in the design space through Latin hypercube to obtain input samples, and the analysis models with different precision are called respectively to generate training response samples; Step 4: To predict the fragment energy field, an improved Bayesian convolutional neural network (BCNN) is constructed with the material constitutive model parameters and working conditions as input x and the energy field y as output. The network mainly consists of linear layers and Bayesian convolutional layers. The input layer and multiple hidden layers use linear mapping to extract nonlinear features from material parameters and working conditions and map them to a high-dimensional feature space. The output layer uses a Bayesian convolution structure to model the local continuity characteristics of the energy field in spatial coordinates; The Bayesian inference mechanism is used to introduce model uncertainty modeling capabilities, achieving a joint estimation of the mean and variance of the energy prediction value at each spatial point. The bias term of the convolutional output layer is set to 0 to ensure the physical consistency and structural simplicity of the prediction results, and to conform to the actual law that energy in space exhibits smooth attenuation or symmetrical diffusion during the energy field generation process. The KL divergence regularization term is introduced during the training process to constrain the consistency of the prior and posterior distributions, thereby enhancing the energy field finite element simulation analysis model's ability to express the energy field's spatial distribution pattern. Analytical expressions for the energy field prediction mean and prediction variance under arbitrary input conditions are constructed. This BCNN structure not only improves prediction accuracy but also provides reliable confidence intervals under finite samples. Step 5: The input and output samples at a certain precision level are sampled with replacement to construct multiple task subsets to form a task set to support task-level meta-learning training. During the training phase, data at different credibility levels are input step by step in the order from low precision to high precision. The model-independent meta-learning MAML method is used to continuously optimize the initial parameters of the shared model through each layer of task training, so that the parameters can quickly adapt to the energy field prediction requirements of the current training task. During the training process, an explicit cross-credibility feature transfer link is constructed to mine the deep feature information contained in samples of different precisions, and explicitly transfer it to a higher credibility model through the network structure to enhance the physical expressiveness and prediction consistency of the features. Through the meta-learning-driven step-by-step training mechanism, the knowledge transfer and rapid adaptation of the energy field from low-precision to high-precision samples are realized. When high-precision samples are introduced, the network already has good initialization capabilities, and only a small amount of high-cost and high-precision simulation data is required to achieve rapid convergence and high-precision prediction, significantly reducing the training cost and the computing resources required for high-precision modeling. Step 6: Introduce the scarce experimental data in practice. The energy field grid points measured in the physical experiment are not as dense as the gridded energy field in step 2, and the output energy field data are not measured completely at the same grid points. Therefore, combined with the multi-credibility neural network trained in step 5, linear interpolation is used to obtain the output data at the energy field grid points in the physical experiment, so that the finite element simulation analysis model and the experimental output data are consistent. The experimental data is used to train the multi-credibility neural network and update its parameters, further improving the consistency between the BCNN network prediction and the experiment. Step 7: Based on the currently constructed multi-credibility Bayesian convolutional neural network, energy field prediction is performed, and the accuracy of the Bayesian convolutional neural network is verified through the test set. If the accuracy meets the requirements, the construction of the multi-credibility Bayesian convolutional neural network is completed, otherwise it proceeds to step 8; In step eight, the maximum a posteriori variance estimation expression is established by combining the prediction variance in step four. The input position with the largest a posteriori variance is identified in the global input space as the most critical sampling point in the current stage. At the same time, several candidate points with a level close to the maximum variance are selected as multi-point supplementary samples. A screening mechanism for a mutually exclusive hypersphere structure in high-dimensional space is established. A high-dimensional hypersphere region with a certain radius is constructed in the input space with the selected key point as the center, and is defined as an exclusive region. Subsequent candidate points are only adopted in regions that do not fall into the existing hypersphere. In the hypersphere construction, the radius of the hypersphere is determined by the scale and distribution characteristics of the input variables to ensure that the regions have clear boundaries and no overlap. All selected sample points constitute a set of spatially exclusive and globally uniformly distributed sampling points in the input space. This screening mechanism can effectively guide sampling to concentrate in areas with high model uncertainty, enhance the information content of the samples, and avoid the aggregation and stacking problems of sampling points in the input space, thereby improving the diversity and distribution rationality of the experimental design. Step 9: A cost-effectiveness index is constructed that comprehensively considers both prediction gain and computational cost to guide the selection of cost-effective sample analysis models. This index integrates the simulation computing resource consumption required for the accuracy level of the analysis model and its contribution to improving energy field prediction accuracy, thereby achieving a quantitative measurement of cost-effectiveness. The analysis models are sorted according to the cost-effectiveness index, and priority is given to the analysis models that have greater marginal benefits in improving prediction accuracy and relatively low computational costs, so as to construct a set of experimental design inputs with high cost-effectiveness, low redundancy and high contribution.

3. The Bayesian deep active learning-guided energy field prediction experiment design method according to claim 2, characterized in that: In step one, High-order units are used for meshing, and local encrypted meshes are used for key areas to construct a high-precision finite element simulation analysis model, which is denoted as y3. Linear units such as C3D4 tetrahedron units are used for meshing, and non-critical geometric features are removed to obtain a medium-precision analysis model, which is denoted as y2. Shell units or beam units are used instead of solid units to simplify the aircraft geometry and obtain a low-precision analysis model, which is denoted as y1. High-order units include hexahedron units or quadratic tetrahedron units. Key areas include stress concentration areas and key load-bearing component areas.

4. The Bayesian deep active learning-guided energy field prediction experiment design method according to claim 3, characterized in that: The implementation method of step 2 is: The specific implementation method of step 2 is: Step 2.1: For the fragment energy field, the finite element simulation analysis model generates an energy field that includes the position, mass, and velocity of each fragment. The energy field is expressed in the form of a matrix: in, and Respectively represent the horizontal and vertical coordinates, mass and velocity of the fragments; Step 2.2: Determine the maximum damage range W of the aircraft's energy field p and L p , grid the energy field and divide it into G square grids K with side length b rt (r=1,…,r p ; t=1,…,t p ), the coordinates of the center point of each square grid are In order to make the gridded energy field more regular, define W p and L p is an integer multiple of b, that is, r p =W p / b,t p =L p / b,r p ×t p =G; Step 2.3: Combine the grid division in step 2.2 to transform the energy field into a clustered energy field. The clustered fragment energy field becomes a matrix consisting of the grid center point and the clustered kinetic energy field quantity. Combined with the grid division, the kinetic energy in each square is statistically obtained as follows: The matrix representation of the energy field after aggregation of a certain precision is shown in formula (3), and this matrix is ​​used as the output data of energy field prediction; Through the rasterization processing in step 2, the output results of analysis models with different precision are unified in format and size, and a rasterized energy field is obtained, which facilitates the construction of a multi-credibility model.

5. The Bayesian deep active learning-guided energy field prediction experiment design method according to claim 4, characterized in that: The implementation method of step three is: According to the given number of samples [n1, n2, n3] of the energy field finite element simulation analysis model with different precision, the input samples are obtained by sampling the input variables in the design space through Latin hypercube Call analysis models of different precisions respectively to generate training response samples Sample response It is the energy field aggregation matrix after the gridding process in step 2; the input variables include the material constitutive model parameters and working conditions; The energy field finite element simulation analysis model with higher accuracy provides fewer samples, and the analysis model with lower accuracy provides more samples, that is, n1 is the largest and n3 is the smallest; the input and output sample data sets are {D1, D2, D3} and {d1, d2, d3}, respectively.

6. The Bayesian deep active learning-guided energy field prediction experiment design method according to claim 5, characterized in that: The specific implementation method of step four is: Step 4.1: Define a deep neural network with L layers: Among them, w L and b L are the weights and biases of the Lth layer (i.e., the output layer) of the network; is the iterative value of the input variable x after the first L-1 layer network operation; θ - Represents all network parameters of the first L-1 layer; f θ Indicates that the final network parameter is a deep neural network of θ; Step 4.2: In the deep neural network defined in step 4.1, w and b are both fixed values. In order to improve the robustness of the network, it is assumed that the weights and biases are changed from fixed values ​​to obey a certain probability distribution. On the basis of the fully connected neural network, only the output layer is set to the Bayesian convolution layer, so that the output layer is unbiased. This is the basic structure of the Bayesian convolutional neural network, which can ensure the physical consistency and structural simplicity of the prediction results, and conform to the actual law that energy in space is smoothly attenuated or symmetrically diffused during the generation of the energy field. The corresponding BCNN is expressed as follows: Among them, θ - Represents the network parameters of other layers, is the output vector of the penultimate layer; Step 4.3: Let the network parameters of the Bayesian convolutional neural network be θ, and p(θ) be the prior distribution of the parameters, which is a standard normal distribution. Given a training set {X, Y}, where X is the input data and Y is the output response data, based on the Bayesian formula, the posterior probability of θ is as follows: Where p(Y|X,θ) is the likelihood function, ∫p(Y|X,θ)p(θ)dθ is the marginal integral; The variational inference method is used to calculate the integral. The basic idea is to establish a simple distribution that obeys the normal distribution to approximate the posterior distribution p(θ|X,Y). By adjusting the mean and variance of the simple distribution, the Kullback-Leibler (KL) divergence between the simple distribution and the posterior distribution is minimized to obtain the optimal parameter estimate θ. * Therefore, in Bayesian network training, the network weights and biases are set to be normally distributed based on the variational inference method and the distribution type is kept unchanged, while the mean and variance are continuously updated during the training process. Step 4.4: Combined with the network parameters obtained in step 4.3, based on the trained Bayesian convolutional neural network, the posterior distribution of the Bayesian convolutional neural network response prediction at the input position x is: p(x)~N(α(x),η(x)) (7) in: Where, Expressing hope; The above formula (8) is calculated using Gauss integral numerical integration. Among them, t k and g k They represent the Gaussian integral node and integral weight corresponding to the weight w of the output layer, respectively, and the distribution mean μ of w w and standard deviation σ w Decide; By analyzing expressions (9) and (10), the predicted mean and variance of each square of the predicted aggregate energy field are obtained. The BCNN predicted mean is output as the final prediction result, and the predicted variance will serve the subsequent active learning experiment design process; In step 5, the input and output samples at a certain level of accuracy {D t ,d t }(t=1,2,3) perform sampling with replacement and construct multiple task subsets T i (i=1,…,K); high-precision samples are {D3,d3}; In step six, the test data is {D e ,d e }.

7. The Bayesian deep active learning-guided energy field prediction experiment design method according to claim 6, characterized in that: The specific implementation method of step seven is: Based on the currently constructed multi-credibility Bayesian convolutional neural network, a test set is generated on a high-precision energy field finite element simulation analysis model, or experimental data is used as a test set to calculate the root mean square error (RMSE) of the network prediction to test the accuracy of the Bayesian convolutional neural network; the RMSE is defined as follows: Among them, m represents the number of samples in the test set, y i Indicates high-precision energy field response value, Represents the energy field prediction value based on multi-credibility Bayesian convolutional neural network; If the accuracy does not meet the requirements, that is, RMSE>Δ, new samples need to be drawn, where Δ is the set threshold.

8. The Bayesian deep active learning-guided energy field prediction experiment design method according to claim 7, characterized in that: The specific implementation method of step eight is: The Bayesian convolutional neural network can provide the advantage of response prediction posterior variance, and establish a multi-point sampling method based on maximum posterior variance; considering that for deep learning, if too few samples are extracted each time, the accuracy of the BCNN network will not be significantly improved, and the sampling process will be very lengthy, but the number of samples extracted each time cannot be too large, otherwise the advantage of sequence sampling cannot be utilized; therefore, based on experience, the upper limit of the number of samples extracted each time is set to n S ; Establish a maximum a posteriori variance search strategy. According to the prediction variance given in step 4.4, the prediction method of each square in the predicted aggregated energy field of any input position is summed as the posterior variance of the input position. The input position with the largest posterior variance is selected as the key input sample, and several points with posterior variances close to the maximum posterior variance are selected as candidate input samples. In order to avoid the stacking of samples near a certain input position and limit the overall improvement of network accuracy, a distance-based sample screening principle is proposed. According to the Euclidean distance between any two points in the key sample and the candidate sample, a set of distances that are not too close to each other (d≥d t ) and the overall posterior variance is larger, then all valid input samples of this sequence sampling are obtained; by setting the distance threshold d t To avoid samples being too close together: Among them, d max Indicates the maximum value of all dimensional variation ranges of the current sample input space. It represents the maximum Euclidean distance between the candidate sample and the key sample, and β is the correction parameter. Since the variables of different dimensions have different ranges of variation, in order to avoid the impact of excessively large or small ranges of individual dimensions, the ranges of variation of all dimensions need to be normalized before calculating the distance.

9. The Bayesian deep active learning-guided energy field prediction experiment design method according to claim 8, characterized in that: The specific implementation method of step nine is: Step 9.1: Establish a cost-effectiveness index (CEI) that takes into account the maximum cost-effectiveness of the sample; Where, subscript t represents the tth analysis model y in the low-precision energy field analysis model t (x); C t represents y t The cost of (x) can be the modeling time cost or labor cost, the computational cost of calling the model once, or a combination thereof; Corr t Indicates the input sample position y t The closer the value is to 1, the more likely y is to be positive at this input sample. t The closer the prediction accuracy of (x) is to y3(x); Step 9.2: Corr t (x) is represented by y t The posterior distribution p of the BCNN response predictions for (x) and y3(x) t The distance between (x) and p3(x) is calculated by introducing the Wasserstein distance criterion to quantify the distance between the two distributions. Regarding the calculation of the posterior distribution, all low-precision models y can be obtained in the process of multi-credibility model fusion. t Bayesian Convolutional Neural Network for (x) Without calling the real analysis model, it can be based on the trained Bayesian convolutional neural network Using formula (8), we can get the posterior distribution p of the response prediction at the input position x: t (x)~N(α t (x),η t (x)); Step 9.3: Determine the analytical model (including analytical model and test) to be called at the new sample input location, denote the analytical model with the largest CEI value as M*, obtain the energy field prediction response data of M* at the input sample location, and minimize the cost while ensuring the improvement of the neural network accuracy; Add the samples extracted from the sequence to the old samples, and repeat steps five to eight based on the updated sample set until the energy prediction accuracy index of the multi-credibility Bayesian convolutional neural network meets the requirements, and obtain the energy field prediction experiment design results guided by Bayesian deep active learning.

10. The Bayesian deep active learning guided energy field prediction experiment design method according to claim 2, 3, 4, 5, 6, 7, 8 or 9, characterized in that: It also includes step ten. After the multi-credibility Bayesian convolutional neural network prediction model is constructed, the aircraft energy field is predicted based on the energy field finite element simulation analysis model to obtain energy field prediction results that are consistent with the test data. While improving the energy field modeling speed and reducing the test cost, the accuracy of aircraft damage assessment is guaranteed, thereby improving the accuracy and efficiency of firepower allocation and firepower planning.

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