Modeling method of double-weight stacking deformation prediction integrated model based on complex sample orientation

Abstract

The invention relates to the technical field of integrated learning deformation prediction, in particular to a double-weight stacking deformation prediction integrated model modeling method based on complex sample guidance, and the method comprises the steps: building five heterogeneous base models: CLAnet, RBF, MLP, CNN and XGBoost; establishing a support vector regression machine as a meta-model; constructing a secondary integration model on the basis of a stacking framework; a complex sample-oriented five-fold cross validation strategy is adopted to optimize training set distribution, and learning of complex samples is dynamically enhanced; by calculating an error index of each base learner, an initial weight is manually allocated to the base model before the meta-model automatically and implicitly allocates the weight, and metadata set distribution is optimized; and a whale optimization algorithm is introduced to adjust hyper-parameters of each model. According to the integrated prediction model, the problems that a single model is insufficient in generalization ability to complex samples and limited in modeling ability of a multivariable coupling relation can be solved by integrating different learning modes of each base model to features and by means of the quadratic fitting ability of the meta-model.

Description

Technical Field

[0001] The present invention relates to the technical field of ensemble learning deformation prediction, and in particular to a modeling method of a dual-weight stacked deformation prediction ensemble model based on complex sample guidance. Background Art

[0002] As the external carrier of a fighter aircraft's conformal antenna, the antenna skin bears the core responsibility of ensuring stealth, aerodynamic performance, and mechanical strength. It is also a key guarantee for fully leveraging the conformal antenna's advantages of flexibility, adaptability, and integration. High-quality antenna skin fabrication provides a solid foundation for improving the overall performance of fighter aircraft, significantly promoting the advancement of defense and military technology, and has become a new requirement for modern information-based warfare. However, antenna skin deformation during fabrication is unavoidable, and this deformation directly impacts conformal antenna performance. Therefore, understanding the deformation patterns during antenna skin fabrication is crucial for controlling conformal antenna quality. Currently, validation of antenna skin co-curing fabrication schemes is primarily accomplished through repeated fabrication experiments using actual prototypes. This process exhibits multi-material, multi-process, and multi-parameter characteristics. Due to the complex physical and chemical reactions involved in the co-curing process, the mechanisms and patterns of how process parameters influence skin deformation remain unclear. Therefore, based on data generated during antenna skin prototype fabrication, the relationship between fabrication process parameters and skin deformation is clarified, thereby developing an antenna skin deformation prediction model. This is key to controlling skin deformation through process parameter adjustment during antenna skin fabrication.

[0003] Because the antenna skin co-curing process is subject to the combined influence of numerous thermal, electrical, mechanical, and magnetic mechanisms, analytical and numerical methods have become common approaches for deformation prediction. With the development of artificial intelligence (AI), researchers have gradually applied AI to the field of composite co-curing molding. AI-based methods can deeply explore the complex mapping relationship between process parameters and deformation, performing high-precision continuous fitting of the two with rapid computational speed. The application of AI technology in the field of composite co-curing molding can be divided into three categories based on theoretical foundations and model learning methods: statistical learning-based prediction methods, machine learning-based prediction methods, and deep learning-based prediction methods.

[0004] Among machine learning methods, prediction methods based on ensemble algorithms are a hot research topic in this field. These methods utilize the diversity and complementarity of weak learners to form a strong learner that can reduce bias and variance, thereby improving the overall performance of the model. Khodadadi et al. used CatBoost to predict the compressive strength of carbon fiber reinforced polymers, addressing the problem that traditional analytical models often overestimate the bearing capacity. They also demonstrated that CatBoost is superior to AdaBoost in applications. Guo et al. eliminated abnormal data through cluster analysis, performed data dimensionality reduction through principal component analysis, and established an XGBoost model to predict the mechanical properties of high-performance fiber-reinforced cement-based composites. Daghigh et al. used a decision tree regressor (DTR) as a weak learner for an adaptive boosting regressor (ABR) to construct a prediction model for the fracture toughness of multi-scale bio-nanocomposites.

[0005] Currently, the mainstream algorithms for ensemble learning fall into three categories: parallel ensemble algorithms, serial ensemble algorithms, and stacked ensemble algorithms. Parallel ensemble algorithms train independent and non-dependent weak learners in parallel, and a typical example is the Bagging algorithm. Serial ensemble algorithms employ a serial training approach, integrating learning by correcting the errors of previous weak learners with subsequent weak learners. Learners exhibit strong dependencies, and a representative example is the Boosting algorithm. Stacked ensemble algorithms, also known as Stacking algorithms, are similar to parallel ensemble algorithms in that weak learners are generated in parallel. However, they are unique in that they leverage the diversity and complementarity of weak learners by training a meta-learner and using it to dynamically integrate the outputs of each weak learner, thereby improving prediction accuracy and generalization.

[0006] However, existing research on antenna skins is limited, and relevant prediction studies have primarily focused on mechanical and mechanical properties, while research on deformation prediction during co-curing is limited. Because antenna skin co-curing is influenced by factors such as different materials, process flows, and process parameters, the deformation mechanisms and patterns are unclear. Existing deformation prediction studies in the literature have primarily focused on applying simple models to clarify the problem, making it difficult to apply deformation prediction to complex processes with unclear mechanisms. Summary of the Invention

[0007] The purpose of the present invention is to provide a dual-weight stacking deformation prediction integrated model modeling method based on complex sample guidance, which is used to predict the deformation of antenna skin during co-curing preparation with high precision, thereby improving the prediction accuracy and model robustness.

[0008] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0009] A complex sample-guided dual-weight stacking deformation prediction integrated model modeling method includes the following steps:

[0010] S1: Construct five heterogeneous base models, including CLAnet network, radial basis function neural network, multi-layer perceptron, convolutional neural network and extreme gradient boosting machine;

[0011] S2: A complex sample-oriented five-fold cross-validation strategy is used to train each base model, and the hyperparameters of each base model are optimized using the whale algorithm. During the validation phase, samples with a prediction error exceeding 20% ​​are marked as complex samples and moved into the training set to retrain the folded base model.

[0012] S3: Calculate the corresponding mean absolute error based on the cross-validation results of each fold of each base model, and calculate the weight of the predicted value of each fold of each base model according to the mean absolute error, which is used to explicitly assign the first weight and generate the training set and test set of the meta-model;

[0013] S4: Construct a support vector regression machine as a meta-model, using a radial basis kernel function as the kernel function, and optimize its hyperparameters using the whale algorithm. The hyperparameters include the penalty coefficient C, the kernel coefficient γ, and the error tolerance band width ε.

[0014] S5: The weighted metadata dataset is input into the SVR for training, and a second weight is implicitly assigned to each input feature to form a final complex sample-guided dual-weight stacked deformation prediction integration model.

[0015] Furthermore, the three-channel multidimensional regression focusing network (CLAnet) is a customized neural network model, whose structure includes a three-channel CNN feature extraction layer, an LSTM feature learning layer, an attention mechanism focusing layer, and a fully connected layer.

[0016] On the other hand, a data-driven method for predicting deformation of antenna skin co-curing preparation includes the following steps:

[0017] S1: Perform preliminary cleaning, missing value processing, and outlier detection on the antenna skin co-curing preparation data. Key features are screened using recursive feature elimination and random forest. Data enhancement is performed using random scaling, Gaussian noise addition, and Mixup hybrid methods. Numerical data is normalized and categorical data is encoded.

[0018] S2: Construct a three-channel multidimensional regression focusing network model CLANet, which includes a three-channel CNN feature extraction layer, an LSTM feature learning layer, an attention mechanism focusing layer, and a hyperparameter optimization layer based on the whale algorithm;

[0019] S3: The three-channel multidimensional regression focusing network model is used as the base model together with the radial basis function network, multilayer perceptron, convolutional neural network, and XGBoost model. The preprocessed data is input into each base model. The base model is trained using a complex sample-guided five-fold cross-validation strategy. The first weight is calculated by calculating the average absolute error of the prediction value of each fold to optimize the metadata set distribution. The support vector regression meta-model is used for double-weight stacking integration to output the final deformation prediction value.

[0020] Furthermore, the method for constructing the three-channel multidimensional regression focusing network model in step S2 includes: extracting multi-scale features based on a three-channel convolutional neural network (CNN), learning spatiotemporal nonlinear relationships through a long short-term memory network (LSTM), dynamically allocating feature weights in combination with an attention mechanism, and optimizing network hyperparameters using a whale algorithm.

[0021] Beneficial effects of the present invention:

[0022] The present invention introduces a complex sample-oriented five-fold cross-validation training mechanism, that is, in each cross-validation iteration, samples with prediction errors exceeding the threshold are identified, and marked as complex samples, and moved into the training set for retraining to enhance the model's recognition and learning capabilities for such samples. It abandons the problem of insufficient information utilization in traditional static data division methods, effectively strengthens the attention paid to samples with high information density and high prediction difficulty in the training phase, and thus establishes a more adaptive prediction mapping function. The strategy of dynamically migrating complex samples during the cross-validation process enhances the diversity of data distribution and the pertinence of model training, which helps to improve the model's ability to model the complex relationships between nonlinear, non-stationary, and highly coupled process variables in the antenna skin preparation process, and ultimately significantly improves the convergence, consistency, and robustness of the model's prediction results for complex deformation samples in actual production.

[0023] The present invention introduces a dual-weighted mechanism into the metadata dataset construction process in stacked ensemble learning. On the one hand, it assigns a static importance evaluation to each base learner based on the global error level. On the other hand, it constructs a fine-grained dynamic adjustment strategy based on the performance fluctuations of each fold during the cross-validation process, thereby avoiding the problem that the influence of the base model in the conventional staking architecture is roughly averaged and the advantages of the local optimal model cannot be reflected. It can combine the different characteristics between learners, the advantages of the RBF network in the local fine fitting process, the expressive power of the CNN model in high-dimensional space feature extraction, and the strength of XGBoost in nonlinear rule discrimination, and differentially assign weights based on stability and adaptability, effectively improving the structural effectiveness of the ensemble model in deformation prediction tasks with strong data heterogeneity and feature instability, so that the learning results of different models can be retained and strengthened in the fusion.

[0024] The stacking model of the present invention is based on the base model system of five typical heterogeneous learners: CLAnet, RBF, MLP, CNN and XGBoost. Each model has obvious differences and complementarities in the construction principle, forming a base learning layer with strong diversity. Among them, the RBF network uses the Gaussian radial kernel function to extract the nonlinear features of specific local areas in the input space, the MLP fully relies on the activation function to realize deep interactive relationship modeling, and the CNN abstractly extracts the spatial distribution characteristics of the input process parameters through local connection and weight sharing mechanism. XGBoost gradually captures the residual information through the serial weighted iteration of the CART tree structure, and realizes the fine correction of high-frequency error signals that are difficult to fit by traditional models. CLAnet integrates the attention mechanism and the convolutional feature extraction path in the integrated structure, which enhances the model's responsiveness to important channel scale inputs and makes the key feature expression more centralized and controllable. On this basis, a kernel-based support vector regression (SVR) machine is used as a meta-learner, and radial basis kernel mapping is introduced to increase the separability of feature vectors in high-dimensional space. A whale optimization algorithm is then used to perform a joint global search of the penalty coefficient, kernel width coefficient, and error tolerance variable to avoid local optimality and underfitting / overfitting problems caused by artificial parameter settings. This multi-level nonlinear modeling process, from kernel-based feature space transformation to prediction error texture learning at the integration layer, achieves end-to-end, highly complex nonlinear fitting from input features to output labels, adapting to the practical technical difficulties of the antenna skin co-curing preparation process, where process parameters are strongly coupled and the physical process is difficult to analyze.

[0025] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0027] Figure 1 This is the overall framework diagram of the dual-weight stacking deformation prediction integrated model based on complex sample guidance;

[0028] Figure 2 This is a schematic diagram of the five-fold cross-validation process of the base learner;

[0029] Figure 3 This is a schematic diagram of the cross-validation process based on complex sample guidance;

[0030] Figure 4 This is a schematic diagram of part of the construction process of the dual-weight stacking deformation prediction integrated model based on complex sample guidance;

[0031] Figure 5 It is a schematic diagram of part of the collected data;

[0032] Figure 6 This is a schematic diagram of the antenna skin deformation prediction value based on the complex sample-guided dual-weight stacking integrated model;

[0033] Figure 7 This is a comparison chart of the prediction results of the dual-weight stacked deformation prediction integrated model based on complex sample guidance;

[0034] Figure 8 It is a scatter plot comparing the predicted value of the antenna skin deformation of the integrated model with the actual value. DETAILED DESCRIPTION

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0036] Example 1

[0037] The present embodiment provides a complex sample-guided dual-weighted stacking deformation prediction integrated model modeling method, comprising the following steps:

[0038] S1: Construct five heterogeneous base models, including CLAnet network, radial basis function neural network, multi-layer perceptron, convolutional neural network and extreme gradient boosting machine;

[0039] S2: A complex sample-oriented five-fold cross-validation strategy is used to train each base model, and the hyperparameters of each base model are optimized using the whale algorithm. During the validation phase, samples with a prediction error exceeding 20% ​​are marked as complex samples and moved into the training set to retrain the folded base model.

[0040] S3: Calculate the corresponding mean absolute error based on the cross-validation results of each fold of each base model, and calculate the weight of the predicted value of each fold of each base model according to the mean absolute error, which is used to explicitly assign the first weight and generate the training set and test set of the meta-model;

[0041] S4: Construct a support vector regression machine as a meta-model, using a radial basis kernel function as the kernel function, and optimize its hyperparameters using the whale algorithm. The hyperparameters include the penalty coefficient C, the kernel coefficient γ, and the error tolerance band width ε.

[0042] S5: The weighted metadata dataset is input into the SVR for training, and a second weight is implicitly assigned to each input feature to form a final complex sample-guided dual-weight stacked deformation prediction integration model.

[0043] Example 2

[0044] In order to address the problems of insufficient generalization ability of a single model for complex samples and limited modeling ability for multivariate coupling relationships, the present invention constructs a two-level integrated model based on stacking to further meet the high-precision requirements for deformation prediction in the co-curing preparation of antenna skins. By integrating the different learning methods of each base model for features and leveraging the quadratic fitting ability of the meta-model, the prediction accuracy and generalization performance of the model can be improved. At present, there is no unified standard for the selection of base models, which are generally required to be diverse and complementary, and to have a certain degree of predictive ability.

[0045] This example uses the CLAnet network, along with RBF, MLP, CNN, and XGBoost, as the base models for stacking ensemble learning. RBF uses the nonlinear transformation of radial basis functions to map low-dimensional problems to a high-dimensional space for fitting. MLP has a simple and flexible structure, using the chain rule to backpropagate errors to optimize weights and parameters. CNN leverages weight sharing and translation invariance to balance efficiency and accuracy. XGBoost, as an ensemble learner for the boosting strategy, improves prediction performance through serial iteration. These four base learners, with distinct structures, diverse principles, and complementary approaches, meet the basic requirements for base model selection.

[0046] The stacking ensemble's architecture is highly flexible, allowing linear regression, decision trees, neural networks, and kernel methods to serve as meta-learners. Linear regression is suitable for simpler tasks, while neural networks are suited to scenarios with larger data volumes. To address the complex mapping relationships and limited sample size in antenna skin deformation prediction, the SVR kernel method is employed as a meta-learner. Through the kernel's nonlinear mapping and tolerance band design, SVR effectively fits the base model output while tolerating some noise and improving model generalization.

[0047] In addition, this embodiment improves the traditional cross-validation and stacking ensemble learning, and constructs a dual-weight stacking deformation prediction ensemble model based on complex sample guidance, whose structure is as follows: Figure 1As shown in the figure. Each base model is trained separately using complex sample-guided five-fold cross-validation to generate metadata. The metadata is manually weighted and then input into SVR for training and prediction. This integrated model achieves higher prediction accuracy than a single model or a simple integrated model by leveraging the synergy between multiple models and multi-layer models, taking advantage of the differences between base models and the intelligent fusion of meta-models. Complex sample guidance helps the base model to discover deep laws, while manual weighting quantifies the performance of each base model in advance and guides the learning direction of the meta-model. This integrated model takes into account both local feature extraction and global learning capabilities, effectively improving the accuracy of deformation prediction in antenna skin co-curing preparation.

[0048] Construction of dual-weight stacked integrated basis model

[0049] RBF construction

[0050] The radial basis function (RBF) neural network is a typical three-layer feedforward neural network. Its input layer receives data, and its output layer is a fully connected layer. The core of the network lies in the radial basis layer. The radial basis layer uses radial basis functions to map the input space from a low-dimensional space to a high-dimensional space. Data in low-dimensional space is typically feature-poor, making it difficult to fully express the data's inherent properties and relationships. Mapping data to a high-dimensional space can uncover more hidden features and enrich the data's feature representation. Complex nonlinear relationships in low-dimensional space are difficult to accurately fit, while the model's degrees of freedom are increased in high-dimensional space, enabling it to better fit complex functional relationships.

[0051] The value of the radial basis function is determined only by the distance from the center point, that is, Φ(x,a)=Φ(||xa||), and the Euclidean distance is generally used for distance measurement. In this embodiment, the Gaussian kernel is selected as the radial basis function. The Gaussian function can approximate any function with arbitrary precision. Since the Gaussian function has an obvious response only near the center point, it is more sensitive to local features and has a better fitting effect on local details of complex mapping relationships. The RBF network using the Gaussian kernel has the characteristics of high computational efficiency and simple form. Its two most core parameters are the center and width of the Gaussian kernel. The expression of the Gaussian function is as follows:

[0052]

[0053] Among them, x is the input space, σ is the parameter that controls the width of the Gaussian kernel, and a iRepresents the center of the i-th basis function. The Gaussian kernel width controls the width of the kernel function. Its response area expands as the width value increases, and the function curve becomes flatter. Appropriate width can make the input features form relatively separated clusters in high-dimensional space, improving feature discrimination and nonlinear fitting capabilities. The kernel center determines the position of the receptive field of the Gaussian kernel in the input space and guides the fitting direction. Reasonable selection of the center can enrich feature representation and optimize network training. Gaussian kernels at different positions can extract features from different scales. The closer the Gaussian kernel center is to the key position of the data distribution, the better the convergence effect and the faster the convergence speed. The K-means clustering algorithm is used to determine the number and position of the centers. The core formula of the K-means algorithm is as follows:

[0054]

[0055] Among them, a k Represents the center of each cluster. The optimization goal of the K-means algorithm is to minimize the value of J.

[0056] Radial basis functions with varying centers and widths construct several locally sensitive response regions. When data flows through the radial basis function, each radial basis function produces a varying degree of response based on the distance between the input and its own center. The smaller the distance, the greater the response. RBF's ability to fit nonlinearities in high-dimensional space is highly compatible with the task of exploring the complex deformation patterns affecting antenna skins, so it was chosen as one of the basis models.

[0057] MLP construction

[0058] The multi-layer perceptron, or MLP, is a feedforward neural network that is an improvement on the single-layer perceptron. The single-layer perceptron consists of only an input layer and an output layer and can only solve linear problems. The MLP architecture adds several hidden layers between the input and output layers and utilizes the nonlinear variation of the activation function to give the MLP the ability to solve nonlinear problems. The MLP structure is flexible and easy to expand. Different numbers of hidden layers and activation functions can be selected according to different task requirements and the scale of the problem. The sigmoid function, tanh function, and relu function are the three most commonly used activation functions. Among them, the relu function has the characteristics of alleviating gradient vanishing, sparse activation, and simple and efficient calculation. The relu function is selected as the activation function of the MLP, and its calculation formula is as follows:

[0059] f(x)=max(0,x) (3)

[0060] The ReLU function does not require complex computations; it simply compares the input to 0. Neurons are activated only when the input is greater than 0. This mechanism promotes sparse activation and helps alleviate the vanishing gradient problem. The MLP weight update relies on the backpropagation algorithm, at the core of which is the chain rule. The complex multi-layer structure of the MLP can be viewed as a multi-layer composite function, making direct calculation of its gradient difficult. However, the chain rule simplifies this process by decomposing the local gradients of each layer.

[0061] The MLP uses recursive feature extraction to map high-dimensional features into a low-dimensional space, thereby uncovering more hidden patterns in the data. Its simple structure differs significantly from several other base models, forming a complementary relationship and improving the prediction accuracy of stacked ensembles.

[0062] CNN construction

[0063] A one-dimensional convolutional neural network is selected as one of the base learners. The one-dimensional convolutional and pooling layers perform downsampling operations to extract local features. The activation function can undergo nonlinear changes. The output of the last hidden layer is flattened and then integrated into the final prediction result by a fully connected layer. The weight sharing property of the CNN convolution process ensures that the same features at different locations in the input space have the same abstract representation, making the CNN translation-invariant in regression prediction, ensuring that the model is unaffected by changes in feature position. Weight sharing and local connections also improve the efficiency of CNN in regression prediction tasks.

[0064] XGBoost Build

[0065] XGBoost is a serial Boosting algorithm built on the gradient boosting framework. It forms a strong learner through iterative training of modified weak learners. XGBoost offers a variety of weak learners, such as Classification and Regression Trees (CART) and Multivariate Additive Regression Trees (DART). CART is chosen as XGBoost's weak learner due to its strong feature representation capabilities and good data adaptability. In regression prediction tasks, the CART tree's recursive partitioning of input data can better mine complex relationships within the data. In a CART tree, each internal node matches a feature splitting condition, each branch matches a splitting result, and each leaf node matches a predicted value. This clear structure intuitively demonstrates the decision-making process and enhances the model's interpretability.

[0066] The core of XGBoost is weighted bias iterative optimization and regularization to control complexity. It also uses a second-order Taylor expansion of the loss function to improve convergence speed. XGBoost's optimization objective includes the loss function and the regularization term, and minimizing this objective controls the split point and complexity of the decision tree. Each iteration fits the error of the previous iteration, and the final prediction is the sum of the predictions of each decision tree. Its prediction model is expressed as follows:

[0067]

[0068] Where N is the number of decision trees, f n represents the nth decision tree. The formula for minimizing the objective function is shown in Equation 5.

[0069]

[0070] Here, l is the loss function, which measures the deviation between the predicted value and the true value. Ω is the regularization term, which controls the number of model nodes and the complexity of the weights. Its calculation formula is shown in Equation 6, where T and w represent the number and weights of leaf nodes, respectively. γ is the leaf node penalty coefficient, and λ is the weight decay coefficient.

[0071]

[0072] The main parameters of XGBoost and their meanings are shown in Table 1. During the experimental verification process, the whale algorithm was still used to perform a global search for the optimal hyperparameter combination.

[0073] Table 1 Main parameters of XGBoost and their meanings

[0074]

[0075] In the table, the colsample_bytree parameter controls the random sampling ratio, increasing model diversity and reducing overfitting risk. The combination of alpha and reg_lambda forms elastic net regularization, combining the feature selection capabilities of L1 regularization with the overfitting prevention capabilities of L2 regularization. n_estimators sets the maximum number of iterations. Increasing the number of trees can capture more information and reduce bias, but it also consumes more training resources.

[0076] SVR metamodel construction

[0077] This embodiment uses support vector regression (SVR) as a meta-model to perform secondary fitting on the preliminary prediction values ​​of the five constructed base models to fully utilize the advantages of each base model and balance the local feature extraction and global learning capabilities of each base model. The SVR regression algorithm is similar to the principle of the RBF neural network. It also uses the kernel function technique to map features in a low-dimensional space to a high-dimensional space and fit complex nonlinear relationships in the high-dimensional space. SVR allows the existence of small noise points by introducing slack variables to improve the generalization ability of the model. Specifically, SVR defines an insensitive loss function. When the error is below a certain threshold, the error is considered acceptable and no loss is incurred. When the error exceeds the threshold, a corresponding slack variable penalty is generated. The goal of SVR training is to find an optimal hyperplane that allows as many data points as possible to be within the error tolerance band while minimizing the error in the tolerance band.

[0078] When using the WOA algorithm for SVR hyperparameter optimization, the three main parameters are penalty coefficient C, ε, and gamma. C controls the severity of the slack variable penalty, ε controls the width of the error tolerance band, and the number of support vectors decreases as ε increases. Gamma, a parameter introduced by the radial basis function kernel, controls the model's perceptual range and fitting granularity.

[0079] Construction of a dual-weight stacking integration framework for complex samples

[0080] In the stacking ensemble learning framework, in order to avoid noise features being fitted by the base model and thus affecting the quality of the meta-data set, cross-validation is usually used to train the base model. The cross-validation method does not divide the original data set into fixed and mutually exclusive training sets and test sets, but divides it into K parts, and uses K-1 parts of data to train the base model each time, and the remaining 1 part of the data is used for verification, and the process is repeated K times. In this embodiment, the deformation prediction of the antenna skin co-curing preparation is a small sample prediction task. Cross-validation does not need to divide independent test sets, so that all samples participate in training to improve data utilization. At the same time, cross-validation can generate prediction values ​​of the same scale as the training set, providing richer data for the meta-model and further solving the small sample problem. Taking five-fold cross-validation as an example, the process is as follows: Figure 2 shown.

[0081] According to the Stacking integration steps:

[0082] (1) Divide the data set: Divide the original data set into a training set and a generation set.

[0083] (2) Training base models: Use cross-validation to train each base model separately on the base model training set.

[0084] (3) Base model prediction: The predicted fold data in the cross-validation is input into the base model trained in the previous step to generate a first-level output vector, which is then combined with the original label to form a new data set.

[0085] (4) Training the metamodel: Use the new dataset formed in the previous step as the input of the metamodel to train the metamodel.

[0086] (5) Integrated model prediction: The generated set is input into each base model, the average value of the first-level output vector of each base model on each fold is taken, and the trained meta-model is input into it, and the meta-model generates the prediction result.

[0087] In five iterations, each fold of the test data generates a corresponding prediction value. The prediction values ​​of each base model are combined to train the SVR model. In each iteration, the test data used to construct the meta-test set also generates a prediction value. The five prediction values ​​generated for the same data point in the five iterations are arithmetic averaged. The prediction values ​​of each base model are combined as the meta-test sample to verify the ensemble model.

[0088] The value of K is typically 3, 5, or 10. Larger folds increase the amount of training data and reduce bias, but they also increase the number of iterations and computational cost. Smaller folds are simpler and less expensive to implement, but they provide insufficient data utilization. To meet the high-precision, micro-deformation prediction requirements for antenna skin co-curing, 5-fold cross-validation is used for stacking ensemble learning, trading a moderate increase in computational cost for higher prediction accuracy. Cross-validation not only alleviates the small sample size issue but also enables the model to fully utilize complete information, allowing the base learner to capture diverse distributional features across different folds of data, thereby enhancing the meta-model's ability to learn from the base learner's performance across different data distributions.

[0089] In conventional cross-validation, the data partitioning of each fold is fixed, and the model learns on a static data distribution. When the data contains complex samples, this static partitioning often does not work well because the information of complex samples is not fully mined in the data space. To this end, a cross-validation strategy based on complex sample guidance is proposed: in each iteration, if a complex sample appears in the prediction set, it is moved to the training set. Complex samples are defined as samples with a prediction value error of more than 20%, which are moved into the training set and then retrained. The cross-validation process based on complex sample guidance is as follows: Figure 3 shown.

[0090] Compared to conventional cross-validation, the improved method proposed in this example offers significant advantages. By incorporating complex samples into each training round, the model can more deeply explore the mapping relationship between antenna skin co-curing manufacturing process parameters and deformation. Leveraging the multi-round nature of cross-validation, each iteration optimizes the training set distribution based on feedback from the previous round. Unlike simply increasing the sample size, this method specifically incorporates complex, information-rich samples, avoiding the impact of redundant data.

[0091] In ensemble learning, in addition to learning methods such as stacking, averaging and weighting are also commonly used. The averaging method directly takes the arithmetic mean of the predictions of each base learner as the final prediction. This method is simple and easy to understand, but it assumes that each base learner contributes equally, obscuring the differences between base learners and often resulting in lower prediction accuracy. The weighting method assigns a weight to the prediction results of each base learner and calculates the final result through weighted summation. The weight coefficient is calculated using evaluation metrics, as shown in Equation 7, where EVA refers to error metrics such as mean absolute error and mean squared error. The weight coefficient is calculated by normalizing the error metrics, giving base models with smaller errors greater weights, highlighting their importance. The weighting method effectively integrates the different learning capabilities of each base model for features, rationally combining their strengths to improve model prediction accuracy.

[0092]

[0093] Traditional stacked ensemble learning implicitly assigns weights to each base model through meta-model training. While this method can fit the nonlinear relationship between the base model's first-level predictions and the true value, it directly uses the base model outputs as input, lacks the guidance of evaluation metrics, and is less interpretable than weighted methods. Furthermore, traditional stacked ensemble learning uses the average of the base model outputs as the meta-model prediction set during cross-validation, facing similar issues as averaging ensembles and obscuring the advantages of superior fold learners.

[0094] In response to the above problems, the traditional stacked ensemble learning is improved, and a dual-weight stacked ensemble learning model is proposed in combination with the weighted method. This model assigns weights to the metadata set and each fold prediction result respectively, instead of directly inputting the metadata set and averaging the prediction value of each fold. It incorporates the guidance of the base model evaluation index to avoid the performance of the excellent fold learner being masked. Before the meta-model automatically and implicitly assigns weights, the initial weights are manually assigned to the base model, and combined with complex sample-guided cross-validation, a dual-weight stacked ensemble learning model based on complex sample guidance is constructed. Part of its construction process is as follows: Figure 4 shown.

[0095] The error index is calculated by comparing the predicted value of the base learner after adjusting the complex samples of each fold with the true value. The mean absolute error is selected as the evaluation index. The w of each fold is calculated according to Formula 7. i The values ​​of are then weighted and summed to generate partial training and test data for the meta-model. CLAnet, RBF, MLP, CNN, and XGBoost all employ complex sample-guided, two-weighted, stacked five-fold cross-validation for training. The data from the five base models is integrated to form a meta-dataset for training the SVR model. During meta-model training and testing, base models with better performance are given greater weight to fully leverage the strengths of each model.

[0096] Experimental verification and analysis

[0097] The experimental data of this embodiment are obtained from the actual co-curing preparation of antenna skin samples. The process parameters such as layer angle, mold type, curing temperature, and holding time are obtained from the preparation process, and the deformation label is obtained from the 3D scanning results of the sample. Some of the collected data are as follows: Figure 5 shown.

[0098] Based on the data collected during the co-curing preparation of antenna skins, the multi-dimensional data preprocessing scheme for antenna skin co-curing preparation is used to preprocess the data, taking into account its high feature dimension, large amount of deformation annotation data, small number of data samples, and high data coupling.

[0099] Initial data cleaning: irrelevant features with no predictive value are removed from the original data set, including the experiment number and the experiment time; dead value variables with constant values ​​are removed, including the type of matrix material and the type of reinforcement material; for the deformation label, only the label with the largest absolute value of the deformation variable among all labels is retained, and its absolute value is taken as the final deformation variable output, and all other labels are removed; the retained original features include the heterogeneous prepreg ply angle, ply configuration L, mold type M, four curing temperature parameters (curing temperature 1 to 4), heating rate, cooling rate, two holding time parameters (holding time 1 to 2), pre-compaction time, two curing pressure parameters (curing pressure 1 to 2) and vacuum degree.

[0100] Missing value processing: Missing variables are identified through the missing value distribution diagram. If the missing ratio is ≤1% (specifically, 2 samples are missing in 200 samples), the samples with missing values ​​are directly removed to avoid noise introduced by interpolation. The missing variables include the layup configuration L and the mold type M. The missing data of the mold type is included in the missing data of the layup configuration. After sample deletion, 198 valid samples are retained.

[0101] Outlier detection and verification: Statistical analysis is performed on numerical variables to calculate the mean, standard deviation, maximum value, minimum value, and median. Based on the 3σ principle, data points are verified to see if they exceed three times the standard deviation. The data distribution is analyzed using a box plot. If all samples are within the upper and lower whiskers and the median line is close to the center of the box, the data are judged to have no outliers and all samples are retained for subsequent processing.

[0102] Key feature screening: Recursive feature elimination (RFE) and random forest model are used to jointly screen features, including:

[0103] Build a random forest model, configure the maximum depth and minimum number of split samples hyperparameters, and use the mean absolute error (MAE) as the evaluation metric;

[0104] After the first training, the feature importance scores are calculated and normalized to generate a preliminary feature ranking;

[0105] Iteratively remove the least important features, retrain the model and update the feature ranking until the feature subset is empty;

[0106] According to the curve of MAE changing with the number of features, the 13 features with the lowest MAE were selected as the optimal subset, and the features eliminated were vacuum degree and pre-compaction time. The feature importance ranking showed that curing temperature, curing pressure and holding time contributed most to the prediction of deformation.

[0107] Hybrid data augmentation: We used a combination of three augmentation methods on the 198 screened samples to expand the data volume to 602 items, including:

[0108] Random scaling: linearly scale the numerical features in the range [0.95, 1.05], while the categorical features (ply configuration L, mold type M) remain unchanged;

[0109] Add Gaussian noise: Superimpose normal distribution noise with a mean of 0 and a variance of 5% of the original data variance on the numerical features.

[0110] Mixup: Randomly select two samples from samples with the same category features (ply configuration L, mold type M), generate a fusion coefficient λ (λ∈[0,1]) according to the Beta distribution, and generate a new sample:

[0111]

[0112] Among them, (x i ,y i ) and (x j ,y j ) are two randomly selected samples from the original data. λ is the fusion coefficient, which ranges from [0 to 1] and is randomly generated using a Beta distribution. The enhanced data is checked for process parameter ranges, and data that exceeds engineering constraints is eliminated to ensure the physical rationality of the enhanced data.

[0113] Normalization of numerical data and encoding of categorical data:

[0114] Normalization: Perform linear normalization on numerical features and map them to the interval [0, 1]. The formula is:

[0115]

[0116] Among them, x is the data before normalization, x min and x maxThe normalization operation maps the maximum value to 1 and the minimum value to 0, and the remaining data is linearly distributed in the interval [0, 1].

[0117] For non-gradient descent models (such as XGBoost), the normalization step is omitted;

[0118] Category data encoding:

[0119] Embedding is used in the neural network model to assign unique indices to the ply configuration L and mold type M, mapping them into two-dimensional continuous vectors, which are initialized to random values ​​and optimized through model training.

[0120] Onehot encoding is used for non-neural network models (such as XGBoost and RBF networks) to generate binary sparse vector representations.

[0121] Through the steps of preliminary cleaning, key feature screening, data enhancement, etc., a total of 602 data samples were obtained, each data sample containing 13 features and 1 deformation label. The effectiveness of the antenna skin deformation prediction based on the complex sample-guided dual-weight stacking integration model proposed in this embodiment is verified. First, the WOA algorithm is used to perform a global search on the hyperparameters of each base model and the integrated model to obtain the optimal hyperparameter combination of each model. Then, the antenna skin deformation is predicted using each base model and the integrated model based on the optimal hyperparameters, and the prediction results are evaluated using four evaluation indicators: mean absolute error (MAE), root mean square error (RMSE), determination coefficient (R2) and accuracy (Acc). Finally, the effectiveness of the complex sample-guided method and the dual-weight stacking integration method proposed in the present invention are verified by ablation experiments.

[0122] Experimental parameter settings

[0123] This embodiment uses mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R²), and accuracy (Acc) as evaluation metrics for the predicted and true values ​​of antenna skin deformation. A global search of hyperparameters for each base model and metamodel is performed using the WOA algorithm. Tables 2, 3, and 4 show the hyperparameter configurations for some models.

[0124] Table 2 RBF base model hyperparameter configuration

[0125]

[0126] In the table, batch_size indicates the number of samples contained in the sample subset input each time; epoch indicates the number of times the entire training set completes training; learning_rate indicates the learning rate; rbf_type indicates the radial basis function type; hidden_size indicates the number of radial basis functions.

[0127] Table 3 XGBoost base model hyperparameter configuration

[0128]

[0129] The meaning of each parameter in the table is detailed in Table 1.

[0130] Table 4 SVR metamodel hyperparameter configuration

[0131]

[0132]

[0133] In the table, kernel represents the kernel function type; C represents the penalty coefficient for controlling the penalty intensity of the slack variable; gamma represents the coefficient of the rbf kernel; and epsilon represents the error tolerance band width.

[0134] Results and analysis of base model and integrated model

[0135] The results of the antenna skin co-curing preparation data preprocessing were input into the dual-weight stacking deformation prediction integrated model based on complex sample guidance constructed in this embodiment. After five-fold cross-validation of the base model and quadratic fitting of the meta-model, the prediction results of the test data were as follows: Figure 6 As shown. According to the evaluation index calculation formula, based on the calculation of actual deformation value and predicted deformation value, the results of each evaluation index are: MAE equals 0.107, RMSE equals 0.127, R2 equals 0.965, Acc equals 95.4%. It can be seen that the average absolute error of deformation is only 0.107mm, and the average deformation prediction accuracy of the test sample is as high as 95.4%. All evaluation indicators are better than WOA-CLAnet, which proves the effectiveness of the integrated model constructed by the present invention in improving the deformation prediction accuracy of antenna skin co-curing preparation. The comparison results of deformation prediction value and true value are shown in Figure 7 shown.

[0136] from Figure 7 It can be seen that the trend fluctuation curve of the antenna skin deformation prediction value and the trend fluctuation curve of the true value have a high degree of overlap, there are fewer data points with large absolute errors, and the antenna skin deformation prediction value of each data point is close to the true value. Figure 8This is a scatter plot comparing the predicted and true values ​​of the antenna skin deformation of the integrated model. It can be seen from the figure that all data points are distributed near the contour lines, and there are no abnormal data points that deviate far away.

[0137] Table 5 shows the experimental results for antenna skin deformation prediction using various base models. RBF and XGBoost use one-hot encoding for categorical features, while MLP, CNN, and WOA-CLAnet use embedded encoding. Because feature scale does not affect XGBoost's split point decision, data normalization is not performed during deformation prediction using the XGBoost base models. Because each base model employed five-fold cross-validation, the evaluation metrics in Table 5 are the averages of the metrics across each fold. The stacking-up model in the table represents the constructed dual-weight stacking deformation prediction ensemble model based on complex sample guidance.

[0138] Table 5 Experimental results of antenna skin deformation prediction for base model and integrated model

[0139]

[0140] The experimental results in Table 5 show that the complex sample-guided dual-weight stacking deformation prediction ensemble model constructed in this embodiment achieves optimal performance across all evaluation metrics for deformation prediction during antenna skin co-curing. For example, compared to the five base models (RBF, MLP, CNN, XGBoost, and WOA-CLAnet), the deformation prediction accuracy improves by 8.2%, 11.1%, 6.5%, 5.3%, and 1.9%, respectively, and the mean absolute error of deformation decreases by 0.179mm, 0.243mm, 0.143mm, 0.119mm, and 0.046mm, respectively. The experimental results demonstrate that stacking ensembles can form a strong ensemble model by combining the different learning methods of each weak base model and leveraging the diversity and complementarity of each base model. This further validates the effectiveness of the constructed complex sample-guided dual-weight stacking deformation prediction ensemble model in improving the accuracy of deformation prediction during antenna skin co-curing.

[0141] Ablation experiment results and analysis

[0142] This paper proposes a complex sample-guided five-fold cross-validation method and a dual-weight stacking ensemble method for deformation prediction during antenna skin co-curing. To verify their effectiveness, ablation experiments were designed for comparison. The ablation test results are shown in Table 6. In the table, Stacking-up2 is a dual-weight stacking ensemble model without complex sample guidance, and Stacking-up3 is a single-weight stacking ensemble model with complex sample guidance. All ablation models use the same data preprocessing method, and other non-ablation components remain completely consistent.

[0143] Table 6 Ablation test results of the integrated model for antenna skin deformation prediction

[0144]

[0145] Table 6 shows that compared to Stacking-up, Stacking-up2, and Stacking-up3, the values ​​of each evaluation metric in antenna skin co-curing deformation prediction decreased to varying degrees. For example, Stacking-up2's deformation mean absolute error increased by 30.8%, and its deformation root mean square error increased by 54.5%. Ablation experiments validate the effectiveness of the complex sample-guided five-fold cross-validation method and dual-weighted stacking ensemble method proposed in this paper for antenna skin deformation prediction.

[0146] The present invention establishes five heterogeneous base models: CLAnet, RBF, MLP, CNN, and XGBoost; establishes a support vector regression machine as a meta-model; constructs a two-level integrated model based on a stacking framework; uses a complex sample-guided five-fold cross-validation strategy to optimize the training set distribution and dynamically enhance learning of complex samples; calculates the error indicators of each base learner and manually assigns initial weights to the base models before the meta-model automatically and implicitly assigns weights to optimize the meta-data set distribution; and introduces a whale optimization algorithm to adjust the hyperparameters of each model. The resulting integrated prediction model, by integrating the different learning methods of each base model for features and leveraging the quadratic fitting capabilities of the meta-model, can address the problems of insufficient generalization ability of a single model for complex samples and limited modeling capabilities for multivariate coupling relationships. It has the advantage of improving the deformation prediction accuracy of antenna skin co-curing preparation and can provide auxiliary decision support for the rapid verification of antenna skin design solutions.

[0147] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A modeling method of a dual-weight stacking deformation prediction integrated model based on complex sample guidance, characterized in that: The following steps are involved: S1: Construct five heterogeneous base models, including CLAnet network, radial basis function neural network, multi-layer perceptron, convolutional neural network and extreme gradient boosting machine; S2: A complex sample-oriented five-fold cross-validation strategy is used to train each base model, and the hyperparameters of each base model are optimized using the whale algorithm. During the validation phase, samples with a prediction error exceeding 20% ​​are marked as complex samples and moved into the training set to retrain the folded base model. S3: Calculate the corresponding mean absolute error based on the cross-validation results of each fold of each base model, and calculate the weight of the predicted value of each fold of each base model according to the mean absolute error, which is used to explicitly assign the first weight and generate the training set and test set of the meta-model; S4: Construct a support vector regression machine as a meta-model, using a radial basis kernel function as the kernel function, and optimize its hyperparameters using the whale algorithm. The hyperparameters include the penalty coefficient C, the kernel coefficient γ, and the error tolerance band width ε. S5: The weighted metadata dataset is input into the SVR for training, and a second weight is implicitly assigned to each input feature to form a final complex sample-guided dual-weight stacked deformation prediction integration model.

2. The complex sample-guided dual-weighted stacking deformation prediction integrated model modeling method according to claim 1, characterized in that: The step S1 comprises: The CLAnet network, RBF, MLP, CNN, and XGBoost are used as the base model for stacking ensemble learning. The Gaussian kernel is selected as the radial basis function of the RBF. The expression of the Gaussian function is as follows: Among them, x is the input space, σ is the parameter that controls the width of the Gaussian kernel, and a i represents the center of the i-th basis function; The K-means clustering algorithm is used to determine the number and location of centers. The core formula of the K-means algorithm is as follows: Among them, a k Represents the center of each cluster, and the optimization goal is to minimize the value of J; The relu function is selected as the activation function of MLP, and its calculation formula is as follows: f(x)=max(0,x) (3) A one-dimensional convolutional neural network is selected as one of the base learners. The one-dimensional convolutional layer and the pooling layer perform downsampling operations to extract local features. The activation function can be nonlinear. The output of the last hidden layer is flattened and then integrated into the final prediction result by the fully connected layer. Select CART as the weak learner of XGBoost; XGBoost's optimization objectives include the loss function and the regularization term. By minimizing this objective, the split point and complexity of the decision tree are controlled. The new round of iteration will fit the error of the previous round, and the final prediction value is the sum of each decision tree. Its prediction model is expressed as follows: Where N is the number of decision trees, f n represents the nth decision tree; the formula for minimizing the objective function is as shown in Equation 5; Where l is the loss function, which measures the deviation between the predicted value and the true value; Ω is the regularization term, which is used to control the number of model nodes and the complexity of the weights. Its calculation formula is as shown in Equation 6. Among them, T and w represent the number and weight of leaf nodes respectively, γ is the leaf node penalty coefficient, and λ is the weight decay coefficient.

3. The complex sample-guided dual-weighted stacking deformation prediction integrated model modeling method according to claim 1, characterized in that: The step S3 includes: calculating the error index by using the predicted value of the base learner after adjusting the complex sample of each fold and the true value, and calculating each fold w according to the following formula i Value: Where, MAE refers to the mean absolute error; The first weight is explicitly assigned to generate the metadata dataset, and the learning direction of the metamodel is guided by manual weighting, forming a dual-weight stacking integration framework.

4. The complex sample-guided dual-weighted stacking deformation prediction integrated model modeling method according to claim 1, characterized in that: The step S4 includes: using the WOA algorithm to optimize the hyperparameters of SVR, including the penalty coefficient C, the error tolerance band width ε, and the kernel coefficient gamma, wherein: C controls the slack variable penalty strength, ε controls the error tolerance band width, the number of support vectors decreases as ε increases, and gamma controls the perception range and fitting granularity of the model.

5. The complex sample-guided dual-weighted stacking deformation prediction integrated model modeling method according to claim 1, characterized in that: The step S5 includes: implicitly assigning a second weight to the meta-model through a support vector regression machine, and training the meta-model in combination with the explicitly weighted meta-data set, to ultimately form a dual-weight collaborative integrated prediction model.

6. A data-driven method for predicting deformation during co-curing of antenna skins, characterized by: The following steps are involved: S1: Perform preliminary cleaning, missing value processing, and outlier detection on the antenna skin co-curing preparation data. Key features are screened using recursive feature elimination and random forest. Data enhancement is performed using random scaling, Gaussian noise addition, and Mixup hybrid methods. Numerical data is normalized and categorical data is encoded. S2: Construct a three-channel multidimensional regression focusing network model CLANet, which includes a three-channel CNN feature extraction layer, an LSTM feature learning layer, an attention mechanism focusing layer, and a hyperparameter optimization layer based on the whale algorithm; S3: The three-channel multidimensional regression focusing network model is used as the base model together with the radial basis function network, multilayer perceptron, convolutional neural network, and XGBoost model. The preprocessed data is input into each base model. The base model is trained using a complex sample-guided five-fold cross-validation strategy. The first weight is calculated by calculating the average absolute error of the prediction value of each fold to optimize the metadata set distribution. The support vector regression meta-model is used for double-weight stacking integration to output the final deformation prediction value.

7. The data-driven method for predicting deformation of antenna skin co-curing according to claim 6, characterized in that: The method for constructing the three-channel multidimensional regression focusing network model in step S2 includes: extracting multi-scale features based on a three-channel convolutional neural network, learning spatiotemporal nonlinear relationships through a long short-term memory network, dynamically allocating feature weights in combination with an attention mechanism, and optimizing network hyperparameters using a whale algorithm.

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