Antenna skin co-curing deformation prediction method based on three-channel multi-dimensional regression focusing network

Abstract

The invention relates to the technical field of deformation prediction, in particular to an antenna skin co-curing deformation prediction method based on a three-channel multi-dimensional regression focusing network, and the method comprises the steps: designing a three-channel convolutional neural network feature extraction layer, and achieving the multi-scale feature fusion through a differential convolution kernel and a pooling strategy, and space coupling characteristics of process parameters such as temperature, pressure intensity and layering configuration are fully excavated. Secondly, a complex non-linear relation between modeling process parameters and deformation of the long-short-term memory network is introduced, and feature weights are dynamically distributed by combining an attention mechanism focusing layer, so that the model is focused on key features with relatively great influence; the whale optimization algorithm is adopted to globally search the optimal hyper-parameter combination, and the convergence efficiency and generalization ability of the model are improved. The problems of insufficient multi-dimensional feature extraction and low micro deformation prediction precision are solved, the accuracy and stability of antenna skin co-curing millimeter-level deformation prediction are remarkably improved, and auxiliary decision support can be provided for rapid verification of an antenna skin co-curing design scheme.

Description

Technical Field

[0001] The present invention relates to the technical field of deformation prediction, and in particular to an antenna skin co-curing deformation prediction method based on a three-channel multi-dimensional regression focusing network. Background Art

[0002] Conformal antennas are advanced antenna systems that closely match the surface geometry of a carrier and closely follow its contours. They are typically integrated into the skin in a non-planar form to achieve a seamless fusion of function and form. In new-generation fighter aircraft, the antenna skin, as the external carrier of the conformal antenna, bears the core responsibility of ensuring stealth performance, aerodynamic performance, and mechanical strength. It is also the key guarantee for fully leveraging the flexibility, adaptability, and integration advantages of conformal antennas. High-quality preparation of antenna skins is a solid foundation for improving the overall performance of fighter aircraft, significantly promoting the advancement of national defense and military technology, and has become the latest requirement for information-based warfare in modern warfare.

[0003] In new-generation fighter aircraft, antenna skins are fabricated using co-curing of fiber composite materials. Fiber composites offer the advantages of high strength and lightweight, enabling the antenna skin to withstand significant mechanical loads and maintain high maneuverability. The core of the co-curing process is to utilize the adhesive properties of low-density resins to replace fasteners such as metal screws, allowing the antenna skin to be molded in an integrated manner. This avoids the interface weaknesses associated with traditional fastening methods and significantly improves the antenna skin's overall performance, including corrosion resistance, electromagnetic properties, and reliability. However, deformation of the antenna skin during the fabrication process is unavoidable, and this deformation directly impacts the performance of the conformal antenna. Therefore, understanding the deformation patterns during the fabrication process is crucial for controlling the quality of the conformal antenna. Currently, validation of antenna skin co-curing fabrication methods is primarily accomplished through repeated fabrication experiments using actual prototypes. Adjustment of process parameters cannot be rapidly adjusted, hindering the real-time nature of design verification. The fabrication process involves multiple materials, multiple processes, and multiple parameters, and involves complex physical and chemical reactions. Consequently, the mechanisms and patterns of how process parameters influence skin deformation remain unclear. Since data-driven deformation prediction technology can quickly verify design schemes in a zero-cost, high-efficiency manner, and can analyze the strong coupling relationship between variables and variables, and variables and deformations in the co-curing preparation process through the interpretability of the model, it has become a key technical support for the high-precision preparation of antenna skins.

[0004] Deformation prediction is a common problem, such as deformation prediction during the use of mechanical parts, mountain deformation prediction in geology, and deformation prediction in composite material preparation. Deformation prediction is to infer the corresponding deformation based on a set of deformation influencing factors. Specifically, it can be described as follows: Assume that there are n factors that affect the deformation, denoted by X = {x1, x2, ..., x n}, there exists a set Y representing the deformation, Y={y1,y2,...,ym The task of deformation prediction is to accurately predict the corresponding deformation set Y based on the deformation influencing factor X. Currently, deformation prediction has been widely used in fields such as geological disaster prediction and component life prediction.

[0005] While deformation prediction has achieved promising results in numerous applications, practical applications in specialized fields still present numerous challenges, particularly in predicting small deformations in antenna skins. First, the co-curing data for antenna skin fabrication contains multiple physical quantities, such as temperatures and pressures, as well as variables at multiple time scales and categorical variables such as layup configuration. This diverse feature information makes it challenging to extract more useful features from this multidimensional feature set. Second, the complex physical and chemical reactions during the co-curing process lead to highly complex nonlinear mapping relationships between process parameters and deformation, making accurate capture extremely challenging. Antenna skins are used in new-generation fighter aircraft, and the deformation of actual fabricated antenna skin samples must be controlled at the millimeter level. This presents a typical problem in small deformation prediction, which has been a challenge in the field due to the difficulty in accurately measuring data and the high precision required for prediction. Therefore, this paper focuses on addressing the issues of existing methods for antenna skin co-curing deformation prediction, such as insufficient multidimensional feature extraction, low small deformation prediction accuracy, and inaccurate fitting of complex mapping relationships. The paper investigates how to extract more useful features and accurately fit complex nonlinear mapping relationships to improve small deformation prediction accuracy.

[0006] Deformation prediction is generally categorized into time-series regression and non-time-series regression. Time-series regression primarily uses historical data to predict future deformation. Due to its time-dependence and dynamic nature, time-series prediction often employs more complex network models, such as Transformers or large models. Non-time-series regression, on the other hand, lacks time dependence, and the data does not change periodically over time. Scrambling the order of input data does not affect the results. The influencing factors and deformation generally have a relatively fixed mechanistic relationship, so relatively simple regression algorithms can often achieve highly accurate predictions. When the data is complex and the mapping relationship is ambiguous, a lightweight neural network can be used to fit the mapping relationship. This can achieve highly accurate predictions while avoiding the high cost of complex models. Summary of the Invention

[0007] The purpose of the present invention is to provide an antenna skin co-curing deformation prediction method based on a three-channel multidimensional regression focusing network. The three-channel CNN extracts multi-scale features, combines the LSTM modeling nonlinear mapping relationship, introduces the attention mechanism to dynamically focus on key features, and uses the whale algorithm to optimize hyperparameters. The problems of insufficient multi-dimensional feature extraction and low accuracy of small deformation prediction are solved, and the accuracy and stability of millimeter-level deformation prediction of antenna skin co-curing are significantly improved.

[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 method for predicting antenna skin co-curing deformation based on a three-channel multidimensional regression focusing network includes the following steps:

[0010] S1: Construct a three-channel convolutional neural network (CNN) feature extraction layer to perform multi-scale feature extraction on the preprocessed process parameter data:

[0011] The first channel performs two one-dimensional convolution operations and average pooling operations;

[0012] The second channel performs two one-dimensional convolution operations and maximum pooling operations;

[0013] The third channel performs a single one-dimensional convolution operation to retain the original features;

[0014] Fuse the feature vectors output by the three channels to generate fused features;

[0015] S2: Inputting the fused features into the long short-term memory network (LSTM) feature learning layer, and modeling the nonlinear mapping relationship between process parameters and deformation through the gating mechanism of forget gate, input gate, and output gate;

[0016] S3: Set up an attention mechanism focusing layer at the LSTM output to dynamically assign feature weights:

[0017] Calculate attention score based on LSTM hidden state;

[0018] Use the softmax function to normalize the attention score and generate the weight coefficient;

[0019] Perform weighted summation on the hidden states to generate a focused feature vector;

[0020] S4: Use the Whale Optimization Algorithm (WOA) to globally optimize the hyperparameters of the CNN, LSTM, and attention layers:

[0021] Initialize the whale population and set the hyperparameter search range;

[0022] Iteratively optimize parameters through encircling prey, spiral position update, and random search mechanisms;

[0023] The optimal parameter combination is selected using the mean absolute error (MAE) as the fitness function;

[0024] S5: The optimized network model is passed through the fully connected layer to output the deformation prediction value, and the prediction accuracy is evaluated based on MAE, root mean square error (RMSE), and determination coefficient (R2).

[0025] Furthermore, the pre-processing in step S1 includes the following sub-steps:

[0026] S1.1: Preliminary data cleaning: Remove irrelevant features with no predictive value from the original data set, including experiment number, experiment time, etc.; remove dead value variables with constant values, including matrix material type, reinforcement material type, etc.; for deformation labels, only retain the label with the largest absolute value of deformation variable among all labels, and remove all other labels; the retained original features include heterogeneous prepreg ply angle, ply configuration, mold type, 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.

[0027] S1.2: Missing value processing: Identify missing variables through the missing value distribution diagram. If the missing ratio is ≤1% (specifically, 2 samples are missing in 200 samples), directly remove the samples with missing values ​​to avoid noise introduced by interpolation. The missing variables include layup configuration and mold type, and the missing data of mold type is included in the missing data of layup configuration. After sample deletion, 198 valid samples are retained.

[0028] S1.3: Outlier detection and verification: Perform statistical analysis on numerical variables and calculate the mean, standard deviation, maximum, minimum, and median. Verify whether the data points exceed the range of three times the standard deviation based on the 3σ principle, and analyze the data distribution with the box plot. If all samples are within the upper and lower whiskers and the median line is close to the center of the box, it is determined that the data have no outliers and all samples are retained for subsequent processing.

[0029] S1.4: Key feature screening: Recursive feature elimination (RFE) and random forest model are used to jointly screen features, including:

[0030] Build a random forest model, configure hyperparameters such as maximum depth and minimum number of split samples, and use mean absolute error (MAE) as the evaluation metric;

[0031] After the first training, the feature importance scores are calculated and normalized to generate a preliminary feature ranking;

[0032] Iteratively remove the least important features, retrain the model and update the feature ranking until the feature subset is empty;

[0033] 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.

[0034] S1.5: Hybrid data augmentation: We use a combination of three augmentation methods on the 198 screened samples to expand the data volume to 602 items, including:

[0035] 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;

[0036] 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.

[0037] 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:

[0038]

[0039] 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.

[0040] S1.6: Normalization of numerical data and encoding of categorical data:

[0041] Normalization: Perform linear normalization on numerical features and map them to the interval [0, 1]. The formula is:

[0042]

[0043] Among them, x is the data before normalization, x min and x max The 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].

[0044] Category data encoding:

[0045] Embedding is used to assign unique indexes to the ply configuration L and mold type M, map them into two-dimensional continuous vectors, initialize them to random values ​​and optimize them through model training.

[0046] Furthermore, the LSTM includes a forget gate, an input gate, and an output gate;

[0047] The calculation formula of the forget gate is as shown in formula 1. The input of the forget gate is the output data h of the previous step. t-1 and the current input data x t , the output f is obtained through the activation function σ t Where W is the matrix information and b is the offset.

[0048] f t =σ(W f ·[h t-1 ,x t ]+b f ) (1)

[0049] The calculation formulas of the input gate are shown in Equations 2 and 3. Equation 2 determines which information to update, and Equation 3 generates candidate memories. The combination of the two equations controls the degree of inclusion of new information.

[0050] i t =σ(W i ·[h t-1 ,x t ]+b i ) (2)

[0051]

[0052] According to the results of the forget gate and input gate, the memory unit is updated. The calculation formula is as shown in formula 4. The memory unit C t Retains information in long-term memory.

[0053]

[0054] The calculation formulas of the output gate are as shown in Equations 5 and 6. Equation 5 completes information screening, and Equation 6 generates the hidden state for the current prediction.

[0055] o t =σ(W o ·[h t-1 ,x t ]+b o ) (5)

[0056] h t =o t *tanh(C t ) (6)

[0057] The output of the three-channel CNN feature extraction layer is used as the input of LSTM, and the powerful nonlinear expression ability of LSTM is used to fit the nonlinear mapping relationship between the antenna skin co-curing process parameters and deformation.

[0058] Furthermore, the attention mechanism includes:

[0059] (1) Using the state S at the previous moment t-1 and the hidden layer node value h i Calculate the attention score e ki , to determine the importance of the current feature to the output value, e ki The calculation formula is as follows:

[0060] e ki =V T tanh(WS t-1 +Uh i +b) (7)

[0061] Where V, W, U are the attention mechanism weight matrices, and b is the bias. Using the V matrix to perform a linear transformation on the result after the tanh function can better learn the correlation between input and output. t-1 Contains the network's accumulated learning experience, and the W matrix can integrate it with the latest input. ki Represents the degree of association between input node i and output node k, e ki The larger the value is, the greater the influence of the corresponding process parameters on the antenna skin deformation is.

[0062] (2) Use the softmax function to calculate the attention score e ki Normalize, the result of normalization is the weight coefficient a ki , a ki The value of is in the interval [0, 1], and the weight coefficient represents the relative importance of the output node k to different input nodes. ki The calculation formula is as follows, where T x The length of the input sequence

[0063]

[0064] (3) The weight coefficient a ki and the LSTM hidden layer state vector h i Perform inner product operation, the result of the operation is the output o of the Attention layer t , o t The calculation formula is as follows:

[0065]

[0066] Furthermore, the parameter optimization process of the whale optimization algorithm includes two stages: development and exploration. The development stage includes the prey encirclement stage and the bubble net attack stage, and the exploration stage is the prey search stage.

[0067] The core formula for the encirclement phase is as follows:

[0068] D=|C·X prey -X (t) | (10)

[0069] X (t+1) =X pred -A·D (11)

[0070] Where D is a transition vector, A and C are parameter variables, and X pred is the position vector of the target prey in the current whale group, X (t) is the position vector of each whale itself, and t is the current iteration number.

[0071] The bubble net attack phase includes two mechanisms: shrinking and surrounding, and spiral position update. The core formula is as follows:

[0072]

[0073] Where D′ is the absolute value of the distance between the individual whale position and the target prey position, b is the shape constant in the spiral formula, and l is a random number uniformly distributed between [0, 1]. p is the probability of selecting the two mechanisms of shrinking and wrapping and spiral position update, and its value is a random number uniformly distributed between [0, 1]. t To select the threshold, it is generally assumed that the probability of selecting the two strategies is equal, that is, p t =0.5.

[0074] The prey search phase is based on the fact that the current surrounding fish school is not optimal during the actual predation process, and a random search strategy is adopted to obtain better exploration capabilities. The core formula of the prey search phase is as follows, where X r Represents a randomly selected individual whale:

[0075] D=|C·X r -X (t) | (13)

[0076] X (t+1) =X r -A·D (14)

[0077] The Whale Algorithm is used to iteratively optimize hyperparameters such as the hidden layer dimension and the number of LSTM layers in the CLANet network. The optimal parameter combination found by WOA is used to train the CLANet network, which can obtain better evaluation index values ​​and faster training speed.

[0078] Beneficial effects of the present invention:

[0079] In view of the high feature dimension and strong data coupling of the antenna skin co-curing preparation data, the present invention designs a three-channel convolutional neural network feature extraction layer. This design effectively solves the problem of insufficient extraction capability of traditional single-channel CNN when processing high-dimensional coupled features. The first channel emphasizes the extraction of the overall trend and average features of the process parameters through two one-dimensional convolutions and average pooling, which helps to capture the macroscopic physical and chemical reaction influencing paths; the second channel uses two one-dimensional convolutions and maximum pooling to keenly capture local extreme values ​​or abnormal features, which are often "hot spots" that reflect the key influence of microscopic local effects and extreme process conditions on deformation; and the third channel only performs a single one-dimensional convolution, which maintains the integrity of the original features and prevents the loss of detailed features that may be introduced by multiple pooling. The fusion of the three-channel features forms a diversified representation covering different scales and receptive fields, which enhances the model's ability to capture complex coupling relationships, especially the interactive effects of temperature, pressure, and ply configuration. The three-channel convolutional neural network feature extraction layer can fully explore the intrinsic patterns and potential representations in the data, thus laying a solid foundation for subsequent nonlinear mapping and significantly improving the prediction accuracy and stability of small deformations of the antenna skin.

[0080] Considering the highly nonlinear and dynamic mapping relationship between the process parameters and deformation variables involved in the co-curing deformation prediction of the antenna skin, the present invention adopts an LSTM feature learning layer containing a forget gate, an input gate, and an output gate as the core regression model. LSTM achieves selective memory and forgetting of information through a gating mechanism, meticulously managing the interaction between input data and historical states, effectively overcoming the vanishing gradient problem of traditional recurrent neural networks. The forget gate can filter out information that is irrelevant or outdated to the current prediction, preventing redundant information from interfering with model training; the input gate determines which new information should be updated, and dynamically accumulates and updates the factors affecting the deformation in combination with candidate memories; the output gate is responsible for screening the final output, ensuring that the hidden state that contributes most to future deformation predictions is saved and transmitted. By using the multi-scale features extracted by the three-channel CNN as the LSTM input, the model can effectively mine the complex coupling relationship between process parameters and deformation in both time and space dimensions, capturing the complex nonlinear mapping relationship between factors such as curing temperature, curing pressure, and layup method and deformation. It can not only complete the accurate fitting of nonlinear functions, but also reveal the potential causal relationship between micro-process parameters and macro-deformation, providing theoretical support and reliable implementation path for high-precision millimeter-level micro-deformation prediction.

[0081] Because the various process parameters involved in the antenna skin co-curing process vary in their impact on deformation, traditional CNN-LSTM models lack an explicit mechanism for distinguishing the importance of each feature, diluting the contribution of key features and affecting the accuracy of the final prediction. To address this issue, the present invention introduces an attention mechanism based on the LSTM hidden state. By calculating the tanh transform mapping between the current hidden state and the historical state, a dynamic attention score is generated, reflecting the contribution of different features to deformation prediction. The score is then normalized using the softmax function to obtain a weight coefficient ranging from 0 to 1, enabling the model to selectively focus on feature dimensions with the most significant impact on deformation, such as key parameters such as curing temperature, curing pressure, and holding time. By weighted summation of the hidden layer states, a targeted focused feature vector is output, significantly improving the model's sensitivity and recognition of subtle deformation changes. This not only improves prediction accuracy and model robustness, but also provides a quantitative analysis basis for key feature weights in engineering practice, helping process engineers understand and optimize the manufacturing process and enhance the quality control of antenna skin products.

[0082] The performance of neural networks is highly dependent on hyperparameter configuration. The reasonable selection of parameters such as LSTM hidden layer dimension, number of layers and number of convolutional layer channels directly affects the expression ability and generalization performance of the model. In view of the high-dimensional, non-convex and complex characteristics of the hyperparameter space, the present invention adopts the whale optimization algorithm (WOA) to perform a global search, and finds the optimal hyperparameter combination by simulating the surrounding prey, foam net attack and random search strategy in the whale's predation behavior. Specifically, the position of the whale population is updated by surrounding the prey, spiral position update and random search mechanism to achieve global optimization of the hyperparameter combination, ensuring the comprehensiveness and efficiency of the search. WOA uses the mean absolute error (MAE) as the fitness function to ensure that the selected parameter combination can minimize the actual prediction error. It not only ensures that the prediction performance of the model is optimal, but also significantly improves the training speed and convergence efficiency, and reduces the cost of manual parameter adjustment.

[0083] 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

[0084] 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.

[0085] Figure 1 This is a schematic diagram of the overall framework of the three-channel multidimensional regression focusing network model;

[0086] Figure 2 It is a schematic diagram of the one-dimensional convolution principle;

[0087] Figure 3 It is a schematic diagram of the one-dimensional pooling principle;

[0088] Figure 4 This is a schematic diagram of the three-channel CNN feature extraction layer structure;

[0089] Figure 5 This is a schematic diagram of the internal structure of LSTM;

[0090] Figure 6 It is a schematic diagram of part of the collected data;

[0091] Figure 7 This is a schematic diagram of the WOA-CLAnet antenna skin deformation prediction value;

[0092] Figure 8 This is a schematic diagram comparing the WOA-CLAnet antenna skin deformation prediction results;

[0093] Figure 9This is a scatter plot diagram comparing the WOA-CLAnet antenna skin deformation prediction value and the actual value. DETAILED DESCRIPTION

[0094] 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.

[0095] Example 1

[0096] The present embodiment provides a method for predicting antenna skin co-curing deformation based on a three-channel multidimensional regression focusing network, comprising the following steps:

[0097] S1: Construct a three-channel convolutional neural network (CNN) feature extraction layer to perform multi-scale feature extraction on the preprocessed process parameter data:

[0098] The first channel performs two one-dimensional convolution operations and average pooling operations;

[0099] The second channel performs two one-dimensional convolution operations and maximum pooling operations;

[0100] The third channel performs a single one-dimensional convolution operation to retain the original features;

[0101] Fuse the feature vectors output by the three channels to generate fused features;

[0102] S2: Inputting the fused features into the long short-term memory network (LSTM) feature learning layer, and modeling the nonlinear mapping relationship between process parameters and deformation through the gating mechanism of forget gate, input gate, and output gate;

[0103] S3: Set up an attention mechanism focusing layer at the LSTM output to dynamically assign feature weights:

[0104] Calculate attention score based on LSTM hidden state;

[0105] Use the softmax function to normalize the attention score and generate the weight coefficient;

[0106] Perform weighted summation on the hidden states to generate a focused feature vector;

[0107] S4: Use the Whale Optimization Algorithm (WOA) to globally optimize the hyperparameters of the CNN, LSTM, and attention layers:

[0108] Initialize the whale population and set the hyperparameter search range;

[0109] Iteratively optimize parameters through encircling prey, spiral position update, and random search mechanisms;

[0110] The optimal parameter combination is selected using the mean absolute error (MAE) as the fitness function;

[0111] S5: The optimized network model is passed through the fully connected layer to output the deformation prediction value, and the prediction accuracy is evaluated based on indicators such as MAE, root mean square error (RMSE), and determination coefficient (R2).

[0112] Example 2

[0113] In order to solve the problems of insufficient multi-dimensional feature extraction, low accuracy of small deformation prediction and inaccurate fitting of complex mapping relationships in existing methods for predicting antenna skin co-curing deformation, this embodiment proposes a three-channel multi-dimensional regression focusing network model (WOA-CLANet) for predicting antenna skin co-curing deformation. The overall framework is as follows: Figure 1 As shown in the figure, WOA-CLANet consists of a three-channel CNN feature extraction layer, an LSTM feature learning layer, an attention mechanism focusing layer, a fully connected layer, and a hyperparameter optimization layer based on the whale algorithm. By combining the spatiotemporal advantages of CNN and LSTM and incorporating the attention mechanism, the WOA-CLANet network not only enables in-depth mining of antenna skin co-curing fabrication data, but also further analyzes and expresses key features, reducing the impact of secondary features on deformation prediction, thereby improving the overall performance of the model.

[0114] First, the data preprocessing results are fed into the feature extraction layer. To address the incomplete feature extraction of a single-channel CNN, a three-channel CNN is used to extract comprehensive, multi-angle features from the data, providing an abstract representation of key features for the LSTM network. The LSTM receives the fused three-channel features from the CNN output and, leveraging its temporal dimension mining and nonlinear fitting capabilities, accurately fits the mapping relationship between process parameters and deformation. To address the lack of explicit differentiation of feature importance, an attention mechanism focusing layer assigns different weight coefficients to the hidden layer states of the LSTM to describe the influence of different features on antenna skin deformation, improving model accuracy and enhancing model interpretability. A fully connected layer applies linear transformations to the output of the attention mechanism focusing layer, resulting in the predicted antenna skin deformation value. To achieve higher prediction accuracy and accelerate training, a global search of hyperparameters for the CNN, LSTM, and attention layers is performed using the whale algorithm to identify the optimal hyperparameter combination.

[0115] Three-channel CNN feature extraction layer

[0116] Since the data prepared by co-curing the antenna skin has the characteristics of high feature dimension and strong data coupling, the complexity of the data is significantly increased. If the results of data preprocessing are directly input into the LSTM network for training, the redundant information in the data can easily cause the model to over-rely on the local patterns of specific samples, and the complex spatial distribution of the data places extremely high demands on the model's expressive ability. To ensure the accuracy of deformation prediction, LSTM requires a deeper network structure to capture complex patterns, but deep networks will significantly increase the number of parameters, resulting in increased training complexity, and a single LSTM network has poor generalization and limited ability to model spatial features. To address the above problems, this embodiment introduces a CNN neural network for feature extraction.

[0117] CNN's local receptive field, weight sharing, and pooling operations reduce the number of parameters and computational complexity, enabling multi-scale feature extraction. Through multiple layers of convolution and pooling, features at each level are gradually extracted to achieve a highly abstract global representation of the data, facilitating the next layer of the LSTM network to analyze the complex structure and patterns of the data. The core structure of a CNN is composed of convolutional and pooling layers.

[0118] (1) Convolutional layer

[0119] The fixed-length sliding of the convolution kernel realizes the local receptive field and weight sharing of CNN, and realizes data filtering and dimensionality reduction through convolution operation. Since the data prepared by antenna skin co-curing is one-dimensional data, a one-dimensional convolution operation is performed. The one-dimensional convolution operation process is as follows: Figure 2 As shown in the figure, the convolution kernel slides from top to bottom according to the set step size, and a convolution operation is performed each time it slides. The result tensor formed after the sliding is the abstract feature representation of the process parameters.

[0120] (2) Pooling layer

[0121] Through pooling operations, features are further selected in regions in the low-dimensional vector output by the convolution layer to reduce the data dimension to a lower level. The most commonly used pooling operations are maximum pooling and average pooling. Maximum pooling takes the maximum value in the pooling area, and average pooling takes the arithmetic average of all values ​​in the pooling area. The maximum pooling and average pooling processes are as follows: Figure 3 Although the pooling operation will cause some data loss, it retains the most representative local features, which has a positive impact on improving accuracy and reducing training time.

[0122] Traditional single-channel convolutional neural networks are widely used for extracting features from one-dimensional data for regression or time series prediction, and they perform relatively well in these tasks. However, when the data has many features and the interactions between them are complex, the effectiveness of single-channel CNN feature extraction deteriorates. The co-curing preparation of antenna skins involves complex chemical reactions and physical processes such as thermal expansion and contraction. Process parameters such as temperature, pressure, mold type, and layup method can significantly affect the progression of these physical and chemical reactions, thereby inducing deformation. Consequently, complex coupling relationships exist between features and between features and deformation, and the feature extraction capabilities of traditional single-channel CNNs are no longer sufficient to meet these complex feature extraction requirements.

[0123] To solve this problem, the present invention improves the traditional single-channel CNN feature extraction and adopts three-channel CNN for feature extraction. The improved three-channel CNN feature extraction layer structure is as follows: Figure 4 As shown in the figure, each channel has different convolution and pooling operations. The features extracted from the three channels are fused to generate the fused features that are input into the LSTM network. The convolution and pooling operations in each channel are independent of each other. Different convolution kernel sizes and differentiated pooling operations can capture the multi-scale features of the complex process parameters of the antenna skin. For example, large convolution kernels focus on relatively global and abstract features, while small convolution kernels focus on local details. After feature fusion, these different-scale features complement each other, increasing feature diversity through different receptive fields. This enables the model to explore the deep relationships between the antenna skin process parameters and helps discover the hidden nonlinear mapping between process parameters and deformation.

[0124] The feature extraction methods of the three channels are as follows: the preprocessed fusion data is first subjected to convolution operation and then to average pooling operation, and repeated twice, thereby realizing feature extraction and feature dimensionality reduction, while retaining the average feature information of the entire data; the second channel first performs convolution operation and then performs maximum pooling operation, and also repeats twice. The maximum pooling operation retains the strongest local response features; the third channel only performs convolution operation on the input data once to retain more original data features and prevent the other two channels from missing original features.

[0125] LSTM feature learning layer

[0126] The LSTM network performs well in time series prediction or classification tasks. The present invention uses it to predict the deformation of antenna skin co-curing preparation. The main reason is that the influence of process parameters on deformation is fuzzy, and there is a complex nonlinear mapping relationship between the two. LSTM has powerful nonlinear modeling capabilities and can explore the hidden nonlinear laws between process parameters and deformation.

[0127] LSTM is based on Recurrent Neural Network (RNN). LSTM introduces a gate structure based on RNN, which enables the model to have selective memory capabilities, thereby solving the problem of gradient vanishing when RNN processes long sequence inputs. The gate structure consists of a point multiplication operation and a sigmoid activation function. LSTM achieves selective operation on data information through the gate structure. The internal structure of LSTM is as follows Figure 5 As shown in the figure, the core parts from left to right are the forget gate, input gate, and output gate.

[0128] The calculation formula of the forget gate is as shown in formula 1. The input of the forget gate is the output data h of the previous step. t-1 and the current input data x t , the output f is obtained through the activation function σ t Where W is the matrix information and b is the offset.

[0129] f t =σ(W f ·[h t-1 ,x t ]+b f ) (1)

[0130] The calculation formulas of the input gate are shown in Equations 2 and 3. Equation 2 determines which information to update, and Equation 3 generates candidate memories. The combination of the two equations controls the degree of inclusion of new information.

[0131] i t =σ(W i ·[h t-1 ,x t ]+b i ) (2)

[0132]

[0133] According to the results of the forget gate and input gate, the memory unit is updated. The calculation formula is as shown in formula 4. The memory unit C t Retains information in long-term memory.

[0134]

[0135] The calculation formulas of the output gate are as shown in Equations 5 and 6. Equation 5 completes information screening, and Equation 6 generates the hidden state for the current prediction.

[0136] o t =σ(W o ·[h t-1 ,x t ]+b o ) (5)

[0137] h t=o t *tanh(C t ) (6)

[0138] The output of the three-channel CNN feature extraction layer is used as the input to the LSTM, leveraging the LSTM's powerful nonlinear representation capabilities to fit the nonlinear mapping relationship between the antenna skin co-curing manufacturing process parameters and deformation. The combination of CNN and LSTM enables in-depth mining of antenna skin co-curing manufacturing data from both temporal and spatial dimensions, facilitating accurate prediction of antenna skin deformation.

[0139] Attention mechanism focusing layer

[0140] Although CNN-LSTM performs well in regression prediction tasks, its fully connected layer only implicitly fuses features through linear transformation when mapping the LSTM output to a shape variable. It lacks an explicit mechanism for distinguishing the importance of each feature, resulting in insufficient attention paid to key features. This is especially true when processing high-dimensional, complex data such as those produced by co-curing antenna skins. Prediction accuracy and robustness still need to be improved. To address this issue, the present invention introduces an Attention mechanism that explicitly assigns different weight coefficients to different feature vectors, allowing the model to focus on key features with greater influence. The calculation process of the Attention mechanism is as follows:

[0141] (1) Using the state S at the previous moment t-1 and the hidden layer node value h i Calculate the attention score e ki , to determine the importance of the current feature to the output value, e ki The calculation formula is as follows:

[0142] e ki =V T tanh(WS t-1 +Uh i +b) (7)

[0143] Where V, W, U are the attention mechanism weight matrices, and b is the bias. Using the V matrix to perform a linear transformation on the result after the tanh function can better learn the correlation between input and output. t-1 Contains the network's accumulated learning experience, and the W matrix can integrate it with the latest input. ki Represents the degree of association between input node i and output node k, e ki The larger the value is, the greater the influence of the corresponding process parameters on the antenna skin deformation is.

[0144] (2) Use the softmax function to calculate the attention score e ki Normalize, the result of normalization is the weight coefficient a ki , aki The value of is in the interval [0, 1], and the weight coefficient represents the relative importance of the output node k to different input nodes. ki The calculation formula is as follows, where T x The length of the input sequence

[0145]

[0146] (3) The weight coefficient a ki and the LSTM hidden layer state vector h i Perform inner product operation, the result of the operation is the output o of the Attention layer t , o t The calculation formula is as follows:

[0147]

[0148] Hyperparameter optimization layer based on the whale algorithm

[0149] Model parameter adjustment is a key step in neural network training. Appropriate parameters can improve model performance and training efficiency, and enhance model generalization ability. In this embodiment, the Whale Optimization Algorithm (WOA) with strong global search and adaptive capabilities is selected to optimize hyperparameters. The optimal solution iteration method of WOA simulates the strategy of updating the position of fish schools during whale predation. The simulation process of the whale algorithm can be divided into two stages: development and exploration. The development stage includes the prey encirclement stage and the foam net attack stage, and the exploration stage is the prey search stage.

[0150] The core formula for the encirclement phase is as follows:

[0151] D=|C·X prey -X (t) | (10)

[0152] X (t+1) =X pred -A·D (11)

[0153] Where D is a transition vector, A and C are parameter variables, and X pred is the position vector of the target prey in the current whale group, X (t) is the position vector of each whale itself, and t is the current iteration number.

[0154] The bubble net attack phase includes two mechanisms: shrinking and surrounding, and spiral position update. The core formula is as follows:

[0155]

[0156] Where D′ is the absolute value of the distance between the individual whale position and the target prey position, b is the shape constant in the spiral formula, and l is a random number uniformly distributed between [0, 1]. p is the probability of selecting the two mechanisms of shrinking and wrapping and spiral position update, and its value is a random number uniformly distributed between [0, 1]. t To select the threshold, it is generally assumed that the probability of selecting the two strategies is equal, that is, p t =0.5.

[0157] The prey search phase is based on the fact that the current surrounding fish school is not optimal during the actual predation process, and a random search strategy is adopted to obtain better exploration capabilities. The core formula of the prey search phase is as follows, where X r Represents a randomly selected individual whale:

[0158] D=|C·X r -X (t) | (13)

[0159] X (t+1) =X r -A·D (14)

[0160] The Whale Algorithm is used to iteratively optimize hyperparameters such as the hidden layer dimension and the number of LSTM layers in the CLANet network. The optimal parameter combination found by WOA is used to train the CLANet network, which can obtain better evaluation index values ​​and faster training speed.

[0161] Experimental verification and analysis

[0162] Based on data from antenna skin co-curing and preprocessing multidimensional data, the proposed three-channel multidimensional regression focusing network model for antenna skin deformation prediction was validated. First, antenna skin deformation was predicted using the three-channel multidimensional focusing network, and the prediction results were measured using metrics such as mean absolute error, coefficient of determination, and accuracy. The effectiveness of the proposed method was then analyzed by comparing the prediction results with those of four baseline models. Finally, ablation experiments were conducted to verify the effectiveness of the three-channel CNN feature extraction layer and the attention mechanism focusing layer.

[0163] Experimental environment and parameter settings

[0164] This example uses Python and the deep learning framework Pytorch to build the model. The complexity of deep learning models and their reliance on large amounts of input data necessitate a high level of hardware support for the model training process. The experimental environment configuration for this example is shown in Table 1.

[0165] Table 1 Deformation prediction experimental environment configuration

[0166]

[0167] The performance of a neural network depends largely on the hyperparameter configuration of the model architecture, which directly affects the convergence, generalization, and computational efficiency of the neural network. Since the combination space of hyperparameters is usually high-dimensional and non-convex, it is difficult for general parameter adjustment methods to simultaneously ensure efficiency and optimality. Therefore, this embodiment uses the WOA algorithm to perform a global search for the optimal hyperparameter combination. The final model hyperparameter configuration is shown in Table 2.

[0168] Table 2 Hyperparameter configuration of three-way multidimensional regression focusing network

[0169]

[0170]

[0171] 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 and the step size of each update of the model parameters; out_channels1, out_channels2, and out_channels3 respectively indicate the number of output channels of the three parallel CNN feature extraction layers; hidden_size(LSTM) and hidden_size(Attention) indicate the size of the hidden layer dimension; and num_layers indicates the number of LSTM layers.

[0172] Evaluation indicators

[0173] In the performance evaluation of regression tasks, the evaluation indicators can not only reflect the prediction accuracy of the model, but also quantify the limitations and applicability of the model from different perspectives. In this embodiment, the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R 2 ) and accuracy (Acc) are used to comprehensively evaluate the established three-channel multidimensional regression focusing network model for antenna skin deformation prediction.

[0174] MAE measures the overall deviation of the model's prediction results by calculating the average error between the predicted value and the true value. The dimension of MAE is consistent with the original data, and no additional processing such as squaring the error value is performed, which can intuitively explain the actual meaning of the error. Its calculation formula is shown in Equation 15, where y i is the true deformation value, is the corresponding model prediction value, and n is the total number of evaluation samples.

[0175]

[0176] RMSE performs a square root operation on the prediction error. The deviation is amplified in the result, making RMSE more sensitive to outliers. It can comprehensively reflect the size of the prediction error and its distribution characteristics. Its calculation formula is as follows:

[0177]

[0178] R 2 It is a dimensionless evaluation index that reflects the model's ability to fit the data. Its calculation formula is shown in Equation 17, where The mean of the true deformation. R 2 The value of is usually between 0 and 1. The closer it is to 1, the closer the predicted value is to the true value, and the better the prediction effect of the model.

[0179]

[0180] Acc is a relative evaluation index that reflects the relative accuracy of the deformation prediction value and can reflect the prediction consistency of the model in different numerical ranges. Its calculation formula is as follows:

[0181]

[0182] Comparison Model

[0183] In order to verify the feasibility and effectiveness of the proposed method for predicting the deformation of antenna skin co-curing preparation, a comparative analysis was conducted with four models that performed well in structured data regression prediction tasks during the experiment. The four comparison models were LightGBM, CatBoost, AdaBoost, and GPR.

[0184] LightGBM: An improved ensemble prediction algorithm based on the gradient boosted decision tree (GBDT). It converts continuous input features into discrete histograms, reducing computational complexity. It also replaces the mid-level growing strategy used in most GBDT tools with a leaf growing strategy and imposes a depth limit. It also uses unilateral gradient sampling to reduce the number of small gradient data samples and uses mutually exclusive feature bundling for data dimensionality reduction, further accelerating computation.

[0185] CatBoost: This algorithm automatically processes categorical features based on the conditional probability of the target variable and dynamically adjusts the encoding method during training, reducing the number of categorical data encoding steps in feature engineering. It also uses a symmetric decision tree as the base learner, with all leaf nodes applying the same judgment criteria, reducing model complexity. Ordered boosting ensures that each data point's own information is not factored into residual calculations, minimizing the possibility of target leakage.

[0186] AdaBoost: A classic boosting algorithm that dynamically adjusts the weights of samples through serial iterations, prompting subsequent learners to tend to correct the errors of the previous round of training.

[0187] GPR: A nonparametric regression method based on Bayesian theory. It establishes a covariance matrix based on the model's inputs and outputs and uses Bayesian inference to obtain the mean of the posterior Gaussian distribution, which serves as the predicted value. GPR does not require a specific function form to be defined in advance; it is driven entirely by the input data.

[0188] Experimental results and analysis

[0189] 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 6 shown.

[0190] Based on the data collected during the co-curing preparation of antenna skins, a multidimensional data preprocessing scheme for antenna skin co-curing was adopted 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. Through preliminary cleaning, key feature screening, data enhancement and other steps, a total of 602 data samples were obtained, each containing 13 features and 1 deformation label. Based on the preprocessing results, the effectiveness of the proposed three-channel multidimensional regression focusing network model in predicting antenna skin deformation was verified.

[0191] (1) Analysis of experimental results

[0192] After data preprocessing, the original antenna skin co-curing preparation data set is input into the established three-channel multi-dimensional regression focusing network model. The prediction results of the test data are as follows: Figure 7 According to the evaluation index calculation formula, based on the calculation of actual deformation value and predicted deformation value, the evaluation index results are: MAE equals 0.159, RMSE equals 0.191, R 2 =0.921, Acc = 93.1%. It can be seen that the average absolute error of deformation is only 0.159mm, the coefficient of determination is close to 1, and the average accuracy of deformation prediction of the test sample exceeds 90%, which proves the effectiveness of the model built in this embodiment for deformation prediction of antenna skin co-curing preparation. The comparison results of deformation prediction value and actual value are shown in the figure. Figure 8 shown.

[0193] from Figure 8It can be seen from the above that the fluctuation trend of the antenna skin deformation prediction value of the test set is consistent with the true value, and the predicted value of most samples is very close to the true value. On the upper side of the prediction result graph, the absolute error of some data points is large, but the deformation value of these data points is large, so the relative error is small, which can ensure the accuracy of the prediction. In order to further intuitively analyze the distribution relationship between the antenna skin deformation prediction value and the true value, the following is drawn: Figure 9 The comparison scatter plot of the predicted and actual values ​​of the antenna skin deformation is shown. As can be seen from the figure, all data points are distributed near the contour lines, and no data points deviate far away.

[0194] (2) Analysis of comparative experimental results

[0195] Comparative experiments were conducted using four comparison models on a preprocessed dataset of antenna skins prepared by co-curing. Regarding categorical data encoding, AdaBoost and GPR both use one-hot encoding. LightGBM and CatBoost, due to their ability to process categorical features, do not preprocess categorical data. The experimental results for each comparison model are shown in Table 3.

[0196] Table 3 Comparison of antenna skin deformation prediction results of each model

[0197]

[0198] The results of the model comparison experiments show that the WOA-CLAnet model constructed in this example achieves optimal values ​​across all metrics for the antenna skin co-curing deformation prediction task. Specifically, compared to the LightGBM, CatBoost, AdaBoost, and GPR models, the MAE values ​​of WOA-CLAnet decreased by 0.104mm, 0.065mm, 0.16mm, and 0.263mm, respectively. The RMSE values ​​decreased by 0.138mm, 0.097mm, 0.191mm, and 0.307mm, respectively. The coefficient of determination values ​​increased by 0.155, 0.101, 0.237, and 0.458, respectively. The Accuracy values ​​increased by 4.7%, 3.1%, 7.4%, and 11.8%, respectively.

[0199] The antenna skin co-curing deformation prediction task studied in this example features minimal deformation. Although the absolute reductions in mean absolute error and root mean square error compared to the comparison model are limited, the relative improvement in accuracy is significant. The comparative experimental results further validate the effectiveness of the three-channel multidimensional regression focusing network model constructed in this example for deformation prediction in antenna skin co-curing.

[0200] (3) Analysis of ablation experiment results

[0201] A feature extraction layer and an attention mechanism layer were introduced, and a three-channel CNN feature extraction method was proposed for deformation prediction in antenna skin co-curing. To verify its effectiveness, an ablation experiment was designed for comparison. The ablation experiment results are shown in Table 4. In the table, to distinguish it from the ablation model, the model of this embodiment is denoted as WOA-3CLAnet. WOA-LAnet is an ablation model without a feature extraction layer, WOA-1CLAnet is a single-channel CNN feature extraction and ablation model, and WOA-3CLnet is an ablation model without an attention mechanism layer. All ablation models use embedded coding for categorical variables, and other non-ablation parts remain completely consistent.

[0202] Table 4 Antenna skin deformation prediction ablation experiment results

[0203]

[0204]

[0205] Table 4 shows that the performance of WOA-LAnet, WOA-1CLAnet, and WOA-3CLnet in deformation prediction for antenna skin co-curing fabrication shows varying degrees of decline across all evaluation metrics. For example, WOA-LAnet's accuracy dropped by 7.3%, its coefficient of determination decreased from 0.921 to 0.673, and its mean absolute error increased by 101.9%. Ablation experiments validate the effectiveness of the feature extraction layer and attention mechanism layer introduced in this example, as well as the proposed three-channel CNN feature extraction method.

[0206] In summary, the three-channel multidimensional regression focusing network model for antenna skin deformation prediction proposed in the present invention combines the feature extraction and nonlinear fitting capabilities of three-channel CNN and LSTM in the time and space dimensions, and explicitly gives higher weights to important features through the attention mechanism, which can effectively predict the deformation of antenna skin co-curing preparation.

[0207] To address the problems of existing methods such as insufficient multidimensional feature extraction, low precision in predicting small deformations, and inaccurate fitting of complex mapping relationships, this paper proposes a three-channel multidimensional regression focusing network model. Each channel of the three-channel CNN feature extraction layer uses different convolution and pooling operations to capture multi-scale features and perform fusion operations. The LSTM feature learning layer has powerful nonlinear modeling capabilities. Combined with the three-channel CNN feature extraction layer, it can accurately fit complex nonlinear relationships in both time and space. The attention mechanism aggregation layer calculates attention scores to obtain weight coefficients, solving the problem of lack of explicit distinction of feature importance. The hyperparameter optimization layer based on the whale algorithm obtains the optimal combination of hyperparameters through global search, improving the overall effectiveness and efficiency of the model.

[0208] 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 method for predicting antenna skin co-curing deformation based on a three-channel multidimensional regression focusing network, characterized in that: The following steps are involved: S1: Construct a three-channel convolutional neural network feature extraction layer to perform multi-scale feature extraction on the preprocessed process parameter data: The first channel performs two one-dimensional convolution operations and average pooling operations; The second channel performs two one-dimensional convolution operations and maximum pooling operations; The third channel performs a single one-dimensional convolution operation to retain the original features; Fuse the feature vectors output by the three channels to generate fused features; S2: Inputting the fusion features into the long short-term memory network feature learning layer, and modeling the nonlinear mapping relationship between process parameters and deformation through the gating mechanism of forget gate, input gate, and output gate; S3: Set up an attention mechanism focusing layer at the LSTM output to dynamically assign feature weights: Calculate attention score based on LSTM hidden state; Use the softmax function to normalize the attention score and generate the weight coefficient; Perform weighted summation on the hidden states to generate a focused feature vector; S4: Use the whale optimization algorithm to globally optimize the hyperparameters of the CNN, LSTM, and attention mechanism layers: Initialize the whale population and set the hyperparameter search range; Iteratively optimize parameters through encircling prey, spiral position update, and random search mechanisms; The optimal parameter combination is selected using the mean absolute error as the fitness function; S5: The optimized network model is outputted through the fully connected layer to predict the deformation, thus completing the deformation prediction of the antenna skin co-curing. The prediction accuracy is evaluated based on indicators such as MAE, root mean square error, and determination coefficient.

2. The antenna skin co-curing deformation prediction method based on a three-channel multidimensional regression focusing network according to claim 1 is characterized in that: The pre-processing in step S1 includes the following sub-steps: S1.1: Preliminary data cleaning: Remove irrelevant features with no predictive value from the original data set, including but not limited to the experiment number and experiment time; remove dead-value variables with constant values, including but not limited to the type of matrix material and the type of reinforcement material; for deformation labels, only retain the label with the largest absolute value of the deformation variable among all labels, and remove all other labels; retain the original features including the heterogeneous prepreg ply angle, ply configuration, mold type, four curing temperature parameters, heating rate, cooling rate, two holding time parameters, pre-compaction time, two curing pressure parameters, and vacuum degree; S1.2: Missing value handling: Identify missing variables through the missing value distribution diagram; the missing variables include ply configuration and mold type; S1.3: Outlier Detection and Verification: Perform statistical analysis on numerical variables and calculate the mean, standard deviation, maximum, minimum, and median. Use the 3σ principle to verify whether the data points are outside the range of three times the standard deviation. Combined with box plot analysis, the data distribution is analyzed. If all samples are within the upper and lower whiskers and the median line is close to the center of the box, the data is judged to have no outliers and all samples are retained for subsequent processing. S1.4: Key feature screening: Recursive feature elimination and random forest model are used to jointly screen features, including: Build a random forest model, configure hyperparameters including but not limited to maximum depth and minimum number of split samples, and use mean absolute error as the evaluation metric; After the first training, the feature importance scores are calculated and normalized to generate a preliminary feature ranking; Iteratively remove the least important features, retrain the model and update the feature ranking until the feature subset is empty; Based on the MAE versus feature number curve, the features with the lowest MAE were selected as the optimal subset. 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 deformation prediction. S1.5: Hybrid Data Augmentation: A combination of three augmentation methods is used on the filtered samples to expand the data volume, including: Random scaling: linearly scale the numerical features in the range [0.95, 1.05], while the categorical features remain unchanged; 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; Mixup enhancement: Randomly select two samples from samples with the same category features, generate a fusion coefficient λ (λ∈[0,1]) according to the Beta distribution, and generate a new sample: 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 is in the interval [0, 1] and is randomly generated using the Beta distribution; the process parameter range of the enhanced data is checked, and data that exceeds the engineering constraints is eliminated to ensure the physical rationality of the enhanced data; S1.6: Normalization of numerical data and encoding of categorical data: Normalization: Perform linear normalization on numerical features and map them to the interval [0, 1]. The formula is: Among them, x is the data before normalization, x min and x max are the maximum and minimum values ​​in the data before normalization; the normalization operation maps the maximum value to 1 and the minimum value to 0, and the remaining data is distributed linearly in the interval [0, 1]; Category data encoding: Embedded coding is used to assign unique indexes to the ply configuration L and mold type M, map them into two-dimensional continuous vectors, initialize them to random values ​​and optimize them through model training.

3. The antenna skin co-curing deformation prediction method based on a three-channel multidimensional regression focusing network according to claim 1 is characterized in that: The LSTM includes a forget gate, an input gate, and an output gate; The calculation formula of the forget gate is as shown in formula 1. The input of the forget gate is the output data h of the previous step. t-1 and the current input data x t , the output f is obtained through the activation function σ t ;W is the matrix information, b is the offset; f t =σ(W f ·[h t-1 ,x t ]+b f ) (1) The calculation formulas for the input gate are shown in Equations 2 and 3. Equation 2 determines which information to update, and Equation 3 generates candidate memories. The combination of the two equations controls the degree of inclusion of new information. i t =σ(W i ·[h t-1 ,x t ]+b i ) (2) According to the results of the forget gate and input gate, the memory unit is updated. The calculation formula is as shown in formula 4. The memory unit C t Long-term memory information is retained; The calculation formula of the output gate is as shown in Equation 5 and Equation 6. Equation 5 completes information screening, and Equation 6 generates the hidden state for the current prediction; the t =σ(W o ·[h t-1 ,x t ]+b o ) (5) h t =o t *tanh(C t ) (6) The output of the three-channel CNN feature extraction layer is used as the input of LSTM, and the powerful nonlinear expression ability of LSTM is used to fit the nonlinear mapping relationship between the antenna skin co-curing process parameters and deformation.

4. The antenna skin co-curing deformation prediction method based on a three-channel multidimensional regression focusing network according to claim 1 is characterized in that: The attention mechanism includes: (1) Using the state S at the previous moment t-1 and the hidden layer node value h i Calculate the attention score e ki , to determine the importance of the current feature to the output value, e ki The calculation formula is as follows: e ki =V T fishy(WS) t-1 +Uh i +b) (7) Among them, V, W, and U are the weight matrices of the attention mechanism, and b is the bias; using the V matrix to perform a linear transformation on the result after the tanh function can better learn the correlation between input and output, S t-1 Contains the network's accumulated learning experience, and the W matrix can integrate it with the latest input; e ki Represents the degree of association between input node i and output node k, e ki The larger the value of , the greater the influence of the corresponding process parameters on the antenna skin deformation; (2) Use the softmax function to calculate the attention score e ki Normalize, the result of normalization is the weight coefficient a ki , a ki The value of is in the interval [0, 1], and the weight coefficient represents the relative importance of the output node k to different input nodes. ki The calculation formula is as follows, where T x The length of the input sequence (3) The weight coefficient a ki and the LSTM hidden layer state vector h i Perform inner product operation, the result of the operation is the output o of the Attention layer t , o t The calculation formula is as follows:

5. The antenna skin co-curing deformation prediction method based on a three-channel multi-dimensional regression focusing network according to claim 1 is characterized in that: The parameter optimization process of the whale optimization algorithm includes two stages: development and exploration. The development stage includes the prey encirclement stage and the bubble net attack stage, and the exploration stage is the prey search stage. The core formula for the encirclement phase is as follows: D=|C·X prey -X (t) | (10) X (t+1) =X pred -A·D (11) Where D is a transition vector, A and C are parameter variables, and X pred is the position vector of the target prey in the current whale group, X (t) is the position vector of each whale itself, and t is the current iteration number; The bubble net attack phase includes two mechanisms: shrinking and surrounding, and spiral position update. The core formula is as follows: Where D′ is the absolute value of the distance between the individual whale position and the target prey position, b is the shape constant in the spiral formula, l is a random number uniformly distributed between [0, 1]; p is the selection probability of the two mechanisms of shrinking and wrapping and spiral position update, and its value is a random number uniformly distributed between [0, 1]; p t To select the threshold, it is generally assumed that the probability of selecting the two strategies is equal, that is, p t =0.5; The prey-seeking stage is based on the fact that the current fish school is not optimal in the actual predation process, and a random search strategy is adopted to obtain better exploration capabilities. The core formula of the prey-seeking stage is as follows, where X r Represents a randomly selected individual whale: D=|C·X r -X (t) | (13) X (t+1) =X r -A·D (14) The whale algorithm is used to iteratively optimize the hidden layer dimension and the number of LSTM layers in the CLANet network. The CLANet network is trained with the optimal parameter combination found by WOA to obtain better evaluation index values ​​and faster training speed.

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