AUV structure stress real-time prediction method based on convolution auto-encoder
By combining convolutional autoencoders and deep learning neural networks, the problem of capturing nonlinear features and predicting stress fields in AUV structures in real time was solved, achieving efficient and accurate stress field prediction and improving computational efficiency and generalization ability.
Patent Information
- Application Number
- CN202511412951.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-29
- Publication Date
- 2026-01-30
AI Technical Summary
Existing linear reduced-order models have insufficient ability to capture nonlinear features and limited generalization performance when dealing with the stress field of AUV structures, making it difficult to achieve real-time high-precision prediction.
A method based on convolutional autoencoders is adopted to establish a mapping relationship between input conditions and stress response through nonlinear feature extraction and deep learning neural networks, thereby achieving efficient real-time prediction.
It achieves high-precision and rapid prediction of stress in AUV structures, improves computational efficiency by several orders of magnitude, has strong generalization ability, and the average relative error can be controlled within 1%.
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Abstract
Description
Technical Field
[0001] This application belongs to the field of data science and physical field simulation technology, specifically relating to a real-time stress prediction method for AUV structures based on a convolutional autoencoder. Background Technology
[0002] High-fidelity numerical simulation technology, as an important research tool in modern engineering, has wide applications in structural design, performance evaluation, and safety analysis. For complex equipment such as autonomous underwater vehicles (AUVs), accurate simulation of their structural stress fields using the finite element method has become a key approach to assessing their mechanical behavior under actual operating conditions. However, such high-precision simulations typically rely on full-order models, consuming enormous computational resources, with a single analysis often taking hours or even days, severely limiting their application in real-time prediction and rapid multi-condition evaluation.
[0003] To overcome the aforementioned computational bottlenecks, reduced-order modeling (ROM) techniques have been proposed and extensively studied. Traditional linear ROM methods, such as orthogonal eigenvalue decomposition (POD) and its Galerkin projection form, reduce the model size by projecting high-dimensional physical fields onto a low-dimensional subspace spanned by dominant modes. Although these methods improve computational efficiency to some extent, they are inherently based on linear assumptions and rely on pre-defined global basis functions, exhibiting significant limitations when dealing with stress field prediction problems under strongly nonlinear, multi-physics coupled, and complex boundary conditions. Specifically, linear ROM methods struggle to effectively capture local gradients, singularities, and nonlinear interactions between modes in structural responses, resulting in deficiencies in prediction accuracy and generalization ability.
[0004] Furthermore, traditional ROMs typically require tight coupling with the solver. Their offline phase still requires a large amount of full-order simulation data to construct the dimension-reduced basis, and their online phase also requires solving the dimension-reduced system equations, which still incurs certain computational overhead and makes it difficult to achieve true real-time prediction.
[0005] Therefore, although existing linear ROM methods provide a certain approach for rapid analysis of complex physical fields, they still have fundamental shortcomings when dealing with real-time prediction problems of physical fields with highly nonlinear, time-varying, and localized characteristics, such as the stress field of AUV structures. Summary of the Invention
[0006] To address the shortcomings of existing linear reduced-order models in predicting the stress field of AUV structures, such as insufficient nonlinear feature capture and limited generalization performance, this application provides a real-time AUV structure stress prediction method based on a convolutional autoencoder. This method can adaptively extract nonlinear features of the flow field and establish an accurate mapping relationship between the input conditions and the full-field stress response, thereby achieving high-precision and high-efficiency real-time prediction of the stress field of AUV structures and significantly improving computational efficiency and model generalization ability.
[0007] To achieve the above technical objectives, this application specifically adopts the following technical solution: In one aspect of this application, a method for real-time prediction of stress in AUV structures based on a convolutional autoencoder is provided, comprising the following steps: S1. A trained convolutional autoencoder is used to extract nonlinear features from the high-dimensional structural stress field data to obtain a low-dimensional representation. S2. A deep learning neural network is used to establish a mapping relationship between the input working conditions and the low-dimensional representation, and to predict the low-dimensional features under the new working conditions; S3. The low-dimensional features predicted by the convolutional autoencoder are reconstructed to obtain high-dimensional structural stress field data. The convolutional autoencoder includes an encoder, a latent space, and a decoder. The encoder extracts features and reduces the dimensionality of the input high-dimensional structural stress field data through convolutional layers and pooling layers to obtain a low-dimensional latent space representation. The decoder is used to reconstruct the low-dimensional latent space representation through a transposed convolutional layer to restore the high-dimensional structural stress field data.
[0008] In one embodiment, the encoder includes a convolutional layer, an activation function layer, and a pooling layer connected in sequence; the convolutional layer uses a one-dimensional convolutional kernel to extract local features, and the pooling layer is used to reduce the spatial resolution of the feature map output by the convolutional layer.
[0009] In one implementation, the activation function is the PReLU function.
[0010] In one implementation, the decoder includes a fully connected layer and a transposed convolutional layer connected in sequence; the low-dimensional latent space representation is extended to a dimension matching the encoder end through the fully connected layer, and then the high-dimensional structural stress field data is reconstructed by progressive upsampling through the transposed convolutional layer.
[0011] In one implementation, the loss function used when training the convolutional autoencoder is the mean squared error loss function, the expression of which is:
[0012] in, m For the sample size, To reconstruct the data, This is the original input data.
[0013] In one implementation, the deep learning neural network in step S2 includes an input layer, a hidden layer, and an output layer; the hidden layer contains multiple fully connected layers and a PReLU activation function; the deep learning neural network is trained using a backpropagation algorithm and a gradient descent optimization algorithm, and the loss function is the mean squared error loss.
[0014] In one implementation, the input of the deep learning neural network is the operating conditions, and the output is nonlinear low-dimensional features. The mapping relationship between the two is established through layer-by-layer nonlinear mapping.
[0015] In one implementation, the decoder includes a fully connected layer and a transposed convolutional layer connected in sequence; the reconstruction process in step S3 includes: expanding the dimension of the predicted low-dimensional features through the fully connected layer, restoring them to a feature map through an anti-flattening operation, and then gradually upsampling and restoring them to high-dimensional structural stress field data through the transposed convolutional layer.
[0016] In one implementation, the high-dimensional structural stress field data is obtained through finite element simulation, including structural stress field distribution data under different working conditions.
[0017] In one embodiment, the AUV structural stress real-time prediction method further includes an error assessment step: verifying the prediction accuracy by calculating the average relative error between the high-dimensional structural stress field data reconstructed in step S3 and the corresponding high-dimensional structural stress field data obtained through simulation.
[0018] In another aspect of this application, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the above-described method for real-time prediction of stress in AUV structures.
[0019] The beneficial effects of this application are as follows: 1) This application overcomes the accuracy bottleneck of traditional linear dimensionality reduction methods. By utilizing the powerful nonlinear feature extraction capability of convolutional autoencoders, it can adaptively capture complex local details and global modes in stress fields, overcoming the inherent limitations of linear methods such as POD in characterizing strongly nonlinear physical fields, thereby achieving higher prediction accuracy.
[0020] 2) Near real-time ultra-efficient computation is achieved. This method establishes a direct nonlinear mapping from input working parameters to low-dimensional features through a deep learning neural network. In the prediction stage, it completely avoids the cumbersome full-order numerical simulation process. Only one forward network calculation and fast decoding are needed to obtain the full-field stress results in seconds. The computational efficiency is improved by several orders of magnitude compared with the traditional finite element method.
[0021] 3) It possesses excellent generalization ability and engineering practical value. The constructed model learns the inherent laws between working conditions and physical fields, and can also make accurate predictions for new working conditions not covered by the training data. The average relative error can be controlled within 1% (such as 0.87% in the example), which is robust and provides reliable technical support for the real-time status monitoring, rapid design and operation optimization of AUVs. Attached Figure Description
[0022] Figure 1 This is a schematic diagram of the training process of the convolutional model according to an embodiment of this application; Figure 2 This is a schematic diagram of the process of establishing the mapping relationship between input conditions and nonlinear dimensionality reduction features using a deep learning neural network in an embodiment of this application; Figure 3 This is a flowchart illustrating the real-time prediction of structural stress field under new working conditions in an embodiment of this application. Figure 4 These are the stress field cloud diagrams of the actual underwater glider structure under four different working conditions according to the embodiments of this application; Figure 5 These are cloud diagrams of the predicted stress field of an underwater glider structure under four different operating conditions according to embodiments of this application; Figure 6 These are the difference cloud maps of the predicted structural stress field under four different working conditions in the embodiments of this application. Detailed Implementation
[0023] The technical solution of this application will be clearly and completely described below with reference to specific embodiments. However, those skilled in the art will understand that the embodiments described below are only some embodiments of this application, not all embodiments, and are only used to illustrate this application, and should not be regarded as limiting the scope of this application. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0024] In one specific embodiment of this application, a method for real-time prediction of stress in AUV structures based on a convolutional autoencoder is provided, comprising the following steps: S1. A trained convolutional autoencoder (CAE) is used to extract nonlinear features from the high-dimensional structural stress field data to obtain a low-dimensional representation. The convolutional autoencoder consists of three core parts: encoder, latent space, and decoder.
[0025] The encoder extracts and reduces the dimensionality of the input high-dimensional structural stress field data layer by layer through a series of convolutional and pooling layers, and finally compresses it into a low-dimensional latent space representation. The latent space, as the bottleneck layer, stores the most essential features of the input data, and its dimensionality is much lower than that of the original data. The decoder then performs progressive upsampling and reconstruction of the latent space representation through a transposed convolutional layer to restore the high-dimensional structural stress field data with the same dimensionality as the original input.
[0026] In some embodiments, the encoder consists of a convolutional layer, an activation function layer, and a pooling layer connected in sequence. The convolutional layer uses a one-dimensional convolutional kernel for local feature extraction, preferably with a kernel size of 3 and a stride of 1, and performs zero-padding (padding=1) to maintain the spatial size of the feature map. The activation function layer uses a parameterized rectified linear unit (PReLU) as the activation function to enhance the model's non-linear expressive power. The pooling layer uses max pooling, preferably with a pooling window size of 2 and a stride of 2, thereby reducing the spatial resolution of the feature map by half.
[0027] Understandably, the above structure can be repeatedly stacked with multiple modules to progressively extract and compress features.
[0028] In some embodiments, the decoder includes a fully connected layer and a transposed convolutional layer connected in sequence. The fully connected layer first expands the low-dimensional vector in the latent space to a size that matches the dimension of the feature map at the end of the encoder. The transposed convolutional layer performs progressive upsampling through multiple layers of transposed convolutions, with each layer combined with the PReLU activation function and batch normalization to progressively reconstruct the high-dimensional structural stress field data.
[0029] In some embodiments, the mean squared error (MSE) is used as the loss function when training the convolutional autoencoder, and its expression is: (1) in, m For the sample size, For the first k Reconstructed data of each sample, For the first k The original input data for each sample. By minimizing this loss function, the model can learn an efficient low-dimensional representation of the input data and possess good reconstruction capabilities.
[0030] S2. A deep learning neural network is used to establish a mapping relationship between the input operating conditions and the low-dimensional representation, and to predict the low-dimensional features under the new operating conditions.
[0031] The deep learning neural network establishes a mapping relationship from input operating conditions to output low-dimensional features through layer-by-layer nonlinear transformations. Specifically, the input operating conditions first enter the network through the input layer, undergo feature transformation and abstraction through multiple hidden layers, and the output of each layer serves as the input of the next layer. Finally, the output layer generates a low-dimensional feature representation consistent with the target dimension.
[0032] After training, the deep learning neural network can perform forward propagation calculations on new input working conditions and output corresponding low-dimensional feature prediction values, thereby achieving fast and accurate prediction of the low-dimensional representation of the structural stress field under new working conditions.
[0033] In some embodiments, the deep learning neural network is a multi-layer fully connected feedforward neural network, including an input layer, multiple hidden layers, and an output layer. The number of neurons in the input layer is consistent with the dimension of the operating conditions, and the number of neurons in the output layer is consistent with the dimension of the low-dimensional features. The hidden layers consist of several fully connected layers, each followed by a parameterized rectified linear unit (PReLU) as an activation function to introduce nonlinear transformation capabilities and enhance the model's ability to fit complex mapping relationships. It is understood that the number of hidden layers and the size of each hidden layer can be flexibly adjusted, allowing the deep learning neural network to learn function representations of varying complexity.
[0034] The training process of the deep learning neural network is based on a supervised learning mechanism, utilizing a known working condition matrix. X n×d and its corresponding nonlinear dimensionality-reduced feature matrix extracted by a convolutional autoencoder. Y n×r As training data, among which, n For the sample size, d For the dimension of working conditions, r It is a low-dimensional feature dimension.
[0035] The deep learning neural network j Layer i The input and output of a unit are determined by the following formula: (2) (3) in, Indicates determining the ( ) j -1) All neurons in layer 1 j The first in the layer i The weighting coefficients of the influence of each neuron. It is the firstj The first layer i Neuron bias Indicates the ( j -1) The output of layer neurons, where σ is a non-linear activation function.
[0036] In some embodiments, the activation function is a crucial component of the deep learning neural network. By introducing a nonlinear transformation, it converts the input signal into a nonlinear output, enabling the deep learning neural network to learn functions of arbitrary complexity. The formula for PReLU is as follows: (4) Here, 'a' is a learnable parameter, typically initialized to a small positive value and updated using the backpropagation algorithm during training.
[0037] In some implementations, the backpropagation algorithm is used during training to calculate the gradient of the loss function with respect to the network parameters, and the gradient descent optimization algorithm is used to iteratively update the weights and bias parameters of each layer until the model converges or reaches the preset number of training iterations. The deep learning neural network is optimized by minimizing the mean squared error (MSE) loss function between the predicted and true values, which is defined as follows: (5) in, These are the predicted features output by the network. These are true low-dimensional features.
[0038] S3. The low-dimensional features predicted by the predicted low-dimensional features are reconstructed using the decoder part of the convolutional autoencoder to obtain high-dimensional structural stress field data.
[0039] In some embodiments, the decoder is composed of a fully connected layer and a transposed convolutional layer connected in sequence, which reconstructs and restores the low-dimensional feature vectors predicted by the deep learning neural network into complete high-dimensional structural stress field data.
[0040] The reconstruction process specifically includes the following steps: First, the predicted low-dimensional feature vector is input into a fully connected layer. Through linear transformation and dimensionality expansion, it is mapped to a higher-dimensional vector that matches the latent representation at the encoder end, thereby restoring the feature information capacity. Subsequently, the expanded vector is converted back into a feature map with spatial structural features through deflattening to adapt to the processing format of the transposed convolutional layer. The feature map is then input into an upsampling module consisting of multiple transposed convolutional layers. Each transposed convolutional layer uses a convolutional kernel of a preset size and performs spatial upsampling operations with a specified sliding stride (e.g., stride of 2) to gradually restore the spatial dimension and resolution of the data. Preferably, batch normalization and PReLU activation functions can be introduced between each transposed convolutional layer to enhance training stability and nonlinear expressive power. Finally, the number of channels is adjusted to the same dimension as the original structural stress field data through the last transposed convolutional layer, completing the end-to-end reconstruction from low-dimensional features to a high-dimensional structural stress field.
[0041] In some embodiments, the high-dimensional structural stress field data is obtained through finite element simulation, specifically including structural stress field distribution data corresponding to different operating conditions of the AUV (such as different recovery speeds, pitch angles, etc.). This data is organized in the form of field distribution cloud maps or grid node stress value matrices, serving as the basic dataset for training and validating convolutional autoencoders.
[0042] In some embodiments, the AUV structural stress real-time prediction method further includes an error assessment step to verify the accuracy and reliability of the prediction method. This step is achieved by calculating the error between the high-dimensional structural stress field data reconstructed by the decoder and the corresponding real stress field data obtained through finite element simulation. Through this error assessment, the prediction accuracy can be quantified, ensuring its effectiveness in practical engineering applications.
[0043] In another specific embodiment of this application, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the above-described method for real-time prediction of AUV structural stress.
[0044] In some embodiments, the computer-readable storage medium is a non-transitory computer-readable storage medium, such as, but not limited to, read-only memory (ROM), random access memory (RAM), optical disc read-only memory (CD-ROM), magnetic tape, floppy disk, optical storage device, magnetic storage device, or any combination thereof. The computer program stored on the storage medium contains computer-executable instructions that, when loaded and executed by a processor (e.g., a central processing unit (CPU), graphics processing unit (GPU), or tensor processing unit (TPU), control a computing device to perform all steps of the real-time stress prediction method for AUV structures.
[0045] Specifically, when the program is executed by the processor, it can perform the following steps: nonlinear dimensionality reduction of the high-dimensional structural stress field data by the encoder part of the convolutional autoencoder to extract low-dimensional feature representations; establish a mapping relationship between the input working conditions and the low-dimensional representations using a deep learning neural network, and predict the low-dimensional features under the new working conditions; reconstruct the predicted low-dimensional features using the decoder part of the convolutional autoencoder to obtain high-dimensional structural stress field data; and optionally, perform error evaluation on the reconstructed high-dimensional structural stress field data to verify the prediction accuracy.
[0046] Exemplary embodiments The underwater glider structural stress field dataset used in this embodiment was obtained through structural simulation of the underwater glider at different recovery speeds and pitch angles from the water surface. (Refer to...) Figure 1 As shown, 180 samples were generated using the design of experiments method, and the structural stress field results for each sample were obtained through structural stress field simulation as the training set. Similarly, 20 samples were generated using the design of experiments method, and the corresponding structural stress field results were obtained as the test set. Then, the convolutional autoencoder was trained using the training set data. By inputting the same working conditions as the test set, the convolutional autoencoder predicted the corresponding structural stress field results, which were then compared and verified with the simulation test set.
[0047] (1) Nonlinear dimensionality reduction feature extraction Structural stress field simulations were performed on 180 training samples. The simulation results for each sample were read to obtain the equivalent elastic stress value at the corresponding grid node, forming an N×M matrix Y. Here, N is the number of grid nodes, and M is the number of training samples, i.e., M=180. The training samples are the simulation input conditions, i.e., an M×2 matrix X. A one-dimensional convolutional model was trained using the training dataset, including encoding and decoding. The encoding process involved progressively extracting features from the training dataset through three consecutive convolutional blocks. Each convolutional block contained a convolutional layer that maintained spatial dimensions (kernel size 3, stride 1, zero padding on both sides of the input data), a ReLU activation function, and a max pooling layer with halved dimensions (pooling window size 2). The number of channels was progressively increased from the initial input channels to 32. Subsequently, the three-dimensional features were converted into vectors through a flattening operation, and then progressively reduced in dimensionality through a four-layer fully connected network, resulting in a dimension of 10. The decoding process is as follows: The dimensionality is expanded through a fully connected layer, then deflattened to restore the feature map to be parsable by the convolutional kernel. Three transposed convolutional layers are used for progressive upsampling (with a stride of 2), and output padding is used to adjust the output size. Finally, the transposed convolution restores the channel count to the input dimension, achieving reconstruction from low-dimensional features to the original data distribution. The convolutional model training process iteratively encodes and decodes until the maximum number of iterations is met. After training, the non-linear dimensionality reduction features can be obtained by executing the encoding process. .
[0048] (2) Nonlinear dimensionality reduction feature prediction Reference Figure 2 As shown, the simulation condition matrix is constructed using the input load conditions of the structural stress field. A simulation condition matrix is established using a deep learning neural network. With nonlinear dimensionality reduction feature matrix Mapping relationship between .in n =180, d =2, r =10. Input data is implemented step-by-step using stacked fully connected layers and the parameterized nonlinear activation function (PReLU). To output features The nonlinear mapping. Specifically: input data The model is progressively expanded to 128 dimensions through linear layers (from 16 to 64 and then to 128), using the PReLU activation function to capture complex nonlinear relationships and enhance the model's ability to represent high-dimensional features. A reverse symmetric structure (from 128 to 64, then to 16, and finally to a nonlinear dimensionality reduction of 10 dimensions) gradually compresses the feature dimensions, with each layer employing PReLU to maintain a nonlinear transformation, progressively focusing high-order features onto the target output dimension and avoiding information loss.
[0049] (3) Nonlinear dimensionality reduction feature reconstruction Reference Figure 3 As shown, after training the deep learning neural network according to the above process, when given new simulation conditions... At that time, with only 20 test samples, the predicted value of the nonlinear dimensionality reduction feature can be obtained. .in, nn =20. Predicted nonlinear dimensionality reduction characteristics After expanding the dimension through a fully connected layer, the feature map is restored to a parsable feature map by the convolution kernel using deflattening. Then, it is upsampled stepwise through three layers of transposed convolution (with a sliding stride of 2), and the output size is adjusted by output padding. Finally, the number of channels is restored to the input dimension through the transposed convolution kernel, thus realizing the reconstruction from low-dimensional features to the original data distribution.
[0050] (4) Comparative verification The predicted stress field of the complete structure was calculated based on the last 20 input load conditions. The average relative error between the simulation results and the actual results is 0.8772%. A schematic diagram of the structural stress field corresponding to one of the samples is drawn, as shown below. Figure 4 , Figure 5 As shown, the predicted difference results are as follows: Figure 6 As shown.
[0051] Although the embodiments of this application have been described above in conjunction with the accompanying drawings, this application is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of this application, and these are all within the scope of protection of this application.
Claims
1. A method for real-time prediction of structural stress of an AUV based on a convolutional autoencoder, characterized in that, The method comprises the following steps: S1, using a trained convolutional autoencoder to perform nonlinear feature extraction on high-dimensional structural stress field data to obtain low-dimensional representation; S2, using a deep learning neural network to establish a mapping relationship between input working conditions and the low-dimensional representation, and to predict low-dimensional features under new working conditions; S3, using a decoder part of the convolutional autoencoder to reconstruct the predicted low-dimensional features to obtain high-dimensional structural stress field data; The convolutional autoencoder comprises an encoder, a latent space, and a decoder; the encoder performs feature extraction and dimension reduction on the input high-dimensional structural stress field data through convolutional layers and pooling layers to obtain low-dimensional latent space representation; The decoder is used to reconstruct the low-dimensional latent space representation through transposed convolutional layers to restore it to high-dimensional structural stress field data.
2. The AUV structural stress real-time prediction method according to claim 1, characterized in that, The encoder comprises convolutional layers, activation function layers, and pooling layers connected in sequence; the convolutional layers use one-dimensional convolutional kernels for local feature extraction, and the pooling layers are used to reduce the spatial resolution of the feature maps output by the convolutional layers.
3. The AUV structural stress real-time prediction method according to claim 2, characterized in that, The activation function is a PReLU function.
4. The AUV structural stress real-time prediction method according to claim 1, characterized in that, The decoder comprises fully connected layers and transposed convolutional layers connected in sequence; the low-dimensional latent space representation is expanded to a dimension matching the end of the encoder through the fully connected layers, and then gradually up-sampled to reconstruct high-dimensional structural stress field data through the transposed convolutional layers.
5. The AUV structural stress real-time prediction method according to claim 1, characterized in that, The loss function used when training the convolutional autoencoder is a mean square error loss function, and its expression is: wherein, m is the number of samples, is the reconstructed data, is the original input data.
6. The AUV structural stress real-time prediction method according to claim 1, characterized in that, The deep learning neural network in step S2 comprises an input layer, a hidden layer, and an output layer; the hidden layer comprises multiple fully connected layers and PReLU activation functions; the deep learning neural network is trained through a backpropagation algorithm and a gradient descent optimization algorithm, and the loss function is a mean square error loss.
7. The AUV structural stress real-time prediction method according to claim 1, characterized in that, The input of the deep learning neural network is working conditions, and the output is nonlinear low-dimensional features, and a mapping relationship between the two is established through layer-by-layer nonlinear mapping.
8. The AUV structural stress real-time prediction method according to claim 1, characterized in that, The decoder comprises fully connected layers and transposed convolutional layers connected in sequence; the reconstruction process in step S3 comprises: expanding the dimension of the predicted low-dimensional features through the fully connected layers, restoring them to feature maps through an inverse flattening operation, and then gradually up-sampling them to restore them to high-dimensional structural stress field data through the transposed convolutional layers.
9. The AUV structural stress real-time prediction method according to claim 1, characterized in that, The AUV structural stress real-time prediction method further comprises an error evaluation step: verifying the prediction accuracy by calculating the average relative error between the high-dimensional structural stress field data reconstructed in step S3 and the corresponding high-dimensional structural stress field data obtained through simulation.
10. A computer-readable storage medium, characterized in that, A computer program is stored thereon, which is executed by a processor to implement the AUV structural stress real-time prediction method of any one of claims 1-9.
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