An intelligent prediction method for space-time evolution of high-dimensional physical field in forming manufacturing

Abstract

The present application relates to the technical field of physical field evolution prediction, in particular to a high-dimensional physical field space-time evolution intelligent prediction method in forming manufacturing, which comprises encoding the preprocessed high-dimensional physical field historical time data into low-dimensional potential representation, extracting a historical evolution feature sequence from the potential representation sequence, and using a multilayer perception machine to learn and obtain external environment disturbance influence features corresponding to the process environment parameters; the historical evolution feature sequence and the external environment disturbance influence features are adaptively fused through a multi-head attention mechanism to obtain a potential representation prediction value at the next time; and the potential representation prediction value at the next time is reconstructed through decoding to obtain a high-dimensional physical field prediction result at the next time. The present application realizes accurate prediction of the evolution of the high-dimensional physical field disturbed by the environment.

Description

Technical Field

[0001] This invention relates to the field of physical field evolution prediction technology, and specifically to an intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing. Background Technology

[0002] In high-end manufacturing fields such as aerospace, rail transportation, and energy, the forming and manufacturing process of complex components (such as spinning, forging, and additive manufacturing) is a dynamic evolution process involving strong coupling of multiple physical fields. The evolution of physical fields (such as stress fields, strain fields, and temperature fields) directly determines the stability of the processing and the microstructure and macroscopic properties of the final product. Therefore, accurate prediction of the evolution of physical fields during manufacturing is a key prerequisite for optimizing process parameters, proactively controlling defects, and ensuring product quality.

[0003] However, the evolution of the physical field exhibits extremely high spatiotemporal complexity. Specifically, in the spatial dimension, the physical field variables in local regions of the workpiece (such as stress, strain, or temperature at contact interfaces and deformation concentration areas) often undergo drastic gradient changes, easily forming highly non-uniform spatial distribution patterns and exhibiting significant multi-scale heterogeneity. Simultaneously, due to constraints such as material continuity and energy conservation, the local distribution of physical field variables must satisfy global consistency requirements. This coupling effect between drastic local changes and global constraints makes the physical field exhibit a high-dimensional complex state that is difficult to characterize using simple low-dimensional descriptions. In the temporal dimension, the evolution of the physical field exhibits a "dual-source driven" characteristic, meaning it is influenced by both internal historical dependence and external environmental regulation. Specifically, its current state is not only dominated by the cumulative effect of historical loading paths but also accompanied by nonlinear interventions from the external environment (such as adjustments to process parameters). This coupling effect of spatial and temporal complexity poses a significant challenge to the accurate prediction and modeling of high-dimensional physical field evolution during the forming and manufacturing process.

[0004] Existing methods for predicting the evolution of physical fields are primarily based on theoretical derivations. These methods analyze the physical mechanisms of the manufacturing process and, combined with fundamental theories such as materials mechanics, heat transfer, and plastic deformation theory, derive governing equations or empirical formulas for the evolution of physical fields. Because the manufacturing process involves high spatial dimensions and complex distributions of field variables, theoretical derivation methods often require simplification of the spatial distribution of the physical field during the solution process. This includes assuming uniform distribution of field variables in certain regions, ignoring local gradient changes, and simplifying high-dimensional problems into low-dimensional problems to reduce the difficulty of solving. Furthermore, these methods typically model and solve for specific combinations of process parameters. When external process parameters (such as feed rate, temperature, and loading rate) change, the model needs to be rebuilt or its parameters adjusted, lacking the ability to respond in real time to dynamic parameter changes.

[0005] Defects and shortcomings of existing technology: High-dimensional physical fields suffer from severe spatial information loss, making it impossible to simultaneously consider local features and global topology. Existing theoretical derivations often require significant simplification of the spatial distribution of the physical field to reduce solution difficulty. For example, they may assume uniform distribution of field variables in certain regions, ignoring the drastic changes in local gradients in key areas such as contact interfaces and deformation concentration zones; or they may simplify three-dimensional high-dimensional problems into two-dimensional or even one-dimensional problems, resulting in an incomplete representation of the true spatial topology of the physical field. While this simplification makes the governing equations solvable, it causes severe loss of spatial information. On the one hand, detailed features in local regions (such as stress concentration and abrupt temperature gradient changes) are averaged or ignored, making it difficult for prediction results to accurately reflect the true state of these key locations, hindering the basis for defect warning and local process adjustments. On the other hand, spatial simplification assumptions introduced to meet solution requirements may violate global constraints that the physical field should satisfy (such as material continuity and energy conservation), leading to a distribution of the predicted physical field that does not conform to physical laws. Therefore, existing methods struggle to maintain the integrity and physical rationality of the global topology while preserving local detailed features.

[0006] Without considering the cumulative effects of historical processes, it is impossible to incorporate nonlinear disturbances from the external environment into time-series predictions. Existing theoretical derivation methods typically solve for the final physical field distribution based on a given combination of initial boundary conditions and process parameters. This modeling approach has two shortcomings: First, existing methods usually do not consider the cumulative effects of historical loading paths. In actual manufacturing processes, the deformation history experienced by materials significantly influences the final physical field state; phenomena such as work hardening and residual stress accumulation are closely related to historical processes. However, theoretical derivation methods often only base their solutions on current boundary conditions and load states, lacking modeling of the temporal evolution of the physical field and failing to capture the impact of historical cumulative effects on the current state. Second, existing methods lack a mechanism to incorporate the influence of external process environment parameters into time-series predictions. In actual production, external process parameters dynamically adjust over time, generating nonlinear disturbances to the evolution of the physical field. This makes it impossible for existing methods to effectively embed the dynamic disturbances of external environmental parameters into the time-series prediction model of the physical field. It also makes it impossible to simultaneously consider the coupling effect of historical evolution and external environmental disturbances, making it difficult for the prediction results to accurately reflect the actual evolution behavior of the physical field under environmental disturbances during the actual manufacturing process.

[0007] Low model prediction efficiency and poor generalization ability: Traditional deep learning methods typically perform operations directly on the original high-dimensional space (such as high-resolution grids), leading to the "curse of dimensionality," a huge number of model parameters, extremely high computational resource consumption, and long inference time. In addition, most existing data-driven prediction models are "black box" models trained "end-to-end" on data under single, fixed operating conditions, without effectively decoupling and embedding interference from external process parameters. Once the process parameters or external environment change during manufacturing, the prediction accuracy of the original model will drop precipitously, requiring the collection of a large amount of new operating condition data and retraining the model from scratch. Summary of the Invention

[0008] To address the shortcomings in the aforementioned background technology, this invention provides an intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing. This method solves the problems of existing technologies being unable to fully preserve the topological structure of high-dimensional physical fields in low-dimensional space, and being unable to effectively integrate the nonlinear interference of external environmental parameters into the time-series prediction model, thereby achieving accurate prediction of the evolution of high-dimensional physical fields affected by environmental disturbances.

[0009] The first objective of this invention is to provide an intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing processes, used for predicting the physical fields during the manufacturing process of structural components, including: Collect historical data of the high-dimensional physical field to be predicted during the manufacturing process of the structural component and the corresponding process environment parameters; perform dimensional unification, position normalization and numerical standardization preprocessing on the historical data of the high-dimensional physical field in sequence. The preprocessed high-dimensional physical field historical data is encoded into a low-dimensional latent representation, and the latent representations of multiple consecutive times are selected to form a latent representation sequence; wherein, the encoding adopts a variational autoencoder; Historical evolution feature sequences are extracted from the latent representation sequence, and the corresponding process environment parameters are learned using a multilayer perceptron to obtain the external environmental interference influence features. The historical evolution feature sequences and the external environmental interference influence features are adaptively fused through a multi-head attention mechanism to obtain the latent representation prediction value for the next time step. The high-dimensional physical field prediction result for the next time step is obtained by decoding and reconstructing the latent representation prediction value for the next time step.

[0010] In one embodiment, the process environment parameters are composed of process initial parameters, process parameters, and time location parameters assembled in sequence.

[0011] In one embodiment, the corresponding process environment parameters are learned using a multilayer perceptron to acquire the characteristics of external environmental interference, including: A multilayer perceptron is used to learn the nonlinear interference mode of the process environment parameters on the evolution of the physical field through multilayer nonlinear transformation of multiple hidden layers, and output a high-dimensional feature vector representing the influence of external environmental interference. Each hidden layer contains linear transformation and nonlinear activation operations.

[0012] In one embodiment, the historical evolutionary feature sequence and the features affected by external environmental disturbances are adaptively fused using a multi-head attention mechanism, including: A multi-head attention mechanism is adopted, in which the features affected by external environmental interference are linearly projected as the query vector, and the historical evolution feature sequence is linearly projected as the key vector and value vector respectively. The attention weight distribution is obtained by calculating the scaling dot product similarity between the query vector and the key vector and then normalizing it with softmax. The attention weights are used to perform a weighted summation on the value vector to obtain the fused feature representation.

[0013] In one embodiment, a long short-term memory network is used when extracting historical evolution feature sequences from the latent representation sequence.

[0014] In one embodiment, a multi-layer feedforward neural network is used to encode the preprocessed high-dimensional physical field historical moment data; and a multi-layer feedforward neural network structure symmetrical to the encoder is used to reconstruct the latent representation prediction value of the next moment through decoding.

[0015] In one embodiment, the method further includes: if it is necessary to predict a more distant future time, adding the prediction result to the historical sequence and updating the input sequence through encoding to perform rolling prediction; otherwise, the process ends.

[0016] The second objective of this invention is to provide a system for intelligent prediction of the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing, comprising a data acquisition module, a spatial encoding module, a temporal modeling module, a parameter embedding module, and a dynamic fusion module; The data acquisition module is used to collect historical data of structural components in the high-dimensional physical field to be predicted and the corresponding process environment parameters; and to perform dimensional unification, position normalization and numerical standardization preprocessing on the historical data of the high-dimensional physical field in sequence. The spatial coding module includes an encoder and a decoder; the encoder is used to encode the preprocessed high-dimensional physical field historical moment data into a low-dimensional latent representation, and select the latent representations of multiple consecutive moments to form a latent representation sequence; the latent representation prediction value of the next moment is reconstructed by decoding to obtain the high-dimensional physical field prediction result of the next moment. The time modeling module is used to extract historical evolution feature sequences from the latent representation sequence; The parameter embedding module is used to learn the external environmental interference characteristics of the corresponding process environment parameters using a multilayer perceptron. The dynamic fusion module is used to adaptively fuse historical evolution feature sequences and external environmental interference features through a multi-head attention mechanism to obtain the potential representation prediction value for the next time step.

[0017] In one embodiment, the spatial coding module is trained using preprocessed high-dimensional physical field historical data, and the optimization objective is to minimize the weighted sum of reconstruction loss and distribution regularization loss during the training process.

[0018] In one embodiment, the time modeling module, parameter embedding module, and dynamic fusion module are built by training with well-organized training data, and the mean square error between the predicted latent representation and the true latent representation is taken as the optimization objective. The well-organized training data consists of encoding historical physical field data into a latent representation sequence using an encoder in a trained spatial coding module, and organizing the training data using a sliding window method. The sliding window has a length of T, and the latent representations of the first T time steps and the corresponding process environment parameters are used as inputs within each window. The latent representation at time step T+1 is used as the prediction target.

[0019] The present invention has at least the following beneficial effects: This invention provides an intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing. This method employs a variational autoencoder to achieve nonlinear dimensionality reduction of high-dimensional physical fields, compressing physical field data from hundreds to thousands of dimensions into a potential space of a dozen dimensions while fully preserving the spatial topology and local details of the physical field. It overcomes the problem of complete loss of spatial information caused by existing scalarization methods and also overcomes the limitation of linear dimensionality reduction methods in capturing nonlinear features. This allows the prediction results to accurately reflect the true state of the physical field at each spatial location, providing a reliable basis for defect localization and process optimization.

[0020] This invention captures historical evolution patterns through a Long Short-Term Memory (LSTM) network, learns the nonlinear interference effects of external process parameters through a Multilayer Perceptron (MLP), and achieves adaptive fusion of the two through a multi-head attention mechanism. The model can automatically adjust the relative weights of historical cumulative effects and external environmental disturbances according to different operating conditions without manual intervention. This overcomes the shortcomings of existing technologies that ignore historical path dependence and cannot integrate external environmental influences, significantly improving prediction accuracy and robustness under dynamically changing process parameters.

[0021] This invention significantly reduces computational complexity through low-dimensional latent space modeling, achieving prediction times in the millisecond to second range, thus meeting real-time control requirements. The trained model exhibits excellent generalization ability to changes in process parameters, eliminating the need for retraining for new operating conditions. By adjusting network parameters, it can flexibly adapt to different manufacturing processes. Attached Figure Description

[0022] Figure 1 Flowchart of an intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing provided by the present invention; Figure 2 Flowchart for constructing a collaborative prediction model for the spatiotemporal evolution of high-dimensional physical fields; Figure 3 A schematic diagram of the spinning process (A) and the evolution behavior of the flange deformation field (B). Detailed Implementation

[0023] In order to illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following detailed description is provided in conjunction with the embodiments.

[0024] The purpose of this invention is to provide a method for predicting the spatiotemporal evolution of high-dimensional physical fields during the forming and manufacturing process. This method aims to solve the problems of existing technologies being unable to fully preserve the topological structure of high-dimensional physical fields in low-dimensional space, and being unable to effectively integrate the nonlinear disturbances of external environmental parameters into the time-series prediction model, thereby achieving accurate prediction of the evolution of high-dimensional physical fields affected by environmental disturbances.

[0025] To achieve the above objectives, see Figure 1 As shown, a high-dimensional physical field spatiotemporal evolution intelligent prediction method for forming and manufacturing is used for physical field prediction in the structural component manufacturing process, including: S1. Collect historical data of the high-dimensional physical field to be predicted during the manufacturing process of the structural component and the corresponding process environment parameters; perform dimensional unification, position normalization and numerical standardization preprocessing on the historical data of the high-dimensional physical field in sequence. The process environment parameters are composed of initial process parameters, process parameters, and time and location parameters arranged in sequence.

[0026] S2. Encode the preprocessed high-dimensional physical field historical time data into low-dimensional latent representations, and select latent representations from multiple consecutive time points to form a latent representation sequence; S3. Extract the historical evolution feature sequence from the latent representation sequence, and use a multilayer perceptron to learn the external environmental interference influence features of the corresponding process environment parameters; adaptively fuse the historical evolution feature sequence and the external environmental interference influence features through a multi-head attention mechanism to obtain the latent representation prediction value for the next time step. Long Short-Term Memory (LSTM) networks are used when extracting historical evolution feature sequences from latent representation sequences.

[0027] The historical evolutionary feature sequence and the features affected by external environmental disturbances are adaptively fused through a multi-head attention mechanism, including: A multi-head attention mechanism is adopted, in which the features affected by external environmental interference are linearly projected as the query vector, and the historical evolution feature sequence is linearly projected as the key vector and value vector respectively. The attention weight distribution is obtained by calculating the scaling dot product similarity between the query vector and the key vector and then normalizing it with softmax. The attention weights are used to perform a weighted summation on the value vector to obtain the fused feature representation.

[0028] The corresponding process environment parameters are learned using a multilayer perceptron to obtain the characteristics of external environmental interference, including: A multilayer perceptron is used to learn the nonlinear interference mode of the process environment parameters on the evolution of the physical field through multilayer nonlinear transformation of multiple hidden layers, and output a high-dimensional feature vector representing the influence of external environmental interference. Each hidden layer contains linear transformation and nonlinear activation operations.

[0029] S4. Reconstruct the latent representation prediction value for the next time step through decoding to obtain the high-dimensional physical field prediction result for the next time step.

[0030] When encoding the preprocessed high-dimensional physical field historical moment data, a multi-layer feedforward neural network is used; when reconstructing the latent representation prediction value of the next moment through decoding, a multi-layer feedforward neural network structure symmetrical to the encoder is used.

[0031] The invention also includes: if it is necessary to predict a more distant future time, the prediction result is added to the historical sequence and the input sequence is updated by encoding to perform rolling prediction; otherwise, the prediction ends.

[0032] To illustrate the intelligent prediction of the spatiotemporal evolution of high-dimensional physical fields in forming manufacturing provided by this invention, a system for the intelligent prediction method of the spatiotemporal evolution of high-dimensional physical fields in forming manufacturing is provided, including a data acquisition module, a spatial encoding module, a time modeling module, a parameter embedding module, and a dynamic fusion module. The data acquisition module is used to collect historical data of structural components in the high-dimensional physical field to be predicted and the corresponding process environment parameters; and to perform dimensional unification, position normalization and numerical standardization preprocessing on the historical data of the high-dimensional physical field in sequence. The spatial coding module includes an encoder and a decoder; the encoder is used to encode the preprocessed high-dimensional physical field historical moment data into a low-dimensional latent representation, and select the latent representations of multiple consecutive moments to form a latent representation sequence; the latent representation prediction value of the next moment is reconstructed by decoding to obtain the high-dimensional physical field prediction result of the next moment. The time modeling module is used to extract historical evolution feature sequences from the latent representation sequence; The parameter embedding module is used to learn the external environmental interference characteristics of the corresponding process environment parameters using a multilayer perceptron. The dynamic fusion module is used to adaptively fuse historical evolution feature sequences and external environmental interference features through a multi-head attention mechanism to obtain the potential representation prediction value for the next time step.

[0033] In this invention, a spatial encoding module encodes high-dimensional physical field distribution data into low-dimensional latent representations and reconstructs them; a temporal modeling module extracts the historical evolution patterns of the latent representation sequences; a parameter embedding module learns the nonlinear interference effects of external process environment parameters on the evolution of the physical field; and a dynamic fusion module fuses historical evolution information and external environmental interference effects through an attention mechanism to generate prediction results. The high-dimensional physical fields include temperature fields, stress fields, deformation fields, and flow fields.

[0034] The spatial coding module is trained using preprocessed high-dimensional physical field historical data. During the training process, minimizing the weighted sum of reconstruction loss and distribution regularization loss is used as the optimization objective.

[0035] For example, the spatial coding module employs a variational autoencoder structure, including an encoder and a decoder. The encoder uses a multi-layer feedforward neural network structure, containing... n There are 1 hidden layer, with the number of neurons in each layer decreasing sequentially. The output is divided into... w dimensional mean vector sum w A variance vector is generated by sampling noise from a standard normal distribution through a reparameterization mechanism, multiplying the noise element-wise with the variance vector, and then adding the mean vector. w The decoder employs a multi-layer feedforward neural network structure symmetrical to the encoder, which contains 12 latent variables. w Dimensional latent variables through n Each hidden layer is expanded layer by layer to the original dimension L, thereby reconstructing the physical field.

[0036] Specifically, the training objectives of the encoder and decoder include reconstruction loss and distribution regularization loss. The reconstruction loss uses mean squared error to measure the difference between the input and the reconstruction, while the distribution regularization loss uses KL divergence to constrain the distribution of latent variables to be close to a standard normal distribution. The two losses are weighted and summed to form the total loss function.

[0037] The time modeling module, parameter embedding module, and dynamic fusion module are built using well-organized training data, and the optimization objective is to minimize the mean square error between the predicted latent representation and the true latent representation. The well-organized training data consists of encoding historical physical field data into a latent representation sequence using an encoder in a trained spatial coding module, and organizing the training data using a sliding window method. The sliding window has a length of T, and the latent representations of the first T time steps and the corresponding process environment parameters are used as inputs within each window. The latent representation at time step T+1 is used as the prediction target.

[0038] For example, the temporal modeling module employs a Long Short-Term Memory (LSTM) network structure, incorporating three gating mechanisms: a forget gate, an input gate, and an output gate. The forget gate determines the degree to which historical information is retained in the cell state, the input gate determines the degree to which current input information is stored, and the output gate determines the degree to which the cell state outputs information to the hidden state. A K-layer stacked structure is used, with the first layer receiving the sequence of latent variables, and subsequent layers receiving the hidden state sequence from the previous layer, enabling multi-timescale feature extraction. Simultaneously, a random deactivation mechanism is implemented at the output of each layer, randomly setting some dimensions of the hidden state to zero with a set probability during training to prevent overfitting.

[0039] The parameter embedding module employs a multilayer perceptron (MLP) structure. The input is an external process environment parameter vector, which is constructed by sequentially concatenating initial process parameters, process parameters, and time-location parameters. Through multilayer nonlinear transformations across M hidden layers, it learns the nonlinear interference patterns of the process environment parameters on the evolution of the physical field, outputting a high-dimensional feature vector representing the influence of external environmental interference. Each hidden layer includes linear transformations and nonlinear activation operations. The parameter embedding module uses a symmetrical hourglass-shaped network structure, with the middle layer having the largest dimension and the two end layers having smaller dimensions.

[0040] The dynamic fusion module employs a multi-head attention mechanism. It uses the external environmental interference features output by the parameter embedding module as the query vector through linear projection, and the historical evolution feature sequence output by the temporal modeling module as the key and value vectors through different linear projections, respectively. The attention weight distribution is obtained by calculating the scaled dot product similarity between the query vector and the key vector and then normalizing it using softmax. The value vectors are then weighted and summed using these attention weights to obtain the fused feature representation. The multi-head attention mechanism includes H attention heads, each independently calculating attention and fusing in different feature subspaces. The H fusion results are concatenated and linearly transformed to obtain the final fused feature. The dynamic fusion module uses a residual fusion structure, concatenating the last-moment hidden state output by the temporal modeling module with the fused feature output by the attention, and then generating the latent representation prediction value through a fully connected layer.

[0041] This invention is based on a system for intelligent prediction of the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing. During the prediction process, see [link to system]. Figure 2 As shown, it includes two stages: model training and evolutionary prediction. Model training phase: (1) Collect historical physical field data and corresponding process environment parameter data of the manufacturing process, and perform dimensional unification, position normalization and numerical standardization preprocessing on the physical field data; (2) Construct the variational autoencoder structure of the spatial coding module (VAE), train the encoder and decoder using the preprocessed physical field data, and optimize the goal of minimizing the weighted sum of reconstruction loss and distribution regularization loss. After training, fix the parameters of the spatial coding module. (3) Use the trained encoder to encode the physical field history data into a potential representation sequence, organize the training data in a sliding window manner, slide the time window of length T, use the potential representation of the first T time moments and the corresponding process environment parameters in each window as input, and use the potential representation of the T+1 time moment as the prediction target. (4) Construct a time modeling module (LSTM), a parameter embedding module (MLP), and a dynamic fusion module (Attention). Train the above three modules using well-organized training data. The optimization objective is to minimize the mean square error between the predicted latent representation and the true latent representation. After training, save all module parameters.

[0042] Evolutionary prediction stage: (5) Collect historical data of the physical field to be predicted during the manufacturing process and the corresponding process environment parameter data, and perform the same dimensional unification, position normalization and numerical standardization preprocessing on the physical field data as in the training stage; (6) Input the preprocessed physical field data at each time step into the encoder of the spatial coding module to obtain the data at each time step. w The latent representation is selected from the latent representations of the most recent T time steps to form the input sequence; (7) Input the latent representation sequence into the time modeling module (LSTM), extract historical evolution features through the long short-term memory network, and output the hidden state sequence at each time step; (8) Input the process environment parameter vector corresponding to the current moment into the parameter embedding module (MLP) to learn the feature vector of external environmental interference; (9) Input the historical evolution feature sequence and the external environmental interference influence features into the dynamic fusion module, and achieve adaptive fusion through the multi-head attention mechanism to generate the potential representation prediction value for the next time step; (10) Input the predicted latent representation into the decoder of the spatial coding module and reconstruct the high-dimensional physical field prediction result for the next time step; (11) If it is necessary to predict a more distant future time, add the prediction result to the historical sequence to update the input sequence, return to step (7) to perform rolling prediction, otherwise end.

[0043] To further illustrate the intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing provided by this invention, specific examples are used for explanation.

[0044] This embodiment uses the spatiotemporal evolution prediction of the flange deformation field during spinning as an example to explain in detail the implementation process of the method of the present invention; see [link to relevant documentation]. Figure 3 As shown, Figure 3 Image (A) illustrates the forming process of a flange by spinning with a rotary wheel. Figure 3 Figure (B) shows the deformation field evolution behavior of the flange from time a to time b.

[0045] (1) Data acquisition and preprocessing: Deformation field data of the flange at different times during the spinning process were collected. The deformation field data were obtained through two methods: finite element simulation and experimental measurement. The finite element simulation used ABAQUS software to establish the spinning model, and the experimental measurement used measuring equipment to obtain the deformation data of the actual forming process. The deformation field data at each time point includes the three-dimensional spatial coordinate information of the flange circumferential direction.

[0046] The three-dimensional Cartesian coordinates (x, y, z) are converted to cylindrical coordinates (r, θ, z), where z is the axial coordinate, θ is the circumferential angle, and r is the radial coordinate. The deformation field data is projected onto the cylindrical surface, and the circumferential angle θ and axial coordinate z are extracted to form a two-dimensional point cloud sequence (θ, z). The data is resampled to L=360 angle nodes uniformly distributed circumferentially with an angle interval of 1° through linear interpolation to obtain a fixed-length circumferential deformation sequence.

[0047] For each deformed waveform, perform position normalization: calculate the average value of the axial coordinates of each point on the waveform. Subtracting this average value from the axial coordinates of all points yields the normalized coordinates z' = z - This eliminates the influence of overall axial displacement.

[0048] The Z-Score standardization method is used to scale the data: the global mean μ and global standard deviation σ of all data points in all training samples are calculated, and each data point is standardized according to the formula z''=(z'-μ) / σ so that the data mean is 0 and the standard deviation is 1.

[0049] Collect process environment parameter data at each corresponding moment, including: initial billet diameter D0 ranging from 150-450mm, feed ratio f ranging from 0.4-2.65mm / r, and mandrel rotation speed n. m The value range is 40-130 rpm, the half-cone angle α ranges from 18.75-76°, and the time position parameter p... Defined as the ratio of the current spinning position to the total forming stroke, the value ranges from 0 to 1, where 0 indicates the start of forming and 1 indicates the end of forming. The above parameters are then concatenated in sequence into a unified process environment parameter vector.

[0050] Through orthogonal experimental design, spinning forming data under different combinations of process parameters were collected, covering typical working conditions within the range of parameter values. The forming process under each combination of process parameters includes deformation field data for several time steps. A total of 6062 samples were collected and divided into training set and test set in an 8:2 ratio. The training set contains 4850 samples and the test set contains 1212 samples.

[0051] (2) Spatial coding module training: Construct a variational autoencoder structure, the encoder containing n =There are two hidden layers. The first hidden layer contains 180 neurons, and the second hidden layer contains 90 neurons. The output layer is divided into a mean output branch and a variance output branch, and each branch outputs... w =13-dimensional vector, each layer uses ReLU as the activation function, the encoder input dimension is 360, corresponding to the axial coordinate values ​​of 360 circumferential sampling points.

[0052] The decoder adopts a network structure symmetrical to the encoder, containing two hidden layers. The first hidden layer contains 90 neurons, and the second hidden layer contains 180 neurons. The output layer is restored to 360 dimensions, corresponding to the axial coordinate values ​​of the reconstructed 360 circumferential sampling points. Each layer uses ReLU as the activation function. The input dimension of the decoder is 13, corresponding to 13-dimensional latent variables.

[0053] The variational autoencoder was trained using 4850 deformation field samples from the training set. The training objective function was a weighted sum of reconstruction loss and KL divergence loss, where the reconstruction loss was calculated using mean squared error, and the KL divergence was used to constrain the distribution of latent variables to approximate a standard normal distribution. The weight coefficient β was set to 0.001. The Adam optimizer was used for parameter optimization, with a learning rate of 0.0001 and a batch size of 256. During training, the training set was further divided, and 20% was extracted as a validation set to monitor the training progress. When the decrease in the validation set loss was less than 0.001 for 1000 consecutive epochs, the model was considered to have converged, and training was automatically stopped.

[0054] After training, all parameters of the fixed spatial coding module are no longer updated. Reconstruction tests are performed on the training and test sets. The encoder can compress the 360-dimensional deformable field data into a 13-dimensional latent representation, and the decoder can reconstruct the 360-dimensional deformable field from the 13-dimensional latent representation. The mean absolute error (MAE) of reconstruction on the training set is 0.15 mm, and the mean absolute error (MAE) of reconstruction on the test set is 0.17 mm. This verifies that the spatial coding module can retain the key spatial features of the deformable field while significantly reducing the data dimensionality.

[0055] (3) Training of the time series prediction module: The time series prediction module includes a time modeling module, a parameter embedding module, and a dynamic fusion module. It uses a trained encoder with fixed parameters to encode all deformation field samples in the training set into a 13-dimensional latent representation. For the time series data of each forming process, the corresponding latent representation time series is obtained.

[0056] The training data is organized using a sliding window approach. The time window length is set to T=5, and the window slides over the time series of each forming process with a step size of 1. For each window position, the 13-dimensional latent representation and the corresponding process environment parameter vector of the first 5 time moments are extracted as model inputs, and the 13-dimensional latent representation of the 6th time moment is used as the prediction target. Through the sliding window, a large number of training sample pairs are generated from the forming process data of the training set.

[0057] The temporal modeling module is constructed using a K=3 stacked Long Short-Term Memory (LSTM) network structure, with each layer having a hidden state dimension of 128. The first LSTM layer receives a potential representation sequence of length 5 (13 dimensions per time step) as input and outputs a hidden state sequence of 5 time steps (128 dimensions per time step). The second LSTM layer receives the hidden state sequence of the first layer as input and outputs a new hidden state sequence. The third LSTM layer receives the hidden state sequence of the second layer as input and outputs the final hidden state sequence. Dropout operations are implemented at the output of each LSTM layer, with a deactivation probability of 0.162 to prevent overfitting.

[0058] The parameter embedding module is constructed using a multilayer perceptron structure with M=3 layers, arranged in a symmetrical hourglass shape. The input layer receives a vector of process environment parameters, containing five parameters: D0, f, n. m α, p The first hidden layer contains 16 neurons, the second hidden layer (intermediate layer) contains 32 neurons, and the third hidden layer contains 16 neurons. The output is a 16-dimensional feature vector of external environmental interference. Each layer uses LeakyReLU as the activation function.

[0059] A dynamic fusion module is constructed: a multi-head attention mechanism is adopted, with H=3 attention heads, each with a dimension of 21. The 16-dimensional feature vector output by the parameter embedding module is used as the query vector, and the 128-dimensional hidden states at each time step output by the temporal modeling module are used as the key and value vectors. Each attention head maps the query, key, and value to a 21-dimensional subspace through a learnable linear transformation matrix. Attention weights are calculated in the subspace and weighted fusion is performed. The outputs of the three attention heads are concatenated to form a 63-dimensional vector, which is then linearly transformed to obtain the fused feature. The fused feature is concatenated with the hidden state at the last time step of the temporal modeling module, and a 13-dimensional latent representation prediction value is generated through a fully connected layer. The fully connected layer contains 256 neurons and uses LeakyReLU as the activation function.

[0060] The time series prediction module was trained using well-organized training data. The optimization objective was to minimize the mean squared error between the predicted 13-dimensional latent representation and the true 13-dimensional latent representation. The RMSprop optimizer was used, and the learning rate was set to 4.65 × 10⁻⁶. -5 The batch size was set to 256. The OneCycleLR learning rate scheduling strategy was adopted, in which the learning rate first increased linearly from the initial value to the maximum value (the warm-up phase accounts for 41.1% of the total training rounds), and then decayed cosinely to below the initial value; during the training process, the parameters of the spatial encoding module remained fixed.

[0061] After training, the loss of the time series prediction module on the training set stabilized at around 0.087, verifying that the module can effectively learn the temporal evolution law of the physical field in the latent space.

[0062] (4) Implementation of physical field evolution prediction: For the spinning process to be predicted, the physical field evolution is predicted according to the following steps: a) Collect flange deformation field data at the first 5 moments of the forming process. The deformation field data can come from online measurements or existing partial forming data.

[0063] b) Perform the same preprocessing on the collected deformation field data as in the training phase. Specifically, this includes: coordinate transformation (converting Cartesian coordinates to cylindrical coordinates and projecting), resampling (interpolating to 360 uniformly distributed circumferential nodes), position normalization (subtracting the axial average coordinates), and numerical standardization (using the global mean μ and standard deviation σ calculated in the training phase for Z-score standardization).

[0064] c) Collect process environment parameter data at 5 corresponding time points, including initial billet diameter D0, feed ratio f, and mandrel rotation speed n. m The half-cone angle α and the time position parameter p at each moment. .

[0065] d) Input the preprocessed 360-dimensional deformation field data at 5 time points into the encoder of the trained spatial coding module in sequence to obtain 13-dimensional latent representations at 5 time points, which are then arranged in chronological order to form a latent representation sequence of length 5.

[0066] e) Input the latent representation sequence into the trained temporal modeling module, and perform forward propagation computation through a 3-layer stacked long short-term memory network to obtain a hidden state sequence of 5 time steps (128 dimensions at each time step).

[0067] f) The process environment parameter vector corresponding to the 6th time (the time to be predicted) (including D0, f, n) m α, p r The trained parameter embedding module is input, and forward propagation calculation is performed through a 3-layer multilayer perceptron to obtain a 16-dimensional feature vector of external environmental interference effects.

[0068] (g) Input the hidden state sequence obtained in step (e) and the external environment influence feature vector obtained in step (f) into the trained dynamic fusion module. Using a multi-head attention mechanism, with the external environment influence feature as the query and the hidden state at each time step as the key and value, calculate the attention weights and perform weighted fusion. After concatenating the fusion result with the hidden state at the last time step, generate the 13-dimensional latent representation prediction value for the 6th time step through a fully connected layer.

[0069] h) The predicted 13-dimensional latent representation is input into the decoder of the trained spatial coding module. Through forward propagation calculation with 2 hidden layers, the 360-dimensional deformation field prediction result (axial coordinates of 360 circumferential nodes) at the 6th time step is reconstructed.

[0070] i) Perform destandardization on the reconstructed 360-dimensional prediction results, that is, multiply by the standard deviation σ and add the mean μ to restore the numerical scale of the original data and obtain the actual deformation field prediction results.

[0071] j) If it is necessary to predict the 7th time point and further into the future, perform rolling prediction: add the prediction result of the 6th time point (after encoding to obtain a 13-dimensional latent representation) to the historical sequence, and remove the data of the 1st time point, keeping the sequence length at 5. Repeat steps (5) to (9) using the updated sequence to predict the 7th time point. And so on, multi-step rolling prediction can be performed.

[0072] (5) Validation of prediction results: The training model's prediction performance was validated using 1212 samples from the test set.

[0073] For quantitative evaluation, the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) were calculated between the predicted and actual values. On the training set, the RMSE was 0.2392 mm, the MAE was 0.1384 mm, and the R² was 0.945. On the test set, the RMSE was 0.3139 mm, the MAE was 0.1639 mm, and the R² was 0.9027. The performance metrics on the training and test sets were similar, indicating that the model has good generalization ability and no obvious overfitting was observed.

[0074] In terms of qualitative evaluation, typical samples from the training and test sets were selected for visualization analysis. Figure 3 By plotting the predicted deformed waveform and the actual deformed waveform in the same coordinate system for comparison, it was observed that the predicted waveform and the actual waveform are highly consistent, and the overall outline, peak and valley positions and local details of the waveform can be accurately captured.

[0075] Existing methods use deep neural networks to directly establish the mapping relationship between process parameters and scalar feature values ​​of the deformation field, simplifying the complex deformation field into a mapping relationship of maximum fluctuation value. The method of this invention is compared with the existing method (Comparison Model 1: DNN) on the same test set. The comparison results, as shown in Table 1, show that the RMSE of the existing method on the test set is 0.3732 mm, which is 15.9% higher than that of the method of this invention. The second comparison method embeds a variational autoencoder (VAE-DNN) into the existing method, i.e., Comparison Model 2, to verify the ability of the existing method to predict the entire deformation field. This method does not introduce temporal modeling and dynamic fusion mechanisms, and its RMSE on the test set is 0.4087 mm, which is 23.2% higher than that of the method of this invention. The results show that the method of this invention significantly improves the prediction accuracy through temporal modeling and dynamic fusion mechanisms.

[0076] Table 1 Comparison of prediction results between existing methods and the model established in this invention

[0077] (6) Parameter adjustment and adaptation: Depending on the specific application requirements, the following key parameters can be adjusted: Potential spatial dimensions w For physical fields with simple spatial distributions, a smaller value (e.g., 10) can be used; for physical fields with complex spatial distributions, a larger value (e.g., 15-20) can be used. Through grid search, when w increases from 5 to 13, the reconstruction error is significantly reduced; beyond 13, the performance improvement is not significant.

[0078] Time window length T: For processes whose evolution is mainly influenced by recent history, a smaller value (e.g., 3-5) can be used; for processes with long-term cumulative effects, a larger value (e.g., 7-10) can be used. In this embodiment, T=5 can balance prediction accuracy and computational efficiency.

[0079] Number of attention heads H: Increasing the number of attention heads can improve fusion capability, but it also increases computational load. In this embodiment, H=3 achieves a good performance balance.

[0080] Through system parameter optimization, the network configuration determined in this embodiment can achieve optimal performance in the flange deformation field prediction task during the spinning process.

[0081] This embodiment details the specific implementation process of the method of the present invention in the spinning forming process, including the complete process of data acquisition, model training, prediction implementation, and effect verification. The method of the present invention is also applicable to the prediction of physical fields in other forming and manufacturing processes, such as stress field prediction in forging and temperature field prediction in additive manufacturing. It is only necessary to adjust the network structure parameters and data preprocessing methods according to the specific application.

[0082] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for intelligent prediction of the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing, characterized in that, Physical field prediction for structural component manufacturing processes, including: Collect historical data of the high-dimensional physical field to be predicted during the manufacturing process of the structural component and the corresponding process environment parameters; perform dimensional unification, position normalization and numerical standardization preprocessing on the historical data of the high-dimensional physical field in sequence. The preprocessed high-dimensional physical field historical data is encoded into a low-dimensional latent representation, and the latent representations of multiple consecutive times are selected to form a latent representation sequence; wherein, the encoding adopts a variational autoencoder; The latent representation sequence is input into the temporal modeling module LSTM, and historical evolution features are extracted through the Long Short-Term Memory network to output the hidden state sequence at each time step. The process environment parameter vector corresponding to the current moment is input into the parameter embedding module MLP to learn the feature vector of the influence of external environmental interference. The historical evolution feature sequence and the features affected by external environmental interference are input into the dynamic fusion module, and adaptive fusion is achieved through a multi-head attention mechanism to generate the potential representation prediction value for the next time step. The predicted latent representation is input into the decoder of the spatial encoding module, and the high-dimensional physical field prediction result for the next time step is reconstructed. The high-dimensional physical field prediction result for the next time step is obtained by decoding and reconstructing the latent representation prediction value for the next time step. If it is necessary to predict a more distant future moment, the prediction result is added to the historical sequence to update the input sequence. The process of extracting the hidden state sequence through the Long Short-Term Memory network and generating the potential representation prediction value for the next moment is returned, and rolling prediction is performed; otherwise, the process ends. The corresponding process environment parameters are learned using a multilayer perceptron to obtain the characteristics of external environmental interference, including: A multilayer perceptron is used to learn the nonlinear interference mode of the process environment parameters on the evolution of the physical field through multilayer nonlinear transformation of multiple hidden layers, and output a high-dimensional feature vector representing the influence of external environmental interference. Each hidden layer contains linear transformation and nonlinear activation operations.

2. The intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing according to claim 1, characterized in that, The process environment parameters are composed of initial process parameters, process parameters, and time and location parameters arranged in sequence.

3. The intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing according to claim 1, characterized in that, The historical evolutionary feature sequence and the features affected by external environmental disturbances are adaptively fused through a multi-head attention mechanism, including: A multi-head attention mechanism is adopted, in which the features affected by external environmental interference are linearly projected as the query vector, and the historical evolution feature sequence is linearly projected as the key vector and value vector respectively. The attention weight distribution is obtained by calculating the scaling dot product similarity between the query vector and the key vector and then normalizing it with softmax. The attention weights are used to perform a weighted summation on the value vector to obtain the fused feature representation.

4. The intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing according to claim 1, characterized in that, Long Short-Term Memory (LSTM) networks are used when extracting historical evolution feature sequences from latent representation sequences.

5. The intelligent prediction method for the spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing according to claim 1, characterized in that, When encoding the preprocessed high-dimensional physical field historical moment data, a multi-layer feedforward neural network is used; when reconstructing the latent representation prediction value of the next moment through decoding, a multi-layer feedforward neural network structure symmetrical to the encoder is used.

6. A system for the intelligent prediction method of spatiotemporal evolution of high-dimensional physical fields in forming and manufacturing as described in claim 1, characterized in that, It includes a data acquisition module, a spatial coding module, a temporal modeling module, a parameter embedding module, and a dynamic fusion module; The data acquisition module is used to collect historical data of the structural components in the high-dimensional physical field to be predicted and the corresponding process environment parameters. The historical data of high-dimensional physical fields are preprocessed by dimensional unification, location normalization and numerical standardization in sequence; The spatial coding module includes an encoder and a decoder; the encoder is used to encode the preprocessed high-dimensional physical field historical moment data into a low-dimensional latent representation, and select the latent representations of multiple consecutive moments to form a latent representation sequence; the latent representation prediction value of the next moment is reconstructed by decoding to obtain the high-dimensional physical field prediction result of the next moment. The time modeling module is used to extract historical evolution feature sequences from the latent representation sequence; The parameter embedding module is used to learn the external environmental interference characteristics of the corresponding process environment parameters using a multilayer perceptron. The dynamic fusion module is used to adaptively fuse historical evolution feature sequences and external environmental interference features through a multi-head attention mechanism to obtain the potential representation prediction value for the next time step.

7. The system according to claim 6, characterized in that, The spatial coding module is trained using preprocessed high-dimensional physical field historical data. During the training process, minimizing the weighted sum of reconstruction loss and distribution regularization loss is used as the optimization objective.

8. The system according to claim 6, characterized in that, The time modeling module, parameter embedding module, and dynamic fusion module are built using well-organized training data, and the optimization objective is to minimize the mean square error between the predicted latent representation and the true latent representation. The well-organized training data consists of encoding historical physical field data into a latent representation sequence using an encoder in a trained spatial coding module, and organizing the training data using a sliding window method. The sliding window has a length of T, and the latent representations of the first T time steps and the corresponding process environment parameters are used as inputs within each window. The latent representation at time step T+1 is used as the prediction target.

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