Method for reconstructing non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging

Abstract

The present application discloses a method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency-domain bridging, which relates to the technical field of stress field reconstruction. The method includes: first, obtaining the geometric model of the target complex component, identifying the degree of non-uniformity of the stress distribution corresponding to the geometric boundary features and dividing it into multiple sub-regions; then, aiming at the spatial frequency characteristics of the stress distribution in each sub-region, constructing a physics-informed neural network embedded with the elastic mechanics mechanism equation, and training to obtain the stress field sub-network model of each sub-region; then, transforming the spatial-domain stress field output by the sub-network to the frequency domain, establishing a frequency-domain dynamic link between sub-regions through a frequency-domain bridging module, and reconstructing the overall non-uniform stress field of the component through inverse transformation; finally, through a variable fidelity cascaded neural operator network, gradually fusing multi-source stress field data to complete the improvement of fidelity. The method of the present application takes into account both the solution efficiency and the multi-scale stress fitting accuracy, and eliminates the boundary discontinuity problem of segmentation and splicing.

Description

Technical Field

[0001] This application relates to the field of stress field reconstruction technology, and in particular to a method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging. Background Technology

[0002] Key load-bearing components of high-end equipment such as advanced CNC machine tools and nuclear reactor main loops, including precision guide rail joints and primary loop pipe bends, are subjected to complex alternating loads under long-term continuous service conditions. These components exhibit significant non-uniform stress distributions, and their stress state directly determines the equipment's service performance. Accurately reconstructing the non-uniform stress field under complex geometric boundaries is of crucial theoretical and engineering value for equipment structural optimization design, accuracy assurance, and life assessment.

[0003] Currently, engineering practice mainly relies on finite element analysis to solve stress fields. However, for complex geometric models, the finite element method has cumbersome preprocessing and long calculation time, making it difficult to meet the needs of rapid iterative design of multiple schemes or online state awareness.

[0004] In recent years, physical information neural networks (PINs) have achieved deep integration of mechanistic equations and measured data by embedding the control equations as regularization terms into the loss function, opening up new paths for efficient solutions to physical fields. However, complex components often contain features such as abrupt curvature changes, concave corners, protrusions, and holes, and their stress fields exhibit multi-scale spatial distribution characteristics—high-frequency stress gradients exist in regions with abrupt geometric feature changes, while low-frequency, gradual changes occur far from these regions. When using a single PIN for end-to-end training of the overall model, the limited frequency band representation capabilities of the network structure and activation function make it difficult to accurately fit the stress distribution where high and low frequencies coexist within the same framework, resulting in severely insufficient solution accuracy for stress concentration regions. If the complex geometry is divided into finite segments and sub-networks are trained separately to alleviate the above contradictions, the stress and displacement continuity conditions at the boundaries of each sub-region are difficult to accurately satisfy through post-processing. The overall stress field after splicing often exhibits non-physical steps or discontinuities at the junctions, destroying the physical consistency of the reconstruction results. Furthermore, due to differences in node density and accuracy, existing technologies make it difficult to cross-integrate simulation data and measured data, thus failing to effectively improve the accuracy of stress field reconstruction through multi-source data. Summary of the Invention

[0005] The purpose of this application is to provide a method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging, which can achieve efficient and high-precision reconstruction of the non-uniform stress field of complex components.

[0006] To achieve the above objectives, this application provides the following solution: A method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging includes the following steps: Obtain the geometric model of the target complex component, identify the degree of stress distribution non-uniformity corresponding to the geometric boundary features of the geometric model, and divide the geometric model into multiple sub-regions based on the degree of stress distribution non-uniformity.

[0007] For each sub-region, a physical information neural network embedding the elasticity mechanism equation is constructed based on the spatial frequency characteristics of the stress distribution within the sub-region, and the stress field sub-network model corresponding to each sub-region is trained.

[0008] The spatial domain stress field data output by each sub-network model is transformed to the frequency domain, and a dynamic link of the stress field in different sub-regions is established in the frequency domain through the frequency domain bridging module.

[0009] The stress field information in the dynamic link established in the frequency domain is inversely transformed to reconstruct the overall non-uniform stress field of the target complex component in the spatial domain.

[0010] A variable-fidelity cascaded neural operator network is constructed. Multi-source stress field data with different sources and accuracies are input into the variable-fidelity cascaded neural operator network step by step. The fidelity of the reconstructed overall non-uniform stress field is improved to obtain the final overall non-uniform stress field.

[0011] Optionally, the geometric model of the target complex component is obtained, the degree of stress distribution non-uniformity corresponding to the geometric boundary features of the geometric model is identified, and the geometric model is divided into multiple sub-regions based on the degree of stress distribution non-uniformity. This specifically includes the following steps: Obtain the geometric model of the target complex component, extract the geometric boundary features of the geometric model, and identify regions with drastic curvature changes, regions with abrupt feature changes, and smooth regions.

[0012] Based on the identification results, the degree of non-uniformity of stress distribution in each region is analyzed. According to the degree of non-uniformity of stress distribution, regions with concentrated stress are independently divided into separate sub-regions, while regions with mild stress are merged or independently divided into sub-regions.

[0013] Optionally, based on the spatial frequency characteristics of stress distribution within a sub-region, a physical information neural network embedding the elasticity mechanism equation is constructed, and the stress field sub-network model corresponding to each sub-region is trained. This specifically includes the following steps: For sub-regions with gentle stress, a fully connected network with fewer layers and fewer neurons than preset values ​​is used, and the density of the first sampling point is set.

[0014] For sub-regions with stress concentration, a physical information neural network fused with graph neural networks is used, and a second sampling point density is set; wherein, the second sampling point density is higher than the first sampling point density.

[0015] The elasticity mechanism equation is embedded as a regularization term into the loss function of each physical information neural network. The stress field sub-network model corresponding to each sub-region is obtained by minimizing the loss function. The loss function is composed of data-driven terms and physical-driven terms, and the physical-driven terms are constructed by the embedded elasticity mechanism equation.

[0016] Optionally, the elasticity mechanism equations include equilibrium differential equations, geometric equations, constitutive equations, and deformation compatibility equations.

[0017] Optionally, the frequency domain bridging module employs a piecewise recursive graph Transformer network; it transforms the spatial domain stress field data output by each sub-network model to the frequency domain, and establishes dynamic links of stress fields in different sub-regions within the frequency domain through the frequency domain bridging module, specifically through the following steps: The spatial domain stress field data is converted to the frequency domain by using Fourier transform to obtain the spectral characteristics of the stress field in each sub-region.

[0018] The frequency domain bridging module uses the spectral characteristics of the stress field in each sub-region as input. The dynamic correlation of stress characteristics between different sub-regions under different frequency bands is learned and established through the attention mechanism of the frequency domain bridging module. The frequency domain bridging module is jointly driven and trained by combining the working condition spectrum data of the target complex component and the multi-source stress field data.

[0019] The stress field information in the dynamic link established in the frequency domain is inversely transformed. Specifically, the stress field information coupled by the dynamic link established in the frequency domain is transformed back to the spatial domain through inverse Fourier transform.

[0020] Optionally, the variable fidelity cascaded neural operator network includes multiple neural operator subnetworks cascaded sequentially, with each neural operator subnetwork corresponding to a fidelity level.

[0021] The first-level neural operator subnetwork receives first-level fidelity stress field data for training and outputs first-level stress field prediction results.

[0022] Subsequent neural operator subnetworks at each level sequentially receive the stress field prediction results output by the previous neural operator subnetwork, and perform fusion training by combining the stress field data of the corresponding fidelity level.

[0023] The final level of the neural operator subnetwork outputs the final non-uniform stress field of the target complex component.

[0024] Optionally, subsequent neural operator subnetworks, except for the first-level neural operator subnetwork, are fused and trained using a residual learning mechanism. The residual field between the stress field data corresponding to the current level and the stress field prediction result output by the previous level subnetwork is used as the learning target. Multi-source stress field data are adaptively fused through a confidence weighting strategy and an attention mechanism, while physical consistency constraints are applied.

[0025] Optionally, the multi-source stress field data includes low-fidelity stress field data, medium-fidelity stress field data, and high-fidelity stress field data; the low-fidelity stress field data includes at least one of the following: simplified model coarse-grid finite element analysis results of the target complex component, empirical formula calculation results, and reduced-order model output results; the medium-fidelity stress field data includes at least one of the following: conventional mesh density finite element analysis results and key region local refinement sub-model analysis results; the high-fidelity stress field data includes at least one of the following: fine-grid high-order element finite element calculation results, measured stress data, scaled-down model test verification data, and prototype measurement data.

[0026] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging. In this method, the degree of non-uniformity of stress distribution corresponding to the geometric boundary features of the target complex component's geometric model is identified, and the geometric model is segmented into multiple sub-regions based on this degree of non-uniformity. This decouples high-frequency stress concentration regions from low-frequency smooth regions, solving the technical challenge of a single physical information neural network being unable to simultaneously fit multi-scale stress distributions. For each sub-region, a physical information neural network embedding elasticity mechanism equations is constructed based on the spatial frequency characteristics of the stress distribution within the sub-region. This trains a stress field sub-network model corresponding to each sub-region, allowing the network structure to be adapted to the stress characteristics of different regions, balancing the efficiency of stress field solution with the fitting accuracy of local stress concentration regions. Simultaneously, embedding the mechanical mechanism equations ensures the physical compliance of the solution results. The spatial domain stress field data output by each sub-network model is transformed to the frequency domain, and then bridged in the frequency domain. The block establishes dynamic links between stress fields in different sub-regions in the frequency domain, enabling continuous transmission and coupling of stress information at the boundaries of adjacent sub-regions. This fundamentally eliminates the non-physical steps and discontinuities that occur when splicing stress fields after traditional segmentation solutions, ensuring the physical consistency of the overall stress field. The stress field information in the dynamic links established in the frequency domain is inversely transformed to reconstruct the overall non-uniform stress field of the target complex component in the spatial domain, fully preserving the high-frequency gradient characteristics of stress concentration areas and the low-frequency distribution characteristics of smooth areas. Finally, a variable-fidelity cascaded neural operator network is constructed, inputting multi-source stress field data of different sources and accuracies level by level. The reconstructed overall non-uniform stress field undergoes fidelity enhancement processing to obtain the final overall non-uniform stress field. This allows for the gradual fusion of multi-source heterogeneous stress data, overcoming the limitation of cross-fusion between simulation and measured data due to differences in node density and accuracy, significantly improving the fidelity and engineering practical value of the stress field reconstruction results. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart illustrating a method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging, as provided in an embodiment of this application.

[0029] Figure 2 This is a flowchart of step A1 in a method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging, provided in an embodiment of this application.

[0030] Figure 3 This is a flowchart of step A2 in a method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging, provided as an embodiment of this application.

[0031] Figure 4 This is a flowchart of step A3 in a method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging, provided as an embodiment of this application. Detailed Implementation

[0032] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0033] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0034] This application provides a method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging. In an exemplary embodiment, such as... Figure 1 As shown, it includes the following steps: A1. Obtain the geometric model of the target complex component, identify the degree of stress distribution non-uniformity corresponding to the geometric boundary features of the geometric model, and divide the geometric model into multiple sub-regions based on the degree of stress distribution non-uniformity. For example... Figure 2 As shown, step A1 specifically includes the following steps: A11. Obtain the geometric model of the target complex component, extract the geometric boundary features of the geometric model, and identify regions with drastic curvature changes, regions with abrupt feature changes, and smooth regions.

[0035] In this embodiment, the target complex component is the elbow section of the primary loop piping of the nuclear reactor. This elbow section is a key load-bearing component of high-end nuclear equipment, which withstands high-temperature and high-pressure fluid loads and alternating mechanical loads during service, resulting in significant non-uniformity in internal stress distribution. First, a three-dimensional geometric model of the elbow section of the primary loop piping is obtained. The geometric features of this elbow section include an inlet straight pipe, a 90° bend curvature abrupt change region, an outlet straight pipe, and a locally reinforcing boss. An integrally formed reinforcing boss with an outer diameter of 1200 mm and a height of 50 mm is located at the midpoint of the outer convex surface of the bend. The geometric boundary features of this three-dimensional geometric model are extracted using computer-aided design software, identifying regions with drastic curvature changes, the root region of the boss, and the smooth straight pipe region. Based on the identification results, the degree of non-uniformity in stress distribution in each region is analyzed.

[0036] A12. Based on the identification results, analyze the degree of non-uniformity of stress distribution in each region. According to the degree of non-uniformity of stress distribution, the region with concentrated stress is independently divided into a separate sub-region, and the region with gentle stress is merged or independently divided into a sub-region.

[0037] Based on the degree of stress distribution non-uniformity, the geometric model is adaptively divided into five sub-regions: the inlet straight pipe sub-region, where stress distribution is gentle and non-uniformity is low; the elbow inner curvature abrupt change sub-region, where stress concentration exists and non-uniformity is high; the elbow outer curvature abrupt change sub-region, where stress concentration exists and non-uniformity is high; the reinforcing boss root sub-region, where stress concentration exists and non-uniformity is high; and the outlet straight pipe sub-region, where stress distribution is gentle and non-uniformity is low. Stress concentration regions are independently divided into separate sub-regions, while regions with gentle stress distribution can be merged or divided separately based on geometric continuity.

[0038] It is understood that the identification of geometric boundary features in step A1 can be completed by curvature calculation and geometric feature recognition algorithm. The degree of non-uniformity of stress distribution can be quantitatively evaluated by preset stress gradient threshold and degree of geometric feature mutation. The number of sub-regions after segmentation can be adaptively adjusted according to the geometric complexity of the component, and is not limited to the 5 in this embodiment.

[0039] A2. For each sub-region, based on the spatial frequency characteristics of stress distribution within the sub-region, a physical information neural network embedding the elasticity mechanism equations is constructed, and trained to obtain the stress field sub-network model corresponding to each sub-region. For example... Figure 3 As shown, step A2 specifically includes the following steps: A21. For sub-regions with gentle stress, a fully connected network with fewer layers and fewer neurons than preset values ​​is used, and the density of the first sampling point is set.

[0040] A22. For sub-regions with stress concentration, a physical information neural network with fused graph neural network is used to set a second sampling point density; wherein, the second sampling point density is higher than the first sampling point density.

[0041] In this embodiment, a Physical Information Neural Network (PINN) is constructed to match the spatial frequency characteristics of stress distribution in different sub-regions. For the inlet and outlet straight pipe sub-regions with gentle stress distribution, the stress distribution is dominated by low-frequency components with small gradient changes. Therefore, a standard fully connected network with shallow layers and fewer neurons is used, and the spatial sampling point density is set to a lower first sampling point density. This reduces computational complexity and improves efficiency while ensuring solution accuracy. For the sub-regions with stress concentration, such as the inner and outer sides of the elbow and the root of the reinforcing boss, the stress distribution contains a large number of high-frequency components with drastic stress gradient changes. Therefore, a G-PINN model with fused graph neural networks is used. The graph neural network captures the topological relationships between nodes, enhancing the ability to capture local stress abrupt changes. At the same time, a deeper network structure and a higher second sampling point density are used, where the second sampling point density is higher than the first sampling point density, to ensure the fitting accuracy of the stress concentration region.

[0042] A23. The elasticity mechanism equation is embedded as a regularization term into the loss function of each physical information neural network. The stress field sub-network model corresponding to each sub-region is obtained by minimizing the loss function. The loss function is composed of data-driven terms and physical-driven terms. The physical-driven terms are constructed by the embedded elasticity mechanism equation.

[0043] The elasticity mechanism equations are embedded as regularization terms in the loss functions of each sub-network. In this embodiment, the elasticity mechanism equations include the equilibrium differential equations, geometric equations, constitutive equations, and deformation compatibility equations of three-dimensional elasticity, ensuring that the stress field output by the network satisfies the basic physical laws of solid mechanics. The loss function is composed of data-driven and physics-driven terms. The data-driven term is constructed based on the stress label data of the sampling points, and the physics-driven term is constructed based on the residuals of the embedded elasticity mechanism equations. The physical information neural networks are iteratively trained by minimizing the total loss function, and the stress field sub-network model corresponding to each sub-region is obtained after convergence. Each sub-network model outputs the spatial domain stress field data of the corresponding sub-region, including the stress tensor components and displacement components of each node.

[0044] It is understandable that the network structure of the physical information neural network can be adaptively adjusted according to the stress distribution characteristics of the sub-region. The activation function can be Swish, Tanh and ReLU, which are suitable for physical information neural networks. The sampling points can be arranged using Latin hypercube sampling, adaptive random sampling and other methods.

[0045] In a specific embodiment targeting the bend section of the primary loop piping in a nuclear reactor, a 6-layer fully connected PINN network is constructed for the two stress-relieving sub-regions: the inlet straight pipe region and the outlet straight pipe region. The number of neurons in a single hidden layer is 64, the activation function is the Swish function, and the spatial sampling points are sampled using Latin hypercube sampling at a density of 20 points / cm². 3 .

[0046] For the three stress concentration sub-regions—the inner side of the elbow, the outer side of the elbow, and the root of the reinforcing boss—a G-PINN model integrating a graph neural network was constructed. The graph neural network used 8 graph convolutional layers, and the PINN part used a 10-layer fully connected network. The number of neurons in a single hidden layer was 128, the activation function was the Tanh function, and adaptive encrypted sampling was used for spatial sampling points, with a sampling point density of 150 points / cm². 3 The sampling points at the locations of abrupt changes in curvature are the focus of the encryption.

[0047] The Adam optimizer is used to iteratively train each sub-network, with an initial learning rate set to 1e. -4 The training iterations were 50,000 times, and the loss function converged to 1e -6 Training is stopped at this point, and the stress field sub-network model corresponding to each sub-region is obtained. Each sub-network outputs the spatial domain stress field data of the corresponding sub-region, including 6 stress tensor components and 3 displacement components.

[0048] A3. Transform the spatial domain stress field data output by each sub-network model to the frequency domain, and establish dynamic links between the stress fields of different sub-regions in the frequency domain through the frequency domain bridging module. In this embodiment, the frequency domain bridging module adopts a piecewise recursive graph Transformer network. Figure 4 As shown, step A3 specifically includes the following steps: A31. The spatial domain stress field data is converted to the frequency domain by Fourier transform to obtain the spectral characteristics of the stress field in each sub-region.

[0049] In this embodiment, a piecewise recursive graph Transformer network is constructed as a frequency domain bridging module. First, the spatial domain stress field data output from each sub-network model is transformed to the frequency domain using a forward Fourier transform to obtain the spectral features corresponding to the stress field of each sub-region. These spectral features contain stress amplitude and phase information for different frequency bands. Using the spectral features of the stress field in each sub-region as input to the piecewise recursive graph Transformer network, the network learns and establishes dynamic correlations between stress features in different frequency bands and between different sub-regions through its self-attention and cross-attention mechanisms, focusing on capturing the spectral matching relationships at the boundaries of adjacent sub-regions.

[0050] A32. Using the spectral characteristics of the stress field in each sub-region as the input of the frequency domain bridging module, the frequency domain bridging module learns and establishes the dynamic correlation of stress characteristics between different sub-regions under different frequency bands through the attention mechanism of the frequency domain bridging module. Combined with the working condition spectrum data of the target complex component and the multi-source stress field data, the frequency domain bridging module is jointly driven and trained.

[0051] By combining the operating condition spectrum data of the primary loop piping of the nuclear reactor with simulated or measured multi-source stress field data, a joint drive training was conducted on the frequency domain bridging module. The operating condition spectrum data includes load information of different frequency bands experienced by the piping during service: 0-10Hz low-frequency band, corresponding to slowly varying loads such as thermal expansion, pressure fluctuations, and earthquakes; 10-100Hz mid-frequency band, corresponding to loads such as pump rotation frequency and fluid pulsation; and 100-1000Hz high-frequency band, corresponding to impact loads such as fluid excitation and rapid valve opening and closing. Through joint drive training, the frequency domain bridging module learns the stress transmission patterns at the boundaries of adjacent sub-regions under different load frequency bands, achieving continuous transmission and physical consistency coupling of stress information at the boundaries of adjacent sub-regions. This ensures that the coupled stress field satisfies the conditions of stress continuity and displacement continuity at the boundaries.

[0052] In another optional embodiment, the transformation of spatial domain stress field data to the frequency domain can be achieved using frequency domain transformation methods such as Fast Fourier Transform and Discrete Cosine Transform. The network structure of the frequency domain bridging module can be adjusted according to the number of sub-regions and boundary complexity, and is not limited to the piecewise recursive graph Transformer network in this embodiment.

[0053] In a specific embodiment targeting the bend section of the primary loop piping of a nuclear reactor, a segmented recursive graph Transformer network is constructed as a frequency domain bridging module. This network contains 4 Transformer coding layers, with 8 attention heads and a feedforward network dimension of 512.

[0054] The spatial domain stress field data output from the five sub-networks were transformed to the frequency domain using a three-dimensional fast Fourier transform to obtain the spectral characteristics of the stress field in each sub-region. The spectral range covers 0-1000Hz, fully matching the full-condition load frequency band of the primary loop pipeline in a nuclear power plant.

[0055] The spectral characteristics of each sub-region are input into the frequency domain bridging module. Through self-attention and cross-attention mechanisms, the dynamic correlation of stress characteristics between sub-regions under different frequency bands is learned, with a focus on capturing the spectral matching relationship at the boundary of adjacent sub-regions. Combining the actual operating condition spectrum data of the primary loop of the nuclear power plant (including 0-10Hz thermal expansion slow-varying load, 10-50Hz main pump rotation frequency load, 50-500Hz fluid pulsation load, and 500-1000Hz impact load), as well as the historical finite element simulation data and on-site strain gauge measured data of the elbow section, the frequency domain bridging module is jointly driven and trained. The training iterations are 30,000 times to achieve continuous transmission and physical consistency coupling of stress information at the boundary of adjacent sub-regions, ensuring stress continuity and displacement continuity at the boundary.

[0056] A4. Perform an inverse transform on the stress field information in the dynamic link established in the frequency domain to reconstruct the overall non-uniform stress field of the target complex component in the spatial domain. Specifically, the inverse transform on the stress field information in the dynamic link established in the frequency domain is performed by converting the stress field information coupled by the dynamic link established in the frequency domain back to the spatial domain using an inverse Fourier transform.

[0057] In a specific embodiment targeting the elbow section of the primary loop piping in a nuclear reactor, a dynamic link is established in the frequency domain based on a piecewise recursive graph Transformer network. After the full boundary coupling of the stress fields of the five sub-regions in the frequency domain is completed, an inverse Fourier transform is used to convert the coupled stress field information of the five sub-regions back to the spatial domain, obtaining the overall non-uniform stress field of the entire elbow section of the primary loop piping in the spatial domain. This overall non-uniform stress field is continuous and smooth at the boundaries of each sub-region, without the non-physical steps or discontinuities produced by traditional segmentation and splicing methods. At the same time, it completely preserves the high-frequency stress gradient characteristics of the stress concentration region and the low-frequency stress distribution characteristics of the smooth region.

[0058] A5. Construct a variable fidelity cascaded neural operator network, input multi-source stress field data of different sources and accuracies into the variable fidelity cascaded neural operator network step by step, and perform fidelity enhancement processing on the reconstructed overall non-uniform stress field to obtain the final overall non-uniform stress field.

[0059] In this embodiment, the variable fidelity cascaded neural operator network includes multiple cascaded neural operator subnetworks, each corresponding to a fidelity level. The first-level neural operator subnetwork receives stress field data at the first-level fidelity for training and outputs the first-level stress field prediction result. Subsequent neural operator subnetworks sequentially receive the stress field prediction results output by the previous-level neural operator subnetwork and combine them with the stress field data at the corresponding fidelity level for fusion training. The last-level neural operator subnetwork outputs the final non-uniform stress field of the target complex component.

[0060] In an exemplary embodiment, subsequent neural operator subnetworks, except for the first-level neural operator subnetwork, are fused and trained using a residual learning mechanism. The residual field between the stress field data corresponding to the current level and the stress field prediction result output by the previous level subnetwork is used as the learning target. The multi-source stress field data are adaptively fused through a confidence weighting strategy and an attention mechanism, while physical consistency constraints are applied.

[0061] In another exemplary embodiment of this application, the variable fidelity cascaded neural operator network is configured as a three-level cascaded structure, corresponding to low fidelity, medium fidelity, and high fidelity levels, respectively. Each level of the neural operator subnetwork uses Fourier neural operators as the core layer, possessing the ability to learn the global mapping of the spatial stress field. First, a multi-fidelity dataset is constructed, with multi-source stress field data divided into three fidelity levels: low-fidelity stress field data, including simplified model coarse mesh (20,000 elements) finite element analysis results, empirical formula calculation results, and reduced-order model output results, characterized by large data volume, fast calculation speed, and wide coverage but limited accuracy; medium-fidelity stress field data, including conventional mesh density (200,000 elements) finite element analysis results and key region local refined sub-model analysis results, with moderate accuracy and computational cost; and high-fidelity stress field data, including fine mesh high-order element (2 million elements) finite element calculation results, pipeline stress measurement data collected by strain gauges and fiber optic sensors, and scaled-down model test verification data, characterized by high accuracy and strong realism but limited data volume. The overall non-uniform stress field reconstructed in step S4 is used as the basic input, combined with the above multi-source stress field data to form a multi-fidelity dataset.

[0062] However, it is understandable that the number of cascade levels in the variable fidelity cascaded neural operator network can be adjusted according to the number of fidelity levels of the multi-source data, and is not limited to the three-level cascade structure limited in the above embodiments. The neural operator sub-network can adopt a variety of neural operator structures suitable for physical field learning, such as Fourier neural operators and graph neural operators.

[0063] The stress field results obtained by reconstructing the overall non-uniform stress field of the elbow section of the primary loop pipeline in this embodiment were compared with the high-precision finite element benchmark solution and field measured data under the same operating conditions. The verification results are as follows: the average relative error of the overall stress field is much lower than that of the traditional single PINN method, and the relative error of the peak stress in stress concentration areas such as the root of the reinforcing boss and the inner side of the bend is much lower than that of the traditional segmentation and splicing method. At the same time, the stress continuity error at the boundary of each sub-region does not have the non-physical step phenomenon of the traditional method. In addition, the time consumed by the single-condition stress field reconstruction is much less than that consumed by the same precision finite element analysis, which greatly improves the solution efficiency.

[0064] The method for reconstructing non-uniform stress fields of complex components based on boundary segmentation and frequency domain bridging provided in the above embodiments of this application divides the component into multiple sub-regions by identifying the degree of non-uniformity of stress distribution corresponding to the geometric boundary features of the complex component. This decouples the high-frequency stress concentration region from the low-frequency smooth region, solving the technical problem that a single physical information neural network cannot simultaneously fit multi-scale stress distributions. By constructing a frequency domain bridging module, dynamic links are established between sub-regions in the frequency domain, realizing the continuous transmission of stress information between adjacent boundaries and physical consistency constraints. This fundamentally eliminates the step and discontinuity problem of stress field splicing after segmentation and solution. By fusing multi-source stress field data step by step through a variable fidelity cascaded neural operator network, the limitation of the difficulty in cross-fusion between simulation data and measured data due to differences in node density and accuracy is overcome. This effectively improves the accuracy and fidelity of stress field reconstruction while taking into account solution efficiency, and can meet the needs of rapid iterative design and online status perception of multiple schemes for key components of high-end equipment.

[0065] It should be noted that the component working condition data, stress measurement data and related model data involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of related data are carried out in accordance with the relevant data protection laws and policies of the country where the application is located and with the authorization of the owner of the corresponding device.

[0066] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0067] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging, characterized in that, include: Obtain the geometric model of the target complex component, identify the degree of stress distribution non-uniformity corresponding to the geometric boundary features of the geometric model, and divide the geometric model into multiple sub-regions based on the degree of stress distribution non-uniformity; For each sub-region, a physical information neural network embedding the elasticity mechanism equation is constructed based on the spatial frequency characteristics of the stress distribution within the sub-region, and the stress field sub-network model corresponding to each sub-region is trained. The spatial domain stress field data output by each sub-network model is transformed to the frequency domain, and a dynamic link of the stress field of different sub-regions is established in the frequency domain through the frequency domain bridging module. The stress field information in the dynamic link established in the frequency domain is inversely transformed to reconstruct the overall non-uniform stress field of the target complex component in the spatial domain. A variable-fidelity cascaded neural operator network is constructed, and multi-source stress field data with different sources and precisions are input into the variable-fidelity cascaded neural operator network step by step. The fidelity of the reconstructed overall non-uniform stress field is improved to obtain the final overall non-uniform stress field.

2. The method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging according to claim 1, characterized in that, Obtain the geometric model of the target complex component, identify the degree of stress distribution non-uniformity corresponding to the geometric boundary features of the geometric model, and divide the geometric model into multiple sub-regions based on the degree of stress distribution non-uniformity, specifically including: Obtain the geometric model of the target complex component, extract the geometric boundary features of the geometric model, and identify regions with drastic curvature changes, regions with abrupt feature changes, and smooth regions; Based on the identification results, the degree of non-uniformity of stress distribution in each region is analyzed. According to the degree of non-uniformity of stress distribution, the region with concentrated stress is independently divided into a separate sub-region, and the region with mild stress is merged or independently divided into a sub-region.

3. The method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging according to claim 1, characterized in that, Based on the spatial frequency characteristics of stress distribution within the sub-regions, a physical information neural network embedding the elasticity mechanism equations is constructed, and the stress field sub-network model corresponding to each sub-region is trained, specifically including: For sub-regions with gentle stress, a fully connected network with fewer layers and fewer neurons than a preset value is used, and the density of the first sampling point is set. For sub-regions with stress concentration, a physical information neural network fused with graph neural networks is used, and a second sampling point density is set; wherein, the second sampling point density is higher than the first sampling point density; The elasticity mechanism equation is embedded as a regularization term into the loss function of each physical information neural network. The stress field sub-network model corresponding to each sub-region is obtained by minimizing the loss function. The loss function is composed of data-driven terms and physical-driven terms, and the physical-driven terms are constructed by the embedded elasticity mechanism equation.

4. The method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging according to claim 1, characterized in that, The elasticity mechanism equations include equilibrium differential equations, geometric equations, constitutive equations, and deformation compatibility equations.

5. The method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging according to claim 1, characterized in that, The frequency domain bridging module employs a piecewise recursive graph Transformer network; it transforms the spatial domain stress field data output by each sub-network model to the frequency domain, and establishes dynamic links between stress fields in different sub-regions within the frequency domain through the frequency domain bridging module, specifically: The spatial domain stress field data is converted to the frequency domain by using the Fourier forward transform to obtain the spectral characteristics of the stress field in each sub-region. The spectral characteristics of the stress field in each sub-region are used as the input of the frequency domain bridging module. The attention mechanism of the frequency domain bridging module is used to learn and establish the dynamic correlation of stress characteristics between different sub-regions in different frequency bands. The frequency domain bridging module is jointly driven and trained by combining the working condition spectrum data of the target complex component and the multi-source stress field data. The stress field information in the dynamic link established in the frequency domain is inversely transformed. Specifically, the stress field information coupled by the dynamic link established in the frequency domain is transformed back to the spatial domain through inverse Fourier transform.

6. The method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging according to claim 1, characterized in that, The variable fidelity cascaded neural operator network includes multiple neural operator subnetworks cascaded sequentially, and each neural operator subnetwork corresponds to a fidelity level; The first-level neural operator subnetwork receives first-level fidelity stress field data for training and outputs first-level stress field prediction results. Subsequent neural operator subnetworks at each level sequentially receive the stress field prediction results output by the previous neural operator subnetwork, and perform fusion training by combining the stress field data of the corresponding fidelity level; The final level of the neural operator subnetwork outputs the final non-uniform stress field of the target complex component.

7. The method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging according to claim 6, characterized in that, In addition to the first-level neural operator subnetwork, subsequent levels of neural operator subnetworks are trained using a residual learning mechanism. The residual field between the stress field data corresponding to the current level and the stress field prediction result output by the previous level subnetwork is used as the learning target. Multi-source stress field data are adaptively fused through a confidence weighting strategy and an attention mechanism, while physical consistency constraints are applied.

8. The method for reconstructing the non-uniform stress field of complex components based on boundary segmentation and frequency domain bridging according to claim 6, characterized in that, The multi-source stress field data includes low-fidelity stress field data, medium-fidelity stress field data, and high-fidelity stress field data; The low-fidelity stress field data includes at least one of the following: simplified model coarse-grid finite element analysis results of the target complex component, empirical formula calculation results, and reduced-order model output results; the medium-fidelity stress field data includes at least one of the following: conventional mesh density finite element analysis results and local refined sub-model analysis results of key regions; the high-fidelity stress field data includes at least one of the following: fine-grid high-order element finite element calculation results, measured stress data, scaled-down model test verification data, and prototype measurement data.

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