Fourier-neuron-operator-based aircraft load case analysis method and system

Abstract

The application belongs to the technical field of aircraft load analysis, in order to solve the problem of inaccurate load analysis, an aircraft load working condition analysis method and system based on Fourier neural operator are proposed, the global internal force condition of the target section is integrated into the initial global section feature to obtain a global feature vector; according to the section geometry coding vector of the target section, the geometric correlation between the target section and each reference section is calculated to determine the geometric context vector of the target section; based on the global feature vector and the geometric context vector of the target section, the node-level stress prediction result of the target section of the aircraft structure is obtained by using the Fourier neural operator, and the load working condition dangerous priority ranking of the target section is obtained by combining the load working condition dangerous priority priori knowledge corrected by sparse high-fidelity data distillation, so that the accuracy and stability of the load analysis are improved while the high calculation efficiency is maintained.

Description

Technical Field

[0001] This invention belongs to the technical field of aircraft load analysis, and particularly relates to a method and system for aircraft load condition analysis based on Fourier neural operators. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In modern aircraft structural design, load case hazard priority assessment is a crucial step in structural optimization and safety margin design. Traditional load case analysis methods, such as the design point method, parametric analysis method, and load envelope method, are expensive in terms of time and manpower, and rely on manual experience in drawing and analysis. However, high-fidelity finite element method (FEM) calculations are costly and have a limited number of load cases, making it difficult to cover all potential load states in the early stages of structural iteration; while low-fidelity models, although computationally efficient, have insufficient accuracy and cannot directly guide the structural optimization of safety-sensitive parts.

[0004] Existing multifidelity learning methods primarily focus on mechanical response prediction or model calibration, rather than the quantification and ranking of load condition hazard priorities. Predicting the mechanical response of large-scale elements or nodes remains computationally complex and expensive in terms of time and cost. Furthermore, most methods rely on fixed meshes or regular domains, making them unsuitable for irregular node clouds and cross-scale configuration transfer problems in complex aircraft structures. Especially when there are significant differences in stress distribution across sections such as the wing and tail, traditional methods struggle to achieve effective transfer and unified modeling between different sections and locations. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention provides an aircraft load condition analysis method and system based on Fourier neural operators, which improves the accuracy and stability of load analysis while maintaining high computational efficiency.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides an aircraft load condition analysis method based on Fourier neural operators, including:

[0008] The geometric and stress information of the target cross section of the aircraft structure under different load conditions is encoded and the feature dimension is increased to obtain the initial global cross section features. The global internal force conditions of the target cross section are then incorporated into the initial global cross section features to obtain the global feature vector.

[0009] Based on the cross-sectional geometric coding vector of the target cross-section, calculate the geometric correlation between the target cross-section and each reference cross-section, and determine the geometric context vector of the target cross-section;

[0010] Based on the global feature vector and geometric context vector of the target section, the nodal stress prediction results of the target section of the aircraft structure are obtained by using Fourier neural operators. Based on the nodal stress prediction results of the target section, the load condition hazard priority ranking of the target section is obtained by combining the prior knowledge of load condition hazard priority corrected by sparse high-fidelity data distillation.

[0011] Secondly, the present invention provides an aircraft load condition analysis system based on Fourier neural operators, comprising:

[0012] The data feature encoding and dimensionality enhancement module is configured to: encode and enhance the geometric and stress information of the target cross section of the aircraft structure under different load conditions to obtain the initial global cross section features; and integrate the global internal force conditions of the target cross section into the initial global cross section features to obtain the global feature vector.

[0013] The geometry perception and context aggregation module is configured to: calculate the geometric correlation between the target cross section and each reference cross section based on the cross section geometry encoding vector of the target cross section, and determine the geometric context vector of the target cross section;

[0014] The Fourier neural operator module is configured to: based on the global feature vector and geometric context vector of the target section, use the Fourier neural operator to predict the nodal-level stress prediction results of the target section of the aircraft structure, and based on the nodal-level stress prediction results of the target section, combine the load condition hazard priority prior knowledge corrected by sparse high-fidelity data distillation to obtain the load condition hazard priority ranking of the target section.

[0015] Thirdly, the present invention provides an electronic device including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in the first aspect.

[0016] Fourthly, the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in the first aspect.

[0017] The above one or more technical solutions have the following beneficial effects:

[0018] In this invention, the geometric and stress information of the target cross section of the aircraft structure is encoded and its features are upgraded. The macroscopic global internal force conditions are integrated into the global cross-sectional stress characteristics, thus maintaining efficient feature expression capabilities even under geometrically irregular conditions. This provides a unified cross-scale description space for stress field prediction of complex structures. By quantitatively measuring the geometric similarity between different cross sections, the geometric perception and knowledge transfer capabilities of the model are significantly improved, enabling generalization of load condition prediction across cross sections and structural scales. The use of Fourier neural operators enables dynamic adjustment of frequency domain feature mapping, allowing the Fourier neural operators to adaptively adjust the response function under different structural scales and cross-sectional configurations. This improves the accuracy and stability of stress field prediction and load condition hazard ranking while maintaining high computational efficiency.

[0019] In this invention, local response accuracy is constrained by stress field prediction error, while global hazard priority consistency is constrained by Spearman ranking consistency loss. This joint optimization mechanism effectively resolves the conflict between stress accuracy and engineering ranking objectives, achieving a balance between interpretability and practicality of the model results.

[0020] In this invention, low-fidelity finite element method (FEM) results are corrected by distillation of sparse high-fidelity data, establishing a multi-fidelity prior knowledge framework. This enables the model to significantly improve the accuracy of identifying hazardous load conditions with limited high-precision samples, overcoming the problem of large deviations in traditional low-fidelity analysis results and achieving high-precision load risk assessment with low computational cost. This invention reduces the computational load of finite element methods and, combined with multi-fidelity distillation, reduces reliance on high-fidelity samples, significantly reducing computational costs while maintaining high accuracy, providing rapid load screening capabilities for the early stages of aircraft design.

[0021] In this invention, through the modular design of geometrically conditional neural operators, the model trained on the wing section can be quickly transferred to the horizontal tail or other structural parts, realizing a unified load evaluation framework between different configurations, and providing a scalable technical foundation for future intelligent, multi-configuration structural design.

[0022] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0024] Figure 1 This is a flowchart of the aircraft load condition analysis method based on Fourier neural operators in Embodiment 1 of the present invention. Detailed Implementation

[0025] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0026] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0027] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0028] Example 1

[0029] like Figure 1 As shown, this embodiment discloses an aircraft load condition analysis method based on Fourier neural operators, including:

[0030] The geometric and stress information of the target cross section of the aircraft structure under different load conditions is encoded and the feature dimension is increased to obtain the initial global cross section features. The global internal force conditions of the target cross section are then incorporated into the initial global cross section features to obtain the global feature vector.

[0031] Based on the cross-sectional geometric coding vector of the target cross-section, calculate the geometric correlation between the target cross-section and each reference cross-section, and determine the geometric context vector of the target cross-section;

[0032] Based on the global feature vector and geometric context vector of the target section, the nodal stress prediction results of the target section of the aircraft structure are obtained by using Fourier neural operators. Based on the nodal stress prediction results of the target section, the load condition hazard priority ranking of the target section is obtained by combining the prior knowledge of load condition hazard priority corrected by sparse high-fidelity data distillation.

[0033] The overall framework of this embodiment includes: prior knowledge construction, data preprocessing, data encoding and dimensionality enhancement, geometric encoding, geometric perception and context aggregation, Fourier neural operators, and multi-task learning and loss function design.

[0034] The following is a detailed description of each part involved in this embodiment:

[0035] In this embodiment, the prior knowledge aims to accurately define the hazard priority of load conditions for a specific cross-section, which is then used for subsequent neural operator learning. This involves defining the hazard priority of load conditions based on structural response, defining the hazard priority of load conditions based on high-dimensional envelope relationships, performing load condition analysis by fusing structural response and aerodynamic load data, and distilling correction of sparse high-fidelity data, ultimately realizing the construction of a prior knowledge system.

[0036] (1) Definition of hazard priority based on structural response.

[0037] This stage aims to establish a hazard index characterized by statistics showing that the stress of nodes or elements exceeds a threshold, using stress data output from the finite element model.

[0038] Let the stress distribution corresponding to the i-th load condition be... for:

[0039] (1)

[0040] Where N is the total number of load conditions and n is the number of structural units.

[0041] Define several sets of stress thresholds :

[0042] (2)

[0043] This corresponds to different levels of hazardous areas, such as material yield, fatigue limit, and crack initiation threshold. For each threshold... Count the number of units exceeding the threshold. :

[0044] (3)

[0045] in, This is an indicator function.

[0046] Set threshold weight coefficient vector Comprehensive stress characteristics It can be represented as:

[0047] (4)

[0048] This yields the overall hazard score for each load condition:

[0049] (5)

[0050] Where m refers to the number of elements in the threshold weight coefficient vector, i.e. the number of thresholds; the superscript T indicates transpose.

[0051] according to By sorting all load cases from largest to smallest, a load case hazard priority sequence based on structural response can be obtained. :

[0052] (6)

[0053] This method can quantify the degree of danger of a chemical condition from the perspective of structural response, providing response domain characteristics for subsequent multimodal fusion.

[0054] (2) Definition of working condition hazard priority based on high-dimensional envelope relationship.

[0055] Considering the multidimensional differences in aerodynamic loads and structural internal forces under different load conditions, let's define eight-dimensional mechanical parameters for each load condition. for:

[0056] (7)

[0057] in, It refers to the internal forces of the cross section in the three directions of x, y, and z. This refers to the cross-sectional moment in the x, y, and z directions; The resultant force and resultant moment correspond to a higher degree of sensitivity to the level of danger.

[0058] First, consider the i-th load condition. Perform normalization preprocessing:

[0059] (8)

[0060] Define the weight matrix :

[0061] (9)

[0062] Among them, corresponding The weight is relatively high, so it can be taken = = 0.3, and the remaining weights are adjusted according to the average percentage of the parameters.

[0063] The comparison rules based on high-dimensional dominance relations are as follows:

[0064] For any two load cases (i, j), if the following conditions are met:

[0065] (10)

[0066] Then, working condition (i) governs working condition (j), denoted as .

[0067] Therefore, the dominance matrix is ​​constructed:

[0068] (11)

[0069] Domination scores for each load condition are obtained by counting the number of dominations:

[0070] (12)

[0071] The final danger priority ranking sequence based on high-dimensional envelope relations is obtained as follows:

[0072] (13)

[0073] This method enables nonlinear dominance analysis under multidimensional load conditions, reflecting the potential danger level of each working condition under the global mechanical envelope. This refers to sorting in descending order.

[0074] (3) The structural response and aerodynamic load data are fused for working condition analysis, and the two methods are fused to obtain the final result.

[0075] To combine the advantages of the two sorting results, this embodiment designs a fusion algorithm based on the sorting consistency index.

[0076] Let the ranking result based on structural response be The sorting based on envelope relationship is After normalizing the calculation results according to formulas (5) and (12), the standardized scores are obtained respectively. and Define the ranking difference index:

[0077] (14)

[0078] in, This refers to the load case i based on the structural response ranking results. The sorting order within. This refers to the sorting results based on envelope relationships. The sorting order within.

[0079] The fusion weights are adaptively selected based on the magnitude of the difference. :

[0080] (15)

[0081] Final overall hazard score The calculation formula is:

[0082] (16)

[0083] Based on the final comprehensive risk score Arranged in descending order, the hazard priority sequence of the integrated working conditions is obtained. :

[0084] (17)

[0085] This process integrates stress field characteristics and load envelope characteristics, improving the robustness and physical consistency of load condition hazard assessment. This refers to sorting in descending order.

[0086] In practical engineering, high-fidelity finite element models can only obtain accurate structural response results for a small number of load conditions (e.g., only 12 out of 160 load conditions). To correct potential biases in low-fidelity finite element models, this embodiment introduces sparse high-fidelity data distillation to correct the results of low-fidelity models, thereby improving the reliability of hazardous condition identification.

[0087] Let the fused sorting obtained from the low-fidelity finite element model be The low-fidelity finite element model is a ranking obtained by fusing the above two methods: hazard priority based on structural response and hazard priority based on high-dimensional envelope relationships; let the accurate ranking obtained by the high-fidelity finite element model be... Since the stress field of the high-fidelity model is accurate, it is only necessary to use a hazard priority ranking method based on structural response to obtain an accurate ranking.

[0088] Minimize the sorting consistency error between the two using optimization algorithms (such as genetic algorithms or Bayesian optimization):

[0089] (18)

[0090] Where M represents the amount of high-fidelity data. This is a set of adjustable parameters in low-fidelity or sorting fusion models, used to adjust the behavior of low-fidelity sorting algorithms. It is the objective function (loss function) used for distillation correction of sparse high-fidelity data, measuring the inconsistency between low-fidelity and high-fidelity rankings. It is the fusion sorting in the low-fidelity finite element model . It is an accurate sorting obtained from a high-fidelity finite element model.

[0091] After optimization, the prior knowledge sorting will be updated. :

[0092] (19)

[0093] in, These are the optimal parameter values ​​obtained after optimization, that is, the... The smallest set of parameters. Further... The parameter set refers to the fusion weights when fusing the two methods mentioned above. By modulating the fusion weights within different ranges, the ranking results are altered to obtain the ranking result that best fits the high-fidelity model. This yields a corrected load condition hazard priority result, providing a high-precision prior supervision signal for the neural operator.

[0094] In this embodiment, all load case data of the foundation section are extracted in batches from the Hypermash result file for preprocessing. The extracted data includes geometric and field data: section node coordinates (x, y, z), node stress σ, and global load data: section internal forces (F). x , F y , F z M x M y M z ).

[0095] The extracted data undergoes preprocessing, specifically including:

[0096] Coordinate system standardization: The coordinates of all nodes in each section are transformed to a local coordinate system with the centroid of the section as the origin and the principal axes as the coordinate axes. This eliminates the influence of global position and orientation, allowing the model to focus on local geometry and stress characteristics.

[0097] (20)

[0098] in, Let i be the global coordinates. The coordinates of the centroid of the cross section are... Let be the rotation transformation matrix. These are the coordinates of node i after standardization.

[0099] Data normalization:

[0100] (1) Node coordinates: Min-Max scaling or standardization (subtract the mean, divide by the standard deviation) using the dimensions of each section.

[0101] (2) Nodal stress: Normalized according to cross section and working condition. Key point: For training stability, quantile normalization or direct normalization to [-1, 1] can be considered.

[0102] (twenty one)

[0103] in, Let be the normalized coordinates of node i; The coordinates of node i are the standardized coordinates; This is the mean of the coordinates of all nodes in the cross section; The standard deviation of the coordinates of all nodes in the cross section; This is the average stress at all nodes of the cross section; The standard deviation of the stress at all nodes of the cross section; The original stress at node i; This is the normalized value of the stress at node i.

[0104] (3) Internal forces in the cross section: This is a global conditional variable. Each component differs greatly (it must be scaled separately). Use the StandardScaler and save its parameters for inference.

[0105] (twenty two)

[0106] in, This refers to the standardized eight-dimensional mechanical parameters; It refers to the mean value of each mechanical parameter. This refers to the standard deviation of each mechanical parameter; It is a very small positive number, so we avoid dividing it by zero.

[0107] Sample construction (section-operating condition sample):

[0108] Form a dataset of standard input tuples:

[0109] (twenty three)

[0110] in, To standardize the node coordinate matrix, For the nodal stress tensor, This is the normalized internal force vector; This refers to the load condition number; This refers to the section number.

[0111] To address the challenge of effectively unifying the representation of node-level and cross-sectional features in the irregular meshes of complex aircraft structures, this embodiment constructs a multi-level feature encoding framework based on DGCNN and FiLM modulation. This framework achieves deep fusion of node coordinates, stress distribution, and macroscopic cross-sectional internal force features, thus maintaining efficient feature representation capabilities even under geometrically irregular conditions. This provides a unified cross-scale description space for stress field prediction of complex structures.

[0112] In this embodiment, the irregular node point cloud of the aircraft structural cross section is encoded into a global feature vector of fixed dimension to achieve a unified representation of geometric information, stress information and global internal force conditions, thereby providing efficient and generalizable feature input for downstream stress field prediction and load condition hazard ranking.

[0113] (1) Input and output definition.

[0114] Input 1: Node feature matrix , This refers to the feature dimension of a node. Each node contains normalized three-dimensional coordinates (x, y, z) and a stress vector. If the material properties of a node are known, it can also be added as an additional feature.

[0115] Input 2: Global condition vector , representing the normalized internal forces of the cross section, for example (F x , F y , F z M x M y M z ,F r M r ), where K refers to the dimension of the global condition vector.

[0116] Output 1: Node-level features , used for subsequent neural operator processing; This refers to the feature dimension of the output node.

[0117] Output 2: Global cross-sectional feature vector It is used for section-level representation and conditional fusion.

[0118] (2) Construction of irregular point cloud structure.

[0119] Treating the cross-section nodes as a graph structure, and using the k-nearest neighbor (KNN) method to define the features of each node. Find neighboring nodes:

[0120] (twenty four)

[0121] in, For nodes The set of neighboring nodes, The number of neighbors.

[0122] Edge features between nodes This is represented as a concatenation of neighborhood differences and central node features:

[0123] (25)

[0124] This edge feature can capture local geometric and stress variation relationships.

[0125] (3) Node feature encoding.

[0126] Node features are updated through multi-layer edge convolution (EdgeConv). Each convolution layer first learns edge features through a multi-layer perceptron (MLP), and then pools the neighborhood features.

[0127] (26)

[0128] By stacking convolutions layer by layer, the GNNEncoder model is able to capture multi-scale local structures and complex stress-geometric interactions between nodes.

[0129] This embodiment uses a stacked GNNEncoder model of three EdgeConv nodes to capture multi-scale local structures and complex stress-geometric interactions between nodes.

[0130] (4) Global cross-sectional feature aggregation.

[0131] To obtain a global representation of the cross-section, attention-weighted pooling is used to combine node-level features. Aggregate into a global vector :

[0132] (27)

[0133] in, For trainable attention vectors, The node weight is represented by the superscript T, which indicates transpose.

[0134] Attention mechanisms allow the GNNEncoder model to automatically learn which nodes contribute more to cross-sectional features, thereby improving its encoding expressive power.

[0135] (5) Global section internal force conditions injection and fusion.

[0136] Project the normalized internal force vector F onto the feature space:

[0137] (28)

[0138] in, This refers to the weight vector. It refers to the bias vector.

[0139] Two fusion strategies are provided here, which can be selected based on the training results:

[0140] Concatenation + MLP Fusion: First, geometric features and internal force features are concatenated, and then mapped to the global feature space through MLP. .

[0141] FiLM feature modulation: Scaling and offset coefficients are generated using internal forces to perform feature-level modulation of geometric features. The FiLM method can flexibly adjust the contribution of each feature dimension while preserving the original geometric information.

[0142] The final output includes node-level encoded features and cross-sectional global features.

[0143] In this embodiment, geometric coding is used to explicitly quantify the geometric differences between different cross sections. Geometric coding is constructed based on the coordinate information of all nodes in each cross section, providing geometric awareness and context aggregation capabilities for subsequent models. It is a key component for realizing cross-scale prediction difference quantification.

[0144] The node coordinate matrix is ​​converted to tensor format, and the dimensions are adjusted to [1, 3, number of nodes]. The geometric encoder consists of three concatenated edge convolutions, each layer of which sequentially includes edge convolution, batch normalization, and ReLU activation. The 3D coordinates are progressively enlarged to a 128-dimensional feature space. Global average pooling is then applied to the node features to generate a fixed-dimensional geometric encoding vector.

[0145] Geometric coding can effectively quantify cross-sectional geometric differences, and the generated geometric codes provide geometric context information for subsequent load condition prediction.

[0146] To address the challenges of significant differences in geometric morphology across different cross-sections, irregular node distribution, and difficulties in cross-configuration prediction in complex aircraft structures, this embodiment proposes a geometric perception context aggregation method based on an attention mechanism. This method can automatically learn the geometric similarity between cross-sections under multi-section conditions, constructing a learnable geometric knowledge base. It enables geometric perception and mechanical knowledge transfer for unseen cross-sections, thereby providing cross-section geometric condition functions for subsequent neural operators and improving the generalization ability of stress prediction and hazard ranking. Specifically, it includes:

[0147] (1) Geometric encoding extraction.

[0148] For any target cross section Extract its node coordinate data The cross-sectional geometric encoding vector is obtained through a geometric encoding network (such as DGCNN or GNN structure):

[0149] (29)

[0150] in, This represents a geometric encoder, with the input being the cross-section node coordinate matrix. The output is a geometric representation vector. This encoding process relies solely on geometry and does not involve load or stress information; it is used to characterize the inherent geometric features of the cross-section.

[0151] (2) Construct a geometric knowledge base.

[0152] During the overall model training phase, several typical cross-sections were selected. Composition of reference section set And extract the corresponding geometric code for each reference section. .

[0153] These encodings are mapped to key-value pairs (Key, Value) through a learnable linear transformation:

[0154] (30)

[0155] in, , This refers to the number of dimensions of the cross section. This refers to the feature dimension of the cross-section node. These are the trainable matrix parameters, used to generate the matching key and knowledge value, respectively.

[0156] This forms a learnable geometric knowledge base. :

[0157] (31)

[0158] Where M represents the number of cross sections.

[0159] This knowledge base stores the geometric features and mechanical semantics of various typical cross sections, providing a basis for subsequent geometric alignment and knowledge transfer.

[0160] (3) Attention-based geometric similarity measure.

[0161] Target cross section Geometric encoding Projection as query vector :

[0162] (32)

[0163] in, It is a trainable matrix.

[0164] The geometric correlation between the target section and the reference section is calculated using Scaled Dot-Product Attention:

[0165] (33)

[0166] Attention weights are obtained after normalization. :

[0167] (34)

[0168] in, Reflecting the target cross section With the The similarity of reference sections in geometric feature space. The larger the value, the closer the geometry and potential mechanical behavior of the two are.

[0169] (4) Geometric context aggregation.

[0170] Based on attention weight For the feature vectors of all reference sections in the knowledge base By performing a weighted summation, we obtain the geometric context vector c of the target cross-section:

[0171] (35)

[0172] The geometric context vector c can be viewed as the geometric and mechanical prior information most relevant to the target cross section, automatically retrieved and fused from the knowledge base. It reflects the "analogous object" of the target cross section in a mechanical sense, that is, "how to process the current input according to the behavior rules of a known cross section".

[0173] (5) Conditionalized neural operators.

[0174] The geometric context vector c is input as a geometric condition function into the subsequent Fourier neural operator, modulating the feature mapping process inside the Fourier neural operator.

[0175] Conditional injection is achieved through feature-wise linear modulation (FiLM):

[0176] (36)

[0177] in, and Generated from the geometric context vector c via an MLP network. This represents the intermediate feature tensor within the neural operator layer. This approach can adaptively adjust the mapping rules according to the geometric context of different cross-sections without changing the main structure of the operator, thus achieving cross-section generalization.

[0178] In this embodiment, a continuous stress field prediction operator for cross-sectional structures is established using Fourier neural operators, which can directly predict the nodal-level stress response after inputting finite nodal features. Based on the spectral domain feature modeling capability of the Fourier Neural Operator (FNO), combined with the conditional vector output from the aforementioned geometrically aware context aggregation step, adaptive adjustment to different cross-sectional geometric features is achieved, thereby maintaining high accuracy and strong generalization ability in multi-structure and multi-scale scenarios.

[0179] The global cross-sectional feature vector obtained by the Fourier neural operator receiving data feature encoding and dimensionality increase step As input It accepts the geometrically conditionalized vector c.

[0180] In each spectral domain mapping layer, the operator performs the following steps:

[0181] (1) Fourier transform:

[0182] (37)

[0183] in, For frequency coordinates, This represents the Fourier transform.

[0184] (2) Spectral domain weighting:

[0185] Keep only the previous one A low-frequency mode is used to control the computational load, and a learnable weighting matrix is ​​applied to it. :

[0186] (38)

[0187] (3) Inverse Fourier Transform:

[0188] (39)

[0189] in, This represents the inverse Fourier transform.

[0190] (4) Residual fusion and conditional modulation:

[0191] (40)

[0192] Through this operation, while maintaining the advantages of spectral domain modeling, the operator uses the FiLM method to modulate the geometrically conditional vector c onto the weights and biases of each layer, achieving adaptive adjustment to the geometric context, thereby maintaining stable prediction performance under different cross sections and structural scales.

[0193] This embodiment proposes a multi-layer conditional embedding strategy to enhance the model's expressive power on complex structures, namely, introducing an independent FiLM module in each spectral domain layer of FNO:

[0194] (41)

[0195] in, and The two symbols represent two learnable parameters in the FiLM module, used to scale and shift the features, respectively. This is the weight matrix for the t-th layer, used for feature transformation. This design allows features at different levels to be influenced by the geometric context to varying degrees: low-level features focus on adjusting local node deformation; mid-level features are responsible for the overall influence of the cross-sectional macro-geometry; and high-level features focus on cross-sectional migration and mechanical consistency. This hierarchical conditional modulation mechanism effectively enhances the model's interpretability and cross-domain transfer performance.

[0196] (5) Output mapping and prediction results:

[0197] (42)

[0198] in, It is the dimension of the last layer of hidden features. This refers to the weight matrix of the output layer. This refers to the bias term of the output layer. This refers to the hidden features of the last layer. These are the predicted values ​​for node-level stress. Eight-dimensional stress components corresponding to the cross-section nodes .

[0199] This embodiment of hazardous load identification and dual-objective optimization aims to simultaneously optimize the accuracy of nodal-level stress field prediction and the consistency of load condition hazard ranking, thereby achieving high-precision identification and intelligent ranking of structural responses under complex flight load conditions. Based on the stress field predicted by the Fourier neural operator, a dual-objective loss function is constructed by introducing a hazard priority definition based on structural response, balancing prediction accuracy and engineering interpretability.

[0200] The dual-objective loss function includes a stress field prediction error term. Consistency loss term with sorting .

[0201] (1) Stress field prediction loss The difference between the predicted node stress and the actual stress in the finite element method used to constrain the output of the neural operator.

[0202] Depending on the data characteristics, mean squared error (MSE) or Huber Loss, which is more robust to outliers, can be used:

[0203] (43)

[0204] in, This refers to the predicted stress value. This refers to the actual stress value. , is the Huber threshold constant. It is the unit code for the i-th working condition of a cross section.

[0205] (2) Order consistency loss : Ranking loss based on Spearman correlation coefficient.

[0206] Directly minimize the Spearman correlation (i.e., ranking consistency) difference:

[0207] (44)

[0208] in, This refers to the Spearman coefficient calculation function. It refers to the ranking result obtained from prior knowledge. This refers to the ranking result predicted by the neural operator.

[0209] (45)

[0210] in, The first The ranking of each working condition in the prior ranking and the predicted ranking. When the predicted order is exactly the same as the actual order, it means that the predicted order is completely consistent with the actual order. The result obtained by the Fourier neural operator is the predicted stress value of each node. The predicted stress value is substituted into the danger priority ranking method based on structural response in step 2 to obtain the predicted order.

[0211] (3) Total loss function :

[0212] (46)

[0213] in The balancing coefficient is dynamically adjusted based on the task weights. This loss function achieves the unification of stress prediction and task-oriented objectives by simultaneously optimizing "local stress accuracy" and "global hazard ranking consistency".

[0214] This embodiment introduces a geometric perception and context aggregation mechanism, and achieves adaptive learning of geometric differences through a sparse cross-section knowledge base and dynamic adjustment of attention weights. It combines Fourier neural operator (FNO) to reduce complexity, and designs a joint loss function to balance stress field accuracy and hazard ranking consistency, thereby achieving high-precision prediction and hazard assessment across scales and cross sections.

[0215] This embodiment corrects low-fidelity finite element results by distilling sparse high-fidelity data and establishes a multi-fidelity prior knowledge framework. This enables the model to significantly improve the accuracy of identifying dangerous load conditions with limited high-precision samples, overcomes the problem of large deviations in traditional low-fidelity analysis results, and achieves high-precision load risk assessment with low computational cost.

[0216] This embodiment utilizes a fusion strategy of Graph Neural Network (DGCNN) and Feature Modulation (FiLM) to achieve unified encoding of node-level local stress features and macroscopic cross-sectional internal force features. This design breaks through the limitations of traditional finite element modeling that relies on regular meshes, enabling the model to directly handle irregular nodes in complex structures such as wings and horizontal stabilizers. It achieves end-to-end learning of cross-sectional structural responses and supports unified representation and cross-sectional modeling of complex irregular structures.

[0217] This embodiment establishes a learnable geometric knowledge base and introduces an attention mechanism, enabling the quantitative measurement of geometric similarity between different cross sections and adaptively generating geometric context vectors as conditional inputs. This mechanism significantly enhances the model's geometric perception and knowledge transfer capabilities, achieving generalized load condition prediction across cross sections and structural scales.

[0218] In this embodiment, the geometric context vector is embedded into the Fourier neural operator through the FiLM module to achieve dynamic adjustment of the frequency domain feature mapping. This enables the operator to adaptively adjust the response function under different structural scales and cross-sectional configurations, thereby improving the accuracy and stability of stress field prediction while maintaining high computational efficiency.

[0219] This embodiment designs a dual-objective loss function: constraining local response accuracy with stress field prediction error (MSE / Huber) and constraining global hazard priority consistency with Spearman ranking consistency loss. This joint optimization mechanism effectively resolves the objective conflict between "stress accuracy" and "engineering ranking," achieving a balance between the interpretability and practicality of the model results.

[0220] By using frequency domain convolution and low-mode truncation with Fourier neural operators, this embodiment reduces the computational complexity of traditional finite element methods from... Down to By combining multi-fidelity distillation to reduce reliance on high-fidelity samples, computational costs are significantly reduced while maintaining high accuracy, providing rapid load screening capabilities for the early stages of aircraft design.

[0221] This embodiment, through the modular design of geometrically conditional neural operators, enables models trained on wing sections to be quickly transferred to horizontal stabilizers or other structural parts, realizing a unified load evaluation framework across different configurations and providing a scalable technical foundation for future intelligent, multi-configuration structural design.

[0222] Example 2

[0223] The purpose of this embodiment is to provide an aircraft load condition analysis system based on Fourier neural operators, including:

[0224] The data feature encoding and dimensionality enhancement module is configured to: encode and enhance the geometric and stress information of the target cross section of the aircraft structure under different load conditions to obtain the initial global cross section features; and integrate the global internal force conditions of the target cross section into the initial global cross section features to obtain the global feature vector.

[0225] The geometry perception and context aggregation module is configured to: calculate the geometric correlation between the target cross section and each reference cross section based on the cross section geometry encoding vector of the target cross section, and determine the geometric context vector of the target cross section;

[0226] The Fourier neural operator module is configured to: based on the global feature vector and geometric context vector of the target section, use the Fourier neural operator to predict the nodal-level stress prediction results of the target section of the aircraft structure, and based on the nodal-level stress prediction results of the target section, combine the load condition hazard priority prior knowledge corrected by sparse high-fidelity data distillation to obtain the load condition hazard priority ranking of the target section.

[0227] In further embodiments, the following is also provided:

[0228] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When executed by the processor, the computer instructions perform the method described in Embodiment 1. For brevity, further details are omitted here.

[0229] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0230] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.

[0231] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in Embodiment 1.

[0232] The method in Embodiment 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0233] A computer program product includes a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0234] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer-executable instructions, such as instructions included in program modules, which execute in a device on a target real or virtual processor to perform the processes / methods described above. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc., that perform specific tasks or implement specific abstract data types. In various embodiments, the functionality of program modules can be combined or divided among program modules as needed. The machine-executable instructions for the program modules can execute within a local or distributed device. In a distributed device, the program modules can reside in both local and remote storage media.

[0235] The computer program code used to implement the methods of the present invention may be written in one or more programming languages. This computer program code may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the computer or other programmable data processing device, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a computer, partially on a computer, as a stand-alone software package, partially on a computer and partially on a remote computer, or entirely on a remote computer or server.

[0236] In the context of this invention, computer program code or related data may be carried by any suitable carrier to enable a device, apparatus, or processor to perform the various processes and operations described above. Examples of carriers include signals, computer-readable media, and the like. Examples of signals may include electrical, optical, radio, sound, or other forms of propagation signals, such as carrier waves, infrared signals, etc.

[0237] Those skilled in the art will recognize that the units and algorithm steps described in conjunction with the embodiments herein can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0238] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. An aircraft load condition analysis method based on Fourier neural operators, characterized in that, include: The geometric and stress information of the target cross section of the aircraft structure under different load conditions is encoded and the feature dimension is increased. The nodes of the target cross section are regarded as a graph structure, the edge features between nodes are determined, and the node features are updated by multi-layer edge convolution to obtain the node features. Attention-based weighted pooling is used to aggregate node-level features into initial global cross-sectional features, and the global stress conditions of the target cross-section are incorporated into the initial global cross-sectional features to obtain a global feature vector. Based on the cross-sectional geometric coding vector of the target cross-section, calculate the geometric correlation between the target cross-section and each reference cross-section, and determine the geometric context vector of the target cross-section; In each spectral domain mapping layer, the global feature vector of the target cross section is subjected to Fourier transform, followed by spectral domain weighting and inverse Fourier transform. The global feature vector and the result of the inverse Fourier transform are fused by residual, and conditional modulation is performed based on the geometric context vector of the target section to obtain the node-level stress prediction result of the target section of the aircraft structure; wherein, the stress field prediction loss function and the ranking consistency loss function are used as the loss functions for training the Fourier neural operator. The order consistency loss function is: ； in, This refers to the Spearman coefficient calculation function. This refers to the load condition hazard priority ranking result obtained from prior knowledge of load condition hazard priority after distillation correction using sparse high-fidelity data. This refers to the ranking result predicted by the neural operator.

2. The aircraft load condition analysis method based on Fourier neural operators as described in claim 1, characterized in that, The geometric and stress information of the aircraft structural target section under different load conditions is encoded and its features are upgraded to obtain initial global section features. The global stress conditions of the target section are then integrated into the global section stress features to obtain a global feature vector, specifically: Treat the target cross-section nodes as a graph structure, determine the edge features between nodes, and update the node features through multi-layer edge convolution to obtain the node features; Attention-based weighted pooling is used to aggregate node-level features into initial global cross-sectional features; The global stress conditions are projected onto the feature space to obtain the global section stress characteristics; The global cross-sectional features and global cross-sectional stress features are fused to obtain the global feature vector.

3. The aircraft load condition analysis method based on Fourier neural operators as described in claim 1, characterized in that, Based on the cross-sectional geometric encoding vector of the target cross-section, the geometric correlation between the target cross-section and the reference cross-section is calculated, and the geometric context vector of the target cross-section is determined, specifically as follows: Based on the cross-sectional geometric encoding vector of the target cross section, the geometric correlation between the target cross section and the reference cross section is calculated by scaling dot product attention, thereby determining the similarity between the target cross section and different reference cross sections in the geometric feature space; The geometric context vector of the target cross section is obtained by weighted summation of the feature vectors of all reference cross sections based on the calculated similarity.

4. The aircraft load condition analysis method based on Fourier neural operators as described in claim 1, characterized in that, The prior knowledge of load condition hazard priority, corrected by distillation of sparse high-fidelity data, is constructed as follows: The algorithm minimizes the consistency error between the load condition hazard priority ranking obtained from the low-fidelity simulation model and the load condition hazard priority ranking obtained from the high-fidelity simulation model. Based on the optimization results, the load condition hazard priority ranking results obtained from the low-fidelity simulation model are updated to obtain the corrected load condition hazard priority prior knowledge.

5. The aircraft load condition analysis method based on Fourier neural operators as described in claim 4, characterized in that, The load condition hazard priority ranking obtained from the low-fidelity simulation model is as follows: Based on the stress distribution corresponding to each load condition and several preset stress thresholds, the number of nodes or elements exceeding each stress threshold is counted to determine the comprehensive hazard score of each load condition. The comprehensive hazard scores of each load condition are then sorted to obtain a load condition hazard priority sequence based on structural response. Based on the mechanical parameters corresponding to each load condition, and based on the dominance relationship between any two load conditions, a dominance matrix is ​​constructed. The dominance count is counted to obtain the dominance score of each load condition. Based on the dominance score of each load condition, a load condition danger priority ranking sequence based on high-dimensional envelope relationship is obtained. By fusing the load condition hazard priority sequence based on structural response and the load condition hazard priority ranking sequence based on high-dimensional envelope relationship, the final load condition hazard priority ranking sequence is obtained.

6. An aircraft load condition analysis system based on Fourier neural operators, characterized in that, include: The data feature encoding and dimensionality enhancement module is configured to: encode and enhance the geometric and stress information of the target cross section of the aircraft structure under different load conditions; treat the nodes of the target cross section as a graph structure; determine the edge features between nodes; and update the node features through multi-layer edge convolution to obtain the node features. Attention-based weighted pooling is used to aggregate node-level features into initial global cross-sectional features, and the global stress conditions of the target cross-section are incorporated into the initial global cross-sectional features to obtain a global feature vector. The geometry perception and context aggregation module is configured to: calculate the geometric correlation between the target cross section and each reference cross section based on the cross section geometry encoding vector of the target cross section, and determine the geometric context vector of the target cross section; The Fourier neural operator module is configured to perform a Fourier transform on the global feature vector of the target cross section in each spectral domain mapping layer, followed by spectral domain weighting and inverse Fourier transform. The global feature vector and the result of the inverse Fourier transform are fused by residual, and conditional modulation is performed based on the geometric context vector of the target section to obtain the node-level stress prediction result of the target section of the aircraft structure; wherein, the stress field prediction loss function and the ranking consistency loss function are used as the loss functions for training the Fourier neural operator. The order consistency loss function is: ； in, This refers to the Spearman coefficient calculation function. This refers to the load condition hazard priority ranking result obtained from prior knowledge of load condition hazard priority after distillation correction using sparse high-fidelity data. This refers to the ranking result predicted by the neural operator.

7. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the method according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, perform the method described in any one of claims 1-5.

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