Method for predicting multi-axial fatigue life of welded structure based on differentiable interface search

Abstract

The application discloses a welding structure multi-axial fatigue life prediction method based on a differentiable critical surface search, and belongs to the technical field of fatigue life evaluation of aero-engine welding components. Multi-axial stress-strain time history data, material attribute data and weld geometry feature data of a dangerous point of a welding structure are acquired; a deep neural network model containing a differentiable critical surface search module is constructed to output a critical surface unit normal vector; the stress-strain tensor is differentially projected based on the unit normal vector to obtain normal stress, shear stress, normal strain and engineering shear strain time sequence characteristics; the time sequence characteristics are input into a sequence coding network to generate a damage feature vector, which is fused with material attributes and weld geometry features to predict fatigue life; a composite loss function is formed by a data error term and a multi-axial fatigue criterion physical constraint term to synchronously optimize the critical surface search module and the life prediction network. The application can improve the accuracy and physical consistency of fatigue life prediction under non-proportional multi-axial load.

Description

Technical Field

[0001] This invention relates to the field of fatigue life assessment and health monitoring technology for key components of aero-engines, and in particular to a method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search. Background Technology

[0002] Welded connections are common in critical components of aero-engines, such as integral bladed disks and casings. These welded structures typically endure high temperatures, high pressures, high speeds, and thermo-mechanical coupled loads during service. The stress and strain states at critical points exhibit significant multiaxial and non-proportional characteristics. Under non-proportional multiaxial loads, the principal stress axis directions, stress component ratios, and shear strain amplitudes change over time, making the fatigue damage accumulation process more complex than under uniaxial or proportional multiaxial loads. Accurate prediction of the fatigue life of welded structures is crucial for the safe service of critical aero-engine components.

[0003] Existing multiaxial fatigue life prediction methods typically include physical criterion methods based on critical surfaces, engineering assessment methods based on equivalent stress or structural stress, and data-driven prediction methods. Critical surface methods based on the Fatemi-Socie criterion can reflect fatigue damage factors such as shear strain and normal stress, but they usually require manual pre-setting, traversal searching, or offline calculation of the critical surface. The critical surface determination process is separated from the life prediction model, making it difficult to adaptively optimize based on specific load history during model training. Engineering assessment methods based on equivalent stress, SN curves, or damage accumulation are suitable for some engineering scenarios, but their comprehensive characterization ability for complex non-proportional load paths, material property differences, and weld geometry is limited. Data-driven methods based on deep learning can fit complex load-life relationships, but without the constraint of multiaxial fatigue damage criteria, they are prone to problems such as insufficient physical interpretation and unstable generalization ability under non-training conditions.

[0004] Furthermore, the fatigue behavior of welded structures is not only affected by multiaxial stress-strain time histories, but also by weld geometry features such as material properties, weld toe radius, weld toe angle, and plate thickness. Existing methods often struggle to unify critical surface search, stress-strain tensor projection, non-proportional load path memory feature extraction, material and weld geometry fusion, and physical criterion constraints into a predictive framework that can be trained end-to-end.

[0005] Existing technical solutions (such as CN202510142525.7) attempt to introduce physical information into neural networks, but their use of attention mechanisms to weight different features still fails to solve the problem of automatic search and localization of the critical surface during model training. Another prediction scheme for welded structures (CN202510753768.4) combines a physical model with support vector regression, but it is not an end-to-end deep learning method and does not involve differentiable critical surface search. Therefore, there is an urgent need for a method that can embed the critical surface search process into a neural network and optimize it end-to-end in a differentiable manner. Summary of the Invention

[0006] The purpose of this invention is to provide a multiaxial fatigue life prediction method for welded structures based on differentiable critical surface search, which addresses the problems of separation between critical surface search and life prediction processes, insufficient physical consistency of purely data-driven models, and inadequate utilization of the geometric features of welded structures in existing multiaxial fatigue life prediction methods. This method constructs the critical surface search process as a differentiable parameter learning task in a deep neural network, enabling the critical surface direction to be optimized synchronously with the life prediction network during model training, and incorporating multiaxial fatigue damage criteria to physically constrain the prediction results.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search includes the following steps:

[0009] Step S1: Obtain multiaxial stress-strain time history data, material property data, and weld geometric feature data of the predicted critical points in the welded structure to construct an initial dataset;

[0010] Step S2: Construct a deep neural network model that includes a differentiable critical surface search module. The differentiable critical surface search module is a parameterized subnetwork and outputs a unit normal vector parameter representing the maximum fatigue damage plane.

[0011] Step S3: Based on the unit normal vector parameter, perform differentiable projection on the stress tensor and strain tensor in the multiaxial stress-strain time history data to obtain the normal stress time sequence, shear stress time sequence, normal strain time sequence and engineering shear strain time sequence on the critical surface.

[0012] Step S4: Input the program sequence for normal stress, shear stress, normal strain, and engineering shear strain into the sequence feature encoding network to generate a damage feature vector containing non-proportional load path memory.

[0013] Step S5: Fuse the damage feature vector with the material property data and weld geometric feature data, and predict the fatigue life of the predicted critical point of the welded structure based on the fused feature vector;

[0014] Step S6: Train the deep neural network model using a composite loss function that includes a data-driven prediction error term and a multi-axis fatigue criterion physical constraint term. The differentiable critical surface search module is optimized synchronously with the life prediction network.

[0015] Furthermore, the differentiable critical surface search module in step S2 is a fully connected network that receives the vector extracted from the multiaxial stress-strain time history data through statistical features as input, and outputs spherical coordinate angle parameters θ and φ representing the direction of the critical surface after being mapped by an activation function; the unit normal vector n is determined by θ and φ.

[0016] Furthermore, the sequence feature encoding network mentioned in step S4 is a long short-term memory network, a bidirectional long short-term memory network, a gated recurrent unit, a temporal convolutional network, or a Transformer.

[0017] Furthermore, the fusion described in step S5 is a vector concatenation operation; the damage feature vector, the vector obtained after normalizing the material property data, and the vector obtained after normalizing the weld geometric feature data are concatenated into a combined feature vector, which is then input into the subsequent fully connected layer for lifetime prediction.

[0018] Furthermore, the deep neural network model is optimized using a composite loss function during training. The composite loss function includes a data-driven prediction error term and a physical constraint term constructed based on a multi-axis fatigue damage criterion. The physical constraint term is used to ensure physical consistency between the fatigue life predicted by the model and the damage parameters calculated by the multi-axis fatigue damage criterion.

[0019] Furthermore, the composite loss function is expressed as:

[0020] ;

[0021] in, This is the fatigue life vector predicted by the model. This represents the true fatigue life vector. This is the equivalent fatigue life vector calculated based on the multiaxial fatigue damage criterion. To balance hyperparameters, This represents the mean square error.

[0022] Furthermore, the multiaxial fatigue damage criterion is the Fatemi-Socie criterion; the equivalent fatigue life... The following equations are obtained by solving them using differentiable numerical methods:

[0023]

[0024] in For Fatemi-Socie multiaxial fatigue damage parameters, This represents the range of maximum shear strain on the critical surface. This represents the maximum normal stress on that plane. For the material's yield strength, For material constants, The fatigue strength coefficient, The fatigue ductility coefficient, The fatigue strength index, The fatigue ductility index, It is the elastic modulus.

[0025] Furthermore, the weld geometry data mentioned in step S1 includes weld toe radius, weld toe angle, and plate thickness.

[0026] Furthermore, the welded structure is a welded component for an aero-engine. Furthermore, during the training of the deep neural network model in step S6, the gradient of the composite loss function is transmitted to the differentiable critical surface search module via the differentiable projection, simultaneously updating the unit normal vector parameters and the weight parameters of the lifetime prediction network.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) The multiaxial fatigue life prediction method for welded structures based on differentiable critical surface search provided by this invention transforms the critical surface search process, which requires manual pre-setting or offline calculation in traditional multiaxial fatigue theory, into a differentiable parameterized subnetwork in a deep neural network. This subnetwork can automatically locate the maximum damage plane under the current load history and welded structure characteristics by updating the weights synchronously with the main network through the gradient descent algorithm during model training. This mechanism differs from the existing paradigm of "fixed pre-setting" or "external calculation" of the critical surface, enabling the fatigue prediction model to have end-to-end adaptive capability for non-proportional loads.

[0029] (2) The multiaxial fatigue life prediction method for welded structures based on differentiable critical surface search provided by this invention organically combines a sequence feature encoding network with a composite physical loss function based on multiaxial fatigue criteria. On the one hand, the sequence encoding network can effectively capture the load path dependence and temporal memory effect during non-proportional loading; on the other hand, the physical loss function forces the model prediction results to be consistent with the classical multiaxial fatigue damage theory, avoiding physically unreasonable prediction outliers that may occur in a purely data-driven model. This dual mechanism enables the model to possess both the powerful expressive power of deep learning and good physical interpretability and generalization ability.

[0030] (3) The multiaxial fatigue life prediction method for welded structures based on differentiable critical surface search provided by this invention integrates the above-mentioned innovative method with the unique geometric features of welded structures, and is specifically optimized for fatigue prediction of welded joints of aero-engines under non-proportional multiaxial loads. Compared with existing multiaxial fatigue prediction methods for standard material specimens, this invention can more realistically reflect the fatigue behavior of welded structures in actual service environments, and provides a practical and feasible technical solution for intelligent health monitoring of key components of aero-engines. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the overall implementation of the multiaxial fatigue life prediction method for welded structures based on differentiable critical surface search proposed in this invention.

[0032] Figure 2 This is a schematic diagram of the deep neural network model of the multiaxial fatigue life prediction method for welded structures based on differentiable critical surface search proposed in this invention.

[0033] Figure 3 This is a scatter plot comparing the predicted and actual lifes of the multiaxial fatigue life prediction method for welded structures based on differentiable critical surface search proposed in this invention with the FS criterion.

[0034] Figure 4 This is a bar chart comparing the prediction error indices of the multiaxial fatigue life prediction method for welded structures based on differentiable critical surface search proposed in this invention with the FS criterion. Detailed Implementation

[0035] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0036] This embodiment uses the prediction of fatigue life of a critical weld on an integral bladed disk of a certain type of aero-engine as an example to illustrate the implementation process of the present invention in detail. The bladed disk is made of nickel-based superalloy GH4169, and the weld area is subjected to complex non-proportional multiaxial thermo-mechanical coupled loads during service.

[0037] A method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search includes the following steps:

[0038] Step S1: Obtain multiaxial stress-strain time history data, material property data, and weld geometric feature data of the dangerous points to be predicted in the welded structure, and construct an initial dataset;

[0039] Step S2: Construct a deep neural network model that includes a differentiable critical surface search module. The differentiable critical surface search module is a parameterized subnetwork and outputs a unit normal vector parameter representing the maximum fatigue damage plane.

[0040] Step S3: Based on the unit normal vector parameter, perform differentiable projection on the stress tensor and strain tensor in the multiaxial stress-strain time history data to obtain the normal stress time sequence, shear stress time sequence, normal strain time sequence and engineering shear strain time sequence on the critical surface.

[0041] Step S4: Input the program sequence for normal stress, shear stress, normal strain, and engineering shear strain into the sequence feature encoding network to generate a damage feature vector containing non-proportional load path memory.

[0042] Step S5: Fuse the damage feature vector with the material property data and weld geometric feature data, and predict the fatigue life of the predicted critical point of the welded structure based on the fused feature vector;

[0043] Step S6: Train the deep neural network model using a composite loss function that includes a data-driven prediction error term and a multi-axis fatigue criterion physical constraint term. The differentiable critical surface search module is optimized synchronously with the life prediction network.

[0044] Furthermore, the differentiable critical surface search module in step S2 is a fully connected network that receives the vector extracted from the multiaxial stress-strain time history data through statistical features as input, and outputs spherical coordinate angle parameters θ and φ representing the direction of the critical surface after being mapped by an activation function; the unit normal vector n is determined by θ and φ.

[0045] Furthermore, the sequence feature encoding network mentioned in step S4 is a long short-term memory network, a bidirectional long short-term memory network, a gated recurrent unit, a temporal convolutional network, or a Transformer.

[0046] Furthermore, the fusion described in step S5 is a vector concatenation operation; the damage feature vector, the vector obtained after normalizing the material property data, and the vector obtained after normalizing the weld geometric feature data are concatenated into a combined feature vector, which is then input into the subsequent fully connected layer for lifetime prediction.

[0047] Furthermore, the deep neural network model is optimized using a composite loss function during training. The composite loss function includes a data-driven prediction error term and a physical constraint term constructed based on a multi-axis fatigue damage criterion. The physical constraint term is used to ensure physical consistency between the fatigue life predicted by the model and the damage parameters calculated by the multi-axis fatigue damage criterion.

[0048] Furthermore, the composite loss function is expressed as:

[0049] ;

[0050] in, This is the fatigue life vector predicted by the model. This represents the true fatigue life vector. This is the equivalent fatigue life vector calculated based on the multiaxial fatigue damage criterion. To balance hyperparameters, This represents the mean square error.

[0051] Furthermore, the multiaxial fatigue damage criterion is the Fatemi-Socie criterion; the equivalent fatigue life... The following equations are obtained by solving them using differentiable numerical methods:

[0052]

[0053] in For Fatemi-Socie multiaxial fatigue damage parameters, This represents the range of maximum shear strain on the critical surface. This represents the maximum normal stress on that plane. For the material's yield strength, For material constants, The fatigue strength coefficient, The fatigue ductility coefficient, The fatigue strength index, The fatigue ductility index, It is the elastic modulus.

[0054] Furthermore, the weld geometry data mentioned in step S1 includes weld toe radius, weld toe angle, and plate thickness.

[0055] Furthermore, the welded structure is a welded component for an aero-engine. Furthermore, during the training of the deep neural network model in step S6, the gradient of the composite loss function is transmitted to the differentiable critical surface search module via the differentiable projection, simultaneously updating the unit normal vector parameters and the weight parameters of the lifetime prediction network.

[0056] like Figure 1 As shown, the specific steps of the present invention are as follows:

[0057] Step S1: Construct the initial dataset.

[0058] From the finite element simulation results of this type of engine, stress-strain tensor time history data of critical weld nodes within a complete takeoff and landing cycle were extracted. A complete cycle was sampled at equal time intervals. Each time step records the stress and strain tensors. The stress components are... The strain components are ,in Represents the normal stress component. Represents the shear stress components. Represents the normal strain component. Represents the shear strain components. There are three coordinate axes. Therefore, the stress time history data of each sample has a dimension of 100×6, and the strain time history data also has a dimension of 100×6.

[0059] Simultaneously, acquire the material's property data at this service temperature, specifically the elastic modulus. Yield strength ,tensile strength Material constants fatigue strength coefficient fatigue ductility coefficient Fatigue strength index and fatigue ductility index .

[0060] Obtain weld geometry data, including: weld toe radius. weld toe angle , plate thickness .

[0061] Finally, the actual fatigue life of the critical point is obtained through testing or simulation. This was used as the training label. In this embodiment, a total of 150 samples were collected under different non-proportional loading paths, of which 120 were used as the training set and the remaining 30 as the test set. Each sample's... Distribution 8.2×10 3 Up to 2.7×10 6 Between loops.

[0062] Step S2: Construct a deep neural network model that includes a differentiable critical surface search module.

[0063] like Figure 2 As shown, a complete deep neural network model is constructed. The structure of the differentiable critical surface search module is as follows: the input layer receives data on the entire... Stress time program list and The 12-dimensional statistical feature vector is obtained by concatenating the program sequences after global average pooling during strain testing; the hidden layer contains 32 neurons and uses the ReLU activation function; the output layer contains 2 neurons, which are processed by... After activation function processing, the azimuth angle is linearly mapped to the spherical coordinate system. and polar angle These two angles uniquely determine a unit spatial normal vector. The plane defined by this normal vector is the critical surface found by the model search.

[0064] During the initial training iteration, the weight parameters of this sub-network are randomly initialized. In subsequent backpropagation stages, the gradient of the total loss function is propagated to this sub-network via the differentiable projection operation described in step S3, causing its output to... and The parameters are continuously optimized and eventually converge to the critical surface direction that maximizes the prediction of fatigue damage.

[0065] Step S3: Analyze stress data based on critical surface normal vector parameters.

[0066] Using the spherical coordinate parameters output in step S2 Construct the unit normal vector of the critical surface .

[0067] For the danger point at any time Stress tensor:

[0068]

[0069] Strain tensor:

[0070]

[0071] The projection is analyzed through the following calculation process:

[0072] Calculate the normal stress scalar :

[0073]

[0074] Calculate the magnitude of the shear stress scalar The total stress vector on this plane:

[0075]

[0076] Shear stress vector :

[0077]

[0078] Then the magnitude of the shear stress scalar:

[0079]

[0080] Calculate the normal strain scalar :

[0081]

[0082] Calculate the scalar amplitude of shear strain The total strain vector on this plane:

[0083]

[0084] Shear strain vector :

[0085]

[0086] Then the magnitude of the shear strain scalar:

[0087]

[0088] In the above formula This represents the tensor shear strain amplitude. To conform to the Fatemi-Socie criterion, it is converted to an engineering shear strain amplitude: In all subsequent steps All of these refer to the shear strain amplitude of this project.

[0089] Through the above analysis process, the original dimension was... The stress tensor time history and The strain tensor time history is reconstructed into a dimension of Time-series characteristic vectors with clear fatigue mechanics meaning ,in .

[0090] All the above projection operations pertain to the angle parameter and All of them are continuously differentiable, thus ensuring that the gradients can be backpropagated to the critical surface search subnetwork in step S2 without hindrance during subsequent end-to-end training.

[0091] Step S4: Sequence feature encoding.

[0092] The 100×4 temporal features generated in step S3 are input into a bidirectional long short-term memory network with 128 hidden units for sequence feature encoding. This network reads data progressively along the timeline and continuously updates the cell state through its gating mechanism. and hidden state After reading, the hidden states output by the forward LSTM and backward LSTM at the last time step are concatenated to obtain a 256-dimensional damage feature vector. , which serves as a damage feature vector that encapsulates the damage impact information throughout the entire non-proportional load history.

[0093] Step S5: Feature fusion and lifetime prediction.

[0094] First, the eight continuous numerical data points of the material properties are Z-score normalized. The mean and standard deviation are obtained and saved based on the statistics of the training dataset, resulting in an 8-dimensional material feature vector. The three numerical values ​​of the weld geometry features are also normalized. In this embodiment, they are scaled by dividing by a preset maximum value. The interval is normalized to obtain a 3D geometric eigenvector.

[0095] Then, the 256-dimensional damage feature vector, 8-dimensional material feature vector, and 3-dimensional geometric feature vector output from step S4 are concatenated to form a 267-dimensional combined feature vector.

[0096] Finally, this combined feature vector is fed into a regression network consisting of two fully connected layers and one output layer. Each of the two fully connected layers contains 64 neurons and uses the ReLU activation function; the output layer contains one neuron using a linear activation function, and its output value is the predicted fatigue life. .

[0097] Step S6: Model training.

[0098] Construct a composite loss function consisting of a weighted sum of data-driven terms and physical constraint terms. Its expression is:

[0099] ;

[0100] in, The fatigue life vector directly predicted by the model ( (for batch size) This represents the actual fatigue life vector. This is the equivalent fatigue life vector calculated based on the Fatemi-Socie multiaxial fatigue criterion; To balance hyperparameters, the relative importance of data-driven loss terms and physical constraint terms is balanced; The mean square error between the predicted lifetime and the actual lifetime; The mean square error between the predicted life and the Fatemi-Socie equivalent fatigue life.

[0101] Data-driven items Defined as:

[0102]

[0103] Physical constraints Defined as:

[0104]

[0105] The following equations are obtained by solving them using differentiable numerical methods:

[0106]

[0107] in For Fatemi-Socie multiaxial fatigue damage parameters, This represents the range of maximum shear strain on the critical surface. This represents the maximum normal stress on that plane. For the material's yield strength, For material constants, The fatigue strength coefficient, The fatigue ductility coefficient, The fatigue strength index, The fatigue ductility index, It is the elastic modulus.

[0108] Training was performed using the Adam optimizer with an initial learning rate of 0.001 and a total of 200 epochs. In each epoch, all 120 training samples were iterated over in batches of 64. The entire deep neural network model was trained end-to-end with the goal of minimizing the composite loss function L. During backpropagation, the gradient of the loss function was propagated through all the differential operations described in steps S6, S5, S4, and S3 to the differentiable critical surface search subnetwork in step S2, synchronously updating the decision... and All weight parameters of the angle are used to achieve automatic positioning of the optimal critical surface driven by both data and physical laws.

[0109] After training, the model performance was evaluated on 30 test samples. The predicted cycle lifetime for each sample was calculated. Compared to actual cycle life A comparison was made. The evaluation results on 30 test samples were as follows: the mean absolute percentage error (MAPE) of the method of this invention was 12.3%, and the coefficient of determination was... The MAPE is 0.982; the MAPE of the traditional Fatemi-Socie criterion method is 41.3%. The value is 0.736. Under the load conditions covered by the 30 test samples in this embodiment, the method of the present invention shows significantly better prediction accuracy than the comparative methods, with particularly outstanding advantages under complex loading paths with high non-proportionality. This verifies the effectiveness of the synergistic effect between the differentiable critical surface search module and the physical constraint loss function.

[0110] Once trained, the model can be used to predict the non-proportional multiaxial fatigue life of the weld under similar load spectra. When a new stress-strain time sequence is input, the model will first automatically locate the maximum damage plane through the embedded differentiable critical surface search module, then analyze the stress, encoding sequence, and fused features, and finally output a high-precision fatigue life prediction value.

[0111] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search, characterized in that, Includes the following steps: Step S1: Obtain multiaxial stress-strain time history data, material property data, and weld geometric feature data of the predicted critical points in the welded structure to construct an initial dataset; Step S2: Construct a deep neural network model that includes a differentiable critical surface search module. The differentiable critical surface search module is a parameterized subnetwork and outputs a unit normal vector parameter representing the maximum fatigue damage plane. Step S3: Based on the unit normal vector parameter, perform differentiable projection on the stress tensor and strain tensor in the multiaxial stress-strain time history data to obtain the normal stress time sequence, shear stress time sequence, normal strain time sequence and engineering shear strain time sequence on the critical surface. Step S4: Input the program sequence for normal stress, shear stress, normal strain, and engineering shear strain into the sequence feature encoding network to generate a damage feature vector containing non-proportional load path memory. Step S5: Fuse the damage feature vector with the material property data and weld geometric feature data, and predict the fatigue life of the predicted critical point of the welded structure based on the fused feature vector; Step S6: Train the deep neural network model using a composite loss function that includes a data-driven prediction error term and a multi-axis fatigue criterion physical constraint term. The differentiable critical surface search module is optimized synchronously with the life prediction network.

2. The method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search according to claim 1, characterized in that, The differentiable critical surface search module in step S2 is a fully connected network. It receives the vector extracted from the multiaxial stress-strain time history data through statistical features as input, and the output layer outputs spherical coordinate angle parameters θ and φ representing the direction of the critical surface after being mapped by an activation function. The unit normal vector n is determined by θ and φ.

3. The method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search according to claim 1, characterized in that, The sequence feature encoding network mentioned in step S4 is a long short-term memory network.

4. The method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search according to claim 1, characterized in that, The fusion described in step S5 is a vector concatenation operation; the damage feature vector, the vector obtained after normalizing the material property data, and the vector obtained after normalizing the weld geometric feature data are concatenated into a combined feature vector, which is then input into the subsequent fully connected layer for lifetime prediction.

5. The method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search according to claim 1, characterized in that, The deep neural network model is optimized using a composite loss function during training. The composite loss function includes a data-driven prediction error term and a physical constraint term constructed based on a multi-axis fatigue damage criterion. The physical constraint term is used to ensure that the fatigue life predicted by the model and the damage parameters calculated by the multi-axis fatigue damage criterion maintain physical consistency.

6. The method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search according to claim 5, characterized in that, The composite loss function is expressed as follows: ； in, This is the fatigue life vector predicted by the model. This represents the true fatigue life vector. This is the equivalent fatigue life vector calculated based on the multiaxial fatigue damage criterion. To balance hyperparameters, This represents the mean square error.

7. The method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search according to claim 6, characterized in that, The multiaxial fatigue damage criterion is the Fatemi-Socie criterion; the equivalent fatigue life... The following equations are obtained by solving them using differentiable numerical methods: in For Fatemi-Socie multiaxial fatigue damage parameters, This represents the range of maximum shear strain on the critical surface. This represents the maximum normal stress on that plane. For the material's yield strength, For material constants, The fatigue strength coefficient, The fatigue ductility coefficient, The fatigue strength index, The fatigue ductility index, It is the elastic modulus.

8. The method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search according to claim 1, characterized in that, The weld geometry data mentioned in step S1 includes weld toe radius, weld toe angle, and plate thickness.

9. The method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search according to claim 1, characterized in that, The welded structure is a welded component for an aero-engine.

10. The method for predicting the multiaxial fatigue life of welded structures based on differentiable critical surface search according to claim 1, characterized in that, In step S6, when training the deep neural network model, the gradient of the composite loss function is transmitted to the differentiable critical surface search module via the differentiable projection, and the unit normal vector parameter and the weight parameter of the lifetime prediction network are updated synchronously.

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