Multiaxial fatigue life prediction methods, devices and computer equipment

Abstract

This application relates to the field of materials mechanics and engineering technology, and provides a method, apparatus, and computer device for multiaxial fatigue life prediction. The method includes: acquiring raw data from a multiaxial fatigue test database and obtaining target features based on the raw data; designing multiple initial multiaxial fatigue life prediction equations based on a semi-empirical multiaxial fatigue life prediction method; constructing a corresponding neural network architecture based on each initial multiaxial fatigue life prediction equation; training the neural network architecture by combining the target features and a physical constraint loss function to obtain a target neural network; performing interpolation sampling on each network module of the target neural network to construct an augmented dataset; extracting interpretable quantization equations for each network module based on the augmented dataset through symbolic regression; combining the interpretable quantization equations and, after generalization screening, outputting the final multiaxial fatigue life prediction equation. This method balances accuracy, interpretability, and generalization to meet the needs of engineering applications.

Description

Technical Field

[0001] This application belongs to the field of materials mechanics and engineering technology, and in particular relates to a multiaxial fatigue life prediction method, device and computer equipment. Background Technology

[0002] Among existing multiaxial fatigue life prediction methods, traditional semi-empirical methods, based on experimental observations and empirical inferences, offer strong interpretability but suffer from low prediction accuracy and limited applicability due to their reliance on simplification assumptions. Pure data-driven methods construct implicit associations through neural networks, achieving higher accuracy, but the prediction process is uninterpretable and generalization depends on large datasets. Knowledge-data fusion methods, while introducing prior knowledge constraints, still cannot derive interpretable quantitative equations, exhibiting black-box characteristics. Overall, existing methods struggle to balance prediction accuracy, interpretability, and generalization, falling short of the requirements for engineering applications. Summary of the Invention

[0003] This application provides a multi-axis fatigue life prediction method, apparatus, and computer device, which can solve the technical problem in the prior art that it is difficult to balance prediction accuracy, interpretability, and generalization, and thus cannot meet the needs of engineering applications.

[0004] In a first aspect, embodiments of this application provide a multiaxial fatigue life prediction method, including:

[0005] Raw data is obtained from a multiaxial fatigue test database, and target features are derived based on the raw data.

[0006] Based on a semi-empirical multi-axis fatigue life prediction method, multiple initial multi-axis fatigue life prediction equations are designed. A corresponding neural network architecture is constructed according to each initial multi-axis fatigue life prediction equation. The neural network architecture is trained by combining the target features and physical constraint loss function to obtain the target neural network.

[0007] Interpolation sampling is performed on each network module of the target neural network to construct an enhanced dataset;

[0008] Based on the augmented dataset, interpretable quantization equations for each network module are extracted using symbolic regression. After combining these interpretable quantization equations and performing generalization filtering, the final multiaxial fatigue life prediction equation is output.

[0009] In one possible implementation of the first aspect, obtaining raw data from a multiaxial fatigue test database and obtaining target features based on the raw data includes:

[0010] The raw data is obtained from the multiaxial fatigue test database; wherein, the raw data includes material property characteristics, multiaxial loading path characteristics, and loading environment characteristics;

[0011] Based on the original data, feature engineering is performed to generate an artificial feature set, and the original data and the artificial feature set are subjected to dimensionless processing to output a normalized feature set.

[0012] The normalized feature set is sorted and filtered by feature importance to obtain the initial target features;

[0013] Using multi-axis fatigue life as the output target, a shallow learning algorithm as the regressor, and mean squared error as the regression performance index, the initial target features are filtered to obtain the target features.

[0014] In one possible implementation of the first aspect, the plurality of initial multiaxial fatigue life prediction equations include:

[0015] ;

[0016] ;

[0017] ;

[0018] in, For multi-axis fatigue life, A, B, C, b, and r are network modules to be determined, and D is the multi-axis damage parameter.

[0019] In one possible implementation of the first aspect, the step of constructing a corresponding neural network architecture based on each initial multi-axis fatigue life prediction equation, and training the neural network architecture in conjunction with a preset physical constraint loss function to obtain the target neural network includes:

[0020] A corresponding neural network architecture is constructed based on each initial multi-axis fatigue life prediction equation, so that A, B, C, D, b, and r correspond to independent network modules, and the connection mode between each network module is designed according to the initial multi-axis fatigue life prediction equation.

[0021] By combining a pre-defined physical constraint loss function, each neural network architecture is trained and validated to determine the neural network architecture with the smallest error.

[0022] The target multi-axis fatigue life prediction equation is obtained based on the neural network architecture with minimum error.

[0023] The target neural network is obtained by optimizing the corresponding neural network architecture according to the target multi-axis fatigue life prediction equation and then performing the training and verification steps for each neural network architecture again.

[0024] In one possible implementation of the first aspect, the method further includes:

[0025] Based on prior knowledge of multi-axis fatigue and the correlation between the target features and multi-axis fatigue life, a physical constraint loss function is designed and embedded in each neural network architecture.

[0026] In one possible implementation of the first aspect, the step of interpolating and sampling each network module of the target neural network to construct the augmented dataset includes:

[0027] Interpolation sampling is performed within the feature value space defined by the multiaxial fatigue test database to obtain interpolated sampling data;

[0028] The interpolated sampled data is mixed with the original data to construct an enhanced dataset for each network module.

[0029] In one possible implementation of the first aspect, the step of extracting interpretable quantization equations for each network module based on the augmented dataset using symbolic regression, combining the interpretable quantization equations and performing generalization filtering, and then outputting the final multiaxial fatigue life prediction equation includes:

[0030] The input and output sample data of each network module are obtained from the augmented dataset, and the input and output sample data contains the mapping relationship between the target features and the output of the network module;

[0031] Using mean squared error as the regression performance index, the symbolic regression algorithm is applied to fit the input and output sample data to obtain the interpretable quantization equations of each network module.

[0032] The interpretable quantization equations of each network module are combined according to the functional relationship of the target multiaxial fatigue life prediction equation to generate a symbolic regression combination equation.

[0033] The generalization performance of the symbolic regression combination equation is evaluated, and the equation with the smallest generalization error is selected as the final multiaxial fatigue life prediction equation.

[0034] In one possible implementation of the first aspect, the raw data includes load features; when applying the symbolic regression algorithm, the following constraints are considered:

[0035] The output of the interpretable quantization equation corresponding to D is always greater than 0;

[0036] The output of the interpretable quantization equation corresponding to A is always greater than 0;

[0037] The output of the interpretable quantization equation corresponding to B is always less than 0;

[0038] The output of the interpretable quantization equation corresponding to D increases with the increase of load characteristics.

[0039] Secondly, embodiments of this application provide a multi-axis fatigue life prediction device, comprising:

[0040] The acquisition module is used to acquire raw data from a multiaxial fatigue test database and obtain target features based on the raw data;

[0041] The training module is used to design multiple initial multi-axis fatigue life prediction equations based on a semi-empirical multi-axis fatigue life prediction method, construct a corresponding neural network architecture based on each initial multi-axis fatigue life prediction equation, and train the neural network architecture by combining the target features and physical constraint loss function to obtain the target neural network.

[0042] A construction module is used to perform interpolation sampling on each network module of the target neural network to construct an enhanced dataset;

[0043] The output module is used to extract interpretable quantization equations for each network module based on the augmented dataset through symbolic regression, combine the interpretable quantization equations and output the final multiaxial fatigue life prediction equation after generalization screening.

[0044] Thirdly, embodiments of this application provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the multi-axis fatigue life prediction method described in any one of the first aspects above.

[0045] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the multi-axis fatigue life prediction method described in any one of the first aspects.

[0046] Fifthly, embodiments of this application provide a computer program product that, when run on a computer device, causes the computer device to execute the multi-axis fatigue life prediction method described in any one of the first aspects.

[0047] Compared with existing technologies, the beneficial effects of this application's embodiments are as follows: A neural network architecture is designed based on semi-empirical equations, combined with training using physical constraint loss functions. This integrates the strong fitting capability of data-driven approaches with physical mechanism constraints, effectively capturing nonlinear damage behavior under multi-factor coupling. This overcomes the accuracy limitations of traditional semi-empirical methods due to reliance on simplification assumptions, significantly improving prediction accuracy. Interpretable quantifiable equations are extracted from each module of the target neural network through symbolic regression, ultimately forming an explicit multi-axis fatigue life prediction equation. This process transforms the black-box learning results of the neural network into mathematically meaningful expressions, overcoming the shortcomings of uninterpretable prediction processes in purely data-driven methods and the black-box nature of knowledge-data fusion methods, making the mechanism of the prediction results traceable. An enhanced dataset is constructed by interpolating and sampling each module of the target neural network, supplementing samples in sparse regions of the feature space and reducing the impact of uneven data distribution on the model. In summary, by fusing multi-source information, physical constraint modeling, and interpretable equation extraction, a synergistic improvement in prediction accuracy, interpretability, and generalization is achieved. This effectively solves the technical problem that existing methods struggle to balance these three aspects and cannot meet the needs of engineering applications, providing reliable technical support for multi-axis fatigue life prediction in key engineering fields.

[0048] It is understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a schematic flowchart of a multiaxial fatigue life prediction method provided in an embodiment of this application;

[0051] Figure 2 This is a neural network architecture provided in one embodiment of this application;

[0052] Figure 3a A schematic diagram showing the comparison between the multiaxial fatigue life prediction results and the actual life using the critical surface method is presented.

[0053] Figure 3b A schematic diagram showing the comparison between the multi-axis fatigue life prediction results of support vector machine and the actual fatigue life is presented.

[0054] Figure 3c A schematic diagram showing the comparison between the multi-axis fatigue life prediction results of random forest and the actual life is presented.

[0055] Figure 3d A schematic diagram showing the comparison between the multi-axis fatigue life prediction results and the actual life of a multilayer sensor is presented.

[0056] Figure 3e A schematic diagram showing the comparison between the multiaxial fatigue life prediction results and the actual fatigue life of the method provided in this application is presented.

[0057] Figure 4 This is a schematic diagram of the structure of the multi-axis fatigue life prediction device provided in the embodiments of this application;

[0058] Figure 5 This is a schematic diagram of the structure of the computer device provided in the embodiments of this application. Detailed Implementation

[0059] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0060] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0061] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0062] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0063] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0064] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0065] Multiaxial fatigue, as one of the most dangerous forms of fatigue failure, is widely present in key engineering fields such as high-speed rail, nuclear industry, and aerospace. Essentially, it is the fatigue failure phenomenon that occurs in materials under multi-directional cyclic loading. Due to the complex characteristics of multiaxial fatigue, including numerous influencing factors, significant coupling effects among these factors, and anisotropic damage accumulation and failure behavior, traditional uniaxial life determination methods are no longer able to accurately predict and handle its lifespan.

[0066] Current mainstream methods for predicting multiaxial fatigue life can be divided into two categories: traditional semi-empirical methods and data-driven methods. Traditional semi-empirical methods are based on experimental observation and empirical inference, mainly focusing on two issues: "how to measure multiaxial fatigue damage" and "how damage accumulates." Regarding damage measurement, although various damage parameters based on stress, strain, energy, and property degradation have been developed, their construction process relies on empirical assumptions. Regarding damage accumulation, the commonly used linear accumulation models (such as the Palmgren-Miner model) simplify the nonlinear interaction between materials and loads, resulting in insufficient prediction accuracy, while existing nonlinear accumulation models still have limited applicability.

[0067] To overcome the limitations of semi-empirical methods, data-driven methods have received widespread attention in recent years, and can be further divided into pure data-driven methods and knowledge-data fusion methods. Pure data-driven methods directly construct the implicit correlation between input features and fatigue life through neural networks, achieving high accuracy and efficiency in life prediction. However, the prediction process is not subject to physical constraints, is not interpretable, and its generalization performance heavily relies on large datasets, limiting its reliability. Although knowledge-data fusion methods introduce multi-axis fatigue prior knowledge as constraints to reduce data requirements, they still cannot derive interpretable quantitative equations between multi-axis fatigue life and influencing factors, making the "black box" problem difficult to overcome.

[0068] In summary, existing methods have obvious shortcomings: traditional semi-empirical methods are highly interpretable but lack accuracy and applicability, while data-driven methods have high accuracy but face the dilemma of lack of interpretability and dependence on real-time data input for generalization. As a result, the reliability and generalization of their prediction results are difficult to meet the requirements of engineering applications, and there is significant room for improvement.

[0069] To solve the above problems, Figure 1 A schematic flowchart of a multiaxial fatigue life prediction method provided in this application is shown.

[0070] S101, Obtain raw data from the multiaxial fatigue test database, and obtain target features based on the raw data.

[0071] Among them, the multiaxial fatigue test database refers to the structured dataset that stores fatigue test data of materials under multiaxial cyclic loading, including raw results such as material properties, loading conditions, environmental parameters and corresponding fatigue life.

[0072] Raw data refers to unprocessed feature data directly obtained from the database, including but not limited to material property features, multiaxial loading path features, and loading environment features. Material property features include inherent material properties such as elastic modulus, Poisson's ratio, and yield strength; multiaxial loading path features include loading condition parameters such as stress amplitude, strain amplitude, load frequency, and phase difference; and loading environment features include environmental influence parameters such as temperature, humidity, and corrosive media.

[0073] Among them, target features refer to the key features that play a decisive role in the prediction of multiaxial fatigue life after being screened out through feature engineering.

[0074] In an optional embodiment, S101 obtains raw data from a multiaxial fatigue test database and derives target features based on the raw data, including:

[0075] Step a1: Obtain the raw data from the multiaxial fatigue test database; wherein the raw data includes material property characteristics, multiaxial loading path characteristics, and loading environment characteristics.

[0076] Step a2: Perform feature engineering based on the original data to generate an artificial feature set, and perform dimensionless processing on the original data and the artificial feature set to output a normalized feature set.

[0077] Feature engineering refers to the process of constructing new features based on domain knowledge to enhance the information density of raw data. Combining prior knowledge of multiaxial fatigue, the generated artificial feature set includes, but is not limited to, damage-related features with clear physical meanings such as Fatemi-Socic parameters and Innce-Glinka parameters. These features can more accurately reflect the material damage behavior under multiaxial loading.

[0078] Dimensionless processing refers to eliminating the dimensional differences between the original data and the different features in the artificial feature set, and transforming the feature values ​​to a uniform numerical range through standardization or normalization algorithms.

[0079] Step a3: Sort and filter the normalized feature set according to feature importance to obtain the initial target features.

[0080] In this process, the importance of each feature in the normalized feature set can be ranked using the Pearson correlation coefficient or mutual information method, and the top few features can be selected as the initial target features.

[0081] In this embodiment, the importance of each feature in the normalized feature set is ranked using the Pearson correlation coefficient or mutual information method, which quantifies the correlation between the feature and multiaxial fatigue life. The Pearson correlation coefficient reflects linear correlation, while mutual information captures overall dependencies, including nonlinear ones. Selecting the top-ranked features as initial target features retains key information while initially reducing feature dimensionality, laying the foundation for more refined feature selection and ensuring that the features input to the model have high relevance and representativeness.

[0082] Step a4: Using multi-axis fatigue life as the output target, a shallow learning algorithm as the regressor, and mean squared error as the regression performance index, the initial target features are screened to obtain the target features.

[0083] In this embodiment, during the process of filtering initial target features to obtain target features, a wrapping method or a filtering method is employed. Multiaxial fatigue life is set as the output target, a shallow learning algorithm is selected as the regressor, and mean squared error is used as the regression performance index. Specifically, the wrapping method iteratively selects a subset of features and uses the regressor to evaluate its predictive performance on multiaxial fatigue life, filtering out the feature combination that minimizes the mean squared error. The filtering method sorts and selects features based on criteria such as the correlation between features and multiaxial fatigue life. Shallow learning algorithms, such as support vector machines, with their effective learning ability of data patterns, can accurately identify key features that have a decisive impact on the prediction accuracy of multiaxial fatigue life during feature filtering. The final target features not only eliminate redundant information but also retain core elements highly correlated with multiaxial fatigue life, providing high-quality input for subsequent modeling processes and helping to improve the accuracy and efficiency of multiaxial fatigue life prediction.

[0084] S102, Design multiple initial multi-axis fatigue life prediction equations based on the semi-empirical multi-axis fatigue life prediction method, construct a corresponding neural network architecture (also known as a modular neural network architecture) according to each initial multi-axis fatigue life prediction equation, and train the neural network architecture by combining the target features and physical constraint loss function to obtain the target neural network.

[0085] In this embodiment of the application, based on a semi-empirical multiaxial fatigue life prediction method, several initial multiaxial fatigue life prediction equations are designed, with typical forms including:

[0086] ;

[0087] ;

[0088] ;

[0089] in, For multi-axis fatigue life, A, B, C, b, and r are network modules to be determined, and D is the multi-axis damage parameter.

[0090] Optionally, a corresponding neural network architecture is constructed based on each initial multi-axis fatigue life prediction equation, and the neural network architecture is trained in conjunction with a preset physical constraint loss function to obtain the target neural network, including:

[0091] Step b1: Construct a corresponding neural network architecture based on each initial multi-axis fatigue life prediction equation, so that A, B, C, D, b, and r correspond to independent network modules, and the connection mode between each network module is designed according to the initial multi-axis fatigue life prediction equation.

[0092] Here, neural network architecture refers to the overall structure of a neural network composed of multiple independent network modules arranged according to specific logic. In this step, the architecture design must follow the following logic:

[0093] Independent network modules: Each parameter (A, B, C, D, b, r) in the equation corresponds to an independent network module. Each network module is responsible for learning the functional relationship between the parameter and the input features (target features).

[0094] Linking pattern: The linking method between network modules is strictly designed according to the mathematical operations (such as addition, multiplication, exponentiation, etc.) of the initial equations to ensure that the network architecture is consistent with the operational logic of the equations. For example, for the equation... In the corresponding architecture, the outputs of network module D and network module C are first added together, and then multiplied with the output of network module A to finally obtain the output related to Nf.

[0095] Each network module includes a DROPOUT layer to prevent the training process from getting trapped in local minima, thus ensuring the model's generalization ability.

[0096] For example, for the equation To construct network modules A, D, b, and C, the outputs of network modules D and B are connected by exponentiation, then multiplied by the output of network module A, and finally connected by addition to the output of network module C, forming the network architecture corresponding to the equation.

[0097] For ease of understanding, a schematic diagram of a neural network architecture coupled with symbolic regression is provided here, such as... Figure 2 As shown.

[0098] Step b2 involves training and validating each neural network architecture using a pre-defined physical constraint loss function to determine the neural network architecture with the smallest error.

[0099] Among them, the physical constraint loss function refers to the loss function designed with reference to prior knowledge of multiaxial fatigue (such as the correlation between key features and fatigue life). It is embedded in each neural network architecture to constrain the network learning process during training, ensuring that the network output conforms to the physical mechanism of multiaxial fatigue (such as the law that damage parameters increase with increasing load), and avoiding fitting results that may violate physical common sense that may occur in pure data-driven approaches.

[0100] This involves training and validating each neural network architecture, comparing the training and validation errors of different neural network architectures, and determining the neural network architecture with the smallest error.

[0101] The training and validation data are obtained by independently and identically sampling from a multiaxial fatigue test database. Several key features (i.e., target features) are selected through feature engineering, such as load frequency, stress amplitude, and temperature. Note that multiaxial fatigue life is not included in these key features; it is the prediction target. These key features selected through feature engineering are then uniformly input into all network modules. When the input features are identical, all network modules perform calculations based on the same operating condition, ensuring physical consistency, preventing information leakage, and simplifying the training process.

[0102] The training and validation processes are described below:

[0103] Data source: Training and validation data were obtained by independent identically distributed sampling from a multi-axis fatigue test database to ensure the representativeness and randomness of the data.

[0104] Input features: The input features of each network module are key features (target features) obtained through prior screening, ensuring high relevance and low redundancy of the input data.

[0105] Specifically, for different neural network architectures, a training process is executed, which calculates the predicted value through forward propagation, calculates the error using the physical constraint loss function, updates the network parameters through backpropagation, evaluates the model's generalization ability through the validation set, and records the training error and validation error.

[0106] In this embodiment, the network is guided to learn functional relationships that conform to physical laws through a physical constraint loss function. At the same time, the optimal architecture is selected through rigorous error comparison. This not only ensures the neural network's ability to fit complex nonlinear relationships of multi-axis fatigue, but also improves the reliability and generalization of the model through physical constraints and error verification. This lays the model foundation for subsequent symbolic regression to extract high-precision and interpretable quantitative equations.

[0107] Optionally, referring to prior knowledge of multi-axis fatigue, and based on the correlation between the target features and multi-axis fatigue life, a physical constraint loss function is designed and embedded into each neural network architecture.

[0108] In this embodiment, the prior knowledge of multiaxial fatigue encompasses fundamental laws verified through practice, such as the damage evolution law of materials under multiaxial cyclic loading (e.g., damage increases with load accumulation) and the anisotropic characteristics of failure behavior. The correlation between target features and multiaxial fatigue life is quantitatively analyzed to clarify the direction and intensity (e.g., positive or negative correlation) of the influence of key features (e.g., stress amplitude, material yield strength) on life. Based on the above, the designed physical constraint loss function transforms physical rules such as "damage parameter output must always be positive" and "damage parameters should monotonically increase as load characteristics increase" into mathematical constraint terms, which, together with conventional prediction error terms, constitute the loss function. When the neural network's prediction results violate these physical laws, the constraint terms significantly increase the loss value, thereby guiding network parameter adjustments during training and forcing the model to learn a mapping relationship consistent with the actual mechanism. Embedding this type of physical constraint loss function into each neural network architecture ensures that networks of different architectures are subject to unified physical rule constraints during the learning process, avoiding "spurious correlations" that may occur due to pure data fitting, and laying a reliable foundation for subsequently selecting the network architecture with the smallest error and extracting interpretable equations.

[0109] Step b3: Based on the neural network architecture with the minimum error, the target multi-axis fatigue life prediction equation is obtained.

[0110] In this embodiment, for the neural network architecture with the smallest error, the output results of each network module (corresponding to parameters A, B, C, D, b, r, etc.) are derived and analyzed to clarify the degree of matching between the functional relationships of each network module and the initial multi-axis fatigue life prediction equation, and to identify possible deviations (such as inconsistencies between the operational logic between network modules and the equation design). Then, based on the analysis results of the network module outputs, the initial multi-axis fatigue life prediction equation is adjusted (such as correcting the operational relationships between parameters, adding or removing parameter terms, etc.) to make the equation more closely match the actual functional relationships learned by the neural network. Simultaneously, the corresponding neural network architecture is optimized based on the adjusted equation (such as correcting the network module connection pattern), and the training and verification process is re-executed to ensure the consistency between the architecture and the equation. After adjustment and retraining, the network model with the best performance and the corresponding multi-axis fatigue life prediction equation are saved. This equation is the target multi-axis fatigue life prediction equation, which retains the physical interpretability of the semi-empirical equation and integrates the nonlinear relationships learned by the neural network, laying the foundation for subsequent extraction of explicit quantization equations.

[0111] In this embodiment, by feeding the fitting results of the neural network back into the equation design, the closed-loop optimization of the data-driven correction empirical equation is realized, so that the target equation not only conforms to the physical mechanism of multiaxial fatigue, but also accurately captures complex nonlinear damage behavior. This overcomes the limitations of the simplification assumptions of traditional semi-empirical equations and provides a core framework for the final generation of prediction equations that are both accurate and interpretable.

[0112] Step b4: Optimize the corresponding neural network architecture according to the target multi-axis fatigue life prediction equation, and repeat the steps of training and validating each neural network architecture to obtain the target neural network.

[0113] In this embodiment, based on the structure of the target multi-axis fatigue life prediction equation (such as the operational relationship between parameters, added or deleted parameter terms), the original neural network architecture is specifically adjusted to correct the connection pattern of each network module (corresponding to A, B, C, D, b, r, etc.) to ensure complete matching with the mathematical operation logic of the equation; if the parameter terms in the equation are added or deleted, the corresponding network modules are added or deleted accordingly, or the neuron structure and number of layers inside the network modules are adjusted to better fit the new functional relationship; the DROPOUT layer in each network module is retained to maintain the generalization ability of the model.

[0114] Next, using the training and validation data from step b2 as input, the optimized neural network architecture is retrained using the physical constraint loss function. The network parameters are continuously adjusted through backpropagation to minimize the degree of deviation between the prediction error and the physical constraints. The model performance is evaluated using a validation set with independent and identically distributed sampling, focusing on the consistency between the training error and the validation error to avoid overfitting. The training process is repeated until the model converges, i.e., the error stabilizes within the preset threshold and the physical constraints are strictly satisfied.

[0115] Finally, the neural network model with the best performance (minimum error and best generalization) after optimization, training and verification is saved as the target neural network. This network not only strictly follows the mathematical framework of the target equation, but also learns the complex nonlinear relationship between each parameter and the target feature through data-driven learning, providing a precise carrier for subsequent analysis of the functional relationship between each network module.

[0116] S103, interpolate sampling is performed on each network module of the target neural network to construct an enhanced dataset.

[0117] Specifically, interpolation sampling is performed within the feature value space defined by the multi-axis fatigue test database to obtain interpolated sampled data; the interpolated sampled data is then mixed with the original data to construct an enhanced dataset for each network module.

[0118] In this embodiment, a feature value space defined by the multiaxial fatigue test database is determined. This space is determined by the actual value range of existing features such as material properties, loading paths, and environmental conditions in the database. This ensures that the interpolation sampling does not exceed a physically reasonable range. For example, the sampled values ​​of features such as load amplitude and temperature must fall within the actual range of experimental observations to avoid subsequent modeling deviations caused by virtual data deviating from reality. Based on this space, interpolation sampling is performed on each network module (corresponding to parameters A, B, C, D, b, and r, respectively). Interpolation sampling fills in the sparse regions of the original experimental data in the feature space by uniformly or adaptively selecting supplementary samples among existing feature data points. For example, sampling points for intermediate gradients are added between high and low load amplitudes to more accurately capture the functional relationship between the input features and output parameters of the network module.

[0119] Subsequently, the supplementary data obtained from interpolation sampling was mixed with the original experimental data in a reasonable proportion to form an augmented dataset for each network module. The original data ensured the authenticity and representativeness of the samples, while the interpolated data expanded the sample coverage. The combination of the two enabled the dataset to not only reflect the actual experimental patterns but also provide more comprehensive input-output distribution information for symbolic regression. This improved the extraction accuracy and stability of the interpretable quantization equations of each network module, laying the data foundation for obtaining a high-precision multi-axis fatigue life prediction equation in the final combination.

[0120] In this process, symbolic regression requires extracting functional relationships for each network module (e.g., A, B, C, D, etc.), and the input-output mapping relationships of different network modules may differ (e.g., network module D is strongly correlated with stress amplitude, while network module A is strongly correlated with temperature). Therefore, the augmented dataset needs to be constructed modularly: for network module D (multiaxial damage parameters), samples from regions of drastic changes in damage parameters in the original data (e.g., high stress amplitude ranges) are added; for network module A (life coefficient), samples from temperature-sensitive ranges (e.g., near the critical temperature of material phase transformation) are added. Through targeted sampling, it is ensured that the augmented dataset for each network module can fully cover the key feature ranges of its functional relationships.

[0121] S104. Based on the enhanced dataset, interpretable quantization equations for each network module are extracted through symbolic regression. After combining the interpretable quantization equations and generalizing them, the final multi-axis fatigue life prediction equation is output.

[0122] Symbolic regression is a technique for mining explicit mathematical expressions from data. In this step, it is used to analyze the input-output function relationship of each network module, derive interpretable quantifiable equations, and use mean squared error as the regression performance index.

[0123] Interpretable quantization equations refer to expressions extracted through symbolic regression that clearly demonstrate the mathematical relationship between input features and network module outputs (such as parameters A, B, C, and D). These equations have clear physical meaning and mathematical form, facilitating the understanding of the influence of each feature on the network module output and overcoming the black-box nature of pure neural networks.

[0124] The physical constraints include: the output of the interpretable quantization equation corresponding to D is always greater than 0; the output of the interpretable quantization equation corresponding to A is always greater than 0; the output of the interpretable quantization equation corresponding to B is always less than 0; and the output of the interpretable quantization equation corresponding to D increases with the increase of load characteristics. These four types of constraints can be achieved by inputting preset data conforming to the physical laws of multiaxial fatigue into the interpretable quantization equation in real time during the symbolic regression process for constraint determination. This can also be described as inputting typical data conforming to physical laws (such as known load characteristics, material properties, etc.) from the multiaxial fatigue test database into the interpretable quantization equation in real time for constraint determination.

[0125] Among them, the generalization performance screening refers to the need to use some data outside the database to evaluate the universality of multiple combinations of interpretable quantifiable equations due to the randomness of symbolic regression, and finally select the equation with the best generalization ability as the result.

[0126] The final multiaxial fatigue life prediction equation represents the final model obtained by combining the interpretable quantization equations of each network module according to the structure of the target multiaxial fatigue life prediction equation and then performing generalization screening. It has high accuracy, strong generalization and interpretability.

[0127] In an optional embodiment, S104, based on the enhanced dataset, extracts interpretable quantization equations for each network module through symbolic regression, combines the interpretable quantization equations, and after generalization screening, outputs the final multi-axis fatigue life prediction equation, including:

[0128] Step c1: Obtain the input and output sample data of each network module from the augmented dataset. The input and output sample data contains the mapping relationship between the target features and the output of the network module.

[0129] The input and output sample data refer to the set of samples extracted from the augmented dataset to describe the relationship between the input and output of the network module. The input is the selected target features, and the output is the prediction result of the corresponding network module (such as the predicted values ​​of A and D).

[0130] Step c2: Using mean squared error as the regression performance index, the symbolic regression algorithm is applied to fit the input and output sample data to obtain the interpretable quantization equations for each network module.

[0131] Symbolic regression is a machine learning method that automatically searches for explicit mathematical equations in data. It does not require pre-defined function forms and generates expressions that conform to data patterns by combining constants, variables, and basic operators. It can directly output interpretable mathematical formulas, rather than implicit mappings from black-box models.

[0132] In this embodiment, mean squared error is used as the regression performance index, and a symbolic regression algorithm is applied to fit the aforementioned input and output sample data. Symbolic regression automatically combines constants, variables, and basic operators to search for explicit mathematical expressions that match the patterns in the sample data, thereby extracting the input-output functional relationship learned by each network module. During this process, four types of constraints must be strictly followed. Finally, through symbolic regression fitting and physical constraint verification, interpretable quantifiable equations for each network module are derived. These equations explicitly describe the functional relationship between the target features and the network module output in mathematical form, laying the foundation for subsequent combination to generate a complete multiaxial fatigue life prediction equation.

[0133] Examples of interpretable quantization equations for each network module are as follows:

[0134] ;

[0135] ;

[0136] ;

[0137] .

[0138] The variables in the above formula have the following meanings: ng is the elastic modulus index; Sy is the yield stress; G is the shear elastic modulus; E is the elastic modulus; K is the hardening coefficient; n is the hardening index; CP-EA is the critical surface normal strain; CP-GAMMA is the critical surface shear strain; Ssa is the critical surface normal stress; Sta is the critical surface shear stress.

[0139] Step c3: Combine the interpretable quantization equations of each network module according to the functional relationship of the target multiaxial fatigue life prediction equation to generate a symbolic regression combined equation.

[0140] Specifically, the parameters corresponding to the interpretable quantization equations of each network module are clearly defined (e.g., parameter A corresponds to the equation of network module A, and parameter D corresponds to the multiaxial damage parameter of network module D, etc.), and these parameters are matched one-to-one with the parameter positions in the target multiaxial fatigue life prediction equation to ensure that each network module equation is embedded in the correct function position. The function relationship combination is based on the operational logic of the target multiaxial fatigue life prediction equation (e.g., addition, multiplication, exponentiation, etc.), combining the equations of each network module. For example, if the target multiaxial fatigue life prediction equation is... Then, the interpretable quantification equations corresponding to A, D, b, and C need to be integrated according to the relationship of "multiplying A and D by the power of b and then adding C" to form a complete symbolic regression combination equation.

[0141] The process involves verifying the mathematical validity of the combined equations (e.g., eliminating logical conflicts) and preliminarily checking for compliance with the physical laws of multiaxial fatigue (e.g., positive life prediction results). This process eliminates obviously unreasonable combinations for subsequent generalization performance screening. Furthermore, this process transforms the implicit associations learned by the neural network into human-understandable mathematical formulas, overcoming the limitations of a black box approach. Symbolic regression facilitates the transformation from a data-driven model to explicit mathematical equations, preserving the fitting accuracy of the neural network while ensuring the reliability and universality of the equations through physical constraints and generalization screening. The final output prediction equations simultaneously meet the requirements of engineering applications for accuracy, interpretability, and generalization ability, completing the closed loop from data to a practical model.

[0142] Step c4: Evaluate the generalization performance of the symbolic regression combination equation and select the equation with the smallest generalization error as the final multiaxial fatigue life prediction equation.

[0143] In this embodiment, independent data outside the multiaxial fatigue test database (i.e., data not involved in model training and symbolic regression) is selected as the evaluation set. This data must cover different materials, loading conditions, and environmental conditions to comprehensively test the generalization ability of the equations. Using mean squared error and mean absolute error as core indicators, the prediction error of each symbolic regression combination equation on the evaluation set is calculated, focusing on the fitting accuracy of the equations to unknown data; the smaller the error, the better the generalization performance. The generalization errors of each equation are compared, and the equation with the smallest error is selected as the final multiaxial fatigue life prediction equation. If multiple equations have similar errors, further selection can be made based on the simplicity of the equations (such as the number of parameters and computational complexity) to ensure that the model has both high accuracy and engineering practicality.

[0144] Among them, the symbolic regression combination equations that are excluded from overfitting are validated by independent data, ensuring that the final output prediction equations not only perform well on the training data, but are also stable and applicable to new multi-axis fatigue conditions, thereby meeting the requirements of engineering applications for model reliability and generalization, and completing the final transformation from theoretical modeling to practical model.

[0145] In this application embodiment, multiaxial fatigue prior knowledge, physical constraints, and multiaxial fatigue test data are integrated to achieve multiaxial fatigue life modeling through multi-information source fusion, and a high-precision multiaxial fatigue life prediction equation is established. At the same time, this application organically combines semi-empirical methods, neural networks, and symbolic regression. While achieving high-precision modeling, it can also discover quantitative equations for multiaxial fatigue life prediction with excellent interpretability and generalization. In principle, it is applicable to different types of materials and multiaxial fatigue conditions. With appropriate adjustments, it can also be applied to other types of fatigue problems. In addition, this application can be applied automatically. In principle, after setting the data, key features, and network architecture, the method can be automatically established and corrected.

[0146] In the embodiments of this application, Figure 3a A schematic diagram showing the comparison between the multiaxial fatigue life prediction results and the actual life using the critical surface method is presented. Figure 3b A schematic diagram showing the comparison between the multi-axis fatigue life prediction results of support vector machine and the actual fatigue life is presented. Figure 3c A schematic diagram showing the comparison between the multi-axis fatigue life prediction results of random forest and the actual life is presented. Figure 3d A schematic diagram showing the comparison between the multi-axis fatigue life prediction results and the actual life of a multilayer sensor is presented. Figure 3eThese diagrams illustrate the comparison between the multi-axis fatigue life prediction results and actual lifespans provided by the method of this application. In these diagrams, the horizontal and vertical axes represent the logarithmic experimental lifespan and the predicted lifespan, respectively. The closer the predicted lifespan is to the diagonal of the diagram, the more accurate it is. As can be seen from these diagrams, the prediction results given by the classical critical surface method, random forest, and support vector machine are all highly dispersed. In contrast, the prediction results from neural networks and the method proposed in this invention are more accurate, less dispersed, and more evenly distributed on both sides of the diagonal of the diagram. Furthermore, the method proposed in this invention not only achieves accurate lifespan prediction but also provides a physically interpretable formula structure, which is the main advantage of this method over neural network methods.

[0147] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0148] Corresponding to the multiaxial fatigue life prediction method described in the above embodiments, Figure 4 A structural block diagram of the multiaxial fatigue life prediction device provided in the embodiments of this application is shown. For ease of explanation, only the parts related to the embodiments of this application are shown.

[0149] Reference Figure 4 The multi-axis fatigue life prediction device includes:

[0150] The acquisition module is used to acquire raw data from a multiaxial fatigue test database and obtain target features based on the raw data;

[0151] The training module is used to design multiple initial multi-axis fatigue life prediction equations based on a semi-empirical multi-axis fatigue life prediction method, construct a corresponding neural network architecture based on each initial multi-axis fatigue life prediction equation, and train the neural network architecture by combining the target features and physical constraint loss function to obtain the target neural network.

[0152] A construction module is used to perform interpolation sampling on each network module of the target neural network to construct an enhanced dataset;

[0153] The output module is used to extract interpretable quantization equations for each network module based on the augmented dataset through symbolic regression, combine the interpretable quantization equations and output the final multiaxial fatigue life prediction equation after generalization screening.

[0154] Optional, the acquisition module is used for:

[0155] The raw data is obtained from the multiaxial fatigue test database; wherein, the raw data includes material property characteristics, multiaxial loading path characteristics, and loading environment characteristics;

[0156] Based on the original data, feature engineering is performed to generate an artificial feature set, and the original data and the artificial feature set are subjected to dimensionless processing to output a normalized feature set.

[0157] The normalized feature set is sorted and filtered by feature importance to obtain the initial target features;

[0158] Using multi-axis fatigue life as the output target, a shallow learning algorithm as the regressor, and mean squared error as the regression performance index, the initial target features are filtered to obtain the target features.

[0159] Optionally, the plurality of initial multiaxial fatigue life prediction equations include:

[0160] ;

[0161] ;

[0162] ;

[0163] in, For multi-axis fatigue life, A, B, C, b, and r are network modules to be determined, and D is the multi-axis damage parameter.

[0164] Optional, training module, used for:

[0165] A corresponding neural network architecture is constructed based on each initial multi-axis fatigue life prediction equation, so that A, B, C, D, b, and r correspond to independent network modules, and the connection mode between each network module is designed according to the initial multi-axis fatigue life prediction equation.

[0166] By combining a pre-defined physical constraint loss function, each neural network architecture is trained and validated to determine the neural network architecture with the smallest error.

[0167] The target multi-axis fatigue life prediction equation is obtained based on the neural network architecture with minimum error.

[0168] The target neural network is obtained by optimizing the corresponding neural network architecture according to the target multi-axis fatigue life prediction equation and then performing the training and verification steps for each neural network architecture again.

[0169] Optional, training module, used for:

[0170] Based on prior knowledge of multi-axis fatigue and the correlation between the target features and multi-axis fatigue life, a physical constraint loss function is designed and embedded in each neural network architecture.

[0171] Optional, building modules, used for:

[0172] Interpolation sampling is performed within the feature value space defined by the multiaxial fatigue test database to obtain interpolated sampling data;

[0173] The interpolated sampled data is mixed with the original data to construct an enhanced dataset for each network module.

[0174] Optional, output module, used for:

[0175] The input and output sample data of each network module are obtained from the augmented dataset, and the input and output sample data contains the mapping relationship between the target features and the output of the network module;

[0176] Using mean squared error as the regression performance index, the symbolic regression algorithm is applied to fit the input and output sample data to obtain the interpretable quantization equations of each network module.

[0177] The interpretable quantization equations of each network module are combined according to the functional relationship of the target multiaxial fatigue life prediction equation to generate a symbolic regression combination equation.

[0178] The generalization performance of the symbolic regression combination equation is evaluated, and the equation with the smallest generalization error is selected as the final multiaxial fatigue life prediction equation.

[0179] Optionally, the original data includes load characteristics; when applying the symbolic regression algorithm, the following constraints are considered:

[0180] The output of the interpretable quantization equation corresponding to D is always greater than 0;

[0181] The output of the interpretable quantization equation corresponding to A is always greater than 0;

[0182] The output of the interpretable quantization equation corresponding to B is always less than 0;

[0183] The output of the interpretable quantization equation corresponding to D increases with the increase of load characteristics.

[0184] It should be noted that the information interaction and execution process between the above modules are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, which will not be repeated here.

[0185] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0186] This application also provides a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, wherein the processor executes the computer program to implement the steps in any of the above method embodiments.

[0187] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps described in the various method embodiments above.

[0188] This application provides a computer program product that, when run on a computer device, enables the computer device to perform the steps described in the above-described method embodiments.

[0189] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying computer program code to a photographing device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0190] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0191] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed 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.

[0192] In the embodiments provided in this application, it should be understood that the disclosed apparatus / computer devices and methods can be implemented in other ways. For example, the apparatus / computer device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings or direct couplings or communication connections may be through some interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0193] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0194] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

[0195] Figure 5 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Figure 5 As shown, the computer device of this embodiment includes: at least one processor 20 ( Figure 5 (Only one is shown in the diagram), memory 21, and computer program 22 stored in said memory 21 and executable on said at least one processor 20, wherein said processor 20 executes said computer program 22 to implement the steps in any of the above embodiments of the multiaxial fatigue life prediction method.

[0196] The computer device may include, but is not limited to, a processor 20 and a memory 21. Those skilled in the art will understand that... Figure 5 The examples of computer devices are merely examples and do not constitute a limitation on computer devices. They may include more or fewer components than shown in the illustration, or combinations of certain components, or different components. For example, they may also include input / output devices, network access devices, etc.

[0197] The processor 20 may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0198] In some embodiments, the memory 21 may be an internal storage unit of the computer device, such as a hard drive or memory. In other embodiments, the memory 21 may be an external storage device of the computer device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, the memory 21 may include both internal and external storage units of the computer device. The memory 21 is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the computer program. The memory 21 can also be used to temporarily store data that has been output or will be output.

Claims

1. A method for predicting multiaxial fatigue life, characterized in that, include: Raw data is obtained from a multiaxial fatigue test database, and target features are derived based on the raw data. Based on a semi-empirical multi-axis fatigue life prediction method, multiple initial multi-axis fatigue life prediction equations are designed. A corresponding neural network architecture is constructed according to each initial multi-axis fatigue life prediction equation. The neural network architecture is trained by combining the target features and physical constraint loss function to obtain the target neural network. Interpolation sampling is performed on each network module of the target neural network to construct an enhanced dataset; Based on the augmented dataset, interpretable quantization equations for each network module are extracted by symbolic regression. After combining the interpretable quantization equations and filtering them through generalization, the final multi-axis fatigue life prediction equation is output. The step of obtaining raw data from a multiaxial fatigue test database and obtaining target features based on the raw data includes: The raw data is obtained from the multiaxial fatigue test database; wherein, the raw data includes material property characteristics, multiaxial loading path characteristics, and loading environment characteristics; Based on the original data, feature engineering is performed to generate an artificial feature set, and the original data and the artificial feature set are subjected to dimensionless processing to output a normalized feature set. The normalized feature set is sorted and filtered by feature importance to obtain the initial target features; Using multi-axis fatigue life as the output target, a shallow learning algorithm as the regressor, and mean squared error as the regression performance index, the initial target features are filtered to obtain the target features.

2. The multiaxial fatigue life prediction method as described in claim 1, characterized in that, The plurality of initial multiaxial fatigue life prediction equations include: ； ； ； in, For multi-axis fatigue life, A, B, C, b, and r are network modules to be determined, and D is the multi-axis damage parameter.

3. The multiaxial fatigue life prediction method as described in claim 2, characterized in that, The step of constructing a corresponding neural network architecture based on each initial multi-axis fatigue life prediction equation, and training the neural network architecture in conjunction with a preset physical constraint loss function to obtain the target neural network includes: A corresponding neural network architecture is constructed based on each initial multi-axis fatigue life prediction equation, so that A, B, C, D, b, and r correspond to independent network modules, and the connection mode between each network module is designed according to the initial multi-axis fatigue life prediction equation. By combining a pre-defined physical constraint loss function, each neural network architecture is trained and validated to determine the neural network architecture with the smallest error. The target multi-axis fatigue life prediction equation is obtained based on the neural network architecture with minimum error. The target neural network is obtained by optimizing the corresponding neural network architecture according to the target multi-axis fatigue life prediction equation and then performing the training and verification steps for each neural network architecture again.

4. The multiaxial fatigue life prediction method as described in claim 3, characterized in that, The method further includes: Based on prior knowledge of multi-axis fatigue and the correlation between the target features and multi-axis fatigue life, a physical constraint loss function is designed and embedded in each neural network architecture.

5. The multiaxial fatigue life prediction method as described in claim 1, characterized in that, The step of interpolating and sampling each network module of the target neural network to construct the augmented dataset includes: Interpolation sampling is performed within the feature value space defined by the multiaxial fatigue test database to obtain interpolated sampling data; The interpolated sampled data is mixed with the original data to construct an enhanced dataset for each network module.

6. The multiaxial fatigue life prediction method as described in claim 3, characterized in that, Based on the enhanced dataset, interpretable quantization equations for each network module are extracted using symbolic regression. These interpretable quantization equations are then combined and filtered through generalization to output the final multi-axis fatigue life prediction equation, including: The input and output sample data of each network module are obtained from the augmented dataset, and the input and output sample data contains the mapping relationship between the target features and the output of the network module; Using mean squared error as the regression performance index, the symbolic regression algorithm is applied to fit the input and output sample data to obtain the interpretable quantization equations of each network module. The interpretable quantization equations of each network module are combined according to the functional relationship of the target multiaxial fatigue life prediction equation to generate a symbolic regression combination equation. The generalization performance of the symbolic regression combination equation is evaluated, and the equation with the smallest generalization error is selected as the final multiaxial fatigue life prediction equation.

7. The multiaxial fatigue life prediction method as described in claim 6, characterized in that, The original data includes load characteristics; when applying the symbolic regression algorithm, the following constraints should be considered: The output of the interpretable quantization equation corresponding to D is always greater than 0; The output of the interpretable quantization equation corresponding to A is always greater than 0; The output of the interpretable quantization equation corresponding to B is always less than 0; The output of the interpretable quantization equation corresponding to D increases with the increase of load characteristics.

8. A multi-axis fatigue life prediction device, characterized in that, include: The acquisition module is used to acquire raw data from a multiaxial fatigue test database and obtain target features based on the raw data; The training module is used to design multiple initial multi-axis fatigue life prediction equations based on a semi-empirical multi-axis fatigue life prediction method, construct a corresponding neural network architecture based on each initial multi-axis fatigue life prediction equation, and train the neural network architecture by combining the target features and physical constraint loss function to obtain the target neural network. A construction module is used to perform interpolation sampling on each network module of the target neural network to construct an enhanced dataset; The output module is used to extract interpretable quantization equations of each network module through symbolic regression based on the augmented dataset, combine the interpretable quantization equations and output the final multi-axis fatigue life prediction equation after generalization screening. The step of obtaining raw data from a multiaxial fatigue test database and obtaining target features based on the raw data includes: The raw data is obtained from the multiaxial fatigue test database; wherein, the raw data includes material property characteristics, multiaxial loading path characteristics, and loading environment characteristics; Based on the original data, feature engineering is performed to generate an artificial feature set, and the original data and the artificial feature set are subjected to dimensionless processing to output a normalized feature set. The normalized feature set is sorted and filtered by feature importance to obtain the initial target features; Using multi-axis fatigue life as the output target, a shallow learning algorithm as the regressor, and mean squared error as the regression performance index, the initial target features are filtered to obtain the target features.

9. A computer device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method as claimed in any one of claims 1 to 7.

Images