A multi-stage variable-amplitude loading method for predicting fatigue life of a digital twin

Abstract

The present application relates to the technical field of structural fatigue life prediction, in particular to a multistage variable amplitude loading modulus double drive fatigue life prediction method, which comprises: carrying out multistage variable amplitude loading uniaxial fatigue test of metal structure to obtain sample data; constructing a physical model to extract a physical feature vector, which takes intrinsic damage dissipation as the core and introduces a nonlinear representation term to capture the load sequence effect; constructing a data-driven model containing NGMM data enhancement, semantic and time sequence coding and Mamba-Transformer collaborative architecture to extract data feature vectors; through full connection layer dimension unification, attention mechanism dynamic fusion and double item loss optimization, outputting fusion prediction value to predict the fatigue life of metal structure. The present application takes into account the physical interpretability and data nonlinear description ability, solves the problem of poor prediction accuracy of existing technology in the aspect of structural multistage variable amplitude loading fatigue life prediction, has strong cross material and working condition adaptability, and significantly improves the prediction accuracy and stability.

Description

A method for predicting fatigue life of multi-stage variable amplitude loading modulus dual drive Technical Field

[0001] This invention relates to the field of structural fatigue life prediction technology. Background Technology

[0002] Currently, in the field of fatigue life prediction under multi-stage variable amplitude loading of structures, the mainstream existing technologies can be divided into three categories based on their technical implementation paths: data-driven methods, physical-mechanical-driven methods, and physical-data fusion methods.

[0003] Data-driven approaches leverage machine learning techniques to build predictive models by uncovering latent patterns in large amounts of experimental data. Their core principle is utilizing the nonlinear mapping capabilities of algorithms to handle complex data relationships, making them a common method for dealing with multivariate and nonlinear problems. In practice, data-driven approaches typically employ both traditional machine learning algorithms and deep learning algorithms.

[0004] The physical mechanics-driven method is a prediction technique based on the principles of classical fatigue mechanics. Its core logic is to reveal the intrinsic mechanism by establishing a physical model of material fatigue damage evolution, thereby transforming microscopic damage into macroscopic failure under load. This is a traditional core technology in the field of structural fatigue life prediction, and it is also the earliest and most theoretically mature method applied in engineering. Based on the degree to which it characterizes the nonlinear effects of fatigue damage accumulation, this type of method is further divided into linear fatigue cumulative damage models and nonlinear fatigue cumulative damage models. The linear fatigue cumulative damage model, represented by Miner's linear cumulative damage rule, assumes that fatigue damage accumulation is independent of the load loading order. It only requires directly summing the damage values ​​corresponding to each load level, and determining structural failure when the cumulative damage value reaches 1. This model has a simple calculation logic, and the computational load is linearly related to the load level, requiring no complex iterations. The nonlinear fatigue cumulative damage model addresses the limitation of linear models in characterizing the load sequence effect. It is constructed based on the nonlinear characteristics of material fatigue mechanics. By introducing parameters such as the damage interaction coefficient and stress ratio correction term, it breaks through the assumption that the load sequence is irrelevant. It can initially capture the nonlinear effect of "high amplitude load accelerates low amplitude damage and low amplitude load inhibits high amplitude damage" in multi-level variable amplitude loading, which is an important direction for the improvement of linear models.

[0005] The essence of the physics-data fusion method is to break down the isolation between data-driven and physics-mechanical-driven approaches. On the one hand, it can solve the problem of weak theoretical support caused by the "black box nature" of data-driven models, while reducing the dependence on massive amounts of labeled experimental data, making it particularly suitable for applications involving multi-stage variable amplitude loading of structures. On the other hand, it can correct parameters in the physics-mechanical model that are difficult to quantify precisely through the data-driven module, solving the problem of large errors in fatigue life prediction by traditional physics-mechanical models under multi-stage variable amplitude loading. Currently, the mainstream fusion methods are mainly implemented in two ways: one is the physical constraint type, which uses physical and mechanical principles as "prior knowledge" for the data model, embedding constraints during the model construction stage to limit the output range of the data-driven model; the other is the parameter optimization type, which uses the physics-mechanical model as a basic framework and utilizes data-driven methods to optimize key parameters of the physics-mechanical model or supplement blind spots in the mechanism.

[0006] Although the three mainstream technologies in the field of fatigue life prediction under multi-stage variable amplitude loading have played a role in their respective scenarios, they all have significant technical shortcomings and performance bottlenecks in practical engineering applications. The accuracy of data-driven models is entirely based on "large-scale, high-quality, full-condition" labeled test data, but data acquisition for fatigue life prediction under multi-stage variable amplitude loading presents an inherent bottleneck. Furthermore, data-driven models only focus on statistical regularities between data points, failing to incorporate the fundamental physical and mechanical laws of fatigue damage, potentially leading to predictions that contradict common sense. The core of multi-stage variable amplitude loading lies in the load sequence effect and the interaction effect between loads—that is, the damage acceleration caused by high stress on low stress and the damage suppression caused by low stress on high stress. Traditional physical and mechanical driving methods have limited ability to characterize these nonlinear interactions. The linear fatigue cumulative damage assumption that "fatigue damage accumulation is independent of the load sequence" completely violates the nonlinear effects of fatigue cumulative damage under multi-stage variable amplitude loading. While existing nonlinear models can overcome the drawback of linear fatigue cumulative damage models not considering the nonlinear effects of fatigue cumulative damage, their nonlinear characteristics directly lead to a computationally far more complex process than linear models. Linear models can directly accumulate fatigue damage at each stage, with the computational load linearly related to the stress level. Nonlinear models, however, require dynamic adjustments to the damage accumulation method based on the stress value and stress sequence at each stage, and some models even require iterative solutions to nonlinear equations, resulting in an exponential increase in computational load. Although fusion methods are superior to single-drive methods, they still suffer from limitations in predicting the fatigue life of structures under multi-stage variable amplitude loading, including insufficient fusion depth and inaccurate capture of nonlinear effects. Most current fusion methods are merely loosely coupled architectures of "physical and mechanical driving model + data-driven model". The two only transmit information through a shallow structure and do not form a strict logical closed loop of mechanism guiding data learning and data feedback mechanism optimization. Nonlinear effects are the core of fatigue cumulative damage under multi-level variable amplitude loading of structures, but the existing physical and mechanical models themselves have significant limitations. This means that even if the data-driven model has powerful performance, it will be unable to accurately capture the evolution law of fatigue cumulative damage due to the mismatch of the basic framework. Summary of the Invention

[0007] To overcome the problem of poor prediction accuracy in the prediction of fatigue life under multi-stage variable amplitude loading of structures in existing technologies, this invention provides a method for predicting fatigue life under multi-stage variable amplitude loading with a dual-drive modulus, comprising the following steps:

[0008] For metal structures, multi-stage variable amplitude loading uniaxial fatigue tests were conducted, and the loading stress, number of loading cycles, and number of cycles from stress acting alone to structural fatigue failure were recorded for each loading stage, which were used as sample data.

[0009] Construct a physical model to extract physical feature vectors from the sample data;

[0010] Build a data-driven model to extract data feature vectors from sample data;

[0011] By fusing physical and data-driven models using feature fusion and prediction methods, the input sample data is used to output fused prediction values ​​as fatigue life prediction results.

[0012] Preferably, the physical model expression is:

[0013] ;

[0014] in, For each level of stress amplitude, This represents the actual number of loading cycles for each stress level. This refers to the number of cycles required to apply stress at each level until fatigue failure. for Under level stress loading, the degradation coefficient characterizing the strength degradation performance of a material is expressed as follows:

[0015] .

[0016] Preferably, constructing a data-driven model specifically involves:

[0017] Semantic and temporal encoding are performed on the sample data to obtain the encoded feature vector; a Mamba-Transformer collaborative architecture model is established, and the encoded feature vector is input into the Mamba-Transformer collaborative architecture model for feature extraction, and the data feature vector is output.

[0018] The Mamba-Transformer collaborative architecture model performs feature extraction as follows:

[0019] The encoded feature vector is input into the first Mamba module. The Mamba module includes linear layers, convolutional layers, a state space, and another linear layer. The linear layer performs dimensional transformation and nonlinear mapping on the input vector. The convolutional layer is used to capture the single-level stress effect in multi-level variable amplitude loading. The state space is used to handle the long-sequence stress interaction effect. The linear layer is used to perform the final transformation on the state space features. The original input features are then preserved through residual connections. Finally, the first Add&Norm process is performed. The feature vector processed by the first Mamba module is input into the multi-head attention module. After the output is processed, the second Add&Norm process is performed. Then, it is input into the second Mamba module. After the output is processed, the third Add&Norm process is performed to obtain the data feature vector.

[0020] Preferably, the method further includes data augmentation of the sample data using a Neural Gaussian Mixture Model (NGMM). The training stopping condition of NGMM is that the reconstruction error of the validation set is ≤0.01 for 5 consecutive rounds. The reconstruction error is equal to the mean lifetime error between the real sample and the model-generated sample / the mean lifetime error of the real sample. After training, the augmented dataset is obtained, and the augmented dataset is semantically encoded and temporally encoded.

[0021] Preferably, the feature fusion and prediction method is as follows:

[0022] The sample data is input into the constructed physical model and data-driven model. The two models output physical feature vectors and data feature vectors respectively. The physical feature vectors output by the physical model are processed through a fully connected layer to unify the dimensions and obtain the adapted physical feature vectors.

[0023] Calculate the similarity between the adapted physical feature vector and the data feature vector. :

[0024] ;

[0025] in, The adapted physical feature vector, For data feature vectors;

[0026] Calculate the self-similarity of data feature vectors :

[0027] ;

[0028] Calculate the weights of physical eigenvectors and data feature vectors :

[0029] ;

[0030] ;

[0031] in, ;

[0032] Calculate the fusion feature vector :

[0033] ;

[0034] Lifetime prediction is performed on the fused feature vectors using both a physical model and a data-driven model. The physical model outputs a deterministic lifetime prediction. Data-driven model outputs lifetime prediction values Calculate the predicted standard deviation for:

[0035] ;

[0036] in, The covariance matrix output by the NGMM model. The diagonal elements of this matrix represent the variance of the corresponding dimension parameter. The weights of the different Gaussian distribution components output by the NGMM model. Based on , , The calculated weighted variance;

[0037] Calculate the fusion prediction value :

[0038] ;

[0039] in, This is a correction factor, and its value is an empirical value of -0.1. For the weights of the physical model, For the data-driven model weights, the two weights are calculated as follows:

[0040] ;

[0041] ;

[0042] in, , These represent the mean absolute errors of the physical model and the data-driven model on the validation set, respectively.

[0043] Preferably, step S4 further includes data preprocessing, using Z-score standardization to unify the data volume:

[0044] ;

[0045] in, These are the standardized sample values. For each sample value in the original sample data, The mean of the original sample data. This represents the standard deviation of the original sample data.

[0046] Preferably, it further includes: calculating the prediction error loss. :

[0047] ;

[0048] in, The total number of training samples, For the first The final fusion of training samples predicts fatigue life. This represents the actual fatigue life of the sample.

[0049] Calculate physical constraint loss :

[0050] ;

[0051] in, This represents the cumulative fatigue damage value output by the physical model. The strength degradation coefficient output by the physical model. This is the maximum strength degradation coefficient of the material;

[0052] By predicting error loss and physical constraint loss The two loss terms are fused and backpropagation is used to optimize the training, resulting in the output. As a result of fatigue life prediction.

[0053] Preferably, the constraint weights for backpropagation optimization training are set to 0.3 in the early stage, 0.5 in the middle stage, and 0.7 in the later stage.

[0054] Preferably, a portion of the sample data is randomly selected as the test set. Backpropagation optimization training is performed using the test set, with the Adam optimizer selected for training, until the test set is optimized. The proportion of samples falling within ±1.5 times the error band is ≥90%, and the average relative error is ≤8%. Output As a result of fatigue life prediction.

[0055] Preferably, it further includes: introducing new sample data; if the amount of newly introduced sample data reaches 15% of the original sample data or a new stress level is introduced, repeat the construction of the physical model, the data-driven model, and the fusion of the physical model and the data-driven model; after passing three-level verification, it is put into use, and the three-level verification is that the new test set indicators meet the standards, the performance degradation of the old test set is ≤5%, and the absolute error of the new stress sample is ≤10%.

[0056] The beneficial effects of this invention are as follows:

[0057] This invention solves the problems of "disconnect between physical laws and data features and weak generalization ability" in traditional fusion methods, enabling the model to have both physical interpretability and data-driven nonlinear characterization ability. It also has stronger adaptability across materials (smooth specimens and welded structures) and across working conditions, and its stability is significantly better than that of pure physical models or pure data-driven models.

[0058] To address the industry bottleneck of scarce multi-stage amplitude fatigue test data for metals, this invention employs a neural Gaussian mixture model (NGMM). By learning the mapping relationships in existing test data, and under the premise of strictly adhering to physical laws, it generates a large number of virtual test samples that meet specific load conditions, effectively supplementing the lack of real data.

[0059] This invention overcomes the single defects of traditional Transformer in processing long sequences, namely "high computational complexity and low efficiency of temporal modeling" and Mamba model, which are "weak global feature capture capabilities". It deeply integrates the two and adopts a progressive logic of "Mamba temporal mining → Transformer global fusion → Mamba temporal refinement" in the module chain to ensure that features are synergistically optimized in the temporal and semantic dimensions.

[0060] This invention takes "intrinsic damage dissipation" as its core framework and makes key improvements to address the inherent defects of traditional physical models: it introduces nonlinear characteristic terms to transform linear damage superposition into nonlinear superposition considering exponential relationships, accurately capturing the load sequence effect of "high stress preloading accelerating low stress damage and low stress preloading inhibiting high stress crack propagation"; it selects a logarithmic function to define the strength degradation coefficient, whose derivative increasing characteristics are highly consistent with the accelerated evolution law of damage in the later stage of fatigue, and can comprehensively cover the strength degradation behavior under different materials and stress levels. Attached Figure Description

[0061] Figure 1 is a schematic diagram of the overall process of the fatigue life prediction method of multi-stage variable amplitude loading modulus dual drive according to an embodiment of the present invention;

[0062] Figure 2 is a schematic diagram of the data-driven model architecture according to an embodiment of the present invention;

[0063] Figure 3 is a schematic diagram of the physical-data fusion-driven prediction model according to an embodiment of the present invention;

[0064] Figure 4 is a schematic diagram of fatigue life prediction results of the physical-data fusion driven model according to an embodiment of the present invention;

[0065] Figure 5 is a schematic diagram comparing the fatigue life prediction errors of the three models in the embodiment of the present invention. Detailed Implementation

[0066] Example 1:

[0067] An embodiment of the present invention provides a method for predicting the fatigue life of a multi-stage variable amplitude loading modulus dual-drive system, as shown in Figures 1-2, comprising the following steps:

[0068] S1. Conduct uniaxial fatigue tests with multi-stage variable amplitude loading on smooth metal specimens or welded joint specimens, and record the stress at each loading stage. Loop loading count And the number of cycles of stress acting alone until structural fatigue failure, i.e., fatigue life. , to obtain sample data.

[0069] S2. Construct a physical model to extract physical feature vectors from the sample data.

[0070] The specific method for constructing the physical model is as follows: taking intrinsic damage dissipation as the core, a basic framework for fatigue cumulative damage is established as follows:

[0071] ;

[0072] in, For each level of stress amplitude, This represents the actual number of loading cycles for each stress level. This refers to the number of cycles required to apply stress at each level until fatigue failure.

[0073] Introducing a nonlinear characterization term It is used to transform linear superposition into nonlinear superposition considering exponential relationships, and can capture the nonlinear deviation of fatigue accumulation rate caused by load sequence and material strength degradation, thereby effectively characterizing the nonlinear effect of fatigue damage accumulation.

[0074] Therefore, the physical model is as follows:

[0075] ;

[0076] in, for Under level stress loading, the degradation coefficient characterizing the strength degradation performance of a material is expressed as follows:

[0077] ;

[0078] This invention uses the slope of the residual strength model characterized by a logarithmic function to define the degradation coefficient. Its derivative characteristics are consistent with the accelerated evolution law of damage in the later stage of fatigue, and can cover the strength degradation behavior of different materials and different stress levels.

[0079] The physical model is used to process the sample data and output physical feature vectors.

[0080] S3. Construct a data-driven model to extract data feature vectors from sample data.

[0081] The specific methods for constructing data-driven models are as follows:

[0082] S31. Data augmentation of sample data is performed using a Neural Gaussian Mixture Model (NGMM). NGMM learns the mapping relationship in the existing data through feature standardization, shared feature layer extraction, and multi-path parallel processing. The training stopping condition of NGMM is that the reconstruction error of the validation set (reconstruction error = mean lifetime error between real samples and model-generated samples / mean lifetime error of real samples) is ≤0.01 for 5 consecutive rounds. Virtual samples need to meet the requirement that the lifetime value is between 1 / 10 and 10 times that of real samples, and the difference in the mean lifetime value is ≤5% when passing the t-test. In small sample scenarios, a large number of virtual samples that maintain physical consistency with real samples are generated to form an expanded dataset.

[0083] S32. Perform semantic encoding and temporal encoding on the expanded dataset to obtain the encoded feature vector;

[0084] Semantic encoding is used to uncover nonlinear physical logic such as "high stress - multiple cycles → rapid damage - short lifespan," mapping the stress amplitude at each level, the number of cycles, and the inter-level relationships between adjacent stress levels into high-dimensional semantic vectors. This injects interpretable physical semantics into the model, preventing the model's output from violating basic principles of fatigue mechanics. Temporal encoding is used to capture the sequential effects and dynamic interactions of multi-level variable amplitude stresses, accurately reconstructing the impact of stress sequence effects and the interaction effects between adjacent stresses on fatigue damage accumulation.

[0085] S33. Establish a Mamba-Transformer collaborative architecture model, input the encoded feature vector into the Mamba-Transformer collaborative architecture model for feature extraction, and output the data feature vector.

[0086] The Mamba-Transformer collaborative architecture model performs feature extraction as follows:

[0087] S331. The encoded feature vectors enter the Mamba module to capture the single-level stress effects and long-sequence stress interaction effects required for multi-level variable amplitude loading fatigue life prediction. The Mamba module includes linear layers, convolutional layers, a state space, and linear layers. The left and right linear layers perform dimensional transformation and nonlinear mapping on the input vectors, transforming the "semantic-temporal" features into a high-dimensional representation suitable for the application scenario of fatigue life prediction. The convolutional layers use small kernel size convolutions to accurately capture the single-level stress effects in multi-level variable amplitude loading. The state space is used to handle long-sequence stress interaction effects. The linear layers are used to perform the final transformation on the state space features. Then, the original input features are preserved through residual connections to reduce the gradient vanishing problem. Finally, the first Add&Norm (feature superposition and normalization) processing is performed to make the feature distribution more stable, ensure the convergence of the model during training, and improve the prediction accuracy.

[0088] S332. Input the feature vector processed by the Mamba module into the multi-head attention module. In order to address the impact of cross-level load interaction effect on fatigue life in multi-level variable amplitude loading fatigue life prediction, the correlation of cross-level stress is deeply explored through multiple attention heads to achieve global fusion.

[0089] S333. The feature vector processed by the multi-head attention module is subjected to a second Add&Norm process to ensure that the feature vector is transmitted without distortion. Then, the feature vector is input into the second Mamba module with the same structure as in step S331 to optimize local details from a global perspective. Finally, a third Add&Norm process is performed to obtain the data feature vector.

[0090] S4. The physical model and the data-driven model are fused using feature fusion and prediction methods. The input sample data is used to output the fused prediction value as the fatigue life prediction result.

[0091] As shown in Figure 3, the feature fusion and prediction method is as follows:

[0092] S41. Preprocess the input sample data, using Z-score standardization to unify the data volume:

[0093] ;

[0094] in, These are the standardized sample values. For each sample value in the original sample data, The mean of the original sample data. The standard deviation of the original sample data is used; after preprocessing, it is ensured that the magnitude of the input data is in the range of [-1,1] to meet the input requirements of the model.

[0095] The preprocessed sample data is randomly divided according to a ratio of "training set: validation set: test set = 7:2:1". During the division, stratified sampling is required to ensure that each stress matching method, such as high stress-low stress loading, low stress-high stress loading, and high stress-low stress-high stress loading, is evenly distributed among these three categories to avoid a certain matching method existing only in the training set. This ensures that the validation set can effectively monitor the model's generalization ability, while guaranteeing that the test set can accurately evaluate the model's predictive performance on unseen stress conditions.

[0096] S42. The partitioned sample data is synchronously input into the physical model and the data-driven model. Since the feature vectors output by the physical model and the data-driven model have different dimensions, the physical feature vectors output by the physical model are processed through a fully connected layer to unify the dimensions, resulting in adapted physical feature vectors.

[0097] The fully connected layer uses ReLU as its activation function. Its input dimension is adapted to the physical model features, and its output dimension is aligned with the data-driven model features. It achieves accurate matching between the physical feature dimension and the data feature dimension by combining linear transformation and nonlinear mapping, while retaining key information related to the physical mechanism and avoiding feature distortion during the dimension matching process.

[0098] S43. An attention mechanism is used to dynamically fuse the adapted physical feature vector and data feature vector.

[0099] First, the similarity between the adapted physical feature vector and the data feature vector is calculated using dot product operations. :

[0100] ;

[0101] in, The adapted physical feature vector, For data feature vectors;

[0102] Calculate the self-similarity of data feature vectors :

[0103] .

[0104] The correlation between two types of feature vectors in the fatigue life prediction task is quantified by dot product operation. The higher the similarity, the more reliable the contribution of the feature to the prediction result, providing an accurate quantitative basis for subsequent weight allocation.

[0105] Secondly, the Softmax function is used to... and Perform normalization processing and calculate the weights of the physical feature vectors. and data feature vectors :

[0106] ;

[0107] ;

[0108] in, .

[0109] In this way, the similarity of abstract concepts is transformed into weight values ​​that can be directly applied within the range of [0,1]. At the same time, the use of exponential operation can amplify the weight ratio of high similarity features, allowing more reliable features to receive more attention, thus solving the drawback of "low-reliability features occupying too much weight and interfering with the role of high-reliability features" in traditional fixed fusion weights.

[0110] Finally, calculate the fused feature vector. :

[0111] ;

[0112] in, The regularization coefficient is set to an empirical value of 0.05. On the one hand, it can constrain the range of differences between the physical model features and the data-driven model features, preventing the fusion result from deviating from the basic laws of mechanics due to excessive feature deviation. On the other hand, it can retain the difference information between features, providing a gradient basis for subsequent model optimization.

[0113] S44. Lifetime prediction is performed on the fused feature vector using both a physical model and a data-driven model. The physical model outputs a deterministic lifetime prediction value. Data-driven model outputs lifetime prediction values The uncertainty interval is:

[0114] ;

[0115] in, The formula for predicting the standard deviation is as follows:

[0116] ;

[0117] in, The covariance matrix in the NGMM model is the covariance of the output layer. The diagonal elements of this matrix represent the variance of the corresponding dimension parameter. In the NGMM model, the mixture weights represent the weights of different Gaussian distribution components in the output layer output. Based on , , The calculated weighted variance.

[0118] Calculate the fusion prediction value :

[0119] ;

[0120] in, This is a correction factor, and its value is an empirical value of -0.1. For the weights of the physical model, For the data-driven model weights, the two weights are calculated as follows:

[0121] ;

[0122] ;

[0123] in, , These represent the mean absolute errors of the physical model and the data-driven model on the validation set, respectively.

[0124] S45. Take the test set and predict the error loss. and physical constraint loss The two-term loss is fused and backpropagation is performed to optimize the prediction, ensuring that the prediction results are close to the actual fatigue life and strictly constraining the prediction process to conform to the basic laws of mechanics.

[0125] Calculate prediction error loss :

[0126] ;

[0127] in, The total number of training samples, For the first The final fusion of training samples predicts fatigue life. This represents the actual fatigue life of the sample.

[0128] Calculate physical constraint loss :

[0129] ;

[0130] in, The fatigue cumulative damage value is based on the output of the physical model. Then the constraint is 0, which conforms to the failure rule. The constraint term is Punish predictions that violate invalid logic; The strength degradation coefficient output by the physical model. The maximum strength degradation coefficient of the material is... Then this constraint is 0, which meets the strength characteristics. The constraint term is The intensity of punishment is degraded and the portrayal is distorted.

[0131] The constraint weights are set using a segmented adaptive adjustment strategy. In the early stage of training, the weights are set to 0.3 to prioritize the model learning mathematical laws and reduce prediction error loss. In the middle stage of training, the weights are set to 0.5 to balance prediction accuracy and physical constraints. In the later stage of training, the weights are set to 0.7 to strengthen physical constraints and ensure that the model output conforms to the basic laws of mechanics, avoiding overfitting in the later stage that could lead to physical violations.

[0132] The Adam optimizer was used to train the model until it reached the test set. The proportion of samples falling within ±1.5 times the error band is ≥90%, and the average relative error is ≤8%. Output As a result of fatigue life prediction.

[0133] S5. Introduce new sample data. If the amount of newly introduced sample data reaches 15% of the existing sample database or a new stress level is introduced, repeat steps S1-S4 to dynamically update and validate the model. The new sample database is divided into stratified sampling according to the ratio of "training set: validation set: test set = 7:2:1". After passing three levels of validation (the new test set indicators meet the standards, the performance degradation of the old test set is ≤5%, and the absolute error of the new stress sample is ≤10%), it can be put into use.

[0134] Example 2:

[0135] This embodiment provides an experimental case, using two-stage variable amplitude loading fatigue test data of two materials commonly used in rail vehicles: Q345 steel (smooth specimen) and ENAW6005 aluminum alloy (welded structure). Q345 steel is commonly used in rail vehicle body structures for secondary support frames, beams, columns, and other non-core load-bearing components such as side walls, end walls, and floor support structures. It can also be used for bogie spring supports and axle box positioning arm auxiliary connectors. ENAW6005 aluminum alloy, as a heat-treatable Al-Mg-Si alloy, is widely used in the manufacturing of rail vehicle body structures and components, especially in subways, light rail, and intercity EMUs. In the body frame, it is commonly used for support structures such as side walls, roof longitudinal beams, and cross beams. In the connection and assembly process, this alloy can be combined with other aluminum alloy components through welding, riveting, etc., and is suitable for components requiring overall structural stability, such as floor support beams and skirt frames. The two-stage variable amplitude loading fatigue test data for the two materials are shown in Tables 1 and 2, respectively.

[0136] Table 1

[0137] ;

[0138] Table 2

[0139] ;

[0140] Based on the fatigue test data of the two materials mentioned above, the fatigue life prediction method of the present invention, using the multi-stage variable amplitude loading modulus dual-drive method, was applied for prediction. The prediction results are shown in Figure 4. The prediction results are then compared with fatigue life prediction results based solely on the data-driven model and solely on the physical mechanics model, as shown in Figure 5. The error calculation formula is as follows:

[0141] ;

[0142] As shown in Figure 4, the fatigue life prediction results of this invention for Q345 steel and ENAW6005 aluminum alloy are generally concentrated, with most data points falling within the ±1.5 life factor range, some within the ±2 life factor range, and only a very few data points approaching the ±3 life factor range. This indicates that it has high accuracy and stability in predicting the fatigue life of both materials. Further analysis of the error comparison in Figure 5 reveals that the prediction error of the pure physical mechanics model fluctuates significantly between the two materials, showing poor adaptability to different materials. In contrast, the errors of the pure data-driven model and the fusion model are more concentrated overall, with smaller fluctuations, demonstrating more stable prediction performance. The error of the fusion model is the lowest among the three materials. A detailed analysis of the prediction results for the two materials follows. First, the materials in the training samples are all smooth, non-welded specimens, with loading methods mainly consisting of rotational bending or tension / compression. The loading scenario for Q345 steel falls within the cyclic loading range of smooth specimens. Therefore, the fusion model's physical model is based on the common mechanical laws of metal fatigue, while the data-driven model learns the loading characteristics of other smooth specimens and transfers them to the prediction of Q345. The synergistic effect of both models effectively reduces prediction errors even in the absence of specific training data, demonstrating good adaptability. ENAW6005 is an Al-Mg-Si alloy, and the fatigue test used a welded joint, which differs significantly from the structure in the training samples. However, as shown in Figure 5, the fusion model's prediction error is still lower than that of the pure data-driven model. This is mainly due to the fact that the fusion physical model itself has a lower prediction error for ENAW6005 aluminum alloy. Based on the universal mechanical mechanism of intrinsic damage dissipation and strength degradation, it is not significantly affected by differences in material structure, providing reliable physical priors for the fusion model, thus achieving error reduction even with significant differences in material types.

[0143] This invention has been described through embodiments. Those skilled in the art will understand that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of this invention.

Claims

1. A method for predicting fatigue life of a multi-stage variable amplitude loading modulus dual-drive system, characterized in that, Includes the following steps: For metal structures, multi-stage variable amplitude loading uniaxial fatigue tests were conducted, recording the loading stress, number of loading cycles, and the number of cycles until the structure failed under stress alone at each stage. This data was used as sample data. A physical model was constructed to extract the physical feature vectors from the sample data. The physical model expression is as follows: ;in, ， For each level of stress amplitude, This represents the actual number of loading cycles for each stress level. This refers to the number of cycles required to apply stress at each level until fatigue failure. for Under level stress loading, the degradation coefficient characterizing the strength degradation performance of a material is expressed as follows: The process involves constructing a data-driven model to extract data feature vectors from sample data. Specifically, this involves semantically and temporally encoding the sample data to obtain encoded feature vectors. A Mamba-Transformer collaborative architecture model is then established, inputting the encoded feature vectors into this model for feature extraction and outputting data feature vectors. The Mamba-Transformer collaborative architecture model performs feature extraction as follows: the encoded feature vectors are input into the first Mamba module. This module includes linear layers, convolutional layers, a state space, and a linear layer. The linear layer performs dimensional transformation and nonlinear mapping on the input vector. The convolutional layer captures single-stage stress effects during multi-stage variable amplitude loading. The state space handles long-order sequences. The system employs a series of stress interaction effects; linear layers are used to perform the final transformation of state space features; residual connections are used to preserve the original input features, and finally, the first Add&Norm process is performed; the feature vector processed by the first Mamba module is input into the multi-head attention module, and after the output, a second Add&Norm process is performed, followed by input into the second Mamba module, and after the output, a third Add&Norm process is performed to obtain the data feature vector; the sample data is augmented using a Neural Gaussian Mixture Model (NGMM). The training stopping condition for NGMM is that the reconstruction error of the validation set is ≤0.01 for 5 consecutive rounds. The reconstruction error is calculated as the mean lifetime error between the real sample and the model-generated sample / the mean lifetime error of the real sample. After training, the augmented dataset is obtained, and semantic and temporal encoding is performed on the augmented dataset. By fusing physical and data-driven models through feature fusion and prediction methods, the input sample data is used to output fused prediction values ​​as fatigue life prediction results.

2. The fatigue life prediction method for multi-stage variable amplitude loading modulus dual-drive according to claim 1, characterized in that, The feature fusion and prediction method specifically involves: inputting sample data into a constructed physical model and a data-driven model; the two models output physical feature vectors and data feature vectors respectively; passing the physical feature vectors output by the physical model through a fully connected layer for dimensionality unification to obtain adapted physical feature vectors; and calculating the similarity between the adapted physical feature vectors and the data feature vectors. ： ;in, The adapted physical feature vector, Given data feature vectors; calculate the self-similarity of the data feature vectors. ： ; Calculate the weights of the physical feature vectors and data feature vectors ： ； ;in, ; Calculate the fusion feature vector ： The fused feature vectors are used to predict lifetimes using both a physical model and a data-driven model. The physical model outputs a deterministic lifetime prediction. Data-driven model outputs lifetime prediction values Calculate the predicted standard deviation for: ;in, ， The covariance matrix output by the NGMM model. The diagonal elements of this matrix represent the variance of the corresponding dimension parameter. The weights of the different Gaussian distribution components output by the NGMM model. For based on 、 、 Calculate the weighted variance; calculate the fused prediction value. ： ;in, This is a correction factor, and its value is an empirical value of -0.

1. For the weights of the physical model, For the data-driven model weights, the two weights are calculated as follows: ； ;in, 、 These represent the mean absolute errors of the physical model and the data-driven model on the validation set, respectively.

3. The fatigue life prediction method for multi-stage variable amplitude loading modulus dual-drive according to claim 2, characterized in that, This also includes data preprocessing, using Z-score standardization to unify the data volume: ;in, These are the standardized sample values. For each sample value in the original sample data, The mean of the original sample data. This represents the standard deviation of the original sample data.

4. The fatigue life prediction method for multi-stage variable amplitude loading modulus dual-drive according to claim 2, characterized in that, Also includes: Calculate prediction error loss ： ;in, The total number of training samples, For the first The final fusion of training samples predicts fatigue life. The true fatigue life of this sample; calculate the physical constraint loss. ： ;in, This represents the cumulative fatigue damage value output by the physical model. The strength degradation coefficient output by the physical model. The maximum strength degradation coefficient of the material; through prediction error loss and physical constraint loss The two loss terms are fused and backpropagation is used to optimize the training, resulting in the output. As a result of fatigue life prediction.

5. The fatigue life prediction method for multi-stage variable amplitude loading modulus dual-drive according to claim 4, characterized in that, The constraint weights for the backpropagation optimization training are set to 0.3 in the early stage, 0.5 in the middle stage, and 0.7 in the later stage.

6. The fatigue life prediction method for multi-stage variable amplitude loading modulus dual-drive according to claim 4, characterized in that, A portion of the sample data is randomly selected as the test set. Backpropagation optimization training is performed using the test set, with the Adam optimizer selected for training, until the test set is fully utilized. The proportion of samples falling within ±1.5 times the error band is ≥90%, and the average relative error is ≤8%. Output As a result of fatigue life prediction.

7. The fatigue life prediction method for multi-stage variable amplitude loading modulus dual-drive according to claim 4, characterized in that, Also includes: Introduce new sample data. If the amount of newly introduced sample data reaches 15% of the original sample data or a new stress level is introduced, repeat the process of constructing the physical model, the data-driven model, and the fusion of the physical model and the data-driven model. After passing three levels of verification, it can be put into use. The three levels of verification are: the new test set indicators meet the standards, the performance degradation of the old test set is ≤5%, and the absolute error of the new stress sample is ≤10%.

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