A gear material multi-axial fatigue life prediction method based on a gated hybrid network

Abstract

The application discloses a gear material multi-axial fatigue life prediction method based on a gated hybrid network, which is used for solving the problem of insufficient life prediction accuracy caused by various loading paths, strong axial and shear coupling of non-proportional multi-axial cyclic load. The method comprises the following steps: obtaining multi-axial fatigue data of a target material, containing loading condition parameters, load path information and fatigue life labels, and extracting equivalent amplitude description information to form static features; constructing a representative loading cycle based on the condition parameters, and discretely sampling axial and shear components into multi-channel time series; dividing and standardizing the data set; establishing a gated hybrid network model, extracting loading history features through residual stacking of time dimension and channel dimension gating hybrid, and adopting a late fusion strategy to fuse static features and output life prediction values; in the training stage, a weak monotonic physical consistency constraint is introduced to improve the prediction stability and generalization ability. The application improves the reliability and applicability of multi-axial fatigue life prediction.

Description

Technical Field

[0001] This invention belongs to the field of fatigue life prediction, specifically involving a gated hybrid network prediction method that uses multi-axis loading path time series and equivalent amplitude features for fusion modeling. Background Technology

[0002] Metallic materials and their components are prone to fatigue damage under alternating loads. The initiation and propagation of fatigue cracks can lead to reduced load-bearing capacity or even failure. Engineering structures often bear multiple load components, including axial and torsional loads, during service, constituting a multiaxial fatigue problem. Compared to uniaxial fatigue, multiaxial fatigue life is significantly affected by load component coupling, phase difference, frequency ratio, and loading path morphology. Especially under non-proportional loading conditions, the material response exhibits stronger nonlinearity and path dependence, making life prediction more challenging. Taking gear transmission systems as an example, during torque transmission through meshing, the tooth root bending effect and the shear effect caused by torsional loads are superimposed. Critical and dangerous locations often exhibit axial-shear coupled multiaxial cyclic loads. Under conditions of variable speed, variable torque, or changing operating conditions, phase difference changes and non-proportional loading path characteristics may also occur, making life more sensitive to the loading path morphology. Existing multiaxial fatigue life assessment methods are mostly based on the equivalent stress / strain or critical plane concept, converting multiaxial loads into scalar damage parameters and then combining them with empirical or semi-empirical life relationships for life calculation. Such methods typically rely on pre-defined equivalence criteria and parameter assumptions. When faced with different materials, different loading paths, and complex working conditions, they often require specific calibration. Furthermore, they have limited ability to characterize factors such as additional load hardening effects caused by non-proportional loading and differences in path morphology, making it difficult to maintain consistent prediction accuracy and generalization ability across multiple loading paths.

[0003] With the development of data-driven methods, life prediction methods based on machine learning or neural networks are increasingly being applied to multiaxial fatigue problems. Among existing data-driven methods, one approach relies on manually constructed features and trained regression models; this type of method is heavily dependent on feature engineering and struggles to fully preserve the temporal structural information of the load history. Another approach attempts to directly use the load history sequence as network input, but multiaxial loading paths vary in length and scale, and there is complex coupling between axial and shear components; with limited sample size, the model is prone to training instability, sensitivity to path type, and insufficient generalization ability. Therefore, a multiaxial fatigue life prediction method is needed that can simultaneously characterize the path features of multiaxial load history, integrate some physical dimensional information, and introduce physical consistency constraints during the training phase to improve adaptability and prediction stability for various loading paths and material scenarios. Summary of the Invention

[0004] The technical problem this invention aims to solve is the insufficient accuracy and stability of multi-axis fatigue life prediction due to diverse loading path types, significant axial-shear coupling, and strong nonlinearity under non-proportional loading conditions. This invention provides a multi-axis fatigue life prediction method that can simultaneously characterize the historical path features of multi-axis loading and integrate equivalent amplitude physical description information. Furthermore, it introduces weak monotonic physical consistency constraints during the training phase, thereby improving the accuracy and stability of fatigue life prediction. This method is also applicable to typical axial-shear coupling conditions such as gear transmission components, and can provide predictive support for engineering material selection, working condition comparison, and life margin analysis.

[0005] The technical solution adopted in this invention is: a method for predicting the multi-axis fatigue life of gear materials based on gated hybrid networks, specifically including the following steps:

[0006] S1: Construction of fatigue test dataset;

[0007] Acquire multiaxial fatigue data of the target material under cyclic loading; the multiaxial fatigue data includes multiaxial loading condition parameters, load path information corresponding to the condition, and fatigue life label; and obtain an equivalent amplitude descriptor to form an equivalent feature vector s;

[0008] S2: Load path time series discretization;

[0009] A representative loading cycle is constructed based on the multi-axis loading condition parameters in step S1; the axial component and shear component are discretized and sampled within the loading cycle period to obtain a multi-channel time series X of length T, which includes an axial channel and a shear channel.

[0010] S3: Using the multi-channel time series X obtained in step S2 and the equivalent amplitude feature vector s obtained in step S1 as input data, and the fatigue life label as output data, construct a dataset.

[0011] S4: Model dataset preprocessing;

[0012] S41: Divide the data to obtain training data and test data;

[0013] S42: Calculate the standardization parameters based on the training dataset, and use the standardization parameters to standardize the training dataset and the test dataset;

[0014] S5: Construct a gated hybrid network model for fatigue life prediction;

[0015] S51: Construct a hybrid backbone network with loaded historical sequences to extract path features of the multi-channel time series X and output path lifetime index;

[0016] S52: In the loaded historical sequence hybrid backbone network, time-gated hybridization and channel-gated hybridization are set to realize information interaction between the time dimension and the channel dimension;

[0017] S53: The path life index and the equivalent amplitude feature vector s are fused in the prediction head network using a late fusion method to output the fatigue life prediction value.

[0018] S54: Construct a loss function that includes a mean squared error loss term and introduces a weak monotonic constraint term;

[0019] S6: Select the optimal gated hybrid network model for fatigue life prediction.

[0020] Preferably, in step S1, the multi-axis loading condition parameters include control waveform information, axial amplitude parameters and shear amplitude parameters, frequency ratio parameters and phase difference parameters, equivalent amplitude parameters, and fatigue life parameters; wherein the axial amplitude parameters include and The shear amplitude parameter includes and The frequency ratio parameter is The phase difference parameter is The equivalent amplitude parameters include and The fatigue life parameter is the test life. .

[0021] More preferably, in step S2, the discretization of the load path time series satisfies the following relationship:

[0022]

[0023] In the formula: and These are the axial and shear strain amplitudes, respectively. and For the corresponding frequency; This represents the phase difference.

[0024] More preferably, in step S41, K-fold cross-validation is used to partition and evaluate the dataset to obtain the optimal model parameters and optimal hyperparameters, specifically including:

[0025] a. Randomly divide the dataset into K non-overlapping subsets;

[0026] b. In each round, select K-1 subsets as training subsets to train the model, and use the remaining 1 subset as validation subset to evaluate the error;

[0027] c. Repeat K rounds, ensuring that each subset is used as a validation subset at least once;

[0028] d. Summarize the verification errors from each round to obtain the error set;

[0029] e. Statistically analyze the error set to obtain the cross-validation average error;

[0030] f. Select or optimize model hyperparameters and determine the target model based on the average error of cross-validation.

[0031] More preferably, in step S42, Z-standardization is applied to the multi-channel time series X and the equivalent amplitude feature vector s; standardization parameters are calculated using the training dataset and used for unified standardization of training and testing data; wherein the standardization of the time series input satisfies:

[0032]

[0033] In the formula: The set of sample indices for the training dataset; The number of training samples, Let be the value of the i-th sample in the k-th channel at time step t; and These are the mean and standard deviation of the training set in the k-th channel, respectively. It is a numerically stable term; the equivalent eigenvector s adopts a normalization method that is isomorphic to it.

[0034] More preferably, in step S51, the loaded historical sequence hybrid backbone network is composed of several gated hybrid modules stacked together; this is designed to comprehensively capture key damage features in complex non-proportional loading paths.

[0035] The core component of the loading history hybrid backbone network is the gated hybrid module. In this module, the time-dimensional gated sublayer is responsible for capturing the long-range dependencies of the loading history in the time dimension. The input load path time series is first normalized by the layer to stabilize the feature distribution. Then, value vectors and gate vectors are generated through two parallel linear mapping paths. After the gate vectors are processed by the GELU activation function, they are multiplied element-wise with the value vectors to achieve selective modulation of the time series information. This gating mechanism enables the model to adaptively identify and enhance key moments in the time series that contribute significantly to fatigue damage, while suppressing redundancy and noise interference. Then, the gated and modulated features are mapped back to the original time dimension through dimensionality reduction projection and form residual connections with the input to ensure the effective propagation of gradients in the deep network.

[0036] More preferably, in step S52, in order to simultaneously model the information interaction of the time dimension and the channel dimension, the gated mixing module adopts a dual-axis serial structure; after completing the time-dimensional gated mixing sub-layer, the feature sequence enters the channel-dimensional gated mixing sub-layer; the input features in this part generate a high-dimensional representation in the channel direction through parallel value mapping and gate mapping, and the gated branch uses the SiLU activation function for nonlinear transformation;

[0037] The concatenated processing of the time dimension and the channel dimension forms a complete gated hybrid module, which is stacked in the loading history hybrid backbone network to deepen the abstract representation of temporal features layer by layer. The deep stacking enables the network to capture multi-scale temporal patterns, from local strain cycle waveforms to global loading path envelopes, all of which can be effectively encoded. At the output of the backbone network, a time dimension projection layer and a channel dimension projection layer are set to compress the time dimension and the channel dimension to scalars, respectively. The time dimension projection layer learns a weighted time aggregation function to automatically identify the moment in the loading history that contributes the most to the lifetime prediction. The channel dimension projection layer learns the relative contribution weights of axial and shear strain components to the comprehensive damage index.

[0038] More preferably, in step S53, in the late fusion part, the core idea of ​​the late fusion strategy is to allow each feature branch to fully develop high-level semantic representations in its own feature space before fusing with the prediction head; in this model, the path lifetime index output by the historical hybrid backbone network is concatenated with the standardized equivalent magnitude descriptor in the feature dimension to form a three-dimensional fusion feature vector; this fusion vector is then input into a lightweight multilayer perceptron prediction head, and after a nonlinear transformation through a hidden layer, the final logarithmic fatigue lifetime prediction value is output;

[0039] The significant advantage of the late fusion strategy lies in the fact that the numerical scale and semantic level of static features are fundamentally different from those of the original time series, which can easily lead to confusion and information interference in the feature space. Late fusion allows the temporal branch to fully learn the abstract representation of the path morphology, while the static branch retains the direct semantics of the physical dimensions. The two achieve true complementarity in the high-level feature space. From a physical perspective, the path lifetime index can be regarded as a correction factor for the baseline lifetime, reflecting the additional impact of the loading path morphology on fatigue damage. The equivalent amplitude descriptor provides key anchoring information for determining the baseline lifetime. The role of the fusion prediction head is to learn how these three factors work together to determine the final fatigue lifetime.

[0040] More preferably, in step S54, the training loss function is a weighted sum of the mean squared error loss and the weak monotonic constraint loss, as shown in the following formula:

[0041]

[0042] In the formula: This is the mean square error loss; The loss is due to the monotonic consistency constraint. These are weighting coefficients; is the predicted lifetime value for the i-th sample; m is the boundary margin parameter;

[0043] The optimal prediction model obtained from the training is used to predict the fatigue life of subsequent test samples, so as to achieve rapid evaluation and analysis of fatigue life under different loading conditions.

[0044] More preferably, in step S6, the gated hybrid network model is iteratively trained using a gradient descent optimization algorithm, and the optimal model parameters are selected based on the average cross-validation error; the sample to be predicted is input into the optimal model after completing the dataset construction and standardization process in steps S1 to S5, and the predicted fatigue life is output.

[0045] The beneficial effects of this invention are as follows: By modeling the time series of multi-axis load paths using a gated hybrid network, path features related to the loading path morphology can be extracted, thereby improving the life characterization capability under various loading path conditions. Simultaneously, a late fusion strategy is employed to complementaryly fuse the path life index obtained from the loading history with the equivalent amplitude descriptor, allowing the model to retain load history information while introducing amplitude anchoring information with physical dimension semantics, thus improving the accuracy of fatigue life prediction. Furthermore, a weak monotonic consistency constraint term is introduced during model training to penalize sample pairs that violate the rule of increasing equivalent variable amplitude without decreasing life prediction, making the prediction results more consistent with engineering physics trends and enhancing the rationality and usability of the prediction results. Therefore, for engineering scenarios such as gears that are prone to non-proportional loading paths under varying working conditions, this invention can improve the stability of the results while maintaining prediction accuracy. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram of the load path serialization of the present invention;

[0048] Figure 3 This is a schematic diagram of the overall structure of the gated hybrid network of the present invention;

[0049] Figure 4 This is a diagram showing the internal structure of the gated hybrid module of the present invention;

[0050] Figure 5 This is a comparison chart of predicted lifetime and experimental lifetime in an example of the present invention; Figure 6 Parameter configuration for the gated hybrid network in this invention example; Detailed Implementation

[0051] To enable those skilled in the art to better understand the implementation details of the present invention, the technical solution of the present invention will be further described below in conjunction with the relevant accompanying drawings.

[0052] This invention proposes a method for predicting the multi-axis fatigue life of gear materials based on gated hybrid networks. The specific steps are detailed below. Figure 1 The specific steps are summarized below.

[0053] S1: Construction of fatigue test dataset;

[0054] Acquire multiaxial fatigue data of the target material under cyclic loading; the multiaxial fatigue data includes multiaxial loading condition parameters, load path information corresponding to the condition, and test life labels. .

[0055] In this embodiment, the multi-axis loading condition parameters include control waveform information, axial amplitude parameters, shear amplitude parameters, and frequency ratio parameters. Phase difference parameter Equivalent amplitude parameters and test life parameters Among them, the axial amplitude parameter includes and The shear amplitude parameter includes and The equivalent amplitude parameters include and .

[0056] In this embodiment, the multiaxial fatigue data were collected from the literature [1] Skibicki D, Pejkowski Ł. Low-cycle multiaxial fatigue behaviour and fatigue life prediction for CuZn37brass using the stress-strain models. International Journal of Fatigue, 2017,102:18–36.

[0057] S2: Load path time series discretization;

[0058] For each multi-axis loading condition, a representative loading cycle is constructed based on the multi-axis loading condition parameters obtained in step S1; within the loading cycle period, the axial component and shear component are discretized and sampled, and the continuous load path is mapped into a multi-channel time series of length T, wherein the multi-channel time series includes an axial channel and a shear channel.

[0059] like Figure 2As shown, the representative loading loop in this embodiment can be represented by the following equation:

[0060]

[0061] In the formula: and These are the axial and shear strain amplitudes, respectively. and For the corresponding frequency; This represents the phase difference.

[0062] By performing discrete sampling on the loading cycle described by equations (1) and (2) within one cycle, a discrete point sequence of the load path can be obtained, and a multi-channel time series X for network input can be further formed, thereby preserving the geometric morphology information and temporal evolution characteristics of the loading path.

[0063] S3: Dataset Construction;

[0064] The multi-channel time series X obtained in step 2 and the equivalent amplitude feature vector s obtained in step S1 are used together as the model input data, and the test lifetime obtained in step S1 is used as the model input data. The dataset used to build the model for training and testing, serving as the output data;

[0065] To facilitate regression training, lifespan labels can be represented in logarithmic form, and the model outputs the corresponding predicted lifespan. The logarithm of .

[0066] S4: Model dataset preprocessing;

[0067] S41: Divide the dataset into a training dataset and a test dataset;

[0068] To improve the reliability and generalization ability of the model evaluation results, and to avoid evaluation bias caused by introducing test set information during the model selection process, this embodiment uses K-fold cross-validation to partition and evaluate the dataset constructed in step S3, thereby obtaining the target model parameters and target hyperparameters, specifically including:

[0069] a. Randomly partition the dataset into K non-overlapping subsets (folds) based on the sample dimension. Ideally, each subset should contain approximately the same number of samples. In small sample scenarios, a fixed random seed can be used to ensure experimental reproducibility. Optionally, to avoid excessive differences in data distribution between different folds, a hierarchical partitioning method can be used to make the statistical distribution of lifetime labels in each subset as consistent as possible.

[0070] b. Component training / validation combination: In the Kth round of cross-validation, one subset is selected as the validation subset, and the remaining K-1 subsets are selected as the training subset; the gated hybrid network model is trained using the training subset, and the validation error is calculated on the validation subset. The validation error can be evaluated using one or more of the following metrics: mean squared error, mean absolute error, or relative error.

[0071] c. Cyclic Coverage Validation: Repeatedly execute K rounds, ensuring that each subset participates in the evaluation as a validation subset at least once, thereby reducing the randomness brought about by a single partition and making the error estimation more stable;

[0072] d. Summarize the error set: Summarize the validation errors obtained in each round to form an error set; optionally, record the changing trends of training loss and validation loss in each round to determine whether the model is overfitting or underfitting.

[0073] e. Statistical cross-validation average error: Statistically analyze the error set to obtain the cross-validation average error (and optional variance or standard deviation) to characterize the average performance and stability of the model under different data partitions.

[0074] f. Select / optimize hyperparameters and determine the target model: Select or optimize network hyperparameters and training hyperparameters based on the cross-validation average error. The hyperparameters include, but are not limited to: number of mixer layers, hidden dimension, hidden layer dimension of prediction head, dropout rate, learning rate, weak monotonic consistency constraint weights and margin parameters, etc. When the cross-validation average error reaches the optimal level or meets the preset threshold, determine the hyperparameter configuration corresponding to the target model.

[0075] Furthermore, to obtain the final deployable prediction model, after completing cross-validation and determining the optimal hyperparameters, the "training subset + validation subset" obtained during the cross-validation process can be merged, and the final model can be retrained using the optimal hyperparameters. A one-time evaluation can be performed on the reserved test dataset to obtain objective generalization performance results that do not participate in any hyperparameter selection process, thereby avoiding performance overestimation caused by test set leakage.

[0076] S42: Standardization process;

[0077] Based on the training dataset, a standardization parameter is calculated, and this parameter is used to standardize the multi-channel time series X and the equivalent amplitude feature vector s of both the training and test datasets to improve numerical conditions and ensure consistent scaling. In this embodiment, the Z-standardization of the time series input satisfies the following equation:

[0078]

[0079] In the formula: The set of sample indices for the training dataset; The number of training samples, Let be the value of the i-th sample in the k-th channel at time step t; and These are the mean and standard deviation of the training set in the k-th channel, respectively. The equivalent feature vector s is a numerically stable term; the equivalent feature vector s is standardized in a manner isomorphic to it; the training set and test set are standardized uniformly using training set statistics, which can avoid scale drift between different data partitions and improve the stability of model training and the consistency of evaluation.

[0080] S5: Construct and train a gated hybrid network model;

[0081] like Figure 3 As shown, a gated hybrid model is constructed and trained based on the dataset preprocessed in step S4. The gated hybrid network model includes a loaded historical sequence hybrid backbone network and a prediction head network. The loaded historical sequence hybrid backbone network models the multi-channel time series X and outputs a path lifetime index. The prediction head network fuses the path lifetime index with the equivalent amplitude feature vector s and outputs the predicted lifetime. The logarithm of .

[0082] S51: The loaded historical sequence hybrid backbone network is composed of several gated hybrid modules stacked together; it is designed to comprehensively capture key damage features in complex non-proportional loading paths. For example... Figure 3 and Figure 4 As shown, the backbone network takes a multi-channel time series X as input. First, it uses linear mapping to increase the dimensionality of the input channels to a preset latent dimension to improve feature representation. Then, it sequentially performs time-channel interaction modeling through multi-layer gated hybrid modules. Each gated hybrid module adopts a "normalization-gated hybridization-residual connection" structure to enhance the stability of deep training and suppress gradient vanishing. At the output of the backbone network, a time-dimensional projection layer and a channel-dimensional projection layer are set: the time-dimensional projection layer is used to perform weighted aggregation of the entire loading history to learn the aggregation result reflecting the "contribution of key time segments"; the channel-dimensional projection layer is used to learn the relative contribution of axial and shear channels (and their combinations) to the comprehensive damage representation. Together, they compress the high-dimensional time series features to form a path lifetime index (i.e., path lifetime representation). This path lifetime index, as a comprehensive characterization of the loading path morphology and historical effects, will be used for subsequent fusion prediction with static equivalent amplitude features.

[0083] The core component of the loading history hybrid backbone network is the gated hybrid module. In this module, the time-dimensional gated sublayer is responsible for capturing the long-range dependencies of the loading history in the time dimension. The input load path time series is first normalized by the layer to stabilize the feature distribution. Then, value vectors and gate vectors are generated through two parallel linear mapping paths. After the gate vectors are processed by the GELU activation function, they are multiplied element-wise with the value vectors to achieve selective modulation of the time series information. This gating mechanism enables the model to adaptively identify and enhance key moments in the time series that contribute significantly to fatigue damage, while suppressing redundancy and noise interference. Then, the gated and modulated features are mapped back to the original time dimension through dimensionality reduction projection and form residual connections with the input to ensure the effective propagation of gradients in the deep network.

[0084] S52: To simultaneously model the information interaction between the time dimension and the channel dimension, the gated hybrid module adopts a dual-axis serial structure. After completing the time-dimensional gated hybrid sub-layer, the feature sequence enters the channel-dimensional gated hybrid sub-layer. The input features in this part generate a high-dimensional representation in the channel direction through parallel value mapping and gate mapping. The gated branch uses the SiLU activation function for nonlinear transformation, thereby achieving adaptive selection and emphasis of the coupling information between channels.

[0085] The concatenated processing of the time dimension and the channel dimension forms a complete gated hybrid module, which is stacked in the loading history hybrid backbone network to deepen the abstract representation of temporal features layer by layer. The deep stacking enables the network to capture multi-scale temporal patterns, from local strain cycle waveforms to global loading path envelopes, all of which can be effectively encoded. At the output of the backbone network, a time dimension projection layer and a channel dimension projection layer are set to compress the time dimension and the channel dimension to scalars, respectively. The time dimension projection layer learns a weighted time aggregation function to automatically identify the moment in the loading history that contributes the most to the lifetime prediction. The channel dimension projection layer learns the relative contribution weights of axial and shear strain components to the comprehensive damage index.

[0086] S53: In the late fusion part, the core idea of ​​the late fusion strategy is to allow each feature branch to fully develop high-level semantic representations in its own feature space before fusing them with the prediction head. In this model, the path lifetime index output by the historical hybrid backbone network is loaded and the equivalent amplitude descriptor after standardization is concatenated in the feature dimension to form a three-dimensional fusion feature vector. This fusion vector is then input into a lightweight multilayer perceptron prediction head, and after a nonlinear transformation through a hidden layer, the final logarithmic fatigue lifetime prediction value is output.

[0087] The significant advantage of the late fusion strategy lies in the fact that the numerical scale and semantic level of static features are fundamentally different from those of the original time series, which can easily lead to confusion and information interference in the feature space. Late fusion allows the temporal branch to fully learn the abstract representation of the path morphology, while the static branch retains the direct semantics of the physical dimensions. The two achieve true complementarity in the high-level feature space. From a physical perspective, the path lifetime index can be regarded as a correction factor for the baseline lifetime, reflecting the additional impact of the loading path morphology on fatigue damage. The equivalent amplitude descriptor provides key anchoring information for determining the baseline lifetime. The role of the fusion prediction head is to learn how these three factors work together to determine the final fatigue lifetime.

[0088] S54: Construct a loss function that includes a mean squared error loss term and introduces a weak monotonic constraint term;

[0089] To balance the accuracy of numerical fitting in lifetime prediction with the reasonableness of the overall lifetime trend under equivalent amplitude changes, this embodiment constructs a composite loss function during the training phase. The training loss function includes a mean squared error loss term and a weak monotonic regularization term, as shown in the following equation:

[0090]

[0091] In the formula: This is the total loss function; This is the mean square error loss; The loss is due to weak monotonic consistency constraints. These are weighting coefficients; Let be the predicted lifetime value for the i-th sample; m is the boundary margin parameter. (Set) The set of sample pairs within a batch is constructed as follows: when the equivalent amplitude constraint corresponding to the i-th sample is greater than the equivalent amplitude constraint corresponding to the j-th sample, the ordered sample pair (i, j) is included in the set. ;

[0092] Its core idea is: for any satisfying Given sample pairs (i, j), we hope to predict lifespan based on trends. When a situation arises that violates the above trend, the amount of violation... If positive, a truncation penalty function is applied. A penalty is imposed on the sample pair; this term is 0 when the trend is not violated, thus avoiding unnecessary gradient intervention on sample pairs that satisfy the trend. The boundary margin parameter m is used to introduce a buffer, which can reduce excessive penalties caused by experimental dispersion, noise, or material discreteness when the equivalent magnitudes of two samples are close, thereby improving training stability and robustness.

[0093] In this embodiment, To control the proportion of the weak monotonic consistency constraint in the total loss, a smaller value is preferred, so that the main driver of model training still comes from... This avoids excessive intervention caused by regularized numerical fitting and avoids gradient instability caused by the introduction of meaningless constraints; the boundary margin parameter m is used to introduce a buffer, which can reduce excessive penalty caused by experimental dispersion and noise when the equivalent amplitudes of two samples are close.

[0094] S6: Iterative optimization and lifetime prediction;

[0095] Gradient descent-type optimization algorithms are used to iteratively train the gated hybrid network model, and the optimal model parameters are selected by cross-validation and averaging the error. The dataset to be predicted is prepared and standardized according to steps S1-S4, and then input into the optimal model to output the predicted lifetime. The logarithm of .

[0096] according to Figure 5 The results show that the horizontal axis represents the experimental lifetime (Cycles), and the vertical axis represents the predicted lifetime (Cycles). The diagonal line represents the ideal case where the predicted lifetime and the experimental lifetime are completely consistent. The figure also shows error dispersion bands centered on the diagonal (e.g., 1.5x and 2x dispersion bands) to visually reflect the range of relative error in the prediction results. To facilitate comparison of prediction performance under different loading path conditions, Figure 5 Different symbols are used to distinguish the loading path type of the samples, including four categories: reverse tension / compression, reverse cyclic torsion, proportional loading, and non-proportional loading. Figure 5 As can be seen, most sample points are distributed near the diagonal, and a large number of samples fall within the 1.5x or 2x dispersion band, indicating that the method of the present invention can achieve good fatigue life prediction on the dataset of this embodiment and maintain a relatively stable error level. Furthermore, from the distribution of loading path categories corresponding to different symbols, it can be seen that the sample points under typical single-component loading conditions such as reverse tension / compression and reverse cyclic torsion are generally close to the diagonal; while for conditions with axial and shear coupling effects and more significant differences in loading path morphology, such as proportional loading and non-proportional loading, the sample points also fall more frequently within the error dispersion band, indicating that the method of the present invention still has good adaptability and prediction stability when facing different loading path morphologies simultaneously.

[0097] Those skilled in the art should understand that the above embodiments are only used to illustrate the basic principles of the present invention and do not mean that the scope of protection of the present invention is limited to this specific implementation. For those skilled in the art, there can be many variations and adjustments in the implementation of the present invention. Any modifications, adjustments and equivalent substitutions within the framework of the basic principles of the present invention should be considered as included within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting the multi-axis fatigue life of gear materials based on gated hybrid networks, characterized in that, Includes the following steps: S1: Construction of fatigue test dataset; Acquire multiaxial fatigue data of the target material under cyclic loading; the multiaxial fatigue data includes multiaxial loading condition parameters, load path information corresponding to the loading condition, and fatigue life label; and obtain an equivalent amplitude descriptor to form an equivalent amplitude feature vector s; S2: Load path time series discretization; A representative loading cycle is constructed based on the multi-axis loading condition parameters in step S1; the axial component and shear component are discretized and sampled within the loading cycle period to obtain a multi-channel time series X of length T, which includes an axial channel and a shear channel. S3: Using the multi-channel time series X obtained in step S2 and the equivalent amplitude feature vector s obtained in step S1 as input data, and the fatigue life label as output data, construct a dataset. S4: Model dataset preprocessing; S41: Divide the dataset into a training dataset and a test dataset; S42: Use Z-standardization to preprocess the model's dataset, improve numerical conditions, and ensure consistent scaling; S5: Construct a gated hybrid network model for fatigue life prediction; S51: Construct a hybrid backbone network with loaded historical sequences to extract path features of the multi-channel time series X and output path lifetime index; S52: In the loaded historical sequence hybrid backbone network, time-gated hybridization and channel-gated hybridization are set to realize information interaction between the time dimension and the channel dimension; S53: The path life index and the equivalent amplitude feature vector s are fused in the prediction head network using a late fusion method to output the fatigue life prediction value. S54: Construct a loss function that includes a mean squared error loss term and introduces a weak monotonic constraint term; S6: Select the optimal gated hybrid network model for fatigue life prediction.

2. The method for predicting multi-axis fatigue life of gear materials based on gated hybrid networks according to claim 1, characterized in that, In step S1, the multi-axis loading condition parameters required for the fatigue dataset include control waveform information and axial amplitude parameters ( , ), shear amplitude parameter ( , ), frequency ratio parameter ( ), phase difference parameter ( ), equivalent amplitude parameters ( , ) and fatigue life parameters ( ).

3. The method for predicting multi-axis fatigue life of gear materials based on gated hybrid networks according to claim 1, characterized in that, In step S2, the discretization of the load path time series satisfies the following relationship: In the formula: and These are the axial and shear strain amplitudes, respectively. and For the corresponding frequency; This represents the phase difference.

4. The method for predicting multi-axis fatigue life of gear materials based on gated hybrid networks according to claim 1, characterized in that, In step S41, K-fold cross-validation is used to partition and evaluate the dataset constructed in step S3 to obtain the optimal model parameters and optimal hyperparameters for fatigue life prediction; the process is as follows: a. Divide the dataset into K non-overlapping subsets in a random manner; b. In each round of cross-validation, select K-1 subsets as training subsets to train the gated hybrid network model, and use the remaining 1 subset as validation subset to evaluate the prediction error of the model on the untrained data. c. Repeat the training and validation process for K rounds, ensuring that each subset is used as a validation subset at least once. d. Calculate the error index on each round of validation subset and summarize them to obtain the cross-validation error set; e. Statistically analyze the cross-validation error set to obtain the average cross-validation error; f. Based on the average error of the cross-validation, select or optimize the model hyperparameters, and determine the target model for fatigue life prediction under the selected hyperparameters.

5. The method for predicting multi-axis fatigue life of gear materials based on gated hybrid networks according to claim 1, characterized in that, In step S42, Z-normalization is used to standardize the multi-channel time series X and the equivalent amplitude feature vector s, in order to improve the numerical conditions and ensure consistent scaling; wherein, the standardization of the time series input is shown in equations (3) and (4): In the formula: The training dataset sample index set; The number of training samples, Let be the value of the i-th sample in the k-th channel at time step t; and These are the mean and standard deviation of the training set in the k-th channel, respectively. It is a numerically stable term; the equivalent eigenvector s adopts a normalization method that is isomorphic to it.

6. The method for predicting multi-axis fatigue life of gear materials based on gated hybrid networks according to claim 1, characterized in that, In step S51, the loading history sequence hybrid backbone network is composed of several gated hybrid modules stacked together; it is designed to comprehensively capture key damage features in complex non-proportional loading paths. The core component of the loading history hybrid backbone network is the gated hybrid module. In this module, the time-dimensional gated sublayer is responsible for capturing the long-range dependencies of the loading history in the time dimension. The input load path time series is first normalized by the layer to stabilize the feature distribution. Then, value vectors and gate vectors are generated through two parallel linear mapping paths. After the gate vectors are processed by the GELU activation function, they are multiplied element-wise with the value vectors to achieve selective modulation of the time series information. This gating mechanism enables the model to adaptively identify and enhance key moments in the time series that contribute significantly to fatigue damage, while suppressing redundancy and noise interference. Then, the gated and modulated features are mapped back to the original time dimension through dimensionality reduction projection and form residual connections with the input to ensure the effective propagation of gradients in the deep network.

7. The method for predicting multi-axis fatigue life of gear materials based on gated hybrid networks according to claim 1, characterized in that, In step S52, the construction of the multi-channel fusion component is described; To simultaneously model the information interaction between the time dimension and the channel dimension, the gated hybrid module adopts a dual-axis serial structure. After completing the time-dimensional gated hybrid sub-layer, the feature sequence enters the channel-dimensional gated hybrid sub-layer. The input features in this part generate a high-dimensional representation in the channel direction through parallel value mapping and gate mapping. The gated branch uses the SiLU activation function for nonlinear transformation. The concatenation of the time dimension and the channel dimension forms a complete gated hybrid module, which is stacked in the loaded historical hybrid backbone network to deepen the abstract representation of time-series features layer by layer. Deep stacking enables the network to capture multi-scale temporal patterns, effectively encoding everything from local strain cyclic waveforms to global loading path envelopes. At the output of the backbone network, a time-dimensional projection layer and a channel-dimensional projection layer are set to compress the time and channel dimensions to scalars, respectively. The time-dimensional projection layer learns a weighted time aggregation function to automatically identify the moment in the loading history that contributes the most to the lifetime prediction. The channel-dimensional projection layer learns the relative contribution weights of axial and shear strain components to the comprehensive damage index.

8. The method for predicting multi-axis fatigue life of gear materials based on gated hybrid networks according to claim 1, characterized in that, In step S53, the late fusion strategy includes fusing the path lifetime index obtained in steps S51 and S52 with the standardized equivalent amplitude feature vector obtained in step S42. The core idea of ​​the late fusion strategy is to allow each feature branch to fully develop high-level semantic representations in its own feature space before fusing them with the prediction head. In this model, the path lifetime index output by the historical hybrid backbone network is loaded and concatenated with the standardized equivalent magnitude descriptor in the feature dimension to form a three-dimensional fusion feature vector. This fusion vector is then input into a lightweight multilayer perceptron prediction head, and after a nonlinear transformation through a hidden layer, the final logarithmic fatigue lifetime prediction value is output. The significant advantage of the late fusion strategy is that the numerical scale and semantic level of static features are fundamentally different from those of the original time series, which can easily lead to confusion and information interference in the feature space. Late fusion allows the time-series branches to fully learn the abstract representation of the path morphology, while the static branches maintain the direct semantics of the physical dimensions. The two achieve true complementarity in the high-level feature space. From a physical perspective, the path lifetime index can be regarded as a correction factor for the baseline lifetime, reflecting the additional impact of the loaded path morphology on fatigue damage. The equivalent amplitude descriptor provides key anchoring information for determining the baseline life; the role of the fusion prediction head is to learn how these three factors work together to determine the final fatigue life.

9. The method for predicting multi-axis fatigue life of gear materials based on gated hybrid networks according to claim 1, characterized in that, In step S54, the training loss function includes a mean squared error loss term and a weak monotonic regularization term, as shown in equation (5): In the formula: This is the mean square error loss; The loss is due to the monotonic consistency constraint. These are weighting coefficients; Let be the predicted life value of the i-th sample; m is the boundary margin parameter; the optimal prediction model obtained by training is used to predict the fatigue life of subsequent test samples, so as to realize the rapid evaluation and analysis of fatigue life under different loading conditions.

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