Method for rapidly identifying fatigue damage state of metal component based on convolutional neural network

Abstract

This invention discloses a rapid method for determining the fatigue damage state of metal components based on a convolutional neural network, comprising the following steps: First, a one-dimensional random load signal is converted into a two-dimensional time-frequency domain image using continuous wavelet transform; then, a ResNet-18 convolutional neural network is used to extract the two-dimensional time-frequency domain image to determine the fatigue failure state of the component under load, while simultaneously identifying different load signal types. This method effectively avoids the tedious and time-consuming steps of constructing finite element models and S-N curves, significantly improving analysis efficiency.

Description

Technical Field

[0001] This invention belongs to the field of civil and mechanical engineering technology, and more specifically, relates to a rapid method for identifying fatigue damage and failure states of metal components based on convolutional neural networks. Background Technology

[0002] Fatigue failure of structural materials typically occurs under alternating stresses far below the yield strength, progressing through three stages: microcrack initiation, propagation, and eventual sudden fracture. This cumulative and irreversible fatigue damage poses a significant challenge to safety-critical fields such as mechanical, aerospace, and civil engineering. Currently, mainstream fatigue life assessment methods face numerous limitations: the finite element method (FEM) is computationally intensive and time-consuming, and its transient analysis is prone to distortion due to accumulated numerical errors when handling long-term cyclic loads; while direct cyclic algorithms effectively reduce computational costs, they are limited to ideal, purely periodic loads. Since components in actual operating conditions are often subjected to complex and irregular variable-amplitude loads, existing analysis methods based on constant-amplitude loads struggle to achieve accurate damage prediction. Therefore, the engineering community urgently needs to develop a new fatigue analysis method that combines accuracy, efficiency, and high reliability to adapt to complex load histories and ensure the long-term safety of critical industrial components. Summary of the Invention

[0003] To address the aforementioned problems, this invention proposes a rapid method for determining the fatigue damage state of metal components based on convolutional neural networks. It directly uses random load signals as input to achieve high-precision end-to-end prediction. This method not only accurately determines the fatigue state of the component ("failed" or "not failed"), but also simultaneously identifies the specific load signal type (e.g., sinusoidal or triangular wave loads). This method effectively avoids the tedious and time-consuming steps of constructing finite element models and SN curves, significantly improving analysis efficiency and providing a highly promising alternative for the rapid identification and prediction of component fatigue failure.

[0004] To solve at least one of the above-mentioned technical problems, according to one aspect of the present invention, a fast method for determining the fatigue damage state of metal components based on a convolutional neural network is provided, comprising the following steps: firstly, using continuous wavelet transform, a one-dimensional random load signal is converted into a two-dimensional time-frequency domain image;

[0005] The two-dimensional time-frequency domain image is extracted using a ResNet-18 convolutional neural network to determine the fatigue failure state of the component under load and to identify different load signal types.

[0006] Furthermore, when using the trained ResNet-18 convolutional neural network to determine the fatigue failure state, the determination results include: "undamaged" and "damaged" states under load.

[0007] Furthermore, the load signal is a sinusoidal load or a triangular load.

[0008] Furthermore, truncated Fourier series are used to represent the periodic displacement response within a single load cycle with period T. (t), the expression is

[0009]

[0010] Where n is the number of Fourier terms, ω represents the angular frequency, and u0, and The displacement coefficient is unknown.

[0011] Furthermore, the finite element method was used to perform fatigue failure analysis and calculation of the structural components.

[0012] Furthermore, a direct loop algorithm is used for analysis.

[0013] According to another aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the method for rapid determination of fatigue damage failure state of metal components based on convolutional neural networks of the present invention.

[0014] According to another aspect of the present invention, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method for rapid determination of fatigue damage failure state of metal components based on convolutional neural networks of the present invention.

[0015] Compared with existing technologies, the beneficial effects of the above-described method of the present invention are as follows:

[0016] This invention only requires inputting the random load signal applied to the component, without the need for intermediate processes such as cumbersome constitutive relations and parameter value determination, as well as additional experiments and finite element models, to achieve rapid identification of fatigue damage and failure of structural components "end to end".

[0017] This invention can not only predict the fatigue damage and failure state of structural components, but also identify the type of load pattern that causes such fatigue damage and failure.

[0018] This invention is fast and accurate, with a fatigue damage prediction accuracy of over 95%. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments will be briefly described below. Obviously, the drawings described below only relate to some embodiments of the present invention and are not intended to limit the present invention.

[0020] Figure 1 This is a flowchart of a preferred embodiment of the present invention;

[0021] Figure 2 This is a diagram of a preferred embodiment of the ResNet-18 convolutional neural network architecture of the present invention;

[0022] Figure 3 This is a schematic diagram of a notched round bar specimen made of SA537 iron according to a preferred embodiment of the present invention;

[0023] Figure 4 This is a schematic diagram of the finite element mesh of a specimen (1 / 4) according to a preferred embodiment of the present invention;

[0024] Figure 5 This is a schematic diagram comparing the test results and finite element results of a preferred embodiment of the present invention.

[0025] Figure 6 This is a schematic diagram of the hysteresis loop characteristics of a specimen under cyclic loading according to a preferred embodiment of the present invention.

[0026] Figure 7 This is a schematic diagram comparing fatigue damage under the same load amplitude but different load carrier patterns, according to a preferred embodiment of the present invention.

[0027] Figure 8 This is a schematic diagram illustrating a preferred embodiment of the present invention with a random sinusoidal load example;

[0028] Figure 9 This is a schematic diagram illustrating a preferred embodiment of the random triangular load of the present invention;

[0029] Figure 10 This is a schematic diagram illustrating time-frequency domain cloud maps under four different operating conditions, representing a preferred embodiment of the present invention.

[0030] Figure 11 This is a schematic diagram of the training accuracy curve of a ResNet-18 convolutional neural network according to a preferred embodiment of the present invention;

[0031] Figure 12 This is a schematic diagram of the training loss curve of a ResNet-18 convolutional neural network according to a preferred embodiment of the present invention;

[0032] Figure 13 This is a schematic diagram of a test set confusion matrix according to a preferred embodiment of the present invention;

[0033] Figure 14 This is a schematic diagram of the F1 score of a test set according to a preferred embodiment of the present invention;

[0034] Figure 15 This is a schematic diagram of the ROC curve of the test set in a preferred embodiment of the present invention. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention.

[0036] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0037] Example 1:

[0038] like Figure 1-15 As shown, this invention provides a fast method for determining the fatigue damage state of metal components based on a ResNet-18 convolutional neural network, comprising the following steps:

[0039] First, continuous wavelet transform is used to convert the one-dimensional random load signal into a two-dimensional time-frequency domain image. Then, ResNet-18 convolutional neural network is used to extract these image features, which can not only determine the fatigue failure state of the component under load, but also identify different load signal types (this invention takes two load signals as examples). For example, in this invention, two load signals are used: one is a sinusoidal load and the other is a triangular load. When the trained ResNet-18 convolutional neural network is used to determine the fatigue failure state, the determination results include: (1) the "undamaged" and "damaged" states under triangular load; (2) the "undamaged" and "damaged" states under sinusoidal load. In addition, as a fast identification method for fatigue failure of structural components, the method of this invention can directly use random load signals as model input and the final identification results as model output, realizing fast and high-precision "end-to-end" prediction of fatigue failure state, effectively avoiding complex and time-consuming steps such as constructing SN curves and finite element models. Therefore, it provides a highly promising alternative for fatigue failure identification and prediction.

[0040] SA537 steel is a commonly used material in pressure vessels and liquefied gas carriers (for example, the manhole of a pressure vessel is usually made of SA537, while the vessel body is mostly made of SA553). To ensure the safety of pressure vessels during service, it is necessary to study the fatigue performance of SA537 steel under different load amplitudes. Therefore, this invention takes the fatigue analysis of an SA537 notched round bar as an example, using variable amplitude loads with two waveforms (triangular load and sinusoidal load) to analyze the fatigue failure state of the SA537 notched round bar under stress. Since it is impossible to conduct countless physical experiments to build a fatigue failure database of SA537 notched round bars under different load amplitudes, experimental data is used to verify the finite element model. Then, by changing the parameters of the finite element model, a fatigue failure response dataset of SA537 notched round bars under different loads is obtained. These datasets are also used to measure the recognition accuracy of the subsequent ResNet-18 convolutional neural network model. Subsequently, random load signals with different waveforms / amplitudes are randomly generated, and continuous wavelet transform is used to transform these generated random load signals, forming a time-frequency domain load signal atlas. Finally, a ResNet-18-based convolutional neural network model is applied to quickly determine the fatigue failure state of the component directly based on these different random load signal maps. The core work of this invention, and the training and testing workflow of the convolutional neural network used, are as follows: Figure 1 As shown.

[0041] Direct Cyclic Algorithm for Fatigue Analysis: Direct cyclic analysis is primarily used to efficiently obtain the stable response of structures under cyclic loading, especially suitable for low-cycle fatigue analysis of large structures with significant inelastic deformation. This invention's method can predict the long-term cyclic behavior of materials without simulating each individual load cycle. Compared to traditional transient analysis, its most significant advantage lies in its extremely high computational efficiency. Transient analysis typically requires simulating a large number of cycles to reach a stable state, resulting in extremely high computational costs for complex or large-scale models; while direct cyclic analysis effectively avoids this computational bottleneck by directly solving the stable response, providing a practical solution to engineering problems that traditional methods struggle to handle. In numerical implementation, the direct cyclic algorithm is a complex numerical technique combining Fourier series and time integrals of nonlinear material behavior, capable of directly calculating the stable cyclic response of a structure through an iterative process. This invention's method utilizes truncated Fourier series to represent the cyclic displacement response within a single load cycle (period T). (t), whose expression is

[0042]

[0043] Where n is the number of Fourier terms, ω represents the angular frequency, and u0, and The displacement coefficient is unknown.

[0044] When using the finite element method to perform fatigue failure analysis on structural components, the direct loop algorithm is mainly used for analysis.

[0045] The ResNet-18 convolutional neural network model is a classic residual network designed to effectively address the performance degradation problem that occurs in deep convolutional neural networks as the number of layers increases. Its core innovation lies in introducing shortcut connections for identity mappings. By skipping one or more layers, the model learns the residual function instead of directly fitting the underlying underlying mapping relationships. Structurally, ResNet-18 consists of 18 weighted layers, specifically designed for efficient image feature extraction. Its front end is a convolutional layer with 64 7×7 kernels (stride 2), followed by a max-pooling layer. The main body consists of four residual blocks, each containing two basic units composed of convolutional layers. The network outputs the final classification or prediction result through a global average pooling layer and a fully connected layer.

[0046] Simulation calculation of a notched round bar made of SA537 iron. The component used in the study is a notched round bar made of SA537 iron. A schematic diagram of the component is shown below. Figure 3 As shown. The specimen is 75 mm in total length, 10 mm in diameter, and has a notch radius of 2 mm. The finite element mesh is as follows. Figure 4 As shown, considering the symmetry of the component, only 1 / 4 of the component is used for finite element modeling. The finite element model consists of 681 four-node bilinear axisymmetric quadrilateral elements.

[0047] The mechanical parameters for the finite element calculation of the SA537 notched round bar were selected based on previous experience. Model verification used experimental data with a sinusoidal load amplitude of 0.0625 mm and an average displacement of 0.125 mm. The finite element numerical simulation employed an elastoplastic constitutive model, and the values ​​of parameters such as Young's modulus E, Poisson's ratio v, yield stress σy, and damage coefficient are listed in Table 1.

[0048] Table 1. Parameter values ​​for finite element simulation

[0049] E (MPa) <![CDATA[2×10 5 ]]> v 0.33 <![CDATA[σ y (MPa)]]> 400 <![CDATA[c1]]> 10.1 <![CDATA[c2]]> -1.439 <![CDATA[Δw0(mJ)]]> 1

[0050] c1 and c2 are material constants considering the damage initiation criterion, and Δw0 is a reference value for the hysteresis energy density per cycle.

[0051] Figure 5 The nonlinear relationship between component damage and the number of load cycles is shown. It can be seen that the finite element simulation results are in excellent agreement with the experimental results, indicating that the finite element model and parameter values ​​are reasonable and can be used to build a database for subsequent convolutional neural network model training.

[0052] Figure 6 This diagram shows the development of the hysteresis loop in an SA537 notched iron round bar under cyclic loading, indicating its gradual failure. It can be seen that the hysteresis loop area gradually decreases with increasing load cycles; simultaneously, the hysteresis loop continuously tilts to the right. These characteristics indicate a gradual deterioration of the mechanical properties of the experimental component, leading to increased damage and eventual failure.

[0053] Figure 7 The damage development of experimental components was compared under cyclic loading with the same amplitude but different waveforms. It can be seen that although the load amplitudes were the same, the different waveforms (one sinusoidal, the other triangular) resulted in different degrees of damage development in the components after the same number of cycles (within the same time frame). This indicates that the damage to the components depends not only on the magnitude of the cyclic load amplitude but also on the waveform shape of the load.

[0054] A rapid method for identifying fatigue damage in structural components based on a ResNet-18 convolutional neural network is proposed. Based on the aforementioned finite element simulation results, it can be seen that component damage depends not only on the amplitude of the applied load but also on the waveform of the load. In the real world, various engineering projects, buildings, and structures experience different loads. For example, high-rise buildings are subjected to significant wind loads, machine vibrations exert constant amplitude vibration loads on the foundation, while hydraulic structures, docks, and ships are subjected to random vibration loads from waves. Therefore, determining whether a structural component has suffered fatigue damage under cyclic loading requires fully considering the different differences in fatigue damage caused by different waveform loads. Since experimentally determining the fatigue damage of each structural component is impractical, finite element simulation can predict fatigue failure of the structural component under cyclic loading. However, finite element modeling is time-consuming and requires consideration of the mechanical properties of the building materials, constitutive relationships, and related parameter determination, making the calculations very cumbersome. Therefore, this invention proposes a fast and relatively accurate method for rapid identification of fatigue damage in structural components. The main features of this method are as follows:

[0055] (1) Only the random load signal applied to the component needs to be input. No intermediate process is required, such as the cumbersome constitutive relationship and parameter value determination, as well as additional experiments and finite element models, to achieve rapid identification of fatigue damage and failure of structural components from end to end.

[0056] (2) It can not only predict the fatigue damage state of structural components, but also identify the type of load waveform that causes such fatigue damage. In this invention, two waveform loads are used as examples for illustration.

[0057] (3) Fast and accurate. Taking two load carrier patterns as examples, the fatigue damage prediction accuracy of the model is over 95%.

[0058] The following is the specific model building and verification process.

[0059] First, a training database for the ResNet-18 convolutional neural network model is established.

[0060] 400 random load time history signals were generated using software and divided into four categories. (1) Random sinusoidal load with a small load amplitude, under which the specimen did not suffer fatigue damage (determined by finite element calculation), this condition is calibrated as SU; (2) Random sinusoidal load with a large load amplitude, under which the specimen suffered fatigue damage (determined by finite element calculation), this condition is calibrated as SD; (3) Random triangular load with a small load amplitude, under which the specimen did not suffer fatigue damage (determined by finite element calculation), this condition is calibrated as SynU; (4) Random triangular load with a large load amplitude, under which the specimen suffered fatigue damage (determined by finite element calculation), this condition is calibrated as SynD. Thus, each training set contains 100 random load time history signals. Figure 8 and Figure 9 The signal time history curves for random sinusoidal load and random triangular load are shown respectively.

[0061] Subsequently, the corresponding time-frequency domain contour maps of these four types of random load signals were obtained through continuous wavelet transform, as follows: Figure 10 As shown. Specifically, Figure 10 (a) shows the three time-frequency domain contour plots of the SynD operating condition. Figure 10 (b) Displays three time-frequency domain contour plots of the SynU operating condition. Figure 10 (c) Shows three time-frequency domain contour plots of the operating condition SD. Figure 10 (d) shows three time-frequency domain contour plots of the SU under load condition. The advantage of continuous wavelet transform is that it converts a one-dimensional random load signal into a two-dimensional time-frequency domain contour plot, thereby containing more load information and improving the prediction accuracy of the ResNet-18 convolutional neural network model.

[0062] The ResNet-18 convolutional neural network was then trained using these 400 time-frequency domain contour maps. For the training dataset split, 70 time-frequency domain contour maps were used for training, 10 for validation, and 20 for testing for each class. Before training, the time-frequency domain contour maps were uniformly adjusted to 224×224 pixels to meet the requirements of the ResNet-18 input layer. For training configuration, the Adam optimizer was selected, with a maximum of 30 training epochs. The accuracy during training varied with the number of iterations as follows: Figure 11 As shown. Figure 11 The accuracy rate shows that as the number of iterations gradually increases, it approaches 1 after approximately 60 iterations. Figure 12This corresponds to the display of the function loss during the training process. As you can see, the loss function value gradually decreases with the increase of the number of iterations until it approaches zero.

[0063] The validation dataset was used to set classification thresholds for the four categories, while the test dataset was used to evaluate the model's classification accuracy. Test results show that the ResNet-18 convolutional neural network achieves an accuracy of 0.975 in predicting the fatigue damage and failure state of structural components. Other metrics are as follows. Figure 13 The result is shown as a confusion matrix, representing the performance of the ResNet-18 convolutional neural network on the test set. It can be observed that, of all four fatigue damage states, only one time-frequency domain contour plot was incorrectly classified from condition SU to condition SD. Figure 14 The F1 scores for the four categories are all above 0.95, indicating that the ResNet-18 convolutional neural network performs excellently in classifying time-frequency domain cloud maps and can fully analyze the information contained in the cloud maps. Figure 15 The receiver operating characteristic (ROC) curves are shown, further demonstrating the excellent classification performance of the ResNet-18 convolutional neural network. The dashed line in the figure represents a random error with a probability of 0.5. By calculating the area under the curve (AUC) of the ROC plot, the average AUC for the model to identify the four types of fatigue damage states is 0.976. These metrics combined confirm that the ResNet-18 convolutional neural network is highly suitable for classifying and predicting time-frequency domain cloud maps in this invention.

[0064] In the real world, structural components are subjected to long-lasting and complex random loads, making accurate prediction of fatigue damage a highly challenging task for engineers. The finite element method (FEM) is widely used due to its low cost, high accuracy, and ability to capture the internal damage evolution and spatial distribution of components (e.g., identifying the location of maximum damage). However, the FEM has some significant drawbacks, including high computational cost and long simulation time. Furthermore, selecting the appropriate model parameters is a major challenge. Inappropriate parameter selection can lead to simulation results that deviate significantly from the actual fatigue damage levels of the components.

[0065] To overcome these limitations and simplify fatigue damage assessment, this invention proposes a rapid method for identifying the fatigue damage state of components based on a ResNet-18 convolutional neural network. In this method, a continuous wavelet transform is first used to convert the random cyclic load signal into a time-frequency domain contour map. These contour maps not only enrich the time-domain features of the random load signal but also impart frequency-domain features. Subsequently, these contour maps are used to train a ResNet-18 convolutional neural network model to classify different fatigue damage states. Results show that the method can accurately identify the fatigue damage and undamaged states of components and distinguish different random load patterns. The accuracy and F1 score of the identification results both exceed 0.95, indicating that the proposed method is a promising tool for assessing fatigue damage under complex cyclic loading conditions.

[0066] Example 2:

[0067] The computer-readable storage medium of this embodiment stores a computer program that, when executed by a processor, implements the steps in the rapid determination method for fatigue damage failure state of metal components based on convolutional neural networks in Embodiment 1.

[0068] The computer-readable storage medium in this embodiment can be an internal storage unit of the terminal, such as the terminal's hard disk or memory; the computer-readable storage medium in this embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc. equipped on the terminal; furthermore, the computer-readable storage medium can include both the terminal's internal storage unit and external storage devices.

[0069] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0070] Example 3:

[0071] The computer device of this embodiment includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the rapid determination method for fatigue damage failure state of metal components based on convolutional neural networks in Embodiment 1.

[0072] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The memory can include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory can also include non-volatile random access memory. For example, the memory can also store device type information.

[0073] Those skilled in the art will understand that the content disclosed in the embodiments can be provided as a method, system, or computer program product. Therefore, this solution can take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this solution can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage) containing computer-usable program code.

[0074] This solution is described with reference to flowchart illustrations and / or block diagrams of methods and computer program products according to embodiments of this solution. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0075] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0076] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0077] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0078] The examples described herein are merely preferred embodiments of the invention and are not intended to limit the concept and scope of the invention. Any modifications and improvements made by those skilled in the art to the technical solutions of the invention without departing from the design concept of the invention should fall within the protection scope of the invention.

[0079] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the specific embodiments described above. The specific embodiments and descriptions in the specification are merely for further illustrating the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the claims and their equivalents.

Claims

1. A method for rapid discrimination of fatigue damage state of metal components based on convolutional neural network, characterized in that, Includes the following steps: First, continuous wavelet transform is used to convert the one-dimensional random load signal into a two-dimensional time-frequency domain image; The two-dimensional time-frequency domain image is extracted using a ResNet-18 convolutional neural network to determine the fatigue failure state of the component under load and to identify different load signal types.

2. The method of claim 1, wherein, When using the trained ResNet-18 convolutional neural network to determine the fatigue failure state, the determination results include "undamaged" and "damaged" states under load.

3. The method of claim 2, wherein, The load signal is a sinusoidal load or a triangular load.

4. The method as described in claim 3, characterized in that, The periodic displacement response within a single load cycle with period T is represented using truncated Fourier series. (t), the expression is ， Where n is the number of Fourier terms, ω represents the angular frequency, and u0, and The displacement coefficient is unknown.

5. The method as described in claim 4, characterized in that, The finite element method is used to perform fatigue failure analysis and calculation of structural components.

6. The method as described in claim 5, characterized in that, The analysis is performed using a direct loop algorithm.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the steps in the method for rapid determination of fatigue damage and failure state of metal components based on convolutional neural networks as described in any one of claims 1 to 6.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the rapid determination method for fatigue damage and failure state of metal components based on convolutional neural networks as described in any one of claims 1 to 6.

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