Multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure

Abstract

The present invention discloses a multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure, which is applied to the field of fatigue reliability. Aiming at the limitations of the existing technology in predicting the metal fatigue life under defect-induced failure, the present invention realizes the uncertainty quantification of fatigue performance and the fitting of low-fidelity fatigue data with physical consistency through a physics-guided Wasserstein generative adversarial network. The concept of transfer learning is introduced, allowing the use of multi-fidelity fatigue data to train the physics-informed neural network during the training process. The influence of manufacturing defects on fatigue performance is embedded as a physical constraint, ensuring the physical consistency of the prediction results of the multi-fidelity physics-informed neural network.

Description

Technical Field

[0001] The present invention belongs to the field of fatigue reliability, and particularly relates to a metal fatigue life prediction technology under defect-induced failure. Background Art

[0002] With the rapid progress of industrialization, major equipment is developing towards precision, complexity, high reliability, and high safety. The fatigue performance of components and structures is usually controlled by defects inevitably introduced during the manufacturing process (casting, forging, and additive manufacturing technologies). These defects significantly reduce the fatigue strength and overall life compared to the theoretical performance of a given microstructure and are also one of the main sources of life dispersion. Due to its significant advantages in the forming and manufacturing of large and complex components, additive manufacturing technology has become one of the cutting-edge technologies promoting the leapfrog development of major equipment in the aerospace and aviation fields. However, the random manufacturing defects introduced by additive manufacturing technology still pose a challenge for its application under fatigue load conditions. The development of major equipment towards high reliability and high safety makes it crucial to comprehensively evaluate the fatigue performance degradation of key components under defect-induced failure for their engineering applications.

[0003] So far, there has been relatively deep accumulation in the research on fatigue failure behavior induced by defects such as additive manufacturing metals. Researchers expect to find a method that can reasonably and reliably predict the metal fatigue life under defect-induced failure. Thanks to the refined characteristics of manufacturing defects provided by computed tomography, studies on the influence of defects on fatigue performance have shown that the size, shape, and location of defects are the main factors affecting fatigue performance. This means that defect-sensitive fatigue modeling is crucial for quantifying the uncertainty of fatigue performance under defect-induced failure. However, due to the large number of manufacturing defects with various shapes, sizes, and irregular distributions in real components, and the complex interaction relationships among them, existing fracture mechanics models are difficult to correctly evaluate the influence of defects on fatigue performance. There is an urgent need to establish a high-precision fatigue life assessment method to ensure the service safety of key components.

[0004] Thanks to the rapid development of data-driven methods, machine learning algorithms with powerful data analysis and fitting capabilities provide a new perspective for exploring fatigue failure behavior induced by defects. However, the data-driven nature of machine learning models determines that their prediction and generalization performance depend on the scale and quality of the constructed training set. Considering the high economic cost and time consumption of fatigue tests, it is difficult to provide a sufficiently large data set to cover the entire observation range in engineering practice. For unknown scenarios outside the prediction training data set, pure data-driven machine learning models are difficult to provide reliable and accurate fatigue life predictions. More importantly, pure data-driven machine learning models are difficult to correctly understand fatigue failure behavior from a small amount of experimental data, which may lead to their fatigue life predictions often not conforming to physical laws. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure, which has significant advantages in improving the prediction performance, generalization ability and effectiveness of the fatigue life prediction model.

[0006] The technical solution adopted by the present invention is: a multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure, including:

[0007] S1. Obtain the test conditions, critical defect geometric characteristics, static mechanical properties of the same grade series of metals and their corresponding fatigue life test results to form an original fatigue database;

[0008] S2. Use physics-informed feature engineering to expand and preprocess the data in the fatigue database to obtain an expanded fatigue database, and divide the data in the expanded fatigue database into a training set and a test set;

[0009] S3. Construct a physics-guided Wasserstein generative adversarial network by using the fracture mechanics model as a physical constraint, and use the data in the training set to train the physics-guided Wasserstein generative adversarial network to obtain a low-fidelity fatigue data set;

[0010] S4. Construct a deep neural network and pre-train the deep neural network according to the low-fidelity fatigue data set;

[0011] S5. Introduce the influence of critical defect geometric characteristics on fatigue performance as a physical constraint in the deep neural network to construct a physics-informed neural network;

[0012] S6. Use the concept of transfer learning to fine-tune the parameters of the physics-informed neural network with the training set data as high-fidelity fatigue data. The construction of the multi-fidelity physics-informed neural network is realized through pre-training with low-fidelity fatigue data and fine-tuning with high-fidelity fatigue data. Use the test set data to test the prediction effect of the multi-fidelity physics-informed neural network to obtain an optimized multi-fidelity physics-informed neural network;

[0013] S7. Adopt an optimized multi-fidelity physics-informed neural network, input the test conditions, critical defect geometric characteristics, and static mechanical properties of a certain metal to be tested, and output its fatigue life prediction result.

[0014] Advantages of the present invention: Uncertainty quantification of fatigue performance and fitting of low-fidelity fatigue data with physical consistency are achieved through a physically-guided Wasserstein generative adversarial network. The concept of transfer learning is introduced, allowing the use of multi-fidelity fatigue data to train a physics-informed neural network during the training process. The influence of manufacturing defects on fatigue performance is embedded as a physical constraint, ensuring the physical consistency of the prediction results of the multi-fidelity physics-informed neural network. Compared with the prior art, the method of the present invention has the following advantages:

[0015] (1) The present invention establishes a multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure by introducing the concept of transfer learning. Based on a generative machine learning algorithm, low-fidelity fatigue data is fitted at low cost. The test data is used as high-fidelity fatigue data, and the influence of defect geometric features on fatigue is introduced as a physical constraint, establishing a set of fatigue life prediction processes based on metal defect characteristics under small sample conditions;

[0016] (2) The present invention constructs a physically-guided Wasserstein generative adversarial network by introducing a fracture mechanics model as a physical constraint. The adversarial learning framework of the Wasserstein generative adversarial network is used to realize the uncertainty quantification of metal fatigue performance under defect-induced failure and capture the potential distribution of critical defect geometric features. The physics-based discriminator established by the fracture mechanics model ensures the physical consistency of the fitted low-fidelity fatigue data, overcoming the inherent shortcomings of traditional models in generating low-fidelity data;

[0017] (3) The present invention comprehensively utilizes low-fidelity and high-fidelity fatigue data, making the life prediction results of metals containing manufacturing defects have small dispersion and high accuracy. The introduced physical constraints further improve the generalization ability and prediction stability of the present invention when facing data outside the training set and ensure the physical consistency of the prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flowchart of the multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure provided by the present invention;

[0019] Figure 2 is a schematic diagram of the physically-guided Wasserstein generative adversarial network structure in an embodiment of the present invention;

[0020] Figure 3 is a schematic diagram of the physics-informed neural network structure in an embodiment of the present invention;

[0021] Figure 4 is a curve graph of the physical loss process of the physics-informed neural network in an embodiment of the present invention;

[0022] Figure 5Schematic diagram of the comparison between the prediction results and experimental results of the additive manufacturing specimens by the method of the present invention. Detailed implementation manners

[0023] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0024] As Figure 1 shown, the embodiments of the present invention disclose a multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure, including the following steps:

[0025] S1. Obtain the test conditions, critical defect geometric features, static mechanical properties of the same grade series of metals and their corresponding fatigue life test results to form an original fatigue database;

[0026] S2. Use physics-informed feature engineering to expand and preprocess the data in the fatigue database, and divide the data in the fatigue database into a training set and a test set;

[0027] S3. Construct a physics-guided Wasserstein generative adversarial network with the fracture mechanics model as a physical constraint, configure the network structure and hyperparameters, and use the training set data to train the physics-guided Wasserstein generative adversarial network to obtain a low-fidelity fatigue data set;

[0028] S4. Construct a deep neural network and pre-train the deep neural network according to the low-fidelity fatigue data set;

[0029] S5. Introduce the influence of critical defect geometric features on fatigue performance as a physical constraint in the deep neural network to construct a physics-informed neural network;

[0030] S6. Use the concept of transfer learning to fine-tune the parameters of the physics-informed neural network with the training set data as high-fidelity fatigue data. The construction of the multi-fidelity physics-informed neural network is realized through pre-training with low-fidelity fatigue data and fine-tuning with high-fidelity fatigue data. Use the test set data to test the prediction effect of the multi-fidelity physics-informed neural network to obtain an optimized multi-fidelity physics-informed neural network;

[0031] S7. Adopt the optimized multi-fidelity physics-informed neural network, input the test conditions, critical defect geometric features, and static mechanical properties of a certain metal to be tested, and output its fatigue life prediction result.

[0032] Next, the above steps of the present invention will be further described.

[0033] S1. Obtain the test conditions, critical defect geometric characteristics, static mechanical properties of metals in the same grade series and their corresponding fatigue life test results to form an original fatigue database. In this embodiment, the material is selected as additively manufactured Ti-6Al-4V. The construction of the original fatigue database specifically includes:

[0034] S11. Define the defect size as the square root of the projected area of the defect perpendicular to the load direction area represents the projected area of the defect perpendicular to the load direction;

[0035] S12. Using the defect size calculated in S11, calculate the relative position of the defect. The functional expression of the relative position of the defect is:

[0036]

[0037] where d represents the distance from the defect to the free surface of the specimen closest;

[0038] S13. Using the defect size calculated in S11, characterize the defect shape by the defect roundness c. The calculation method of the defect roundness is:

[0039]

[0040] where R represents the maximum distance from the geometric center of the projected area to the boundary. The details of the original fatigue database constructed for this material are shown in Table 1.

[0041] Table 1 Fatigue database of additively manufactured Ti-6Al-4V

[0042]

[0043] In Table 1, σ u is the ultimate tensile strength; in this embodiment, considering that there are many data points in the dataset, Table 1 uses the minimum value, maximum value, average value, and standard deviation of each feature to characterize the fatigue database.

[0044] S21. Use the stress intensity factor to characterize the local stress concentration caused by the defect, and use the stress intensity factor as an extended feature;

[0045] Furthermore, the calculation method of the stress intensity factor is:

[0046]

[0047] where △σ represents the stress range and Y represents the position factor.

[0048] S22. Use the normalized S-N curve as the driving force for crack propagation, and use the normalized S-N curve as an extended feature. The functional expression of the normalized S-N curve is:

[0049]

[0050] Among them, N f represents the fatigue life, and σ w represents the fatigue limit. A and B represent material parameters.

[0051] The expression for the fatigue limit is:

[0052]

[0053] Among them, HV represents the Vickers hardness, and σ w represents the fatigue limit. A and B represent material parameters. The expression for the fatigue limit is:

[0054]

[0055] Among them, HV represents the Vickers hardness, and μ represents the position factor. The detailed extended fatigue database constructed by this material is shown in Table 2.

[0056] Table 2 Extended Fatigue Database of Additive Manufactured Ti-6Al-4V

[0057] Feature Minimum value Maximum value Average value Standard deviation △K 8μm 331μm 66.459μm 50.807μm <![CDATA[△σ / σ w > 427.5MPa 799MPa 636.476MPa 100.528MPa Y 0.5 0.65 0.546 0.070

[0058] S23. Normalize the test conditions (△σ), critical defect geometric features ( h, c, d), static mechanical properties (σ u ), and extended features (△K, △σ / σ w , Y) in Tables 1 and 2 to the interval [-1, 1] as the input features for constructing the multi-fidelity physics-informed neural network;

[0059] S24. Perform logarithmic normalization on the fatigue life and normalize the fatigue life to the interval [-1, 1]. The function expression for normalization is:

[0060]

[0061] S3. Use the fracture mechanics model as the physical information to construct a physics-based discriminator. Specifically, introduce the Paris equation as the fracture mechanics model, and its expression is:

[0062]

[0063] Among them, a is the crack length, and C and m are material parameters. Introduce the physics-based discriminator into the Wasserstein generative adversarial network structure. As Figure 2 shown, the optimization objective for constructing the physics-guided Wasserstein generative adversarial network with physical constraints is:

[0064]

[0065]

[0066] Among them, G is the generator, and D p is the physics-based discriminator, and D d is the pure data-driven discriminator, and V W (·) is the Wasserstein distance, and V PW (·) is the optimization objective of the physics-guided Wasserstein generative adversarial network. The structure and parameter settings of the constructed physics-guided Wasserstein generative adversarial network are shown in Table 3.

[0067] Table 3 Structure and Parameter Settings of the Physics-Guided Wasserstein Generative Adversarial Network

[0068]

[0069] In the physics-guided Wasserstein generative adversarial network, the activation function adopts the Leaky-ReLU function, and its function expression is:

[0070]

[0071] Among them, α is a coefficient greater than zero, and x is the input of the neuron in the physics-guided Wasserstein generative adversarial network.

[0072] Use the training set obtained in step S2 to train the physics-guided Wasserstein generative adversarial network constructed in step S3 to fit the potential distributions of the test conditions, critical defect geometric features, static mechanical properties, and corresponding fatigue lives, and realize the uncertainty quantification of the fatigue life. After the physics-guided Wasserstein generative adversarial network is fully trained, use random noise as the input of the generator, and the generator outputs the simulated test conditions, critical defect geometric features, static mechanical properties, and their corresponding fatigue lives, so as to construct a low-fidelity fatigue data set.

[0073] S4. Construct a deep neural network, configure the network structure and hyperparameters, and pre-train the deep neural network according to the low-fidelity fatigue data set, specifically including:

[0074] S41. Configure the number of hidden layers of the deep neural network to be 6 layers. Each hidden layer in its network structure contains 144 neurons, the learning rate is set to 0.001, the regularization coefficient is set to 0, and the activation function adopts the Tanh function, and its function expression is:

[0075]

[0076] S42. Optimize the parameters of the deep neural network using low-fidelity fatigue data, and set the number of training rounds to 500;

[0077] S43. After the deep neural network is fully pre-trained on the low-fidelity fatigue data set, save the pre-trained network structure and parameters of the deep neural network locally.

[0078] S5. Summarize the effects of defect size, defect location, and defect shape on fatigue performance, and extract them into a programmable partial differential inequality form, as shown in Table 4.

[0079] Table 4 Effects of Defect Geometric Features on Fatigue Performance and Their Mathematical Descriptions

[0080]

[0081] Take the effects of defect size, defect location, and defect shape on fatigue performance as the constraint conditions in the optimization process of the deep neural network:

[0082] minLoss mse

[0083]

[0084] where Loss mse is the optimization objective of the deep neural network, and its calculation method is:

[0085]

[0086] where N p,i is the fatigue life predicted by the deep neural network corresponding to the i-th training data, and n is the number of fatigue data used for model training. Further, use the exterior penalty function method to transform this constrained optimization problem into an unconstrained optimization problem to construct a physics-informed neural network:

[0087] minLoss P

[0088] Loss P =(1 - λ)Loss mse +λLoss phy

[0089] where λ is the relaxation factor, Loss P is the loss function of the physics-informed neural network, and Loss phy is the physical loss function. Further, based on the exterior penalty function method, the calculation method of the physical loss function is:

[0090]

[0091]

[0092] Among them, j is the number of high-fidelity fatigue data in the training set. The constructed physics-informed neural network is as Figure 3 shown

[0093] S61. Set the network structure and activation function of the physics-informed neural network to be the same as those of the pre-trained deep neural network;

[0094] S62. Using the concept of transfer learning, let the physics-informed neural network read the network structure and parameters of the pre-trained deep neural network in step S4 saved locally, and limit the number of hidden layers that can be updated to the last layer to retain the feature information extracted from the low-fidelity fatigue data;

[0095] S63. Configure the learning rate of the physics-informed neural network to be 0.001, the regularization coefficient to be 0, and the physical constraint strength to be 0.05;

[0096] S64. Use the fatigue data of the training set as the high-fidelity fatigue data to fine-tune the parameters of the updatable hidden layer, so as to realize the construction of a multi-fidelity physics-informed neural network with a pre-trained deep neural network for low-fidelity fatigue data and a fine-tuned physics-informed neural network for high-fidelity fatigue data. During the fine-tuning process, use Loss P as the optimization target. When the optimization target of the model no longer decreases, it is considered that the prediction performance of the constructed multi-fidelity physics-informed neural network meets the requirements. Use the test set data to test the extrapolation performance of the fine-tuned multi-fidelity physics-informed neural network. Further, as Figure 4 shown, the introduced physical loss ensures the physical consistency of the prediction of the multi-fidelity physics-informed neural network.

[0097] S7. First, perform the test conditions, critical defect geometric features, and static mechanical properties of the additive manufacturing Ti-6Al-4V to be measured, and input them into the multi-fidelity physics-informed neural network after feature expansion for prediction, and output the predicted value of the fatigue life of the additive manufacturing alloy to be measured.

[0098] Figure 5 It is a comparison chart of the prediction results and experimental results according to the method of the present invention. The comparison between the experimental results and the prediction results shows that: by using a multi-fidelity physics-informed neural network to couple low-fidelity and high-fidelity fatigue data, the dispersion of the prediction results of the metal fatigue life under defect-induced failure is small, and the accuracy is relatively high. The introduced physical constraints further improve the generalization ability and prediction stability of the present invention when facing data outside the training set and ensure the physical consistency of the prediction results, which also shows the rationality and effectiveness of the multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure.

[0099] Those of ordinary skill in the art will realize that the embodiments described herein are to assist the reader in understanding the principles of the present invention and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, various changes and modifications can be made to the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure, characterized in that Including: S1. Obtain the test conditions, critical defect geometric features, static mechanical properties of metals in the same grade series and their corresponding fatigue life test results, and form an original fatigue database; S2. Use physical information feature engineering to expand and preprocess the data in the fatigue database to obtain an expanded fatigue database, and divide the data in the expanded fatigue database into a training set and a test set; S3. Construct a physics-guided Wasserstein generative adversarial network by using the fracture mechanics model as a physical constraint, and use the data in the training set to train the physics-guided Wasserstein generative adversarial network to obtain a low-fidelity fatigue data set; S4. Construct a deep neural network and pre-train the deep neural network according to the low-fidelity fatigue data set; S5. Introduce the influence of critical defect geometric features on fatigue performance as a physical constraint in the deep neural network to construct a physics-informed neural network; S6. Use the concept of transfer learning to fine-tune the parameters of the physics-informed neural network with the training set data as high-fidelity fatigue data. The construction of a multi-fidelity physics-informed neural network is realized through pre-training with low-fidelity fatigue data and fine-tuning with high-fidelity fatigue data. Use the test set data to test the prediction effect of the multi-fidelity physics-informed neural network to obtain an optimized multi-fidelity physics-informed neural network; S7. Adopt the optimized multi-fidelity physics-informed neural network, input the test conditions, critical defect geometric features, and static mechanical properties of a certain metal to be tested, and output the predicted result of its fatigue life.

2. The fatigue life prediction method of the multi-fidelity physics-informed neural network under defect-induced failure according to claim 1, wherein The test conditions include the stress range △σ; The geometric characteristics of critical defects include: defect size The relative position h of the defect, the roundness c of the defect, and the distance d from the defect to the free surface of the specimen closest; The static mechanical properties include the ultimate tensile strength σ u ; The fatigue life test results are specifically the stress range △σ, the defect size the relative position h of the defect, the defect roundness c, the distance d from the defect to the nearest distance of the specimen free surface, the ultimate tensile strength σ u and their respective fatigue lives N f .

3. The fatigue life prediction method of the multi-fidelity physics-informed neural network under defect-induced failure according to claim 2, characterized in that The process of expanding the data in the fatigue database is as follows: First, according to the stress range Δσ and the defect size calculate the stress intensity factor ΔK: Where Y represents the position factor; Use the normalized S-N curve as the driving force for crack growth, and use the normalized S-N curve as an expansion feature. The functional expression of the normalized S-N curve is: Among them, N f represents the fatigue life, σ w represents the fatigue limit, and A and B represent material parameters.

4. The multi-fidelity physics-informed neural network fatigue life prediction method under defect-induced failure according to claim 3, wherein, The extended features included in the extended fatigue database are △K, △σ / σ w , and Y.

5. The fatigue life prediction method of the multi-fidelity physics-informed neural network under defect-induced failure according to claim 4, characterized in that The specific implementation process of step S3 is: Introduce the Paris equation as the fracture mechanics model, and its expression is: Where a is the crack length, and C and m are material parameters; Use the fracture mechanics model as a physics-based discriminator; Introduce the physics-based discriminator into the Wasserstein generative adversarial network structure. The optimization objective for constructing the physics-guided Wasserstein generative adversarial network with physical constraints is: Among them, G is the generator, and D p is a physics-based discriminator, and D d is a pure data-driven discriminator. V W (·) is the Wasserstein distance, and V PW (·) is the optimization objective of the physics-guided Wasserstein generative adversarial network; The activation function in the physics-guided Wasserstein generative adversarial network uses the Leaky-ReLU function, and its functional expression is: Where α is a coefficient greater than zero, and x is the input of the neuron in the physics-guided Wasserstein generative adversarial network Use the training set obtained in step S2 to train the constructed physics-guided Wasserstein generative adversarial network to fit the potential distribution of test conditions, critical defect geometric features, static mechanical properties and corresponding fatigue life, and realize the quantification of fatigue life uncertainty. After the physics-guided Wasserstein generative adversarial network training is completed, use random noise as the input of the generator, and the generator outputs the simulated test conditions, critical defect geometric features, static mechanical properties and corresponding fatigue life, so as to construct a low-fidelity fatigue data set.

6. The fatigue life prediction method of the multi-fidelity physics-informed neural network under defect-induced failure according to claim 5, wherein, Step S4 specifically includes the following sub-steps: S41. Configure the number of hidden layers of the deep neural network. The number of neurons in each hidden layer in its network structure, set the learning rate and regularization coefficient. The activation function uses the Tanh function, and its function expression is: S42. Use the low-fidelity fatigue dataset to optimize the parameters of the deep neural network and set the number of training epochs; S43. After the deep neural network is trained on the low-fidelity fatigue dataset, save the network structure and parameters of the trained deep neural network to the local.

7. The fatigue life prediction method of the multi-fidelity physics-informed neural network under defect-induced failure according to claim 6, wherein, The physical constraints described in step S5 include: The optimization problem based on physical constraints is: Among them, Loss mse is the optimization objective of the deep neural network, and its calculation method is as follows: Among them, N p,i is the fatigue life predicted by the deep neural network; Use the exterior penalty function method to transform the optimization problem based on physical constraints into an unconstrained optimization problem to construct a physics-informed neural network: minLoss P Loss P =(1 - λ)Loss mse + λLoss phy Among them, λ is the relaxation factor, and Loss P is the loss function of the physics-informed neural network, and Loss phy is the physical loss function.

8. The fatigue life prediction method of the multi-fidelity physics-informed neural network under defect-induced failure according to claim 7, wherein Step S6 includes the following sub-steps: S61. Use the concept of transfer learning to make the physics-informed neural network read the network structure and parameters of the deep neural network trained in step S4 saved locally, and limit the number of updatable hidden layers to the last layer to retain the feature information extracted from the low-fidelity fatigue data; S62. Configure the learning rate, regularization coefficient, and physical constraint strength of the physics-informed neural network; S63. Use the fatigue data of the training set as high-fidelity fatigue data, and fine-tune the parameters of the updatable hidden layer until the prediction performance of the multi-fidelity physics-informed neural network meets the requirements.

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