Fatigue life prediction method based on LSTM-PINN

Abstract

The invention belongs to the technical field of fatigue life prediction, and relates to a fatigue life prediction method based on LSTM-PINN, and the method comprises the steps: building and evaluating a fatigue life data set; dividing and pre-processing an original data set; an LSTM-PINN mixed life prediction model is built; determining hyper-parameters in the LSTM and PINN sub-models and integrating physical information; training the built model by using the data set; evaluating the performance of the model by using R2 and RMSE indexes, and repeating the previous step under the condition that the performance of the model is insufficient until the prediction performance of the model meets the requirement; carrying out life prediction based on the trained LSTM-PINN mixed life prediction model; according to the method, the LSTM (Long Short-Term Memory Neural Network) and the PINN (Physical Information Neural Network) are combined, and the original loading path information can be used for fatigue life prediction, so that the fatigue life prediction process is reliable and efficient.

Description

Technical Field

[0001] The present invention belongs to the technical field of fatigue life prediction, and particularly relates to a fatigue life prediction method based on LSTM (Long Short-Term Memory Neural Network)-PINN (Physics-Informed Neural Network). Background Art

[0002] With the rapid development of modern industrial technology, key structural components and members in fields such as aerospace, automotive manufacturing, and ship engineering often bear complex load conditions during service, such as variable amplitude loads, multiaxial stress states, and high-frequency vibrations. These complex load environments lead to the accumulation of fatigue damage in materials during long-term use, which in turn causes fatigue failure, seriously affecting the safety and reliability of engineering structures. Therefore, fatigue life prediction has become the core research content in engineering structure design, health monitoring, and safety assessment, and has important engineering significance and economic value.

[0003] In recent years, with the progress of science and technology, the application of machine learning technologies such as neural networks in life prediction has made remarkable progress, especially in fields such as materials, mechanical components, and structural health monitoring. Due to its improved non-linear description ability, parallel processing ability, and superior generalization ability, machine learning methods are very suitable for making up for the deficiencies of traditional methods. By combining advanced technologies such as deep learning and reinforcement learning, neural networks can learn potential laws and trends from a large amount of data, thereby improving the accuracy and reliability of life prediction.

[0004] However, existing machine learning methods usually require processing of original load data for life prediction under complex loading paths, and some unnecessary human errors may be introduced in this process.

[0005] To address the above limitations and improve the model's ability to identify complex loading path information, a hybrid life prediction model combining LSTM and PINN is proposed. LSTM can effectively learn the non-linear relationship between complex load history and fatigue damage, improving the accuracy of fatigue life prediction. By integrating physical laws and prior knowledge into the loss function of the neural network using PINN, the prediction accuracy and generalization ability can be further enhanced. Directly using the original loading path information and the mechanical properties of materials as inputs, the prediction of fatigue life is realized. Summary of the Invention

[0006] The object of the present invention is to overcome the deficiencies in the prior art and propose a fatigue life prediction method based on LSTM-PINN, which can reliably and efficiently realize fatigue life prediction.

[0007] To achieve the object of the present invention, the following technical solutions will be adopted for implementation.

[0008] A fatigue life prediction method based on LSTM-PINN, comprising:

[0009] Step 1: Collect fatigue life data through experiments and investigations (mainly including the mechanical property information of materials and the loading path information of fatigue tests), build a fatigue life dataset and evaluate the reliability of the dataset;

[0010] Step 2: Divide and preprocess the original dataset. Randomly divide the dataset into a training set and a test set with a ratio of 4:1, and transform the material mechanical property data based on the Z-score normalization method;

[0011] Step 3: Build LSTM and PINN sub-models respectively based on Python and combine them into a complete hybrid life prediction model. Specifically, use LSTM to extract the effective information in the loading path, combine the output of LSTM with the mechanical properties of materials as the input of PINN, and take the fatigue life as the output to achieve the integration of physical information;

[0012] Step 4: Determine the hyperparameter configuration (such as activation function, etc.) of each sub-model to make the performance of the overall model meet the requirements;

[0013] Step 5: Set reasonable training parameters, use the processed dataset to train the built model, and record the data loss and physical loss during the training process;

[0014] Step 6: Use R 2 and RMSE metrics to evaluate the performance of the model. In the case of insufficient model performance, repeat the previous step until the prediction performance of the model meets the requirements;

[0015] Step 7: Perform life prediction based on the trained LSTM-PINN hybrid life prediction model.

[0016] As a preferred solution of the present invention, the dataset in Step 1 includes the loading path information (such as stress-strain information) of fatigue tests, the mechanical property information of materials, and the fatigue life.

[0017] As a preferred solution of the present invention, the dataset preprocessing process in Step 2:

[0018] The dataset includes three parts, namely loading path information, material mechanical properties, and test fatigue life. The fatigue life information is used as a label and does not need to be normalized. Since the loading path information includes the information of time steps and the differences in loading paths between different materials, these important time series-related information is easily lost during normalization, so the original data is used as the input.

[0019] Therefore, it is only necessary to standardize the dataset of material mechanical properties.

[0020] When normalizing or standardizing, if the mean, standard deviation, minimum value, or maximum value is calculated based on the entire dataset (including the training set and the test set), the model will indirectly "peek" at the information of the test set or the validation set during training. To prevent data leakage in the test set, only the data in the training set is used to calculate the statistics, and then these statistics are applied to the test set.

[0021] Transform the material mechanical property data based on the Z-score standardization method:

[0022]

[0023] where \(X\) is the original data, \(\mu\) is the mean of the data, and \(\sigma\) is the standard deviation of the data.

[0024] After the above transformation, each feature is transformed into a distribution with a mean of 0 and a standard deviation of 1.

[0025] As a further solution of the present invention, in the process of building the LSTM and PINN sub-models in the third step and the expression of the total loss function:

[0026] Building of the LSTM sub-model:

[0027] Generally, when using LSTM, the network output of the last time step of LSTM is usually extracted. However, we found that extracting the outputs of all time steps may be more accurate for predicting fatigue life, but this may increase a part of the training time and cost. Therefore, a compromise method is selected, that is, extracting the output every \(n\) time steps to minimize the network complexity as much as possible while accurately extracting the loading path information.

[0028] The loading path information in the dataset described in the first step mainly includes two dimensions, namely the information of normal strain and shear strain (or normal stress and shear stress). After being processed by LSTM, it is extracted as one-dimensional data to be merged with the mechanical properties of the materials in the dataset as the input of PINN in the next stage.

[0029] Building of the PINN sub-model:

[0030] By modifying the loss function, a PINN model considering physical factors is established. Specifically, the physical information loss function consists of three parts. Among them, Loss p1 indicates that the fatigue life is positively correlated with the yield strength; Loss p2 indicates that the fatigue life is positively correlated with the tensile strength; Loss p3 prevents the predicted fatigue life from being too large.

[0031]

[0032] Loss physics = Loss p1 + Loss p2 + Loss p3

[0033] where N f is the predicted fatigue life; σ y is the yield strength; σ u is the tensile strength; λ1, λ2, λ3, λ4 are hyperparameters.

[0034] The expression of the data-driven loss is as follows:

[0035]

[0036] where y i , are the true value and the model predicted value of the sampling point, respectively.

[0037] The total loss function is the weighted sum of the data-driven loss and the physical loss, and the specific form is:

[0038] Loss All = Loss data + αLoss physics

[0039] where α is the weight coefficient, which controls the relative importance of the data-driven loss and the physical loss.

[0040] The content in the red box is the external input of the PINN part, which are: the loading path information extracted by LSTM, the mechanical properties of the material, and the physical prior knowledge. Specifically, the extracted loading path information is sorted into the corresponding format through a fully connected neural network, and together with the mechanical properties of the material, it constitutes the data input of the PINN. The derivative of the life with respect to the input parameters is obtained through the automatic differentiation function of the network, and the physical information is integrated into the loss function of the network, so as to introduce physical constraints in the process of predicting the fatigue life through the loading path and the mechanical properties of the material.

[0041] As a preferred solution of the present invention, the hyperparameter configuration in the fourth step:

[0042] Configuration of the activation function:

[0043] The selection of the activation function should be realized according to the characteristics of the specific research object. In this paper, the selected activation function is the ReLU function, and its expression is as follows:

[0044] ReLU(x) = max(0, x)

[0045] Where x is the input value. When x > 0, ReLU outputs x; when x ≤ 0, ReLU outputs 0.

[0046] For the fatigue life that is always greater than 0, the use of the ReLU function is undoubtedly more appropriate. It enables the neural network to learn and represent complex non-linear relationships while meeting the physical requirements.

[0047] Setting of the learning rate:

[0048] The learning rate controls the step size of each step in the gradient descent process. If the learning rate is too large, it will lead to unstable training; if the learning rate is too small, it will lead to slow convergence. In this study, the Adam optimization algorithm is adopted because it has strong adaptability and can automatically adjust the learning rate, avoiding the influence caused by a fixed learning rate.

[0049] As a preferred solution of the present invention, R in step six 2 And the RMSE index:

[0050]

[0051] Where y i , And Are respectively the true value, the model prediction value and the average value of the sampling points.

[0052] R 2 Ranges from 0 to 1. The closer it is to 1, the better the model fits the data; RMSE represents the square root of the difference between the predicted value and the actual value, reflecting the average error of the model prediction. The smaller the RMSE, the closer the predicted result of the model is to the actual value, and the better the model performance.

[0053] Beneficial effects

[0054] Compared with the prior art, the present invention adopts a method combining LSTM (Long Short-Term Memory Neural Network) and PINN (Physics-Informed Neural Network), which can use the original loading path information for fatigue life prediction, making the fatigue life prediction process reliable and efficient. Description of the drawings

[0055] Figure 1 Is the flow chart of the present invention;

[0056] Figure 2 Is the schematic diagram of the LSTM sub-model;

[0057] Figure 3 Is the schematic diagram of the PINN sub-model;

[0058] Figure 4Schematic diagram of the ReLU function value

[0059] Figure 5 Schematic diagram of the model training process

[0060] Figure 6 Schematic diagram of the model's life prediction result Specific implementation manners

[0061] The present invention will be further elaborated below in conjunction with the accompanying drawings and embodiments

[0062] As Figures 1 to 4 shown, the present invention provides a fatigue life prediction method based on LSTM (Long Short-Term Memory Neural Network)-PINN (Physics-Informed Neural Network), including the following steps

[0063] Step 1: Establish a fatigue life data set (by means of experiments, etc.), evaluate the data set, and remove the "abnormal" points in the data set; the format of the established data set is shown in Table 1

[0064] Table 1

[0065]

[0066] Step 2: Divide and preprocess the original data set

[0067] Randomly divide the data set into a training set and a test set, with a ratio of 4:1, and transform the material mechanical property data based on the Z-score normalization method

[0068]

[0069] where X is the original data, μ is the mean of the data, and σ is the standard deviation of the data

[0070] After the above transformation, each feature is transformed into a distribution with a mean of 0 and a standard deviation of 1

[0071] Step 3: Build the LSTM and PINN sub-models respectively based on the Python language, and combine them into a complete hybrid life prediction model for physical information integration; the built LSTM and PINN sub-models are respectively as Figure 2 and 3 shown

[0072] Step 4: Determine the hyperparameter configuration (such as activation function, etc.) of each sub-model; the selected activation function is the ReLU function, and the ReLU function value is shown as Figure 4 shown; adopt the Adam optimization algorithm to automatically adjust the learning rate to avoid the influence caused by a fixed learning rate

[0073] The expression of the ReLU function is as follows:

[0074] ReLU(x) = max(0, x)

[0075] Where x is the input value. When x > 0, ReLU outputs x; when x ≤ 0, ReLU outputs 0.

[0076] Step 5: Use the processed dataset to train the established model. The training process of the model is shown as Figure 5 shown.

[0077] Step 6: Use R 2 and the RMSE index to evaluate the prediction performance of the model. In case of insufficient performance, repeat the previous step until the prediction performance of the model meets the requirements.

[0078] R 2 and the RMSE index:

[0079]

[0080] Where, y i , and are the true value, the model prediction value, and the average value of the sampling points respectively.

[0081] R 2 ranges from 0 to 1. The closer it is to 1, the better the model fits the data; RMSE represents the square root of the difference between the predicted value and the actual value, reflecting the average error of the model prediction. The smaller the RMSE, the closer the prediction result of the model is to the actual value, and the better the model performance.

[0082] Step 7: Perform life prediction based on the trained LSTM-PINN hybrid life prediction model; some prediction results are shown as Figure 6 shown.

Claims

1. A fatigue life prediction method based on LSTM-PINN, characterized in that: The prediction method comprises: Step 1: Collect fatigue life data (mainly including mechanical property information of materials and loading path information of fatigue tests) through experiments and surveys, build a fatigue life data set and evaluate the reliability of the data set; Step 2: Divide and pre-process the original data set. Randomly divide the data set into a training set and a test set with a ratio of 4:1, and convert the material mechanical property data based on the Z-score standardization method; Step 3: Based on Python, build LSTM and PINN sub-models respectively, and combine them into a complete hybrid life prediction model. Specifically, use LSTM to extract effective information in the loading path, combine the output of LSTM with the mechanical properties of the material as the input of PINN, and use fatigue life as the output to achieve the integration of physical information; Step 4: Determine the hyperparameter configuration of each sub-model (such as activation function, etc.) so that the performance of the overall model meets the requirements; Step 5: Set reasonable training parameters, use the processed data set to train the built model, and record the data loss and physical loss during the training process; Step 6: Using R 2 The performance of the model is evaluated using the RMSE indicator. If the model performance is insufficient, the previous step is repeated until the prediction performance of the model meets the requirements. Step 7: Perform lifespan prediction based on the trained LSTM-PINN hybrid lifespan prediction model.

2. The fatigue life prediction method based on LSTM-PINN according to claim 1 is characterized in that: The data set in step 1 includes loading path information (such as stress-strain information) of the fatigue test, mechanical property information of the material, and fatigue life.

3. The fatigue life prediction method based on LSTM-PINN according to claim 1 is characterized in that: The data set pre-processing process in step 2: The data set contains three parts, namely, loading path information, material mechanical properties, and test fatigue life. Fatigue life information does not need to be standardized as a label. Since the loading path information contains the information of the time step and the difference in loading paths between different materials, it is easy to lose these important time-related information during normalization, so the original data is used as input. Therefore, only the material mechanical properties need to be normalized in the data set. When normalizing or standardizing, if the mean, standard deviation, minimum, or maximum value is calculated based on the entire data set (including the training set and the test set), the model will indirectly "spy" on the information of the test set or validation set during training. To prevent data leakage in the test set, only use the data of the training set to calculate statistics, and then apply these statistics to the test set. The material mechanical property data is converted based on the Z-score standardization method: Among them, X is the original data, μ is the mean of the data, and σ is the standard deviation of the data. After the above transformation, each feature is converted into a distribution with a mean of 0 and a standard deviation of 1.

4. The fatigue life prediction method based on LSTM-PINN according to claim 1 is characterized in that: The construction process of the LSTM and PINN sub-models in step 3 and the expression of the total loss function are as follows: LSTM sub-model construction: Generally speaking, when using LSTM, the network output of the last time step of LSTM is extracted. However, we found that extracting the output of all time steps may be more accurate for fatigue life prediction, but this may increase the training time and cost. Therefore, a compromise method was chosen, that is, extracting the output once every n time steps, reducing the complexity of the network as much as possible while accurately extracting the loading path information. The loading path information in the data set described in step 1 mainly includes two dimensions, namely, the information of normal strain and shear strain (or normal stress and shear stress). After LSTM processing, it is extracted into one-dimensional data so as to be combined with the mechanical properties of the material in the data set as the input of the next stage PINN. PINN sub-model construction: By modifying the loss function, a PINN model considering physical factors is established. Specifically, the physical information loss function consists of three parts. p1 Indicates that fatigue life is positively correlated with yield strength; Loss p2 Indicates that fatigue life is positively correlated with tensile strength; Loss p3 Prevents predicted fatigue life from being too large. Loss physics =Loss p1 +Loss p2 +Loss p3 Among them, N f To predict fatigue life; σ y is the yield strength; σ u is the tensile strength; λ1, λ2, λ3, λ4 are hyper parameters. The expression of data-driven loss is as follows: Among them, y i , are the true value and model predicted value of the sampling point respectively. The total loss function is the weighted sum of data-driven loss and physical loss, and its specific form is: Loss All =Loss data +αLoss physics Where α is a weight coefficient that controls the relative importance of data-driven loss and physical loss. The contents in the red box are the external inputs of the PINN part, which are: loading path information extracted by LSTM, mechanical properties of materials, and physical prior knowledge. Specifically, the extracted loading path information is organized into a corresponding format through a fully connected neural network, and together with the mechanical properties of the material, it constitutes the data input of PINN. The derivative of the life with respect to the input parameters is obtained through the automatic derivation function of the network, and the physical information is integrated into the loss function of the network, thereby introducing physical constraints in the process of predicting fatigue life through loading path and material mechanical properties.

5. The fatigue life prediction method based on LSTM-PINN according to claim 1 is characterized in that: Hyperparameter configuration in step 4: Configuration of activation function: The choice of activation function should be based on the characteristics of the specific research object. In this paper, the activation function selected is the ReLU function, and its expression is as follows: ReLU(x)=max(0,x) Where x is the input value. When x>0, ReLU outputs x; when x≤0, ReLU outputs 0. For fatigue life that is always greater than 0, the use of the ReLU function is undoubtedly more appropriate. It enables the neural network to learn and represent complex nonlinear relationships while meeting the requirements of physics. Learning rate settings: The learning rate controls the step size of each step in the gradient descent process. A learning rate that is too large will lead to unstable training, while a learning rate that is too small will lead to slow convergence. In this study, the Adam optimization algorithm is used because it is highly adaptable and can automatically adjust the learning rate, avoiding the impact of a fixed learning rate.

6. The fatigue life prediction method based on LSTM-PINN according to claim 1 is characterized in that: R in step 6 2 And the RMSE indicator: Among them, y i , as well as are the true value of the sampling point, the model predicted value and the average value respectively. R 2 The value range is from 0 to 1. The closer to 1, the better the model fits the data. RMSE represents the square root of the difference between the predicted value and the actual value, reflecting the average error of the model prediction. The smaller the RMSE, the closer the model's prediction result is to the actual value, and the better the model performance is.

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