High-low cycle composite fatigue life prediction method based on particle swarm optimization physical information neural network

Abstract

The invention discloses a high-low cycle composite fatigue life prediction method based on a particle swarm optimization physical information neural network, which aims at high-low cycle composite fatigue life prediction of turbine blades under small sample data characteristics, and comprises the following steps of: introducing a classical physical formula of a linear cumulative damage theory into a loss function as a constraint term; training fatigue test data by adopting a neural network model; deducing a constraint space of model parameters according to domain knowledge of high-low cycle composite fatigue life prediction, and converting training of a neural network into a constrained optimization problem; a particle swarm optimization algorithm is adopted to optimize the weight and the threshold value of the neural network, and the learning ability of the neural network under a small sample data set is further improved. The method provided by the invention can predict the fatigue life of the turbine component under the high-low cycle combined load, has high prediction precision under a small sample data set, and provides theoretical support for fatigue life prediction and reliability analysis of the engine turbine component.

Description

Technical Field

[0001] The present invention relates to a method for predicting the high-low cycle composite fatigue life of turbine components, and more particularly, to a method for predicting the high-low cycle composite fatigue life based on a particle swarm optimization physics-informed neural network. Background Art

[0002] With the development of aero-engine technology, the reliability requirements for turbine blades are constantly increasing, and accurately predicting their fatigue life has become crucial. When a turbine blade is in service, it is affected by centrifugal loads, temperature loads, and vibrations, resulting in an increasing probability of failure, especially failures caused by high-low cycle composite fatigue. Due to the extreme working environment of turbine blades, combined with the influence of uncertain factors such as material properties, applied loads, and geometric dimensions, their fatigue performance shows great dispersion, leading to large deviations in the predicted fatigue life results. Most traditional life prediction methods are empirical models based on simplified assumptions, and their prediction accuracy depends on specific material properties and load conditions. They have low accuracy when the sample set is small and are difficult to be used in practical engineering.

[0003] In recent years, with the rapid development of machine learning technology, methods such as random forest (RF) and support vector machine (SVM) have gradually been applied to fatigue life prediction. Although these methods can improve the prediction accuracy, their dependence on large sample data limits their application in small sample scenarios. For fatigue life prediction under small samples, neural network technology can better extract sample feature information. Therefore, it is necessary to conduct research on a method for predicting the high-low cycle composite fatigue life of turbine blades based on neural networks to improve the fatigue life prediction accuracy of turbine blades under small samples. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the high-low cycle composite fatigue life based on a particle swarm optimization physics-informed neural network to solve the problems of low accuracy in predicting the high-low cycle composite fatigue life and strong dependence on large samples existing in the prior art.

[0005] To achieve the purpose of the present invention, the technical solution adopted is: A method for predicting the high-low cycle composite fatigue life based on a particle swarm optimization physics-informed neural network, comprising the following steps:

[0006] Step 1, normalize the fatigue test data to ensure that the numerical values of different features are distributed within a unified range;

[0007] Step 2, embed the classical formula of the linear cumulative damage model, the Miner's rule, into the loss function to construct a new loss function;

[0008] Step 3: According to the domain knowledge of high-low cycle composite fatigue life prediction and combining the relationship between the input and output of the neural network, deduce the restricted space of the model parameters, and transform the training of the neural network into a constrained optimization problem;

[0009] Step 4: Use the particle swarm optimization algorithm to optimize the model parameters of the neural network to improve the efficiency and prediction accuracy of the model;

[0010] Step 5: Extract the optimal particle swarm obtained in the particle swarm optimization algorithm, reassign it to the neural network for training, and use the test set to verify the performance of the proposed model;

[0011] Step 6: Optimize the model structure of the neural network and the hyperparameters of the particle swarm algorithm, such as the number of particles, population size, learning factor, etc., and improve the accuracy and stability of the model through iterative improvement;

[0012] Step 7: Based on the finally trained neural network model, carry out the life prediction of high-low cycle composite fatigue.

[0013] Further, in Step 1, the normalization process is the maximum-minimum normalization process, which scales the original data to a specific range ([0, 1]) for data preprocessing. The formula is:

[0014]

[0015] where x is the original data value, x min is the minimum value of this feature, x max is the maximum value of this feature, and x' is the value after normalization.

[0016] Further, in Step 2, the linear cumulative damage model is extended to the Miner's rule under high-low cycle composite loads. The formula is:

[0017]

[0018] where D is the cumulative fatigue damage, n i is the number of high-cycle load applications in the i-th composite cycle block, N fH,i is the high-cycle fatigue life of the i-th composite cycle block, N fL,i is the low-cycle fatigue life of the i-th composite cycle block.

[0019] Further, in Step 2, a new loss function is constructed as:

[0020] L = LMSE + λ(Nf - Nminer) 2

[0021] where L MSE is the mean squared error loss term of the traditional neural network, Nf is the fatigue life predicted by the neural network, N miner is the fatigue life calculated according to the Miner's rule, and λ is the introduced balance coefficient.

[0022] Furthermore, in step 2, to ensure the integrity of the Miner's rule, λ is taken as 2.

[0023] Furthermore, in step 3, according to the physical properties and domain knowledge of high-low cycle composite fatigue, the life of high-low cycle composite fatigue should satisfy the following conditions: (1) The fatigue life N f should decrease with the increase of high cycle stress, and the curvature of the high cycle stress-fatigue life curve decreases with the increase of high cycle stress, that is and (2) The fatigue life N f should decrease with the increase of the damage parameter, and the curvature of the damage parameter-fatigue life curve decreases with the increase of high cycle stress, that is and

[0024] Furthermore, in step 3, according to the domain knowledge of high-low cycle composite fatigue life prediction and combining the relationship between the input and output of the neural network, there is:

[0025]

[0026] Furthermore, in step 3, when determining the positive and negative of, select the maximum value corresponding to each feature in all samples to determine the positive and negative of.

[0027] Furthermore, in step 4, use the particle swarm optimization algorithm to optimize the weights and thresholds of the neural network to minimize the fitness function value of the particle swarm algorithm, and its fitness function is:

[0028] Fitness = L MSE + μ × Penalty

[0029] where Fitness is the fitness function, Penalty is the penalty term, and μ is a balance coefficient. To ensure that the penalty term is scaled to the same order of magnitude as L MSE the same order of magnitude, μ is taken as 0.01.

[0030] Furthermore, in step 5, the way to extract the optimal particle swarm obtained in the particle swarm optimization algorithm is: flatten the optimal particle swarm obtained in the particle swarm optimization algorithm into a one-dimensional vector.

[0031] Furthermore, optimize and adjust the parameters of the particle swarm algorithm and the structure of the neural network to improve the performance of the physical information neural network model.

[0032] The beneficial effects of the present invention are as follows:

[0033] In the present invention, the formula rule of the linear damage accumulation theory is introduced into the loss function of the neural network to construct a new loss function. According to the domain knowledge of high-low cycle composite fatigue life prediction, the constraint space of the model parameters is deduced, and the training of the neural network is transformed into a constrained optimization problem. The particle swarm optimization algorithm is used to optimize the weights and thresholds of the neural network, which can effectively solve the problem that the model falls into the local optimal solution during the training process and further improve the prediction accuracy of the model. The method proposed by the present invention has a simple process and high prediction accuracy in the case of few samples, and can provide theoretical support for the life determination of complex structures such as turbine blades. Description of the Drawings

[0034] The drawings illustrate exemplary embodiments of the present invention and, together with the description thereof, are used to explain the principles of the present invention. These drawings are included to provide a further understanding of the present invention and are included in this specification and form a part of this specification.

[0035] Figure 1 is the load spectrum of the high-low cycle composite fatigue test for the turbine blade;

[0036] Figure 2 is the structure of the neural network model;

[0037] Figure 3 is the comparison between the experimental results and the prediction results of four different turbine blade materials and components; Detailed Embodiments

[0038] The following further describes the present invention in detail with reference to the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the relevant content and do not limit the present invention. In addition, it should be noted that, for the sake of description, only the parts related to the present invention are shown in the drawings.

[0039] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the drawings and embodiments.

[0040] A method for predicting the high-low cycle composite fatigue life based on a particle swarm optimization physical information neural network provided by the present invention includes the following steps:

[0041] Step 1, as Figure 1The high-low cycle composite fatigue test load spectrum of the turbine blade shown. First, the test data under the high-low cycle composite fatigue test load are normalized to ensure that the numerical values of different characteristics are distributed within a unified range. For the small sample data characteristics of the turbine blade, 5 groups of data samples are selected as the training set for different materials.

[0042] Step 2: Incorporate the physical law of high-low cycle composite fatigue damage into the loss function in combination with Miner's rule. Miner's rule superimposes the low-cycle fatigue damage and high-cycle fatigue damage of each load block, and the formula is as follows:

[0043]

[0044] where D is the cumulative fatigue damage, n i is the number of high-cycle load applications in the i-th composite cycle block, N fH,i is the high-cycle fatigue life of the i-th composite cycle block, N fL,i is the low-cycle fatigue life of the i-th composite cycle block.

[0045] When the cumulative fatigue damage reaches its critical value of 1, it is considered that fatigue failure occurs, and thus the high-low cycle composite fatigue life can be calculated, that is:

[0046]

[0047] where N fH is the high-cycle fatigue life, N fL is the low-cycle fatigue life.

[0048] Combined with the mean squared error loss term and introducing a balance coefficient λ, a new loss function is constructed as:

[0049] L = L MSE + λ(N f - N miner ) 2 (3)

[0050] where L MSE is the mean squared error loss term of the traditional neural network, N f is the fatigue life predicted by the neural network, N miner is the fatigue life calculated by Miner's rule.

[0051] Furthermore, to maintain the integrity of Miner's rule and prevent it from overly affecting the prediction performance of the model, the balance coefficient λ is taken as 2.

[0052] Step 3: As Figure 2 shown in the structure of the neural network model, the mathematical expression from the input layer to the hidden layer and in between is:

[0053]

[0054] Among them, refers to the output before activation of the hidden layer.

[0055] The mathematical expression from the hidden layer to the output layer is:

[0056]

[0057] Among them, is the connection weight from the input layer to the hidden layer, is the connection weight from the hidden layer to the output layer, is the threshold of the hidden layer, is the threshold of the output layer, g (2) (a) is the activation function of the hidden layer, g (3) (a) is the activation function of the output layer.

[0058] Furthermore, the hidden layer uses tanh as the activation function, and the output layer uses ReLU as the activation function. Their expressions are as follows:

[0059]

[0060] Relu: g (z) = max(0, z) (9)

[0061] According to the physical properties and domain knowledge of high-low cycle composite fatigue life prediction, the life of high-low cycle composite fatigue should satisfy the following conditions: (1) The fatigue life N f should decrease with the increase of high-cycle stress, and the curvature of the high-cycle stress-fatigue life curve should decrease with the increase of high-cycle stress, that is and (2) The fatigue life N f should decrease with the increase of the damage parameter, and the curvature of the damage parameter-fatigue life curve should decrease with the increase of high-cycle stress, that is and Thus, it can be obtained that:

[0062]

[0063] Substitute into There is:

[0064]

[0065] ① When , there is:

[0066]

[0067] Thus, further derivation gives:

[0068]

[0069] ② When , there is:

[0070]

[0071] Further derivation gives:

[0072]

[0073] Combining equations (15) and (17) gives:

[0074]

[0075] Furthermore, when determining the sign of , the maximum value corresponding to each feature in all samples is selected to judge the sign of .

[0076] Step 4: Use the particle swarm optimization algorithm to optimize the constrained neural network, and form a one-dimensional vector from the weights and thresholds of the neural network as the particle position in the particle swarm optimization algorithm, there is:

[0077]

[0078] Furthermore, by continuously iterating to update the particle position to minimize the fitness function of the neural network, combining the mean square error loss term and the penalty term, and introducing a balance coefficient, the fitness function is constructed as:

[0079] Fitness = L MSE + μ × Penalty (21)

[0080] where Fitness is the fitness function, μ is a balance coefficient, Penalty is the penalty term, and the magnitude of the penalty term is determined by the number of neurons violating the physical constraints in each generation of particles.

[0081] Furthermore, to scale the penalty term to the same order of magnitude as L MSE , the balance coefficient μ is taken as 0.01.

[0082] Step 5: Extract the optimal particle swarm obtained after particle swarm optimization, reassign it to the neural network for training, and use the test set to verify the performance of the proposed model.

[0083] Step 6: According to the verified results, further optimize the model structure of the neural network and the hyperparameters of the particle swarm optimization algorithm.

[0084] Step 7: Carry out the life prediction of high-low cycle composite fatigue according to the parameters of the updated particle swarm optimization algorithm and the model structure of the neural network.

[0085] To verify the effectiveness of a high-low cycle composite fatigue life prediction method based on particle swarm optimization physics-informed neural network proposed by the present invention, the life values predicted by this method are compared with the experimental values of turbine blade components and specimen parts under high-low cycle composite fatigue tests. The results show that, compared with the experimental values, the particle swarm optimization algorithm-neural network model proposed by the present invention exhibits a good prediction trend in the prediction results under all materials and working conditions, and the vast majority of points fall within the ±2 life scatter bands, as Figure 3 shown. It can be seen from this that for small sample data, the particle swarm optimization algorithm-neural network model has high accuracy and performance in fatigue life prediction. Aiming at the small sample characteristics of turbine blades, this method introduces the classical formula of linear damage accumulation theory as a constraint term into the loss function for the model training of the neural network, and then derives the search space for restricting the model parameters according to the domain knowledge of high-low cycle composite fatigue of turbine blades, and combines the global optimization ability of the particle swarm optimization algorithm. Therefore, the method proposed by the present invention can significantly improve the prediction accuracy of the high-low cycle composite fatigue life of turbine blades under small samples. The present invention is not limited to the engine turbine blades under high-low cycle composite loads, and is also applicable to the fatigue life prediction of aero-engine rotor components under complex loads, etc.

[0086] Those skilled in the art should understand that the above embodiments are only for clearly illustrating the present invention, rather than limiting the scope of the present invention. For those skilled in the art, other changes or modifications can be made on the basis of the above disclosure, and these changes or modifications are still within the scope of the present invention.

Claims

1. A method for predicting the high and low cycle composite fatigue life based on a particle swarm optimization physical information neural network, characterized in that, It includes the following steps: Step 1: Normalize the fatigue test data; Step 2: Embed the classical formula rule of the linear cumulative damage model into the loss function to construct a new loss function; Step 3: Derive the restricted space of the model parameters according to the domain knowledge of high-low cycle composite fatigue life prediction and combining the relationship between the input and output of the neural network; Step 4: Optimize the model parameters of the neural network using the particle swarm optimization algorithm; Step 5: Extract the optimal particle swarm obtained in the particle swarm optimization algorithm and reassign it to the neural network model for training to verify the performance of the proposed model; Step 6: Optimize the model structure of the neural network and the hyperparameters of the particle swarm optimization algorithm, and improve the accuracy and stability of the model; Step 7: Conduct high-low cycle composite fatigue life prediction based on the trained neural network model.

2. The high-low cycle composite fatigue life prediction method based on a particle swarm optimization physical information neural network according to claim 1, wherein In Step 1, the normalization process is the maximum-minimum normalization process, which scales the original data to a specific range for data preprocessing. The formula is: where x is the original data value, x min and x max represent the minimum and maximum values of this feature respectively, and x′ is the value after normalization.

3. The high-low cycle composite fatigue life prediction method based on a particle swarm optimization physical information neural network according to claim 1, wherein, In Step 2, the linear cumulative damage model is the Miner's rule extended to high-low cycle composite loads.

4. The high-low cycle composite fatigue life prediction method based on a particle swarm optimization physical information neural network according to claim 1, characterized in that In Step 2, the new loss function is constructed as: L = L MSE + λ(N f - N min er ) 2 Among them, L MSE is the mean square error loss term of the traditional neural network, N f is the fatigue life predicted by the neural network, N miner is the fatigue life calculated according to the Miner's rule, and λ is the introduced balance coefficient.

5. The high-low cycle composite fatigue life prediction method based on a particle swarm optimization physical information neural network according to claim 1, wherein In step 3, the life of high-low cycle composite fatigue should satisfy the following conditions: (1) The fatigue life N f should decrease with the increase of high cycle stress, and the curvature of the high cycle stress-fatigue life curve should decrease with the increase of high cycle stress, that is and (2) The fatigue life N f should decrease with the increase of the damage parameter, and the curvature of the damage parameter-fatigue life curve should decrease with the increase of high cycle stress, that is and 6. The high-low cycle composite fatigue life prediction method based on a particle swarm optimization physical information neural network according to claim 1, wherein In Step 3, according to the domain knowledge of high-low cycle composite fatigue life prediction and combining the relationship between the input and output of the neural network, there is:

7. The high-low cycle composite fatigue life prediction method based on a particle swarm optimization physical information neural network according to claim 1, wherein In Step 4, use the particle swarm optimization algorithm to optimize the weights and thresholds of the neural network to minimize the fitness function value of the particle swarm optimization algorithm. Its fitness function is: Fitness = L MSE + μ × Penalty Among them, Fitness is the fitness function, Penalty is the penalty term, and μ is the balance coefficient of 0.

01.

8. The high-low cycle composite fatigue life prediction method based on a particle swarm optimization physical information neural network according to claim 1, wherein, In Step 5, the method of extracting the optimal particle swarm obtained in the particle swarm optimization algorithm is: flatten the optimal particle swarm obtained in the particle swarm optimization algorithm into a one-dimensional vector.

9. The high-low cycle composite fatigue life prediction method based on a particle swarm optimization physical information neural network according to claim 1, characterized in that In Step 6, optimize and adjust the parameters of the particle swarm algorithm and the structure of the neural network to improve the performance of the physical information neural network model.

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