Complex equipment probability fatigue life prediction method based on physical information neural network

Abstract

The application discloses a complex equipment probability fatigue life prediction method based on a physical information neural network, and belongs to the field of complex equipment fatigue analysis. First, fatigue life data of complex equipment materials are grouped according to stress, and non-parametric probability estimation, linear regression and maximum entropy modeling are used for adaptive mixed uncertainty quantification. Then, a physical guide neural network is trained based on the obtained standard deviation data, and the standard deviation under missing or limited data stress is supplemented. Then, a Bayesian physical information neural network is trained based on the supplemented standard deviation data and the fatigue life data, and the pre-trained Bayesian neural network is sampled multiple times to obtain a PSN curve, which is used for probability fatigue life prediction of complex equipment. The application significantly improves the accuracy and stability of the probability fatigue life prediction of complex equipment, and ensures the physical consistency of the prediction result.

Description

Technical Field

[0001] This invention belongs to the field of fatigue analysis of complex equipment, specifically involving a method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network. Background Technology

[0002] In probabilistic fatigue life prediction of complex equipment, traditional deterministic analysis-based life assessment methods often fail to meet engineering reliability requirements due to uncertainties in material microstructure, randomness of loads, and multiphysics coupling effects. While existing probabilistic fatigue life prediction methods can achieve high-precision characterization of fatigue life uncertainty, most rely on purely data-driven approaches, exhibiting inherent flaws such as poor physical consistency and weak interpretability. Some methods, although incorporating physical information, only apply to the mean SN curve, failing to guarantee good physical consistency for SN curves of other failure rates. Therefore, how to fully integrate physical information into the PSN curve to characterize fatigue life uncertainty has become a crucial issue in probabilistic fatigue life prediction. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies and achieve effective prediction of probabilistic fatigue life of complex equipment, this invention adopts the following technical solution:

[0004] A probabilistic fatigue life prediction method for complex equipment based on physical information neural networks includes the following steps:

[0005] Step S1: Group the fatigue life data of complex equipment materials according to stress. Perform nonparametric probability estimation and normality test on the data under each stress. For fatigue life data that pass the test, fit the data to a normal distribution based on the results of the nonparametric probability estimation. For fatigue life data that fail the test, fit the data to a maximum entropy distribution.

[0006] Step S2: Construct a physical-guided neural network to predict the missing standard deviation. Based on the fitted standard deviation data and the stress of the fatigue life data, train the physical-guided neural network to predict the standard deviation through the stress, and supplement the standard deviation under missing or limited data stress.

[0007] Step S3: Construct a Bayesian physical information neural network for predicting probabilistic fatigue life. The stress of the fatigue life data is used as the input, and the logarithmic fatigue life data is output. During the training process, the neural network parameters are sampled and predicted multiple times. The standard deviation of the predicted fatigue life under each stress is calculated. At the same time, a composite loss function is constructed based on the stress of the fatigue life data, the logarithmic fatigue life data, and the standard deviation generated by the physical guidance neural network.

[0008] Step S4: Based on the predictions of the pre-trained Bayesian physical information neural network, obtain the PSN curve, and combine it with the requirements of complex equipment to determine the fatigue life under a specific failure rate for probabilistic fatigue life prediction.

[0009] Further, step S1 includes the following steps:

[0010] Step S1.1: Obtain fatigue life data and stress of complex equipment, perform nonparametric probability estimation on the fatigue life data under each stress, and obtain the failure rate corresponding to each fatigue life data.

[0011]

[0012] in, Indicates failure rate. This represents the fatigue life data corresponding to the i-th stress amplitude, This indicates the number of fatigue life data points corresponding to the stress amplitude. Indicates the number of stress amplitudes;

[0013] Step S1.2: Perform a normality test on the fatigue life data;

[0014]

[0015] in, This indicates that fatigue life data follows a log-normal distribution. This represents the probability of observing a given data point under the assumption that fatigue life data follows a log-normal distribution. Indicates the significance level;

[0016] Step S1.3: For fatigue life data that has passed the normality test, calculate the logarithmic mean and standard deviation of fatigue life data under each stress, and accumulate the standard normal quantiles corresponding to the failure probability. Use the mean and standard deviation as slope and intercept to perform linear regression on the quantiles to obtain the logarithmic value of fatigue life data.

[0017]

[0018]

[0019] in, This represents the logarithmic value of fatigue life data. and Let represent the logarithmic mean and standard deviation of fatigue life data j under the i-th stress amplitude, respectively. Indicates the cumulative failure probability The corresponding standard normal quantile, The inverse cumulative distribution function of the standard normal distribution;

[0020] Step 1.4: For fatigue life data that fails the normality test, calculate the moment constraint equation based on the fatigue life data, and fit the distribution using the maximum entropy algorithm of the first few statistical moments to obtain the most unbiased probability density function estimate.

[0021] Furthermore, in step 1.4, the Lagrange multipliers of the four moments are calculated by solving the moment constraint equations to obtain the probability density function of the logarithmic fatigue life under each stress; normalization constraints and fourth-order moment constraint equations are constructed, where the fourth moments are the mean, standard deviation, kurtosis, and skewness of the logarithmic fatigue life, respectively.

[0022] probability density function The definition is as follows:

[0023]

[0024] in, Let Lagrange multipliers represent the t-th moment of fatigue life data under the i-th stress amplitude. These multipliers are calculated by solving the moment constraint equations, which are as follows:

[0025]

[0026] in, Represents the probability density function. Represents the integral term. This represents the fatigue life data under the i-th stress amplitude. Step moment;

[0027] in , where represent the mean, variance, skewness, and kurtosis of fatigue life data, respectively, and their calculation formulas are as follows:

[0028]

[0029]

[0030]

[0031]

[0032] Further, step S2 includes the following steps:

[0033] Step S2.1: Construct a physics-guided neural network model, using stress amplitude as input and outputting the corresponding prediction standard deviation;

[0034] Step S2.2: Add a physical constraint to the physical-guided neural network that the fatigue life standard deviation decreases with increasing stress:

[0035] ;

[0036] Step S2.3: Train the physical guidance neural network using the standard deviation data, generate predicted values ​​through forward propagation, quantify the difference between the predicted and actual values ​​using the mean squared error loss function, and then calculate the gradient and update the weights through backpropagation.

[0037]

[0038] in, Indicates the number of stress amplitudes. The standard deviation of the forecast is represented by the standard deviation of the forecast. This represents the standard deviation of the uncertainty quantification strategy estimate;

[0039] The combination of physics-guided neural networks and physical information is achieved through weight constraints, which are as follows:

[0040]

[0041] in, This represents the input layer of the neural network to the first hidden layer. The weights of each neuron, Indicates the first hidden layer. The first neuron is transferred to the second hidden layer. The weights of each neuron, Indicates the second hidden layer. The weights from one neuron to the output layer neurons.

[0042] Further, step S3 includes the following steps:

[0043] Step S3.1: Construct a Bayesian physical information neural network, using stress amplitude as input, and output logarithmic fatigue life. The network parameters follow a normal distribution;

[0044] Step S3.2: Maximize the evidence lower bound ELBO based on variational inference, and construct a composite loss function in combination with prior physical information to ensure prediction accuracy and physical consistency. The prior physical information includes the fatigue life standard deviation decreasing with increasing stress, the logarithmic fatigue life monotonically increasing with decreasing stress, and the curvature of the SN curve increasing with increasing stress.

[0045] The definition of prior physical information is as follows:

[0046]

[0047]

[0048]

[0049] The composite loss function consists of an evidence lower bound and a physical constraint penalty term, which are used as data fitting terms. Weighting coefficients are added to enhance the fitting effect and physical consistency. The physical constraint penalty term is obtained based on the predicted logarithmic fatigue life data and the partial derivative of the standard deviation with respect to stress.

[0050]

[0051] in, and These represent the weighting coefficients, It indicates the lower bound of evidence and represents the data fitting term;

[0052] Step S3.3: Train a Bayesian physical information neural network based on the fatigue life standard deviation prediction results and fatigue life data. In the forward propagation, generate multiple prediction values ​​through Monte Carlo sampling. Based on the composite loss function, backpropagate to update the normal distribution parameters of the network parameters and continuously perform iterative updates.

[0053] Furthermore, in step S3.2, the lower bound of evidence consists of the likelihood function of the observed data given the network parameters, the prior function of the weights, and the distribution function of the weight parameters given the normal distribution parameters.

[0054] Furthermore, the physical constraint penalty term in step S3.2 includes a first physical constraint function in which fatigue life monotonically increases as stress decreases. This is achieved by constructing a state indicator function of the first derivative of logarithmic fatigue life with respect to stress. If the first derivative of logarithmic fatigue life with respect to stress is greater than zero, the state indicator function is one; otherwise, it is zero.

[0055] Furthermore, the physical constraint penalty term in step S3.2 includes a second physical constraint function in which the curvature of the SN curve increases with increasing stress. This is achieved by constructing a state indicator function of the second derivative of logarithmic fatigue life with respect to stress. If the second derivative of logarithmic fatigue life with respect to stress is less than zero, the state indicator function is one; otherwise, it is zero.

[0056] Furthermore, the physical constraint penalty term in step S3.2 includes a third physical constraint function in which the fatigue life standard deviation decreases as stress increases. This is achieved by constructing the mean square error function between the standard deviation and the predicted fatigue life standard deviation.

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] in, , and These represent the first, second, and third physical constraint penalty terms, respectively. Represents the expectation function, This represents the likelihood of observed data given network parameters. Represents the prior knowledge of the weights. This represents the distribution of the weight parameters after considering the parameters of a normal distribution. Represents the state indication function, when The value is 1 if it is true, and 0 otherwise. This represents the expected standard deviation obtained from the physical-guided neural network. This represents the standard deviation of fatigue life under various stresses calculated after multiple samplings of the output from a Bayesian neural network. This represents the number of Monte Carlo samplings performed on the Bayesian neural network.

[0064] Furthermore, in step S4, the physical information neural network adopts a Bayesian physical information neural network, which obtains a set of fatigue life prediction values ​​under a given input stress through Monte Carlo sampling, constructs a prediction distribution from it, realizes the construction of the PSN curve, and extracts specific quantiles from the prediction distribution for probabilistic fatigue life prediction of complex equipment.

[0065] The advantages and beneficial effects of this invention are as follows:

[0066] The prediction method of this invention estimates the fatigue life distribution by predicting multiple output points instead of distribution parameters. This method incorporates physical information while ensuring prediction accuracy, improving the physical consistency of the prediction results. Furthermore, this invention proposes an adaptive hybrid uncertainty quantification strategy, which eliminates dependence on predefined distribution assumptions, reduces subjective errors, and can flexibly and objectively estimate the fatigue life probability distribution under various stress conditions. This invention also constructs a physics-guided neural network to estimate the standard deviation to supplement missing or limited datasets, enabling relatively accurate model training even with small sample sizes, thereby avoiding degenerate results such as zero variance. Attached Figure Description

[0067] Figure 1 This is a flowchart of the method in an embodiment of the present invention.

[0068] Figure 2 This is a schematic diagram of the physical guidance neural network structure in an embodiment of the present invention.

[0069] Figure 3This is a schematic diagram of the Bayesian physical information neural network structure in an embodiment of the present invention.

[0070] Figure 4 This is a comparison chart of the PSN curves of 7-series aluminum alloys predicted by different methods in the embodiments of the present invention.

[0071] Figure 5 This is a comparison chart of the PSN curves of 2024-T4 aluminum alloy predicted by different methods in the embodiments of the present invention.

[0072] Figure 6 This is a comparison chart of the PSN curves of SAE 8620 steel predicted by different methods in the embodiments of the present invention. Detailed Implementation

[0073] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0074] A probabilistic fatigue life prediction method for complex equipment based on a physical information neural network (PIN) first groups fatigue life data of complex equipment materials according to stress. Nonparametric probability estimation and Shapiro-Wilk normality tests are then performed on the data under each stress. Data passing the test are fitted with a normal distribution, while data failing are fitted with a maximum entropy distribution. The standard deviation data obtained from the fitted data is used to train a physical-guided neural network (PSN). The standard deviations under missing or limited data stresses are then supplemented. Based on the standard deviations predicted by the PSN and the fatigue life data, a Bayesian physical information neural network (PSN) is trained. Multiple samplings are performed on the pre-trained Bayesian neural network to obtain the PSN curve, which is then used for probabilistic fatigue life prediction of complex equipment. Figure 1 As shown, the prediction method of the present invention specifically includes the following steps:

[0075] Step S1: For the estimation of unbiased fatigue life distribution under different stress amplitudes, adaptive hybrid uncertainty quantification is performed using nonparametric probability estimation, linear regression, and maximum entropy modeling; specifically, it includes the following sub-steps:

[0076] Step S1.1: Based on the fatigue life sample dataset The nonparametric probability estimation method is used to calculate the corresponding fatigue life for each fatigue life, and the calculation method is as follows:

[0077]

[0078] in, For stress amplitude, The stress amplitude is The amount of fatigue life data at that time. Stress amplitude The next fatigue life is arranged in ascending order. One fatigue life data point;

[0079] Step S1.2: Perform a normality assessment on the fatigue life data, using a significance level of 100%. The Shapiro-Wilk method is used to test the hypothesis. Fatigue life follows a log-normal distribution, and the test rules are as follows:

[0080]

[0081] in, To test the returned p-value, we need to represent the hypothesis. The probability of observing given data;

[0082] Step S1.3: For the dataset that passes the normality test, fit it to a log-normal distribution. The parameters of the normal distribution are estimated by linear regression, and the calculation method is as follows:

[0083]

[0084] in, and Stress amplitude The mean and standard deviation of the logarithmic fatigue life. This represents the logarithmic value of fatigue life. Cumulative failure probability The corresponding standard normal quantile, quantile The calculation is as follows:

[0085]

[0086] in, It is the inverse cumulative distribution function of the standard normal distribution;

[0087] Step 1.4: For datasets that fail the normality test, use the maximum entropy algorithm based on the first four statistical moments to fit the distribution. Combined with moment estimation, the maximum entropy algorithm can obtain the most unbiased probability density function estimate. probability density function The definition is as follows:

[0088]

[0089] in, For the Lagrange multipliers, their calculation is obtained by solving the moment constraint equations, which are as follows:

[0090]

[0091] in, Stress amplitude The first fatigue life data The moments, representing the mean, variance, skewness, and kurtosis of fatigue life data, are calculated using the following formulas:

[0092]

[0093]

[0094]

[0095]

[0096] Step S2: Based on the standard deviation data after adaptive mixed uncertainty quantization, a physical-guided neural network is constructed to predict the missing standard deviation. This network serves as a first-stage model of the Bayesian physical information neural network and is used for estimating the fatigue life standard deviation under finite or missing sample stress amplitudes. The constructed neural network structure is as follows: Figure 2 As shown; specifically including the following sub-steps:

[0097] Step S2.1: Construct a fully connected neural network model containing one input layer, one output layer, and two hidden layers. The hidden layers use the hyperbolic tangent activation function, and the output layer uses the exponential linear unit activation function. The neural network is configured with stress amplitude... As input, the corresponding predicted standard deviation is output. ;

[0098] Step S2.2: Add a physical constraint to the physical-guided neural network that the standard deviation of fatigue life decreases with increasing stress. The expression for the physical constraint is as follows:

[0099]

[0100] Step S2.3: Train the physics-guided neural network using the standard deviation data estimated by the uncertainty quantification strategy. The model generates predicted values ​​through forward propagation, quantifies the difference between the predicted and actual values ​​using the mean squared error loss function, and then calculates the gradient and updates the weights through backpropagation. The loss function... The definition is as follows:

[0101]

[0102] in, The number of stress amplitudes, The standard deviation of the forecast. This represents the standard deviation of the uncertainty quantification strategy estimate.

[0103] The combination of neural network models and physical information is achieved through weight constraints, which are as follows:

[0104]

[0105] in, For the input layer of the neural network to the first hidden layer The weights of each neuron, For the first hidden layer The first neuron is transferred to the second hidden layer. The weights of each neuron, For the second hidden layer The weights from one neuron to the output layer neurons.

[0106] Step S3: Combining the fatigue life standard deviation prediction results of the first-stage model, construct a two-stage Bayesian physical information neural network model for probabilistic fatigue life prediction. The Bayesian neural network structure is as follows: Figure 3 As shown; specifically including the following sub-steps:

[0107] Step S3.1: Construct a fully connected Bayesian neural network model, consisting of one input layer, one output layer, and two hidden layers. The hidden layers use the hyperbolic tangent activation function, and the output layer uses the exponential linear unit activation function. The neural network is configured with stress amplitude... As input, the output is the logarithmic fatigue life. The network parameters follow a normal distribution;

[0108] Step S3.2: Maximize the evidence lower bound ELBO based on variational inference, and construct a composite loss function by combining prior physical information to ensure prediction accuracy and physical consistency. The prior physical information includes the decrease in fatigue life standard deviation with increasing stress, the monotonically increasing fatigue life with decreasing stress, and the increase in curvature of the SN curve with increasing stress. The prior physical information is defined as follows:

[0109]

[0110]

[0111]

[0112] Among them, the composite loss function The definition is as follows:

[0113]

[0114] in, and These are the weighting coefficients. The lower bound of evidence represents the data fitting term. , and This is a physical constraint penalty term. , , and The calculation is as follows:

[0115]

[0116]

[0117]

[0118]

[0119] in, This represents the likelihood of the observed data given the network parameters. Represents the prior knowledge of the weights. This represents the distribution of the weight parameters after considering the parameters of a normal distribution. Expressing expectations, This refers to the total fatigue life for training purposes. For the state indication function, when The value is 1 if it is true, and 0 otherwise. The expected standard deviation obtained by the physical-guided neural network. This represents the standard deviation of fatigue life under various stresses calculated after multiple samplings of the output from a Bayesian neural network. The calculation is as follows:

[0120]

[0121] in, The number of Monte Carlo samplings for the Bayesian neural network.

[0122] Step S3.3: Train a Bayesian physical information neural network based on the fatigue life standard deviation prediction results and fatigue life data of the first-stage model. During forward propagation, the model generates multiple prediction values ​​through Monte Carlo sampling. Based on the composite loss function, backpropagation updates the normal distribution parameters of the network parameters and continuously iterates and updates the network.

[0123] Step S4: Obtain the PSN curve based on the pre-trained Bayesian Physical Information Neural Network prediction model. Combined with the requirements of complex equipment, determine the fatigue life under a specific failure rate for probabilistic fatigue life prediction, as detailed below:

[0124] Extensive Monte Carlo sampling is performed on the pre-trained Bayesian Physical Information Neural Network prediction model to obtain a set of fatigue life prediction values ​​under a given input stress. From these values, a prediction distribution is constructed to realize the construction of the PSN curve. Specific quantiles are extracted from the prediction distribution for probabilistic fatigue life prediction of complex equipment.

[0125] Example 1

[0126] To verify the effectiveness of the method of the present invention, this implementation example uses a 7-series aluminum alloy case given by Song et al., and the fatigue life data is shown in Table 1:

[0127] Table 1

[0128]

[0129] In this embodiment, the fatigue life data under various stresses are subjected to a normality test. Based on the test results, it is determined whether to fit the data according to a normal distribution or a maximum entropy distribution. Then, the physical guided neural network proposed in this invention is trained using the fitted standard deviation data. The learning rate of the neural network is 0.005, and the number of iterations is 10,000. Next, the standard deviation of fatigue life under various stresses predicted by the one-stage model and the fatigue life data are used to train the Bayesian physical information neural network. The learning rate of the network is 0.005, and the number of iterations is 20,000. Each iteration samples the Bayesian neural network 10 times to calculate the standard deviation. When using the pre-trained Bayesian neural network for fatigue life prediction, the neural network is sampled 1000 times to obtain the fatigue life distribution under a given stress. Compared with the methods proposed by Ling et al. and Chen et al., the obtained PSN curve is as follows: Figure 4 As shown, (a) is the method of this invention, (b) is the method of Ling et al., and (c) is the method of Chen et al. It can be seen that on the SN curve with a survival rate of 97.5%, the method proposed in this invention satisfies the physical law that fatigue life decreases with increasing stress, while the other two methods do not. Furthermore, the probabilistic fatigue life prediction errors on the test set were also compared. and failure probability prediction error The calculation formula is as follows:

[0130]

[0131]

[0132] in, The fatigue life count for the test set. This represents the fatigue life corresponding to the failure rate in the predicted distribution. This represents the failure probability corresponding to fatigue life in the predicted distribution.

[0133] To ensure the statistical reliability of the evaluation results, the model was trained and evaluated repeatedly using cross-validation at different stress amplitudes. Each time, fatigue life data at randomly selected stress amplitudes were used as the test set, with the remainder used for training. After repeating this process multiple times, the average test results are shown in Table 2.

[0134] Table 2

[0135]

[0136] As can be seen from the results in Table 2, the method proposed in this invention achieves the best prediction accuracy while satisfying physical consistency. Compared with the method proposed by Ling, this method is superior. and These figures were reduced by 23% and 17% respectively, compared to the method proposed by Chen. and The results reduced the stress amplitude by 17% and 9% respectively. In addition, the standard deviation obtained by cross-validation of this invention was the smallest, indicating that the prediction stability was better under different stress amplitude datasets.

[0137] Example 2

[0138] To verify the effectiveness of the method of the present invention, this embodiment uses a 2024-T4 aluminum alloy case given by Shimokawa et al., and the fatigue life data is shown in Table 3:

[0139] Table 3

[0140]

[0141] In this embodiment, the fatigue life data under various stresses are subjected to a normality test. Based on the test results, it is determined whether to fit the data according to a normal distribution or a maximum entropy distribution. Then, the physical guided neural network proposed in this invention is trained using the fitted standard deviation data. The learning rate of the neural network is 0.005, and the number of iterations is 10,000. Next, the standard deviation of fatigue life under various stresses predicted by the one-stage model and the fatigue life data are used to train the Bayesian physical information neural network. The learning rate of the network is 0.005, and the number of iterations is 20,000. In each iteration, the Bayesian neural network is sampled 10 times to calculate the standard deviation. When using the pre-trained Bayesian neural network to predict fatigue life, the neural network is sampled 1,000 times to obtain the fatigue life distribution under a given stress. Compared with the methods proposed by Ling et al. and Chen et al., the obtained PSN curve is as follows: Figure 5 As shown, (a) is the method of this invention, (b) is the method of Ling et al., and (c) is the method of Chen et al. It is evident that on the SN curve with a survival rate of 97.5%, the method proposed in this invention satisfies the physical law that fatigue life decreases with increasing stress, while the other two methods do not. Furthermore, the probabilistic fatigue life prediction errors on the test set were also compared. and failure probability prediction error .

[0142] To ensure the statistical reliability of the evaluation results, the model was trained and evaluated repeatedly using cross-validation at different stress amplitudes. Each time, fatigue life data at randomly selected stress amplitudes were used as the test set, with the remainder used for training. After repeating this process multiple times, the average test results are shown in Table 4.

[0143] Table 4

[0144]

[0145] As can be seen from the results in Table 4, the method proposed in this invention achieves the best prediction accuracy while satisfying physical consistency. Compared with the method proposed by Ling, this method is superior. and These figures were reduced by 72% and 59% respectively, compared to the method proposed by Chen. and The results reduced the stress amplitude by 43% and 20% respectively. In addition, the standard deviation obtained by cross-validation of this invention was the smallest, indicating that the prediction stability was better under different stress amplitude datasets.

[0146] Example 3

[0147] To verify the effectiveness of the method of the present invention, this implementation example uses an SAE8620 steel case given by Pujol et al., and the fatigue life data is shown in Table 5:

[0148] Table 5

[0149]

[0150] In this embodiment, there are many cases where fatigue life data for various stress amplitudes is scarce or missing. With limited data, it's difficult to guarantee the accuracy of the fit. Therefore, a normality test is performed on samples with 14 or more fatigue life data points for each stress amplitude. Based on the test results, it's determined whether to fit according to a normal distribution or a maximum entropy distribution. Then, the physical guidance neural network proposed in this invention is trained using the fitted standard deviation data. The neural network has a learning rate of 0.005 and 10,000 iterations. A one-stage model is then used to predict the standard deviation of fatigue life under stress, including missing data. The standard deviation and all fatigue life data are used to train a Bayesian physical information neural network. The network has a learning rate of 0.005 and 20,000 iterations. Each iteration samples the Bayesian neural network 10 times to calculate the standard deviation. When using the pre-trained Bayesian neural network for fatigue life prediction, the neural network is sampled 1000 times to obtain the fatigue life distribution under a given stress. Compared with the methods proposed by Ling et al. and Chen et al., the obtained PSN curve is as follows: Figure 6As shown, (a) is the method of this invention, (b) is the method of Ling et al., and (c) is the method of Chen et al. It can be seen that on the SN curve with a survival rate of 97.5%, the method proposed in this invention satisfies the physical law that fatigue life decreases with increasing stress, while the other two methods do not. Furthermore, the probabilistic fatigue life prediction errors on the test set were also compared. and failure probability prediction error .

[0151] To mitigate the impact of insufficient test samples, all test sets included at least 14 fatigue life samples to ensure the reliability of the validation results on the test sets. Each model was trained and evaluated through repeated cross-validation at different stress amplitudes. Each time, fatigue life data at randomly selected stress amplitudes were used as the test set, with the remainder used for training. This process was repeated multiple times, and the average test results are shown in Table 6.

[0152] Table 6

[0153]

[0154] As can be seen from the results in Table 6, the method proposed in this invention achieves the best prediction accuracy while satisfying physical consistency. Compared with the method proposed by Ling, this method is superior. and These figures were reduced by 26% and 43% respectively, compared to the method proposed by Chen. and The reductions were 6% and 25% respectively. Meanwhile, the standard deviation obtained from the cross-validation of this invention, although... While not as good as Chen's method, it still achieved the second-best result. The result was even better, indicating that the model has good robustness.

[0155] The above embodiments effectively demonstrate the effectiveness and superiority of the probabilistic fatigue life prediction method for complex equipment based on Bayesian physical information neural network proposed in this invention. It can effectively improve the prediction accuracy while satisfying physical consistency, and also has good stability, thus improving the reliability of probabilistic fatigue life prediction.

[0156] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the probabilistic fatigue life of complex equipment based on physical information neural networks, characterized in that... Includes the following steps: Step S1: Group the fatigue life data of complex equipment materials according to stress, perform nonparametric probability estimation and normality test on the data under each stress, fit the fatigue life data that passes the test to a normal distribution based on the results of nonparametric probability estimation, and fit the fatigue life data that fails the test to a maximum entropy distribution. Step S2: Construct a physical-guided neural network to predict the missing standard deviation. Based on the fitted standard deviation data and the stress of the fatigue life data, train the physical-guided neural network to predict the standard deviation through the stress. Step S3: Construct a physical information neural network for predicting probabilistic fatigue life. The stress of the fatigue life data is used as the input, and the logarithmic fatigue life data is output. During the training process, the parameters of the neural network are sampled and predicted multiple times. The standard deviation of the predicted fatigue life under each stress is calculated. At the same time, a composite loss function is constructed based on the stress of the fatigue life data, the logarithmic fatigue life data, and the standard deviation generated by the physical guidance neural network. Step S4: Based on the prediction of the pre-trained physical information neural network, obtain the PSN curve, and combine it with the requirements of complex equipment to determine the fatigue life under a specific failure rate for probabilistic fatigue life prediction.

2. The method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network according to claim 1, characterized in that: Step S1 includes the following steps: Step S1.1: Obtain fatigue life data and stress of complex equipment, perform nonparametric probability estimation on fatigue life data under each stress, and obtain the failure rate corresponding to each fatigue life data. Step S1.2: Perform normality testing on fatigue life data under various stresses; Step S1.3: For fatigue life data that has passed the normality test, calculate the standard normal quantile corresponding to the failure rate, perform linear regression on the logarithmic fatigue life and the standard normal quantile, and obtain the slope and intercept of the fitted line as the standard deviation and mean of the logarithmic fatigue life data under each stress. Step S1.4: For fatigue life data that fails the normality test, calculate the moment constraint equation based on the fatigue life data, and fit the distribution using the maximum entropy algorithm of the first few statistical moments to obtain the most unbiased probability density function estimate.

3. The method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network according to claim 2, characterized in that: In step S1.4, the Lagrange multipliers of the four moments are calculated by solving the moment constraint equations to obtain the probability density function of the logarithmic fatigue life under each stress. Normalization constraints and fourth-order moment constraint equations are constructed. The fourth moments are the mean, standard deviation, kurtosis, and skewness of the logarithmic fatigue life, respectively. The mean moment is the average value of the logarithmic fatigue life data based on the number of stresses. The variance moment is the square root of the average value of the logarithmic fatigue life data based on the number of stresses after subtracting the mean moment from the logarithmic fatigue life data. The skewness moment is the cube of the ratio of the logarithmic fatigue life data to the mean moment and the variance moment based on the number of stresses. The kurtosis moment is the fourth power of the ratio of the logarithmic fatigue life data to the mean moment and the variance moment based on the number of stresses.

4. The method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network according to claim 1, characterized in that: Step S2 includes the following steps: Step S2.1: Construct a physics-guided neural network model, using stress amplitude as input and outputting the corresponding prediction standard deviation; Step S2.2: Add a physical constraint to the physical-guided neural network that the standard deviation of fatigue life decreases as stress increases; Step S2.3: Train the physical guidance neural network using the standard deviation data, generate predicted values ​​through forward propagation, quantify the difference between the predicted and actual values ​​using the mean squared error loss function, and then calculate the gradient and update the weights through backpropagation. The combination of physics-guided neural networks and physical information is achieved through constraint weights.

5. The method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network according to claim 1, characterized in that: Step S3 includes the following steps: Step S3.1: Construct a physical information neural network, using stress amplitude as input and outputting logarithmic fatigue life. The network parameters follow a normal distribution. Step S3.2: Maximize the lower bound of evidence based on variational inference, and construct a composite loss function by combining prior physical information. The prior physical information includes the fact that the standard deviation of fatigue life decreases with increasing stress, fatigue life increases monotonically with decreasing stress, and the curvature of the SN curve increases with increasing stress. The composite loss function consists of an evidence lower bound and a physical constraint penalty term, which are used as data fitting terms. Weighting coefficients are added to enhance the fitting effect and physical consistency. The physical constraint penalty term is obtained based on the predicted logarithmic fatigue life data and the partial derivative of the standard deviation with respect to stress. Step S3.3: Train the physical information neural network based on the fatigue life standard deviation prediction results and fatigue life data. In the forward propagation, generate multiple predicted values ​​through Monte Carlo sampling. Based on the composite loss function, backpropagate to update the normal distribution parameters of the network and continuously perform iterative updates.

6. The method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network according to claim 5, characterized in that: In step S3.2, the lower bound of evidence consists of the likelihood function of the observed data after the network parameters are given, the prior function of the weights, and the distribution function of the weight parameters after the normal distribution parameters are given.

7. The method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network according to claim 5, characterized in that: The physical constraint penalty term in step S3.2 includes a first physical constraint function in which fatigue life monotonically increases as stress decreases. This is achieved by constructing a state indicator function of the first derivative of logarithmic fatigue life with respect to stress. If the first derivative of logarithmic fatigue life with respect to stress is greater than zero, the state indicator function is one; otherwise, it is zero.

8. The method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network according to claim 5, characterized in that: The physical constraint penalty term in step S3.2 includes a second physical constraint function in which the curvature of the SN curve increases with increasing stress. This is achieved by constructing a state indicator function of the second derivative of logarithmic fatigue life with respect to stress. If the second derivative of logarithmic fatigue life with respect to stress is less than zero, the state indicator function is one; otherwise, it is zero.

9. The method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network according to claim 5, characterized in that: The physical constraint penalty term in step S3.2 includes a third physical constraint function that states that the fatigue life standard deviation decreases as stress increases. This is achieved by constructing the mean square error function of the standard deviation and the predicted fatigue life standard deviation.

10. The method for predicting the probabilistic fatigue life of complex equipment based on a physical information neural network according to claim 1, characterized in that: In step S4, the physical information neural network adopts a Bayesian physical information neural network. Through Monte Carlo sampling, a set of fatigue life prediction values ​​under a given input stress is obtained. From these values, a prediction distribution is constructed to realize the construction of the PSN curve. Specific quantiles are extracted from the prediction distribution for probabilistic fatigue life prediction of complex equipment.

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