Aircraft landing gear outer cylinder yield strength prediction method based on physical information deep neural network

Abstract

The invention provides an aircraft landing gear outer cylinder yield strength prediction method based on a physical information deep neural network, and relates to the technical field of intelligent manufacturing. The process data comprises transfer time, forging time, forge piece initial forging temperature, forge piece final forging temperature, size after final forging of the forge piece and forging speed of the free forging blank making and die forging forming stage; preprocessing the process data to obtain processed data; correlation analysis is conducted on the processed data, and contribution degree analysis is conducted on the processed data on the yield strength; according to a correlation analysis result and a contribution degree analysis result, screening out a modeling target process parameter from the processing data; and inputting the target process parameters to the trained deep neural network based on the physical information to obtain a predicted yield strength value of the outer cylinder of the aircraft landing gear. According to the method, the number of sample points required for constructing the model can be reduced on the premise of ensuring the interpretability of the model.

Description

Technical Field

[0001] The present application relates to the technical field of intelligent manufacturing, and specifically relates to a method for predicting the yield strength of an aircraft landing gear outer cylinder based on a physics-informed deep neural network. Background Art

[0002] As an important component for supporting an aircraft, the aircraft landing gear needs to withstand huge impact forces from the fuselage weight and the vertical direction during the takeoff and landing stages of the aircraft. Therefore, the material thereof must have extremely high yield strength. The outer cylinder of the aircraft landing gear is produced by a hot forming forging process. The forming process has multiple heating times and a long process flow, and the yield strength of the formed part is affected by many process parameters. Traditional yield strength detection uses destructive tests to measure, which is not only costly, but also requires complex experimental designs, sample preparation, sample calibration, and stretching and other steps.

[0003] With the development of machine learning technology, more and more scholars use machine learning models to predict the physical properties of hot-formed products. However, as a black-box model, machine learning can only extract limited data features and the correlation relationships between data, and cannot explain the physical laws of objective phenomena. And a sufficiently robust pure data-driven machine learning model must have a large amount of training data, which means a large amount of time and economic costs. Therefore, a method is needed to reduce the number of sample points required for building a model while ensuring the interpretability of the model. Summary of the Invention

[0004] The present application provides a method for predicting the yield strength of an aircraft landing gear outer cylinder based on a physics-informed deep neural network, which can reduce the number of sample points required for building a model while ensuring the interpretability of the model.

[0005] In the first aspect of the present application, a method for predicting the yield strength of an aircraft landing gear outer cylinder based on a physics-informed deep neural network is provided. The method includes:

[0006] Collecting process data of the aircraft landing gear at different process stages, where the process data includes transfer time, forging time, initial forging temperature of the forging, final forging temperature of the forging, final forging size of the forging, and forging speed during the free forging blanking and die forging forming stages;

[0007] Preprocessing the process data to obtain processed data;

[0008] Performing a correlation analysis on the processed data, and performing a contribution degree analysis on the processed data to the yield strength;

[0009] According to the results of the correlation analysis and the results of the contribution degree analysis, screening out the target process parameters for modeling from the processed data;

[0010] Input the target process parameters into the trained physics-informed deep neural network to obtain the predicted yield strength value of the aircraft landing gear outer cylinder.

[0011] Based on the above technical solutions, preferably, performing a correlation analysis on the processed data and an analysis of the contribution degree of the processed data to the yield strength specifically includes:

[0012] Performing a correlation analysis on different processed data using the Pearson correlation coefficient;

[0013] Performing a random forest contribution degree analysis on the processed data to calculate the contribution degree of the processed data to the yield strength.

[0014] Based on the above technical solutions, preferably, before inputting the target process parameters into the trained physics-informed deep neural network to obtain the predicted yield strength value of the aircraft landing gear outer cylinder, the method further includes:

[0015] Reducing the value of the loss function corresponding to the physics-informed deep neural network through forward propagation and backward propagation. The loss function includes a pure data-driven yield strength loss function and a physics-informed yield strength loss function. Among them, the pure data-driven yield strength loss function is defined by the square of the difference between the experimentally measured value and the predicted yield strength value, and the physics-informed yield strength loss function is constructed according to the physical laws of the yield strength and the forging temperature and forging time of the forging.

[0016] Based on the above technical solutions, preferably, the pure data-driven yield strength loss function is defined by the square of the difference between the experimentally measured value and the predicted yield strength value, and the specific expression of the pure data-driven yield strength loss function is as follows:

[0017]

[0018] where σ s ' is the predicted yield strength value, and σ s is the experimentally measured value.

[0019] Based on the above technical solutions, preferably, the physics-informed yield strength loss function constructed according to the physical laws of the yield strength and the forging temperature and forging time of the forging specifically further includes:

[0020] Based on the influence of the forging temperature and forging speed on the yield strength during the landing gear forging process and the saturation effect of the forging temperature and forging speed on the yield strength, constructing the physical constraints of the physics-informed deep neural network;

[0021] Determine an optimization objective for training the physics-informed deep neural network according to the physical constraints;

[0022] For the optimization objective, the optimization objective with the penalty function is changed to an unconstrained optimization problem, and the physics-informed yield strength loss function is constructed. The physics-informed yield strength loss function is expressed as follows:

[0023]

[0024] Where, is the first derivative of the yield strength with respect to the forging temperature, is the first derivative of the yield strength with respect to the forging time, is the second derivative of the yield strength with respect to the forging time.

[0025] On the basis of the above technical solutions, preferably, before inputting the target process parameters into the trained physics-informed deep neural network to obtain the predicted yield strength value of the aircraft landing gear outer cylinder, the method further includes:

[0026] Calculate the deviation degree between the experimental measurement value and the yield strength prediction value by using the mean absolute percentage error to obtain the mean relative error;

[0027] Calculate the fitting coefficient of the physics-informed deep neural network based on the model measurement value, the actual measurement value, and the average value of the actual measurement value;

[0028] Use the mean relative error and the coefficient of determination to measure the prediction accuracy of the physics-informed deep neural network.

[0029] On the basis of the above technical solutions, preferably, the preprocessing of the process data to obtain the processed data specifically includes:

[0030] Use the K-nearest neighbor algorithm to fill in the missing values of the process data to obtain the intermediate data, which is specifically processed by the following formula:

[0031]

[0032] Where, L(x i , x j ) is the Lagrangian distance between two adjacent process data, F is the feature index excluding the missing point, and x is the calculated missing value;

[0033] Normalize the intermediate data to obtain the processed data, which is specifically processed by the following formula:

[0034]

[0035] Among them, x * is the processed data, with a range of [0, 1]. x is the value of the process feature, and x max is the maximum value of the process feature, and x min is the minimum value of the process feature.

[0036] In the second aspect of the present application, a prediction device for the yield strength of the outer cylinder of an aircraft landing gear based on a physics-informed deep neural network is provided. The device is used to execute the method for predicting the yield strength of the outer cylinder of an aircraft landing gear based on a physics-informed deep neural network as described in any one of the above. The device includes an acquisition module, a processing module, and an output module, where:

[0037] The acquisition module is used to collect the process data of the aircraft landing gear at different process stages. The process data includes the transfer time, forging time, initial forging temperature of the forging, final forging temperature of the forging, final size of the forging after forging, and forging speed in the free forging blanking and die forging forming stages;

[0038] The processing module is used to preprocess the process data to obtain processed data;

[0039] The processing module is used to perform a correlation analysis on the processed data and analyze the contribution degree of the processed data to the yield strength;

[0040] The processing module is used to screen out the target process parameters for modeling from the processed data according to the results of the correlation analysis and the results of the contribution degree analysis;

[0041] The output module is used to input the target process parameters into the trained physics-informed deep neural network to obtain the predicted yield strength value of the outer cylinder of the aircraft landing gear.

[0042] Based on the above technical solutions, preferably, the processing module is used to perform a correlation analysis on different processed data by using the Pearson correlation coefficient;

[0043] The processing module is used to perform a random forest contribution degree analysis on the processed data to calculate the contribution degree of the processed data to the yield strength.

[0044] Based on the above technical solutions, preferably, the processing module is used to reduce the value of the loss function corresponding to the physics-informed deep neural network through forward propagation and backward propagation. The loss function includes a pure data-driven yield strength loss function and a physics-informed yield strength loss function. Among them, the pure data-driven yield strength loss function is defined by the square of the difference between the experimentally measured value and the predicted yield strength value, and the physics-informed yield strength loss function is constructed according to the physical laws of the yield strength and the forging temperature and forging time of the forging.

[0045] Based on the above technical solutions, preferably, the processing module is used to define the pure data-driven yield strength loss function by the square of the difference between the experimental measurement value and the predicted yield strength value. The specific expression of the pure data-driven yield strength loss function is as follows:

[0046]

[0047] where σ s ' is the predicted yield strength value, and σ s is the experimental measurement value.

[0048] Based on the above technical solutions, preferably, considering the influence of forging temperature and forging speed on the yield strength during the landing gear forging process, as well as the saturation effect of forging temperature and forging speed on the yield strength, construct the physical constraints of the physics-informed deep neural network;

[0049] The processing module is used to determine the optimization objective for training the physics-informed deep neural network according to the physical constraints;

[0050] The processing module is used to transform the optimization objective with a penalty function into an unconstrained optimization problem for the above optimization objective, and construct the physical information yield strength loss function, which is expressed as follows:

[0051]

[0052] where is the first-order derivative of the yield strength with respect to the forging temperature, is the first-order derivative of the yield strength with respect to the forging time, is the second-order derivative of the yield strength with respect to the forging time.

[0053] Based on the above technical solutions, preferably, the processing module is used to calculate the deviation degree between the experimental measurement value and the predicted yield strength value by the mean absolute percentage error to obtain the mean relative error;

[0054] The processing module is used to calculate the fitting coefficient of the physics-informed deep neural network based on the model measurement value, the actual measurement value, and the average value of the actual measurement value;

[0055] The processing module is used to measure the prediction accuracy of the physics-informed deep neural network by using the mean relative error and the coefficient of determination.

[0056] Based on the above technical solutions, preferably, the processing module is used to fill in the missing values of the process data by using the K-nearest neighbor algorithm to obtain intermediate data, and the specific processing is as follows:

[0057]

[0058] where L(x i ,x j ) is the Lagrangian distance between two adjacent process data, F is the feature index that does not include the missing point, and x is the calculated missing value;

[0059] The processing module is used to perform normalization processing on the intermediate data to obtain the processed data, and the specific processing is as follows:

[0060]

[0061] where x * is the processed data, with a range of [0, 1], x is the value of the process feature, x max is the maximum value of the process feature, and x min is the minimum value of the process feature.

[0062] In the third aspect of the present application, an electronic device is provided, including a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are both used to communicate with other devices, and the processor is used to execute the instructions stored in the memory so that the electronic device executes the method described in any one of the above.

[0063] In the fourth aspect of the present application, a computer-readable storage medium is provided. The computer-readable storage medium stores instructions, and when the instructions are executed, the method described in any one of the above is executed.

[0064] In summary, one or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages:

[0065] 1. By introducing physical information constraints, the physical laws between forging temperature, forging time and yield strength are incorporated into the training process of the deep neural network, enabling the model to follow the known physical mechanisms while learning data features, thereby reducing the dependence on large-scale data samples and improving the modeling efficiency. Compared with pure data-driven deep learning methods, using physical information to guide model optimization allows the model to effectively learn and generalize reasonable yield strength prediction results even when the number of samples is small. In addition, key process parameters are screened out through correlation analysis and contribution analysis to avoid redundant information interfering with model training, improve data utilization, further reduce the required amount of data samples, and ensure the physical interpretability and engineering applicability of the prediction results.

[0066] 2. Analyze the linear correlation between different process parameters through Pearson correlation coefficient to identify redundant or highly correlated features, thereby reducing the dimension of the input data, improving the computational efficiency and stability of the model. At the same time, use random forest contribution analysis to evaluate the influence degree of each process parameter on the yield strength, ensuring that the selected input features have a significant contribution to the model prediction and enhancing the physical interpretability of the model. Combining these two analysis methods can reduce unnecessary computational overhead while ensuring the prediction accuracy of the model, improve data utilization, and enhance the generalization ability of the model under different working conditions, making the yield strength prediction more accurate and reliable.

[0067] 3. Combine the pure data-driven yield strength loss function and the physical information yield strength loss function constructed based on physical laws. During the neural network training process, calculate the loss value through forward propagation and adjust the weights through backward propagation to optimize the model prediction performance. The pure data-driven loss function ensures that the model can effectively fit the experimental data, while the physical information loss function guarantees that the model prediction results conform to the physical laws of the material forming process by introducing the physical constraints of forging temperature, forging time and yield strength. This method can not only improve the accuracy of yield strength prediction, but also reduce the sample size required for training, enhance the generalization ability and physical interpretability of the model, and enable it to stably provide reasonable prediction results under different process conditions.

[0068] 4. Calculate the mean absolute percentage error to measure the deviation between the experimental measurement value and the yield strength prediction value, so as to quantitatively evaluate the error level of the model and ensure the reliability of the prediction results. At the same time, evaluate the goodness of fit of the model by calculating the coefficient of determination to measure the explanatory ability of the prediction value to the actual measurement value and ensure the effective learning of the model for the data trend. Combining these two indicators can comprehensively measure the prediction accuracy of the physical information-based deep neural network, ensure the stability and generalization ability of the model under different process conditions, improve the accuracy of yield strength prediction, and enhance the feasibility and credibility of the model in engineering applications. Description of the Drawings

[0069] Figure 1 It is a schematic flow chart of a method for predicting the yield strength of an aircraft landing gear outer cylinder based on a physics-informed deep neural network disclosed in an embodiment of the present application;

[0070] Figure 2 It is a schematic module diagram of a device for predicting the yield strength of an aircraft landing gear outer cylinder based on a physics-informed deep neural network disclosed in an embodiment of the present application;

[0071] Figure 3 It is a schematic structural diagram of an electronic device.

[0072] Explanation of reference numerals: 201, acquisition module; 202, processing module; 203, output module; 301, processor; 302, communication bus; 303, user interface; 304, network interface; 305, memory. Detailed implementation manners

[0073] In order to enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments.

[0074] In the description of the embodiments of the present application, words such as "for example" or "for illustration" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as "for example" or "for illustration" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Specifically, the use of words such as "for example" or "for illustration" is intended to present relevant concepts in a specific manner.

[0075] In the description of the embodiments of the present application, the meaning of the term "plurality" refers to two or more. For example, a plurality of systems refers to two or more systems, and a plurality of screen terminals refers to two or more screen terminals. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the technical features indicated. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. The terms "include", "comprise", "have" and their variants all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0076] When a machine learning model is trained, it requires a large number of data samples, resulting in high modeling costs in terms of both capital and time. For a pure data-driven machine learning model, to extract the hidden data features behind the samples and establish the mapping relationship between the input and output, a huge amount of data is needed. Moreover, collecting and analyzing data samples consumes a great deal of time and computational cost. Additionally, the trained model, which is a black-box model of input and output, lacks physical interpretability. To address the above problems, by introducing physical constraint relationships to guide the modeling process, the amount of data required for modeling can be reduced to a certain extent, and the model can also have a certain physical meaning.

[0077] This embodiment discloses a method for predicting the yield strength of the outer cylinder of an aircraft landing gear based on a physics-informed deep neural network, referring to Figure 1 , and includes the following steps S110 - S150:

[0078] S110, collect the process data of the aircraft landing gear at different process stages.

[0079] The method for predicting the yield strength of the outer cylinder of an aircraft landing gear based on a physics-informed deep neural network disclosed in the embodiments of this application is applied to a server. The server includes, but is not limited to, electronic devices such as mobile phones, tablet computers, wearable devices, and PCs (Personal Computers). It can also be a background server running the method for predicting the yield strength of the outer cylinder of an aircraft landing gear based on a physics-informed deep neural network. The server can be implemented by an independent server or a server cluster composed of multiple servers.

[0080] When collecting the process data of the aircraft landing gear at different process stages, the key process parameters in the free forging blanking and die forging forming stages need to be covered to ensure the integrity and accuracy of the data. Specifically, first, high-precision sensor devices, including infrared thermal imagers, speed sensors, and binocular cameras, are required to collect the parameters involved in the free forging and die forging processes in real time. The determination of the transfer time needs to be calculated by combining the length of the transfer path and the transfer speed to ensure the accuracy of the data; the forging time needs to be measured by combining the number of strokes of the press and the single stamping time, and high-frequency data recording technology is used to capture transient changes; the initial forging temperature and final forging temperature of the forgings are continuously monitored using infrared temperature measurement equipment or thermocouples, and data correction is performed in combination with temperature field simulation; the dimensions of the forgings after final forging are measured using a laser measurement system or a high-precision coordinate measuring machine to ensure the reliability of the final dimension data; the determination of the forging speed needs to be double-verified by combining the speed control parameters of the press and the actual measurement data to ensure that it reflects the actual forging conditions. All the collected data needs to be preprocessed, including data cleaning, outlier detection, and normalization, to improve the data quality and the accuracy of subsequent modeling. Finally, these data are stored in the SQL Server database to provide basic data support for the subsequent yield strength prediction model based on the physics-informed deep neural network.

[0081] S120, preprocess the process data to obtain processed data.

[0082] When preprocessing the process data to obtain processed data, missing value filling needs to be carried out first. During the data collection process, due to sensor accuracy limitations, data transmission interference, or measurement environment changes, some process data may have missing values. To solve this problem, the K-nearest neighbor algorithm is used to fill in the missing values. Specifically, first, calculate the Lagrangian distance between the current sample and other samples, and this distance is calculated according to the formula:

[0083]

[0084] is calculated, where x i and x j represent the feature vectors of two samples respectively, F represents the feature index that does not contain the missing point, and the K nearest samples are determined by calculating the distance between samples. Then, according to the average value of the corresponding features in the K nearest samples:

[0085]

[0086] Fill in the missing values through the average value, so that the filled data is as close as possible to the actual distribution, and reduce the impact of abnormal data on subsequent analysis. Next, normalize the filled intermediate data to eliminate the dimensional differences between different process data and enhance the comparability of the data. The specific method is to use the min-max normalization formula:

[0087]

[0088] where x * is the processed data, with a range of [0, 1], x is the value of the process feature, and x max is the maximum value of the process feature, and x min is the minimum value of the process feature.

[0089] Through normalization, all process data is converted to the [0, 1] interval, ensuring that process data with different dimensions has a consistent numerical range, providing a stable data basis for subsequent machine learning modeling and analysis. After the above preprocessing steps, the processed data for subsequent analysis is finally obtained, which can effectively reduce noise, improve the overall quality of the data and the reliability of modeling.

[0090] S130, perform a correlation analysis on the processed data and an analysis of the contribution degree of the processed data to the yield strength.

[0091] When performing a correlation analysis and a contribution degree analysis on the processed data, it is first necessary to calculate the correlation between different processed data using the Pearson correlation coefficient to determine which process data has a strong linear correlation. Specifically, first extract each process data variable from the normalized processed data set, calculate its mean and variance, and calculate the correlation between each variable. The specific calculation is through the following formula:

[0092]

[0093] where r is the correlation degree of different processed data, X i , X j are different processed data, var(X i )·var(X j ) is the variance between different processed data, and cov(X i , X j ) is the covariance between different processed data. The calculated r value ranges from [-1, 1]. When the r value is close to 1, it indicates a high positive correlation between the two variables; when it is close to -1, it indicates a high negative correlation; when it is close to 0, it indicates no obvious correlation. After analyzing the correlation results, screen the highly correlated process data to reduce data redundancy and improve the calculation efficiency of the model.

[0094] After completing the correlation analysis, it is necessary to further calculate the contribution degree of the processed data to the yield strength in order to screen out the key process data that has a greater impact on the yield strength. The random forest model is used for the contribution degree analysis, and the mean decrease accuracy (MDA) is calculated to evaluate the contribution degree of each process data. In specific implementation, first, a random forest (RF) regression model is constructed and the data set is trained to form multiple decision trees. For each decision tree, a part of the samples are randomly selected as out-of-bag (OOB) samples, and the prediction error of the OOB samples is calculated. Then, without changing other variables, the values of a certain process data are randomly shuffled, and the prediction error of the OOB samples is calculated again, which is specifically calculated by the following formula:

[0095]

[0096] where T is the number of random trees in the RF, (X i ,Y i ) is the sample, X i is the sample corresponding to the processed data, Y i is the sample corresponding to the yield strength, D t is the out-of-bag sample set of the random tree t, D t j is the sample set formed after the j-th dimension is swapped, R k (X i ) is the predicted output of the yield strength of the sample X i , Y i k is the k-th dimension output considering multi-objective regression.

[0097] If a certain process data has a greater impact on the yield strength, the MDA value after its replacement increases, otherwise the impact is smaller. Finally, the process data with higher contribution degree is screened out according to the size of the MDA value and is used for subsequent deep neural network model training to improve the prediction accuracy and physical interpretability of the model.

[0098] S140. According to the results of the correlation analysis and the contribution degree analysis, the target process parameters for modeling are screened out from the processed data.

[0099] When screening the target process parameters for modeling from the processed data, it is first necessary to comprehensively utilize the results of correlation analysis and contribution analysis to ensure that the input parameters can not only avoid redundant information but also effectively represent the factors that have the most significant impact on the yield strength. Specifically, first, use the correlation matrix obtained from the Pearson correlation coefficient analysis to calculate the correlation coefficient r value pairwise for all process data, and use a certain correlation threshold (for example, |r|>0.8) as the standard to screen out parameters with too high correlation to avoid data redundancy and multicollinearity problems. For parameter pairs with too high correlation, select the parameter with a larger contribution to the yield strength and retain it, and eliminate the parameter with a lower contribution to improve the stability of the model.

[0100] Next, according to the results of the random forest contribution analysis, screen out the process data that has the greatest impact on the yield strength. First, sort the MDA values of all parameters and set a contribution threshold (such as the top 10 parameters with the highest contribution, or parameters with a contribution accounting for more than 80% of the total contribution), retain the process data with high contribution, and eliminate the parameters with lower contribution. In specific implementation, first normalize the MDA values so that the total contribution of each parameter is normalized to 1, then calculate the cumulative contribution, and select the parameters whose cumulative contribution reaches the set standard.

[0101] In the final screening stage, comprehensively considering the results of correlation analysis and contribution analysis, if a certain process data has a high contribution but is highly correlated with other parameters, it may be processed by means of combined dimensionality reduction or feature engineering, such as using principal component analysis (PCA) for dimensionality compression, or selecting the most representative parameters based on expert knowledge. In addition, for parameters with low contribution, even if their correlation is low, they can be directly eliminated to reduce the model complexity and improve the calculation efficiency.

[0102] The finally obtained target process parameters for modeling should have the following characteristics: one is that the correlation between them is low to reduce the interference of multicollinearity on model training; the other is that the contribution to the yield strength is high to ensure that the input features can reflect the impact of the process on the yield strength during the landing gear forming process to the greatest extent. After the screening is completed, these target process parameters will be used as the input features of the deep neural network model for further prediction modeling of the yield strength to improve the accuracy and physical interpretability of the model.

[0103] S150, input the target process parameters into the trained physics-informed deep neural network to obtain the predicted yield strength value of the aircraft landing gear outer cylinder.

[0104] In a possible implementation, before inputting target process parameters into a trained physics-informed deep neural network to obtain the predicted yield strength value of the aircraft landing gear outer cylinder, the method further includes: reducing the value of the loss function corresponding to the physics-informed deep neural network through forward propagation and backward propagation. The loss function includes a purely data-driven yield strength loss function and a physics-informed yield strength loss function. Among them, the purely data-driven yield strength loss function is defined by the square of the difference between the experimental measurement value and the yield strength prediction value, and the physics-informed yield strength loss function is constructed based on the physical laws of yield strength, forging temperature, and forging time of the forging.

[0105] Specifically, in the process of training a physics-informed deep neural network to predict the yield strength of the aircraft landing gear outer cylinder, it is first necessary to construct a loss function to guide model optimization. The loss function consists of a purely data-driven yield strength loss function and a physics-informed yield strength loss function. The purely data-driven yield strength loss function is calculated by the square of the error between the experimental measurement value and the yield strength prediction value, and its expression is:

[0106]

[0107] where σ s ' is the predicted yield strength value, and σ s is the experimental measurement value.

[0108] Minimizing the loss function enables the model to more accurately fit the experimental data.

[0109] The physics-informed yield strength loss function is constructed based on the physical relationship between yield strength, forging temperature, and forging time. The first-order and second-order derivatives of yield strength with respect to forging temperature and time are used to constrain the model output to balance the impact of physical loss on overall optimization. During the training process, the loss value is calculated through forward propagation, and the weight is adjusted by using the backpropagation algorithm to calculate the gradient of the loss function with respect to the network parameters, so that the value of the loss function gradually decreases. In the optimization process, the gradient descent algorithm or the Adam optimization algorithm is used to improve the convergence speed and ensure the training stability. Finally, when the loss function reaches the convergence criterion or the number of training iterations reaches the set value, the network model is trained and can input target process parameters to predict the yield strength of the aircraft landing gear outer cylinder. Through this method, not only the prediction accuracy of the model is improved, but also its physical interpretability and generalization ability are enhanced.

[0110] Furthermore, when constructing the physical-information-based yield strength loss function of the deep neural network, it is first necessary to analyze the influence of forging temperature and forging speed on the yield strength during the forging process of the aircraft landing gear and consider its saturation effect. As the forging temperature increases, the yield strength of the metal material usually decreases, while the increase in forging time can improve the yield strength in the initial stage. However, when it exceeds a certain threshold, due to the dynamic recrystallization and grain growth effects of the microstructure, the yield strength decreases instead. Therefore, based on these physical laws, physical constraints are constructed, that is, to ensure that the temperature gradient and time gradient of the yield strength conform to the physical laws, and at the same time, a second-order derivative constraint is imposed on the time change rate of the yield strength to avoid non-physical prediction results. The influence of forging temperature and forging speed on the yield strength and the saturation effect during the landing gear forging process can be expressed by the formula:

[0111]

[0112] Among them, is the first derivative of the yield strength with respect to the forging temperature, is the first derivative of the yield strength with respect to the forging time, is the second derivative of the yield strength with respect to the forging time.

[0113] When determining the optimization objective for training the deep neural network, it is necessary to formalize the above physical constraints and optimize them in combination with the training process of the neural network. The optimization objective is set as: the predicted value of the network should not only match the experimental data but also satisfy the physical constraints, that is, the derivatives of the yield strength with respect to the forging temperature and forging time satisfy reasonable physical laws. In particular, it is necessary to ensure that the first derivative of the yield strength with respect to the temperature is non-positive to reflect its decreasing trend, and to ensure that the derivative of the yield strength with respect to time shows a trend of being positive first and then negative to reflect the saturation effect of the forging time. The optimization objective can be expressed as:

[0114]

[0115] To convert the optimization objective into a trainable unconstrained optimization problem, the penalty function method is used to adjust the structure of the loss function, that is:

[0116]

[0117] In the formula, η is the relaxation factor, and f(·) is the penalty function. The specific approach is to introduce a non-negative constraint term, so that when the physical law is violated, the corresponding loss term increases, thereby guiding the model to automatically satisfy the physical constraints during the optimization process. The physical-information-based yield strength loss function is expressed as follows:

[0118]

[0119] Among them, is the first derivative of the yield strength with respect to the forging temperature, is the first derivative of the yield strength with respect to the forging time, is the second derivative of the yield strength with respect to the forging time. Among them, the first term ensures that the yield strength does not increase abnormally with the increase of the forging temperature, the second term ensures that the yield strength increases within a reasonable forging time range, and the third term ensures that the rate of change of the yield strength with respect to time conforms to physical laws, that is, it prevents abnormal oscillations or unreasonable trends in the predicted values.

[0120] Finally, during the neural network training process, the loss function of the model is jointly composed of the data-driven loss function and the physical-information yield strength loss function, and is iteratively optimized through the gradient descent or Adam optimization algorithm, so that the prediction results can not only minimize the error of the experimental data, but also satisfy the physical constraints of the forging temperature and time on the yield strength, thereby improving the physical interpretability, generalization ability and robustness of the prediction model.

[0121] Furthermore, when evaluating the prediction model of the yield strength of the aircraft landing gear outer cylinder based on the physics-informed deep neural network, the mean absolute percentage error (MAPE) and the coefficient of determination (R 2 ) are used to measure the prediction accuracy of the model, and the SHAP value is used to analyze the interpretability of the model. First, calculate the MAPE to measure the average relative error of the model, which can reflect the deviation degree between the experimental measurement value and the yield strength prediction value. Its calculation formula is:

[0122]

[0123] where, σ s i ' is the i-th yield strength prediction value, σ s i is the i-th experimental measurement value, and n is the number of samples.

[0124] When calculating, sum and average the errors of all test set samples, and then convert them into percentages. The smaller the MAPE value, the smaller the prediction error and the higher the model accuracy.

[0125] Next, calculate the coefficient of determination (R 2 ) to measure the goodness of fit of the model, and its formula is:

[0126]

[0127] where, y i is the actual measurement value, is the model prediction value, is the average value of all actual measurements. The numerator calculates the sum of the squared errors between the model prediction values and the actual measurement values, and the denominator calculates the sum of the squared errors of the actual measurement values relative to their mean. When R 2 is close to 1, it indicates that the model has a high degree of fitting to the data and the prediction results are relatively accurate; when R 2 is low, it shows that the prediction effect of the model is poor, and it may be necessary to optimize the neural network structure or adjust the feature selection strategy.

[0128] Finally, to analyze the interpretability of the model, SHAP (Shapley Additive Explanations) values are used to quantify the impact of each input feature on the prediction results. The SHAP method is based on cooperative game theory and evaluates the importance by calculating the marginal contribution of each process data to the predicted value of yield strength under different combinations. In specific implementation, first, apply the SHAP interpretation framework to the trained neural network model, calculate the SHAP values of each input process data, and generate the SHAP importance ranking graph and the dependence graph to visually display the impact direction and degree of each process data on the yield strength. The positive or negative of the SHAP value indicates whether the feature enhances or reduces the predicted value, and the absolute value size indicates the strength of the impact. By analyzing the SHAP values, it is possible to identify which process data contribute the most to the yield strength, thereby optimizing the forging process and improving the quality control level of the production process. Finally, evaluate the prediction performance of the model through MAPE and R 2 and improve the interpretability of the model by combining SHAP analysis, making the application of the physics-informed deep neural network in the prediction of landing gear yield strength more reliable and with stronger engineering usability.

[0129] After the data preprocessing is completed, the target process parameters are input into the trained deep neural network, which has been optimized based on physical information and trained by combining data-driven methods. The forward propagation process of the network first passes through the input layer, transfers the target process parameters to the hidden layer, and calculates the high-dimensional feature mapping through multiple neurons and non-linear activation functions (such as ReLU or Leaky ReLU) in the hidden layer, and transfers information layer by layer to learn the complex relationship between the process parameters and the yield strength.

[0130] During the forward propagation process, the model calculates the target process parameters by combining the learned weight parameters and outputs the predicted yield strength value. Since the physical information constraints have been integrated into the deep neural network, when calculating the predicted value, the physical law constraints of the yield strength on the forging temperature and forging time will be implicitly satisfied to ensure the physical consistency of the output. Finally, at the output layer of the network, the predicted yield strength value is finally calculated through the linear regression layer or the regression activation function and the prediction result is output.

[0131] This embodiment also discloses an aircraft landing gear outer cylinder yield strength prediction device based on a physics-informed deep neural network. The device is used to execute the aircraft landing gear outer cylinder yield strength prediction method based on the physics-informed deep neural network as described in any one of the above, with reference to Figure 2 , the device includes an acquisition module 201, a processing module 202, and an output module 203, where:

[0132] The acquisition module 201 is used to collect the process data of the aircraft landing gear in different process stages. The process data includes the transfer time, forging time, initial forging temperature of the forging, final forging temperature of the forging, final forging size of the forging, and forging speed in the free forging blanking and die forging forming stages.

[0133] The processing module 202 is used to preprocess the process data to obtain processed data.

[0134] The processing module 202 is used to perform a correlation analysis on the processed data and analyze the contribution degree of the processed data to the yield strength.

[0135] The processing module 202 is used to screen out the target process parameters for modeling from the processed data according to the results of the correlation analysis and the contribution degree analysis.

[0136] The output module 203 is used to input the target process parameters into the trained physics-informed deep neural network to obtain the predicted yield strength value of the aircraft landing gear outer cylinder.

[0137] In a possible implementation manner, the processing module 202 is used to perform a correlation analysis on different processed data by using the Pearson correlation coefficient.

[0138] The processing module 202 is used to perform a random forest contribution degree analysis on the processed data to calculate the contribution degree of the processed data to the yield strength.

[0139] In a possible implementation manner, the processing module 202 is used to reduce the value of the loss function corresponding to the physics-informed deep neural network through forward propagation and backward propagation. The loss function includes a pure data-driven yield strength loss function and a physics-informed yield strength loss function. Among them, the pure data-driven yield strength loss function is defined by the square of the difference between the experimentally measured value and the yield strength prediction value, and the physics-informed yield strength loss function is constructed according to the physical laws of the yield strength and the forging temperature and forging time of the forging.

[0140] In a possible implementation manner, the processing module 202 is used to define the pure data-driven yield strength loss function by the square of the difference between the experimentally measured value and the yield strength prediction value. The specific expression of the pure data-driven yield strength loss function is as follows:

[0141]

[0142] Among them, σ s ' is the predicted value of the yield strength, and σ s is the experimentally measured value.

[0143] In a possible implementation manner, based on the influence of forging temperature and forging speed on the yield strength during the forging process of the landing gear, as well as the saturation effect of forging temperature and forging speed on the yield strength, physical constraints of a deep neural network based on physical information are constructed.

[0144] The processing module 202 is configured to determine an optimization objective for training a deep neural network based on physical information according to the physical constraints.

[0145] The processing module 202 is configured to change the optimization objective with a penalty function into an unconstrained optimization problem for the optimization objective, and construct a physical information yield strength loss function, and the physical information yield strength loss function is expressed as follows:

[0146]

[0147] Among them, is the first derivative of the yield strength with respect to the forging temperature, is the first derivative of the yield strength with respect to the forging time, is the second derivative of the yield strength with respect to the forging time.

[0148] In a possible implementation manner, the processing module 202 is configured to calculate the deviation degree between the experimentally measured value and the predicted value of the yield strength by using the mean absolute percentage error to obtain the mean relative error.

[0149] The processing module 202 is configured to calculate the fitting coefficient of the deep neural network based on physical information based on the model measurement value, the actual measurement value, and the average value of the actual measurement value.

[0150] The processing module 202 is configured to measure the prediction accuracy of the deep neural network based on physical information by using the mean relative error and the coefficient of determination.

[0151] In a possible implementation manner, the processing module 202 is configured to fill in the missing values of the process data by using the K-nearest neighbor algorithm to obtain intermediate data, and specifically process through the following formula:

[0152]

[0153] Among them, L(x i , x j ) is the Lagrangian distance between two adjacent process data, F is the feature index that does not include the missing point, and x is the calculated missing value.

[0154] The processing module 202 is configured to perform normalization processing on the intermediate data to obtain processed data, and specifically process it through the following formula:

[0155]

[0156] where x * is the processed data, and the range is [0, 1], x is the value of the process feature, x max is the maximum value of the process feature, x min is the minimum value of the process feature.

[0157] It should be noted that: when the device provided in the above embodiment realizes its functions, only the division of the above function modules is used for illustration. In practical applications, the above functions can be allocated to different function modules according to needs, that is, the internal structure of the device is divided into different function modules to complete all or part of the functions described above. In addition, the device and method embodiments provided in the above embodiment belong to the same concept, and the specific implementation process can be seen in the method embodiment, which will not be elaborated here.

[0158] This embodiment also discloses an electronic device. Referring to Figure 3 , the electronic device may include: at least one processor 301, at least one communication bus 302, a user interface 303, a network interface 304, and at least one memory 305.

[0159] Among them, the communication bus 302 is used to realize the connection and communication between these components.

[0160] Among them, the user interface 303 may include a display screen (Display) and a camera (Camera). Optionally, the user interface 303 may also include a standard wired interface and a wireless interface.

[0161] Among them, the network interface 304 may optionally include a standard wired interface and a wireless interface (such as a WI-FI interface).

[0162] Among them, the processor 301 may include one or more processing cores. The processor 301 connects various parts within the entire server through various interfaces and lines, and executes various functions of the server and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory 305, and by calling the data stored in the memory 305. Optionally, the processor 301 may be implemented in at least one hardware form of digital signal processing (DSP), field-programmable gate array (FPGA), or programmable logic array (PLA). The processor 301 may integrate a combination of one or more of a central processing unit (CPU), a graphics processing unit (GPU), and a modem, etc. Among them, the CPU mainly processes the operating system, user interface, application programs, etc.; the GPU is responsible for rendering and drawing the content to be displayed on the display screen; the modem is used to process wireless communication. It can be understood that the above-mentioned modem may not be integrated into the processor 301 and may be implemented separately by a single chip.

[0163] Among them, the memory 305 may include random access memory (RAM) and may also include read-only memory. Optionally, the memory includes a non-transitory computer-readable storage medium. The memory 305 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 305 may include a program storage area and a data storage area. Among them, the program storage area may store instructions for implementing the operating system, instructions for at least one function (such as touch function, sound playback function, image playback function, etc.), instructions for implementing the above-mentioned method embodiments, etc.; the data storage area may store the data involved in the above-mentioned method embodiments. Optionally, the memory 305 may further be at least one storage device located far from the aforementioned processor 301. As a computer storage medium, the memory 305 may include an operating system, a network communication module, a user interface 303 module, and an application program for the method for predicting the yield strength of the outer cylinder of an aircraft landing gear based on physical information deep neural network.

[0164] In Figure 3In the electronic device shown, the user interface 303 is mainly used to provide an interface for the user to input and obtain the data input by the user; and the processor 301 can be used to call the application program stored in the memory 305 for the method for predicting the yield strength of the outer cylinder of the aircraft landing gear based on the physical information deep neural network. When executed by one or more processors 301, the electronic device is caused to execute the method as described in one or more of the above embodiments.

[0165] It should be noted that, for the foregoing method embodiments, for the sake of simple description, they are all expressed as a series of action combinations. However, those skilled in the art should know that this application is not limited by the described action sequence, because according to this application, certain steps can be performed in other sequences or simultaneously. Secondly, those skilled in the art should also know that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0166] In the above embodiments, the descriptions of the respective embodiments have their own emphases. For the parts not detailed in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0167] In several embodiments provided by this application, it should be understood that the disclosed device can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed mutual coupling or direct coupling or communication connection can be through some service interfaces. The indirect coupling or communication connection of the device or unit can be in an electrical or other form.

[0168] The units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they can be located in one place, or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0169] In addition, in each embodiment of this application, the functional units can be integrated in one processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above integrated units can be implemented in the form of hardware or in the form of software functional units.

[0170] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a memory 305 and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present application. The aforementioned memory 305 includes various media that can store program codes, such as USB flash drives, mobile hard disks, magnetic disks, or optical discs.

[0171] The present application also discloses a computer-readable storage medium storing instructions. When executed by one or more processors 301, it causes the electronic device to execute one or more of the methods as described in the above embodiments.

[0172] The foregoing are only exemplary embodiments of the present disclosure and should not be used to limit the scope of the present disclosure. That is, any equivalent changes and modifications made in accordance with the teachings of the present disclosure still fall within the scope covered by the present disclosure. Those skilled in the art will readily think of other embodiments of the present disclosure after considering the specification and practice of the present disclosure. The present application aims to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common general knowledge or conventional technical means in the technical field not described in the present disclosure. The specification and embodiments are only regarded as exemplary, and the scope and spirit of the present disclosure are defined by the claims.

Claims

1. A method for predicting the yield strength of an aircraft landing gear outer tube based on a physical information deep neural network, characterized in that: The method comprises: Collecting process data of the aircraft landing gear at different process stages, the process data includes the transfer time, forging time, forging initial forging temperature, forging final forging temperature, forging size after final forging, and forging speed in the free forging billet and die forging forming stages; Preprocessing the process data to obtain processed data; performing a correlation analysis on the processed data, and performing a contribution analysis on the processed data to the yield strength; According to the result of the correlation analysis and the result of the contribution analysis, the target process parameters for modeling are screened out from the processing data; The target process parameters are input into a trained deep neural network based on physical information to obtain a predicted yield strength value of an outer tube of an aircraft landing gear.

2. The method for predicting the yield strength of an aircraft landing gear outer tube based on a physical information deep neural network according to claim 1 is characterized in that: The performing correlation analysis on the processed data and performing contribution analysis on the processed data to the yield strength specifically includes: The Pearson correlation coefficient is used to perform correlation analysis on the different processed data; A random forest contribution analysis is performed on the processed data to calculate the contribution of the processed data to the yield strength.

3. The method for predicting the yield strength of an aircraft landing gear outer tube based on a physical information deep neural network according to claim 1, characterized in that: Before inputting the target process parameters into the trained physical information-based deep neural network to obtain the predicted yield strength value of the aircraft landing gear outer tube, the method further includes: The value of the loss function corresponding to the deep neural network based on physical information is reduced by forward propagation and back propagation, and the loss function includes a pure data-driven yield strength loss function and a physical information yield strength loss function, wherein the pure data-driven yield strength loss function is defined by the square of the difference between the experimental measurement value and the yield strength prediction value, and the physical information yield strength loss function is constructed according to the physical laws of yield strength and forging temperature and forging time of forgings.

4. The method for predicting the yield strength of an aircraft landing gear outer tube based on a physical information deep neural network according to claim 3 is characterized in that: The pure data-driven yield strength loss function is defined by the square of the difference between the experimental measurement value and the yield strength prediction value. The specific expression of the pure data-driven yield strength loss function is as follows: Among them, σ s ' is the predicted value of yield strength, σ s are the experimental measurements.

5. The method for predicting the yield strength of an aircraft landing gear outer tube based on a physical information deep neural network according to claim 3 is characterized in that: The physical information yield strength loss function constructed according to the physical laws of yield strength, forging temperature and forging time of forgings specifically includes: Based on the influence of forging temperature and forging speed on yield strength during the landing gear forging process, and the saturation effect of forging temperature and forging speed on yield strength, physical constraints of the deep neural network based on physical information are constructed; Determining an optimization target for training the physics-based deep neural network based on the physical constraints; For the optimization objective, the optimization objective using the penalty function is changed to an unconstrained optimization problem, and the physical information yield strength loss function is constructed. The physical information yield strength loss function is expressed as follows: in, is the first-order derivative of yield strength with respect to forging temperature, is the first-order derivative of yield strength with respect to forging time, is the second-order derivative of yield strength with respect to forging time.

6. The method for predicting the yield strength of an aircraft landing gear outer tube based on a physical information deep neural network according to claim 3, characterized in that: Before inputting the target process parameters into the trained physical information-based deep neural network to obtain the predicted yield strength value of the aircraft landing gear outer tube, the method further includes: The average absolute percentage error is used to calculate the degree of deviation between the experimental measurement value and the yield strength prediction value to obtain the average relative error; Calculating the physical information-based deep neural network fitting coefficient based on the model measurement value, the actual measurement value and the average value of the actual measurement value; The average relative error and the coefficient of determination are used to measure the prediction accuracy of the deep neural network based on physical information.

7. The method for predicting the yield strength of an aircraft landing gear outer tube based on a physical information deep neural network according to claim 1, characterized in that: The preprocessing of the process data to obtain processed data specifically includes: Using a K-nearest neighbor algorithm to fill missing values ​​in the process data to obtain intermediate data; The intermediate data is normalized to obtain the processed data.

8. An aircraft landing gear outer tube yield strength prediction device based on physical information deep neural network, characterized in that: The device is used to execute the aircraft landing gear outer barrel yield strength prediction method based on physical information deep neural network according to any one of claims 1 to 7, and the device comprises an acquisition module (201), a processing module (202) and an output module (203), wherein: The acquisition module (201) is used to collect process data of the aircraft landing gear at different process stages, wherein the process data includes the transportation time, forging time, forging initial forging temperature, forging final forging temperature, forging size after final forging, and forging speed in the free forging billet and die forging forming stages; The processing module (202) is used to pre-process the process data to obtain processed data; The processing module (202) is used to perform a correlation analysis on the processed data and a contribution analysis on the yield strength of the processed data; The processing module (202) is used to select target process parameters for modeling from the processing data according to the result of the correlation analysis and the result of the contribution analysis; The output module (203) is used to input the target process parameters into the trained physical information-based deep neural network to obtain the predicted yield strength value of the aircraft landing gear outer tube.

9. An electronic device, characterized in that: The electronic device comprises a processor (301), a communication bus (302), a user interface (303), a network interface (304) and a memory (305), wherein the memory (305) is used to store instructions, the user interface (303) and the network interface (304) are both used to communicate with other devices, the communication bus (302) is used to realize connection and communication between components in the electronic device, and the processor (301) is used to execute the instructions stored in the memory (305) so that the electronic device executes the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores instructions, and when the instructions are executed, the method according to any one of claims 1 to 7 is performed.

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