Method for predicting yield strength of aircraft landing gear outer tube based on physical information deep neural network

Abstract

The application 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 method comprises the following steps: collecting process data of an aircraft landing gear at different process stages, wherein the process data comprises transfer time, forging time, initial forging temperature of a forging piece, final forging temperature of the forging piece, size of the forging piece after final forging, and forging speed at the free forging blank and die forging forming stages; preprocessing the process data to obtain processed data; performing correlation analysis on the processed data and contribution degree analysis on the processed data to the yield strength; selecting target process parameters for modeling from the processed data according to the results of the correlation analysis and the contribution degree analysis; and inputting the target process parameters into a trained deep neural network based on physical information to obtain a predicted yield strength value of the aircraft landing gear outer cylinder. The application can reduce the number of sample points required for constructing a model while ensuring the interpretability of the model.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent manufacturing, and in particular to an aircraft landing gear outer cylinder yield strength prediction method based on a physical information deep neural network. BACKGROUND

[0002] The aircraft landing gear is an important component for supporting the aircraft, and needs to bear the huge impact force from the weight of the aircraft body and the vertical direction during the take-off and landing stages of the aircraft. Therefore, the material of the aircraft landing gear must have extremely high yield strength. The aircraft landing gear outer cylinder is produced by hot forming forging, and the forming process has many times of heating and a long process flow. The yield strength of the formed part is affected by many process parameters. Traditional yield strength detection uses destructive testing to measure, which is not only expensive, but also needs to go through complex experimental design, sample preparation, sample calibration and tensile testing 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 data correlation, and cannot explain the physical laws of objective phenomena. Moreover, a sufficiently robust data-driven machine learning model must have a large amount of training data, which means a large amount of time and economic cost. Therefore, a method is needed to reduce the number of sample points required to build a model while ensuring model interpretability. SUMMARY

[0004] The present application provides an aircraft landing gear outer cylinder yield strength prediction method based on a physical information deep neural network, which can reduce the number of sample points required to build a model while ensuring model interpretability.

[0005] In a first aspect of the present application, an aircraft landing gear outer cylinder yield strength prediction method based on a physical information deep neural network is provided, the method comprising:

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

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

[0008] Performing correlation analysis on the processed data and contribution degree analysis of the processed data on yield strength;

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

[0010] input the target process parameter into the trained deep neural network based on physical information to obtain a predicted yield strength value of the outer cylinder of the aircraft landing gear.

[0011] Based on the above technical solutions, preferably, the processing data is subjected to correlation analysis, and the contribution of the processing data to the yield strength is analyzed, specifically including:

[0012] The Pearson correlation coefficient is used to analyze the correlation of different processing data;

[0013] The processing data is subjected to random forest contribution analysis to calculate the contribution of the processing data to the yield strength.

[0014] Based on the above technical solutions, preferably, before the input of the target process parameter into the trained deep neural network based on physical information to obtain a predicted yield strength value of the outer cylinder of the aircraft landing gear, the method further includes:

[0015] The value of the loss function corresponding to the deep neural network based on physical information is reduced by forward propagation and back propagation, the loss function including 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 law of yield strength and forging temperature and forging time.

[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 experimental measurement value and the yield strength prediction value, and the specific expression of the pure data-driven yield strength loss function is as follows:

[0017]

[0018] wherein, σ s is the yield strength prediction value, and σ s is the experimental measurement value.

[0019] Based on the above technical solutions, preferably, the physical information yield strength loss function constructed according to the physical law of yield strength and forging temperature and forging time further includes:

[0020] Based on the influence of forging temperature and forging speed on yield strength during the forging process of the landing gear, and the saturation effect of forging temperature and forging speed on yield strength, the physical constraints of the deep neural network based on physical information are constructed.

[0021] According to the physical constraint, an optimization objective for training the deep neural network based on physical information is determined;

[0022] For the optimization objective, the optimization objective with a penalty function is changed into an unconstrained optimization problem, and a physical information yield strength loss function is constructed, and the physical information yield strength loss function is expressed as follows:

[0023]

[0024] Wherein, is a first-order derivative of the yield strength with respect to the forging temperature, is a first-order derivative of the yield strength with respect to the forging time, is a second-order derivative of the yield strength with respect to the forging time.

[0025] On the basis of the above technical scheme, preferably, before the input of the target process parameters into the trained deep neural network based on physical information to obtain the predicted yield strength value of the aircraft landing gear outer cylinder, the method further comprises:

[0026] The average relative error is obtained by calculating the deviation degree between the experimental measurement value and the yield strength prediction value by using the mean absolute percentage error;

[0027] Based on the model measurement value, the actual measurement value and the average value of the actual measurement value, the fitting coefficient of the deep neural network based on physical information is calculated;

[0028] The average relative error and the determination coefficient are used to measure the prediction accuracy of the deep neural network based on physical information.

[0029] On the basis of the above technical scheme, preferably, the pre-processing of the process data to obtain the processed data specifically comprises:

[0030] The K-neighbor algorithm is used to fill in the missing values of the process data to obtain intermediate data, and the intermediate data is processed by the following formula:

[0031]

[0032] Wherein, L(x i ,x j ) is the Lagrange distance between the adjacent two process data, F is the feature index not containing the missing point, and x is the calculated missing value;

[0033] The intermediate data is normalized to obtain the processed data, and the processed data is processed by the following formula:

[0034]

[0035] wherein, x * is the process feature, x max is the maximum value of the process feature, x min is the minimum value of the process feature.

[0036] In a second aspect of the present application, a physical information deep neural network based aircraft landing gear outer cylinder yield strength prediction device is provided, which is used to perform the physical information deep neural network based aircraft landing gear outer cylinder yield strength prediction method according to any one of the above aspects. The device comprises an acquisition module, a processing module, and an output module, wherein:

[0037] The acquisition module is configured to collect process data of an aircraft landing gear at different process stages, wherein the process data comprises transfer time, forging time, initial forging temperature of a forging piece, final forging temperature of the forging piece, size of the forging piece after final forging, and forging speed at the free forging blanking stage and the die forging forming stage.

[0038] The processing module is configured to pre-process the process data to obtain processed data.

[0039] The processing module is configured to perform correlation analysis on the processed data and contribution degree analysis of the processed data on yield strength.

[0040] The processing module is configured to filter out 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 configured to input the target process parameters into the trained physical information deep neural network to obtain a predicted yield strength value of the aircraft landing gear outer cylinder.

[0042] In the above technical solution, preferably, the processing module is configured to perform correlation analysis on different processed data using a Pearson correlation coefficient.

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

[0044] In the above technical solution, preferably, the processing module is configured to reduce the value of a loss function corresponding to the physical information deep neural network by forward propagation and back propagation, wherein the loss function comprises a pure data driven yield strength loss function and a physical information yield strength loss function. The pure data driven yield strength loss function is defined by the square of the difference between an experimental measured value and a yield strength prediction value, and the physical information yield strength loss function is constructed according to the physical law of yield strength and forging temperature and forging time of a forging piece.

[0045] Preferably, the processing module is configured to define the pure data-driven yield strength loss function by squaring the difference between the experimental measurement value and the yield strength prediction value, and the specific expression of the pure data-driven yield strength loss function is as follows:

[0046]

[0047] wherein σ s is the yield strength prediction value, σ s is the experimental measurement value.

[0048] Preferably, based on the influence of the forging temperature and the forging speed on the yield strength and the saturation effect of the forging temperature and the forging speed on the yield strength in the landing gear forging process, the physical constraint of the deep neural network based on physical information is constructed.

[0049] The processing module is configured to determine an optimization objective for training the deep neural network based on physical information according to the physical constraint.

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

[0051]

[0052] wherein, 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] Preferably, the processing module is configured to 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 average relative error.

[0054] The processing module 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.

[0055] The processing module is configured to measure the prediction accuracy of the deep neural network based on physical information by using the average relative error and the coefficient of determination.

[0056] On the basis of the above technical solutions, preferably, the processing module is configured to fill missing values in the process data by using a K-neighbor algorithm to obtain intermediate data, and specifically by using the following formula:

[0057]

[0058] wherein, L(x i ,x j ) is the Lagrange distance between two adjacent process data, F is a feature index not containing missing points, and x is the calculated missing value.

[0059] The processing module is configured to normalize the intermediate data to obtain the processing data, and specifically by using the following formula:

[0060]

[0061] wherein, x * is the processing data, ranging from 0 to 1, x is a numerical value of a process feature, x max is a maximum value of the process feature, and x min is a minimum value of the process feature.

[0062] In a third aspect of the present application, an electronic device is provided, which includes a processor, a memory, a user interface, and a network interface, the memory is configured to store instructions, the user interface and the network interface are both configured to communicate with other devices, and the processor is configured to execute the instructions stored in the memory to enable the electronic device to perform the method according to any one of the preceding aspects.

[0063] In a fourth aspect of the present application, a computer-readable storage medium is provided, which stores instructions, and when the instructions are executed, the method according to any one of the preceding aspects is performed.

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

[0065] 1. The present application introduces physical information constraints during the training process of deep neural networks, incorporating the physical laws between forging temperature, forging time and yield strength, so that the model learns data features while following known physical mechanisms, thereby reducing the dependence on large-scale data samples and improving modeling efficiency. Compared with pure data-driven deep learning methods, the use of physical information to guide model optimization enables the model to effectively learn and generalize reasonable yield strength prediction results even with a small number of samples. In addition, through correlation analysis and contribution analysis, key process parameters are selected to avoid redundant information interference with model training, improve data utilization, and further reduce the required data sample size while ensuring the physical interpretability and engineering applicability of the prediction results.

[0066] 2. By analyzing the linear correlation between different process parameters through Pearson correlation coefficient, redundant or highly correlated features are identified, thereby reducing the dimensionality of input data, improving model calculation efficiency and stability. At the same time, random forest contribution analysis is used to evaluate the influence of each process parameter on yield strength, ensuring that the selected input features have a significant contribution to model prediction, and improving the physical interpretability of the model. Combined with these two analysis methods, unnecessary computational overhead can be reduced while ensuring model prediction accuracy, improving data utilization, and enhancing the model's ability to generalize to different conditions, making yield strength prediction more accurate and reliable.

[0067] 3. Combined with the pure data-driven yield strength loss function and the physical information yield strength loss function constructed based on physical laws, the loss value is calculated through forward propagation during neural network training, and the weights are adjusted through back 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 introduces the physical constraints of forging temperature, forging time and yield strength to ensure that the model prediction results conform to the physical laws of the material forming process. This method not only improves the accuracy of yield strength prediction, but also reduces the required sample size, enhances the model's generalization ability and physical interpretability, and provides reasonable prediction results under different process conditions.

[0068] 4. Calculate the mean absolute percentage error to measure the degree of deviation between experimental measurements and yield strength prediction values, to quantitatively evaluate the error level of the model and ensure the reliability of the prediction results. At the same time, the determination coefficient is calculated to evaluate the goodness of fit of the model, to measure the explanatory power of the predicted values to the actual measurements, and to ensure the effective learning of the model on the data trend. Combined with these two indicators, the prediction accuracy of the deep neural network based on physical information can be comprehensively measured, ensuring the stability and generalization ability of the model under different process conditions, improving the accuracy of yield strength prediction, and enhancing the feasibility and credibility of the model in engineering applications. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 is a flow diagram of a method for predicting the yield strength of an aircraft landing gear outer tube based on a physical information deep neural network according to an embodiment of the present application.

[0070] Figure 2 is a module diagram of a device for predicting the yield strength of an aircraft landing gear outer tube based on a physical information deep neural network according to an embodiment of the present application.

[0071] Figure 3 is a structural diagram of an electronic device according to an embodiment of the present application.

[0072] Legend: 201, acquisition module; 202, processing module; 203, output module; 301, processor; 302, communication bus; 303, user interface; 304, network interface; 305, memory. DETAILED DESCRIPTION

[0073] In order for those skilled in the art to better understand the technical solutions in the specification, the technical solutions in the specification will be clearly and completely described below in conjunction with the drawings in the embodiments of the specification. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments.

[0074] In the description of the embodiments of the present application, the words such as "for example" or "for instance" are used to mean an example, illustration or description. Any embodiment or design solution described as "for example" or "for instance" in the embodiments of the present application should not be interpreted as more preferred or more advantageous than other embodiments or design solutions. Rather, the words such as "for example" or "for instance" are intended to present the relevant concept in a specific manner.

[0075] In the description of the embodiments of the present application, the term "a plurality of" means two or more. For example, a plurality of systems means two or more systems, and a plurality of screen terminals means two or more screen terminals. In addition, the terms "first" and "second" are used for description purposes only, and should not be interpreted or implied to indicate or imply relative importance or implicitly indicate the indicated technical features. Therefore, the features defined with "first" and "second" can explicitly or implicitly include one or more of the features. The terms "include", "contain", "have" and their variants mean "include but are not limited to", unless otherwise specifically emphasized.

[0076] Machine learning model needs a large amount of data samples when training, which leads to the problem of large modeling fund and time cost. For pure data-driven machine learning model, it is necessary to extract the data features hidden behind the samples and establish the mapping relationship between the input and the output, which requires a large amount of data. Collecting and analyzing data samples will consume a lot of time and computing cost. In addition, the trained model, that is, a black box model of input and output, lacks physical interpretability. In view of the above problems, the modeling process is guided by introducing physical constraint relationship, which can reduce the amount of data required for modeling to a certain extent, and make the model contain certain physical meaning.

[0077] The embodiment discloses an aircraft landing gear outer cylinder yield strength prediction method based on a physical information deep neural network, referring to Figure 1 , comprising the following steps S110-S150:

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

[0079] The aircraft landing gear outer cylinder yield strength prediction method based on the physical information deep neural network disclosed in the embodiment is applied to a server. The server includes but is not limited to electronic devices such as mobile phones, tablet computers, wearable devices, PC (Personal Computer), and the like. The server can also be a background server running the aircraft landing gear outer cylinder yield strength prediction method based on the physical information deep neural network. The server can be realized by an independent server or a server cluster composed of multiple servers.

[0080] In the process of collecting the process data of the aircraft landing gear at different process stages, the key process parameters of the free forging blank and the die forging forming stage need to be covered to ensure the integrity and accuracy of the data. Specifically, first of all, high-precision sensor equipment, including an infrared thermal imager, a speed sensor and a binocular camera, is needed to collect the parameters involved in the free forging and die forging process in real time. The determination of the transfer time needs to be combined with the length of the transmission path and the transfer speed to ensure the accuracy of the data; the forging time needs to be combined with the stroke number of the press and the single stamping time to measure, and high-frequency data recording technology is used to capture transient changes; the initial forging temperature and the final forging temperature of the forging are continuously monitored by using infrared temperature measurement equipment or thermocouples, and the data are corrected by combining temperature field simulation; the size of the forged part after final forging needs to be measured by using a laser measurement system or a high-precision three-coordinate measuring machine to ensure the reliability of the final size data; the determination of the forging speed needs to be combined with the speed control parameters of the press and the actual measured data for double verification to ensure that it reflects the actual forging working condition. All the collected data need to be preprocessed, including data cleaning, outlier detection and normalization processing, 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 physical information deep neural network.

[0081] In S120, the process data is preprocessed to obtain processed data.

[0082] When the process data is preprocessed to obtain processed data, first of all, missing value filling needs to be performed. During the data collection process, due to the limitation of sensor accuracy, data transmission interference or changes in the measurement environment, some process data may have missing values. To solve this problem, K- nearest neighbor algorithm is used to fill the missing values. Specifically, first of all, the Lagrange distance between the current sample and other samples is calculated, and the distance is based on the formula:

[0083]

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

[0085]

[0086] The missing values are filled by the average value, so that the filled data is as close to the actual distribution as possible, reducing the influence of abnormal data on subsequent analysis. Next, the filled intermediate data is normalized to eliminate the dimensional differences between different process data and enhance the comparability of the data. The specific method is to use the minimum-maximum normalization formula:

[0087]

[0088] wherein x * is the processing data, ranging from [0, 1], x is the numerical 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.

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

[0090] S130, correlation analysis is performed on the processing data, and contribution analysis of the processing data to the yield strength is performed.

[0091] In the correlation analysis and contribution analysis of the processing data, first, the Pearson correlation coefficient is used to calculate the correlation between different processing data to determine which process data has strong linear correlation. Specifically, first, extract each process data variable from the normalized processing data set, calculate the mean and variance, and calculate the correlation between each variable, which is calculated by the following formula:

[0092]

[0093] wherein r is the correlation of different processing data, X i and X j are different processing data, var(X i )·var(X j ) is the variance between different processing data, and cov(X i , X j ) is the covariance between different processing data. The calculated r value ranges between [-1, 1], when r value is close to 1, it indicates that the two variables are highly positively correlated, close to -1, it indicates that they are highly negatively correlated, close to 0, it indicates that there is no obvious correlation. After analyzing the correlation results, the highly correlated process data is filtered to reduce data redundancy and improve the calculation efficiency of the model.

[0094] After the correlation analysis is completed, the contribution of the process data to the yield strength needs to be further calculated and processed to screen out key process data that have greater impact on the yield strength. A random forest model is used for contribution analysis, and the contribution of each process data is evaluated by calculating the mean decrease accuracy (MDA). 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 value of a certain process data is randomly disturbed, and the prediction error of the OOB samples is calculated again. The prediction error is calculated by the following formula:

[0095]

[0096] wherein 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 process 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 jth dimension exchange, R k (X i ) is the yield strength prediction output of the sample X i , Y i k is the kth dimension output considering the multi-target regression.

[0097] If a certain process data has greater impact on the yield strength, the MDA value after replacement increases, otherwise the impact is smaller. Finally, according to the size of the MDA value, the process data with higher contribution is screened out, 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 results of the contribution analysis, the target process parameters for modeling are screened out from the process data.

[0099] In the process of screening the target process parameters for modeling from the processing data, firstly, the results of correlation analysis and contribution analysis are comprehensively utilized to ensure that the input parameters can avoid redundant information and effectively represent the factors that have the most significant influence on the yield strength. Specifically, firstly, the correlation matrix obtained by using Pearson correlation coefficient analysis is used to calculate the correlation r value between all process data, and a certain correlation threshold (for example, |r|>0.8) is used as a standard to screen out parameters with too high correlation to avoid data redundancy and multicollinearity problems. For the parameters with too high correlation, the parameter with higher contribution to the yield strength is selected to remain, and the parameter with lower contribution is removed to improve the stability of the model.

[0100] Next, according to the results of random forest contribution analysis, the process data that has the most significant influence on the yield strength is screened out. Firstly, the MDA values of all parameters are sorted, and a contribution threshold (such as the top 10 parameters with the highest contribution, or parameters with a contribution of more than 80% of the total contribution) is set to retain process data with high contribution and remove parameters with low contribution. In specific implementation, the MDA values are first normalized so that the sum of the contribution of each parameter is normalized to 1, then the cumulative contribution is calculated, and the parameters with cumulative contribution reaching the set standard are selected.

[0101] In the final screening stage, the results of correlation analysis and contribution analysis are comprehensively utilized. If the contribution of a certain process data is high but highly correlated with other parameters, it can be processed by dimensionality reduction or feature engineering means, such as using principal component analysis (PCA) for dimensionality reduction, 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 removed to reduce the complexity of the model and improve the calculation efficiency.

[0102] The final target process parameters for modeling should have the following characteristics: first, the correlation between them is low to reduce the interference of multicollinearity on model training; second, the contribution to the yield strength is high to ensure that the input features can reflect the influence of the process on the yield strength in the landing gear forming process to the greatest extent. After screening, these target process parameters will be used as input features of the deep neural network model to further predict the yield strength of the aircraft landing gear outer cylinder to improve the accuracy and physical interpretability of the model.

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

[0104] In a possible implementation, before inputting the target process parameter into the trained deep neural network based on physical information to obtain the predicted yield strength value of the aircraft landing gear outer cylinder, the method further comprises: reducing the value of the loss function corresponding to the deep neural network based on physical information through forward propagation and back propagation, the loss function comprising 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 law of yield strength and forging temperature and time of a forging piece.

[0105] Specifically, in the process of training the deep neural network based on physical information to predict the yield strength of the aircraft landing gear outer cylinder, it is necessary to first construct a loss function to guide model optimization, and the loss function is composed of a pure data-driven yield strength loss function and a physical information yield strength loss function. The pure 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] wherein σ s is the yield strength prediction value, σ s is the experimental measurement value.

[0108] Minimization of the loss function can make the model more accurately fit the experimental data.

[0109] The physical information yield strength loss function is constructed based on the physical relationship between yield strength and forging temperature and time, and the first and second order derivatives of yield strength with respect to forging temperature and time are used to constrain the model output, so as to balance the influence of physical loss on overall optimization. In the training process, the loss value is calculated by forward propagation, and the weight is adjusted by calculating the gradient of the loss function with respect to the network parameters using the back propagation algorithm, 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 standard or the number of training iterations reaches the set value, the network model is trained and can input the target process parameter 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 the physical interpretability and generalization ability of the model are enhanced.

[0110] Further, in constructing the physical information yield strength loss function of the deep neural network based on physical information, firstly, the influence of forging temperature and forging speed on yield strength in the forging process of aircraft landing gear and the saturation effect thereof need to be analyzed. With the increase of forging temperature, the yield strength of metal material generally decreases, while the increase of forging time can increase the yield strength at the initial stage, but when exceeding a certain threshold, the yield strength decreases due to the dynamic recrystallization and grain growth effect of microstructure. Therefore, based on these physical laws, the physical constraint condition is constructed, that is, to ensure that the temperature gradient and time gradient of yield strength conform to the physical laws, and to conduct second-order derivative constraint on the time variation rate of yield strength to avoid non-physical prediction results. The influence of forging temperature and forging speed on yield strength and the saturation effect thereof in the forging process of landing gear can be expressed by the following formula:

[0111]

[0112] wherein, 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.

[0113] In determining the optimization objective for training the deep neural network, the above physical constraint condition needs to be formalized and combined with the training process of neural network for optimization. The optimization objective is set as follows: the predicted value of the network not only matches the experimental data, but also meets the physical constraint, that is, the derivatives of yield strength with respect to forging temperature and forging time meet reasonable physical laws, especially to ensure that the first-order derivative of yield strength with respect to temperature is a non-positive value to reflect its downward trend, and to ensure that the derivative of yield strength with respect to time presents a trend of first positive and then negative to reflect the saturation effect of forging time. The optimization objective can be expressed as:

[0114]

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

[0116]

[0117] In the formula, η is a relaxation factor, and f(·) is a penalty function. The specific method 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 meet the physical constraint in the optimization process. The physical information yield strength loss function is expressed as follows:

[0118]

[0119] wherein, the first order derivative of yield strength with respect to forging temperature, the first order derivative of yield strength with respect to forging time, the second order derivative of yield strength with respect to forging time. The first term ensures that the yield strength does not abnormally increase with the increase of forging temperature, the second term ensures that the yield strength increases within a reasonable forging time range, and the third term ensures that the change rate of yield strength with respect to time conforms to the physical law, i.e. to prevent the predicted value from abnormal oscillation or unreasonable trend.

[0120] Finally, in the neural network training process, the loss function of the model is 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 result not only minimizes the error of experimental data, but also meets the physical constraints of forging temperature and time on yield strength, thereby improving the physical interpretability, generalization ability and robustness of the prediction model.

[0121] Further, in the evaluation of the aircraft landing gear outer cylinder yield strength prediction model based on the physical information deep neural network, the mean absolute percentage error (MAPE) and the determination coefficient (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, the MAPE is calculated to measure the average relative error of the model, which can reflect the deviation between the experimental measured value and the yield strength predicted value. Its calculation formula is:

[0122]

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

[0124] In the calculation, the errors of all test set samples are summed and averaged, and then converted to percentage. The smaller the MAPE value, the smaller the prediction error and the higher the model accuracy.

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

[0126]

[0127] where y i is the actual measured value, is the model predicted value, is the average of all actual measured values. The numerator part calculates the sum of squared errors between the model predicted values and the actual measured values, and the denominator part calculates the sum of squared errors of the actual measured values relative to their mean. When R 2 approaches 1, it indicates that the model has a high degree of fitting to the data and the prediction result is more accurate; when R 2 is lower, it indicates that the prediction effect of the model is poor, and the neural network structure may need to be optimized or the feature selection strategy may need to be adjusted.

[0128] Finally, in order to analyze the explainability of the model, SHAP (Shapley Additive Explanations) values are used to quantify the influence of each input feature on the prediction result. The SHAP method is based on cooperative game theory, which evaluates the importance of each process data by calculating its marginal contribution to the yield strength prediction value under different combinations. In specific implementation, first, the SHAP explanation framework is applied to the trained neural network model to calculate the SHAP value of each input process data, and SHAP importance ranking chart and dependence chart are generated to intuitively display the influence direction and degree of each process data on the yield strength. The positive and negative of the SHAP value represents the promotion or reduction of the feature to the prediction value, and the absolute value size represents the strength of the influence. By analyzing the SHAP value, it can be identified which process data contributes most to the yield strength, so as to optimize the forging process and improve the quality control level of the production process. Finally, the prediction performance of the model is evaluated by MAPE and R 2 , and the explainability of the model is improved by combining SHAP analysis, making the application of deep neural networks based on physical information in landing gear yield strength prediction more reliable and more engineering usable.

[0129] After 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, transmits the target process parameters to the hidden layer, calculates the high-dimensional feature mapping in the hidden layer through multiple neurons and nonlinear activation functions (such as ReLU or Leaky ReLU), and transmits information layer by layer to learn the complex relationship between process parameters and yield strength.

[0130] In the forward propagation process, the model will calculate the target process parameters based on the learned weight parameters and output the predicted yield strength value. Since the deep neural network has integrated physical information constraints, when calculating the prediction value, it will implicitly satisfy the physical law constraints of yield strength on forging temperature and forging time, ensuring the physical consistency of the output. Finally, in the output layer of the network, the predicted yield strength value is calculated through a linear regression layer or a regression activation function, and the prediction result

[0131] The embodiment also discloses an aircraft landing gear outer cylinder yield strength prediction device based on a physical information deep neural network, which is used for executing the aircraft landing gear outer cylinder yield strength prediction method based on the physical information deep neural network. Figure 2 The device comprises an acquisition module 201, a processing module 202, and an output module 203.

[0132] The acquisition module 201 is used for collecting process data of the aircraft landing gear at different process stages, wherein the process data comprises transfer time, forging time, initial forging temperature of a forging piece, final forging temperature of the forging piece, size after the final forging of the forging piece, and forging speed at the free forging blank and die forging forming stages.

[0133] The processing module 202 is used for preprocessing the process data to obtain processing data.

[0134] The processing module 202 is used for performing correlation analysis on the processing data and performing contribution degree analysis on the processing data to the yield strength.

[0135] The processing module 202 is used for screening target process parameters for modeling from the processing data according to a result of the correlation analysis and a result of the contribution degree analysis.

[0136] The output module 203 is used for 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 aircraft landing gear outer cylinder.

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

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

[0139] In a possible implementation, the processing module 202 is used for reducing a value of a loss function corresponding to the deep neural network based on the physical information by forward propagation and backward propagation, wherein the loss function comprises a pure data-driven yield strength loss function and a physical information yield strength loss function, the pure data-driven yield strength loss function is defined by a square of a difference between an experimental measurement value and a yield strength prediction value, and the physical information yield strength loss function is constructed according to a physical law of the yield strength and forging temperature and forging time of a forging piece.

[0140] In a possible implementation, the processing module 202 is used for defining the pure data-driven yield strength loss function by a square of a difference between an experimental measurement value and a yield strength prediction value, and a specific expression of the pure data-driven yield strength loss function is as follows:

[0141]

[0142] wherein σ s is the yield strength prediction value, σ s is the experimental measured value.

[0143] In a possible implementation, a physical constraint of the deep neural network based on physical information is constructed based on the influence of the forging temperature and the forging speed on the yield strength in the landing gear forging process and the saturation effect of the forging temperature and the forging speed on the yield strength.

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

[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, which is expressed as follows:

[0146]

[0147] wherein, is a first-order derivative of the yield strength with respect to the forging temperature, is a first-order derivative of the yield strength with respect to the forging time, is a second-order derivative of the yield strength with respect to the forging time.

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

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

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

[0151] In a possible implementation, the processing module 202 is configured to perform missing value filling on the process data by using a K-neighbor algorithm to obtain intermediate data, and specifically processes by using the following formula:

[0152]

[0153] wherein, L(x i ,x j ) is a Lagrange distance between two adjacent process data, F is a feature index not containing a missing point, and x is a calculated missing value.

[0154] The processing module 202 is configured to normalize the intermediate data to obtain processing data, and the normalization is performed according to the following formula:

[0155]

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

[0157] It should be noted that the device provided in the above embodiments is only used as an example to divide the above functional modules to achieve the functions thereof, and in actual applications, the above functions can be completed by different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules to complete all or part of the above-described functions. In addition, the device and method embodiments provided in the above embodiments belong to the same concept, and the specific implementation process is described in the method embodiments, which will not be described here.

[0158] The embodiment further discloses an electronic device, which refers to Figure 3 The electronic device can 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] The communication bus 302 is configured to realize the connection and communication between the components.

[0160] The user interface 303 can include a display screen (Display) and a camera (Camera), and the optional user interface 303 can further include a standard wired interface and a wireless interface.

[0161] The network interface 304 can optionally include a standard wired interface and a wireless interface (such as a WI-FI interface).

[0162] The processor 301 can include one or more processing cores. The processor 301 connects various parts within the server through various interfaces and lines, performs 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 calling data stored in the memory 305. Alternatively, the processor 301 can be implemented in at least one of a hardware form of a digital signal processing (DSP), a field-programmable gate array (FPGA), and a programmable logic array (PLA). The processor 301 can integrate a combination of one or several of a central processing unit (CPU), a graphics processing unit (GPU), and a modem. Among them, the CPU mainly processes operating systems, user interfaces, and application programs; the GPU is responsible for rendering and drawing the content to be displayed on the display screen; and the modem is used for processing wireless communication. It can be understood that the above-mentioned modem can also not be integrated into the processor 301, but can be realized by a separate chip.

[0163] The memory 305 can include a random access memory (RAM) and a read-only memory (ROM). Optionally, the memory includes a non-transitory computer-readable storage medium. The memory 305 can be used to store instructions, programs, codes, code sets or instruction sets. The memory 305 can include a program storage area and a data storage area, wherein the program storage area can store instructions for implementing an operating system, instructions for at least one function (such as a touch function, a sound playing function, an image playing function, etc.), instructions for implementing the above-mentioned various method embodiments, etc.; the data storage area can store data involved in the above-mentioned various method embodiments, etc. The memory 305 can also be at least one storage device located away from the aforementioned processor 301. As a computer storage medium, the memory 305 can include an operating system, a network communication module, a user interface 303 module, and an application program of the aircraft landing gear outer cylinder yield strength prediction method 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 user input, and obtain data input by the user; and the processor 301 can be used to invoke an application program of the aircraft landing gear outer cylinder yield strength prediction method based on a physical information deep neural network stored in the memory 305, and when executed by one or more processors 301, cause the electronic device to perform the method of one or more of the above-described embodiments.

[0165] It should be noted that, for the foregoing method embodiments, in order to simply describe, they are all described as a series of action combinations, but those skilled in the art should know that the present application is not limited to the order of the actions described, because according to the present application, certain steps can be performed in other order or at the same time. Secondly, those skilled in the art should know that the embodiments described in the specification all belong to preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0166] In the above embodiments, the description of each embodiment has its own focus, and the parts not described in detail in a certain embodiment can be referred to the related description of other embodiments.

[0167] In several embodiments provided by the present application, it should be understood that the disclosed device can be implemented in other ways. For example, the device embodiments described above are only schematic. The division of units is only a logical function division. There can be another division manner in actual implementation, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some services interfaces, devices or units, and can be electrical or other forms.

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

[0169] In addition, each functional unit in each embodiment of the present application can be integrated into a processing unit, or each unit can exist physically, or two or more units can be integrated into one unit. The integrated unit can be realized in the form of hardware, or in the form of a software functional unit.

[0170] The integrated unit, if implemented in the form of a software function unit and sold or used as an independent product, can be stored in a computer readable memory. Based on such understanding, the technical solutions of the present application essentially or say the part that contributes to the prior art or the whole or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a memory 305 and includes a plurality of 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 embodiments of the present application. The aforementioned memory 305 includes: a U disk, a mobile hard disk, a magnetic or optical disk and various program code storage media.

[0171] The present application also discloses a computer readable storage medium, which stores instructions. When executed by one or more processors 301, the instructions cause an electronic device to perform the method of one or more of the above embodiments.

[0172] The above is only exemplary embodiments of the present disclosure, which cannot limit the scope of the present disclosure. That is, any equivalent changes and modifications made in accordance with the teachings of the present disclosure are still within the scope of the present disclosure. Other embodiments of the present disclosure will be readily apparent to those skilled in the art upon considering the specification and practicing the disclosure. The present application is intended to cover any variations, uses or adaptive changes of the present disclosure that follow the general principles of the present disclosure and include common knowledge or conventional techniques in the art that are not described in the present disclosure. The specification and examples are only considered 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 an aircraft landing gear at different process stages, the process data comprising transfer time, forging time, initial forging temperature of a forging piece, final forging temperature of the forging piece, size of the forging piece after final forging, and forging speed of free forging blanking and die forging forming stages; Preprocessing the process data to obtain processed data; Performing correlation analysis on the processed data and contribution degree analysis of the processed data on yield strength; According to the results of the correlation analysis and the results of the contribution degree analysis, filtering out target process parameters for modeling from the processed data; Inputting the target process parameters into a trained deep neural network based on physical information to obtain a predicted yield strength value of an outer cylinder of the aircraft landing gear; Before the inputting the target process parameters into the trained deep neural network based on physical information to obtain the predicted yield strength value of the outer cylinder of the aircraft landing gear, the method further comprises: Reducing the value of a loss function corresponding to the deep neural network based on physical information through forward propagation and back propagation, the loss function comprising 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 an experimental measurement value and a yield strength prediction value, and the physical information yield strength loss function is constructed according to the physical law of yield strength and forging temperature and forging time of a forging piece.

2. The method of claim 1, wherein the method is based on a physical information deep neural network for predicting the yield strength of the aircraft landing gear outer tube. The correlation analysis on the processed data and the contribution degree analysis of the processed data on yield strength specifically comprises: Performing correlation analysis on different processed data by using Pearson correlation coefficients; Performing random forest contribution degree analysis on the processed data to calculate the contribution degree of the processed data to yield strength.

3. The method of claim 1, wherein the method is based on a physical information deep neural network for predicting the yield strength of the aircraft landing gear outer tube. The pure data-driven yield strength loss function is specifically defined by the square of the difference between an experimental measurement value and a yield strength prediction value, and the specific expression of the pure data-driven yield strength loss function is as follows: where σ s is the yield strength prediction value, σ s is the experimental measured value, and n is the number of samples.

4. The method of claim 1, wherein the method is based on a physical information deep neural network for predicting the yield strength of the aircraft landing gear outer tube. The physical information yield strength loss function constructed according to the physical law of yield strength and forging temperature and forging time of a forging piece further comprises: Based on the influence of forging temperature and forging speed on yield strength and the saturation effect of forging temperature and forging speed on yield strength in the forging process of the landing gear, constructing a physical constraint of the deep neural network based on physical information; According to the physical constraint, determining an optimization objective for training the deep neural network based on physical information; For the optimization objective, the optimization objective with a penalty function is changed into an unconstrained optimization problem, and the physical information yield strength loss function is constructed, which is represented as follows: wherein, 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, n is the number of samples.

5. The method of claim 1, wherein, Before the inputting the target process parameters into the trained deep neural network based on physical information to obtain the predicted yield strength value of the outer cylinder of the aircraft landing gear, the method further comprises: Calculating the deviation degree between the experimental measurement value and the yield strength prediction value by using mean absolute percentage error to obtain the average relative error; The fitting coefficients of the physical information based deep neural network are calculated based on the model measurement values, the actual measurement values and the average values of the actual measurement values; The average relative error and the determination coefficient are used to measure the prediction accuracy of the physical information based deep neural network.

6. The method of claim 1, wherein, The preprocessing of the process data to obtain the processed data specifically includes: The K-neighbor algorithm is used to fill in the missing values of the process data to obtain intermediate data; The intermediate data is normalized to obtain the processed data.

7. An aircraft landing gear outer tube yield strength prediction device based on physical information deep neural network, characterized by, The device is used to execute the aircraft landing gear outer cylinder yield strength prediction method based on the physical information deep neural network, and the device includes 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, and the process data includes transfer time, forging time, initial forging temperature, final forging temperature, final forging size and forging speed of the free forging blank and die forging forming stage; The processing module (202) is used to preprocess the process data to obtain processed data; The processing module (202) is used to analyze the correlation of the processed data and analyze the contribution degree of the processed data to the yield strength; The processing module (202) is used to filter 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; 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 aircraft landing gear outer cylinder yield strength value.

8. An electronic device, comprising: The electronic device includes a processor (301), a communication bus (302), a user interface (303), a network interface (304) and a memory (305), the memory (305) is used to store instructions, the user interface (303) and the network interface (304) are used to communicate with other devices, the communication bus (302) is used to realize the connection and communication between the components in the electronic device, and the processor (301) is used to execute the instructions stored in the memory (305) to make the electronic device execute the method.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium stores instructions, when the instructions are executed, the method of any one of claims 1-6 is executed.

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