Rubber material fatigue life prediction method based on physical-data fusion driving

Abstract

The invention relates to the field of material fatigue life prediction, and particularly discloses a rubber material fatigue life prediction method based on physical-data fusion driving, and the method comprises the following steps: S1, obtaining rubber fatigue life data through a test; s2, constructing a fatigue life prediction physical model based on continuous medium mechanics; s3, preprocessing the predicted life and test data of the physical model; s4, determining the number of nodes of an input layer, a hidden layer and an output layer in the BP neural network model according to the preprocessed data; s5, determining a connection weight and a threshold value of the BP neural network model by adopting a gradient descent method by taking the minimum mean square error between the actually measured life and the predicted life as a target; and S6, in combination with the connection weight and the threshold, establishing a rubber material fatigue life prediction model based on physical-data fusion driving. According to the physical-data fusion driving method in the scheme, the rubber fatigue life prediction precision can be improved, and the failure risk of rubber products in practical application is reduced.

Description

Technical Field

[0001] The invention relates to the technical field of material fatigue life prediction, and specifically provides a rubber material fatigue life prediction method based on physics-data fusion drive. Background Art

[0002] Natural rubber has been widely used in key equipment fields such as automobiles, aerospace, and rail transit due to its unique viscoelasticity, excellent wear resistance, and good corrosion resistance. However, during the service of these equipment, rubber is inevitably subjected to the cyclic action of alternating loads, which makes it very prone to fatigue failure. As a vibration reduction and sealing material, the fatigue life of rubber is crucial and directly related to the safety and reliability of the equipment. Once the rubber fails due to fatigue, it will not only seriously affect its vibration reduction and sealing performance, resulting in a significant decrease in the operating stability and safety of the equipment, but also significantly shorten the service life of the equipment, and may even cause the equipment to fail prematurely, causing huge economic losses and potential safety risks. Therefore, conducting research on rubber fatigue life assessment methods and accurately assessing the fatigue life of rubber are of great significance to ensure the safety and reliability of equipment.

[0003] At present, the rubber fatigue life assessment methods are mainly divided into bench test method and model prediction method. The bench test method can provide relatively reliable fatigue life assessment results, but in practical applications, the bench test method faces the problems of long test cycle and high economic cost, which largely limits the widespread application of the bench test method. Compared with the bench test method, the model prediction method can achieve accurate assessment of rubber fatigue life by establishing a rubber fatigue life prediction model, and has the advantages of high efficiency and economy. Therefore, the model prediction method has become the key research direction of the current rubber fatigue life assessment method.

[0004] Existing rubber fatigue life prediction modeling methods mainly cover two categories: physical models and data-driven models. Physical models are usually based on the mechanical properties and damage evolution laws of rubber, such as the crack initiation method based on continuum mechanics and the crack propagation method based on fracture mechanics. Among them, the crack initiation method establishes a prediction model by constructing a power function relationship between fatigue damage parameters and fatigue life, and the crack propagation law constructs a prediction model by establishing a power function relationship between crack propagation rate and crack growth rate. It can be seen that physical modeling methods all require the establishment of a clear mathematical model.

[0005] In fact, the fatigue life of rubber depends on many factors, such as mechanical load, ambient temperature, material hardness, etc. It is difficult to establish an effective mathematical model to comprehensively consider the impact of multiple factors on the fatigue life of rubber. Data-driven models, such as BP neural networks and support vector machines, have unique advantages in processing multi-dimensional, nonlinear relationships and data-driven modeling. They can effectively extract the potential relationship between material properties and complex working condition data, thereby realizing fatigue life prediction.

[0006] Compared with physical models, data-driven models do not require the establishment of complex mathematical models. However, the accuracy of data-driven models, especially neural network models, depends largely on the number and quality of training samples. Under small sample conditions, the prediction accuracy is often low and it is difficult to meet the requirements of high-precision prediction. Although the support vector machine model shows good results in processing small sample data sets, its accuracy is significantly affected by parameters such as kernel function and penalty factor. Therefore, in view of the respective limitations of physical models and data-driven models, it is urgent to develop a new model that can accurately predict rubber fatigue life.

[0007] As a hybrid modeling technology, the physical-data fusion driven model significantly improves the accuracy and reliability of model prediction by combining the theoretical advantages of the physical model with the efficiency of the data-driven model. Currently, the physical-data fusion driven model has been successfully applied to the fatigue life prediction of metal materials. Unlike metal materials, rubber is a polymer material with large deformation, nonlinearity, and fatigue characteristics that are closely related to temperature. There is no research on the use of physical information neural network models to predict rubber fatigue life. Summary of the invention

[0008] In order to solve the above problems, the present invention provides a method for predicting the fatigue life of rubber materials based on physics-data fusion drive.

[0009] The present invention provides a method for predicting fatigue life of rubber materials based on physics-data fusion drive, comprising the following steps: S1. Obtaining fatigue life data of rubber through experiments. The fatigue life data to be obtained include the corresponding fatigue life times under different ambient temperatures, different material hardnesses and different strain amplitudes; S2. Construct a fatigue life prediction physical model based on continuum mechanics. The fatigue life prediction physical model includes the power function equation: N = Aε d ,in, N is the fatigue life times, ε is the strain amplitude, A and d is the material parameter; S3, preprocessing the predicted life and test data of the fatigue life prediction physical model; S4. Determine the number of nodes in the input layer, hidden layer, and output layer of the BP neural network model based on the preprocessed data; S5. Taking the minimum mean square error between the measured life and the predicted life as the goal, the connection weights and thresholds of the BP neural network model are determined by using the gradient descent method; S6. Combine the connection weights and thresholds to establish a rubber material fatigue life prediction model driven by physics-data fusion.

[0010] Furthermore, in S2, the least squares method is used to fit the power function relationship between the measured fatigue life and the strain amplitude to establish a fatigue life prediction physical model based on continuum mechanics.

[0011] Furthermore, when preprocessing the predicted life and test data of the fatigue life prediction physical model in S3, maximum-minimum value normalization processing is performed and the test set and training set are divided.

[0012] Furthermore, the input sample 1 of the BP neural network model in S4 is X =[ x 1, x 2,…, x m ],in, x i ( i =1, 2,…, m ) is the i The physical model corresponding to each working condition predicts the life, ambient temperature, material hardness and strain amplitude; the output sample 2 of the BP neural network model is Y =[ y 1, y 2,…, y n ],in, y j ( j =1, 2,…, n ) is the j The measured fatigue life corresponding to each working condition.

[0013] Furthermore, the number of nodes in the hidden layer is obtained by formula 1: l =2 P +1; among them, l is the number of hidden layer nodes, P is the number of nodes in the input layer.

[0014] Furthermore, step S5 specifically includes the following sub-steps: S51, determining a nonlinear mapping relationship between input variables and output variables of the BP neural network model; S52: Determine the connection weight and threshold of the BP neural network model.

[0015] Further, in step S51, according to the mapping relationship of the artificial neural network, the nonlinear mapping relationship between the input and output of the BP neural network model is expressed by Formula 2 and Formula 3; Formula 2 is: ; Formula 3 is ;in, H represents the output of the hidden layer; and Respectively represent the connection weights from the input layer to the hidden layer, and from the hidden layer to the output layer; k represents the hidden layer k nodes; a k and b j Respectively represent the thresholds from the input layer to the hidden layer and from the hidden layer to the output layer; f 1( x )and f 2( x ) are the activation functions of the hidden layer and the output layer respectively.

[0016] Further, f 1( x ) is expressed as Formula 4, which is: ; f 2( x ) is expressed as Formula 5, which is: ;in, represents the natural exponential function, express The reciprocal of Represents the input variable.

[0017] Furthermore, the BP neural network model in S52 uses the mean square error function as the learning objective function of the model, and adopts the gradient descent method to obtain the connection weights and thresholds of the model; the mathematical expression of the mean square error function is Formula 6, which is: ;in, M_S_E is the mean square error; Q is the number of training samples of the BP neural network model; For the g The actual output life of the BP neural network model corresponding to the training samples; For the g The actual life of rubber corresponding to the training samples.

[0018] Furthermore, Formula 7 and Formula 8 are used to normalize the predicted life of the physical model and the test data. Formula 7 is: ; Formula 8 is: ;in, and They are the normalized input samples and output samples respectively; x max and x min are the maximum and minimum values ​​of the input samples respectively; y max and y min are the maximum and minimum values ​​of the output samples respectively; x i For the i The physical model corresponding to each operating condition predicts the life, ambient temperature, material hardness and strain amplitude; y j For the j The measured fatigue life corresponding to each working condition.

[0019] Compared with the prior art, the present invention can achieve the following beneficial effects: the fatigue life prediction method proposed in the present invention can comprehensively consider the influence of strain amplitude, ambient temperature and material hardness on rubber fatigue life, and effectively integrates the advantages of both physical models and data-driven models. It can not only avoid the problem of difficulty in model construction and limited accuracy caused by the complex characteristics of rubber materials when relying solely on physical models, but also overcome the defect of insufficient prediction accuracy of traditional data-driven models in the case of small sample data, realize the synergy and complementarity between the two, and significantly improve the accuracy and reliability of rubber fatigue life prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a flow chart of a rubber fatigue life prediction method based on physics-data fusion drive provided in an embodiment of the present invention; Figure 2 It is a fitting effect diagram of the rubber fatigue life prediction physical model provided according to an embodiment of the present invention; wherein, Figure (a) is a fitting effect diagram of the rubber material fatigue life prediction model established when the material hardness is N45 and the ambient temperature is 23°C; Figure (b) is a fitting effect diagram of the rubber material fatigue life prediction model established when the material hardness is N50 and the ambient temperature is 23°C; Figure (c) is a fitting effect diagram of the rubber material fatigue life prediction model established when the material hardness is N50 and the ambient temperature is 60°C; Figure (d) is a fitting effect diagram of the rubber material fatigue life prediction model established when the material hardness is N45 and the ambient temperature is 90°C; Figure (e) is a fitting effect diagram of the rubber material fatigue life prediction model established when the material hardness is N50 and the ambient temperature is 90°C; Figure 3 1 is a schematic diagram of prediction results of a training set provided in an embodiment of the present invention; wherein line 1 represents the predicted lifespan, and line 2 represents the measured lifespan; Figure 4 1 is a schematic diagram of the prediction results of the test set provided according to an embodiment of the present invention; wherein line 1 represents the predicted lifespan, and line 2 represents the measured lifespan; Figure 5 It is a schematic diagram of the predicted life and measured life distribution of the data-physics fusion driven model provided according to an embodiment of the present invention; wherein, Line 1 represents a 2.0 times dispersion line, Line 2 represents a 1.5 times dispersion line, and Line 3 represents an equal life line. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following Figure 1-5 It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0022] A fatigue life prediction method for rubber materials based on physics-data fusion drive. Figure 1 As shown, the following steps are included: S1. Obtain the fatigue life data of rubber through experiments. The fatigue life data required to be obtained include the corresponding fatigue life times under different ambient temperatures, different material hardnesses and different strain amplitudes; different ambient temperatures such as 23°C, 60°C, 90°C, and different material hardnesses such as N45 and N50.

[0023] S2. Construct a fatigue life prediction physical model based on continuum mechanics. Specifically, the least squares method is used to fit the power function relationship between the measured fatigue life and the strain amplitude to establish a fatigue life prediction physical model based on continuum mechanics. The fatigue life prediction physical model includes the power function equation: N = Aε d ,in, N is the fatigue life times, ε is the strain amplitude, A and d is the material parameter. The least square method is used to fit the measured fatigue life and strain amplitude, and a physical model for predicting rubber fatigue life is established. Figure 2 shown.

[0024] S3. Preprocessing the predicted life and test data of the fatigue life prediction physical model. When preprocessing the predicted life and test data of the fatigue life prediction physical model, perform maximum-minimum value normalization processing, divide the test set and the training set, and the normalized mathematical expression is Formula 9, which is: ,in, and They are the normalized input samples and output samples respectively; and are the maximum and minimum values ​​of the input samples respectively; and are the maximum and minimum values ​​of the output samples, respectively. The total number of samples is 24, and 18 samples are randomly selected as training sets to train the BP neural network model; the remaining 6 samples are used as test sets to verify the accuracy and universality of the trained BP neural network model.

[0025] S4. According to the preprocessed data, determine the number of nodes in the input layer, hidden layer, and output layer of the BP neural network model. The structure of the BP network model is as follows: Figure 3 As shown. The input sample of the BP neural network model is X =[ x 1, x 2,…, x m ],in, x i ( i =1, 2,…, m ) is the i The physical model corresponding to each working condition predicts the life, ambient temperature, material hardness and strain amplitude; the output sample 2 of the BP neural network model is Y =[ y 1, y 2,…, y n ],in, y j ( j =1, 2,…, n ) is the j The measured fatigue life corresponding to each working condition.

[0026] The number of nodes in the model input layer is 4, the number of nodes in the model output layer is 1, and the number of nodes in the hidden layer is obtained by formula 1: l =2 P +1; among them, l is the number of hidden layer nodes, P is the number of nodes in the input layer; the number of nodes in the hidden layer is calculated by formula 1 l is 9.

[0027] S5, with the goal of minimizing the mean square error between the measured life and the predicted life, the gradient descent method is used to determine the connection weights and thresholds of the BP neural network model. Step S5 specifically includes the following sub-steps: S51, determine the nonlinear mapping relationship between the input variables and output variables of the BP neural network model. In step S51, according to the mapping relationship of the artificial neural network, the nonlinear mapping relationship between the input and output of the BP neural network model is expressed by formula 2 and formula 3; formula 2 is: ; Formula 3 is ;in, H represents the output of the hidden layer; and Respectively represent the connection weights from the input layer to the hidden layer, and from the hidden layer to the output layer; k represents the hidden layer k nodes; l Indicates the number of nodes in the hidden layer; a k and b j Respectively represent the thresholds from the input layer to the hidden layer and from the hidden layer to the output layer; f 1( x )and f 2( x ) are the activation functions of the hidden layer and the output layer respectively.

[0028] f 1( x ) is expressed as Formula 4, which is: ; f 2( x ) is expressed as Formula 5, which is: ;in, represents the natural exponential function, express The countdown of Represents the input variable.

[0029] S52, determine the connection weights and thresholds of the BP neural network model. In S52, the BP neural network model uses the mean square error function as the learning objective function of the model, and uses the gradient descent method to obtain the connection weights and thresholds of the model; the mathematical expression of the mean square error function is Formula 6, which is: ;in, M_S_E is the mean square error; Q is the number of training samples of the BP neural network model; For the g The actual output life of the BP neural network model corresponding to the training samples; For the g The actual life of rubber corresponding to the training samples.

[0030] Formula 7 and Formula 8 are used to normalize the predicted life of the physical model and the test data. Formula 7 is: ; Formula 8 is: ;in, and They are the normalized input samples and output samples respectively; x max and x min are the maximum and minimum values ​​of the input samples respectively; y max and y min are the maximum and minimum values ​​of the output samples respectively; x i For the i The physical model corresponding to each working condition predicts the life, ambient temperature, material hardness and strain amplitude, that is, x i Indicates i input variables; y j For the j The measured fatigue life corresponding to each working condition is y j Indicates j output variables.

[0031] S6: Combine the connection weights and thresholds to establish a rubber material fatigue life prediction model driven by physics-data fusion to achieve accurate prediction of rubber fatigue life. The results are as follows Figure 4~Figure 5 shown.

[0032] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. Those skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A method for predicting fatigue life of rubber materials based on physics-data fusion drive, characterized in that: The steps include: S1. Obtaining fatigue life data of rubber through experiments. The fatigue life data to be obtained include the corresponding fatigue life times under different ambient temperatures, different material hardnesses and different strain amplitudes; S2. Construct a fatigue life prediction physical model based on continuum mechanics. The fatigue life prediction physical model includes the power function equation: N = Aε d ,in, N is the fatigue life times, ε is the strain amplitude, A and d is the material parameter; S3, preprocessing the predicted life and test data of the fatigue life prediction physical model; S4. Determine the number of nodes in the input layer, hidden layer, and output layer of the BP neural network model based on the preprocessed data; S5. Taking the minimum mean square error between the measured life and the predicted life as the goal, the connection weights and thresholds of the BP neural network model are determined by using the gradient descent method; S6. Combine the connection weights and thresholds to establish a rubber material fatigue life prediction model driven by physics-data fusion.

2. The method for predicting fatigue life of rubber materials based on physics-data fusion drive according to claim 1 is characterized in that: In S2, the least squares method is used to fit the power function relationship between the measured fatigue life and the strain amplitude to establish a physical model for fatigue life prediction based on continuum mechanics.

3. The method for predicting fatigue life of rubber materials based on physics-data fusion drive according to claim 1 is characterized in that: In S3, when preprocessing the predicted life and test data of the fatigue life prediction physical model, maximum-minimum value normalization processing is performed and the test set and training set are divided.

4. The method for predicting fatigue life of rubber materials based on physics-data fusion drive according to claim 1, characterized in that: The input sample of the BP neural network model in S4 is X =[ x 1, x 2,…, x m ],in, x i ( i =1, 2,…, m ) is the i The physical model corresponding to each working condition predicts the life, ambient temperature, material hardness and strain amplitude; the output sample 2 of the BP neural network model is Y =[ y 1, y 2,…, y n ],in, y j ( j =1, 2,…, n ) is the j The measured fatigue life corresponding to each working condition.

5. The method for predicting fatigue life of rubber materials based on physics-data fusion drive according to claim 4 is characterized in that: The number of nodes in the hidden layer is obtained by formula 1: l =2 P +1; among them, l is the number of hidden layer nodes, P is the number of nodes in the input layer.

6. The method for predicting fatigue life of rubber materials based on physics-data fusion drive according to claim 1, characterized in that: Step S5 specifically includes the following sub-steps: S51, determining a nonlinear mapping relationship between input variables and output variables of the BP neural network model; S52: Determine the connection weight and threshold of the BP neural network model.

7. The method for predicting fatigue life of rubber materials based on physics-data fusion drive according to claim 6 is characterized in that: In step S51, according to the mapping relationship of the artificial neural network, the nonlinear mapping relationship between the input and output of the BP neural network model is expressed by Formula 2 and Formula 3; Formula 2 is: ; Formula 3 is ;in, H represents the output of the hidden layer; and Respectively represent the connection weights from the input layer to the hidden layer, and from the hidden layer to the output layer; k represents the hidden layer k nodes; a k and b j Respectively represent the thresholds from the input layer to the hidden layer and from the hidden layer to the output layer; f 1( x )and f 2( x ) are the activation functions of the hidden layer and the output layer respectively.

8. The method for predicting fatigue life of rubber materials based on physics-data fusion drive according to claim 7 is characterized in that: f 1( x ) is expressed as Formula 4, which is: ; f 2( x ) is expressed as Formula 5, which is: ;in, represents the natural exponential function, express The countdown of Represents the input variable.

9. The method for predicting fatigue life of rubber materials based on physics-data fusion drive according to claim 8, characterized in that: The BP neural network model in S52 uses the mean square error function as the learning objective function of the model, and adopts the gradient descent method to obtain the connection weights and thresholds of the model; the mathematical expression of the mean square error function is Formula 6, which is: ;in, M_S_E is the mean square error; Q is the number of training samples of the BP neural network model; For the g The actual output life of the BP neural network model corresponding to the training samples; For the g The actual life of rubber corresponding to the training samples.

10. According to the method for predicting fatigue life of rubber materials based on physics-data fusion drive in claim 9, formula 7 and formula 8 are used to normalize the predicted life of the physical model and the test data, and formula 7 is: ; Formula 8 is: ;in, and They are the normalized input samples and output samples respectively; x max and x min are the maximum and minimum values ​​of the input samples respectively; y max and y min are the maximum and minimum values ​​of the output samples respectively; x i For the i The physical model corresponding to each operating condition predicts the life, ambient temperature, material hardness and strain amplitude; y j For the j The measured fatigue life corresponding to each working condition.

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