Gear fatigue life prediction model and method for establishing prediction model

Abstract

The invention discloses a gear fatigue life prediction model and a method for establishing the prediction model, according to the prediction model, a CTab-GAN + generator and XGBoost are combined to form the gear life prediction model, the input parameters are friction coefficient, elastic modulus, Poisson's ratio, tensile strength and contact stress, and the output parameter is gear life. The method for establishing the prediction model comprises the following steps: 1, selecting an input parameter and an output parameter; 2, generating a large amount of synthetic data by using a CTab-GAN + generator, and predicting the fatigue life of different gears under different working conditions by using an XGBoost algorithm; and 3, evaluating the feasibility and accuracy of a prediction result, and analyzing the influence of different factors on the service life of the gear through an SHAP explanation model. The gear fatigue life prediction method has the technical effect that the accuracy of fatigue life prediction of different gears under different conditions is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical manufacturing, and specifically relates to a gear fatigue life prediction model combining data enhancement and machine learning algorithms and a method for establishing the prediction model, which is a method for accurately predicting the gear fatigue life. Background Art

[0002] Fatigue life prediction is an important task in materials science or mechanical engineering. Fatigue is the process of damage and fracture of materials under alternating loads, which often occurs in parts in the fields of machinery, electronics, aviation, aerospace, etc. In these fields, technicians need to predict the damage and fracture process of materials under alternating loads based on the stress-strain relationship, load and other conditions of the materials, and then predict the life of the materials to ensure that they can work safely and reliably.

[0003] Existing fatigue life prediction methods are usually based on test data and empirical formulas, which require a large number of tests and data processing, and consume a lot of resources and time. At the same time, the accuracy and reliability of existing fatigue life prediction models are limited by the quality of experimental data and the applicability of the models, and are only applicable to specific materials and load conditions. The complexity and uncertainty of actual working conditions will also affect the accuracy of fatigue life prediction.

[0004] With the development of machine learning and deep learning technology, fatigue life prediction methods have also been improved and optimized. CN111324989A proposed a gear contact fatigue life prediction method based on GA-BP neural network on June 23, 2020. This method uses GA-BP neural network to establish a gear contact fatigue life prediction model. By inputting the structural characteristic parameters and material parameters of the gear, the gear contact fatigue life is predicted. Compared with the gear contact fatigue life prediction method based on the physical model, it has low cost and high prediction accuracy. However, this method requires a large amount of original data to construct the GA-BP neural network, and can only predict gears with the same material as the original data (such as 20MnCr5, 18Cr2Ni4WA, AISI4118, 16MnCr5).

[0005] Machine learning and deep learning technologies predict the results of new data by learning the characteristics of existing sample data. Compared with traditional methods, they are more convenient and have higher accuracy. However, ordinary machine learning models require a large amount of raw data to build neural networks. It is very difficult to obtain the life of gears. The large amount of data required will consume a lot of time and resources. At the same time, the current methods cannot predict the life of gears that are different from the original data type, and the model is not very versatile, which limits the development of gear research.

[0006] The technical background of GAN generation network for data enhancement can be traced back to 2014, when the concept of generative adversarial network (GAN) was proposed by Goodfellow et al. GAN is a deep learning model consisting of two sub-models: generator and discriminator. The generator tries to generate samples similar to real data, while the discriminator tries to distinguish between generated samples and real samples. The two sub-models are constantly competing, gradually improving the generator's ability to generate samples during the training process. Therefore, after training, the GAN generation network can generate new data samples by learning the distribution of real data, thereby expanding the training data set. These new samples are similar to but not exactly the same as the real data, which can effectively increase the diversity of the data. Data enhancement methods have been widely used in many fields to solve the problem of insufficient data in deep learning applications.

[0007] Due to the complexity of fatigue data, there are still great limitations in directly applying the GAN generation network to fatigue life prediction. For example, the training of the GAN generation network also requires a certain amount of input data, and it is very difficult to obtain gear fatigue life test data, which greatly limits the accuracy of the generated data. In addition, the fatigue life of gears is affected by multiple factors including friction coefficient, Poisson's ratio, tensile strength, contact stress, etc. Ordinary GAN generation networks may not be able to handle the results of the interaction of some multiple factors in gear life prediction well, and the accuracy of the prediction will be greatly affected. At present, the models that use GAN generation networks for prediction often only consider the role of 1 to 2 factors, and can only predict the same type of gear under the same working conditions. The versatility of the model is poor.

[0008] At the same time, there are still some shortcomings in the technology of GAN generation network in tabular data generation, including how to maintain the structure and relationship of data, how to ensure the authenticity and validity of generated data, etc. In order to solve these problems, the enhanced generative adversarial network of CTAB-GAN+ is introduced. According to the document "CTAB-GAN+: Enhancing Tabular Data Synthesis", Zhao, Zilong et al. ArXiv abs / 2204.00401(2022):n.pag. ("CTAB-GAN+: Enhanced Tabular Data Synthesis", Zhao, Zilong), a CTAB-GAN+ generator was recorded in April 2022, which belongs to a new GAN generation network model. In addition to the basic generator G and discriminator D in the GAN generation network, Wasserstein distance plus gradient penalty are added to reduce the problems of gradient explosion and gradient disappearance, further enhancing the stability and effectiveness of GAN training. At the same time, the CTAB-GAN+ generator contains a noise vector plus a conditional vector. Some features of the generated data can be controlled by controlling the conditional vector, such as specifying the sum or average of rows and columns, so that the generated data has a certain controllability and predictability, which has great flexibility and usability in practical applications. Compared with other existing generation models, the CTAB-GAN+ generator has better performance and effect, can achieve effective control in the generation process, and make the generated data more realistic and robust, which shows that the model has great advantages and practicality in the field of structured data generation.

[0009] The document "XGBoost: A Scalable Tree Boosting System.", Chen, T., & Guestrin, C. (2016). Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ("XGBoost: A Scalable Tree Boosting System", Tianqi Chen, Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining) disclosed XGBoost (Extreme Gradient Boosting), developed by Tianqi Chen in 2016. It was the fastest before Gradient boost and was the preferred Boosting method. The basic components of XGboost are decision trees, which are also called "weak learners". Each "decision tree" is the model with the smallest objective function value. Only when the objective function value of this "decision tree" is the smallest will it be selected as a "weak learner". These "weak learners" together constitute XGboost. The decision trees that make up XGBoost have a sequence, and the generation of the next decision tree will take into account the prediction results of the previous decision tree, that is, the deviation of the previous decision tree is taken into account. The data set used to generate each decision tree is the entire data set, so the generation of each decision tree can be regarded as a complete decision tree generation process. The new sample enters each decision tree of XGBoost in turn, and each decision tree has a prediction value until it enters all "weak learners" (decision trees). Finally, the "values ​​in each decision tree" are added together to obtain the final prediction result. Since it contains hyperparameters, many adjustments can be made, such as regularization hyperparameters to prevent overfitting. However, in order to improve the accuracy and stability of the XGBoost prediction model, a large amount of training data and optimization algorithms are required. At the same time, the prediction results need to be evaluated and verified to ensure the reliability and applicability of the prediction model. Summary of the invention

[0010] In view of the problems existing in the existing gear fatigue life prediction technology, the technical problem to be solved by the present invention is to provide a gear fatigue life prediction model, which can improve the accuracy of fatigue life prediction of different gears under different conditions. The present invention also provides a method for establishing a gear fatigue life prediction model.

[0011] In order to solve the above technical problems,

[0012] The present invention provides a gear fatigue life prediction model, which is composed of a CTab-GAN+ generator and an XGBoost. The input parameters are friction coefficient, elastic modulus, Poisson's ratio, tensile strength and contact stress, and the output parameter is gear life.

[0013] The present invention also provides a method for establishing a gear fatigue life prediction model, comprising the following steps:

[0014] Step 1: Select the input parameters as friction coefficient, elastic modulus, Poisson's ratio, tensile strength and contact stress, and the output parameter as gear life;

[0015] Step 2: Generate a large amount of synthetic data using the CTab-GAN+ generator, and then use the XGBoost algorithm to predict the fatigue life of different gears under different working conditions;

[0016] Step 3: Evaluate the feasibility and accuracy of the prediction results, and analyze the impact of different factors on gear life through the SHapley Additive exPlanations (Shapley Additive Explanation Model, abbreviated as SHAP) explanation model.

[0017] The CTAB-GAN+ generator is different from the general GAN ​​network. This network is specially trained and generated for tabular data. It uses Wasserstein distance plus gradient penalty to further enhance the stability and effectiveness of GAN training. At the same time, the CTAB-GAN+ generator adds a new auxiliary component to improve the overall performance of regression tasks. Its advantages mainly include two aspects:

[0018] 1. Strong controllability: The CTAB-GAN+ generator can control some features of the generated data through conditional features, such as specifying the average value of rows and / or columns, etc., so that the generated data has a certain degree of controllability and predictability, which has great flexibility and usability in practical applications.

[0019] 2. High quality: Compared with other existing generative models, the CTAB-GAN+ generator has better performance and effects, can achieve effective control in the generation process, and the generated data is more realistic and robust. It has great advantages and practicality in the field of structured data generation.

[0020] XGBoost is a machine learning algorithm based on gradient boosting decision trees. It has the advantages of high efficiency, accuracy and interpretability, and has been widely used in various fields. Compared with other Boosting methods, XGBoost adds a regularization term to the objective function to control the complexity of the model, making the learned model simpler and preventing overfitting. At the same time, XGBoost not only uses the first-order derivative, but also the second-order derivative, and the loss is more accurate. Applying XGBoost to gear life prediction can make full use of test data and empirical knowledge to establish a high-precision prediction model. The XGBoost algorithm can also handle high-dimensional, nonlinear and non-stationary data, and is suitable for various types of gears.

[0021] Compared with the existing machine learning gear fatigue life prediction technology, the technical effects of the present invention are:

[0022] The CTab-GAN+ generator can generate a large amount of synthetic data based on real data sets, increasing the amount of data to improve the accuracy of the model. At the same time, the XGBoost algorithm can effectively mine the characteristics of the data. Combining the two data processing techniques improves the accuracy of predicting the fatigue life of gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The accompanying drawings of the present invention are as follows:

[0024] Figure 1 Comparison chart of the original data of Example 1 and the prediction results of the CTab-GAN+ generator enhanced data (10000

[0025] Enhancement amount);

[0026] Figure 2 This is the SHAP ranking diagram of the gear life prediction model combining CTab-GAN+ generator and XGBoost;

[0027] Figure 3 This is the feature ranking diagram of the gear life prediction model combining CTab-GAN+ generator and XGBoost;

[0028] Figure 4 This is a comparison chart of the original data of Example 2 and the prediction results of the CTab-GAN+ generator enhanced data. DETAILED DESCRIPTION

[0029] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0030] The gear fatigue life prediction model of the present invention is a gear life prediction model composed of a CTab-GAN+ generator and XGBoost. The input parameters are friction coefficient, elastic modulus, Poisson's ratio, tensile strength and contact stress, and the output parameter is gear life.

[0031] Example 1: A gear life prediction model method combining CTab-GAN+ generator and XGBoost is established, and the following steps are taken:

[0032] Step 1: Take the five parameters of friction coefficient, elastic modulus, Poisson's ratio, tensile strength and contact stress as input parameters, and the output parameter is the life of the corresponding gear.

[0033] This implementation uses 18 sets of POM gear and PEEK gear fatigue life experimental data as original training data; 5 sets of POM gear and PEEK gear fatigue life experimental data as test data. The parameter range of the original data is shown in Table 1:

[0034] Table 1 Parameter range of original data

[0035] Friction coefficient Elastic modulus Poisson's ratio Tensile Strength Contact stress Gear fatigue life 0.04，0.09 1800～4050 0.38，0.35 60，100 50～155 4～6

[0036] Step 2: Use the CTAB-GAN+ generator to perform data enhancement on the 18 sets of original data. Select the enhancement type as regression and the enhancement target as gear life. The total amount of data after data enhancement is 1000, 5000, and 10000 respectively. The default parameter selection of the CTAB-GAN+ generator is formula 1:

[0037] CTABGAN(class_dim=(256,256,256),random_dim=100,num_channels=64,l

[0038] 2scale=1e-5, batch_size=500, epochs=30000) (1)

[0039] The XGBoost prediction model is used to predict the enhanced data set to obtain the life data of the gear under specific conditions. The default parameter selection of the XGBoost model is formula 2:

[0040] XGBRegressor(n_estimators=100, learning_rate=0.1, gamma=0,

[0041] subsample=0.8,colsample_bytree=0.9, max_depth=2) (2)

[0042] Step 3: Evaluate the feasibility and accuracy of the prediction results and analyze the impact of different factors on gear life through the SHAP interpretation model

[0043] Concentration is used instead of the traditional root mean square error to compare the accuracy of the prediction. Since the fatigue life of specimens with the same material and size under the same conditions may vary from hundreds to hundreds of thousands, the root mean square error may generate results of different orders of magnitude in fatigue research. Therefore, concentration considering the logarithmic transformation difference is introduced to compare the accuracy.

[0044] According to the literature "A new cyclical generative adversarial network based data augmentation method for multiaxial fatigue life prediction", Xingyue Sun, KunZhou, Shouwen Shi, Kai Song, Xu Chen, International Journal of Fatigue, Volume, 162, 2022, 106996, ISSN 0142-1123 ("Multiaxial fatigue life prediction data augmentation method based on cyclic generative adversarial network", Xingyue Sun et al., International Journal of Fatigue, vol. 162, 2022, 106996, ISSN 0142-1123), concentration is recorded as a new evaluation criterion for prediction results. Concentration is defined as:

[0045]

[0046] In formula (3), n is the number of samples;

[0047]

[0048] In formula (4): Y i,exp is the experimental fatigue life of sample i, Y i,pre To predict life span, the distribution δ lg,i It can effectively reflect the concentration of prediction results and describe the stability of the XGBoost prediction model.

[0049] If the concentration C of the enhanced data is lower than the concentration of the original data at different enhancement amounts, the corresponding XGBoost prediction model has the most stable performance. The closer C is to 0, the better and more concentrated the prediction performance obtained by the prediction model.

[0050] Testing of the gear life prediction model combining CTab-GAN+ generator and XGBoost

[0051] Five groups of POM gear and PEEK gear fatigue life experimental data were used as test data, and the original data and CTabGAN+ generator enhanced data were used to verify the feasibility of CTab-GAN+ generator and XGBoost prediction model.

[0052] Test results see Figure 1 ,from Figure 1 It can be seen that the POM and PEEK gear life data enhanced by the CTab-GAN+ generator can better realize the life prediction of POM and PEEK gears, and the error is stable within the 2-fold error band, while the prediction without using enhanced data will exceed the 2-fold error band.

[0053] Calculating the average concentration C of the above test data, we can get Table 2:

[0054] Table 2 Comparison of average concentration C of original data and CTab-GAN+ generator enhanced data

[0055]

[0056] As can be seen from Table 2, the performance of the enhanced data of CTab-GAN+ generator is much better than the prediction performance of the original data. The performance of the enhanced data with 10,000 enhancements is the best, indicating that XGBoost can accurately and completely learn and predict the gear life under different conditions with 10,000 sets of data. 5,000 sets of data are not enough to fully learn the intrinsic factors between the gear life and each input variable. Therefore, compared with 1,000 sets of data, the excess data will mislead the accuracy of life prediction, resulting in a situation where 5,000 enhancements are not as good as 1,000 enhancements. Therefore, 10,000 sets of enhancements are selected as the standard enhancement for model prediction.

[0057] In order to enable the model of the present invention to predict the life of different gears under different working conditions based on the five input parameters of friction coefficient, elastic modulus, Poisson's ratio, tensile strength and contact stress, more input parameters and life data of different gears are needed. Considering the difficulty in obtaining gear fatigue data, it is impossible to obtain a large amount of data for model training, and simulation data is used instead.

[0058] On the basis of the 18 sets of real experimental data in this embodiment, 30 sets of high-quality gear fatigue life simulation data are added to expand the experimental data range and increase the stability and robustness of the enhanced data prediction. The parameter range of the original + simulation data is shown in Table 3:

[0059] Table 3 Parameter range of original + simulation data

[0060]

[0061] The CTab-GAN+ generator was used to enhance the 48 sets of original data to 10,000 data points, and the XGBoost model was used to predict the gear life. The model of the present invention used five parameters as input data and predicted the life of the corresponding gear under the corresponding working conditions through XGBoost. The model of the present invention can effectively predict the fatigue life of different gears under different conditions, providing a new technical approach for gear life prediction.

[0062] The SHAP analysis of the gear life prediction model combining CTab-GAN+ generator and XGBoost is performed, and the prediction model is explained according to the Shapley sum interpretation method (SHAP) described in the literature "A Unified Approach to Interpreting Model Predictions", Lundberg, Scott M. and Su-In Lee, ArXiv abs / 1705.07874 (2017): n.pag. ("Unified Approach to Interpreting Model Predictions", Lundberg et al., ArXiv abs / 1705.07874 (2017): n.pag.). The main idea of ​​SHAP value is Shapley value, which is a method from coalitional game theory. The Shapley value created by Shapley in 1953 is a method to allocate expenditures to players according to their contribution to the total expenditure, where "total expenditure" is the model prediction value of a single instance of the data set, "player" is the feature value of the instance, and "revenue" is the actual prediction of the instance minus the average prediction of all instances. For the ensemble tree model, when doing classification tasks, the model outputs a probability value, so SHAP actually attributes the output value to the shapely value of each feature. By calculating the shapley value of each feature, the influence of the feature on the final output value is measured. The higher the shapley value, the greater the influence of the corresponding factor on the model. Based on SHAP analysis, the influence of each input parameter on the gear life can be obtained. See the interactive SHAP-sorting diagram Figure 2 , feature sorting see Figure 3 .

[0063] from Figure 2 and Figure 3 It can be seen that contact stress, elastic modulus and tensile strength have the greatest impact on gear life. This result is consistent with the traditional fatigue life prediction conclusion, which verifies the feasibility and accuracy of the model of the present invention.

[0064] Example 2: Prediction of the lubrication life data of POK gears and PET gear oil using the prediction model of the present invention

[0065] This embodiment selects 8 groups of POK gear experimental life data and 4 groups of PET gear oil lubrication life data in VDI 2736, and uses the original data and the gear life prediction model combined with the CTab-GAN+ generator and XGBoost for prediction.

[0066] See Table 4 for the corresponding parameter ranges:

[0067] Table 4 Parameter range of PET and POK data

[0068] Friction coefficient Elastic modulus Poisson's ratio Tensile Strength Contact stress Gear fatigue life 0.04，0.09 1300～2000 0.4，0.45 55，58 30～60 5～8

[0069] The present invention is used to synthesize 10,000 data sets, and the corresponding life data is predicted and compared with the original life data in the experiment and VDI2736. Figure 4 The comparison chart shown. Figure 4 It can be seen that the model of the present invention can also well realize the life prediction of other gears except POM and PEEK, and the error is stable within 3 times the error band. The average concentration C of the above data is calculated to obtain Table 5:

[0070] Table 5 Comparison of average concentration C of original data and CTab-GAN+ generator enhanced data

[0071] method Average concentration Enhanced Data C 90.03％ Original data C 363.34％

[0072] It can be seen from Table 5 that the prediction effect of the gear life prediction model combining CTab-GAN+ generator and XGBoost is much better than the prediction of the original data.

Claims

1. A gear fatigue life prediction model, characterized by: By CT The ab-GAN+ generator is combined with XGBoost to form a gear life prediction model. The input parameters are friction coefficient, elastic modulus, Poisson's ratio, tensile strength and contact stress, and the output parameter is gear life.

2. A method for establishing a gear fatigue life prediction model, characterized in that: The following steps are involved: Step 1: Select the input parameters as friction coefficient, elastic modulus, Poisson's ratio, tensile strength and contact stress, and the output parameter as gear life; Step 2: Generate a large amount of synthetic data using the CTab-GAN+ generator, and then use the XGBoost algorithm to predict the fatigue life of different gears under different working conditions; Step 3: Evaluate the feasibility and accuracy of the prediction results and analyze the impact of different factors on gear life through the SHAP interpretation model.

3. The method for establishing a gear fatigue life prediction model according to claim 2, characterized in that: In step 3, assess feasibility and accuracy using the logarithmic transformation of the difference in concentration C as: Where n is the number of samples; Where: Y i,exp is the experimental fatigue life of sample i, Y i,pre To predict the lifespan, δ lg,i It is the distribution situation, reflecting the concentration of the prediction results.

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