A rubber multi-factor aging life prediction method based on response surface-artificial neural network coupling modeling
By using response surface methodology-artificial neural network coupling modeling to generate virtual samples for training the artificial neural network, the accuracy and stability issues of multi-factor aging life prediction for rubber were resolved, achieving high-precision rubber life prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TONGJI UNIV
- Filing Date
- 2026-04-27
- Publication Date
- 2026-07-31
AI Technical Summary
Existing technologies cannot effectively analyze the insufficient accuracy of life prediction for rubber under multi-factor high-order nonlinear coupling, and artificial neural network models have poor generalization ability under small sample conditions, resulting in inaccurate prediction results.
A response surface methodology coupled with an artificial neural network was adopted. By screening key factors of rubber aging, a response surface model was constructed, virtual samples were generated, and an artificial neural network was trained to achieve multi-factor aging life prediction.
While reducing experimental costs, it improved the accuracy and stability of rubber life prediction, and solved the problems of overfitting and insufficient generalization ability under small sample conditions.
Smart Images
Figure CN122494070A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of rubber materials technology, and in particular to a method for predicting the aging life of rubber based on response surface methodology and artificial neural network coupled modeling. Background Technology
[0002] As the core material of sealing systems, the accurate prediction of the service life of polymer elastomer-based sealing elements is a crucial aspect of industrial equipment reliability management. Premature replacement will lead to increased operating and maintenance costs, while delayed failure may cause safety accidents such as media leakage.
[0003] Current rubber life prediction systems mainly rely on the Arrhenius single-factor model based on thermo-oxidative aging. However, rubber is usually subjected to the coupling effects of multiple physicochemical fields such as temperature, humidity, and mechanical strain during use, and there are significant nonlinear synergistic effects among these factors. Traditional models cannot meet the requirements for accurate prediction of rubber life under multi-factor coupling.
[0004] Existing technologies typically rely on response surface methodology (RSM) to analyze the interactions between parameters, such as two-factor RSM models based on the Eyring model. Chinese patent CN121347316A uses an Eyring model to fit aging experimental data of pyrotechnic agents under different temperature and pressure conditions, achieving lifetime prediction under two-factor influences. Chinese patent CN121598768A also uses the Eyring model and particle swarm optimization algorithm to accurately predict the lifespan of rubber under the combined influence of ambient temperature and material hardness. However, these methods have limited analytical capabilities for higher-order nonlinear coupling effects, and when the number of influencing factors exceeds three, their analytical capabilities for the synergistic effects of multiple factors are insufficient, resulting in limited prediction accuracy.
[0005] In contrast, data-driven methods based on artificial neural network models can effectively fit higher-order features and analyze the synergistic effects between multiple factors through hidden layer nodes. Chinese patent CN112989691A, based on an artificial neural network model, predicts the mechanical properties of rubber under the influence of multiple factors such as temperature, humidity, aging time, and stress. However, due to the limited number of training samples (approximately 100 groups), the prediction results show significant bias. In the context of analyzing the coupling effects of multiple factors, the stable convergence of artificial neural network models typically depends on 10... 3 -10 4 The sheer volume of training samples significantly increases experimental costs, while training with only small sample data can easily lead to overfitting or insufficient generalization ability in the model.
[0006] In summary, there is currently a lack of a method for predicting the aging life of rubber based on response surface methodology and artificial neural network coupling modeling, which can solve or partially solve the above problems. Summary of the Invention
[0007] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a method for predicting the aging life of rubber based on response surface modeling and artificial neural network coupling modeling. This method aims to solve or partially solve the problems in the existing technology, such as the difficulty of analyzing the high-order nonlinear coupling effects of multiple factors by response surface model, insufficient prediction accuracy, and the large data requirements and poor generalization ability of artificial neural network model for training.
[0008] The objective of this invention can be achieved through the following technical solutions: According to one aspect of the present invention, a method for predicting the aging life of rubber based on response surface methodology-artificial neural network coupled modeling is provided, the method comprising: S1. Screen the key influencing factors of rubber aging, construct factor groups by orthogonally combining the key influencing factors of rubber aging in pairs, and design experimental parameter groups for each factor group through partial factor design; S2. Based on the experimental parameter set, conduct rubber aging experiments to obtain rubber life experimental data, fit the rubber life experimental data to the Eyring model, and establish a response surface model under the synergistic effect of two factors for each factor group. S3. Evaluate the accuracy of each response surface model sequentially using independent experimental parameter sets. For response surface models with accuracy below a preset threshold, supplement the experimental parameter sets and refit them. S4. Construct an artificial neural network model architecture, generate virtual samples using the response surface model through importance sampling, and train the artificial neural network model based on the virtual samples; S5. Using the trained artificial neural network model, output the multi-factor aging life prediction results of rubber to realize the prediction of rubber life under multi-factor coupling.
[0009] As a preferred technical solution, the key influencing factors of rubber aging include temperature, humidity, acidity, compression, ultraviolet intensity, and ozone content.
[0010] As a preferred technical solution, the rubber aging experiment includes compressing the rubber through a compression mold and then placing it in an environmental simulation chamber for aging according to preset experimental parameters, and recording the residual compressive stress of the rubber at set time points.
[0011] As a preferred technical solution, the rubber life test data refers to the time required for the residual compressive stress of the rubber to decay to a preset percentage of the original compressive stress.
[0012] As a preferred technical solution, the accuracy is evaluated using root mean square error, mean absolute error, and coefficient of determination as evaluation criteria.
[0013] As a preferred technical solution, the artificial neural network model architecture adopts a single hidden layer feedforward structure, with the neurons in the input layer corresponding to the key influencing factors of rubber aging and the neurons in the output layer corresponding to the rubber lifespan.
[0014] As a preferred technical solution, the generation of the virtual samples includes: constructing an importance distribution based on the uncertainty or gradient characteristics of the response surface model, adjusting the sample distribution in the input space using a probability-weighted sampling strategy, and performing sampling.
[0015] As a preferred technical solution, the training process of the artificial neural network model includes: training the artificial neural network model through backpropagation using the SGD optimizer, monitoring the validation set loss using the early stopping method, validating the artificial neural network model, and testing the artificial neural network model on an independent test set by evaluating the root mean square error, mean absolute error, and coefficient of determination.
[0016] According to another aspect of the present invention, an electronic device is provided, comprising one or more processors and a memory, wherein the memory stores one or more programs, the one or more programs including instructions for executing the rubber multi-factor aging life prediction method based on response surface-artificial neural network coupling modeling as described above.
[0017] According to another aspect of the invention, a computer-readable storage medium is provided, comprising one or more programs executable by one or more processors of an electronic device, the one or more programs including instructions for performing the rubber multi-factor aging life prediction method based on response surface-artificial neural network coupling modeling as described above.
[0018] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention combines the physical prior of the response surface model with the high-order nonlinear fitting capability of the artificial neural network model to construct a response surface-artificial neural network coupled model. This solves the problem in the prior art that it is difficult to balance the analytical capability of multi-factor coupling effect with experimental economy. It can achieve high-precision prediction of rubber life while significantly reducing the cost of multi-factor aging experiments.
[0019] (2) This invention generates high-quality virtual samples through response surface model, providing a large amount of data foundation for training artificial neural network models. It solves the problem that existing artificial neural network models are prone to overfitting and generalization defects in multi-factor lifetime prediction due to small sample data. It has the advantages of effectively expanding the training set and improving the convergence stability of the model under small sample data conditions.
[0020] (3) The present invention constructs an importance distribution based on the uncertainty or gradient features of the response surface model and uses probability weighted sampling to generate high-quality virtual samples. This solves the defects of low proportion of high-value samples and a lot of redundant data in the existing virtual sample generation methods. It has the advantages of improving the information density of virtual samples and ensuring efficient convergence of the artificial neural network model training process. Attached Figure Description
[0021] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation
[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.
[0023] Example 1 To address the problems existing in the aforementioned prior art, this embodiment provides a method for predicting the multi-factor aging life of rubber based on response surface methodology and artificial neural network coupled modeling, such as... Figure 1 As shown, it specifically includes: S1. Screen the key influencing factors of rubber aging, construct factor groups by orthogonally combining the key influencing factors of rubber aging in pairs, and design experimental parameter groups for each factor group through partial factor design.
[0024] The key influencing factors of rubber aging are mainly temperature, humidity, acidity, compression, ultraviolet intensity, and ozone content. These factors are orthogonally combined pairwise to construct a total of 15 factor groups. Sufficient experimental parameter sets are designed for each factor group using a partial factorial design (D-optimal design). The number of experimental parameter sets is determined based on the number of undetermined coefficients in the Eyring model. in, For rubber life, , , and For undetermined coefficients, , These are the independent variables of the factors.
[0025] There are 4 undetermined coefficients, meaning at least 4 sets of experimental parameters are required. To ensure the accuracy of the fitting results, 8 sets of experimental parameters are designed for each factor group, resulting in a total of 120 sets of experimental parameters for 15 factor groups.
[0026] S2. Based on the experimental parameter set, conduct rubber aging experiments to obtain rubber life experimental data. Fit the rubber life experimental data to the Eyring model and establish a response surface model under the synergistic effect of two factors for each factor group.
[0027] Cylindrical rubber was compressed using a compression mold and then placed in an environmental simulation chamber for aging according to set experimental parameters. The residual compressive stress of the rubber was recorded at fixed time points. The cylindrical rubber was set to have a diameter of 29 mm and a height of 12.5 mm, and the fixed time points were set at 1, 3, 7, 14, and 28 days. Rubber life refers to the time required for the rubber's compressive stress to decay to 60% of its original compressive stress, which can be obtained by fitting experimental data from the aging experiment. in, This represents the percentage of remaining performance. For undetermined coefficients, The rate constant is For time, It is the exponential coefficient.
[0028] The rubber life data in each factor group were fitted with the Eyring model to obtain a total of 15 response surface models.
[0029] S3. Evaluate the accuracy of each response surface model sequentially using independent experimental parameter sets. For response surface models with accuracy below a preset threshold, supplement the experimental parameter sets and refit them.
[0030] The root mean square error, mean absolute error, and coefficient of determination were used as evaluation criteria to assess the accuracy of the model. For response surface models with an error greater than 5%, the experimental parameter set was further supplemented by D-optimal design and the Eyring model was refitted until a highly accurate response surface model was obtained.
[0031] S4. Build an artificial neural network model architecture, generate virtual samples using the response surface model through importance sampling, and train the artificial neural network model based on the virtual samples.
[0032] An artificial neural network model architecture was constructed, which adopts a single hidden layer feedforward structure containing 10 neurons. The input layer contains 6 neurons corresponding to the key influencing factors of rubber aging, and the output layer contains 1 neuron corresponding to the rubber lifespan.
[0033] Subsequently, an importance distribution is constructed based on the uncertainty or gradient characteristics of the response surface model, and a probability-weighted sampling strategy is used to adjust the sample distribution in the input space, focusing virtual samples on regions with high uncertainty or high gradient characteristics. This yields a sufficient number of virtual samples to meet the training, validation, and testing requirements of the artificial neural network model. This number is determined based on the constructed artificial neural network model architecture: for the training set, each hidden layer neuron from the input layer to the hidden layer requires 6 weights and 1 bias, and each output layer neuron from the hidden layer to the output layer requires 10 weights and 1 bias, for a total of 81 parameters. Following the rule of thumb of 10 times the number of parameters, a total of 810 virtual samples are needed. Based on the ratio of 7:1.5:1.5 between the training, validation, and test sets, at least 1158 virtual samples are required. To fully train the artificial neural network model, the number of virtual samples is set to 1200.
[0034] Finally, based on virtual sample data, the artificial neural network model was trained by backpropagation using the SGD optimizer. The early stopping method was used to monitor the loss on the validation set to validate the artificial neural network model. The artificial neural network model was then tested on an independent test set by evaluating the root mean square error, mean absolute error, and coefficient of determination.
[0035] S5. Using a trained artificial neural network model, output the multi-factor aging life prediction results of rubber to realize the prediction of rubber life under multi-factor coupling.
[0036] Example 2 Based on the foregoing embodiments, this embodiment provides an electronic device, including a processor, an internal bus, a network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then runs it to implement the above-mentioned method for predicting the multi-factor aging life of rubber based on response surface-artificial neural network coupled modeling. Of course, in addition to software implementation, this invention does not exclude other implementation methods, such as logic devices or a combination of hardware and software, that is, the execution subject of the processing flow is not limited to individual logic units, but can also be hardware or logic devices.
[0037] Example 3 Building upon the foregoing embodiments, this embodiment provides a computer-readable storage medium storing a computer program that can be used to execute the aforementioned method for predicting the multi-factor aging life of rubber based on response surface-artificial neural network coupled modeling. Computer-readable media include permanent and non-permanent, removable and non-removable media, and information storage can be achieved by any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient media, such as modulated data signals and carrier waves.
[0038] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A rubber multi-factor aging life prediction method based on a response surface-artificial neural network coupling modeling, characterized in that, The method includes: S1. Screen the key influencing factors of rubber aging, construct factor groups by orthogonally combining the key influencing factors of rubber aging in pairs, and design experimental parameter groups for each factor group through partial factor design; S2. Based on the experimental parameter set, conduct rubber aging experiments to obtain rubber life experimental data, fit the rubber life experimental data to the Eyring model, and establish a response surface model under the synergistic effect of two factors for each factor group. S3. Evaluate the accuracy of each response surface model sequentially using independent experimental parameter sets. For response surface models with accuracy below a preset threshold, supplement the experimental parameter sets and refit them. S4. Construct an artificial neural network model architecture, generate virtual samples using the response surface model through importance sampling, and train the artificial neural network model based on the virtual samples; S5. Using the trained artificial neural network model, output the multi-factor aging life prediction results of rubber to realize the prediction of rubber life under multi-factor coupling.
2. The rubber multi-factor aging life prediction method based on the coupling modeling of response surface-artificial neural network according to claim 1, characterized in that, The key factors affecting rubber aging include temperature, humidity, acidity, compression, ultraviolet intensity, and ozone content.
3. The method for predicting the aging life of rubber based on response surface methodology and artificial neural network coupling modeling as described in claim 1, characterized in that, The rubber aging experiment includes compressing the rubber through a compression mold and then placing it in an environmental simulation chamber for aging according to preset experimental parameters, and recording the residual compressive stress of the rubber at set time points.
4. The method for predicting the aging life of rubber based on response surface methodology and artificial neural network coupling modeling as described in claim 1, characterized in that, The rubber life test data refers to the time required for the residual compressive stress of the rubber to decay to a preset percentage of the original compressive stress.
5. The method for predicting the multi-factor aging life of rubber based on response surface methodology and artificial neural network coupled modeling as described in claim 1, characterized in that, The accuracy is evaluated using root mean square error, mean absolute error, and coefficient of determination as criteria.
6. The method for predicting the aging life of rubber based on response surface methodology and artificial neural network coupling modeling as described in claim 1, characterized in that, The artificial neural network model architecture adopts a single hidden layer feedforward structure, with the neurons in the input layer corresponding to the key influencing factors of rubber aging and the neurons in the output layer corresponding to the rubber lifespan.
7. The method for predicting the multi-factor aging life of rubber based on response surface methodology and artificial neural network coupled modeling as described in claim 1, characterized in that, The generation of the virtual samples includes: constructing an importance distribution based on the uncertainty or gradient characteristics of the response surface model, adjusting the sample distribution in the input space using a probability-weighted sampling strategy, and performing sampling.
8. The method for predicting the aging life of rubber based on response surface methodology and artificial neural network coupled modeling as described in claim 1, characterized in that, The training process of the artificial neural network model includes: backpropagating the artificial neural network model using the SGD optimizer, monitoring the validation set loss using the early stopping method, validating the artificial neural network model, and testing the artificial neural network model on an independent test set by evaluating the root mean square error, mean absolute error, and coefficient of determination.
9. An electronic device, characterized in that, It includes one or more processors and a memory, wherein the memory stores one or more programs, the one or more programs including instructions for executing the rubber multi-factor aging life prediction method based on response surface-artificial neural network coupling modeling as described in any one of claims 1-8.
10. A computer-readable storage medium, characterized in that, Includes one or more programs executable by one or more processors of an electronic device, the one or more programs including instructions for performing the rubber multi-factor aging life prediction method based on response surface-artificial neural network coupling modeling as described in any one of claims 1-8.