A method for establishing a prediction model for the post-curing effect of rubber properties in natural environments

Abstract

The present invention discloses a method for establishing a prediction model for the post-curing effect of rubber properties in a natural environment. By describing the storage performance curve of rubber materials in a real atmospheric environment with piecewise functions and then superimposing the functions of each stage, a performance prediction model for rubber storage in a natural environment is constructed #imgabs0# Using digital tools such as Origin or Matlab to perform curve fitting of custom formulas on the original data group [t1, x1; t2, x2; ……; t n , x n to output specific undetermined parameters a, b, c, and d. The invention effectively predicts the change law of rubber properties over time. By establishing a unified formula for calculating the performance indexes of rubber at each time point under natural environment storage conditions, the regular understanding is promoted to a rational understanding.

Description

Technical Field

[0001] The invention belongs to the field of natural environment testing, and in particular relates to a method for establishing a prediction model for post-curing effects of rubber properties under natural environments. Background Art

[0002] Rubber materials are widely used in insulation sealing, noise reduction and vibration reduction of various types of equipment. Storage aging of rubber materials in natural environments is a common and serious problem, which can easily cause failure of various types of equipment, resulting in huge economic losses and social harm. Natural environment tests that reflect the evolution of rubber material performance are generally time-consuming, requiring several years or even more than ten years. However, the valuable data from long-term tests are difficult to keep up with the rapid development of material research and equipment development. The use of laboratory accelerated aging tests can effectively shorten the test time, but there are inevitable differences with the actual service conditions of the equipment. Due to the long time span, wide spatial distribution and complex and changeable factors affecting performance aging of polymer materials in natural environment tests, their performance aging data usually have the characteristics of small samples and high noise, which restricts the application of many traditional data analysis techniques and increases the difficulty of predicting performance laws.

[0003] When predicting the performance trend of rubber, due to its special performance evolution law, the power function, exponential function, polynomial function, etc. commonly used in metal corrosion aging are not very applicable. The performance evolution of rubber materials generally decreases rapidly in the early stage, and then recovers and rises after a period of time. This highly alienated characteristic is difficult to describe with a simple function form. Therefore, a composite mathematical model is constructed for the performance evolution law of materials with post-curing effects, which is of great significance for effectively predicting the performance changes of rubber materials. Summary of the invention

[0004] In view of the deficiencies in the above-mentioned prior art, the present invention proposes a method for establishing a prediction model for the post-curing effect of rubber properties under natural environment, which can effectively predict the change pattern of rubber properties over time, and improve the regularity understanding to rational understanding by establishing a unified formula for calculating the performance indicators of rubber at each time point under natural environment storage conditions.

[0005] In order to achieve the above object, the technical solution of the present invention is: a method for establishing a prediction model for the post-curing effect of rubber properties under natural environment, which comprises the following steps:

[0006] S1. Conduct atmospheric environment tests on rubber materials to obtain performance values ​​of rubber materials at different storage times in natural environments and draw time-performance curves;

[0007] S2. Construct the performance description function of rubber materials at each stage in the natural environment:

[0008] The early performance degradation process is described by an inverse proportional function in the form of 1 / (t+1);

[0009] Mid-term performance reduction enhancement process uses -e -t Description of exponential function in deformed form;

[0010] The slow performance decline process in the later stage is described by the organic combination of inverse proportional function and exponential function;

[0011] S3. Superimpose the functions of the three stages, and establish a comprehensive prediction model for the curing effect of rubber materials after storage in natural environments:

[0012]

[0013] Where a is the coefficient of the inverse proportional function, a>0;

[0014] b is the pre-exponential factor of the exponential function, b<0;

[0015] d is the exponential function exponential factor, d>0;

[0016] c is a constant to be determined;

[0017] S4. Use Origin or Matlab to analyze the original test data set [t1, x1; t2, x2; ...; t n , x n ] Perform curve fitting of custom formula and output the undetermined parameters a, b, c, d, where t i is the time node parameter; x i It is the performance data measured at the corresponding time node in the natural environment test;

[0018] S5. Substituting the determined parameters into the comprehensive prediction model, a prediction model for the post-curing effect of rubber performance under natural environment is obtained.

[0019] S6. Output the predicted value of rubber performance [t1, x1 p ;t2,x2 p ;……;t n , x n p ], using the predicted value and the true value to evaluate the model, including the sum of variance SSE, root mean square error RMSE, and determination coefficient R 2 Evaluate:

[0020] Residual sum of squares SSE: ∑(xi-x i p ) 2

[0021] Root mean square error RMSE:

[0022] Coefficient of determination R 2 :

[0023] S7. Use relative error Evaluate the error of each node and use the absolute average error Conduct overall model error assessment.

[0024] Use the inverse proportional function 1 / (t+1) and the modified form of the exponential function -e -t The inverse proportional function and exponential function are combined to describe the performance decline in the early stage, the gradual increase in the middle stage, and the slow decline curve in the late stage during the storage process of rubber in the natural environment. It can effectively characterize the post-curing effect of performance evolution and has a great advantage over the single function model. The effectiveness and reliability of the prediction model are verified through a series of model evaluations and model error analysis.

[0025] The prediction model of the present invention is easy to understand, simple and easy to implement, and plays an important supporting role in predicting the evolution trend of rubber material performance and improving the prediction accuracy and reliability of rubber materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a curve diagram of the performance change rule of the rubber stored in the natural environment of the present invention;

[0027] Figure 2 It is a graph of the inverse proportional function and the deformation exponential function;

[0028] Figure 3 It is a curve chart of rubber performance prediction model;

[0029] Figure 4 It is the rubber tensile strength prediction curve diagram of the present invention at Mohe Station;

[0030] Figure 5 It is the rubber tensile strength prediction curve diagram of the present invention at Hainan Station;

[0031] Figure 6 It is a rubber tensile strength prediction curve diagram of the present invention at Jiangjin Station. DETAILED DESCRIPTION

[0032] The present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0033] A kind of Figure 1-3 The method for establishing a prediction model for the post-curing effect of rubber properties under natural environment includes the following steps:

[0034] S1. Conduct atmospheric environment tests on rubber materials to obtain performance values ​​of rubber materials at different storage times in natural environments and draw time-performance curves;

[0035] By conducting atmospheric environment tests on rubber materials, the performance values ​​of rubber materials under different storage times are obtained, and a curve is drawn with the test time as the horizontal axis and the performance value as the vertical axis, such as Figure 1 As shown in the curve, it can be seen that the mechanical properties of rubber products continue to decline for a period of time after leaving the factory. As the internal polymer chain and other microstructures gradually solidify, the performance quickly recovers and strengthens, reaches a peak, and then slowly decreases.

[0036] S2. Construct the performance description function of rubber materials in each stage under natural environment, mainly including the function describing the early performance decline process, the function describing the mid-term decreasing enhancement process and the late slow decline function:

[0037] Depend on Figure 1 It can be seen that the performance curve decreases from rapid to slow in the early stage, and the function value should gradually decrease over time, which can be described by an inverse proportional function. Considering the discontinuity of 1 / t at 0, the performance decrease process of this model in the early stage is described by an inverse proportional function in the form of 1 / (t+1);

[0038] Mid-term performance reduction enhancement process uses -e -t Description of exponential function in deformed form;

[0039] The late performance slow decline process is described by the organic combination of inverse proportional function and exponential function, which can better describe the late slow decline process within a certain range, such as Figure 2 shown.

[0040] S3. Superimpose the functions of the three stages, add appropriate parameters to be determined, and establish a comprehensive prediction model for the curing effect of rubber materials after storage performance in natural environments. Figure 3 :

[0041]

[0042] Where a is the coefficient of the inverse proportional function, a>0;

[0043] b is the pre-exponential factor of the exponential function, b<0;

[0044] d is the exponential function exponential factor, d>0;

[0045] c is a constant to be determined;

[0046] contrast Figure 1 and Figure 3 The change trend of the predicted curve is in line with expectations, which is consistent with the change law of rubber properties under natural environment and can be used for modeling and analysis of rubber properties.

[0047] S4. Use Origin or Matlab to analyze the original test data set [t1, x1; t2, x2; ...; t n , x n ] Perform curve fitting of custom formula and output the undetermined parameters a, b, c, d, where t i is the time node parameter; x i It is the performance data measured at the corresponding time node in the natural environment test;

[0048] S5. Substituting the determined parameters into the comprehensive prediction model, a prediction model for the post-curing effect of rubber performance under natural environment is obtained.

[0049] S6. Output the predicted value of rubber performance [t1, x1 p ;t2,x2 p ;……;t n , x n p ], using the predicted value and the true value to evaluate the model, including the sum of variance SSE, root mean square error RMSE, and determination coefficient R 2 Evaluate:

[0050] Residual sum of squares SSE: ∑(x i -x i p ) 2

[0051] Root mean square error RMSE:

[0052] Coefficient of determination R 2 :

[0053] During the verification process, the closer the residual sum of squares SSE and the root mean square error RMSE are to 0, the better the model is. 2 The closer it is to 1, the better the model is.

[0054] S7. Use relative error Evaluate the error of each node and use the absolute average error Conduct overall model error assessment.

[0055] The steps are as follows:

[0056] (1) Carry out atmospheric environment test on rubber materials according to GJB8893-2017 "Natural Environment Test Method for Military Equipment" to obtain the original data time series group X of atmospheric corrosion weight loss of rubber materials:

[0057] X={t1,x1;t2,x2;…;tn , x n}

[0058] Where x1, x2, …x n They represent the test time of rubber materials in atmospheric environment t1, t2, ...t n The original data of performance test at time; t1, t2, ..., t n are any different positive real numbers; n represents the number of original data of atmospheric corrosion weight loss of metal materials collected during the entire atmospheric environment test period, and n is a positive integer not less than 4.

[0059] (2) Use the time series X of the natural environment test data of rubber materials to determine the parameters of the model, and use mathematical tools such as Origin or Matlab to customize the function:

[0060] Fitting modeling.

[0061] (3) Use the prediction model determined by the parameters to calculate the performance prediction value at the measured time point and output the prediction sequence X p ={t1, x1 p ;t2,x2 p ;……;t n , x n p}. In the formula, x i p The model for this method is calculated at t i Performance data value at a point in time.

[0062] (4) Using the residual sum of squares SSE: ∑(x i -x i p ) 2 , root mean square error RMSE: Coefficient of determination R2: Evaluate the model.

[0063] (5) Use relative error Evaluate the error of each node and use the absolute average error Conduct overall model error assessment.

[0064] In order to better understand the post-curing effect prediction model of the rubber material in the present invention, the following example is used to illustrate the performance evolution law prediction model and effect in this case:

[0065] Example 1: A prediction model for rubber post-curing effect

[0066] (1) Referring to GJB8893-2017 "Natural Environment Test Methods for Military Equipment", a rubber natural environment storage test with a test period of 8 years was carried out at Mohe, Hainan and Jiangjin test stations, and the original data of the tensile strength of a certain type of silicone rubber at test times of 1 year, 2 years, 3 years, 4 years, 6 years and 8 years were obtained, as shown in Table 1.

[0067] Experimental Station Original value 1 year 2 years 3 years 4 years 6 years 8 years Mohe 4.51 2.5 3.51 4.13 4.09 4.18 4.05 Hainan 4.51 2.52 4.18 4.77 4.52 4.53 4.12 Jiangjin 4.51 2.73 4.1 4.1 4.64 4.34 4.36

[0068] Table 1 Changes in tensile strength of a silicone rubber at different test stations (MPa)

[0069] (2) Determine the model parameters and use the custom formula to fit and determine the fitting parameters of different regions, as shown in Table 2. As can be seen from Table 2, b is a negative value, and a, c, and d are all greater than 0. Figure 4-6 The predicted curve of pull-up performance of the test station is shown.

[0070] Experimental Station a b c d Mohe 17.63 -15.25 2.124 0.6014 Hainan 25 -21.85 1.337 0.6709 Jiangjin 17.09 -15.02 2.422 0.6194

[0071] Table 2 Parameters of the prediction model for rubber tensile properties in different regions

[0072] (3) Calculate the predicted value of tensile strength using the prediction model determined by parameters, see Table 3.

[0073] Experimental Station 0 years 1 year 2 years 3 years 4 years 6 years 8 years Mohe 4.497 2.577 3.418 4.019 4.273 4.228 3.958 Hainan 4.486 2.665 3.958 4.666 4.844 4.518 4.012 Jiangjin 4.489 2.881 3.766 4.352 4.579 4.498 4.215

[0074] Table 3 Prediction of rubber tensile properties in different regions

[0075] (4) Using the residual sum of squares SSE = ∑(x i -x i p ) 2 , root mean square error Coefficient of determination Etc. to evaluate the model, where the total deviation sum of squares x is the data average. From the evaluation results (Table 4), the Mohe station data has the best prediction effect, with a determination coefficient of 0.9732 and a root mean square error of only 0.1008. The Jiangjin station fitting determination coefficient is relatively the lowest at 0.8993, and the root mean square error is relatively the largest at 1.881, and the model prediction effect is still relatively ideal.

[0076] Experimental Station SSE R2 RMSE SST Mohe 0.07115 0.9732 0.1008 2.6585 Hainan 0.198 0.9427 0.1682 3.4526 Jiangjin 0.2477 0.8993 0.1881 2.4609

[0077] Table 4 Model evaluation results

[0078] (5) Use relative error Evaluate the error at each time node and use the absolute average error The overall error of the model was evaluated. The error control of each time node was ideal, as shown in Table 5, with a minimum error of 0.29% and a maximum error of 8.15%. The overall error was lowest at Mohe Station at 2.37% and highest at Jiangjin Station at 4.08%.

[0079]

[0080] Table 5 Error evaluation analysis

[0081] The technical solutions provided by the embodiments of the present invention are introduced in detail above. Specific examples are used herein to illustrate the principles and implementation methods of the embodiments of the present invention. The description of the above embodiments is only applicable to help understand the principles of the embodiments of the present invention. At the same time, for those skilled in the art, according to the embodiments of the present invention, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for establishing a prediction model for the post-curing effect of rubber properties under natural environment, characterized in that: The steps include: S1. Conduct atmospheric environment tests on rubber materials to obtain performance values ​​of rubber materials at different storage times in natural environments and draw time-performance curves; S2. Construct the performance description function of rubber materials at each stage in the natural environment: The early performance degradation process is described by an inverse proportional function in the form of 1 / (t+1); Mid-term performance reduction enhancement process uses -e -t Description of exponential function in deformed form; The slow performance decline process in the later stage is described by the organic combination of inverse proportional function and exponential function; S3. Superimpose the functions of the three stages, and establish a comprehensive prediction model for the curing effect of rubber materials after storage in natural environments: Where a is the coefficient of the inverse proportional function, a>0; b is the pre-exponential factor of the exponential function, b<0; d is the exponential function exponential factor, d>0; c is a constant to be determined; S4. Use Origin or Matlab to analyze the original test data set [t1, x1; t2, x2; ...; t n , x n ] Perform curve fitting of custom formula and output the undetermined parameters a, b, c, d, where t i is the time node parameter; x i It is the performance data measured at the corresponding time node in the natural environment test; S5. Substituting the determined parameters into the comprehensive prediction model, a prediction model for the post-curing effect of rubber performance under natural environment is obtained.

2. The method for establishing a prediction model for the post-curing effect of rubber properties under natural environment according to claim 1, characterized in that: The steps also include: S6. Output the predicted value of rubber performance [t1, x1 p ; t2,x2 p ;……;t n , x n p ], using the predicted value and the true value to evaluate the model, including the sum of variance SSE, root mean square error RMSE, and determination coefficient R 2 Evaluate: Residual sum of squares SSE: ∑(x i -x i p ) 2 Root mean square error RMSE: Coefficient of determination R 2 : S7. Use relative error Evaluate the error of each node and use the absolute average error Conduct overall model error assessment.

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