Neural Network Calculator of Rubber Characteristics with Improved Properties

A new technique for the use of Artiﬁ cial Neural Networks (ANN) for the generalization and visual presentation of the results of experimental studies is proposed. The possibility of using ANN for cases for which their use was previously considered impossible is shown. ANN calculators have been created that summarize the results of experimental studies on the eﬀ ect of trans-polynorbornene and basalt ﬁ ber on the characteristics of a rubber compound based on general-purpose rubbers (isoprene SKI-3, butadiene-methylstyrene SKMS-30ARK and butadiene SKD), which also contained vulcanizing agents (N, N′-dithiodimorpholine, thiuram D), vulcanization accelerators (sulfenamide C, 2-mercapto-benzothiazole), vulcanization activators (zinc white, stearic acid), emollients (industrial oil I-12A, rosin) and antioxidants (acetonanil H, diaphene FP). The rubber mixture was prepared on laboratory rollers LB 320 160/160. Subsequently, the rubber mixture was vulcanized in a P-V-100-3RT-2-PCD press. For the resulting vulcanizates, the physical and mechanical properties and their changes were determined after daily exposure to air and in a standard SZhR-1 hydrocarbon liquid at a temperature of 100 °C. We also studied the change in the mass of vulcanizates after exposure to industrial oil I-20A and water. The dynamic parameters (modulus of elasticity and mechanical loss tangent) of vulcanizates, which characterize their noise and vibration-absorbing properties, were studied on a Metravib VHF 104 dynamic mechanical analyzer. The created ANN calculators allow solving a direct problem - interpolating the dependences of all rubber characteristics on the content of basalt ﬁ ber, as well as solving inverse problems - to determine the required content of basalt ﬁ ber to create rubber with the required performance properties. The autonomous executable modules of the calculators developed by ANN were made and can be passed to everyone.


Introduction
It is known that the movement of railway transport creates noise and vibration that has a negative impact on the environment and people. To reduce them, highly elastic rubber pads of rail fasteners are used, which are shock absorbers that reduce resonant vibrations of railway tracks during train movement [1]. To improve the performance properties of rail pads, it is necessary to develop rubber compound formulations through the use of special additives. These include trans-polynorbornene (trans-polybicyclo [2,2,1] hept-2-ene) [2,3], the possibility of using which for rail fasteners was studied in [4,5] to improve sound and vibration absorption. rubber properties. Vibration-absorbing materials also include polymer compositions containing ibrous illers. One of these illers is basalt iber [6]. It is of interest to investigate the combined effect of Trans-Polynorbornene (TPNB) and basalt iber on the properties of rubber gaskets. The purpose of this work was an experimental study of the effect of TPNB and basalt iber on the properties of rubber and the creation of a neural network calculator that allows interpolating the experimental results and determining the formulation of a rubber mixture with speci ied performance properties.

Abstract
A new technique for the use of Artifi cial Neural Networks (ANN) for the generalization and visual presentation of the results of experimental studies is proposed. The possibility of using ANN for cases for which their use was previously considered impossible is shown. ANN calculators have been created that summarize the results of experimental studies on the eff ect of transpolynorbornene and basalt fi ber on the characteristics of a rubber compound based on generalpurpose rubbers (isoprene SKI-3, butadiene-methylstyrene SKMS-30ARK and butadiene SKD), which also contained vulcanizing agents (N, N′-dithiodimorpholine, thiuram D), vulcanization accelerators (sulfenamide C, 2-mercapto-benzothiazole), vulcanization activators (zinc white, stearic acid), emollients (industrial oil I-12A, rosin) and antioxidants (acetonanil H, diaphene FP). The rubber mixture was prepared on laboratory rollers LB 320 160/160. Subsequently, the rubber mixture was vulcanized in a P-V-100-3RT-2-PCD press. For the resulting vulcanizates, the physical and mechanical properties and their changes were determined after daily exposure to air and in a standard SZhR-1 hydrocarbon liquid at a temperature of 100 °C. We also studied the change in the mass of vulcanizates after exposure to industrial oil I-20A and water. The dynamic parameters (modulus of elasticity and mechanical loss tangent) of vulcanizates, which characterize their noise and vibration-absorbing properties, were studied on a Metravib VHF 104 dynamic mechanical analyzer. The created ANN calculators allow solving a direct problem -interpolating the dependences of all rubber characteristics on the content of basalt fi ber, as well as solving inverse problems -to determine the required content of basalt fi ber to create rubber with the required performance properties. The autonomous executable modules of the calculators developed by ANN were made and can be passed to everyone. others). The rubber mixture was prepared on laboratory rolls LB 320 160/160 at a temperature of the rolls of the rolls of 60 °C -70 °C for 15 min. Subsequently, the rubber mixture was vulcanized in a P-V-100-3RT-2-PCD vulcanizing press at a temperature of 143 °C for 25 min. For the resulting vulcanizates, the physical and mechanical properties and their changes after daily exposure to air and in the standard hydrocarbon liquid SZHR-1 at a temperature of 100 °C were determined, and the change in the mass of vulcanizates after exposure to industrial oil I-20A and water at a temperature of 23 °C with within 24 hours was studied. The dynamic parameters (modulus of elasticity and mechanical loss tangent) of vulcanizates, which characterize the noise and vibration-absorbing properties of vulcanizates, were studied on a Metravib VHF 104 dynamic mechanical analyzer at a degree of deformation of 0.01%, a temperature of 30 °C, and a frequency of 1000 Hz. The basalt iber was a staple with a cutting length of 10 mm -12 mm and an elementary iber diameter of 9 -13 μm. Norsorex APX TPNB was a ine-grained white powder with a particle size of 300 -400 μm and a bulk density of 0.35 -0.40 g/cm3. To improve the compatibility of TPNB with the rubber matrix, a rubber-like composition of TPNB was developed with a technological additive -industrial oil I-12A at a mass ratio of 1:1. Subsequently, the resulting TPNB composition was introduced into the rubber mixture, the content of which in all the studied variants was 50.0 wt. h. per 100.0 wt. h. rubbers. At the same time, the irst (basic) version of the rubber mixture did not contain basalt iber, and the second -ifth versions of the mixture were prepared using basalt iber in an amount from 2.0 to 10.0 wt. h. 100.0 wt. h. rubbers. The results of the options and properties of the studied rubber mixture are presented in the Table 1.
To summarize all the dependencies contained in the table, Arti icial Neural Networks (ANN) were used, the rules and examples of their application are given in [7] and with various igures and graphs in [8][9][10][11][12]. One of the main rules of using ANN is that in order to generalize the patterns of an experiment with a large number of variables, a very large number of examples with different data sets is required. Violation of this rule leads to the so-called retraining of the ANN. It is believed that this makes it impossible to use the ANN when summarizing the results of experimental studies. To create an ANN calculator, the domestic analytical platform Deductor (www.basegroup.ru) was used, the results of which are given in [9][10][11][12][13].

Results and discussion
The structure of the ANN calculator for solving the direct problem, corresponding to the experimental data given in the table, was as follows. One neuron in the input layer of the ANN (the only input variable was the content of basalt iber -BF), 12 neurons in the output layer (12 main characteristics of physical-mechanical and dynamic properties are given in the Table), one inner (hidden) layer -6 neurons.
This structure, as well as others, can be seen in the autonomous executable modules of the calculators developed by ANN located at [7]. This module comes with instructions for use. A summary of ANN theory and other various ANN structures is given in [13].
The assessment of the accuracy of the obtained ANN calculator showed that the root-mean-square error of calculations is in the range of 7.1 10-5 ... 3.7 10-3 depending on the calculated characteristic (in units of a speci ic characteristic). The relative interpolation error, depending on the calculated characteristic, ranges from 0 (up to the 4 th digit) to 1%. Comparing these values with the values given in the table, one can estimate the absolute and relative error in the calculation of each speci ic characteristic. These estimates show that the ANN calculator accurately calculates the characteristics of the physical-mechanical and dynamic properties of vulcanizates.
At the same time, following [8], it cannot be argued that real experimental data can be considered as reference, that is, more accurate. The high "smoothing" abilities of the ANN when approximating experimental data burdened with measurement errors and revealing hidden dependencies in the data in some cases allow us to state that the ANN calculations better re lect the real dependences of the experiment, in our case, the real dependences of the characteristics of physical, mechanical and dynamic properties of vulcanizates on the content of basalt iber. This issue requires further research.
The work of the ANN calculator in solving the direct problem from the point of view of interpolation of experimental results is illustrated in Figure 2, which presents the results of calculating the characteristics of the physical-mechanical and dynamic properties of vulcanizates with the content of basalt iber equal to 7 wt. h. Real measurements of such a content of basalt iber were not carried out.
We also created ANN calculators for solving inverse problems, which are formulated as follows: What should be the content of basalt iber in order to obtain the speci ied values of the characteristics of the physical and mechanical properties of vulcanizates? The structure of one of the ANN calculators was as follows: three neurons in the input layer of the ANN (given values of three characteristics of the physical and mechanical properties of vulcanizates, 1 neuron in the output layer (amount of basalt iber), and one inner (hidden) layer -6 neurons.
This structure, as well as others, can be seen in the autonomous executable modules of the calculators developed by ANN located at [11].    equal to approximately 6.06 mass. h. The results of assessing the accuracy of the ANN calculator showed that it has a high accuracy, the root-mean-square error of calculating the BV is in the range of 8.1 10-4 ... 2.4 10-3 wt. h.
The operation of this ANN calculator is illustrated in Figure 4. The screenshots below show the results of calculating the amount of basalt iber, which provides three different sets of values for the characteristics of the physical and mechanical properties of vulcanizates.

Conclusion
A new technique for the use of Arti icial Neural Networks (ANN) for a generalized and visual representation of the results of experimental studies is proposed. ANN calculators have been created that summarize with suf iciently high accuracy the results of experimental studies on the effect of trans-polynorbornene and basalt iber on the characteristics of a rubber compound based on general-purpose rubbers. The ANN calculator allows solving the direct problem -to interpolate the dependences of all rubber characteristics on the content of basalt iber, as well as the inverse problem -to determine the required content of basalt iber to create rubber with the required performance properties. The autonomous executable modules of the calculators developed by ANN were made and can be passed to everyone.