## 3 Data Analysis of Similarity Calculation Method for Infield and Outfield Environmental Tests  
### Data Analysis and Fitting of Environmental Tests  
From the test data shown in Figure 6, it can be seen that the hardening degree of the two kinds of rubber in the vitrification transformation zone is significantly related to temperature. That is, the lower the temperature, the more obvious the hardening. The difference between the infield tests and the outfield tests is also demonstrated. At the same temperature, the springback and elongation of the infield tests are different from those of the outfield test, with the springback and elongation of the infield tests being smaller. In addition, at the same temperature, the hardening of the two materials is more obvious in the infield test environment. Based on a genetic algorithm [22], three curve fitting models were then used to fit the data of the outfield environmental tests: namely, the polynomial, exponential, and Fourier fitting models. The polynomial models for the curves are given by,  
\[y=\sum_{i=1}^{n+1}p_{i}x^{n+1-i} \tag{1}\]  
where \(n+1\) is the order of the polynomial, \(n\) is the degree of the polynomial, and \(1\leq n\leq 9\). The order gives the number of coefficients to be fit, and the degree gives the highest power of the predictor variable. The main advantages of the polynomial fits include reasonable flexibility for data that is not too complicated, and they are linear, which means the fitting process is simple [23]. The one-term and two-term exponential model as given by,  
\[y=ae^{bx}+ce^{dx} \tag{2}\]  
Exponential fits are often used when the rate of change of a quantity is proportional to the initial amount of the quantity [20; 21]. The Fourier series is a sum of sine and cosine functions that describes a periodic signal. It is represented in either the trigonometric form or the exponential form [21]. \[y=a_{0}+\sum_{i=1}^{n}a_{i}cos(iwx)+b_{i}sin(iwx) \tag{3}\]  
where \(a_{0}\) models a constant (intercept) term in the data and is associated with the \(i=0\) cosine term, \(w\) is the fundamental frequency of the signal, \(n\) is the number of terms (harmonics) in the series, and \(1\leq n\leq 8\). These three models are commonly used in curve fitting, and can balance the smoothness of the curve and the accuracy of the data fitting. The goodness of fit \(R^{2}\) was used to evaluate the fitting error of the constitutive model, which is defined as  
\[R^{2}=1-SS_{err}/SS_{tot} \tag{4}\]\[SS_{tot} =\sum_{i=1}^{N}\bigl{(}P_{i}-\overline{P}\bigr{)}^{2} \tag{5}\] \[SS_{err} =\sum_{i=1}^{N}\bigl{(}\hat{P}_{i}-\overline{P}_{i}\bigr{)}^{2} \tag{6}\]  
where \(SS_{err}\) denotes the residual error, \(SS_{tot}\) deviation, \(P_{i}\) test value, \(\overline{P}\) average value of \(P_{i}\), \(\hat{P}_{i}\) model fitting value, and \(N\) the number of test data points participating in the fitting. The larger the \(R^{2}\), the higher the goodness of fit and the smaller the error. The form of polynomial fitting is  
\[f_{1}(T)=p_{1}T^{3}+p_{2}T^{2}+p_{3}T+p_{4} \tag{7}\]  
The form of exponential fitting is  
\[f_{2}(T)\ =\ ae^{(-bT)}+c \tag{8}\]  
The form of Fourier fitting is  
\[f_{3}(T)\ =a_{0}\ +\ a_{1}cos(Tw)\ +\ b_{1}sin(Tw) \tag{9}\]  
The fitting curve parameters of the three fitting methods for the infield and outfield test data are shown in Tables 1-3, and the goodness of fit is shown in Table 4 and Figure 7. The fitting curves of the springback and elongation tests of the two materials based on the three fitting methods are shown in \[y=ae^{bx}+ce^{dx} \tag{2}\]0