## 4 Process and Result
### Prediction of the Chemical Content of Glass before Weathering Based on the ARIMA-LSTM Model  
By solving 4.1, we obtained the results of the relationship between glass weathering and its chemical composition, and using this relationship, we screened 14 chemical elements in two respective types, high potassium and lead-barium, respectively. For high potassium glasses, we have chosen to retain both SiO\({}_{2}\) and K\({}_{2}\)O chemical components. For lead-barium glasses, we chose to retain three chemical components: SiO\({}_{2}\), PbO, and P\({}_{2}\)O\({}_{5}\); all of them have relatively complete data and have strong correlations for modeling analysis. In order to make the model better identify the patterns in the data, the outliers with large deviations are first eliminated. SPSS 24 software was used to detect three abnormal data values with an additive or transient state, and the existence of such outliers would lead to accidental results in the model, leading to wrong conclusions. Taking the SiO\({}_{2}\) content of high potassium glass and lead-barium glass as examples, the outliers of both are shown in Table 2.  
Through the analysis and calculation in Matlab and SPSS, we tested and fitted the data values of all the chemical composition contents changing with the time series and established the ARIMA-LSTM prediction curve model. We found that the parameters of ARIMA(2,1,0)-LSTM can obtain the maximum likelihood value of the model, and the normalized BIC [54] values of 3.160 and 4.160 for the SiO\({}_{2}\) component content in high potassium glass and lead-barium glass, for example, are the smallest values among the parameters. In addition, the smooth R\({}^{2}\) values of the model are 0.960 and 0.934, both close to 1, and both p-values are 0.000, both less than 0.05, so it can be considered that the results of the model are significantly reasonable and can fit well with the prediction model (Table 3). After the initial completion of the estimated time series model based on the chemical composition content, a white noise test of the residuals is required. If the residuals are white noise, then it can indicate that the selected model can identify the laws of the time series data, that is, the model is acceptable; if the residuals are not white noise, then it means that there is still some information not identified; at this time, the model parameters need to be revised to continue to identify this part of the information. The study used [PERSON]'s Q test to determine whether the residuals are white noise [55; 56]: \begin{table}
\begin{tabular}{c c c c c c} \hline
**Relic Number** & **Outlier Type** & **Estimates** & **S.E.** & **t** & **Significance** \\ \hline High potassium 02 & Additive & 23.850 & 3.478 & 6.858 & 0.000 \\ \cline{3-6} High potassium 13 & Transient & Magnitude & 16.260 & 3.478 & 4.675 & 0.001 \\ \cline{3-6}  & Decay factor & 0.829 & 0.266 & 3.114 & 0.011 \\ \hline \multirow{3}{*}{Lead barium 05} & \multirow{3}{*}{Transient} & Magnitude & 31.926 & 4.569 & 6.988 & 0.000 \\ \cline{3-6}  & Decay factor & 0.964 & 0.013 & 76.495 & 0.000 \\ \hline \end{tabular}
\end{table} 
Table 2: Outlier of SiO\({}_{2}\) component content. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Type** & **Fitting Statistics** & **Stationary** & **R\({}^{2}\)** & **RMSE** & **MAPE** & **MaxAPE** & **MAE** & **MaxAE** & **Normalized BIC** \\ \hline High potassium glass & 0.960 & 0.960 & 1.330 & 1.411 & 8.842 & 2.177 & 6.130 & 3.160 \\ Lead-barium glass & 0.934 & 0.934 & 1.523 & 2.105 & 10.624 & 4.001 & 11.250 & 4.160 \\ \hline \end{tabular}
\end{table} 
Table 3: Parameters of the ARIMA-LSTM model for SiO\({}_{2}\) component content in two types of glass. Assuming that the residual \(\{\epsilon_{t}\}\) is a white noise sequence, then \(\rho_{s}=\left\{ \begin{array}{ll}1,s=0\\ 0,s\
eq 0\end{array}