# Water Quality Evaluation and Prediction Based on a Combined Model
## 4 Results and Discussion
### Water Quality Prediction Model  
#### 4.2.1 Water Quality Prediction of Lanzhou Xincheng Bridge Section  
For prediction with the ARIMA model, we used E-views10 software, which is created by IHS Global Inc in the State of California, United States. An original sequence diagram was generated to intuitively judge whether the data sequence was stable, as shown in Figure 7.  
In Figure 7, the \(x\)-axis shows the time in months, and the \(y\)-axis shows dissolved oxygen in milligrams per liter. The series in the figure does not indicate an obvious trend or seasonality, so it was preliminarily judged to be stationary series [35]. For further confirmation, an ADF unit root test was performed. The results show that the ADF test statistic is less than the critical value at levels of 1%, 5% and 10%, so the dissolved oxygen series is stationary and does not require differential processing [36]. An autocorrelation diagram and partial autocorrelation diagram were generated for model order determination, as shown in Figure 8.  
As shown in Figure 8, the trailing and censoring characteristics of the autocorrelation function and partial autocorrelation function are very obvious in the dissolved oxygen data series. The decay of the autocorrelation function is very slow, which is a typical characteristic of trailing. However, the partial autocorrelation function rapidly decays to within two times the standard deviation after two steps, so the AR(2) model is determined. The estimation results of the model are shown in Table 5.  
The R\({}^{2}\) of the model reached 79.34%, and an adaptability test was conducted on the AR(2) model was conducted, i.e., a white noise test of the residuals, as shown in Figure 9[37]:  
As shown in Figure 9, the autocorrelation and partial autocorrelation functions of the residual sequence both fall within two standard deviations, and the P value is significantly greater than 0.05. Therefore, it is a white noise sequence, indicating that the useful information in the original sequence has been extracted and the model has passed the adaptability test. Then, the AR(2) model established in this paper is used to predict the test data. A comparison between the predicted value and the real value is shown in Figure 10.  
Figure 7: Original dissolved oxygen values. Figure 8: Autocorrelation and partial autocorrelation of dissolved oxygen. \begin{table} \begin{tabular}{c c c c c} \hline \hline
**Variable** & **Coefficient** & **Standard Error** & **T Statistic** & \(p\)**Value** \\ \hline C & 8.16 & 0.20 & 40.13 & \textless{}0.001 \\ AR(1) & 0.78 & 0.04 & 20.46 & \textless{}0.001 \\ AR(2) & 0.11 & 0.04 & 2.99 & \textless{}0.001 \\ \hline \hline \end{tabular} 
\begin{tabular}{c c c c c} \hline \hline Autocorrelation & Partial Correlation & AC & PAC & Q-Stat & Prob \\ \hline \hline \multirow{4}{*}{\(\|\)\(\|\)\(\|\)} & \multirow{4}{*}{\(\|\)\(\|\)} & 1 -0.006 & -0.006 & 0.0236 & 0.878 \\  & & 2 -0.052 & -0.052 & 1.8499 & 0.397 \\  & & 3 -0.074 & -0.075 & 5.5660 & 0  
In Figure 10, the \(x\)-axis represents time, the \(y\)-axis represents the concentration of DO, the blue line represents the predicted value of the ARIMA model and the orange line represents the real value. We can intuitively observe that the coincidence degree of the two lines is relatively high, which indicates that the prediction effect of the ARIMA model is strong. Before using wavelet neural network for prediction, the irrelevant noise in the data is removed. The empirical mode decomposition (EMD) of the dissolved oxygen sequence was carried out by MATLAB, as shown in Figure 11:  
The original data series were decomposed into eight intrinsic mode functions (IMFs) and a residual sequence. The frequency decreases from IMF1 to IMF8, and each IMF has its own unique frequency and cycle [38]. Due to the high-frequency property of IMF1 and its chaotic fluctuation trend, it was removed on the basis of the original data sequence too obtain a new sequence after denoising.