## 4 BP Neural Network and Pearson Correlation Analysis
### Computation Analysis
#### 4.2.1 Evaluation of Working Conditions
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Evaluation Indicators** & **Data** & **Remarks** \\ \hline \multirow{6}{*}{Working condition 7} & Sum of Square Errors, \(\mathrm{E_{SSE}}\) & 5.5945\(\cdot 10^{-5}\) & Fit between predicted and actual values \\ \cline{2-4}  & Mean Absolute Error, \(\mathrm{E_{MAE}}\) & 0.00081209 & Average absolute difference between the predicted and actual values \\ \cline{2-4}  & Mean Absolute Percentage Error, \(\mathrm{E_{MAP}}\) & 0.004057 & Error across datasets with varying magnitudes \\ \cline{2-4}  & Mean Square Error, \(\mathrm{E_{MSE}}\) & 1.1189\(\cdot 10^{-6}\) & Mean square error of prediction discrepancies \\ \cline{2-4}  & Root Mean Square Error, \(\mathrm{E_{RMSE}}\) & 0.0010578 & The square root of the mean square differences between predicted and actual values \\ \hline \multirow{6}{*}{Working condition 8} & Sum of Square Errors, \(\mathrm{E_{SSE}}\) & 0.00635 & Fit between predicted and actual values \\ \cline{2-4}  & Mean Absolute Error, \(\mathrm{E_{MAE}}\) & 0.0095017 & Average absolute difference between the predicted and actual values \\ \cline{2-4}  & Mean Absolute Percentage Error, \(\mathrm{E_{MAP}}\) & 0.011281 & Error across datasets with varying magnitudes \\ \cline{2-4}  & Mean Square Error, \(\mathrm{E_{MSE}}\) & 0.00010583 & Mean square error of prediction discrepancies \\ \cline{2-4}  & Root Mean Square Error, \(\mathrm{E_{RMSE}}\) & 0.010288 & The square root of the mean square differences between predicted and actual values \\ \hline \multirow{6}{*}{Working condition 9} & Sum of Square Errors, \(\mathrm{E_{SSE}}\) & 0.00030943 & Fit between predicted and actual values \\ \cline{2-4}  & Mean Absolute Error, \(\mathrm{E_{MAE}}\) & 0.0024449 & Average absolute difference between the predicted and actual values \\ \cline{2-4}  & Mean Absolute Percentage Error, \(\mathrm{E_{MAP}}\) & 0.0061119 & Error across datasets with varying magnitudes \\ \cline{2-4}  & Mean Square Error, \(\mathrm{E_{MSE}}\) & 6.1887\(\cdot 10^{-6}\) & Mean square error of prediction discrepancies \\ \cline{2-4}  & Root Mean Square Error, \(\mathrm{E_{RMSE}}\) & 0.0024877 & The square root of the mean square differences between predicted and actual values \\ \hline \multirow{6}{*}{Working condition 10} & Sum of Square Errors, \(\mathrm{E_{SSE}}\) & 7.5391\(\cdot 10^{-5}\) & Fit between predicted and actual values \\ \cline{2-4}  & Mean Absolute Error, \(\mathrm{E_{MAE}}\) & 0.0011243 & Average absolute difference between the predicted and actual values \\ \cline{2-4}  & Mean Absolute Percentage Error, \(\mathrm{E_{MAP}}\) & 0.0028055 & Error across datasets with varying magnitudes \\ \cline{2-4}  & Mean Square Error, \(\mathrm{E_{MSE}}\) & 1.5078\(\cdot 10^{-6}\) & Mean square error of prediction discrepancies \\ \cline{2-4}  & Root Mean Square Error, \  
As detailed in the table above, the metrics E\({}_{\text{SSE}}\), E\({}_{\text{MAE}}\), E\({}_{\text{MAP}}\), E\({}_{\text{MSE}}\), and E\({}_{\text{RMSE}}\) for the orthogonal experimental working conditions 1-18 demonstrate the fidelity of the BPNN