## 5 Research and Application of Prediction Results  
The blast furnace permeability index data set selected by feature parameters was sorted by time series, and the wavelet neural network (WNN) was applied for prediction to construct the blast furnace permeability index prediction model. The prediction results are shown in Figure 10. The BP neural network (BP) prediction model, the particle swarm optimization BP neural network (PSO-BP) prediction model, and the Xgboost prediction model were also selected for simulation prediction, and the prediction results obtained were compared with those of the wavelet neural network using evaluation indices. Upon a thorough analysis of Figure 10, it becomes evident that the prediction results obtained from the wavelet neural network model closely align with the actual values collected. The model demonstrates an impressive accuracy of 95.71% within an error range of \(\pm\)0.1, making it highly suitable for practical applications in production. Consequently, in this paper, the wavelet neural network model is used to predict the air permeability index of the blast furnace, which can predict the air permeability index of the blast furnace in advance and ensure the smooth operation of the blast furnace. Figure 10: Wavelet neural network model blast furnace permeability index prediction graph. Figure 9: Flow chart of wavelet neural network prediction steps. Four commonly used evaluation indexes, including the RMES (root mean square error), MAE (mean absolute error), MAPE (mean absolute percentage error), and accuracy (model accuracy, error of \(\pm\)0.1), were selected to compare the performance of the above four prediction models and present an intuitive evaluation of the prediction results. The calculation formulae are shown in Equations (10)-(13) [27]:  
\[RMSE=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}}{\left(\hat{y_{i}}-y_{i}\right)^{2}}} \tag{10}\]  
\[MAE=\frac{1}{n}{\sum_{i=1}^{n}}{\left|\hat{y_{i}}-y_{i}\right|} \tag{11}\]  
\[MAPE=\frac{1}{n}{\sum_{i=1}^{n}}{\left|\frac{\hat{y_{i}}-y_{i}}{y_{i}}\right|} \tag{12}\]  
\[ACCURACY=\frac{\dot{n}}{n} \tag{13}\]  
where: \(n\) denotes the total number of samples; \(\hat{y_{i}}\) denotes the predicted value; \(y_{i}\) denotes the true value; and \(\dot{n}\) denotes the number of predicted values within the error allowance. The RMES, MAE, MAPE, and accuracy of the above four prediction models were calculated based on the blast furnace permeability index simulation prediction results as shown in Table 3.  
The comprehensive comparison table above concludes that the wavelet neural network blast furnace permeability index prediction model has the best overall performance and the highest prediction accuracy, and the model accuracy reaches 95.71% at an accuracy error of \(\pm\)0.1. Therefore, the overall performance of the wavelet neural network in predicting the blast furnace permeability index is better than that of the other three models. This wavelet neural network blast furnace permeability index prediction model was put into the actual production of a #2 blast furnace in a steel enterprise. The data set of key parameters in a certain time period was collected, the data of the required characteristic parameters were selected for blast furnace permeability index prediction, and the predicted values were compared to the actual production values, as illustrated in Figure 11.  
By comparing the predicted values of the blast furnace permeability index with the real-time production values, the efficacy of the prediction algorithm is further validated. The utilization of the prediction model's data in the blast furnace production process enables prompt assessments of the furnace's operational conditions, ensuring its smooth operation. This validation from the perspective of actual blast furnace production confirms the effectiveness of the blast furnace permeability index prediction model.