# Research on Slope Stability Prediction Based on MC-BKA-MLP Mixed Model
## 4 (M-C)-BKA-MLP Prediction Model
### Comparison of the Results of Different Models  
To further evaluate and benchmark the performance of the prediction models, the BKA-MLP model was compared against several established models: Random Forest Regression (RF), Support Vector Machine Regression (SVR), Long Short-Term Memory Network (LSTM), Extreme Learning Machine (ELM), and Backpropagation Neural Network (BP). The detailed performance metrics for each model are presented in Table 4. We ranked the four key performance indicators for each model and generated a radar chart to visualize the rankings of the six models, as illustrated in Figure 6. Among them, the MAE and RMSE of the BKA-MLP model are the smallest, R\({}^{2}\) is the largest, and the MBE value is only 0.04%, although not the lowest, so the model has the best fitting effect and the highest feasibility. Second, the BP neural network prediction model, R\({}^{2}\), and RMSE ranked second, MAE and MBE ranked third among the four indexes, and the prediction performance was slightly weaker than that of BKA-MLP. The RF prediction model and ELM prediction model have moderate ranking in the test set, average performance, and feasibility. Among all models, the LSTM and SVR prediction models have the highest MAE, MBE, and RMSE values, along with the lowest R\({}^{2}\) values. Among these models, the error of the LSTM model is approximately one order of magnitude greater than that of the others. This discrepancy arises because the dataset primarily consists of independently distributed samples lacking pronounced time-series characteristics. Therefore, these two models have the worst performance and the lowest feasibility in predicting slope stability.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Prediction Model** & **MAE** & **MBE** & **RMSE** & **R\({}^{2}\)** & **Rank Sum** \\ \hline BKA-MLP & 0.012378 & 0.0004031 & 0.024135 & 0.94993 & 4 \\ RF & 0.020142 & 0.0024439 & 0.047163 & 0.90096 & 12 \\ SVR & 0.0253 & \(-\)0.0130 & 0.0884 & 0.6637 & 21 \\ LSTM & 0.21707 & 0.0077602 & 0.37596 & 0.84635 & 20 \\ ELM & 0.019913 & \(-\)0.0083463 & 0.041278 & 0.88122 & 13 \\ BP & 0.027787 & 0.012915 & 0.039354 & 0.92487 & 14 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results of different prediction models.  
Figure 6: Each model is ranked by four groups of indicators.  
After preliminary screening, the SVR model with poor performance and the LSTM model were abandoned, and the results of the other four models with good performance on the test set were compared, as shown in Figure 7. As can be seen from the figure, the predicted value of the BKA-MLP model is the best fit with the true value, and the difference is the smallest, which indicates that the BKA-MLP prediction model has the best fitting effect and the best prediction performance. The RF model and ELM model have higher predicted values in some samples. The ELM model even has a negative safety factor when predicting data points of sample number 60, which is obviously not in line with reality. The BP neural network performed well on some samples, but the predicted value fluctuated significantly between samples 60 and 120 and was less stable than other models.