# Research on Price Prediction of Construction Materials Based on VMD-SSA-LSTM
## 5 Model Application and Results Discussion
### Results Discussion  
To verify the superiority of the VMD-SSA-LSTM material price prediction model proposed in this paper, as well as the necessity of VMD decomposition and the effectiveness of SSA in optimizing parameters, and to further clarify that the proposed method has significant improvement and enhancement in predicting CMP it is necessary to select the historical price information data of threaded steel bars in CMP as the experimental sample, and use the BP, LSTM, VMD-LSTM, and VMD-SSA-LSTM models for prediction. Then, the researcher should compare the four prediction models. Figure 9 shows the comparison of the prediction effects of the four models. Figure 10a is an error curve graph of the prediction results of the four models, and Figure 10b is the error box plot of the prediction results of the four models. Table 4 shows the comparison of the evaluation index results of all models in the performance of the same experimental sample.  
Figure 10: The comparison of prediction results errors of four models. (**a**) The comparison of standard errors of the 4 prediction models’ curve plot. (**b**) Box line plots of standard error comparisons for each prediction model, representing the distribution of model prediction data.  
Figure 9: Comparison of prediction results of four models.  
From the analysis of the chart and table above, the locally enlarged view indicated by the arrow in Figure 9 shows that all four models exhibit relatively good fitting effects, with the VMD-SSA-LSTM model performing the best. The error curve in Figure 10 indicates that the prediction error range for those models is within [\(-\)0.6, 0.4]. Additionally, the error box plot in Figure 10 reveals that the BP model has the largest error and fluctuates significantly, while the prediction error of the VMD-SSA-LSTM model is the smallest, demonstrating a stable curve trend that indicates high stability. For the LSTM model (i.e., VMD-SSA-LSTM) optimized by VMD decomposition and SSA parameters, the \(RMSE\) and \(MAE\) are reduced by 2.68% and 1.82%, respectively, compared to the VMD-LSTM model; by 2.99% and \(-\)2.57%, respectively, compared to the single LSTM model; and by 41.22% and 45%, respectively, compared to the BP model. Furthermore, the \(R^{2}\) values increase by 0.196%, 0.217%, and 6.566%, respectively. This demonstrates that the VMD-SSA-LSTM model effectively improves prediction accuracy by enhancing data quality through VMD and optimizing LSTM parameters using SSA.  
The empirical results demonstrate that the VMD-SSA-LSTM model achieves significant improvements in prediction accuracy over traditional models. Key findings include the following:  
* The model's RMSE is reduced by 41.22% compared to the BP model and by 2.99% compared to the standalone LSTM model, indicating superior performance in capturing complex price patterns.
* The R\({}^{2}\) value for the VMD-SSA-LSTM model is 96.532%, showcasing its robustness in fitting observed data.  
From a practical perspective, these results highlight the model's utility in real-world scenarios. For instance, construction managers can leverage the improved predictive accuracy to prepare more precise budgets and mitigate financial risks associated with material price volatility. Moreover, the model's ability to process noisy data ensures reliability across diverse market conditions, making it a valuable tool for strategic planning. Unlike conventional models, which often struggle with noisy and nonlinear data, the VMD-SSA-LSTM framework effectively addresses these challenges. The integration of VMD enhances data quality by isolating noise, while SSA optimizes LSTM's learning process, leading to more accurate and stable predictions. These improvements align with previous findings on the benefits of hybrid models but extend their application to the underexplored domain of CMP forecasting.