## 5 Results
### Model Accuracy
Figure 4 shows that the proposed HFL model shows the shortest training time, while FLBM-IoT has the longest, and PPFLB falls in between. The decrease in training time proves that the HFL model is effective when it comes to the large-scale healthcare systems in which the institutions might face some challenges regarding computational resources and may at the same time experience higher latency in real-time decision-making. Privacy preservation is also incorporated in the proposed HFL model which uses LDP, GDP, SMPC, and HE as its methods of privacy preservation. The degree of privacy leakage was assessed using some measures like data fidelity loss, Kullback-Leibler (KL) divergence, and mutual information in order to estimate the vulnerability of the data when used in the training models. The HFL model was able to reduce privacy leakage by 30% compared to the baseline models. It was quantified at 0 for the privacy leakage and 025 for HFL, which is much lower than the 0. The mean values of time domain features for FLBM-IoT were 043 and 0. Patient numbers were similar between groups for PPFLB, 038 as shown in Figure 5. This improvement can be attributed to the multiple layers of privacy-sensitive mechanisms that mask updates at both local and global levels. These results in Figure 5 show that the proposed HFL framework is very useful in minimizing the chances of privacy violation and therefore suits environments that require strong privacy, such as the healthcare domain, where patient privacy is very important. The utility of models and their privacy preservation are two conflicting factors that pose a common problem in federated learning. The proposed Hierarchical Federated Learning (HFL) framework solves this problem by utilizing a Novel Aggregated Gradient Perturbation Mechanism (AGPM). The dynamically adaptive noise addition mechanism controls how much noise is added in the process of updating the gradients so that the result is strong privacy protection with no significant loss of model performance. The success of such a privacy-utility trade-off was considered by considering the model accuracy and privacy leakage together. As illustrated in Figure 5, the proposed HFL model had a model utility score of 84% (compared to the baseline use of resources) and a high classification accuracy score of 97.8%, which is indicated by the green bar. At the same time, it had a very low privacy leakage, around 0.015 \(\pm\) 0.001, as indicated in Figure 4. Comparatively, both the baseline models, FLBM-IoT and PPFLB, showed greater privacy leakages (0.038 and 0.045, respectively) and lower accuracies (91.7% and 89.2%, respectively). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Privacy Method** & **Overhead (\%)** & **Relative Impact** \\ \hline LDP & 3–5\% & Low \\ GDP & 5–7\% & Moderate \\ SMPC & 10–12\% & Noticeable \\ HE & 18–20\% & High \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis of computational overhead by each privacy-preserving technique. Figure 4: Comparison of training time of models. Figure 5: Privacy leakage comparison. More details can be seen in Figure 6, where the utility-privacy trade-off is plotted: the red dots indicate the leakage of privacy, and the blue bars show the accuracy of the model. The HFL model stands in the most preferable position with the highest accuracy and the lowest privacy leakage, which proves its best balance of utility and privacy. This result highlights the effect of the AGPM component, which selectively restricts noise injection, especially in high-dimensional healthcare data, consequently maintaining the predictive potential of the model while protecting patient data. These findings confirm that the suggested HFL framework delivers strong privacy assurances without affecting performance. Figure 6 illustrates the utility-privacy trade-off among the three models: the proposed HFL, FLBM-IoT, and PPFLB.