## 5 Experimental Results and Analysis
### Comparative Experiments  
The proposed CFSFDP-E algorithm takes local density, distance and residual energy into consideration to get the appropriate number of clusters and choose suitable cluster heads. Based on the experiments above, we choose \(E_{f}=E^{2}\) as the form of energy. The normalization of density-energy \(\omega\) and \(\gamma\) can be calculated by \(\omega^{\prime}_{i}(r)=\rho^{\prime}_{i}(r)E_{f,i}^{\prime}(r)\), \(\gamma^{\prime}_{i}(r)=\rho^{\prime}_{i}(r)E_{f,i}^{\prime}(r)\delta^{\prime} _{i}(r)\) for each node in the \(r\) round, respectively. The dynamic threshold is set to \(\eta(r)=2\omega^{\prime}_{\max}(r)t_{dc}(r)\). In order to demonstrate the performance of CFSFDP-E algorithm, several protocols will be compared in this part. The results shown below are all the average values of 20 independent experiments. Figure 6 shows the network lifetime comparison of LEACH-C [10], PEGASIS [11], SEP [12] and CFSFDP-E. The first three protocols are famous and classical. In SEP protocol, there are a percentage of numbers of sensor nodes is equipped with additional energy resources. In this experiment, we set 10 nodes with double energy compared to normal nodes. The area size, number of nodes, location of sink node, length of data packets and control packets and other basic simulation parameters are all the same as those in Table 4.  
From Figure 6, we can also observe that the FND of CFSFDP-E is larger than that of the other protocols, which means it can keep all the nodes alive in most of rounds and the death for first node is  
Figure 5: Distributions of the number of cluster heads in CFSFDP-E and LEACH. (**a**) distribution of the number cluster heads in CFSFDP-E. (**b**) distribution of the number of cluster heads in LEACH. Figure 6: Network lifetime comparison of LEACH-C, PEGASIS, SEP and CFSFDP-E.  
later. Experiments prove that the performance of CFSFDP-E algorithm is better than these classical protocols, indicating that the proposed approach can balance the energy consumption of the network. The protocols of ALEACH [17], C-LEACH [18] and K-LEACH [19] are improvements based on LEACH. They optimize the clustering division and cluster heads selection. ALEACH, C-LEACH and K-LEACH select nodes with high residual energy as cluster heads with different forms of threshold \(T(i)\) shown in (14). ALEACH takes nodes' residual energy and maximum energy into consideration while C-LEACH and K-LEACH considers residual energy and initial energy with different forms to choose clusters heads. Figure 7 is the result for these four protocols and CFSFDP-E algorithm with same parameters in the same experimental scenario shown in Table 4.  
It is obvious that the death of first node of the three improved protocols based on LEACH are all less than 800 rounds, while the FND of CFSFDP-E is over 1000. When first node dies, the residual energy of all nodes will be exhausted in hundreds of rounds. Table 9 and Figure 8 show a network lifetime comparison of the proposed CFSFDP-E, KM-LEACH [3], DBCH [20] and EESCA [21]. KM-LEACH (KMEANS-LEACH) uses the k-means clustering algorithm to form clusters and chooses cluster heads which are the nearest to the centers. The Distance-Based Cluster Head (DBCH) algorithm establishes a new threshold which includes the node energy and distance between node and sink node and distance between cluster head and sink node for measuring the threshold value. The Energy Efficient Structured Clustering Algorithm (EESCA) is a hybrid cluster head selection method with parameter location centrality and nodes' residual energy on the fixed clusters [21]. The area of deployment is exactly divided into four regions based on coordinates. Initially, the nodes which have the minimum average communication distance with other nodes are selected as cluster heads and remain their role until the cluster heads lose its 50% of their energy. This process continues until all the nodes in the cluster lose 50% of their total energy.