Secure and energy-efficient inter- and intra-cluster optimization scheme for smart cities using UAV-assisted wireless sensor networks

Abstract

In recent years, lightweight sensors have become essential for advancing technologies, particularly in wireless sensor networks (WSNs). A persistent challenge in WSNs is maintaining continuous operation while achieving balanced energy consumption across sensor nodes. Wireless mobile energy transmitters (WMETs) provide a promising solution by wirelessly recharging sensor nodes. However, most existing approaches fail to optimize WMET charging locations, resulting in energy imbalance and reduced network coverage. Furthermore, conventional clustering systems often overlook both inter- and intra-cluster energy balancing, degrading overall network performance. Security issues, such as insufficient data encryption, further exacerbate these challenges, leaving WSNs vulnerable to attacks. To address these gaps, we propose the secure and energy-efficient inter- and intra-cluster optimization scheme (SEI2), a novel WMET-based framework that ensures balanced energy utilization among cluster heads (CHs) and member nodes (MNs) while securing data transmission. The SEI2 system incorporates UAVs to dynamically recharge sensor nodes, determining optimal charging locations within clusters to maximize energy efficiency. Additionally, robust data encryption mechanisms are applied at both the CH and base station (BS) levels to safeguard transmitted data. Key parameters considered include node energy levels, data transmission rates, optimal charging locations, and encryption overhead. Experimental evaluations demonstrate that SEI2 improves network lifetime by 35%, reduces compromised data packets by 19%, enhances coverage time by 15%, and significantly minimizes energy variance by 62% for CHs and 88% for MNs. These results highlight SEI2’s potential as a comprehensive solution for extending WSN lifetimes, enhancing energy efficiency, and strengthening data security, making it particularly suitable for smart city applications.

Introduction

A smart city is defined as a network of Internet of Things (IoT)-based systems that transform traditional services into smart, efficient, and sustainable ones. In such systems, WSNs play a vital role by enabling the collection and transmission of data from sensor nodes deployed throughout the city. These sensor nodes, however, are constrained by their limited energy capacity, which directly impacts the network’s operational lifetime ¹. Ensuring energy efficiency in these nodes is crucial, and significant research has focused on improving energy efficiency in sensor nodes ^1–4.

One of the most effective strategies to enhance energy efficiency in WSNs is clustering. Clustering divides the network into groups of sensor nodes, with each group led by a CH responsible for aggregating and forwarding data to a BS ^5,6. While clustering improves energy efficiency by reducing redundant transmissions, it also introduces new challenges. The most significant of these challenges is unbalanced energy consumption, both within clusters (intra-cluster) and between clusters (inter-cluster). Unequal energy depletion among CHs and MNs can lead to early node failures and reduced overall network performance ^7–12. In inter-cluster communication, CHs located closer to the BS tend to handle more data relay traffic, leading to faster energy depletion. Similarly, in intra-cluster communication, MNs that are farther from the CH consume more energy in direct data transmission, further exacerbating the problem of uneven energy consumption. This imbalance can lead to energy holes, premature node failures, and coverage gaps, significantly reducing the network’s lifespan ^13,14.

While various approaches have been proposed to address energy balancing in WSNs, several gaps remain unaddressed. For instance, many studies have focused either on inter-cluster or intra-cluster energy balancing in isolation, failing to address the problem comprehensively. Existing methods that employ multi-hop data transmission or mobile base stations ^12,15–18 often overlook the impact of uneven energy consumption on both CHs and MNs. Additionally, while wireless energy transfer (WET) has gained attention as a solution to replenish energy in sensor nodes, most WET-based systems fail to optimize charging locations within clusters, leading to suboptimal network performance and reduced coverage time ^19–26.

Moreover, existing works focus primarily on extending network lifetime through energy optimization but give insufficient attention to data security, leaving the network vulnerable to cyber threats. Security in WSNs is crucial, especially in smart city applications where sensitive data is transmitted. In resource-constrained environments like WSNs, encryption mechanisms are often computationally expensive, leading to high overheads on CHs and BSs. Thus, many existing solutions either compromise on security or energy efficiency, which can expose the network to eavesdropping, jamming, or node compromise attacks ^5,6,27–29.

To overcome these challenges, this paper proposes a secure and energy-efficient inter- and intra-cluster optimization scheme (SEI2), which addresses both energy efficiency and security in WSNs using WMETs. The key innovation of the SEI2 system lies in its ability to achieve balanced energy consumption across both CHs and MNs while ensuring the security of data transmissions through encryption. The SEI2 system leverages unmanned aerial vehicles (UAVs) equipped with WMETs to wirelessly recharge sensor nodes. By optimizing UAV charging locations within each cluster, the system balances energy consumption among MNs and CHs, ensuring no node is overly drained. Unlike previous WET-based solutions that charge only CHs or operate from a fixed location, SEI2 allows UAVs to visit multiple charging points within clusters, further improving energy distribution. Additionally, the system introduces a time constraint for charging, optimizing UAV schedules to prevent overcharging or undercharging of nodes. In terms of security, SEI2 employs a collaborative data encryption approach. Data is encrypted at both the CH and BS levels, ensuring confidentiality and integrity as data travels across the network. This collaborative encryption mechanism distributes security tasks among ground devices (BS, CHs, and MNs), reducing the computational burden on any single node and improving overall network resilience to attacks.

The SEI2 system provides the following key contributions:

• Energy balancing The system addresses both inter- and intra-cluster energy balancing using WMETs, extending the network’s operational lifetime. The WMET charges both CHs and MNs at multiple locations within a cluster, reducing energy variance and ensuring even energy consumption.

• Optimized charging locations By allowing the UAV to move within clusters and optimize charging locations, SEI2 enhances energy efficiency compared to traditional WET-based approaches that use static charging positions.

• Time-constrained charging The system introduces a time constraint in the charging schedule to optimize energy distribution among MNs and CHs, preventing imbalances in energy consumption.

• Data security The SEI2 model integrates secure data transmission by employing encryption at both CH and BS levels, ensuring that collected data remains protected from potential cyber threats.

• Smart city applications The SEI2 system is tailored for smart city environments where energy efficiency and security are critical, particularly in applications such as environmental monitoring, disaster management, and precision agriculture.

The SEI2 system presents a comprehensive solution that addresses the dual challenges of energy imbalance and security in WSNs. By optimizing energy distribution through WMETs and securing data transmission through encryption, the SEI2 system offers improved network lifetime, coverage time, and resilience to cyber threats. This makes it a promising solution for energy-efficient, secure smart city applications, overcoming the limitations of existing approaches.

The remaining section of the paper is organized as follows: Section 2 provides the related works of the research area. The Problem statement and network model are explained in Sections 3 and 4. the proposed model is introduced in Sect. 5. Simulation results, discussion and conclusion are given in Sects. 6, 7, and 8 respectively.

Related work

In recent years, various approaches have been proposed to achieve balanced energy consumption among sensor nodes in wireless sensor networks (WSNs). For instance, ¹² presents inter- and intra-cluster routing protocols utilizing mobile base stations, where the network area is segmented into sectors. The mobile sink traverses these sectors to achieve more balanced energy consumption. Similarly, ¹⁵ introduces a three-layer framework combining joint rate-aware fuzzy clustering with stable sensor association to enhance resource utilization and energy balancing. This framework addresses load balancing, resource allocation, congestion management, and energy consumption.

In ¹⁶, a joint data collection and recharging scheme is proposed, where a mobile agent simultaneously collects data and transfers energy to nodes. This scheme consists of two steps: constructing clusters to ensure balanced energy consumption among cluster heads (CHs), and scheduling the mobile agent to mitigate charging delays. A location-less energy-efficient algorithm in ¹⁷ aims to balance traffic load among nodes by creating clusters that avoid overburdening nodes closer to gateways, thus achieving a more balanced traffic load.

The energy balanced improved soft-k-means algorithm presented in ¹⁸ focuses on selecting optimal initial cluster centers and creating clusters with an equal number of memberships. Nodes on the edges are reassigned to low-density clusters based on membership probabilities, and a multi-CH scheme is used to balance the traffic load among CHs. Despite these advancements, there remains a gap in addressing the joint inter- and intra-cluster energy balancing issues, which affects overall network performance.

Wireless power transmission (WPT) technology has garnered significant attention for its potential to enhance energy management in WSNs. In ³⁰, a collaborative recharging technique is introduced to minimize charging latency and improve charging throughput by deploying local chargers. Similarly, ³¹ presents a cooperative wireless power transfer approach that aims to maximize the operation time of multi-hop networks through optimization of charging time for each node. In ³², a partial charge scheduling-based approach is proposed to prolong sensor node operation and network lifetime by prioritizing nodes based on their contribution to charging tasks.

In ²⁵, two wireless mobile energy transmitters (WMETs) are used to separately charge CHs and MNs, optimizing their travel paths to minimize energy variance among MNs and balance CH energy. ³³ employs a WET-enabled mobile sink to enhance CH energy saving and balance MN energy. This approach adjusts MN energy consumption to address hotspots around CHs and selects MNs with minimal remaining energy as CHs in subsequent rounds.

The annulus-based energy balanced data collection (AEBDC) approach in ³⁴ aims to mitigate energy holes around the base station (BS) by assigning a wireless charging vehicle to each layer to periodically recharge CHs and candidate CHs, thereby enhancing energy efficiency and minimizing recharging costs. However, many WMET-based studies have not adequately addressed the joint unbalanced energy consumption of MNs and CHs with a single WMET, leading to reduced network performance. Additionally, optimizing WMET charging locations often neglects time limitations, resulting in suboptimal network performance. Furthermore, previous research has not sufficiently considered the joint factors of the number of covered nodes and balanced energy consumption in charging location optimization.

To ensure the security of WSNs, where devices can be jammed, eavesdropped on, or compromised, encryption of exchanged messages is crucial. Recent studies, such as ²⁷, have proposed asymmetric elliptic curve cryptography (ECC) for key generation and a combination of advanced encryption standard (AES) and ECC for data encryption. ²⁸ introduces a decentralized system utilizing blockchain and cryptographic tools to enhance IoT system security, while ²⁹ proposes a path prediction method using Floyd’s algorithm and trust levels for secure and efficient route selection. ⁵ presents an intelligent and secure edge-enabled computing model for sustainable cities, employing deep learning for optimal data routing and integrating distributed hashing with a chaining strategy for enhanced security.

Despite these advancements, many existing schemes impose high network overhead on the base station (BS) or CHs. Collaborative solutions that distribute tasks among the BS, CHs, and MNs increase network efficiency and security. However, a comprehensive solution addressing the mentioned limitations remains lacking.

Problem statement

In recent years, cluster-based approaches have become prevalent in WSNs due to their benefits, including lower energy consumption, reduced load, and extended network lifetime ^35,36. However, these systems often face challenges related to unbalanced energy consumption among nodes, which negatively impacts network lifetime, coverage time, and overall performance ³⁷. While cluster-based approaches have become widespread in WSNs due to their energy-saving benefits, these systems suffer from significant drawbacks that limit their performance and longevity. Specifically, the following key problems exist:

Unbalanced energy consumption among cluster heads (CHs)

In many WSNs, a multi-hop data transfer model is used for communication between clusters. In this model, CHs that are closer to the BS bear a heavier burden, as they must not only manage their own data but also relay traffic from outer clusters. This leads to uneven energy consumption among CHs, causing some CHs to drain their energy faster than others. This phenomenon, known as the "energy hole problem," results in premature network failure, reducing the overall network lifetime. This issue can be mathematically expressed as:

1

Where l and Ni are the length of the data packet and the number of nodes located in the clusters of the ith layer, respectively. Similarly, , , and denote the energy consumed for receiving, aggregating, and transmitting data packets, respectively. Moreover, is the compression ratio. In this study, perfect compression is considered. As a result, the CHs closer to the BS deplete their energy faster than CHs in outer layers, causing early network breakdown and wasting energy from CHs with residual power.

Unbalanced energy consumption among member nodes (MNs)

Within clusters, most intra-cluster routing models use direct data transmission from MNs to the CHs. However, the energy consumption of MNs increases with the distance between them and the CH. This causes MNs farther away from the CH to consume more energy, resulting in unbalanced energy consumption among MNs, which leads to coverage holes when distant MNs die prematurely. This limits the network’s coverage and reduces its operational time. The energy consumption of an MN in a direct transmission model can be expressed as:

2

where is the only variable parameter indicating the distance between MNs and CHs. Based on Eq. (2), there is a direct relationship between the energy consumption of the MNs and their distance to their destinations (the respective CHs). Consequently, the MNs that are farther away from the CHs consume more energy. This unbalanced energy consumption of the MNs leads to coverage holes and reduces the performance of the network.

Security challenges in cluster-based WSNs

In addition to energy consumption issues, data security in clustered WSNs is a critical concern. Wireless communication is vulnerable to attacks such as eavesdropping, jamming, and node compromise. However, most clustering protocols do not provide sufficient data protection. They either impose high overheads on the CHs and BS, or lack robust solutions to prevent intrusions and unauthorized access. This leads to a compromise between network efficiency and security, often leaving the data collected by sensors vulnerable.

Lack of joint solutions for energy balancing and security

Although previous works have proposed solutions to address either energy balancing or data security in WSNs, few have addressed both issues simultaneously. As a result, there is a lack of holistic solutions that can jointly optimize energy efficiency while ensuring secure data transmission in resource-constrained environments.

To overcome these challenges, a collaborative approach is required that balances the energy consumption among CHs and MNs, prevents the formation of energy and coverage holes, and ensures secure communication without overloading the network. The solution must jointly address the following objectives:

1. Energy balancing Minimize the energy disparity among CHs and MNs to enhance the network’s lifetime and coverage.

2. Data security Implement secure data transmission mechanisms that protect against attacks without imposing significant overheads on the network.

3. Optimization of network resources Efficiently manage both energy consumption and data security tasks to prolong network lifetime while maintaining robust performance.

System model and assumptions

As illustrated in ` 1, the network field consists of N rechargeable sensor nodes equipped with GPS, deployed in an uneven or random manner. To facilitate efficient management of the smart city environment, the area is divided into sub-areas, each with a dedicated BS. For energy optimization within each sub-area, a two-dimensional grid-based clustering approach is applied, as shown in Fig. 1. CHs are selected based on their proximity to other nodes and their higher remaining energy ³⁸. This ensures that the CHs chosen are capable of handling the data relaying efficiently, with energy being a critical factor in selection. In the proposed scheme MNs transmit their sensed data directly to their respective CHs. The CHs then forward this data to the BS using a multi-hop data transmission model. Once the data is collected, it is synchronized with cloud storage for further processing. MNs consume energy to transmit data to their respective CHs, while CHs expend energy to aggregate, receive, and transmit data both from within their clusters and from neighboring clusters.

Fig. 1.

Network model.

To achieve inter- and intra-cluster energy balancing, each sub-area is equipped with a UAV that acts as a WMET. The UAV travels between clusters to recharge the batteries of both CHs and MNs wirelessly, ensuring balanced energy consumption across the network. As depicted in Fig. 2, the WMET is powered by solar cells, enabling it to harvest solar energy, while the ground devices are equipped with wireless radio frequency (RF) receiving technology that allows them to receive power wirelessly from the WMET. This architecture not only optimizes energy usage but also prolongs the overall network lifetime by addressing unbalanced energy consumption among nodes in each sub-area..

Fig. 2.

Power energy transmission model.

Secure and energy-efficient inter- and intra-cluster optimization scheme

In this section, we introduce the SEI2 scheme. The SEI2 scheme is designed to address potential threats in data collection and routing between MNs, CHs, and the BS while simultaneously mitigating the occurrence of energy and coverage holes in the network. This dual-focus approach enhances the security, network lifetime, and coverage time of the Wireless Sensor Network (WSN). To achieve these goals, the SEI2 scheme is composed of three key components:

1. Collaborative secure data gathering (CSDG) algorithm This algorithm ensures secure and efficient data transmission from MNs to CHs and from CHs to the BS, protecting against potential cyber threats and minimizing network overhead.

2. Inter-cluster charging time optimization (inter-C2TO) algorithm This algorithm optimizes the charging time of the wireless mobile energy transmitter (WMET) at each cluster to ensure balanced energy consumption across CHs in different clusters, preventing premature energy depletion and network failures.

3. Intra-cluster charge time optimization (intra-CTO) algorithm This algorithm optimizes the charging locations of the WMET within each cluster, focusing on balancing energy consumption among MNs to avoid coverage holes and ensure sustained network performance.

Figure 3 illustrates the overall architecture of the SEI2 scheme, detailing the interaction between these components. The following subsections provide an in-depth explanation of the CSDG, Inter-C2TO, and Intra-CTO algorithms and their roles in achieving balanced energy consumption and enhanced security within the network.

Fig. 3.

SEI2 architecture.

Collaborative secure data gathering algorithm

In this section, we present the security phase for the proposed SEI2 scheme to protect the data from threats. At each time unit, the BS generates key streams with value and a secret code with value from the set of random bits. Then, a new code is created by BS as follows:

3

The BS encrypts the new code using a private key as given and broadcasts it toward CHs. Upon receiving X, the CHs decrypt it from the public key of BS as given .

Furthermore, each CH (jth) generates a secret code with value from the set of random bits and performs Exclusive-OR between received NCBS and generated SCCH as follows:

4

The new CH code is encrypted using a private key as given and broadcasted toward respective MNs. Each MN decrypts the received new code from the public key of ith CH as given .

The MNs perform an encryption on their collected data as Eq. 6 and along with NCCH, MNs forward their collected data to their respective CHs.

5

Where MACID is an authentication code for ith MN. Upon receiving the data, CHs authenticate the entities and re-compute their secret code as following:

6

After successfully verifying the secret code, along with the BS secret code (SCBS) and the CH new code (NCCH), the CHs send their clusters’ data to BS. First, BS authenticates the entities and re-computes a secret code based on the XoR operation between the BS new code and the key streams as follows.

7

After successfully verifying the secret code, BS performs the following decryption to access the received data as following:

8

Afterwards, the received data is transmitted to the cloud storage.

Inter-cluster charging time optimization of WMET algorithm

In multi-hop clustering WSNs, CHs that are closer to the BS need to handle higher traffic load, which deplete their energy faster compared to farther CHs. This situation leads to appear energy holes and waste 90% of energy of the network. To solve this problem, Inter-C2TO attempts to optimize the charging time of WMET at each cluster so that maximized balanced operation time of CHs will be achieved.

In SEI2 , the energy consumption of the CH located at column and row is calculated as follows:

9

Furthermore, the remaining lifetime of CHs located at ith column and jth row can be calculated using the following equation:

10

Where ER denotes the remaining energy level of CH. Based on Eq. (5), the CHs located at the innermost column (i = 1) are known as the critical CHs due to their higher traffic burden. On the other hand, the CHs belonging to the outermost column (i = m) are the safe CHs due to their lower traffic load and longer operation time compared with inner ones. Therefore, the proposed scheme attempts to equalize the remaining lifetime of each CH with the safe CHs.

11

Then,

12

To improve the quality of service, CHs closer to BS have a higher priority to be met by the UAV. Consequently, the UAV moves along a predefined path and stays in each cluster for a limited charging time. To calculate the charging time in each cluster, the UAV is informed about the remaining energy of the safe CHs at the beginning of the charging cycles. Then, it starts to move along clusters and sends a request packet toward the met CH upon arriving at a cluster. CH replies a message consisting of its remaining energy level. Consequently, UAV determines the charging time at the residence CH so that the relation (12) can be established when leaving the cluster. Therefore, the following relation can be concluded:

13

where φ indicates the required energy to achieve balanced remaining operation time of CHs. Consequently, the following equation can be derived:

14

Then, the charging time of UAV at the cluster (i,j) can be determined as follows:

15

Where η denotes the recharging rate of the UAV at each time unit. Accordingly, UAV stays at cluster (i,j) to recharge the battery of CH for a limited τ time.

Intra-Cluster tour optimization of WMET algorithm

In most previous clustering methods, single hop data transmission model is used for communication between MNs and CHs. Based on Eq. (3), an MN consumes energy according to its distance to the destination node. Therefore, the MN farthest from CH consumes its energy earlier than others, resulting in poor environmental monitoring of the dead MN and creating a coverage hole and decreasing the coverage time of the network. The coverage time is defined as the time when the first MN stops its operation due to different reasons.

To overcome this limitation, in this paper, when the UAV arrives at a cluster, it moves along several charging locations within the cluster instead of being static. In other words, the charging time determined in the first algorithm is divided into k charging locations within the cluster. Then, the charging time of the UAV at each charging location will be as follows:

16

UAV stays at each location for ω time unit and recharges the nodes located within its charging range. Then, the received energy level of each MN will be as follows:

17

Where ℇ denotes the received energy level of a node at each time unit, which is calculated as follows:

18

In this paper, the energy transmission model proposed in ³⁹ has been employed to transfer energy from UAV to MNs. In Equation, the P, Gs and Gr denote the transmitted energy level, energy sender and energy receiver, respectively. Likewise, D, η, LP and σ are the distance between energy sender and energy receiver, rectifier efficiency, polarization loss, and the wavelength ⁴⁰.

In the Intra-CTO algorithm, the WMET sends a request packet to the MNs belonging to the residence cluster and asks their remaining energy level upon arriving at the cluster. Then, k charging locations are optimized in such wise that after expiring the charging time at the residence cluster, the minimum variance of the remaining lifetime of MNs is achieved. The remaining lifetime of a MN is calculated as follows:

19

where ER is the remaining energy level and E denotes the energy consumption of a node at each time unit. Let consider L = {L1,L2,…,Lk} is the set of suggested charging locations of UAV, and l = {l1,l2,…,lm} is the set of locations of MNs within the cluster. In the proposed algorithm, first, the distances between nodes and the charging locations need to be determined:

20

If the distance between a MN and a charging location is less than r (d(i,j) ≤ r), then, it will receive energy for a limited ω time and its remaining energy after expiring the charging time at the residence cluster will be:

21

Intra-CTO optimizes the L so that the variance of the remaining lifetime of nodes is minimized as much as possible subject to the CH will be within the charging coverage of UAV in all k charging locations, then the following problem can be formulated:

22

Where LCH denotes the location of CH. After determining the optimal charging locations l = {l1,l2,…,lm}, the UAV moves along locations and stays at each location for a ω time unit to recharge the batteries of the nodes located within its charging range. After expiring charging time (τ), it moves toward the next cluster. Finally, at the end of each charging cycle and expiring the charging time at the last cluster UAV moves toward the charging station to replenish its power supply.

Simulation result

The SEI2 scheme’s performance is evaluated in various network scenarios using numerical simulation experiments in OMNET +  + . The nodes in the experiments regularly generate and send data to the Cluster Heads (CHs), which forward the collected data packets to the Base Station (BS). For the Inter-C2TO algorithm, the simulation area is set to 1000 m × 1000 m with 500 sensor nodes, while the sink is located outside the network field. In contrast, the Intra-CTO algorithm simulation uses a 50 m × 50 m area with 50 Malicious Nodes (MNs). Table 1 summarizes other relevant system parameters.

Table 1.

Simulation parameters.

Parameters	Value
Number of nodes	500
Area of a sub-area	1000 m × 1000 m
Packet size	128 bit
Initial energy of nodes	4 J
Energy dissipated in the op-amp	0.0013e−12
Eelec	50e−9
Speed of WMET	0.5 m/s
Initial Energy of WMET	10 J
Energy replenishment time of WMET	10000 s

Performance evaluation of the collaborative secure data gathering algorithm

The performance of CSDG is assessed against CTOWMC ³⁰ and FEDS ³⁴ under varying numbers of malicious nodes. Figure 4 illustrates the packet delivery ratio for different numbers of malicious nodes. The results indicate that CSDG improves packet delivery compared to other approaches, as it effectively identifies malicious activities and prevents routing performance degradation. Consequently, the CSDG scheme minimizes packet interruptions caused by malicious nodes, thereby enhancing network throughput.

Fig. 4.

Packet delivery ratio versus malicious nodes.

Figure 5 provides a performance evaluation of CSDG compared to other methods under varying malicious nodes. The analysis reveals that CSDG significantly improves data security by reducing the number of compromised packets, due to its secure and consistent routing process. Before forwarding data to the CHs, MNs are authenticated, and once verified, the data is securely transmitted to the BS. CSDG effectively prevents malicious nodes from intercepting or tampering with intelligent data packets.

Fig. 5.

Compromised data packet versus malicious nodes.

Performance evaluation of the inter-cluster charging time optimization algorithm

In this section, the Inter-C2TO algorithm is evaluated and compared with the schemes proposed in ³⁰ and ³⁴ in terms of different evaluation metrics. Figure 6 illustrates the network lifetime against a varying number of nodes. As observed, increasing the number of nodes leads to an increase in the traffic load of CHs coming from the faraway clusters thereby reducing the lifetime of CHs. Likewise, the results show that the Inter-C2TO improves the energy consumption compared to related works among the different number of nodes. This improvement is due to the fact that the load is distributed among CHs sensors. By efficiently distributing the load among the nodes, the energy consumption is significantly reduced and the regeneration and forwarding of data is avoided.

Fig. 6.

Network lifetime.

The variance of the remaining energy of the CHs is shown in Fig. 7. It is obvious that as the number of nodes increases, the traffic load of CHs and the variance of the remaining energy of CHs increases. However, Fig. 7 shows that Inter-C2TO improves the balanced energy consumption of CHs compared to existing approaches. This is because considering the energy of the other CHs when optimizing the charging time of the WMET in each cluster contributes to a significant reduction in the unbalanced energy consumption of the CHs and improved network lifetime.

Fig. 7.

Variance of lifetime of CHs versus number of nodes.

Figure 8 reveals the number of active CHs in three different systems with increasing number of rounds. The goal of this measurement is to show how the proposed algorithm improves the energy savings and network lifetime. As can be observed, Inter-C2TO outperforms the other approaches as it balances the remaining lifetime of the CHs with the safe CHs that have maximum lifetime in the network.

Fig. 8.

Number of alive CHs versus number of nodes.

Figure 9 depicts the computation time of three schemes under different scenarios. Obviously, increasing the number of nodes leads to an increase in the time required to execute the algorithms. Likewise, according to the comparison as depicted in Fig. 9, the proposed inter-C2TO algorithm demonstrates better performance than existing schemes due to moving the WMET along a predefined trajectory among clusters.

Fig. 9.

Computation time versus number of nodes.

Figure 10 illustrates the total traveled trajectory of WMET during a charging cycle against varying network areas with the deployment of 300 nodes. As increasing network area increases the number of clusters, extending the area size leads to an increase in the path traveled by WMET. However, Inter-C2TO achieved higher performance compared to existing schemes, regardless of the increase in the network area. This is due to moving the WMET under a predefined pattern in our proposed Inter-C2TO, which reduces the path length that needs to be passed by WMET.

Fig. 10.

Travelled path versus network area.

Figure 11 shows the system throughput as a function of the number of nodes. In this paper, the system throughput is defined as the effectiveness of the proposed method for balancing the energy of sensor nodes. It is observed that the throughput produced by Inter-C2TO is higher than existing schemes. This is because, in Inter-C2TO algorithm, the charging time of WMET is optimized by balancing the energy consumption of CHs.

Fig. 11.

System throughput of Inter-C2TO VERSUS NUMBER OF NODES.

Performance evaluation of the intra-cluster tour optimization algorithm

The performance of the Intra-CTO algorithm is assessed in this section. Likewise, the results are compared with the schemes proposed in ¹³ and ^41,42 in terms of different evaluation metrics. Figure 12 illustrates the coverage time of the network for different schemes and different number of nodes. As you can see, increasing the number of MNs within a cluster does not affect the network coverage time. Similarly, Intra- CTO improves the performance compared to existing schemes. The reason for the improved coverage time is the movement of the WMET along multiple charging points instead of staying at only one position, which leads to a reduction in the transmission range of the MNs and a reduction in their energy consumption.

Fig. 12.

Coverage time versus number of nodes.

Figure 13 compares the variance of remaining energy of MNs among three different approaches. As can be seen, our proposed scheme outperforms other schemes thanks to utilizing the Intra-CTO algorithm which optimizes the charging locations of WMET using Eq. (17) which leads to balancing the remaining energy of MNs.

Fig. 13.

Variance of energy of MNs versus number of nodes.

Figure 14 depicts the results for the number of alive MNs as time increases. This measurement aims to depict how Intra-CTO enhances the coverage time. According to the evaluation as depicted in Fig. 14, Intra-CTO demonstrates better performance than mobile sink-based and EMSLO schemes due to moving WMET along multiple charging locations that are optimized using the proposed algorithm.

Fig. 14.

Number of dead MNs versus elapsed rounds.

Figure 15 compares the computation time of the proposed Intra-CTO algorithm with the existing schemes. According to Fig. 16, it is obvious that there is no remarkable difference between Intra-CTO and mobile sink-based algorithms. As observed, CTO and mobile sink-based approaches outperform EMSLO due to pre-specifying of the sojourn time of mobile agents in both schemes.

Fig. 15.

Computation time versus number of nodes.

Fig. 16.

System throughput versus number of Nodes.

Figure 16 reveals the system throughout in three approaches under different numbers of MNs. As shown, our proposed scheme achieves better performance thanks to utilizing the Intra-CTO algorithm which optimizes the charging locations of WMET within the cluster to enhance the balanced remaining energy of MNs.

The total travelled path of WMET within a cluster is depicted with respect to different cluster areas in Fig. 17. As can be observed, in our proposed algorithm, WMET traverses a shorter path compared with prior schemes. This is because of considering the constraint presented in Eq. (18), where WMET can only stay at the locations that can cover CH.

Fig. 17.

Intra cluster travelled path versus cluster size.

Discussion

The Secure Energy-Balancing Inter- and Intra-Cluster (SEI2) scheme presented in this paper demonstrates significant improvements in Wireless Sensor Networks (WSNs), particularly in the areas of security, energy efficiency, and network longevity. The SEI2 scheme integrates the Collaborative Secure Data Gathering (CSDG) algorithm, the Inter-Cluster Charging Time Optimization (Inter-C2TO) algorithm, and the Intra-Cluster Tour Optimization (Intra-CTO) algorithm, offering a comprehensive approach to address key challenges in WSNs. This section discusses the implications of these contributions, compares them with existing approaches, and outlines potential areas for future research.

The CSDG algorithm plays a pivotal role in enhancing the security of data transmission within the network. The combination of encryption techniques and authentication protocols ensures the protection of data from MNs to CHs and, ultimately, the BS. This is crucial in WSN environments, where security breaches could compromise sensitive information or disrupt the network’s operational efficiency. Compared to previous solutions, the CSDG algorithm demonstrates improved performance in terms of packet delivery and throughput, even in the presence of malicious nodes. Simulation results show that it outperforms schemes like CTOWMC and FEDS, as it effectively identifies and mitigates security threats. This improvement is largely attributed to the secure routing process that authenticates nodes and prevents packet interception by malicious entities. By ensuring data integrity and minimizing packet losses, CSDG significantly contributes to maintaining the network’s overall performance.

Energy consumption is a critical factor in the design of WSNs, especially in applications like smart cities, where network longevity is a key requirement. The Inter-C2TO algorithm addresses the issue of uneven energy consumption among CHs by optimizing the charging time of the WMET. The algorithm prioritizes CHs that handle higher traffic loads and ensures that their energy consumption is balanced with those located in safer regions of the network. Through efficient energy management, Inter-C2TO enhances the network’s lifetime. The algorithm’s ability to balance the energy consumption of CHs helps prevent energy holes, which are a common issue in clustered WSNs. This balance ensures that no CH is prematurely depleted, which is particularly important in networks where nodes closer to the BS handle more data traffic. As the simulation results reveal, Inter-C2TO extends the network’s operational time compared to previous approaches by distributing the load more evenly among CHs. Additionally, the reduction in the variance of CH lifetimes further indicates that the algorithm successfully mitigates the risk of unbalanced energy depletion.

While Inter-C2TO focuses on balancing energy consumption among CHs, the Intra-CTO algorithm optimizes the charging locations within each cluster to address energy depletion among MNs. By moving the WMET along multiple charging points within a cluster, the algorithm ensures that MNs receive sufficient energy based on their proximity to the CH. This not only reduces the energy consumption of faraway MNs but also extends the network’s coverage time. The performance evaluation of the Intra-CTO algorithm indicates that it enhances the coverage of the network compared to other methods. The ability of the UAV to visit multiple charging locations within a cluster prevents the formation of coverage holes, which occur when MNs run out of energy. Furthermore, the minimization of the variance in the remaining energy of MNs suggests that the algorithm effectively balances energy consumption within the cluster, further extending the network’s lifespan and improving its reliability.

When compared with existing algorithms, such as mobile sink-based approaches and EMSLO, the SEI2 scheme consistently shows better performance in terms of energy efficiency, network lifetime, and coverage. The use of predefined UAV trajectories in Inter-C2TO and the strategic selection of charging points in Intra-CTO contribute to the scheme’s superior performance. The simulation results also highlight the advantage of the SEI2 scheme in terms of computation time, as its optimization processes are more efficient than those of other approaches, even as the number of nodes increases.

Moreover, the integration of both inter- and intra-cluster optimization techniques into a unified scheme allows for a more holistic approach to energy management. The SEI2 scheme not only improves the operational time of CHs but also ensures that MNs remain functional for longer periods, reducing the likelihood of network failures and ensuring sustained performance in smart city applications. While the SEI2 scheme significantly advances the state of energy management and security in WSNs, there are several potential areas for further research. The incorporation of artificial intelligence (AI) into the SEI2 scheme presents an exciting opportunity for future development. AI-driven solutions could enable more dynamic and adaptive energy management, allowing the network to respond to changing conditions in real time. For example, AI could be used to predict energy consumption patterns and optimize UAV paths and charging positions based on the specific needs of the network.

Furthermore, exploring the integration of the SEI2 scheme within more complex and realistic smart city frameworks could provide deeper insights into its effectiveness. By simulating more diverse and large-scale environments, future research could identify additional optimization opportunities and refine the scheme to better handle the complexities of real-world deployments.

The integration of multiple algorithms at the sensor nodes, while beneficial, introduces operational complexity. This complexity could be particularly challenging in real-world deployments involving dense or large-scale WSNs, where the computational and communication overhead at each node could become a limiting factor. As the network size increases, the sensor nodes may struggle to process and manage the additional computational tasks required by the multiple algorithms, potentially leading to increased delays, energy consumption, or even failures in data processing. This issue could be more pronounced in environments with dynamic topologies, node mobility, or external factors such as interference. Future work could explore optimization techniques such as load balancing, data aggregation, or edge computing to reduce the computational burden at the sensor nodes. Additionally, hardware improvements, like incorporating more powerful processing units or low-power chips, could enhance the ability of nodes to handle multiple algorithms efficiently. Adaptive algorithms that can adjust their complexity based on network conditions could also be an area of interest to further reduce operational overhead in large-scale or dense WSNs.

In conclusion, the SEI2 scheme represents a comprehensive solution to the challenges of energy balancing and security in WSNs. By integrating secure data gathering with optimized energy management strategies, it enhances network performance, extends coverage time, and improves the overall efficiency of smart city-based WSNs. The potential for AI-driven advancements further suggests that the SEI2 scheme could continue to evolve, addressing emerging challenges and maximizing its impact in future applications..

Conclusions

In this paper, we introduced the SEI2 scheme to address the challenges of energy balancing and coverage optimization in smart city-based WSNs. The scheme employs a UAV equipped with WET technology, following a predefined mobility pattern, and integrates three key algorithms: Collaborative Secure Data Gathering (CSDG), Inter-Cluster Charging Time Optimization (Inter-C2TO), Intra-Cluster Charge Time Optimization (Intra-CTO) Algorithms. The Collaborative Secure Data Gathering algorithm ensures secure and efficient data transmission between MNs, CHs, and the BS, enhancing both security and operational efficiency. The Inter-Cluster Charging Time Optimization algorithm balances CHs’ operation times by optimizing the UAV’s charging duration in each cluster, while the Charging Position Optimization algorithm strategically determines the UAV’s charging positions to improve MNs’ remaining lifetime and extend network coverage. Key parameters considered in the SEI2 scheme include node energy levels, data transmission rates, charging positions, cluster densities, UAV mobility patterns, encryption overhead, and energy variance metrics. These parameters collectively contribute to the robustness and efficiency of the proposed framework. Simulation results demonstrate that the SEI2 scheme significantly enhances network performance compared to traditional methods, effectively extending network lifetime and improving coverage time through integrated energy balancing and optimized charging strategies. Looking ahead, future work will focus on incorporating artificial intelligence to further enhance the SEI2 scheme. AI can be employed to develop advanced algorithms for dynamic energy management, predictive maintenance, and adaptive optimization of UAV paths and charging positions. Additionally, exploring more realistic frameworks for smart cities and integrating AI-driven solutions could provide deeper insights and further improve network performance. The integration of AI is expected to lead to even more efficient and adaptive WET-based WSNs, addressing emerging challenges and maximizing the potential benefits of the SEI2 scheme. Overall, the SEI2 scheme represents a significant advancement in energy management and coverage optimization for smart city-based WSNs, and future research will build upon this foundation to incorporate AI for enhanced capabilities and performance.

Author contributions

Niayesh Gharaei and Aliaa M. Abdali were responsible for writing the main manuscript text and formulating the overall structure of the paper. Niayesh Gharaei designed and prepared Figures, while both authors contributed to the analysis and interpretation of the results. All authors reviewed and approved the final manuscript.

Data availability

All data generated or analyzed during this study are included in this article.

Competing interests

The authors declare no competing interests.