1 Introduction

The expansion of WSN has made the perspective of communication to the next level and it is also used in various popular applications [1, 2]. The network of WSN is composed of numerous senor nodes with constrained resource and they are instilled with non-researchable batteries. The sensors in the WSN consume more energy during transmission rather than computation. The occurrence ofoverhead in the communication will influence the energy utilization and the reduced overhead decreases the energy consumption that also widens the Life time of the network [3]. The scenario of the network with a huge sensor generally creates a substantial quantity of data. Most of the cases cause complications and high redundancy in the raw data [4]. Hence, an effective design of the protocol is necessary to minimize the redundancy of data and the amount of data transmission.

Data aggregation is a significant paradigm that avoids the redundancy of data and preserves energy [5]. During the process of data aggregation, the sensor node in the sensing field is organized as a tree hierarchy that is rooted at the base station (BS). The node assigned as a non-leaf in the tree will act as an aggregator that fuses the collected data from the child and forwards the aggregated data towards the BS. By this method, aggregated data alone transmitted to the BS, rather than the generated summation of data from every node. Data aggregation can effectively minimize the communication overhead and the lifetime of WSNs are increased [6, 7]. The final decision of every application is determined on the basis of the accuracy result of aggregation and the variation of result gives varied decisions. In the applications of forest fire monitoring and surveillance on the battlefield, such variation in the decision may lead to the critical consequence [8, 9]. Therefore, the accuracy of aggregation is a significant criterion for the data aggregation technique.

The sensor network can alter the people’s way of transmission with the atmosphere and others. The WSN has become an eminent platform for pervasive computing. The sensor network is deployed in most of the personal locations, likely the human body, and house. The effectiveness of data transmission is achieved by a prominent data aggregation scheme. Therefore, data aggregation should address effective data transmission. The atmosphere of application poses a set of constraints in the process of protocol design. The aggregation must be attained with transmission accuracy as high as possible and overhead as low as possible. However, the sensor network has certain limitations on network lifetime and energy constraints [10, 11].

An extensive simulation analysis has been conducted to rectify the limitation using the Trust weighted Secure Data Aggregation algorithm (TESDA) [12]. In the TESDA approach, clustering scheme is incorporated to attain the effectiveness and balances the energy utilization. The TESDA minimizes the overhead and the reduced transmission overhead leads to the collision. The node failure and energy hole issues are rectified using the Optimized Distributed Voronoi-based Collaboration (ODVOC) [13, 14]. The consumption of energy is high and the network lifetime is low in ODVOC protocol. To overcome this issue polydisperse aggregation is used for the data aggregation scheme. The polydisperse aggregation is a population balancing model and aggregation of the node is accomplished by the overlapping spheres. The simulation analysis of the proposed scheme is compared with the existing scheme. The simulation result depicts that the proposed scheme can minimize the overhead and enriches the accuracy of aggregation.

This research article is emphasized as follows: The investigations of aggregation protocol are given in related work section, the methodology of DAOHS-ODVOC- EDGR is given in Sect. 3, the diagrammatical representation of TESDA, ODVOC-EDGR, and DAOHS- ODVOC-EDGR is demonstrated via graph in Sect. 4 and the conclusions, as well as the future suggestions.

2 Related Work

Latha et al. [15] proposed a Trust Assisted- Energy Efficient Aggregation (TA- EEA) approach that enriches the precision of the aggregation process with the constraints like aggregation and reliability. The TA-EEA approach incorporated the congestion control mechanism, energy preservation using duty cycle, and trusted neighbor election scheme for seamless transmission. The utilization of energy was minimized that extended the lifetime of the node. In the context of large scale WSN, the methodology of TA-EEA was failed to attain a better result.

Kaur and Mahajan [16] proposed a hybrid protocol for data aggregation that was a combination of Ant Colony Optimization and Particle Swarm Optimization. This scheme mainly intended to enrich the lifetime of the network and it enriched the dissipation of data by effective energy utilization. ACOPSO utilizes the clustering mechanism for data segregation and the aggregation process was carried by the tree construction process. The sensor network was segmented by clustering and the process may take the time that may lead to data transmission delay.

El Fissaoui et al. [17] projected a data aggregation scheme using a minimum spanning tree (MST) and proposed Mobile Agent Protocol based Energy-aware data aggregation (MAPE). The process of data collection and gathering was attained by an optimal number of mobile agents. The sensor nodes were grouped and the cluster head was elected which in turn attained the data transmission more effective. The MAPE utilized less time to transmit the data and also energy usage is minimum when compared to other aggregation techniques. Gupta et al. [18] discussed the collaborative data processing in WSN where the mobile agent move among the node and the aggregation process has been attained. Through the proposed mechanism bloated state issue was analyzed in mobile agent-based data aggregation technique that minimizes the utilization of energy among the data transmitting active nodes. The response time, usage of energy, and lifetime was improved with the proposed approach. The inspection of the migration of the mobile agent was not considered in the collaborative data aggregation approach that may reduce the performance of the network.

Padmaja and Marutheswar [12] developed a data aggregation scheme called TESDA that optimizes the performance of the data aggregation with the assistance of the clustering process. In the TESDA approach clustering scheme was employed to accomplish the effectiveness of transmission and to balance energy utilization. The TESDA minimizes the overhead and the reduced transmission overhead leads to the situation called a collision.

2.1 Data Aggregation-Based Optimal Hop Selection with ODVOC-EDGR (DAOHS-ODVOC-EDGR) Protocol

This section elaborates the proposed framework for the effective routing of data in accordance with the optimal hops. The initial section denotes the construction procedure of logical topology. In the subsequent section election of appropriate sensor node for data transmission, the effectiveness of data aggregation and forwarding of data using polydisperse data aggregation [18] is described. The packet loss and the hop count delay are minimized with the congestion control mechanism that is presented at the end of the section.

2.2 Construction of Logical Topology and Data Transmission

The construction of topology reduces the issues progressed in the generation of redundant and intense deployment of nodes i.e. intervention, the maximum count of feasible routes, utilization of highest energy to transmit the data to the nodes at the distance position. The control of the topology conserves the connectivity with the utilization of minimal energy. During the construction of logical topology, every sensor node in the network must aware of its position, neighboring node position, and location of the base station (BS). The construction of topology is established by the propagation of the “HELLO” message. The construction of logical topology is established by the sensor node which received the HELLO message. Every node is assigned with a random waiting time to avoid the occurrence of collision during the transmission between the peer nodes. The transmitted “HELLO” message holds the node ID, status buffer, energy level, information of location, and its hop count. Hop count of the “HELLO” message is zero (hc = 0) at the preliminary stage of data transmission. The hop count of the message is increased by one (hc + 1) after every transmission from the BS to its neighboring nodes. The neighbor node with minimum hop count will be elected as a receiver by the transmission node. The node poses the hc one forms the first level and hc two forms the second level of logical topology and so on. The process of construction pursues till all the sensor nodes are included and the orphan nodes are excluded from the construction of hierarchy.

The construction of topology provides assistance in the effective recognization of neighborhood nodes. The protocol is dynamic and the representation of topology alters when the sensor node becomes inactive. The proposed Data Aggregation Optimal Hop Selection with ODVOC-EDGR (DAOHS-ODVOC-EDGR) protocol preserves the energy dissipated in the construction of topology by adhering to the schema-less data delivery mechanism. The overall message transmission and the construction of logical topology in the sensing field are illustrated in Fig. 1.

Fig. 1
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Overall message transmission and the construction of logical topology in the sensing field

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The sensor nodes are deployed densely in the sensing field which generates redundant and highly correlated data. The utilization of energy in WSN is reduced by selectively forwarding the sensed data to the point of aggregation. The WSN necessitates varied levels of sensing reliability in the field of sensing that is sub region (s). The diversified sensing field in WSN is allocated with varied reliability weights (wk,1 ≤ k ≤ rs).The requirement of Quality of Service (QoS) in data transmission delay and the delivery ratio is determined by the weight factors. Based on the requirement of the reliability, the proposed DAOHS-ODVOC-EDGR divides the sensing field into a subsection to preserve energy. The sensor node in the network sense the data transmission within the sensing field (sdense), and the reliability factor (Rf) is allocated to the sensed data. The rate of reliability factor of sensory information is estimated by,

$$ R_{f} = \frac{{S_{Sense} - S_{event} }}{100} $$
(1)

where the distance among the event and node is denoted by Sevent. The progression or the restriction of data transmission is accomplished on the basis of Rf and the transmission is determined by the condition Rf ≥ tRf.The threshold dependability factor of the sensing event tRf is estimated by,

$$ tR_{f} = \frac{100 - Wk}{{100}} $$
(2)

2.3 Election of subsequent Hop-Node using Adaptive Scheme

The electing of the next-hop node to send its own or aggregated data using an adaptive scheme towards the BS that is done by the sensor node and the cost function determines the election of the next-hop node. The cost function is estimated from the robustness of the association among the current and next-hop node, available buffer space, and residual energy. During the process of forwarding the data, the neighbor information table is maintained by ever sensor node that provides assistance in estimating the cost function. The neighbor information table includes robustness of the link (Lr), buffer space (Bufsp), residual energy (Erl), node id (Ndi), and the coordinate position (Nd(x,y)). A node m (Ndm) elects a next-hop node n (Ndn) with the highest cost function values (CoFmax). The CoFmax is estimated by,

$$ CoF_{{max}} = {}_{{i \in Nd}}^{{max}} \left\{ {\left( {E_{{rl,}} + Buf_{{al,i}} + L_{r} } \right.} \right. $$
(3)

where Nd denotes a set of neighbors of Ndj and is considered as the weight factor estimated as the converse of distance among Ndj and Ndi.

$$ a = \frac{1}{{\sqrt {\left( {Nd_{j,x} - Nd_{i,x} } \right)^{2} + \left( {Nd_{j,y} - Nd_{i,y} } \right)^{2} } }} $$
(4)

The residual energy is estimated by

$$ E_{rl,} = E_{lvl,i} - \left\{ {E_{RT} \left( {c,dis_{tr} } \right) + E_{SR} \left( c \right) + \sum\nolimits_{i = 1}^{Nd} {E_{SR} (c)} + E_{agr} } \right\} $$
(5)

The ERT(c,dis) represents the needed energy to propagate c number of bits to certain distance where highest propagation area of sensor node is denoted by distr, the level of energy is denoted by Elvl, the energy used to aggregate the packet is represented by Eagr, the energy used for receiving a packet ESR(c) and it is computed by,

$$ E_{S} \left( c \right) = E_{ele} \times c $$
(6)

The accessible buffer space is estimated from the existing status of the buffer and the count of the expected packet is transmitted from the neighborhood of node Ndj. Generally, Bufsp and Elvl hold the acknowledgment data that is sent to the packet and it will be updated in the table of information. At the preliminary stage, the values of Bufsp and Elvl are assigned at the construction of the logical topology phase. The available range of buffer to a node i is estimated by,

$$ Buf_{avl} = Buf_{{_{sp,i} }} - \sum\nolimits_{i = 1}^{Nd} c $$
(7)

The robustness of the link for the neighbor node is estimated and renewed in the information table acknowledgment information from the neighbor node is received by the node on the sensing field and the strength of the link is estimated by,

$$ L_{r,i} = \frac{{Recv_{sp} }}{{Recv_{no\;of\;bits} }} $$
(8)

where Recvno of bit denotes the count of the bit resided in the acknowledgment data from the neighbor node Ndi. The robustness of the link is the Signal Interference Noise Ratio (SINR) for the link among the node Ndj and Ndi. The signal power received during the transmission is estimated by,

$$ Recv_{{sp}} = \frac{{\left\lceil {Prc\left( d \right)} \right\rceil }}{{Prc\left( {d_{0} } \right)}} = - 10\beta \log \left( {\frac{d}{{d_{0} }}} \right) + Y_{{rdb}} $$
(9)

where Prcv(d) is the arrived mean power with the distance d, which is estimated in relevance to a reference power Pr(d0) at the specific distance d0. The exponent value of path loss is β and the random Gaussian variable with mean zero value Yrdb and the standard deviation.

figure c

The process of data aggregation reduces traffic, delay, and energy usage than the near sink aggregation. An aggregate Agq holds Ndn (Agq) in the sensing region that is represented as overlapping spheres and it is signified as,

$$ Ag_{q} = Ag\left( {Ag_{1} \ldots \ldots \ldots Nd(Ag_{q} ),\;C_{m} } \right. $$
(10)

where nodes in the sensing region Agk, with k belongs 1,. Ndn (Agq), is denoted as

$$ Ag_{i} = Ag(n_{i} ,r_{i} ,x_{i} ) $$
(11)

where Cm is the connectivity matrix, Agq denotes the ni aggregated nodes, is the formulation of the sensing field, ri is the sensing field radius and xi is the midpoint of the formulated region. The process of estimation of gyration reduces the complexities in computation. The degree of overlap among the neighboring node is solved by the center of separation that is equated by,

$$ d_{ij} = \left| {x_{i} - x_{j} } \right| $$
(12)

The nodes in the sensing region are stored in a binary tree and it enriches the performance of the computation by permitting a very effective election. The connectivity at the initial stage determined based on the nature of the node within the sensing region. However, the computation is achieved by binary tree connectivity and it determines the neighbours. A binary tree denotes the branched structure and the representation of closed-loop that is not possible. The successive transmission of data through neighbours is constructed only once in a closed loop.

The connectivity matrix is used for representing a binary tree of dimension Ndn (Agq) * Ndn (Agq) with the matrix element,

$$ C_{i,j} = \left\{ {\begin{array}{*{20}c} {0,\;if\;Ag_{i} \;and\;Ag_{j} \;are\;not\;neighbours} \\ {1,\;if\;Ag_{i} \;and\;Ag_{j} \;are\;not\;neighbours} \\ \end{array} } \right. $$

The packets involved in the aggregation rely on the path of data routing and the schema of routing. In polydisperse data aggregation, the aggregated packet data count varies from node to node may be higher than other data aggregation process. Increased packet creation may lead to the situation called traffic, congestion requirement, and requirement of the buffer. Thus, the process of aggregation is attained for the possible event. The overall methodology of the proposed protocol is demonstrated in Fig. 2.

Fig. 2
figure 2

The overall function of the proposed protocol

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3 Analysis of Simulation

In this section, the simulation effects of the proposed DAOHS-ODVOC-EDGR protocol are depicted and it is evaluated with the existing TESDA and ODVOC-EDGR using Network Simulator (NS-2.34). The simulation is executed under two contexts such as sensing reliability with variations and network density. The parameters incorporated in the simulation are listed in Table 1.

Table 1 Simulation parameters
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3.1 Packet Delivery Ratio

Packet Delivery Ratio (PDR) is estimated as the count of packets delivered in the total count of packets transmitted from the source to the destination node [19]. The algorithm with higher packet delivery is considered as the best algorithm. The process of aggregation is accomplished by considering the delivery time of a sensitive packet in the network. In the DAOHS-ODVOC-EDGR, the transmission schedule is made on the basis of priority that provides assistance to accomplish the limitations of the delay in transmission. Thus, a node with maximal density DAOHS-ODVOC-EDGR performs better PDR value than the TESDA and ODVOC-EDGR. The performance of the algorithm is illustrated in Table 2 and Fig. 3.

Table 2 Comparison of packet delivery ratio
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Fig. 3
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Comparison of packet delivery ratio

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3.2 Delivery Delay

In TESDA, the process of aggregation duration relies on the nodes in the aggregation tree with a downstream process. The size of the tree rises with the compactness of the node and the delay in data transmission is also increases [20]. In the DAOHS-ODVOC-EDGR, the aggregation process and the binary tree construction is attained on the overlapping spheres. The binary tree is effective and the aggregation process is enriched and the process of data transmission is also improved with minimum delivery time. Table 3 and Fig. 4 depict the delivery delay of the proposed and existing algorithm. The data delivery time is minimized in the DAOHS-ODVOC-EDGR protocol effectively.

Table 3 Comparison of delivery delay
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Fig. 4
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Comparison of delivery delay

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3.2.1 Energy Consumption

In the WSN, every node in the transmission network is instilled with the minimum amount of energy and the process of recharging is also difficult [20]. The binary tree construction and aggregation considerably reduce congestion and traffic load. The process of transmission is carried without any hindrance and data transmission is attained in the shortest path. This situation reduces the exhaust of energy in the transmission nodes. The DAOHS-ODVOC- EDGR protocol has reduced the consumption of energy across various network densities and sensing reliability. The energy consumption value of the existing and proposed algorithm is displayed in Tables 4 and 5.

Table4 Comparison of energy consumption
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Table 5 Comparison of energy consumption versus network densities
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In Figs. 5 and 6, the utilization of energy across various network densities is illustrated and from the observation, it is identified that the proposed algorithm utilizes minimum energy.

Fig. 5
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Comparison of energy consumption

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Fig. 6
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Comparison of energy consumption versus network density

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3.2.2 Network Lifetime

The effective hop election in the transmission made the proposed algorithm to attain a longer lifetime [21]. The increased lifetime of the algorithm results in better performance and the values are shown in Table 6. The network lifetime comparison and the efficiency of the proposed algorithm are reflected in Fig. 7.

Table6 Comparison of network lifetime
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Fig. 7
figure 7

Comparison of network lifetime

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3.2.3 Hop Count Delay

The average count of hop in the solution replicates the quality of the transmission path. Figure 8 reflects the hop count delay of TESDA, ODVOC-EDGR, and DAOHS ODVOC-EDGR protocol. The proposed algorithm DAOHS- ODVOC-EDGR identifies the shortest path from the BS to the sink node. Therefore, the transmission path is considered as an optimal, and hop count delay is also minimum [22]. The proposed algorithm has a shorter delay than other algorithm and it is desirable. The algorithm with a longer lifetime also yields very minimum delay. The increase in network density will result in a drop in the lifetime of the network that may increase the hop count delay. Though, a trade-off occurs among both the performance metrics, efficient utilization of resources results in the effectiveness of the algorithm. The proposed algorithm utilizes more sensor nodes to transmit the data than the traditional algorithm and also DAOHS-ODVOC-EDGR performs effectively. The hop count delay is given in Table 7.

Fig. 8
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Comparison of hop count delay

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Table 7 Comparison of hop count delay
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In Fig. 8, hop count delay of the proposed and the existing algorithm is depicted with various network densities. From the observation, it is identified that the proposed algorithm has a better result.

The simulation results prove that the strategy presented by DAOHS- ODVOC-EDGR approach is applicable in both small and large networks and the results demonstrated that the network lifetime using DAOHS-ODVOC-EDGR approach is high when compared to other existing protocols with respect to various network densities respectively. Further, cluster based scheduling enabled the DAOHS- ODVOC-EDGR algorithm to decrease node energy consumption and achieved better load balancing among the nodes. From the results analysis, it has been also evidenced that the computational cost in terms of end to end delay is not improved as expected on increasing the network density. Stress testing in WSN can be considered as the process of determining that the network can continue to operate effectively under challenging circumstances or under high network densities. In this research work, the performance of the network is analyzed using various network densities which has been considered as a stress testing factor. Then, the PDR, End to End Delay, Energy Consumption, Network Lifetime, Communication Overhead and Thorughput has been analyzed and the proposed approach is found better than the existing algorithms under various network densities (stress factor).

4 Conclusion

In this article, a proficient and polydisperse data aggregation scheme with effective usage of energy in WSN is discussed. In the DAOHS-ODVOC-EDGR, the sensing section is segregated into varied overlapping spheres that are dived on the basis of reliability requirements. The proposed protocol permits only a limited number of nodes and the construction of the binary tree is also initiated depends on the necessity. This context minimizes the utilization of energy among the sensor nodes and also the traffic load is reduced. The effective subsequent hop node election enriches the temporal and spatial convergence of the polydisperse data aggregation. The data in the network is aggregated selectively based on the overlapping spheres that improve the network lifetime and PDR value. The delay and the hop count delay are reduced considerably in the proposed algorithm. In the future, the algorithm is altered and tested for a real-time dynamic environment. The effective scheduling procedures incorporated in the aggregation process that can improve the overall performance of the algorithm.