## 3 Energy Consumption of Distributed Solutions under Different Scenarios
### Scenario 1  
The performance of different classes of DKFs used in a WSN have been evaluated and compared in [45]. From [45], we selected three DKFs in which we evaluated their leak detection performance in the context of WWPM systems in [46]. The three DKFs were selected from data fusion strategies--specifically, diffusion, gossip, and consensus. The consensus-based DKF selected was the Information-Weighted Consensus Filter (ICF) proposed by [PERSON] et al. [47], the gossip-based DKF selected was the Sample Greedy Gossip Information-Weighted Consensus Filter (SGG-ICF) proposed by [PERSON] et al. [48], and the selected diffusion-based DKF was the Event-triggered Diffusion-based Kalman Filter (EDKF) proposed by [PERSON] et al. [49]. In [46], we presented the algorithms, operation and detailed explanations for the choice of the selected DKFs. Table 3 provides a summary of the values of the parameters assigned to the various DKF algorithms. However, no work has been done to evaluate the energy consumption of DKFs used in a WSN and more specifically in the context of WWPM. If we have previously demonstrated that distributed \begin{table}
\begin{tabular}{c c} \hline
**Technique** & **Rationale and Components Affected** \\ \hline Distributed computing & Reduces energy consumption by reducing the number of transmissions to the base station \\ \hline Duty cycling & Reduces energy consumption by switching sensor node components (MCU, transceiver, and sensors) to low power modes. \\ \hline Hierarchical Sensing & Reduces energy consumption by performing a tradeoff (compromise) between accuracy and energy consumption. This involves switching between high accuracy high power sensor and low accuracy low power sensor \\ \hline \end{tabular}
\end{table} 
Table 2: Rationale behind each energy conservation technique and the sensor node components affected. computing is feasible on low-end IoT devices and yields similar or superior results compared to centralized computing, the energy aspects in those prior works primarily focused on establishing feasibility and quantifying energy consumption orders. However, in this article, our objective is to conduct a precise evaluation of the IoT device energy consumption in a distributed computing solution. We also investigate hierarchical sensing as a means to prolong the system's lifespan without compromising the leak detection reliability and real-time monitoring. For this reason, in scenario 1, we are interested in assessing the energy consumption of the three selected DKFs whose leak detection performances were evaluated in [46]. In scenario 1, we started with simulations on CupCarbon before proceeding with physical experiments on the laboratory testbed. The simulation platform was fed with real data from the laboratory testbed. The simulation and experimental setups are the same as those described in [46], which was focused on evaluating the leak detection performance of three DKF variants. However, in this study, we focus on the detailed energy evaluation of these algorithms, the impact of using hierarchical sensing and duty cycle on energy consumption, and battery management. The simulation setup is shown in Figure 3 and is composed of two sensor nodes (S1 and S2) and natural event generators (A4 and A5). The natural event generators emulated the physical accelerometer sensors and were loaded with acceleration data collected from the laboratory testbed. The sensor nodes (S1 and S2) were loaded with scripts that implement the selected DKF algorithms during the simulations. Figure 3: Simulation setup in CupCarbon.