Cloud-edge collaborative high-frequency acquisition data processing for distribution network resilience improvement

To realize transparent monitoring and resilience improvement of low-voltage distribution network, both the data acquisition scope and frequency have been greatly expanded. Cloud-edge collaboration leverages the edge server’s real-time response capabilities and the cloud server’s robust data processing power to enhance the performance of high-frequency data acquisition processing. Nonetheless, it continues to confront challenges such as the entanglement of optimization variables, the presence of uncertain information, and a lack of awareness regarding acquisition frequencies. In this paper, we propose a machine learning-based cloud-edge collaborative data processing optimization algorithm to minimize the weighted sum of data processing delay and device energy consumption for distribution network resilience improvement. The joint optimization problem is decoupled into device-edge data offloading subproblem and edge-cloud data splitting subproblem, which are solved by the proposed upper confidence bound (UCB) based frequency-aware device-edge data offloading optimization algorithm and the exponential-weight algorithm for exploration and exploitation (EXP3) based edge-cloud data splitting optimization algorithm, respectively. Simulation results show that the proposed algorithm is superior to existing algorithms in performances of energy consumption and total processing delay.

1 Introduction

With a high proportion of unstable distributed renewable sources, energy storage, and controllable loads connected to the low-voltage distribution network, its transparent monitoring and resilience improvement have become an indispensable requirement Zhou et al. (2022); Yang et al. (2023); Ding et al. (2024); Wang et al. (2018); Chen et al. (2021). A large number of high-frequency acquisition devices need to be deployed in the low-voltage distribution network to collect multi-dimensional operation data such as voltage and current to support continuous monitoring, unmanned control, and fault detection, improving the resilience of distribution network operation Shah et al. (2020); Li et al. (2023); Soltani et al. (2023); Tariq et al. (2020). Compared with conventional devices, both the data acquisition scope and frequency have been greatly expanded. However, due to the limited computation and energy resources of devices, it is difficult to satisfy the stringent and differentiated data processing requirements of electric services Liao et al. (2020); Liu and Cao (2021); Li et al. (2024b), Li et al. (2024c).

Cloud-edge collaboration is a new convergent distributed computing paradigm, which combines the advantages of edge computing and cloud computing Laili et al. (2023); Jiang et al. (2023); Zhang et al. (2021). High-frequency acquisition devices offload the collected data to either edge server or offload the data to cloud server for remote processing. The real-time response capability of edge server and the large data processing capability of cloud server are integrated to improve data processing performance Gao et al. (2022); Dong et al. (2021); Guo et al. (2020); Naeem et al. (2021). However, the application of cloud-edge collaborative high-frequency acquisition data processing for distribution network resilience improvement still faces several challenges.

First, cloud-edge collaborative data processing involves the joint optimization of transmission power selection, edge server selection, and data splitting Long et al. (2023); Wu et al. (2020); Lin et al. (2024). The coupling relationship among optimization variables causes difficulties in solving the joint optimization problem. Second, traditional optimization methods are based on the global state information (GSI), while it is impractical to obtain complete GSI in real-world applications Zhang et al. (2022); Wang et al. (2022); Zhang et al. (2022). Uncertain GSI leads to large deviations in the optimization of cloud-edge collaborative data processing decisions. Last but not least, the data processing performance is affected by the frequency of data acquisition. The data processing optimization without the consideration of acquisition frequency cannot satisfy differentiated data processing requirements of high-frequency acquisition, which degrades the optimization performance Xiao et al. (2022); Cui et al. (2021).

Currently, some works have explored data processing for the distribution network. In Xia et al. (2022), Xia et al. proposed a data processing algorithm based on the Lyapunov optimization framework and the Markov approximation method, the objective of which is to minimize the long-term energy cost while meeting the real-time data processing constraint. However, the above study does not consider the joint optimization of edge server selection, data splitting, and device data transmission power control. In Mu et al. (2019), Mu et al. proposed a data processing method based on the centralized Kuhn-Munkers algorithm for a binary integer linear programming problem, the objective of which is to guarantee the network stability and improve energy saving. In Li et al. (2024a), Li et al. proposed a data processing method based on the three-dimensional learning-matching-based joint selection algorithm of server and container, the objective of which is to reduce the delay of high-priority service. However, the above studies do not consider how to make device data processing decisions under uncertain GSI. In Zhang et al. (2022), Zhang et al. proposed a data processing method based on convolutional neural networks and mathematical methods to solve the problems of sampling period anomalies, sampling reference time anomalies, data noise, and data missing in low-voltage distribution substation area. However, it does not consider the joint optimization of high-frequency acquisition device energy consumption and data processing delay.

Motivated by the above challenges, we propose a machine learning-based cloud-edge collaborative data processing optimization algorithm to minimize the weighted sum of data processing delay and device energy consumption for distribution network resilience improvement. First, we formulate a joint optimization problem of transmission power selection, edge server selection, and data splitting under cloud-edge collaboration. Second, the joint optimization problem is decoupled into device-edge data offloading subproblem and edge-cloud data splitting subproblem and solved by machine learning-based cloud-edge collaborative data processing optimization algorithm. Specifically, devices and edge servers can learn the optimal data offloading and data splitting strategy by upper confidence bound (UCB) based frequency-aware device-edge data offloading optimization and exponential-weight algorithm for exploration and exploitation (EXP3) based edge-cloud data splitting optimization, respectively. Finally, the effectiveness is verified through simulations. The main contributions of this paper are summarized as follows.

$•$ Two-stage joint optimization of transmission power selection, edge server selection, and data splitting under cloud-edge collaboration: We decompose the joint optimization of transmission power selection, edge server selection, and data splitting into two stages. In the first stage, the selection of transmission power and edge server is realized through UCB-based frequency-aware device-edge data offloading optimization algorithm, and in the second stage, the selection of data splitting ratio is realized through EXP3-based edge-cloud data splitting optimization algorithm.

$•$ Cloud-edge collaborative high-frequency acquisition data processing under uncertain GSI: We model the cloud-edge collaborative high-frequency acquisition data processing problem as a multi-armed bandit (MAB) problem and propose a machine learning-based cloud-edge collaborative data processing optimization algorithm, which introduces the acquisition frequency weight into the confidence upper bound calculation formula to achieve frequency awareness. The proposed algorithm optimizes device data offloading and edge-cloud data splitting through historical observations of cloud-edge collaborative processing delay and device energy consumption, integrating edge server and cloud server for collaborative computing.

$•$ Low-delay and low-energy consumption data processing: We formulate the optimization objective as the weighted sum of total data processing delay and energy consumption to achieve simultaneous reduction of delay and energy consumption. The proposed algorithm dynamically selects transmission power, edge server, and data splitting ratio based on the historical observation of weighted sum performance.

This paper is structured as follows. Section 2 formulates the system model and the cloud-edge data processing problem. The proposed machine learning-based cloud-edge collaborative data processing optimization algorithm is presented in Section 3. Simulation results are provided in Section 4. Section 5 concludes this paper.

2 System model

As shown in Figure 1, we consider a cloud-edge collaborative high-frequency acquisition data processing architecture for distribution network resilience improvement, which consists of the device layer, the edge layer, and the cloud layer. In the device layer, the information acquisition devices are deployed on distributed electrical equipment such as photovoltaic and distributed energy storage to collect data to support different services. There exists $N$ devices. The set of which is denoted as $\mathcal{D}=\{d_1,\dots ,d_n,\dots ,d_N\}$. The edge layer and the cloud layer consist of $M$ edge servers and one cloud server, the set of edge servers is denoted as $\mathcal{S}=\{s_1,\dots ,s_m,\dots ,s_M\}$ and the cloud server is denoted as $s_0$. Firstly, devices offload data to edge servers via 5G to reduce the data processing delay. Then, edge servers split the data offloaded from devices and transmit them to the cloud server via optical fiber communication to relieve data processing stress caused by device data growth. Through edge-cloud collaborative data processing, the processing requirements of high-frequency power distribution information acquisition can be met.

Figure 1

Figure 1. Cloud-edge collaborative high-frequency acquisition data processing architecture for distribution network resilience improvement.

The total optimization period is divided into $T$ time slots, and the set is $\mathcal{T}=\{1,\dots ,t,\dots ,T\}$. Each slot includes three stages: device-edge data offloading, edge-cloud data transmission, and edge-cloud collaborative data processing. The maximum time length of each stage is set as ${\tau }_1,{\tau }_2,{\tau }_3$. Denote $x_{n,m}(t)$ as edge server selection variable, where $x_{n,m}(t)=1$ represents that device $d_n$ selects edge server $s_m$ for data offloading in the $t$-th slot, and $x_{n,m}(t)=0$ otherwise.

2.1 Device-edge data offloading model

The power distribution information acquisition devices have differentiated acquisition frequencies. Devices collect data with different volumes in each slot and offload the data to the selected edge server for data processing. Denoting the amount of data collected at $d_n$ in the $t$-th slot as $U_n(t)$, the data stored at $d_n$ are modeled as a data backlog queue $Q_n(t)$, which is evolved as Eq. 1:

$Q_n\left(t+1\right)=Q_n\left(t\right)+U_n\left(t\right)-{\displaystyle \sum _{m=1}^M}{x}_{n,m}\left(t\right)U_{n,m}^{D,E}\left(t\right),(1)$

where U^D,E_n,m (t) represents the amount of data offloaded by d_n to s_m in the t-th slot, which is given by Eq. 2:

$U_{n,m}^{D,E}\left(t\right)=\min \left\{Q_n\left(t\right)+U_n\left(t\right),{\tau }_1{R}_{n,m}\left(t\right)\right\},(2)$

where $R_{n,m}(t)$ represents the rate of data transmission between $d_n$ and $s_m$, which is given by Eq. 3:

$R_{n,m}\left(t\right)=B_{n,m}\left(t\right){\mathrm{l}\mathrm{o}\mathrm{g}}_2\left(1+\frac{P_n\left(t\right)g_{n,m}\left(t\right)}{{\delta }_0+I_{n,m}\left(t\right)}\right),(3)$

where $B_{n,m}(t)$ and $g_{n,m}(t)$ represent the bandwidth and channel gain for data transmission between $d_n$ and $s_m$, respectively. ${\delta }_0$ and $I_{n,m}(t)$ represent Gaussian white noise and electromagnetic interference power between $d_n$ and $s_m$, respectively. $P_n(t)\in {\mathcal{P}}_n$ represents transmission power of $d_n$. ${\mathcal{P}}_n$ is the transmission power set, which contains $L$ levels and can be expressed by Eq. 4:

${\mathcal{P}}_n=\left\{P_{n,min},\dots ,P_{n,min}+\frac{\left(l-1\right)\left(P_{n,max}-P_{n,min}\right)}{L-1},\dots ,P_{n,max}\right\},(4)$

where $L$ is the transmission power level number. $P_{n,min}$ and $P_{n,max}$ represent the minimum transmission power and maximum transmission power of $d_n$, respectively.

Therefore, the transmission delay of data offloading from $d_n$ to $s_m$ in the $t$-th slot is calculated as Eq. 5:

${\tau }_{n,m}^{D,E}\left(t\right)=\min \left\{{\tau }_1,\frac{Q_n\left(t\right)+U_n\left(t\right)}{R_{n,m}\left(t\right)}\right\}.(5)$

The data transmission energy consumption $E_{n,m}(t)$ for data offloading from $d_n$ to $s_m$ in the $t$-th slot is represented as Eq. 6:

$E_{n,m}\left(t\right)=P_n\left(t\right){\tau }_{n,m}^{D,E}\left(t\right).(6)$

2.2 Edge-cloud data splitting model

Edge server $s_m$ maintains data backlog queue $O_{n,m}^E(t)$ for the data offloaded from device $d_n$, which is dynamically evolved as Eq. 7:

$\begin{array}{ll}\hfill O_{n,m}^E\left(t+1\right)& =O_{n,m}^E\left(t\right)+U_{n,m}^{D,E}\left(t\right)\hfill \\ \hfill & -y_{n,m}\left(t\right)U_{n,m}^{D,E}\left(t\right)-U_{n,m}^{E,com}\left(t\right),\hfill \end{array}(7)$

where $U_{n,m}^{E,com}(t)$ is the processed data volume of $s_m$, whose specific explanation is shown in (11). $y_{n,m}(t)\in \mathcal{Y}$ is data splitting ratio, which represents the data splitting ratio of $d_n$ from $s_m$ to $s_0$. $\mathcal{Y}$ is the data splitting ratio set. In order to ensure the data integrity while accomplishing ratio-based data splitting, we discretize the data splitting ratio into $H$ levels Chen et al. (2020), which can be expressed as Eq. 8:

$\begin{array}{l}\mathcal{Y}=\left\{y_{\mathit{min}}\left(t\right),\dots ,y_{\mathit{min}}\left(t\right)+\frac{\left(h-1\right)\left(y_{\mathit{max}}-y_{\mathit{min}}\right)}{H-1},\right.\hfill \\ \left.\dots ,y_{\mathit{max}}\right\}.\hfill \end{array}(8)$

Denote $U_{n,m}^{E,C}(t)$ as the data amount of $d_n$ offloaded from $s_m$ to cloud server $s_0$ in the $t$-th slot, which is given by Eq. 9:

$U_{n,m}^{E,C}\left(t\right)=\min \left\{y_{n,m}\left(t\right)U_{n,m}^{D,E}\left(t\right),{\tau }_2{R}_m^{E,C}\left(t\right)\right\},(9)$

where $R_m^{E,C}(t)$ represents the transmission rate between $s_m$ and $s_0$, whose calculation method is as same as (3).

The transmission delay of data transmitted from $s_m$ to $s_0$ in the $t$-th slot is calculated as Eq. 10:

${\tau }_{n,m}^{E,C}\left(t\right)=\min \left\{{\tau }_2,\frac{y_{n,m}\left(t\right)U_{n,m}^{D,E}\left(t\right)}{R_m^{E,C}\left(t\right)}\right\}.(10)$

2.3 Edge-cloud collaborative data processing model

2.3.1 Edge server data processing delay model

Define the data amount of device $d_n$ processed by edge server $s_m$ in the $t$-th slot as $U_{n,m}^{E,com}(t)$, which is given by Eq. 11:

$\begin{array}{l}\hfill U_{n,m}^{E,com}\left(t\right)=\min \left\{O_{n,m}^E\left(t\right)+\left(1-y_{n,m}\left(t\right)\right)U_{n,m}^{D,E}\left(t\right),\right.\\ \hfill \left.{\tau }_3\frac{f_{n,m}^E\left(t\right)}{{\chi }_n}\right\},\end{array}(11)$

where $f_{n,m}^E(t)$ (cycles/s) is the computing capacity of $s_m$ in the $t$-th slot, and ${\chi }_n$ (cycles/bit) is the data processing complexity of $d_n$. Therefore, the processing delay of $s_m$ in the $t$-th slot is given by Eq. 12:

$\begin{array}{ll}\hfill & {\tau }_{n,m}^{E,com}\left(t\right)=\hfill \\ \hfill & \min \left\{{\tau }_3,{\chi }_n\left[\frac{\left(O_{n,m}^E\left(t\right)+\left(1-y_{n,m}\left(t\right)\right)U_{n,m}^{D,E}\left(t\right)\right)}{f_{n,m}^E\left(t\right)}\right]\right\}.\hfill \end{array}(12)$

2.3.2 Cloud server data processing delay model

Cloud server $s_0$ maintains data backlog queue $Z_{n,m}^C(t)$ for the data of device $d_n$ split from edge server $s_m$, which is dynamically evolved as Eq. 13:

$Z_{n,m}^C\left(t+1\right)=Z_{n,m}^C\left(t\right)+U_{n,m}^{E,C}\left(t\right)-U_{n,m}^{C,com}\left(t\right),(13)$

where $U_{n,m}^{C,com}(t)$ is the cloud server processing data amount, which is given by Eq. 14:

$\begin{array}{l}{U}_{n,m}^{C,com}\left(t\right)=\min \left\{Z_{n,m}^C\left(t\right)+U_{n,m}^{E,C}\left(t\right),\right.\hfill \\ \left.\frac{\left({\tau }_3-{\tau }_{n,m}^{E,C}\left(t\right)\right)f_{n,m}^C\left(t\right)}{{\chi }_n}\right\}.\hfill \end{array}(14)$

The processing delay of $d_n$’s data in $s_0$ is given by Eq. 15:

${\tau }_{n,m}^{C,com}\left(t\right)=\min \left\{{\tau }_3-{\tau }_{n,m}^{E,C}\left(t\right),\frac{{\chi }_n\left(Z_{n,m}^C\left(t\right)+U_{n,m}^{E,C}\left(t\right)\right)}{f_{n,m}^C\left(t\right)}\right\}.(15)$

2.4 Problem formulation

The total delay of high-frequency acquisition data processing consists of the delay of device-edge data offloading, and the maximum value between edge server data processing delay and the sum of edge-cloud data splitting delay and cloud server data processing delay, which is given by Eq. 16:

${\tau }_{n,m}^{\mathit{sum}}\left(t\right)={\tau }_{n,m}^{D,E}\left(t\right)+\max \left\{{\tau }_{n,m}^{E,com}\left(t\right),{\tau }_{n,m}^{E,C}\left(t\right)+{\tau }_{n,m}^{C,com}\left(t\right)\right\}(16)$

In this paper, we aim to address the problem of low delay and low energy consumption edge-cloud collaborative high-frequency acquisition data processing for distribution network resilience improvement. The objective is to minimize the weighted sum of data processing delay and device energy consumption through the joint optimization of transmission power selection, edge server selection, and edge-cloud data splitting ratio selection. The joint optimization problem is formulated as Eq. 17:

$\begin{array}{ll}\hfill & \mathbf{P}\mathbf{1}:\underset{\left\{P_n\left(t\right),x_{n,m}\left(t\right),y_{n,m}\left(t\right)\right\}}{\min }\frac{1}{N}{\displaystyle \sum _{n=1}^N}{\displaystyle \sum _{m=1}^M}{x}_{n,m}\left(t\right){\mathrm{\Upsilon }}_{n,m}\left(t\right)\hfill \\ \hfill \text{s.t.}& C_1:x_{n,m}\left(t\right)\in \left\{\mathrm{0,1}\right\},\forall d_n\in \mathcal{D},\forall s_m\in \mathcal{S},\forall t\in \mathcal{T}\hfill \\ \hfill & C_2:{\displaystyle \sum _{m=1}^M}{x}_{n,m}\left(t\right)=1,\forall d_n\in \mathcal{D},\forall s_m\in \mathcal{S},\hfill \\ \hfill & C_3:{\displaystyle \sum _{n=1}^N}{x}_{n,m}\left(t\right)\le nu{m}_m^{\mathit{max}},\forall d_n\in \mathcal{D},\forall s_m\in \mathcal{S},\hfill \\ \hfill & C_4:P_n\left(t\right)\in \mathcal{P},\forall d_n\in \mathcal{D},\forall s_m\in \mathcal{S},\hfill \\ \hfill & C_5:y_{n,m}\left(t\right)\in \mathcal{Y},\forall d_n\in \mathcal{D},\forall s_m\in \mathcal{S},\hfill \end{array}(17)$

where ${\mathrm{\Upsilon }}_{n,m}(t)={\tau }_{n,m}^{\mathit{sum}}(t)+V_E{E}_{n,m}(t)$, and $V_E$ is the weight of the energy consumption. $C_1$, $C_2$ and $C_3$ are edge server selection constraints, i.e., each device can only select one edge server for data offloading, and the maximum number of devices can be handled by $s_m$ is $nu{m}_m^{\mathit{max}}$. $C_4$ is the transmission power selection constraint and $C_5$ is the data splitting ratio selection constraint.

$\mathbf{P}\mathbf{1}$ involves the device-edge data offloading optimization and edge-cloud data splitting optimization, which can be solved by a time-sequential manner. Specifically, the device-edge data offloading should be first optimized and edge-cloud data splitting should be optimized based on the data offloading strategy. Therefore, $\mathbf{P}\mathbf{1}$ is decomposed into two subproblems, i.e., $\mathbf{S}\mathbf{P}\mathbf{1}$: device-edge data offloading subproblem involving $P_n(t)$ and $x_{n,m}(t)$; $\mathbf{S}\mathbf{P}\mathbf{2}$: edge-cloud data splitting subproblem involving $y_{n,m}(t)$.

3 Machine learning-based cloud-edge collaborative data processing optimization algorithm

In this section, a machine learning-based cloud-edge collaborative data processing optimization algorithm is proposed to solve the optimization problem. The implementation procedure of the machine learning-based cloud-edge collaborative data processing optimization algorithm is shown in Algorithm 1.

Algorithm 1.Machine Learning-based Cloud-Edge Collaborative Data Processing Optimization Algorithm.

1: Input: $\mathcal{D}$, $\mathcal{S}$, $\mathcal{T}$, $\mathcal{P}$, $\mathcal{Y}$, $N$, $M$, $V_E$.

2: Output: $\{x_{n,m}(t)\}$, $\{P_n(t)\}$ and $\{y_{n,m}(t)\}$.

3: For $t$ = 1,2, … ,$T$ do

4: Phase 1: UCB-based frequency-aware device-edge    data offloading optimization

5: For $d_n\in \mathcal{D}$ do

6:  Initialize $a_{l,m}^n(t),x_{n,m}(t)$, and ${\alpha }_{l,m}^n(t)$.

7:  Sequentially select each arm and obtains the     initial reward.

8:  Calculate the confidence upper bound    based on (20).

9:  Select arm $A_{l^{*},m^{*}}^n$ and perform the action $a_{l^{*},m^{*}}^n(t)$     based on (21).

10: Update ${\alpha }_{l^{*},m^{*}}^n(t)$, ${\bar{\alpha }}_{l^{*},m^{*}}^n(t)$, and $r_{l^{*},m^{*}}^n(t)$ based on     (19) and (22) respectively.

11: End for

12: Phase 2: EXP3-based edge-cloud data splitting     optimization

13: For $s_m\in \mathcal{S}$ do

14: Initialize the uniform distribution parameter    $\xi \in (\mathrm{0,1}]$. Set the empirical performance-related     distribution parameter     ${\lambda }_h^{n,m}(t)=1$, $\forall Y_h^{n,m}\in \mathcal{Y}$.

15:  Calculate the probability for selecting      $Y_h^{n,m}$ based on (25).

16:  Calculate the cumulative distribution        function of $pro{b}_h^{n,m}(t)$ based on (26).

17:  Generate a random value $pro{b}_0^{n,m}(t)\in [\mathrm{0,1}]$, and      get the optimal splitting ratio decision      based on (27).

18:  Execute $b_1^{n,m}(t)=1$ and get the reward ${\gamma }_h^{n,m}(t)$     based on (24).

19: Update the empirical performance-related      distribution parameter ${\lambda }_h^{n,m}(t)$ based on      (28) and (29).

20: End for

21: End for

3.1 UCB-based frequency-aware device-edge data offloading optimization

$\mathbf{S}\mathbf{P}\mathbf{1}$ is formulated as Eq. 18:

$\begin{array}{ll}\hfill & \mathbf{S}\mathbf{P}\mathbf{1}:\underset{\left\{P_n\left(t\right),x_{n,m}\left(t\right)\right\}}{\min }\frac{1}{N}{\displaystyle \sum _{n=1}^N}{\displaystyle \sum _{m=1}^M}{x}_{n,m}\left(t\right){\mathrm{\Upsilon }}_{n,m}\left(t\right)\hfill \\ \hfill \text{s.t.}& C_1\sim C_4.\hfill \end{array}(18)$

$\mathbf{S}\mathbf{P}\mathbf{1}$ optimizes the device-edge data offloading process. Its optimization variables involve $P_n(t)$ and $x_{n,m}(t)$. The device obtains the optimal offloading decision by minimizing the weighted sum of ${\tau }_{n,m}^{\mathit{sum}}(t)$ and $E_{n,m}(t)$.

However, the precise knowledge of global state information such as channel quality and edge server computing resources is inaccurate. It is difficult for devices to make the optimal offloading decision. Devices should optimize edge server selection and power selection based on the local state information. Multi-armed bandit (MAB) is an effective solution to solve the combinatorial optimization problem with incomplete information Hashima et al. (2020); Zhao et al. (2020). In each slot, the decision maker selects an arm. Then, the selected arm generates a reward. The goal of the decision maker is to maximize the cumulative reward.

We transform $\mathbf{S}\mathbf{P}\mathbf{1}$ into an MAB problem. The decision maker, arm, action, and reward are described as follows.

$•$ Decision maker: Define the acquisition devices as the decision maker, which makes the edge server selection and power control decision for data offloading.

$•$ Arm: The power ${\mathcal{P}}_n$ and edge server $\mathcal{S}$ are combined to reduce the space complexity of action. Define ${\mathcal{A}}^n=\{A_{\mathrm{1,1}}^n,\dots ,A_{l,m}^n,\dots ,A_{L,M}^n\}$ as the set of arms which satisfy $|{\mathcal{A}}^n|=L\times M$. The arm $A_{l,m}^n$ represents the combination of the power level $l$ and edge server $s_m$. Define the number of times to select $A_{l,m}^n$ as $r_{l,m}^n(t)$.

$•$ Action: Define the arm selection action indicator variable as $a_{l,m}^n(t)$, $a_{l,m}^n(t)=1$ represents that device $d_n$ selects the transmission power $P_n(t)=P_{n,min}+\frac{(l-1)(P_{n,max}-P_{n,min})}{L-1}$ to offload data to the edge server $s_m$.

$•$ Reward: In the $t$-th slot, $d_n$ selects $A_{l,m}^n$ to get the reward ${\alpha }_{l,m}^n(t)$, which is given by Eq. 19:

${\alpha }_{l,m}^n\left(t\right)=-{\mathrm{\Upsilon }}_{n,m}\left(t\right).(19)$

We propose a UCB-based frequency-aware device-edge data offloading optimization algorithm, which introduces the acquisition frequency weight into the confidence upper bound calculation formula to achieve frequency awareness, and addresses the MAB problem of device-edge data offloading. UCB is a low-complexity learning-based algorithm to balance exploitation and exploration. The proposed algorithm enables the acquisition devices to take action based on local state information such as delay. Afterward, combined with the optimization variables ${\tau }_{n,m}^{D,E}(t)$ and $E_{n,m}(t)$, the acquisition devices perceive the obtained reward and updated state information for the next selection Xia et al. (2020).

The implementation procedure of UCB-based frequency-aware device-edge data offloading optimization algorithm is introduced as follows.

3.1.1 Initialization

Initialize $a_{l,m}^n(t)=0$, $x_{n,m}(t)=0$, and ${\alpha }_{l,m}^n(t)=0$, $\forall d_n\in \mathcal{D}$, $\forall s_m\in \mathcal{S}$. When $t\le |{\mathcal{A}}^n|$, device $d_n\in \mathcal{D}$ sequentially selects each arm and obtains the initial reward.

3.1.2 Decision making

$d_n$ calculates the confidence upper bound based on the selection number $r_{l,m}^n(t)$ of $A_{l,m}^n$ in the $t$-th slot, which is expressed by Eq. 20:

${\alpha }_{l,m}^{n,up}\left(t\right)={\bar{\alpha }}_{l,m}^n\left(t-1\right)+\frac{1}{{\beta }_n{\bar{\alpha }}_{l,m}^n\left(t-1\right)}\sqrt{\frac{\ln \left(t\right)}{r_{l,m}^n\left(t-1\right)}},(20)$

where ${\bar{\alpha }}_{l,m}^n(t-1)$ is the average reward before the $(t-1)$-th slot, ${\beta }_n$ is the acquisition frequency weight of $d_n$, $\sqrt{\frac{\ln (t)}{r_{l,m}^n(t)}}$ is the confidence interval of $A_{l,m}^n$, and ${\beta }_n$ is the acquisition frequency weight of $d_n$. If the acquisition frequency weight ${\beta }_n$ of $d_n$ is larger, more data will be collected at each slot. In order to ensure its transmission delay and energy consumption performance, it is necessary to utilize the best possible decision. Thus, the second term indicates that if ${\beta }_n$ is larger and the reward value of the selected arm is higher, the confidence interval is smaller and the device tends to exploit the currently selected arm. If ${\beta }_n$ is smaller and the reward value of the selected arm is lower, the confidence interval is larger and the device tends to explore other arms.

After obtaining ${\alpha }_{l,m}^{n,up}(t)$, $d_n$ selects the arm $A_{l,m}^n$ with the highest confidence upper bound to perform the action, which is expressed by Eq. 21:

$\left\{\begin{array}{ll}\hfill & A_{l^{*},m^{*}}^n=\arg {\max }_{\left\{A_{l^{*},m^{*}}^n\right\}}\left\{{\alpha }_{l,m}^{n,up}\left(t\right)\right\},\hfill \\ \hfill & a_{l^{*},m^{*}}^n\left(t\right)=1.\hfill \end{array}\right.(21)$

3.1.3 Learning process

The device observes delay and energy efficiency performances. Then, gets the reward ${\alpha }_{l^{*},m^{*}}^n(t)$ based on (19). Accordingly, ${\bar{\alpha }}_{l^{*},m^{*}}^n(t)$ and $r_{l^{*},m^{*}}^n(t)$ are updated as Eq. 22:

$\begin{array}{ll}\hfill & {\bar{\alpha }}_{l^{*},m^{*}}^n\left(t\right)=\frac{r_{l^{*},m^{*}}^n\left(t-1\right){\bar{\alpha }}_{l^{*},m^{*}}^n\left(t-1\right)+a_{l^{*},m^{*}}^n\left(t\right){\alpha }_{l^{*},m^{*}}^n\left(t\right)}{r_{l^{*},m^{*}}^n\left(t-1\right)+a_{l^{*},m^{*}}^n\left(t\right)},\hfill \\ \hfill & r_{l^{*},m^{*}}^n\left(t\right)=r_{l^{*},m^{*}}^n\left(t-1\right)+a_{l^{*},m^{*}}^n\left(t\right).\hfill \end{array}(22)$

3.2 EXP3-based edge-cloud data splitting optimization

$\mathbf{S}\mathbf{P}\mathbf{2}$ is formulated as Eq. 23:

$\begin{array}{ll}\hfill & \mathbf{S}\mathbf{P}\mathbf{2}:\underset{\left\{y_{n,m}\left(t\right)\right\}}{\min }\frac{1}{N}{\displaystyle \sum _{n=1}^N}{\displaystyle \sum _{m=1}^M}{\mathrm{\Upsilon }}_{n,m}^{\mathit{Exp}}\left(t\right)\hfill \\ \hfill \text{s.t.}& C_5,\hfill \end{array}(23)$

where ${\mathrm{\Upsilon }}_{n,m}^{\mathit{Exp}}(t)=\max \{{\tau }_{n,m}^{E,com}(t),{\tau }_{n,m}^{E,C}(t)+{\tau }_{n,m}^{C,com}(t)\}$.

Based on the offloading decision obtained by optimizing $\mathbf{S}\mathbf{P}\mathbf{1}$, $\mathbf{S}\mathbf{P}\mathbf{2}$ optimizes the edge-cloud data splitting process. Its optimization variable involves $y_{n,m}(t)$. The edge server obtains the optimal splitting decision by minimizing the delay required to process all data. Similarly, we transform $\mathbf{S}\mathbf{P}\mathbf{2}$ into an MAB problem. The decision maker, arm, action, and reward are described as follows.

$•$ Decision maker: Define the edge server as the decision maker, which makes the splitting ratio decision when conducting edge-cloud data splitting.

$•$ Arm: Define the arm as the total splitting ratio based on $\mathcal{Y}$. The arm $Y_h^{n,m}\in \mathcal{Y}$ indicates that the data splitting level of the $d_n$ specified by the edge server $s_m$ is $h$.

$•$ Action: Define the action indicator variable as $b_h^{n,m}(t)$, $b_h^{n,m}(t)=1$ represents that edge server $s_m$ sets the splitting ratio of the data from $d_n$ as $y_{n,m}(t)=y_{\mathit{min}}+\frac{(h-1)(y_{\mathit{max}}-y_{\mathit{min}})}{H-1}$ in the $t$-th slot.

$•$ Reward: Define ${\gamma }_h^{n,m}$ to represent the reward obtained by $s_m$ of selecting arm $Y_h^{n,m}$, which is given by Eq. 24:

${\gamma }_h^{n,m}\left(t\right)=\frac{1}{{\mathrm{\Upsilon }}_{n,m}^{\mathit{Exp}}\left(t\right)}.(24)$

We propose an EXP3-based edge-cloud data splitting optimization algorithm to address the MAB problem. The core idea is to maintain the probability of a certain arm. Then, the algorithm randomly selects a certain arm each time and updates the weight of the arm based on the observed reward after selection Zhou et al. (2021). Through iteration, this algorithm can ensure that the regret value is within a certain acceptable range.

The implementation procedure of the EXP3-based edge-cloud data splitting optimization algorithm is introduced as follows.

3.2.1 Initialization

Initialize the uniform distribution parameter $\xi \in (\mathrm{0,1}]$. Set the empirical performance-related distribution parameter ${\lambda }_h^{n,m}(t)=1$, $\forall Y_h^{n,m}\in \mathcal{Y}$.

3.2.2 Decision making

In the $t$-th slot, firstly, calculate the probability for selecting $Y_h^{n,m}$, which is given by Eq. 25:

$pro{b}_h^{n,m}\left(t\right)=\left(1-\xi \right)\frac{{\lambda }_h^{n,m}\left(t\right)}{{\sum }_{h=1}^H{\lambda }_h^{n,m}\left(t\right)}+\frac{\xi }{H}.(25)$

Then, calculate the cumulative distribution function of $pro{b}_h^{n,m}(t)$, which is given by Eq. 26:

$F^{n,m}\left(h\right)={\displaystyle \sum _{h=1}^H}pro{b}_h^{n,m}\left(t\right).(26)$

Finally, generate a random value $pro{b}_0^{n,m}(t)\in [\mathrm{0,1}]$, and get the optimal splitting ratio decision, which is given by Eq. 27:

$b_h^{n,m}\left(t\right)=\left\{\begin{array}{cc}1,\hfill & \text{if}{F}^{n,m}\left(h-1\right)\le pro{b}_0^{n,m}\left(t\right)\le F^{n,m}\left(h\right),\hfill \\ 0,\hfill & \text{otherwise}.\hfill \end{array}\right.(27)$

Specially, if $0\le pro{b}_0^{n,m}(t)\le F^{n,m}(1)$, $b_1^{n,m}(t)=1$.

3.2.3 Learning process

The edge server executes the splitting ratio decision $b_1^{n,m}(t)$, gets the reward ${\gamma }_h^{n,m}(t)$ based on (24), and updates the empirical performance-related distribution parameter as Eq. 28:

${\lambda }_h^{n,m}\left(t+1\right)={\lambda }_h^{n,m}\left(t\right)\exp \left(\frac{\eta {\tilde{\gamma }}_h^{n,m}\left(t\right)}{H}\right),(28)$

where $\eta >0$ is the adjustment factor of empirical performance-related distribution parameter and ${\tilde{\gamma }}_h^{n,m}(t)$ is the estimated reward, which is given by Eq. 29:

${\tilde{\gamma }}_h^{n,m}\left(t\right)=\left\{\begin{array}{cc}\frac{{\gamma }_h^{n,m}\left(t\right)}{pro{b}_h^{n,m}\left(t\right)},\hfill & \text{if}{b}_h^{n,m}\left(t\right)=1,\hfill \\ 0,\hfill & \text{otherwise}.\hfill \end{array}\right.(29)$

Finally, the algorithm terminates until $t>T$.

4 Simulation result

In this paper, we take a low-voltage distribution network in a certain area as the simulation scenario to verify the system model and the performance of the proposed algorithm, which includes 10 power distribution acquisition devices, 3 edge servers, and one cloud server. The amount of data collected by a device in each slot distributed within [1.2, 1.8] Mbits. The transmission power and the data splitting ratio contain 5 and 6 levels, respectively. The specific simulation parameters are shown in Table 1 Liao et al. (2022); Yang et al. (2023).

Table 1

Table 1. Simulation parameters.

Two state-of-the-art algorithms are used for comparison. The first one is the multi-index evaluation learning-based computation offloading algorithm (MINCO), which sets the average total data processing delay minimization as the optimization objective, but lacks energy consumption control of device Lu et al. (2023). MINCO considers multiple indices in power internet of things to improve the learning performance of its algorithm, thereby achieving the low-delay computation offloading. The other one is the UCB-advantage actor-critic-based data offloading algorithm (UCB-A3C), which considers energy consumption management and transmission delay optimization Yang et al. (2022). UCB-A3C combines UCB and actor-critic algorithm to enhance the learning ability of its algorithm, and achieves the joint optimization of energy consumption and delay. Meanwhile, both comparison algorithms do not consider data splitting optimization.

Figure 2 shows the weighted sum of total delay and energy consumption versus time slot. The simulation result shows that the proposed algorithm has the lowest weighted sum among the three algorithms. Compared with MINCO and UCB-A3C, the proposed algorithm can decrease the weighted sum performance by 19.69% and 16.05%, respectively. The reason is that the proposed algorithm can coordinate the balance between total delay and energy consumption by adjusting the transmission power of devices and the data splitting ratio of edge servers, which reduces energy consumption while maintaining low delay. However, MINCO merely focuses on delay reduction while the energy consumption balance is neglected. UCB-A3C considers energy consumption management, but the utilization of cloud-edge computing resources is inadequate, resulting in poor weighted sum performance.

Figure 2

Figure 2. The weighted sum of total delay and energy consumption versus time slot.

Figure 3 shows the total delay of data processing versus time slot. It can be seen that the proposed algorithm has the optimal total delay performance of data processing. Compared with MINCO and UCB-A3C, the proposed algorithm can decrease the total delay by 16.91% and 23.11%, respectively. The reason is that both MINCO and UCB-A3C adopt the traditional binary full offloading strategy, and do not take into account the optimization of the edge-cloud data splitting process, which makes them difficult to fully utilize the computing resources of cloud server and edge servers, leading to worse delay performance.

Figure 3

Figure 3. The total delay of data processing versus time slot.

Figure 4 shows the cumulative energy consumption versus time slot. Compared with MINCO and UCB-A3C, the proposed algorithm can reduce the cumulative energy consumption by 15.04% and 9.52% respectively. The reason is that the proposed algorithm can coordinate the balance between total delay and energy consumption through the joint optimization of data offloading and data splitting allocation. MINCO only considers the data offloading delay optimization but ignores the coupling relationship between data transmission power and data offloading delay, which leads to the highest energy consumption. UCB-A3C lacks optimization of edge-cloud data splitting process, and cannot make full use of computing resources of cloud server and edge server, resulting in serious data backlog queue, which consumes more energy for device data offloading.

Figure 4

Figure 4. The cumulative energy consumption versus time slot.

Figure 5 shows the data backlog on device versus acquisition frequency. With the increase of acquisition frequency, the data backlogs of the three algorithms all increase, but the data backlog of the proposed algorithm increases the least. This is because the proposed algorithm can adaptively learn the server and transmission power selection strategies by adjusting the balance between exploration and exploitation through the acquisition frequency awareness. When the acquisition frequency is large, the proposed algorithm will tend to utilize the current optimal strategy to effectively reduce the data backlog. On the contrary, the proposed algorithm will tend to explore other strategies to avoid the optimization falling into local optimality.

Figure 5

Figure 5. The data backlog on device versus acquisition frequency.

Figure 6 shows the total delay and cumulative energy consumption of different algorithms versus computing resources of edge servers. When the computing resources of the edge servers decrease, the total delay of all algorithms increases due to the increase of data processing time. However, the proposed algorithm exhibits a minimal upward trend in terms of total latency and energy consumption. This is because the proposed algorithm transmits part of the data to the cloud server for processing through data splitting of the edge server, so as to relieve the processing pressure of the edge server. At the same time, more edge servers with better performance are available for devices to choose for data offloading, thus reducing data transmission power consumption. However, the binary unloading strategy is adopted in the comparison algorithm, which transmits too much data to the cloud server, and the computing resources of the edge server cannot be fully utilized, resulting in the increase of the total delay performance.

Figure 6

Figure 6. The total delay and cumulative energy consumption of different algorithms versus computing resources of edge servers.

Figure 7 shows the impact of $V_E$ on the total delay and cumulative energy consumption. With the increase of $V_E$, the proposed algorithm pays more attention to energy consumption and ignores the total delay performance. As a result, the total delay gradually increases, and the energy consumption gradually decreases. This result provides a reference for the setting of $V_E$ in practical applications. Reasonable setting can achieve a compromise between the total delay of data processing and device energy consumption performance.

Figure 7

Figure 7. The impact of $V_E$ on the total delay and cumulative energy consumption.

5 Conclusion

In this paper, we investigated the cloud-edge collaborative high-frequency acquisition data processing architecture for distribution network resilience improvement. A machine learning-based cloud-edge collaborative data processing optimization algorithm was proposed to minimize the weighted sum of data processing delay and device energy consumption by jointly optimizing transmission power selection, edge server selection, and data splitting ratio selection. Firstly, we decomposed the optimization problem into two subproblems of device-edge data offloading and edge-cloud data splitting. Then, a UCB-based frequency-aware device-edge data offloading optimization algorithm was employed to address the device-edge data offloading subproblem, and an EXP3-based edge-cloud data splitting optimization algorithm was employed to address the edge-cloud data splitting subproblem. Simulation results demonstrated that the proposed algorithm can achieve superior performance in terms of processing delay and energy consumption. Compared with MINCO and UCB-A3C, the proposed algorithm can decrease the weighted sum performance by 19.69% and 16.05%, respectively.

In the future, we will focus on the combination of high-frequency acquisition data processing with security technologies such as blockchain, encryption authentication, or differential privacy, thereby achieving the joint guarantee of low processing delay, low energy consumption, and high data security and privacy performances.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Author contributions

SD: Conceptualization, Formal Analysis, Funding acquisition, Investigation, Methodology, Writing–original draft, Writing–review and editing. JiZ: Conceptualization, Formal Analysis, Investigation, Methodology, Writing–original draft, Writing–review and editing. TL: Investigation, Methodology, Writing–original draft, Writing–review and editing. YuZ: Software, Validation, Visualization, Writing–original draft. PS: Software, Validation, Writing–review and editing. JZ: Supervision, Visualization, Writing–review and editing. RL: Supervision, Writing–review and editing.

Funding

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This work was supported by Science and Technology Project of China Southern Power Grid Corporation under Grant Number 035900KK52220012 (GDKJXM20220909).

Conflict of interest

Authors SD, JiZ, TL, YZ, PS, JuZ, and RL were employed by the Metrology Center, Guangdong Power Grid Co., Ltd.

The authors declare that this study received funding from the Science and Technology Project of China Southern Power Grid Corporation. The funder had the following involvement in the study: resources, data collection and analysis, software and methodology.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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