# BPDM-GCN: Backup Path Design Method Based on Graph Convolutional Neural Network
## 4 Backup Path Design Method Based on BPDM-GCN  
### Data Transmission Path Optimization Algorithm Based on BPDM-GCN  
In the backup path design of this study, the BPDM-GCN-based data transmission path optimization algorithm aims to optimize the data transmission path in the communication network topology of the wide-area measurement system by combining the GCN and the DDPG algorithm, which provides a weight basis for key links to determine the backup path in the future. The following is a detailed introduction to the specific contents of the algorithm. The BPDM-GCN backup path design method employs an enhanced version of the DDPG algorithm that integrates GCN. Specifically, the GCN neural network replaces the original neural network within the DDPG algorithm to optimize the transmission paths for phasor data across the communication network topology of the wide-area measurement system. The DDPG algorithm, structured within the Actor-Critic framework, comprises two primary components: the Actor network and the Critic network. The Actor network employs a neural network to approximate a strategic function, mapping current network topology state information to corresponding actions within the action space. Meanwhile, the Critic network assesses and directs actions generated by the Actor network based on a defined reward function, aiming to refine and optimize the strategic actions generated by the Actor network. The DDPG algorithm commonly integrates Recurrent Neural Networks and Long Short-Term Memory Networks within the Actor and Critic networks. These neural networks typically demand substantial computational resources during training, particularly when optimizing network topology path weights. However, their adaptability and flexibility can be constrained. In order to improve the operating efficiency and generalization ability of the DDPG algorithm, the graph theory based on the GCN neural network is used to efficiently learn the structural information and link state information of the nodes in the communication network topology of the wide-area measurement system, so that the DDPG algorithm improved based on GCN can efficiently adapt to the communication network topologies of wide-area measurement systems of various scales. The DDPG algorithm framework based on GCN is shown in Figure 2.  
Figure 1: Backup path method architecture. Figure 2 shows the GCN-based DDPG algorithm framework, where the online policy GCN network, target policy GCN network, online \(Q\) GCN network, and target \(Q^{\prime}\) GCN network represent the improved online Actor policy network, target Actor policy network, online \(Q\) Critic network, and target \(Q^{\prime}\) Critic network. The algorithm's generalization capability is effectively enhanced through the parameter sharing and local connectivity properties inherent in the GCN neural network. The experience replay pool \(D\) stores \((s_{t},a_{t},r_{t},s_{t+1})\) data generated during interactions between the agent and the network topology environment, thereby reducing data correlation and enhancing algorithm stability. Green nodes represent normal status information nodes, red nodes (such as node 17) represent nodes with abnormal conditions (such as link failures, high packet loss rates, etc. ), and nodes are numbered 1-30 to identify each node in the network topology.The update process for the online policy network and the target network in the GCN-based DDPG algorithm proceeds as follows. (1) Online network update: The online network includes the online policy GCN network and the online \(Q\) GCN network. The online strategy GCN network generates action \(a_{t}=\mu(s_{t}|\theta^{\mu})\) based on the current network topology state \(s_{t}\) and parameter \(\theta^{\mu}\). \(s_{t}\) and \(a_{t}\) are passed to the online \(Q\) GCN network to generate function \([Q(s_{t},a_{t}|\theta^{Q})\) after iteration. The online \(Q\) GCN network transmits gradient information \(grad[Q]\) to update the online policy GCN network.