# BPDM-GCN: Backup Path Design Method Based on Graph Convolutional Neural Network
## 4 Backup Path Design Method Based on BPDM-GCN
### Theoretical and Practical Correlation of GCN and DDPG Fusion Mechanism  
#### 4.3.1 Benefits of GCN for Dynamic Network Topology Modeling  
The traditional DDPG algorithm uses a fully connected neural network (FCN) or a recurrent neural network (RNN) to process the state space. However, in the communication network of a wide-area measurement system, the connection relationship between nodes has a graph structure characteristic. It is difficult for FCN to capture the dynamic correlation of the topology. Its fixed input dimension and local perception ability are difficult to adapt to the dynamic graph structure characteristics of the wide-area measurement system communication network [19]. This paper uses a graph convolutional neural network (GCN) as the core network of DDPG for the following reasons:  
Figure 3: Backup path based on incremental shortest path tree. (1) Graph structure perception capability: GCN directly models the connection relationship between switch nodes through the spectral domain convolution operation of the adjacency matrix and the node feature matrix, capturing the dynamic changes of the network topology. (2) Parameter sharing and generalization: The convolutional layer of GCN shares the weight matrix between different nodes, avoiding the parameter explosion problem caused by changes in network scale in traditional FCN, and supports generalization training from 14 nodes to 118 nodes. (3) Multi-scale feature fusion: By stacking multiple layers of GCN, the algorithm can simultaneously aggregate local link status (latency, bandwidth) and global topology (node degree, path redundancy), providing high-dimensional semantic features for DDPG. [PERSON] et al. focused mainly on data center networks. To solve the problem that existing algorithms ignore network energy consumption, energy saving and network performance are taken as joint optimization goals. The improved DDPG algorithm is combined with a convolutional neural network to achieve energy-saving routing scheduling [20]. This paper focuses on the communication network of wide-area measurement systems. To solve the problems of poor applicability of existing faulty link recovery algorithms and backup path congestion during network topology migration, the graph convolutional neural network (GCN) and deep deterministic policy gradient algorithms are integrated to optimize the backup path. The differences and innovations in the algorithm design and experimental verification of this paper can be summarized as follows. (1) Innovative algorithm fusion: A backup path algorithm BPDM-GCN based on graph convolutional neural network is proposed to improve deep deterministic policy gradient. When dealing with network topology path weight optimization, the traditional DDPG algorithm, such as the recurrent neural network, has the problems of large computational resource requirement and limited adaptability. In this paper, GCN is used to directly model the node connection relationship in the network topology. Through the spectral domain convolution operation of the adjacency matrix and the node feature matrix, the dynamic changes of the network topology are captured, and the adaptability of the algorithm to the communication network topology of different scales of wide-area measurement systems is improved. (2) Optimization of backup path implementation: A backup path implementation method based on the incremental shortest path tree is designed. Considering the difference in physical distance of nodes in the communication network of the wide-area measurement system, the long backup path will increase the delay of faulty link recovery. According to the link weight output by the BPDM-GCN algorithm, this method uses the incremental shortest path tree algorithm to calculate the shortest backup path from the source node to the destination node. It can dynamically adapt to the changes in network topology and reduce the transmission delay of phasor data in the backup path.