Anomaly Detection Algorithms Based On Graph Signal Processing

In recent years,with the rapid development of the intelligent sensor technology,information communication technology,as well as physical infrastructure networks such as smart grids,traffic networks and meteorological networks,the signal processing technology to process the data from those various irregular networks has aroused increasing attention.However,classical signal processing technologies might not efficiently process the data,due to the complex relationships and interactions between the elements of data residing on irregular networks.Recently,the graph signal processing(GSP)technologies,extended from classical discrete time signal processing(DSP)technologies,could model these data including their complex interactions well,and efficiently process the data residing on nodes of an irregular graph.Additionally,in practical applications,people may naturally encounter the data associated with the edges of a graph.With the help of the Hodge theory,the GSP technologies could be extended to the technologies which could handle the graph signal indexed by edges.In this thesis,based on the anomaly detection technologies in the GSP field,the detection of false data injection attacks(FDIAs)in smart grids is discussed.Specifically,the main research content of this thesis includes the following three parts.(1)The detection of the presence of FDIAs in smart grids is studied,with the system states at each bus of power systems.Based on the graph filter technology of the GSP,with the graph frequency domain analysis of system states,a Graph High Pass Filter(GHPF)detection algorithm is proposed,by exploiting the deviation of the system state under detection from the historical FDIA-free system state baseline.This FDIA detection algorithm is incorporated with both an adjustable cutoff frequency and an adjustable detection threshold.Simulation results validate that compared to the state-of-the-art GHPF detection algorithms,the proposed flexible algorithm can effectively improve the FDIA detection performance and can be easily transplanted to different power systems of different underlying topologies.(2)The locational detection of FDIAs in smart grids is expected to be realized.Based on the graph attention mechanism and graph neural network(GNN)technology,by utilizing either power injection measurements or system state estimates,the Graph Convolutional Attention Network(GCAT)-based FDIA detector is developed.Moreover,simulation results validate the superior locational detection performance of the proposed detector.(3)In the edge space,the locational detection of the presence of FDIAs in smart grids is studied.Utilizing the power measurement data at each branch and bus in smart grids,based on the Hodge theory,a Hodge Aggregation Graph Neural Network(AGNN)-based FDIA detector is proposed,by incorporating the Hodge Laplacian into the GNN architecture.Further,incorporating the graph attention mechanism,a Hodge Aggregation Graph Attention Network(AGAT)-based FDIA detector is proposed.Moreover,a Hodge GCAT-based FDIA detector is also proposed by incorporating a simplex convolution filter.Simulation results show the effectiveness of three proposed detectors.