The security of Unmanned Aerial Vehicle (UAV) swarms is threatened by the deployment of anti-UAV systems under complicated environments such as battlefield. Specifically, the faults caused by anti-UAV systems exhibit sparse and compressible characteristics. In this paper, in order to improve the survivability of UAV swarms under complicated environments, we propose a novel multi-abnormality self-detecting and faults location method, which is based on compressed sensing (CS) and takes account of the communication characteristics of UAV swarms. The method can locate the faults when UAV swarms are suffering physical damages or signal attacks. Simulations confirm that the proposed method performs well in terms of abnormalities detecting and faults location when the faults quantity is less than 17% of the quantity of UAVs.