At present, the structural damage detection of aircraft strength tests is mainly conventional non-destructive testing methods and acoustic emission methods, non-destructive testing methods have the shortcomings of poor real-time performance, high missed detection rate, and only post-event detection, and acoustic emission methods have problems such as sensitivity to materials and easy noise interference. Aiming at the short-time impulsive abnormal sound caused by structural damage, a non-contact acoustic detection method is proposed based on a microphone array and compressed sensing (CS) algorithm. To verify the method, a lateral and forward sound source localization test is conducted for the abnormal sounds that occur in the typical aircraft structural strength test - aircraft landing gear retraction test, and the OMP-SVD algorithm of CS, which combines the orthogonal matching pursuit (OMP) and the singular value decomposition (SVD) is used to solve the problem. The results show that the proposed acoustic detection method can perform real-time high-precision localization of the short-time impulsive abnormal sound generated by the collision of the test object. Compared with the conventional beamforming (CBF) algorithm, the OMP-SVD algorithm performs better for multiple abnormal sounds with different intensities in the low signal-to-noise ratio aircraft strength test environment.