Methods for detection, monitoring, and determination of location of changes in rigid structures with arbitrarily complex geometries are described. Implementations include locating acoustic transducers that generate and receive acoustic signals at multiple locations along a surface of the rigid structure, wherein longitudinal spacing between the transducer locations define measurement zones. Acoustic signals with chosen amplitude-time-frequency characteristics excite multiple vibration modes in the structure within each zone. Small mechanical changes in the inspection zones lead to scattering and attenuation of broadband acoustic signals, which are detectable as changes in received signal characteristics as part of a through-transmission technique. Additional use of short, narrowband pulse acoustic signals as part of a pulse-echo technique allows determination of the relative location of the mechanical change within each zone based on the differential delay profiles.