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Multiple phase-shifted fiber Bragg gratings (MPS-FBGs) are proposed for a novel intensity-type vibration sensing scheme with broadband source based interrogation. In this scheme, the collective and simultaneous operation of the subchannels of MPS-FBG multiplies the total acquired signal power change at a particular channel, considerably enhancing sensitivity. Compared to a standard FBG scheme, our experiment scheme attained significant sensitivity enhancement of nearly 20 dB using 17 phase-shifted FBG. These experimental results agree with the theoretical prediction based on cross-correlation relations. The sensitivity enhancement while retaining the system simplicity would be an attractive option for an economical coarse wavelength division multiplexed (CWDM) vibration sensing system based on a single broadband source.