Abstract: When attempting to identify vibration in a lightweight robots' structure in a telemanipulation system, the conventional vibration identification method experiences bottleneck due to its narrow bandwidth and the low communication frequency of the communication link. As such, there is a need to study ways to reduce the amount of data being transmitted. For this purpose, we studied the problem of vibration identification in mechanical structures for a sub-Nyquist sample, using the ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm, and propose a method for adding sampling points (ASP). We substitute mean value matrices for the correlation matrices used in the conventional ESPRIT algorithm, which overcomes the ill-conditioning problem and reduces the calculation required, while also using sampling data efficiently. Vibration frequencies and attenuation coefficients are respectively identified and then matched in pairs, which resolves the contradiction between frequency de-aliasing and the accurate identification of attenuation coefficients. We use the discrepancy method to match the vibration frequencies.