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We focus on an inverse problem for identifying physical parameters such as Young's modulus and air and structural damping coefficients in the mathematical model of cantilevered beams subject to random disturbance, using dynamic noisy data measured on its vibration taken in a nondestructive manner. First, we describe mathematical models of the cantilevered beam by an Euler-Bernoulli type partial differential equation including parameters to be identified and the measurement equation, taking vibration data including the observation noise. Second, the identification problem using random dynamic data is divided into an estimation problem obtaining the (modal) state estimate and a least-squares problem determining unknown parameters, and then the unknown parameters are determined recursively by using the pair of algorithms alternately. Finally, in order to verify the efficacy of the proposed identification algorithm, simulation studies and experiments are shown.