A Fast Online Estimator of the Two Main Vibration Modes of Flexible Structures From Biased and Noisy Measurements

Vibrations are present in many mechanical structures and machines, and are often associated with their elastic parts. Characterizing these vibrations, i.e., obtaining their frequencies, amplitudes and phases, is of most interest in many applications ranging from the maintenance of civil structures to motion control. This paper presents a method for the online and reliable identification of the defining parameters of two unknown sinusoidal signals through the use of their measured sum in the presence of noise and an offset. It is based on the algebraic derivative approach, defined in the frequency domain, which yields exact calculation formulae for the unknown parameters of the signal, i.e., the amplitudes, phases, and frequencies of the two sinusoids and the value of the constant term. The online estimation is performed in a time interval which is only a fraction of the first full cycle of the slower component of the measured signal. This feature allows the algorithm to be used to monitor time-varying parameters in these vibration signals. This algorithm has been used in experiments with a flexible beam, which is a representative platform of a vibrating mechatronic system. It estimated all the vibration signal parameters quickly and accurately, proved to be insensitive to high-frequency noises, and accurately tracked the time variations of the signal parameters.