Real-time estimations of multi-modal frequencies for smart structures

In this paper, various methods for the real-time estimation of multi-modal frequencies are realized in real time and compared through numerical and experimental tests. These parameter-based frequency estimation methods can be applied to various engineering fields such as communications, radar and adaptive vibration and noise control. Well-known frequency estimation methods are introduced and explained. The Bairstow method is introduced to find the roots of a characteristic equation for estimations of multi-modal frequencies, and the computational efficiency of the Bairstow method is shown quantitatively. For a simple numerical test, we consider two sinusoids of the same amplitudes mixed with various amounts of white noise. The test results show that the auto regressive (AR) and auto regressive and moving average (ARMA) methods are unsuitable in noisy environments. The other methods apart from the AR method have fast tracking capability. From the point of view of computational efficiency, the results reveal that the ARMA method is inefficient, while the cascade notch filter method is very effective. The linearized adaptive notch filter and recursive maximum likelihood methods have average performances. Experimental tests are devised to confirm the feasibility of real-time computations and to impose the severe conditions of drastically different amplitudes and of considerable changes of natural frequencies. We have performed experiments to extract the natural frequencies from the vibration signal of wing-like composite plates in real time. The natural frequencies of the specimen are changed by added masses. Especially, the AR method exhibits a remarkable performance in spite of the severe conditions. This study will be helpful to anyone who needs a frequency estimation algorithm for real-time applications.