document: 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 -LRB- AR -RRB- and auto regressive and moving average -LRB- ARMA -RRB- 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
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extractive_keyphrases: smart structures frequency estimation noise control bairstow method characteristic equation arma cascade notch filter linearized adaptive notch filter recursive maximum likelihood methods vibration signal
abstractive_keyphrases: multi-modal frequencies real-time estimation adaptive vibration control auto regressive and moving average methods real-time computations wing-like composite plates frequency estimation algorithm real-time applications