Kaimal spectrum based H2 optimization of tuned mass dampers for wind turbines

Abstract

The closed-form analytical expression of the objective function of a single degree of freedom system with the tuned mass damper, subjected to Gaussian white noise and Kaimal forcing spectrum, is derived implementing the H₂ optimization technique. To illustrate the procedure, a wind turbine tower with and without the tuned mass damper, subjected to wind load, has been presented. The Kaimal spectrum has been considered to model the effects of wind load. Usually, the parameters of the tuned mass damper is optimized by implementing the H₂ optimization technique on Gaussian white noise even though the system is subject to any other forcing spectrum. Obtaining an analytical closed-form expression of the objective function for a tuned mass damper system considering a real spectrum is very challenging as a real spectrum may contain fractional order of the frequency. Therefore, either objective function can be obtained numerically or an analytical form can be obtained but only for Gaussian white noise as an input forcing spectrum. To address the above-mentioned issue, in this paper, the concept of near identity spectrum is introduced to idealize the Kaimal spectrum with high accuracy from which a closed-form expression of the objective function can be established. Further, histogram plots of the response reduction have been made to show a comparison between the tuned mass damper system optimized with Gaussian white noise and the Kaimal spectrum. The results showed that the displacement response of the tuned mass damper system subjected to the Kaimal spectrum yields better performance if it is optimized according to the Kaimal spectrum rather than Gaussian white noise and vice versa.