Robust adaptive analysis of extreme dynamic responses of wave energy converters

In the current study, a new adaptive binned kernel density estimation method has been introduced. In the proposed new method, Fourier transforms have been utilized to accomplish the convolution rather than performing the convolution by hand. By utilizing the fast Fourier transform, direct and inverse Fourier transforms have been found in a relatively short amount of time when implementing the new method. Upon analyzing the computed results, it has been observed that the newly proposed adaptive binned kernel density estimation distribution curve exhibits a high level of smoothness in the tail region. Furthermore, it demonstrates a strong alignment with the histogram derived from the recorded ocean wave dataset obtained at the NDBC station 46053. These are the major advantages of the proposed new method comparing with other existing methods such as the parametric method, the ordinary KDE method, and Abramson's adaptive KDE method. The specific research gap identified in the field is that none of the existing methods can predict the sea state parameter probability distribution tails both accurately and efficiently, and the proposed new method has successfully addressed this research gap. Upon careful examination of the calculation results, it becomes evident that the projected 50-year extreme power-take-off heaving force value, derived using the newly proposed method, is 1989300N. This value significantly surpasses (by more than 9.5%) the forecasted value of 1816200N obtained through the application of the Rosenblatt-I-SORM contour method. The findings of this study suggest that the newly proposed adaptive binned kernel density estimation method exhibits robustness and demonstrates accurate forecasting capabilities for the 50-year extreme dynamic responses of wave energy converters.