Application of orthogonal algebraic polynomials for description of manoeuvring hydrodynamic forces

The objective of the present study is to investigate the use of orthogonal functions, namely Légendre polynomials, as functions for regression of hydrodynamic hull forces. This method provides several advantages compared to other conventional models based on polynomials. There is an explicit formula for calculating the regression coefficients and these form an unique set. This makes the model much easier to reduce to extend to lower or higher degrees, since the regression coefficients remain the same and can be easily computed. Moreover, orthogonal functions guarantee that the least-squares error is the lowest among all possible choices of regression functions. They also guarantee that each additional term in the expansion reduces the approximation error. They make the computation of the regression coefficients more efficient and they can be easily extended to higher degrees of freedom. In this preliminary investigation, the focus is on the case two variables. The method is introduced from a theoretical point of view, then applied to experimental data for moderate manoeuvres and the advantages of this approach are highlighted.

This paper is protected by copyright and therefore cannot be shared. You may obtain access to the paper directly from the official publisher via the link: Application of orthogonal algebraic polynomials for description of man.
Should you have any questions regarding the publication, please feel free to contact the authors directly.