Estimation of Roll Damping Parameters Using Hermite Wavelets: an Operational Matrix of Derivative Approach

The steady-state ship rolling motion in random beam seas with nonlinear damping and restoring moments are explored mathematically in this work. The Hermite Wavelet Method (HWM) is applied to estimate the parameters in ship roll models. We get the closed-form solutions for the roll angle, damping, and restoring moments using the HWM. Ship motion modeling based on fractional derivatives is also analyzed. The required solution of the governing equation is derived using the operational matrices of Hermite wavelet derivatives. Using operational derivative matrices with the appropriate collocation point, the nonlinear differential equations with boundary conditions are transformed into a system of algebraic equations. The proposed HWM solutions are compared with the results obtained from HPM and OHAM. For small parameter values k and M, the HWM results are much closer to the HPM, OHAM, and numerical MATLAB solutions. Moreover, using HWM is found to be a straightforward, flexible and simple method for solving nonlinear differential equations.