Nonstationary response of floating structures to random waves

Even if ocean waves are treated as a stationary random process, dynamic responses of floating structures to random waves at the transient state are always nonstationary. When nonstationary response statistics is desired, a common technique is to apply Monte Carlo simulations; however, its implementation is costly in computational time. Analytically, this article develops an efficient method for computing nonstationary response statistics, including evolutionary power spectrum and time-varying mean-square values. Assuming a hydrodynamic software has been employed to get various frequency response functions, a prerequisite of the proposed method is to get the elevation-to-motion transfer function formulated in its pole-residue form. The proposed method is applicable to arbitrary wave spectrum and has been based on pole-residue operations implemented in the Laplace domain to obtain closed-form solutions for the response evolutionary power spectrum. Numerical examples choose a single-degree-of-freedom Spar model and a six-degree-of-freedom Floating Production Storage and Offloading model to a Pierson–Moskowitz wave spectrum, and the correctness of the computed mean-square values is verified by Monte Carlo simulations.