Phase-Shifting Filtering Method for Simulating Three-Dimensional Directional Ocean Waves

Ocean wave action is a key environmental load on marine structures, and its numerical simulation is a critical issue in the field of ocean engineering. In stochastic dynamic response analysis and time-variant reliability analysis, say, by the dimension-reduced probability density evolution equation (DR-PDEE), accurate representation of wave excitation through filtering methods is essential. To advance the probability density level analysis in ocean engineering, it is necessary to develop filtering methods for wave fields that align with fundamental physical principles. In this paper, a phase-shifting method for calculating the phase difference between wave elevations at different points on the sea surface based on the Fourier transform and its inverse is first introduced. The method enables the generation of wave elevations in long-crested waves from a single-point signal. To simulate short-crested wave fields, the wave direction is discretized into multiple intervals, and a filtering simulation method based on the linear superposition principle along with the Mitsuyasu-type directional spreading function is proposed using a designed digital filter system. The validity of the proposed method is verified by illustrating three numerical examples: the long-crested wave case, the short-crested wave case, and the case of wave force calculation on two columns in a wave field. The necessity of adopting wave fields for calculating wave loads on large offshore structures is demonstrated. The proposed method can be applied in the dynamic response analysis of various ocean engineering structures.