Cross-mode couplings for the fatigue damage evaluation of trimodal Gaussian processes

In ocean engineering, the fatigue damage evaluation of structures subjected to random stress in the design stage is of great practical interest. The stress can be a single-mode, bimodal or multi-modal Gaussian process. Traditional spectral methods used to focus on establishing a probabilistic model for the rainflow stress cycles to count the accumulation of damage. Recently, authors have developed a state-of-the-art bimodal spectral discretization method which crosses the border of traditional methods by introducing a coupling coefficient xi to reflect the interaction between low- and high-frequency components. The present study extends this accurate bimodal method to solve the more complicated trimodal Gaussian problems. A cubic coefficient is developed to account for cross-mode couplings among low-, medium- and high-frequency components. Extensive comparisons with time-domain rainflow counting method and traditional spectral methods are conducted to validate the high level of accuracy and efficiency of this trimodal method. Moreover, via the proposed trimodal method, the respective contributions of different frequencies and their couplings to the overall fatigue damage in a multi-modal situation can be thoroughly differentiated. Comprehensive case studies including an analysis of a floating wind turbine have evidenced the important role of cross-mode couplings in the total damage of fatigue.