Wave episode based Gaussian process regression for extreme event statistics in ship dynamics: Between the Scylla of Karhunen–Loève convergence and the Charybdis of transient features

Statistical modeling of fully nonlinear hydrodynamic loads on offshore wind turbine monopile foundations using wave episodes and targeted CFD simulations through active sampling

“…[40][41][42][43][44] In addition, scientists have addressed the question of experimental design for these studies-what waves to simulate-with a number of methods, including stochastic wavegroups, 45,46 critical wavegroups, [47][48][49][50] equivalent waves, 51 reduced order wavegroups, 40,52,53 and Karhunen-Loève (KL) wave episodes. 54 While previous studies have explored surrogate models using methods like polynomial-chaos expansion and Kriging, 55 there is a growing interest in utilizing machine learning approaches. However, according to Elyasichamazkoti and Khajehpoor, 56 most existing studies develop surrogate models focusing on specific areas such as fault detection, wind speed and power forecasting, power optimization, and control.…”

“…To handle time series prediction via the surrogate modeling, dimension reduction techniques such as KL and PCA are employed, while the GPR model accounts for nonlinear dependencies, including those associated with extreme events. While similar techniques have been used in ship hull load calculations, 54 wave episode methods have not been applied to estimate hydrodynamic loads on monopile structures before.…”

“…In Section 2, we briefly recapitulate the design of KL wave episodes first described in Guth and Sapsis. 54 In Section 3, we describe the techniques we use to build the surrogate model: GPR, active sampling, and spectrum transfer. In Section 4, we describe our CFD simulation design in the OpenFOAM software, and describe some of the challenges we faced adapting this approach to nonlinear waves.…”

“…In addition, scientists have addressed the question of experimental design for these studies—what waves to simulate—with a number of methods, including stochastic wavegroups, 45,46 critical wavegroups, 47–50 equivalent waves, 51 reduced order wavegroups, 40,52,53 and Karhunen‐Loève (KL) wave episodes 54 . While previous studies have explored surrogate models using methods like polynomial‐chaos expansion and Kriging, 55 there is a growing interest in utilizing machine learning approaches.…”

“…To handle time series prediction via the surrogate modeling, dimension reduction techniques such as KL and PCA are employed, while the GPR model accounts for nonlinear dependencies, including those associated with extreme events. While similar techniques have been used in ship hull load calculations, 54 wave episode methods have not been applied to estimate hydrodynamic loads on monopile structures before. Overall, this work presents a pioneering framework to model short‐term extreme hydrodynamic loads statistics on monopile foundations showcasing its potential in improving the understanding and prediction of extreme loads in offshore wind turbine design.…”