Comparative Study of Time-Domain Fatigue Assessments for an Offshore Wind Turbine Jacket Substructure by Using Conventional Grid-Based and Monte Carlo Sampling Methods

Abstract

Currently, in the design standards for environmental sampling to assess long-term fatigue damage, the grid-based sampling method is used to scan a rectangular grid of meteorological inputs. However, the required simulation cost increases exponentially with the number of environmental parameters, and considerable time and effort are required to characterise the statistical uncertainty of offshore wind turbine (OWT) systems. In this study, a K-type jacket substructure of an OWT was modelled numerically. Time rather than frequency-domain analyses were conducted because of the high nonlinearity of the OWT system. The Monte Carlo (MC) sampling method is well known for its theoretical convergence, which is independent of dimensionality. Conventional grid-based and MC sampling methods were applied for sampling simulation conditions from the probability distributions of four environmental variables. Approximately 10,000 simulations were conducted to compare the computational efficiencies of the two sampling methods, and the statistical uncertainty of the distribution of fatigue damage was assessed. The uncertainty due to the stochastic processes of the wave and wind loads presented considerable influence on the hot-spot stress of welded tubular joints of the jacket-type substructure. This implies that more simulations for each representative short-term environmental condition are required to derive the characteristic fatigue damage. The characteristic fatigue damage results revealed that the MC sampling method yielded the same error level for Grids 1 and 2 (2443 iterations required for both) after 1437 and 516 iterations for K- and KK-joint cases, respectively. This result indicated that the MC method has the potential for a high convergence rate.

Validation of Improved Sampling Concepts for Offshore Wind Turbine Fatigue Design

“…This biased mean value only occurs for measurement data, where the occurrence probability of each bin does not completely match the long-term EC distributions. As postulated before [10,11], MCS outperforms DG. The good performance of MCS is supported by similar sampling and damage distributions (see Figure 10a).…”

“…Turbulent wind and irregular waves are considered in a stochastic process in each bin by conducting simulations of an overall length of one hour (normally divided into six 10 min simulations) per bin, as it is proposed by standards [5]. In industry and some academic studies [9][10][11], the same approach but with finer binning and bins for more EC (e.g., wind direction, wave height and period) is used to increase the accuracy and to reduce the uncertainty at the cost of higher computing times [9].…”

“…The multi-dimensional grid-based approach-used in industry-leads to more accurate approximations of the long-term fatigue damage. However, it was repeatedly shown that it is numerically inefficient [10,11]. Therefore, either meta models [9,13,14], replacing time-domain simulations and reducing the computing time of each model evaluation significantly, are applied or alternative sampling concepts, improving the computational efficiency by reducing the number of model evaluations while conserving the same level of uncertainty, are needed.…”

“…The most frequently applied probabilistic sampling concept is Monte Carlo sampling (MCS). In the context of fatigue design of offshore wind turbine substructures, MCS has recently been investigated by various authors [10,11,16,18,19]. On the one hand, probabilistic approaches can reproduce measurement results more precisely [20] and MCS is more suitable for high-dimensional input spaces [10,11].…”

“…In the context of fatigue design of offshore wind turbine substructures, MCS has recently been investigated by various authors [10,11,16,18,19]. On the one hand, probabilistic approaches can reproduce measurement results more precisely [20] and MCS is more suitable for high-dimensional input spaces [10,11]. On the other hand, fatigue damage approximations using probabilistic approaches and limited samples are quite uncertain [18,19] and MCS becomes inefficient (i.e., converges slowly) for highly non-linear model functions [10].…”