Analysis of the influence of climate change on the fatigue lifetime of offshore wind turbines using imprecise probabilities

When discussing the connection of wind energy and climate change, normally, the potential of wind energy to reduce green house gas emissions is emphasised. Hence, effects of wind energy on climate change are analysed. However, what about the other direction? What is the impact of climate change on wind energy? Recently, the effect of a reversal in global terrestrial stilling,that is, an increase in global wind speeds in the last decade, on the wind energy production has been analysed. Certainly, knowledge about potential changes in energy production is essential to plan future energy supply. Nonetheless, at least similarly important is the effect on loads acting on wind turbines. Increasing loads due to higher wind speeds might reduce wind turbine lifetimes and yield higher costs. Moreover, especially for already existing turbines, it might even affect the structural reliability. Since the impact of climate change on wind turbine loads is largely unknown, it is studied in this work in more detail. For this purpose, different existing models for predicted changes in wind speed and air temperature and their uncertainties are used to forecast the environmental conditions an exemplary offshore wind turbine is exposed to. Subsequently, for this turbine, the lifetime fatigue damages are calculated for different prediction models. It is shown that the expected changes in lifetime fatigue damages are present but relatively small compared to other uncertainties in the fatigue damage calculation

Probabilistic temporal extrapolation of fatigue damage of offshore wind turbine substructures based on strain measurements

Substructures of offshore wind turbines are becoming older and beginning to reach their design lifetimes. Hence, lifetime extensions for offshore wind turbines are becoming not only an interesting research topic but also a relevant option for industry. To make well-founded decisions on possible lifetime extensions, precise fatigue damage predictions are required. In contrast to the design phase, fatigue damage predictions can be based not only on aeroelastic simulations but also on strain measurements. Nonetheless, strain-measurement-based fatigue damage assessments for lifetime extensions have been rarely conducted so far. Simulation-based approaches are much more common, although current standards explicitly recommend the use of measurement-based approaches as well. For measurement-based approaches, the main challenge is that strain data are limited. This means that measurements are only available for a limited period and only at some specific hotspot locations. Hence, spatial and temporal extrapolations are required. Available procedures are not yet standardised and in most cases not validated. This work focusses on extrapolations in time. Several methods for the extrapolation of fatigue damage are assessed. The methods are intended to extrapolate fatigue damage calculated for a limited time period using strain measurement data to a longer time period or another time period, where no such data are available. This could be, for example, a future period, a period prior to the installation of strain gauges or a period after some sensors have failed. The methods are validated using several years of strain measurement data from the German offshore wind farm Alpha Ventus. The performance and user-friendliness of the various methods are compared. It is shown that fatigue damage can be predicted accurately and reliably for periods where no strain data are available. Best results are achieved if wind speed correlations are taken into account by applying a binning approach and if a least some winter months of strain data are available

A co-rotational based anisotropic elasto-plastic model for geometrically non-linear analysis of fibre reinforced polymer composites: Formulation and finite element implementation

Geometrical non-linearity is one of the aspects to be taken into account for accurate analysis of fibre reinforced polymers (FRPs), since large displacements and rotations may be observed in many of its structural applications such as in aircraft wings and wind turbine blades. In this paper, a co-rotational formulation and implementation of an invariant-based anisotropic plasticity model are presented for geometrically non-linear analysis of FRPs. The anisotropic constitutive equations are formulated in the format of isotropic tensors functions. The model assumes an anisotropic pressure-dependent yield function, and in addition to this, a non-associated plastic potential function in order to model realistic plastic deformations in FRPs. The formulation is then cast in the co-rotational framework to consider the geometrical non-linear effects in an efficient manner. The developed model is implemented in the commercial finite element (FE) software ABAQUS/Implicit via the means of the user-defined material subroutine (UMAT). The kinematics within the co-rotational frame is explained briefly while the important aspects regarding the numerical treatment and implementation are discussed in detail. Representative numerical examples at different scales are presented to demonstrate the applicability and robustness of the proposed development

Effect of moisture on the nonlinear viscoelastic fracture behavior of polymer nanocompsites: a finite deformation phase-field model

The mechanisms underlying damage in high-performance polymer nanocomposites are remarkably affected by hygrothermal conditions. In this study, we develop a phase-field formulation to investigate the influence of hygrothermal conditions on the nonlinear viscoelastic fracture behavior of epoxy resins and their nanocomposites at finite deformation. For this, the Helmholtz free energy, capturing the effect of temperature and moisture and nanoparticle contents, is defined based on an additive decomposition of the energy into an equilibrium, a non-equilibrium, and a volumetric contribution with different definitions under tensile and compressive loading. The coupled displacement phase-field problem is solved using a quasi-Newton monolithic algorithm and a staggered solution scheme. Numerical examples show that the monolithic algorithm is more efficient. Simulations are performed to investigate the effect of temperature, deformation rate, and moisture content on the force–displacement response of boehmite nanoparticle/epoxy samples in benchmark numerical problems. Comparing numerical predictions and experimental data for compact-tension tests shows good agreement at different nanoparticle contents. Also, the model’s capability to predict fracture patterns is evaluated using simulations of single-edge notched nanocomposite plates under tensile and shear loading. © 2022, The Author(s)

Assessment of a standard ULS design procedure for offshore wind turbine sub-structures

Sub-structures of offshore wind turbines are designed according to several design load cases (DLCs) that cover various fatigue (FLS) and ultimate limit states (ULS). The required DLCs are given in the current standards, and are supposed, on the one hand, to cover accurately all significant load conditions to guarantee reliability. On the other hand, they should include only necessary conditions to keep computing times manageable. For ULS conditions, the current work addresses the question whether the current design practice is, firstly, sufficient, and secondly, sensible concerning the computing time by only including necessary DLCs. To address this topic, data of five years of normal operation, simulated using a probabilistic approach, is used to extrapolate 20-year ULS loads (comparable to a probabilistic version of DLC 1.1 for substructures). These ULS values are compared to several deterministic DLCs required by current standards. Results show that probabilistic, extrapolated ULS values are fairly high and exceed standard DLC loads. Hence, the current design practice might not always be conservative. Especially, the benefit of an additional DLC for wave peak periods close to the eigenfrequency of the sub-structure is indicated

Very low frequency IEPE accelerometer calibration and application to a wind energy structure

In this work, we present an experimental setup for very low frequency calibration measurements of low-noise integrated electronics piezoelectric (IEPE) accelerometers and a customised signal conditioner design for using IEPE sensors down to 0.05 Hz. AC-response IEPE accelerometers and signal conditioners have amplitude and phase deviations at low frequencies. As the standard calibration procedure in the low-frequency range is technically challenging, IEPE accelerometers with standard signal conditioners are usually used in frequency ranges above 1 Hz. Vibrations on structures with low eigenfrequencies like wind turbines are thus often monitored using DC-coupled micro-electro-mechanical system (MEMS) capacitive accelerometers. This sensor type suffers from higher noise levels compared to IEPE sensors. To apply IEPE sensors instead of MEMS sensors, in this work the calibration of the entire measurement chain of three different IEPE sensors with the customised signal conditioner is performed with a low-frequency centrifuge. The IEPE sensors are modelled using infinite impulse response (IIR) filters to apply the calibration to time-domain measurement data of a wind turbine support structure. This procedure enables an amplitude and phase-accurate vibration analysis with IEPE sensors in the low-frequency range down to 0.05 Hz

Multi-Objective Global Pattern Search: Effective numerical optimisation in structural dynamics

With this work, a novel derivative-free multi-objective optimisation approach for solving engineering problems is presented. State-of-the-art algorithms usually require numerical experimentation in order to tune the algorithm’s multiple parameters to a specific optimisation problem. This issue is effectively tackled by the presented deterministic method which has only a single parameter. The most popular multi-objective optimisation algorithms are based on pseudo-random numbers and need several parameters to adjust the associated probability distributions. Deterministic methods can overcome this issue but have not attracted much research interest in the past decades and are thus seldom applied in practice. The proposed multi-objective algorithm is an extension of the previously introduced deterministic single-objective Global Pattern Search algorithm. It achieves a thorough recovery of the Pareto frontier by tracking a predefined number of non-dominated samples during the optimisation run. To assess the numerical efficiency of the proposed method, it is compared to the well-established NSGA2 algorithm. Convergence is demonstrated and the numerical performance of the proposed optimiser is discussed on the basis of several analytic test functions. Finally, the optimiser is applied to two structural dynamics problems: transfer function estimation and finite element model updating. The introduced algorithm performs well on test functions and robustly converges on the considered practical engineering problems. Hence, this deterministic algorithm can be a viable and beneficial alternative to random-number-based approaches in multi-objective engineering optimisation

MOGPS Supplementary Material

Additional analytical test functions optimised using Multi-Objective Global Pattern Search