In this work, we present four different methodologies for reducing the computational effort of fatigue assessment for offshore wind turbine support structures. To test these methods, we use them to predict the total fatigue damage of several modified support structure designs based on subsets that represent a reduction of about 6-17 times the original size of the load case set. Three of the methods are able to give quite accurate predictions, with expected errors of no more than 4-8%, though there are some limitations due to the variance inherent in some of the methods.
One of the main challenges for the design of offshore wind turbines support structures is the complexity of both the structure itself and the offshore environment. This complexity means that assessing the performance of the structure requires not only the use of detailed models, but also investigating a large number of different scenarios. Specifically, with reference to the standards that the design must conform to (e.g. International Electrotechnical Commision (2009)), there are literally thousands of different design load cases (DLCs) that must be assessed for any given structure, covering both all the various environmental states one expects to encounter at a given site and all the various scenarios that the structure is likely to experience. To summarize, we need to run detailed models and we need to run them many times. For one single assessment of a design, this can be accommodated by ever improving computer hardware and increased access to computer clusters for both institutions and individuals. However, for those wishing to run either probabilistic assessments or to optimize the design (or worse still, both of these at the same time), the large number of DLCs remains an important challenge. One that should be addressed not just by improved hardware, but by improved methodology. This is the main topic of the work to be presented below.
As it stands, it is not possible to completely replace the standard assessment with something new. Rather, one seeks to approximate the results of such full assessments by a less computationally demanding procedure. If the approximation is good enough, it may then serve well as a replacement for the conventional procedure when small deviations from the true estimates (e.g., fatigue damage) are allowable. Especially in a context like optimization, simplifications leading to such small deviations are often expected and, if the size of the deviations can be estimated, one may even incorporate these as modeling errors in a probabilistic analysis. Previous work attempting to find approximate simplified assessments have encountered some success, but have tended to be very simplified (for example in terms of the types of DLCs studied), have struggled to get a sufficiently accurate approximation while also getting a sufficient decrease in analysis time or have faced a combination of these issues. One approach is to completely abandon the time domain and instead attempt to analyze the structure in the frequency domain (see e.g. van der Tempel (2006)), but this approach has its own set of issues and we will here focus on methods in the time domain.
The Markov approach to estimate fatigue damage for a monopile-based offshore wind turbine exposed to aerodynamic and hydrodynamic loading is investigated in this study. The focus of this study is on obtaining the rainflow-counting intensity from a peak-trough counting using the Markov method proposed by Frendahl & Rychlik. The fatigue damage estimated from the rainflow-counting intensity is compared to fatigue damage estimated from the original time-series using the rainflow-counting algorithm. The comparison is performed for different load situations. The study shows that the Markov approach performs the best for load situations where wave loading is dominating the response, making it interesting for load calculations of large-diameter monopiles and monopiles in parked or idling conditions.
Offshore wind turbines are prone to failure from fatigue damage due to their exposure to a significant source of quasi-periodic excitations from wind and waves. A detailed fatigue assessment is based on cycle counting (the rainflow-counting algorithm is widely used) from a large number of load simulations in the time-domain, typically in the order of a few thousand. Detailed fatigue assessment is therefore primarily performed in the final stage of the design process (Seidel et al. 2016), since it is inefficient for sensitivity studies or conceptual design phases where several designs have to be assessed. Simplified and/or reduced models of wind turbines or loads (Muskulus, 2015; Schløer et al., 2016; Ong et al., 2017) or calculations in frequency-domain (Ragan & Manuel, 2007; Seidel 2014; Ziegler et al., 2015) are commonly used to estimate fatigue damage in these situations.
Another method to compute the expected damage was proposed by Frendahl & Rychlik in 1993. Fatigue damage is estimated by assuming that the sequence of local extrema forms a Markov chain. This allows to obtain the rainflow-counting intensity directly from the spectrum of the input loads (referred to load spectrum throughout this paper) without the need for response time series in the time-domain. The fatigue damage can be estimated from the rainflow-counting intensity afterwards. The benefit of this method is the possibility to estimate the total damage from a load spectrum without the need to perform lengthy and computationally demanding simulations in the time-domain. The flowchart for both methods are shown in Fig. 1.
Due to large variability of the offshore environment, the load analysis of an offshore wind turbine is a complex task. It is normally performed in the time domain, by running stochastic simulations. This is usually very time consuming due to the necessity of having long time series in order to obtain results with little bias, or to sample events with a low probability of happening. An alternative is to perform the analysis in the frequency domain. The drawback is that this method is only valid for linear systems, which makes it rather inaccurate for fatigue damage results. Also, there are well-known inaccuracies when estimating fatigue damage from a response spectrum. This paper investigates a novel approach based on probability evolution methods, which can obtain accurate results for linear, as well as non-linear systems. The method is not very well known, and a drawback is that it can be numerically challenging, especially for high-dimensional problems. The benefits of the method are that it evaluates all possible states of the wind turbine without generating a long signal in the time domain. We show how this can be used to efficiently evaluate fatigue damage.
This paper presents a probability density evolution method in the time domain for a simplified wind turbine model with one mode. The cell mapping approach discretizes the two-dimensional phase space (Hsu, 1987). The method is evaluated using both deterministic and random loads and compared to time domain simulations. Different sizes in the discretization of the mesh and in the area of state space covered are investigated, to determine when the method converges towards the final solution. The algorithm has been programmed in Python with the Numba Just-In-Time compiler to help speed up the calculations. How to implement a simple stochastic load model by the cell-mapping method is discussed. The result is a joint response probability density that contains information about the extrema of the structure motion, and how often these occur. This allows for calculating Markov transition probabilities between minima and maxima from the response density, which then makes it possible to estimate fatigue damage. Determining the response probability density is done by many short time-domain integrations, instead of one or more long simulations. The main novelty introduced and demonstrated here is that as soon as one has calculated the cell mapping, one can easily obtain the peak transition matrix and use this to obtain fatigue damage estimates.
In this paper we show how a new idea for how to calculate the derivatives of extrapolated 50-year return values, used in extreme load safety criteria, can be used to estimate the uncertainty in these return values resulting from uncertainty in the simulations and in the load extrapolation procedure itself. The method yields uncertainty estimates with a high degree of accuracy. Additionally, to highlight one of the subtler uncertainties involved in this setting, we also make a small study of how changing the block size used in the extraction of maxima from load time series affects the 50-year return value.
Finding ways to reduce the cost of offshore wind turbine support structures is one of the main objectives of current research on this topic. One of the main challenges involved in cost reduction of structures is the balance between measures that reduce the resistance to loading (like e.g. lighter designs) and the safety requirements. A primary reason for the difficulty posed by this balance is the large amount of uncertainties in the analysis. On the load side there are a lot of uncertainties coming from various sources such as measurements, local variations within windfarms and simplified modeling of the environment. In the structure there are uncertainties such as those related to the production of components and to simplified structural models. The usual solution to this issue is to make designs that are very conservative, scaling preliminary designs as dictated by analysis by large safety factors. Hence, increased knowledge about uncertainty could potentially enable designers to be less conservative and make more economical choices.
Extreme load, or Ultimate Limit State (ULS), criteria present a particular challenge for uncertainty analysis due to the way these are evaluated. Chiefly, this is because of the requirement (Det Norske Veritas, 2014) that extreme loads should be the 50-year return values calculated from the loads obtained by simulations. While this is a standard procedure in the design of wind turbines, it is not trivial. It entails fitting the short term maximum loads to extreme value distributions and then extrapolating from these distributions to the 50-year return value. A considerable amount of work has gone into the study of various aspects of the load extrapolation procedure for wind turbines. A comparison of three different approaches, including a process model, was made by Cheng (2002). A study of the effect of turbulence level on the predicted extreme load was performed by Moriarty et al. (2002). A report discussing, among other things, several aspects of extreme load extrapolation, including selection of threshold values, the statistical uncertainty of the fits, details of both short term and long term statistics and possibilities for model simplification was made by Moriarty et al. (2004). Further studies and discussion of various standard and alternative methods for short term fitting and long term extrapolation methods, as well as details of uncertainty, can be found in, e.g., Saranyasoontorn and Manuel (2006), Ragan and Manuel (2007), Agarwal and Manuel (2007), Fogle et al. (2008), Toft and Sørensen (2009), Agarwal and Manuel (2010) and Dimitrov (2016).
The influence of the accuracy of the weather forecast on the availability and production losses for a given maintenance policy are investigated in this paper. This is done by varying the look ahead time, with accurate weather forecast, of a simulation model. The results show that for the maintenance policy that was chosen for the model, the availability of the wind farm decreases while production losses increase with a longer look ahead time. This is caused, since in the given policy, maintenance actions are not started, if the weather forecast predicts a storm during the time needed for the maintenance action. This also demonstrates the importance of a proper maintenance strategy.
Offshore wind energy is still significantly more expensive than onshore wind energy and not yet economically profitable without governmental subsidies. One of the driving factors is the cost of operations and maintenance in offshore wind farms. Since corrective maintenance causes longer down-times and therefore higher cost, reducing the amount of corrective maintenance and optimizing the scheduling of the corrective maintenance tasks are in the focus of current research. To tackle the problem of optimising the scheduling of corrective maintenance, several models to simulate the scheduling of corrective maintenance have been developed by Douard et al. (2012), Scheu et al. (2012), Dinwoodie et al. (2013), Hofmann and Sperstad (2013), Endrerud et al. (2014) and Endrerud and Liyanage (2015).
These models include different aspects of the maintenance scheduling, such as wind turbine and component failures, spare part and crew gathering times, vessel activation times, wind farm access, repair operations and weather conditions, like wind speed and wave height. All of these influencing factors are subject to uncertainties. However, most models assume constant values for one or more of them. A sensitivity analysis by Martin et al. (2016), using one of the models, has shown that the most important factors influencing the operations and maintenance cost and wind farm availability are access and repair costs as well as failure rates. The influence of the variation in repair times on the maintenance delays due to sea state, the availability and the production losses have been investigated by Seyr and Muskulus (2016a) using an analytical model for the delay from Feuchtwang and Infield (2013). Variations in the repair times and their influence on the availability and production losses were investigated by Seyr and Muskulus (2016b) using the simulation model from Scheu et al. (2012).
The statistical properties of the local slamming forces on the braces of a jacket structure are analyzed based on experimental data. The slamming forces from the plunging breaking waves are first reconstructed by using an inverse method together with the measured response forces in the wave test and the hammer test. The reconstructed forces from five wave cases under the same wave conditions, each including 20 waves, are investigated. The features of the forces regarding the position of the wave in the test, the case number and the location on the braces are discussed. The confidence intervals of the mean peak forces and the mean impulses are given as the statistical estimation of the slamming forces.
The support structures used in the offshore wind industry are exposed to plunging breaking waves at certain locations. These waves exert slamming forces on the structures, which feature high impact forces during short time (Alagan Chella et al., 2012). For the structures exposed to such wave conditions, the slamming forces are necessary to be considered in the design of the offshore wind turbines, which is extensively discussed by various standards and guidelines (IEC, 2009; DNV, 2014; GL, 2009).
The experimental researches on the slamming forces so far mainly focus on monopile structures (or slender cylinders) (Wienke, 2005; Irschik, 2004; Bredmose, 2013). Regarding the slamming forces on jacket structures, a 1:50 scale experiment was first carried out at NTNU (Aashamar, 2012). Later, a larger scale experiment was realized by the WaveSlam Project, in which a 1:8 model of a jacket structure was used (Arntsen and Gudmestad, 2014). As the first experimental research for jacket structures at this scale, the WaveSlam Project provides many valuable data for the investigation of the slamming loads on such structures.
The concept of floating wind turbines is as old as the idea of offshore wind turbines itself. In order to use the vast offshore wind resources, Heronemus proposed floating wind turbines already in 1972. However, it took about 20 years to even produce electricity with fixed offshore wind turbines: in 1991, the offshore wind park “Vindeby” was commissioned, featuring eleven turbines with monopile substructures. Only two years after that, the FLOAT project (cf. Tong, 1998) was accomplished. FLOAT proposed to mount a three-bladed horizontal axis wind turbine on a spar-type floater with catenary mooring lines and also realized a model test with this concept. From then on, a lot of different concepts for floating wind turbines have been proposed and investigated. This lead to the world’s first full-scale floating wind turbine, the Hywind prototype, which was installed in 2009. Since then, more concepts have been proposed, more prototypes have been realized, and a lot more research has been done with respect to floating wind turbines. The reasons for pursuing floating wind energy in contrast to continuing working with fixed-bottom offshore wind turbines are manifold. Floating wind turbines can be installed with less noise emission compared to fixed-bottom wind turbines, as piling is typically not necessary. Furthermore, depending on the floating concept and localocation, the system can be assembled from the quay and/or in sheltered waters, and is then towed to the location with standard offshore vessels (in contrast to specialized and expensive installation vessels that are used for fixed-bottom offshore wind turbines). The time needed for costly marine operations, such as installation of the turbines, is thereby significantly reduced.
However, the most important argument for floating wind turbines is their independence on water depth compared to fixed-bottom substructures. The feasibility of the latter has an economic limit that strongly depends on the water depth. This limit is softer for floating wind turbines. Hence, floating wind energy is especially interesting when sites for fixed-bottom wind turbines become scarce (e. g. in the UK) or when mainly deep water sites are available (e. g. in Japan, Norway, or the USA).
Offshore wind turbines are getting bigger and are being installed in deeper waters (Arapogianni et al., 2013). This results in a huge interest of both the industry and research community to bring floating offshore wind turbines into the market at a reasonable cost of energy. Henderson and Witcher (2010) and Wang et al. (2010) reviewed the state of the art of floating wind energy previously. However, since 2010 the number of publications dealing with floating wind energy has grown exceptionally (James and Costa Ros, 2015). The recent review by Tande et al. (2015) focuses more on a general overview of existing prototypes than on details and research aspects. This motivates the need for a more recent, in-depth review of the research on floating wind energy. We present and discuss the current
state of the art in terms of design and dynamics of floating wind turbines, taking into account the latest literature. In addition, current challenges for floating wind turbines are summarized, special issues are discussed, and recommendations for future work and research are given.
Schafhirt, Sebastian (Norwegian University of Science and Technology) | Verkaik, Niels (Keppel Verolme BV) | Salman, Yilmaz (Keppel Verolme BV) | Muskulus, Michael (Norwegian University of Science and Technology)
The most accurate analysis of an offshore wind turbine is still a timeconsuming and computational demanding simulation in the timedomain. In order to accelerate the analysis, a substructuring technique, which is based on the principle of superposition of impulse responses was combined with the power of modern general purpose graphics processing units. This gives the ability to perform a simplified analysis of an offshore wind turbine with complex lattice support structure forty times faster than specialized commercial available state-of-the-art software is capable of running it, without a loss in accuracy. Implications for research and practice are discussed.
For offshore wind structures located in shallow water, slamming loads resulting from plunging breaking waves are important for the fatigue assessment during the design. This study investigates the slamming loads on the bracings of a truss structure, based on the analyses of the local force data measured in a 1:8 scale experiment. A hammer test analysis is conducted to check the properties of the structure. A wave test analysis is carried out to estimate the slamming loads. An Optimization based Deconvolution (ODC) method, which uses the linearity of the structure, is proposed for the estimation. The optimal values of eight parameters representing the slamming loads are obtained. This local force model demonstrates an astonishingly good reconstruction of the experimental results, given the simplicity of the approach.
It is shown how to reconstruct the total rotor loads from complex numerical wind turbine simulations of support structures, using a simplified one-dimensional equation of motion with effective parameters determined through simple numerical experiments. The reconstructed forces match the original forces very well with only a few percent differences in response and fatigue lifetime. This is in strong contrast to what happens when one naïvely uses the element forces, which leads to a resonance problem. The method opens up the possibility for detailed studies of rotor loads and aerodynamic damping by numerical simulations.