Evaluation of the fatigue limit state (FLS) for offshore wind turbine foundations is normally based on deterministic design approaches, where partial safety factors are used to account for load and resistance uncertainties. In this paper, the propagation of uncertainties related to structural, environmental and fatigue damage model parameters is evaluated by performing Monte Carlo fatigue simulations of a reference Gravity Based Foundation (GBF) supporting a 5 MW offshore wind turbine. A linear model for concrete fatigue damage is formulated based on the S-N approach, and fatigue structural reliability is evaluated using the FORM technique. Results indicate that the uncertainty related to wind turbulence intensity has the highest influence on fatigue loads during power production. Adopting a probabilistic damage model for concrete also increases the fatigue damage standard deviation by 60% and 85% for structures in water and in air, respectively. In addition, the assumption on Miner’s rule uncertainty has a large influence on the structural reliability. A reduction of this uncertainty from Δcov=0.40 to Δcov=0.30 could increase the annual reliability index by 22%.
In the detailed design of offshore wind turbine (OWT) foundations, the structure has to be evaluated for fatigue to ensure that the structure withstands environmental loads throughout its intended design life (typically 25 years). Current design standards are based on deterministic approaches, where partial safety factors are used to account for uncertainties in loads and resistance models. This approach, however, can either be over conservative or unsafe. It has been shown that target reliability level for OWTs can be lowered compared to other fixed offshore structures due to lower risks and consequences related to failure (Marquez-Dominguez & Sorensen, 2012). Moreover, uncertainties related to environmental inputs, which affect reliability assessments, are site-specific. To achieve more robust and cost-effective solutions, relevant sources of uncertainties have to be accounted for when performing reliability analyses and calibration of safety factors.
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).
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.
Dragt, R. C. (Netherlands Institute for Applied Scientific Research (TNO)) | Allaix, D. L. (Netherlands Institute for Applied Scientific Research (TNO), Eindhoven University of Technology) | Maljaars, J. (Keppel Verolme BV) | Tuitman, J. T. (Keppel Verolme BV) | Salman, Y. | Otheguy, M.
Fatigue is one of the main design drivers for offshore wind substructures. Using Fracture Mechanics methods, load sequence effects such as crack growth retardation due to large load peaks can be included in the fatigue damage estimation. Due to the sequence dependency, a method is required that represents the sequences of loads in the design or maintenance procedures.
This paper presents a methodology to deal with this challenge. First, a framework is presented for coupling between the design load cases and the Fracture Mechanics methods, resulting into the requirements for loads and load sequences. Second, a 2-stage Markov Chain Monte Carlo model is presented which is able to create realistic loading sequences based on measurement data. The method is elaborated for fluctuating wind loads.
One of the main design drivers for Offshore Wind Turbine (OWT) substructures is fatigue. Current standards (e.g.; DNVGL, 2016; IEC, 2009) specify a wide range of operational conditions, such as normal operation, parked condition and fault conditions, and the environmental conditions (combinations of wind, wave and current conditions) that are to be included in the fatigue assessment. Every single combination is used as input for a time domain simulation, which results in a stress history at given (hot)spots in the structure. Prescribed Stress Concentration Factors (SCF) are used to account for structural details. Standards prescribe that a 1-hour period is simulated (by either simulating 6 times a 10-minute realization or a 1-hour realization) per load combination. The total analysis requires several thousands of individual 1-hour long time-domain simulations, each typically containing several thousands of stress cycles.
The stress history is used to estimate the fatigue damage in a structural detail during its intended lifetime. Fatigue damage is referred to as the utilization of the total fatigue capacity of a structural detail expressed in terms of life. For every stress history, the number of occurring cycles for each stress range are counted using the Rainflow Counting method. The appropriate SN-curve is selected from the design standard and used to determine the number of cycles to failure for each stress range. The damage contribution per range of stress cycles is defined as the ratio between the occurring number of cycles and the number of cycles per stress range. The damage contributions of all stress cycles are summed in agreement with the damage accumulation rule of Palmgren-Miner in order to arrive at the total fatigue damage. The result is multiplied by a Design Fatigue Factor (DFF) in order to arrive at a certain probability of failure, which amongst others accounts for difficulties encountered during inspection or repair of a specific detail and for the risk of structural failure (DNVGL, 2016). The final result is the estimated design fatigue damage for this particular hotspot, for a particular environmental and operational condition.
According to the previous researchers, the bottom mounted offshore structure experienced ice-induced vibrations by the drifting level ice. In this study, a new ice breaking model based on the Matlock-method is proposed to explain the documented characteristics of ice-induced vibrations in many studies. A numerical simulation is performed by coupling the ice model with aero-hydro-servo-elastic numerical simulator, FAST. With this developed program, the monopile type wind turbine was examined in parked and operating conditions. The present results show that this model is capable of describing the three distinct ice crushing modes (intermittent ice crushing, frequency lock-in, and continuous brittle crushing), which are reported in both experimental tests and field data. In addition, it was found that the dynamics of tower and blades in two different conditions were dependent on the ice velocity.
As the arctic offshore wind turbine has become a promising renewable energy system, several studies about the interaction of the wind turbines with ice have been carried out numerically and experimentally. Barker et al.(2005) conducted ice model tests with cones and vertical cylinder types of tower configurations in mean sea level. With this test results, Gravesen et al.(2005) analyzed the four distinguished ice failure modes and developed the design procedures to estimate extreme and combined ice loads. Some researchers (Heinonen et al.(2011); Hetmanczyk et al.(2011); Jussila et al.(2013)) investigated the wind turbine dynamics with ice numerically. They have integrated the ice load calculation models in the wind turbine simulation tool, OneWind. Yu et al.(2014, 2016) developed and added the ice loading module into FAST to consider the interaction between level ice and monopile-type offshore wind turbines. The model was based on the Matlock method with and without zonal concept. The numerical study of the monopile wind turbines in level ice(Shi et al.(2016)) was performed in parked and operating conditions. The pile with a conical waterline shape was modeled for level ice to fail in bending. They reported the ice-induced resonances at tower natural periods.
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.
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 time-consuming and computational demanding simulation in the time-domain. In order to accelerate the analysis, a sub structuring 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 performa 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.
A new numerical methodology is presented for simulation of dynamic behavior of floating offshore wind turbines. Wind forces are computed in the time domain through application of blade element momentum theory using the instantaneous wind velocities, blade pitch angles, and resulting rotor speed. Equations of motion are developed and solved in Euler-space, such that no small-angle assumptions are required in the solution; vessel motions are included in wind and wave force calculations. Aero-elastic effects are quantified using the industry-standard subroutine AeroDyn, with blade pitch-angles computed by the "DISCON" subroutine, both open-source and publicly available from the National Renewable Energy Lab (NREL). Effectiveness is demonstrated through a series of examples, first a case for small-angle motion is compared with results from an industry standard simulation tool for the spar-based NREL OC3-Hywind with constant wind speed and no waves; next, the same environmental conditions are applied to a smaller spar-based floater for which standard simulation tools would not be applicable. Finally, a case is presented including irregular winds and waves.
Assessment of the structural integrity of an offshore wind turbine requires simulation of its structural response for many combinations of the wave and wind conditions that represent its lifetime loads. Modeling the dependence between the wind speed, wave height and wave period is very expensive because it requires a large amount of data. Assuming independence can lead to inaccurate estimation of the probability of failure. Some researchers assume that the wave height follows a standard distribution conditioned upon wind speed. We propose an alternative method that uses a copula to approximate the joint probability distribution of the wind speed, and the significant wave height. We believe that this approach is more complete because we obtain the joint distribution of the above quantities without making any assumption on their conditional distributions. To test the quality of the proposed approach, we use Monte Carlo simulation to generate sample values of the wind speed and wave heights, and validate the model with the available data.
Milatz, Marius (Institute of Geotechnical Engineering and Construction Management Hamburg University of Technology (TUHH)) | Reimann, Katja (Institute of Geotechnical Engineering and Construction Management Hamburg University of Technology (TUHH)) | Grabe, Jurgen (Institute of Geotechnical Engineering and Construction Management Hamburg University of Technology (TUHH))
Numerical simulations of hydro sound emissions due to offshore pile driving are presented in this paper. With the help of the finite element method (FEM) the propagation of sound waves evoked by a single hammer impact on an idealised monopile structure is simulated, taking into consideration the influence of ram energy and boundary conditions such as the seabed. The research presented in this paper investigates the possibility of a future prognosis of hydro sound emissions when offshore piles are driven into the ground. The aim is to develop technology that helps wind farms to be constructed without endangering noise-sensitive marine mammals.
1. Offshore Noise Emissions
1.1 Hydro sound as a consequence of impact driving
With the fast development of renewable energies and a growing awareness of ecological and sustainable issues, the wind energy industry has begun to reach for very rough and difficult, but promising regions to build new wind farms, particularly the vast and windy offshore areas surrounding the German coasts. In order to cope with enormous wind and wave loading, a pile foundation is, in most cases, chosen as the foundation system of a wind turbine. All loads have to be directed into the seabed with large steel piles which have to be driven into the seabed by means of impact hammers. Depending on the pile type, the diameter and especially the density of the subsoil, the impact energy is the most important factor in successfully driving the pile to its required depth. These oscillations lead to a sound pressure wave propagating in radial direction from the pile into the sea. Simultaneously, due to the dynamic reaction force at the pile toe, the seabed area close to the pile acts as a source of hydro sound, whose intensity is still a question of research.