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The need for cost-effective support structure designs for offshore wind turbines has led to continued interest in the development of design optimization methods. So far, almost no studies have considered the effect of uncertainty, and hence probabilistic constraints, on the support structure design optimization problem. In this work, we present a general methodology that implements recent developments in gradient-based design optimization, in particular the use of analytical gradients, within the context of reliability-based design optimization methods. Gradient-based optimization is typically more efficient and has more well-defined convergence properties than gradient-free methods, making this the preferred paradigm for reliability-based optimization where possible. By an assumed factorization of the uncertain response into a design-independent, probabilistic part and a design-dependent but completely deterministic part, it is possible to computationally decouple the reliability analysis from the design optimization. Furthermore, this decoupling makes no further assumption about the functional nature of the stochastic response, meaning that high-fidelity surrogate modeling through Gaussian process regression of the probabilistic part can be performed while using analytical gradient-based methods for the design optimization. We apply this methodology to several different cases based around a uniform cantilever beam and the OC3 Monopile and different loading and constraint scenarios. The results demonstrate the viability of the approach in terms of obtaining reliable, optimal support structure designs and furthermore show that in practice only a limited amount of additional computational effort is required compared to deterministic design optimization. While there are some limitations in the applied cases, and some further refinement might be necessary for applications to high-fidelity design scenarios, the demonstrated capabilities of the proposed methodology show that efficient reliability-based optimization for offshore wind turbine support structures is feasible. [ABSTRACT FROM AUTHOR]

A complete fatigue assessment for operational conditions for offshore wind turbines involves simulating thousands of environmental states. For applications such as optimization, where this assessment needs to be repeated many times, that presents a significant computational problem. Here, we propose a novel way of reducing the number of simulated environmental states (load cases) while maintaining an acceptable accuracy. From one full fatigue analysis of a base design, the OC3 monopile (with the NREL 5MW turbine), the distribution of fatigue damage per load case can be used to estimate the lifetime fatigue damage of a range of modified designs. Using importance sampling and a specially adapted two‐stage filtering procedure, we obtain pseudo‐optimal sets of load cases from which the fatigue damage is estimated. This is applied to seven different designs that have been modified to emulate iterations of an optimization loop. For several of these designs, sampling less than 1% of all load cases can give damage estimates with median errors of less than 2%. Even for the most severe cases, using 3% of the environmental states yields a maximum error of 10%. While further refinement is possible, the method is considered viable for applications within design optimization and preliminary design. [ABSTRACT FROM AUTHOR]

This paper reviews the state of the art in offshore wind farm operations and maintenance with a focus on decision support models for the scheduling of maintenance. Factors influential to maintenance planning are collected from the literature and their inclusion in state-of-the-art models is discussed. Methods for modeling and optimization are presented. The methods currently used and possible alternatives are discussed. The existing models are already able to aid the decision-making process. They can be improved by applying more advanced mathematical methods, including uncertainties in the input, regarding more of the influential factors, and by collecting, analyzing, and subsequently using more accurate data. [ABSTRACT FROM AUTHOR]

During the bidding or very early design phases of jacket structures for offshore wind turbines, there may be very limited information available on meteorological conditions, soil conditions, turbine specifications, etc. However, it is still important to quickly produce near‐optimal designs with production costs similar to that of the final support structure. Numerical optimization methods can be used to this purpose. This paper investigates three gradient‐based optimization methods, where preliminary designs are produced by mass optimization. The mass is reduced by changing tube diameter and thickness of the structural members, and the optimization considers both frequency and fatigue constraints. The three methods are based on (1) damage equivalent loads, (2) quasi‐static analysis, and (3) dynamic analysis. The optimizations are conducted using in‐house software JADOP (jacket design optimization), and the optimized designs are evaluated using state‐of‐the‐art integrated time‐domain simulation software FEDEM Windpower. The findings show that each analysis can be applied with success. However, if excitations of structural frequencies contribute significantly to the overall damage, special care must be taken with quasi‐static and static modeling. It is observed that wave loading does not contribute considerably to the fatigue damage. Additionally, the aerodynamic loading does not change significantly with changes of tube geometry within the optimization ranges. The optimized designs are partly driven by reducing stress concentration factors, which can be achieved by reducing the chord diameter to thickness ratio. Thus, the optimized designs resemble each other to a certain extent. [ABSTRACT FROM AUTHOR]

The large amount of computational effort required for a full fatigue assessment of offshore wind turbine support structures under operational conditions can make these analyses prohibitive, especially for applications like design optimization, for which the analysis would have to be repeated for each iteration of the process. To combat this issue, we present a simple procedure for reducing the number of load cases required for an accurate fatigue assessment. After training on one full fatigue analysis of a base design, the method can be applied to establish a deterministic, reduced sampling set to be used for a family of related designs. The method is based on sorting the load cases by their severity, measured as the product of fatigue damage and probability of occurrence, and then calculating the relative error resulting from using only the most severe load cases to estimate the total fatigue damage. By assuming this error to be approximately constant, one can then estimate the fatigue damage of other designs using just these load cases. The method yields a maximum error of about 6% when using around 30 load cases (out of 3647) and, for most cases, errors of less than 1%-2% can be expected for sample sizes in the range 15-60. One of the main points in favor of the method is its simplicity when compared to more advanced sampling-based approaches. Though there are possibilities for further improvements, the presented version of the method can be used without further modifications and is especially useful for design optimization and preliminary design. We end the paper by noting some possibilities for future work that extend or improve upon the method. [ABSTRACT FROM AUTHOR]

Decoupled load simulations are a computationally efficient method to perform a dynamic analysis of an offshore wind turbine. Modelling the dynamic interactions between rotor and support structure, especially the damping caused by the rotating rotor, is of importance, since it influences the structural response significantly and has a major impact on estimating fatigue lifetime. Linear damping is usually used for this purpose, but experimentally and analytically derived formulas to calculate an aerodynamic damping ratio often show discrepancies to measurement and simulation data. In this study decoupled simulation methods with reduced and full rotor loads are compared to an integrated simulation. The accuracy of decoupled methods is evaluated and an optimization is performed to obtain aerodynamic damping ratios for different wind speeds that provide the best results with respect to variance and equivalent fatigue loads at distinct output locations. Results show that aerodynamic damping is not linear, but it is possible to match desired output using decoupled models. Moreover, damping ratios obtained from the empirical study suggest that aerodynamic damping increases for higher wind speeds. [ABSTRACT FROM AUTHOR]

For some applications in structural optimization, it is required to have constraints on the extreme loads that represent long term loading conditions. This usually involves a statistical extrapolation procedure that fits maxima from simulated load time series to short term extreme value distributions and then extrapolates to an n-year return value. Often such situations are highly simplified because of the apparent complexity involved in evaluating the sensitivity of such constraints. However, such simplification is not necessary. In this study, we present a method to evaluate the sensitivities of such extrapolated extreme load constraints in a semi-analytical way. The method uses the implicit function theorem to obtain local derivatives at the points defined by the solution of the maximum likelihood estimate that is used to calculate the parameters of the short term extreme value distributions. Comparing with high accuracy finite difference estimates, the method is shown to give reasonably accurate values. We also demonstrate how the method can be used to estimate the uncertainty of the estimated n-year return value caused by uncertainty in both the maximum likelihood estimate and inherent uncertainties in the data. The method then is applied to a simple optimization example and shown to perform very well compared with using finite difference estimates for the sensitivities. Finally, we note that the method is in principle fairly general and could be applied to similar problems that do not specifically involve statistical extrapolation. [ABSTRACT FROM AUTHOR]

Operators need accurate knowledge on structural reserves to decide about lifetime extension of offshore wind turbines. Load monitoring enables us to directly compare design loads with real loading histories of the support structure in order to calculate its remaining useful lifetime. Monitoring of every hot spot is technically and financially not feasible. This paper presents a novel idea for load monitoring of monopiles. It requires strain measurements at only one level convenient for sensor installation, such as tower bottom. Measurements are converted into damage equivalent loads for 10 min time intervals. Damage equivalent loads are extrapolated to other locations of the structure with a simulation model and statistical algorithm. For this, structural loads at all locations of the monopile are calculated with aero-hydro-elastic software and updated finite element models. Damage equivalent loads at unmeasured locations are predicted from the simulation results with a k-nearest neighbor regression algorithm. The extrapolation was tested with numerical simulations of an 8MW offshore wind turbine. Results show that damage can be predicted with an error of 1-3% if this is done conditional on mean wind speed, which is very promising. The load monitoring concept is simple, cheap and easy to implement. This makes it ideal for making decisions on lifetime extension of monopiles. [ABSTRACT FROM AUTHOR]

The estimation of fatigue lifetime for an offshore wind turbine support structure requires a large number of time-domain simulations. It is an important question whether it is possible to reduce the number of load cases while retaining a high level of accuracy of the results. We present a novel method for simplified fatigue load assessments based on statistical regression models that estimate fatigue damage during power production. The main idea is to predict the total fatigue damage only and not also the individual damage values for each load case. We demonstrate the method for a jacket-type support structure. Reducing the number of simulated load cases from 21 to 3, the total fatigue damage estimate exhibited a maximum error of about 6% compared with the complete assessment. As a consequence, a significant amount of simulation time can be saved, in the order of a factor of seven. This quick fatigue assessment is especially interesting in the application of structural optimization, with a large number of iterations. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The ultimate capacity of support structures is checked with extreme loads. This is straightforward when the limit state equations depend on a single load component, and it has become common to report maxima for each load component. However, if more than one load component is influential, e.g., both axial force and bending moments, it is not straightforward how to define an extreme load. The combination of univariate maxima can be too conservative, and many different combinations of load components can result in the worst value of the limit state equations. The use of contemporaneous load vectors is typically non-conservative. Therefore, in practice, limit state checks are done for each possible load vector, from each time step of a simulation. This is not feasible when performing reliability assessments and structural optimization, where additional, time-consuming computations are involved for each load vector. We therefore propose to use Pareto-optimal loads, which are a small set of loads that together represent all possible worst case scenarios. Simulations with two reference wind turbines show that this approach can be very useful for jacket structures, whereas the design of monopiles is often governed by the bending moment only. Even in this case, the approach might be useful when approaching the structural limits during optimization. [ABSTRACT FROM AUTHOR]

Stochastic representations of turbulent wind and irregular waves are used in time domain simulations of offshore wind turbines. The variability due to finite sampling of this input loading is an important source of simulation error. For the OC4 reference jacket structure with a 5 MW wind turbine, an error of 12-34% for ultimate loads and 6-12% for fatigue loads can occur with a probability of 1%, for simulations with a total simulation length of 60 min and various load cases. In terms of fatigue life, in the worst case, the lifetime of a joint was thereby overestimated by 29%. The size of this error can be critical, i.e., ultimate or fatigue limits can be exceeded, with probability depending on the choice of number of random seeds and simulation length. The analysis is based on a large simulation study with about 30,000 time domain simulations. Probability density functions of response variables are estimated and analyzed in terms of confidence intervals; i.e., how probable it is to obtain results significantly different from the expected value when using a finite number of simulations. This simulation error can be reduced to the same extent, either using several short simulations with different stochastic representations of the wind field or one long simulation with corresponding total length of the wind field. When using several short-term simulations, it is important that ultimate and fatigue loads are calculated based on the complete, properly combined set of results, in order to prevent a systematic bias in the estimated loads. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT A simple method, based in the frequency domain, was developed for calculating the dynamic response of a stall-regulated wind turbine. Emphasis is placed on two aspects of the method, which are necessary in order to obtain a reasonable linearization of behavior when the blades are stalled. First, the tangential (in-plane) component of turbulence is included, in addition to the axial component. Second, the linearized relationship between lift coefficient and angle-of-attack is adjusted to account for the effects of dynamic stall: separate linearizations are used for excitation and damping of vibration. A thorough comparison is made between linear and non-linear dynamic-stall methods, with the conclusion that the accuracy of the linear method depends upon the frequency and amplitude of oscillation. The linear dynamic-stall method is accurate at blade vibrational frequencies, but it can be inaccurate at frequencies in the vicinity of 1P or below, when the angle-of-attack oscillates with an amplitude of 3° or more. Load spectra of a Nordtank 500 turbine, calculated using the frequency-domain method, are compared with measurements. The frequency-domain method provides estimates of load spectra and aerodynamic damping (stability) that are useful for preliminary design and optimization, but the method lacks sufficient accuracy and generality to be used for certification. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Asthma and COPD are chronic respiratory diseases that fluctuate widely with regard to clinical symptoms and airway obstruction, complicating treatment and prediction of exacerbations. Time series of respiratory impedance obtained by the forced oscillation technique are a convenient tool to study the respiratory system with high temporal resolution. In previous studies it was suggested that power-law-like fluctuations exist also in the healthy lung and that respiratory system impedance variability differs in asthma. In this study we elucidate such differences in a population of well-characterized subjects with asthma (n = 13, GINA 1+2), COPD (n = 12, GOLD I+II), and controls (n = 10) from time series at single frequency (12 min, f = 8 Hz). Maximum likelihood estimation did not rule out power-law behavior, accepting the null hypothesis in 17/35 cases (P > 0.05) and with significant differences in exponents for COPD (P < 0.03). Detrended fluctuation analysis exhibited scaling exponents close to 0.5, indicating few correlations, with no differences between groups (P > 0.14). In a second approach, we considered asthma and COPD as dynamic diseases, corresponding to changes of unknown parameters in a deterministic system. The similarity in shape between the combined probability distributions of normalized resistance and reactance was quantified by Wasserstein distances and reliably distinguished the two diseases (cross-validated predictive accuracy 0.80; sensitivity 0.83, specificity 0.77 for COPD). Wasserstein distances between 3+3 dimensional phase space reconstructions resulted in marginally better classification (accuracy 0.84, sensitivity 0.83, specificity 0.85). These latter findings suggest that the dynamics of respiratory impedance contain valuable information for the diagnosis and monitoring of patients with asthma and COPD, whereas the value of the stochastic approach is not clear presently. [ABSTRACT FROM AUTHOR]

We discuss aspects of biological relevance to the modelling of bio-computation in a multiset rewriting system context: turnover, robustness against perturbations, and the dataflow programming paradigm. The systems under consideration are maximally parallel and asynchronous parallel membrane systems, the latter corresponding to computation in which the notion of time is operationally meaningless. A natural geometrical setting which seems promising for the study of computational processes in general multiset rewriting systems is presented. Configuration space corresponds to a subset of the lattice ${\bf N}^d_0$, d ∈ N, and state transitions correspond to vector addition. The similarities and differences with Vector Addition Systems and Petri nets are discussed. Symbolic dynamics are introduced on special partitions of configuration space and we indicate different notions of complexity for membrane systems based on this and related concepts such as graph complexity and minimal automata. Some examples of synchronized, pipelined dataflow computations are given and decompositions into functional subunits are briefly commented on. [ABSTRACT FROM AUTHOR]

Optimization of the maintenance policies for offshore wind parks is an important step in lowering the costs of energy production from wind. The yield from wind energy production is expected to fall, which will increase the need to be cost efficient. In this article, the Markov decision process is presented and how it can be applied to evaluate different policies for corrective maintenance planning. In the case study, we show an alternative to the current state-of-the-art policy for corrective maintenance that will achieve a cost-reduction when energy production prices drop below the current levels. The presented method can be extended and applied to evaluate additional policies, with some examples provided. [ABSTRACT FROM AUTHOR]

To maintain the increasing interest and development in offshore wind energy, novel training tools for engineers and researchers are needed. Concurrently, educational outreach activities are in demand to inform the public about the importance of offshore wind energy. In this paper, the development of a serious game about the design and management of offshore wind farms is presented to address such demands. Such a serious game may enable a new audience to explore the field of offshore wind as well as provide researchers entering the field a better understanding of the intricacies of the industry. This requires a simulation that is realistic but also effective in teaching information and engaging outreach. Ultimately, increased public support and expanded training tools are desired to improve decision-making and to provide opportunities to test and integrate innovative solutions. The work presented here includes the game design and implementation of a prototype game. The game design involves building a game framework and developing a simplified simulation. This simulation addresses weather prediction, offshore wind farm design, operation and maintenance, energy demand, climate change, and finance. Playtesting of the prototype demonstrated immersion and informed decision-making of the players and surveys revealed that knowledge had increased while playing the game. Recommendations for future versions of the game are listed. [ABSTRACT FROM AUTHOR]

The cover image, by Jacob Oest et al., is based on the Research Article On gradient‐based optimization of jacket structures for offshore wind turbines, https://doi.org/10.1002/we.2206. [ABSTRACT FROM AUTHOR]