Estimation Of Extreme Loads Research Articles

Bayes Inference of Structural Safety under Extreme Wind Loads Based upon a Peak-Over-Threshold Process of Exceedances

In the present paper, the process of estimating the important statistical properties of extreme wind loads on structures is investigated by considering the effect of large variability. In fact, for the safety design and operating conditions of structures such as the ones characterizing tall buildings, wind towers, and offshore structures, it is of interest to obtain the best possible estimates of extreme wind loads on structures, the recurrence frequency, the return periods, and other stochastic properties, given the available statistical data. In this paper, a Bayes estimation of extreme load values is investigated in the framework of structural safety analysis. The evaluation of extreme values of the wind loads on the structures is performed via a combined employment of a Poisson process model for the peak-over-threshold characterization and an adequate characterization of the parent distribution which generates the base wind load values. In particular, the present investigation is based upon a key parameter for assessing the safety of structures, i.e., a proper safety index referred to a given extreme value of wind speed. The attention is focused upon the estimation process, for which the presented procedure proposes an adequate Bayesian approach based upon prior assumptions regarding (1) the Weibull probability that wind speed is higher than a prefixed threshold value, and (2) the frequency of the Poisson process of gusts. In the last part of the investigation, a large set of numerical simulations is analyzed to evaluate the feasibility and efficiency of the above estimation method and with the objective to analyze and compare the presented approach with the classical Maximum Likelihood method. Moreover, the robustness of the proposed Bayes estimation is also investigated with successful results, both with respect to the assumed parameter prior distributions and with respect to the Weibull distribution of the wind speed values.

Statistical extrapolation methods and empirical formulae for estimating extreme loads on operating wind turbine towers

The wind turbine tower is designed against extreme load during power production with the return period of 50 years. The statistical extrapolation method is widely used to estimate the extreme load of wind turbine tower and is recommended by the IEC Standard 61400–1. However, various statistical extrapolation methods were used in previous studies and their accuracy and efficiency have not been evaluated comprehensively, which is investigated in this research. The validation procedure is assessed by simulating the one-year load of the reference wind turbine. It is found the fitting before aggregation methods with peak loads extracted by block maxima or peak over threshold techniques and three-parameter Weibull fitting function have the best accuracy and robustness. 60 samples for each wind speed are enough and the data below rated wind speed can be neglected for the optimal statistical extrapolation methods. In addition, an empirical formula for the extreme load estimation of wind turbine tower is proposed considering both the mean and fluctuating moment caused by the thrust force on the rotor, drag forces on the tower and nacelle and the gravities of nacelle and rotor. The extrapolation factor is modelled based on the estimated extreme load by the statistical extrapolation method. The proposed empirical formula shows good accuracy for both short-term and long-term extreme loads of wind turbine tower at various wind conditions.

Sensitivity analysis of extreme loads acting on a point-absorbing wave energy converter

There are many uncertainties associated with the estimation of extreme loads acting on a wave energy converter (WEC). In this study we perform a sensitivity analysis of extreme loads acting on the Uppsala University (UU) WEC concept. The UU WEC consists of a bottom-mounted linear generator that is connected to a surface buoy with a taut mooring line. The maximum stroke length of the linear generator is enforced by end-stop springs. Initially, a Variation Mode and Effect Analysis (VMEA) was carried out in order to identify the largest input uncertainties. The system was then modelled in the time-domain solver WEC-SIM coupled to the dynamic mooring solver Moody. A sensitivity analysis was made by generating a surrogate model based on polynomial chaos expansions, which rapidly evaluates the maximum loads on the mooring line and the end-stops. The sensitivities are ranked using the Sobol index method. We investigated two sea states using equivalent regular waves (ERW) and irregular wave (IRW) trains. We found that the ERW approach significantly underestimate the maximum loads. Interestingly, the ERW predicted wave height and period as the most important parameters for the maximum mooring tension, whereas the tension in IRW was most sensitive to the drag coefficient of the surface buoy. The end-stop loads were most sensitive to the PTO damping coefficient.

Probabilistic Response and Short-Term Extreme Load Estimation of Offshore Monopile Wind Turbine Towers by Probability Density Evolution Method

Probabilistic Response and Short-Term Extreme Load Estimation of Offshore Monopile Wind Turbine Towers by Probability Density Evolution Method

The DeRisk database: Extreme design waves for offshore wind turbines

The estimation of extreme loads from waves is an essential part of the design of offshore wind turbines. Standard design codes suggest either to use simplified methodologies based on regular waves, or to perform fully-nonlinear computations. The former may not provide an accurate representation of the real extreme waves, while the latter is too computationally intensive for fast design iterations. Here, we address these limitations by using the fully-nonlinear solver OceanWave3D to establish the DeRisk database, a large dataset of extreme wave kinematics in a two-dimensional domain. From the database, which is open and freely available, a designer can easily extract fully-nonlinear wave kinematics for a wave condition and water depth of interest by identifying a suitable computation in the database and, if needed, by Froude-scaling the kinematics. This will ultimately enable quicker estimations of nonlinear wave loads, speeding up design evaluations. The database sea states cover a range of nondimensional depth of about h∗∈[3.0⋅10−3,6.5⋅10−2] and of nondimensional significant wave height of HS∗∈[1.0⋅10−3,8.0⋅10−3], where h∗=h/(gTP2)[−] and HS∗=HS/(gTP2)[−].The fully-nonlinear solver is validated against the DeRisk model-scale experiments, where a number of long-crested sea state realizations are generated at two different water depths, 33.0[m] and 20.0[m], and the induced force on a stiff monopile with a diameter of D=7.0[m] is measured.Comparison with the experiments shows that the database predicts maximum crest elevations at both depths very accurately. Predictions of the in-line force, obtained by application of the Rainey slender body force model with the database wave kinematics, are accurate for milder storms. However, for stronger storms, where slamming loads from breaking waves dominate, the force computations from the database kinematics provide slightly nonconservative force estimates compared with the standard methodologies such as the embedded stream function and the WiFi JIP model. This discrepancy is mainly due to the lack of a slamming load model in the applied force model. A procedure to add slamming loads to OceanWave3D and to the DeRisk database is currently being developed.

Site-Specific Extreme Load Estimation of a Long-Span Cable-Stayed Bridge

To provide benefit for design, rating, evaluation and management of signature bridges, site-specific extreme wind speeds, structural temperatures, and traffic load effects of a long-span cable-stayed bridge were estimated using relatively long-term structural health monitoring (SHM) data and compared with respective design values in this paper. The generalized Pareto distribution was adopted and briefly introduced to predict the extreme values in consideration of its advantage in making full use of limited measurement data available. The configuration and characteristics of the 3rd Nanjing Yangtze River Bridge and its SHM system were then presented. The extreme wind speed at the deck level and the four extreme temperatures of the bridge were estimated and compared with the corresponding design values. After a brief introduction to the simulation of traffic load effects, five extreme traffic load effects were finally estimated and compared with the design ones. The comparative results showed that the site-specific extreme wind speed, uniform girder temperature change, and five traffic load effects are all lower than the respective design values. The site-specific extreme vertical and transverse girder temperature differences and the site-specific extreme tower temperature difference were, however, larger than the respective design values.

A Method for the Prediction of Extreme Ship Responses Using Design-Event Theory and Computational Fluid Dynamics

The design of a naval vessel requires accurate estimation of the extreme loads and motions that it will experience during its lifetime. Operation in large seaways in which the ship-wave interaction is highly nonlinear and transient leads to design events such as maximum internal loads due to global wave bending, local slamming loads, extreme roll, combinations of the global wave bending and local slamming, and many others. In this article, a method is presented that allows for nonlinear analysis to be used to predict events with user-specified rareness. The core of the method combines probability, frequency, and time-domain analyses to generate short time-window sea environments that lead to extreme dynamical events. The Office of Naval Research Tumblehome geometry is analyzed for the extreme roll angle when advancing in stern quartering irregular seas. 1. Introduction The design of a naval vessel requires accurate estimation of extreme loads and motions that it will experience during its lifetime. Specific quantities of interest are the maximum slamming load during wet-deck impact, maximum acceleration at different locations on the vessel, maximum green-water load on the bow structure or helicopter deck, maximum roll angle, or frequency of occurrence of capsize, to name a few. It is important to recognize that a ship lifetime is decades long, and the exposure time in different severe storms over the lifetime is of the order of weeks, if not months. Furthermore, because of the random nature of the sea and, hence, the dynamical response of the ship, the extreme response is also random and should be characterized statistically. This means that a single lifetime realization in a given seaway by either model tests or numerical simulation only gives one sample of the extreme response, and multiple lifetime realizations are required to characterize the extreme response.

Extreme load estimation of the wind turbine tower during power production

Wind turbines have to be designed against extreme load during power production with the recurrence period of 50 years. This extreme load is usually calculated through statistical extrapolation. However, large uncertainties exist in the estimation of the extreme load. This study aims to reduce these uncertainties in the statistical extrapolation by using systematic simulations. First, a new criterion is proposed for the data sets to be used for the statistical extrapolation and the resulting uncertainty satisfies the requirement in the standard for prediction of wind load. Then, a new extrapolation factor for load extrapolation is proposed and the predicted maximum tower bending moments at all the heights show favorable agreement with measurement. Finally, empirical formulae are proposed to estimate the expected value of the maximum tower bending moment and the predicted values show good agreement with the numerical simulations.

Adaptive stratified importance sampling: hybridization of extrapolation and importance sampling Monte Carlo methods for estimation of wind turbine extreme loads

Abstract. Wind turbine extreme load estimation is especially difficult because turbulent inflow drives nonlinear turbine physics and control strategies; thus there can be huge differences in turbine response to essentially equivalent environmental conditions. The two main current approaches, extrapolation and Monte Carlo sampling, are both unsatisfying: extrapolation-based methods are dangerous because by definition they make predictions outside the range of available data, but Monte Carlo methods converge too slowly to routinely reach the desired 50-year return period estimates. Thus a search for a better method is warranted. Here we introduce an adaptive stratified importance sampling approach that allows for treating the choice of environmental conditions at which to run simulations as a stochastic optimization problem that minimizes the variance of unbiased estimates of extreme loads. Furthermore, the framework, built on the traditional bin-based approach used in extrapolation methods, provides a close connection between sampling and extrapolation, and thus allows the solution of the stochastic optimization (i.e., the optimal distribution of simulations in different wind speed bins) to guide and recalibrate the extrapolation. Results show that indeed this is a promising approach, as the variance of both the Monte Carlo and extrapolation estimates are reduced quickly by the adaptive procedure. We conclude, however, that due to the extreme response variability in turbine loads to the same environmental conditions, our method and any similar method quickly reaches its fundamental limits, and that therefore our efforts going forward are best spent elucidating the underlying causes of the response variability.

Threshold Selection for POT Framework in the Extreme Vehicle Loads Analysis Based on Multiple Criteria

Extreme value of vehicle load plays an important role in bridge design and risk assessment. Peaks over threshold (POT) is a method commonly used in extreme load estimation. The selection of thresholds for the POT method is extremely crucial, but the selected optimal threshold varies under different test criteria. Therefore, a method to select the suitable threshold is developed based on multiple criteria decision analysis (MCDA) in the paper. In MCDA, Chi‐Square (χ2) test, Kolmogorov–Smirnov (K–S) test, and Root Mean Square Error (RMSE) in probability distribution functions (PDF) are employed as the test criteria and the weight of these criteria is calculated using the entropy method. Finally, vehicle loads obtained from simulation and field measurement are adopted to validate the effectiveness and feasibility of the proposed method. The results indicate that the proposed MCDA is a useful and complementary tool for threshold selection in the extreme value analysis.

Prediction of extreme loads on ultra-large containerships with structural hydroelasticity

Design rules for very large seagoing vessels are undergoing changes owing to the hydroelasticity of the ship. The hydroelasticity of the ship is in the form of wave-induced vibrations such as springing and whipping, which are known to aggravate fatigue and extreme loads. The present study deals with a method for the estimation of extreme loads. The method consists of a preliminary analysis of linear responses of motions and loads, and a sequential analysis of the nonlinear extreme load. First, a full-time series of the linear response is obtained using response amplitude operators and wave spectra. Next, the candidate waves of extreme event are extracted from the full-time series based on the linear response. The linear response may be a motion or a load depending on the target value of the sequential analysis. Finally, the sequential analysis is conducted using a fully coupled model of the three-dimensional Rankine panel method, three-dimensional finite-element method, and two-dimensional generalized Wagner model with the candidate waves. The method is validated for a nonlinear hogging moment in a short-term sea state and applied for a long-term prediction of an extreme hogging moment on an ultra-large containership. The extreme values of linear and nonlinear loads are compared in terms of the most probable value and probabilistic distribution.

Statistical Estimation of Extreme Loads for the Design of Offshore Wind Turbines during Non-Operational Conditions

The International Electrotechnical Commission (IEC) design standard (IEC 61400-3) for offshore wind turbines includes a design load case which considers loads on the turbine during extreme conditions, when the wind turbine is not operating and the blades are feathered. The recommendation of this design standard is to simulate 6 one-hour periods, each with wind and wave fields modeled as random processes, and to calculate design loads as the mean of the maximum from the six simulations. Previous studies have investigated this recommendation for fixed bottom offshore wind turbines and raised concerns about the stability of the estimate of the design load calculated using these guidelines. The research presented in this paper calculates statistics of extreme design loads as a function of the number of one-hour simulations considered for three offshore wind turbine support structures: a fixed-bottom turbine supported by a monopile and two floating turbines, a spar buoy and a semi-submersible. The study considers one extreme design load, the moment at the tower base, one set of 50-year metocean conditions representive of the Northeast U.S. Atlantic coast, and five combinations of wind and wave models, including linear and nonlinear representations of irregular waves. The data generated from this study are used to assess the stability of the estimate of the extreme load for various numbers of one-hour simulations for each turbine type. The study shows that, for the considered metocean conditions and models, the monopile exhibits the least stability in the estimate of the extreme load and therefore requires more one-hour simulations to have comparable stability as the two floating support structures. Explanations for this result are provided along with a probabilistic formulation for estimating variability of design loads more efficiently, using fewer one-hour simulations.

Effects of Waves and Currents on Extreme Loads on a Jacket

In lack of simultaneous data of metocean parameters such as wind, waves, and currents, Norwegian design regulations presently recommend a conservative combination of metocean parameters for estimation of characteristic metocean loads on offshore structures. A simplified parametric load model for a jacket, based on waves and currents, is assumed. Several approaches to load estimation are investigated and the following are considered: different averaging length of extreme currents, the effect of peak-over-threshold approach for estimation of extreme wave and currents compared to all-sea states approach and extreme load estimation directly from a load time series. When compared to the recommended approach, all other approaches yield a reduced estimated characteristic metocean load. The purpose of this study is to indicate the possible conservatism in the Norwegian design regulations for estimation of quasi-static loads on a jacket. The results are intended to be illustrative and not suitable for use in specific design calculations.

Statistical Extrapolation Methods for Estimating Wind Turbine Extreme Loads

With the introduction of the third edition of the International Electrotechnical Commission (IEC) Standard 61400-1, designers of wind turbines are now explicitly required, in one of the prescribed load cases, to use statistical extrapolation techniques to determine nominal design loads. In this study, we use field data from a utility-scale 1.5MW turbine sited in Lamar, Colorado to compare the performance of several alternative techniques for statistical extrapolation of rotor and tower loads—these include the method of global maxima, the peak-over-threshold method, and a four-moment process model approach. Using each of these three options, 50-year return loads are estimated for the selected wind turbine. We conclude that the peak-over-threshold method is the superior approach, and we examine important details intrinsic to this method, including selection of the level of the threshold to be employed, the parametric distribution used in fitting, and the assumption of statistical independence between successive peaks. While we are primarily interested in the prediction of extreme loads, we are also interested in assessing the uncertainty in our predictions as a function of the amount of data used. Towards this end, we first obtain estimates of extreme loads associated with target reliability levels by making use of all of the data available, and then we obtain similar estimates using only subsets of the data. From these separate estimates, conclusions are made regarding what constitutes a sufficient amount of data upon which to base a statistical extrapolation. While this study makes use of field data in addressing statistical load extrapolation issues, the findings should also be useful in simulation-based attempts at deriving wind turbine design load levels where similar questions regarding extrapolation techniques, distribution choices, and amount of data needed are just as relevant.

Wind turbine measurement technique—an open laboratory for educational purposes

AbstractAs part of the International Master of Science Programme in Wind Energy at the Technical University of Denmark (DTU), a complete interactive wind turbine measurement laboratory (WTMLAB) was developed. A 500kW stall regulated wind turbine was instrumented with sensors for recording (i) turbine operational parameters, (ii) meteorological conditions, (iii) electrical quantities and (iv) mechanical loads. The data acquisition system was PC based, and it was combined with a MySQL® database for data management. The system enabled online access for real‐time recordings, which were used both for demonstration purposes, for individual student exercises and for scientific investigations. The automatic data acquisition system furthermore enabled recording of extreme and fatigue loads together with a long‐term event registration. Long‐term registration of wind turbine loads resulted in a unique database of non‐commercial time series, which would be available for practicing fatigue calculations and extreme load estimation in basic wind turbine courses. Power quality analysis was carried out based on high‐speed‐sampled, three‐phase voltage and current signals. The wide spectrum of sensors enabled a detailed study of the correlation between meteorological, mechanical and electrical quantities. Measurements were recorded with a PC placed at the wind turbine site at Risø. The PC could be remotely controlled from DTU, which gave the students the opportunity to work on an operating wind turbine. The WTMLAB was included in a new course entitled Wind Turbine Measurement Techniques. Copyright © 2007 John Wiley & Sons, Ltd.