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The dynamic response and reliability analysis of a 13.2 MW offshore wind turbine supported by a moored semi-submersible platform is the subject of this study. Loads data for the extreme response analysis involve time-domain simulations for a range of sea states representative of expected site-specific metocean conditions. To gain deeper insight into the dynamic behavior of this system and to obtain long-term loads efficiently and accurately, two studies are carried out sequentially. First, the short-term response of the integrated system is studied based on 1-h simulations for sea states identified using the Environmental Contour method for a 50-year return period. Response extremes for the integrated wind turbine system as well as system sensitivity to metocean conditions are studied. Next, the long-term response associated with the 50-year return period is estimated using statistical extrapolation based on loads derived from the 1-h simulations. Inverse First-Order Reliability Method procedures are employed to seek appropriate response quantile levels, e.g., the median response for 2D Inverse FORM. A more comprehensive 3D approach, which accounts for system response uncertainties, improves long-term response estimates. A proposed adaptive procedure in the 3D approach helps determine the number of simulations needed to guarantee accuracy in the long-term response estimation.

Marine risers are susceptible to sustained vortex-induced vibration (VIV) because of their slenderness and light damping. Commonly used tools for analyzing VIV and the associated fatigue damage are based on the finite element method and rely on simplifying assumptions on the riser's physical model, the flow conditions, and characteristics of the response. In order to assess the influence of VIV and to ensure the integrity of the riser, field monitoring campaigns are often undertaken wherein data loggers such as strain sensors and/or accelerometers are installed on such risers. Given the recorded riser's dynamic response, empirical techniques can be used in VIV-related fatigue estimation. These empirical techniques make direct use of the measurements and are intrinsically dependent on the actual current profiles. Damage estimation can be undertaken for the different current profiles encountered and can account explicitly even for complex riser response characteristics. With a significant amount of data, “short-term” fatigue damage probability distributions, conditional on current, can be established. If the relative frequency of different current types is known from a separate metocean study, the short-term fatigue damage distributions can be combined with the current distributions to yield an integrated “long-term” fatigue damage model, which then can be used to predict the long-term cumulative fatigue damage for the instrumented riser. Non-parametric statistical techniques (that do not assume a specific function for the underlying distribution as parametric techniques do) are employed to describe the short-term fatigue damage data. In this study, data from the Norwegian Deepwater Programme (NDP) model riser experiments are used to demonstrate the effectiveness of empirical procedures and non-parametric statistics applied to field measurements to predict long-term fatigue damage, life, and probability of fatigue failure.

Many floating offshore wind turbine (FOWT) concepts are light displacement platforms moored in shallow water and exposed to significant storms with high winds. Shock loads (also called snap loads) on the mooring lines can occur when an FOWT experiences large wave- and wind-induced motions. A typical snap event is characterized by a temporary slackness in the line followed by a sharp spike in tension whose magnitude can considerably exceed typical values of local tension maxima. In this study, we investigate seven experimental tests of a moored FOWT under survival storm conditions (i.e., a 100-year storm). For all these cases, the significant wave height and peak wave period are held constant at 10.5 m and 14.3 s respectively, while the wind speed is varied from 0 to 30.5 m/s. The wind conditions range from a steady wind to turbulent wind characterized by a chosen spectrum. Several snap events are found to result in the windward mooring line. The duration of these events range from 7.5 to 10.5 s, and the maximum tension values recorded are 37–68% higher than the corresponding cyclic non-snap tension maxima. The dynamic tension in the measured time histories are separated into snap-induced events and those that are not associated with a snap event based on criteria specified in marine operation practices; probability distributions of these separate events are analyzed. The exceedance probability curve of the dynamic tension in the higher ranges contributed to by snap-induced tension shows different characteristics compared to the lower tension range values that are related to the cyclic dynamic tension. There appears to be a clear demarcation point for this change in the probability curve characteristics. We propose a composite Weibull probability distribution for the mooring line dynamic tension that incorporates the effects of snap events. The model is composed of two Weibull distributions with different characteristics on either side of a transition tension value, and whose parameters are estimated from test data. The transition tension is related to the maximum cyclic dynamic tension in an extreme storm event, as specified by recommended practices. The proposed distribution model provides a good fit to the measured tension data, particularly in the extreme range. A design extreme value is developed for systems where snap loads are generally non-existent or are associated with very low probabilities of occurrence. When the shock load incidence probability is higher, the developed composite Weibull distribution model could offer a good starting point for the prediction of extreme dynamic tensions of a FOWT mooring system.

In complex stochastic high-dimensional reliability studies, polynomial chaos expansion (PCE) has been widely used to build surrogate models in lieu of prohibitively expensive Monte Carlo simulation (MCS). PCE relies on parametric distributions for associated variables and appropriate basis functions. However, incomplete or imperfect information on the stochastic variables can limit its use; accepted parametric forms for variable distributions, for instance, may not be justified when variables display multimodal character or mixed discrete-continuous support. Also, the dependency structure among the random variables may be complex, which can make probabilistic mapping or transformation to independent variables needed for PCE cumbersome. Nonlinearities in such transformations can affect the accuracy of PCE surrogate models and lead to slower convergence relative to “truth” system computations of desired QoIs (quantities of interest). To address these challenges, a distribution-free PCE approach is proposed. We compute joint raw moments of underlying random input variables for Gram-Schmidt orthogonalization in developing surrogate models. Using illustrative examples, we demonstrate the proposed approach as an efficient and accurate surrogate model-building alternative to traditional PCE.

The effects of automatic indoor set point temperature setbacks using smart thermostats in response to time-of-use (TOU) electricity rates structures on occupant thermal comfort are evaluated for representative single family residential buildings located in 3 climate zones with dominant cooling loads. Building energy models (BEM) of single family homes are evaluated using a full factorial experimental design to create a response surface which provides a continuous function to evaluate the impact of four design variables on long-term thermal comfort indices, including Average Percent of People Dissatisfied (Average PPD), and Percentage Outside Thermal Comfort Zone (POS). These design variables include indoor set point temperature, degrees of setback temperature in cooling mode, building thermal mass, and air exchange rate for each climate zone. These are compared to the relative energy savings resulting from TOU thermostat setbacks while considering other design variables. A second-order response surface is found to provide a reasonable fit to BEM simulation in- and out-of-sample data. The set point temperature is the most influential of the variables studied in decreasing long-term thermal comfort, while reducing HVAC electricity use. The thermostat setback has the strongest influence on thermal comfort in a hot-dry climate, while the most HVAC energy savings is able to be achieved in the mixed-humid climate zone. The results are tabulated for weighing the costs and benefits of TOU electricity rates for homes with different characteristics, in climate zones with air conditioning-dominate energy consumption.

Stress wave stimulation of geological formations has potential applications in petroleum engineering, hydro-geology, and environmental engineering. The stimulation can be applied using wave sources whose spatio-temporal characteristics are designed to focus the emitted wave energy into the target region. Typically, the design process involves numerical simulations of the underlying wave physics, and assumes a perfect knowledge of the material properties and the overall geometry of the geostructure. In practice, however, precise knowledge of the properties of the geological formations is elusive, and quantification of the reliability of a deterministic approach is crucial for evaluating the technical and economical feasibility of the design. In this article, we discuss a methodology that could be used to quantify the uncertainty in the wave energy delivery. We formulate the wave propagation problem for a two-dimensional, layered, isotropic, elastic solid truncated using hybrid perfectly-matched-layers (PMLs), and containing a target elastic or poroelastic inclusion. We define a wave motion metric to quantify the amount of the delivered wave energy. We, then, treat the material properties of the layers as random variables, and perform a first-order uncertainty analysis of the formation to compute the probabilities of failure to achieve threshold values of the motion metric. We illustrate the uncertainty quantification procedure using synthetic data.

Design of an offshore wind turbine requires estimation of loads on its rotor, tower and supporting structure. These loads are obtained by time-domain simulations of the coupled aero-servo-hydro-elastic model of the wind turbine. Accuracy of predicted loads depends on assumptions made in the simulation models employed, both for the turbine and for the input wind and wave conditions. Currently, waves are simulated using a linear irregular wave theory that is not appropriate for nonlinear waves, which are even more pronounced in shallow water depths where wind farms are typically sited. The present study investigates the use of irregular nonlinear (second-order) waves for estimating loads on the support structure (monopile) of an offshore wind turbine. We present the theory for the irregular nonlinear model and incorporate it in the commonly used wind turbine simulation software, FAST, which had been developed by National Renewable Energy Laboratory (NREL), but which had the modeling capability only for irregular linear waves. We use an efficient algorithm for computation of nonlinear wave elevation and kinematics, so that a large number of time-domain simulations, which are required for prediction of long-term loads using statistical extrapolation, can easily be performed. To illustrate the influence of the alternative wave models, we compute loads at the base of the monopile of the NREL 5MW baseline wind turbine model using linear and nonlinear irregular wave models. We show that for a given environmental condition (i.e., the mean wind speed and the significant wave height), extreme loads are larger when computed using the nonlinear wave model. We finally compute long-term loads, which are required for a design load case according to the International Electrotechnical Commission guidelines, using the inverse first-order reliability method. We discuss a convergence criteria that may be used to predict accurate 20-year loads and discuss wind versus wave dominance in the load prediction. We show that 20-year long-term loads can be significantly higher when the nonlinear wave model is used.

When there is interest in estimating long-term extreme loads for an offshore wind turbine using simulation, statistical extrapolation is the method of choice. While the method itself is rather well-established, simulation effort can be intractable if uncertainty in predicted extreme loads and efficiency in the selected extrapolation procedure are not specifically addressed. Our aim in this study is to address these questions in predicting blade and tower extreme loads based on stochastic response simulations of a 5 MW offshore turbine. We illustrate the use of the peak-over-threshold method to predict long-term extreme loads. To derive these long-term loads, we employ an efficient inverse reliability approach which is shown to predict reasonably accurate long-term loads when compared to the more expensive direct integration of conditional load distributions for different environmental (wind and wave) conditions. Fundamental to the inverse reliability approach is the issue of whether turbine response variability conditional on environmental conditions is modeled in detail or whether only gross conditional statistics of this conditional response are included. We derive long-term loads for both these cases, and demonstrate that careful inclusion of response variability not only greatly influences such long-term load predictions but it also identifies different environmental conditions that bring about these long-term loads compared with when response variability is only approximately modeled. As we shall see, for this turbine, a major source of response variability for both the blade and tower arises from blade pitch control actions due to which a large number of simulations are required to obtain stable distribution tails for the turbine loads studied.

When stochastic simulation of inflow turbulence random fields is employed in the analysis or design of wind turbines in normal operating states, it is common to use well-established standard spectral models represented in terms of parameters that are usually treated as fixed or deterministic values. Studies have suggested, though, that many of these spectral parameters can exhibit some degree of variability. It is not unreasonable to expect, then, that derived flow fields based on simulation with such spectral models can be in turn highly variable for different realizations. Turbine load and performance variability would also be expected to result if response simulations are carried out with these variable flow fields. The aim here is to assess the extent of variability in derived inflow turbulence fields that arises from the noted variability in spectral model parameters. Simulation of these parameters as random variables forms the basis of this study. A commercial-sized 1.5 MW concept wind turbine is considered in the numerical studies. Variability in turbulence power spectra at field points on the rotor plane and in turbulence coherence functions for separations on the order of a rotor diameter and smaller is studied. Using time domain simulations, variability in various wind turbine response measures is also studied where the focus is on statistics such as response root-mean-square and 10-min extreme estimates. It is seen that while variability in inflow turbulence spectra can be great, the variability in turbine loads is generally considerably lower. One exception is for turbine yaw loads whose larger variability arises due to sensitivity to a coherence decay parameter that is itself highly variable. Finally, because reduced-order representations of turbulence random fields using empirical orthogonal decomposition techniques allow useful physical insights into spatial patterns of flow, variability in the energy distribution and the shapes of such empirical eigenmodes is studied and a simplified model is proposed that retains key variability sources in a limited number of modes and that accurately preserves overall inflow turbulence field uncertainty.

The reliability of wind turbines against extreme loads is the focus of this study. A procedure to establish nominal loads for use in a conventional load-and-resistance-factor-design format is presented. The procedure, based on an inverse reliability approach, permits inclusion of randomness in the gross wind environment as well as in the extreme response given wind conditions. A detailed example is presented where three alternative nominal load definitions are used to estimate extreme bending loads for a 600 kW three-bladed horizontal-axis wind turbine. Only operating loads—here, flapwise (out-of-plane) bending moments—at a blade root are considered but the procedure described may be applied to estimate other loads and response measures of interest in wind turbine design. Results suggest that a full random characterization of both wind conditions and short-term maximum response (given wind conditions) will yield extreme design loads that might be approximated reasonably well by simpler models that include only the randomness in the wind environment but that account for response variability by employing appropriately derived “higher-than-median” fractiles of the extreme bending load conditional on inflow parameter values.

Using a random effects model that takes into consideration the correlation of data recorded by a single seismic event, a database consisting of 195 recordings from 17 recent events is employed to develop empirical attenuation relationships for the geometric mean of horizontal peak ground acceleration and 5-percent damped spectral acceleration ( S a ). The recordings employed are obtained from strong motion stations operating in Northwestern Turkey and resulted from events that include the Kocaeli ( M w =7.4) and the Duzce ( M w =7.1) earthquakes and their aftershocks as well as other events. By studying differences in standard errors, the random effects model is compared with a fixed effects model that does not account for distinctions between intra- and inter-event variability. Effects of local site conditions are included in the empirical relationships developed. The dependence on frequency of the various model parameters is also studied. Frequency-dependent attenuation coefficients for the proposed random effects models developed are summarized in tables to facilitate their use.

When the specification of safety goals for offshore jacket platforms is made in explicit “probability of failure” terms, a design procedure may be developed that rationally derives design load return periods and levels for sizing. One such procedure is described here. Using information on the probabilistic description of annual maximum wave heights, an ultimate-level wave height is first estimated that establishes a load level against which performance will in the end be confirmed. From this ultimate-level load, one derives a lower level of load (and associated design-level wave height) to be employed for sizing members by assuming/anticipating the reserve strength characteristics of the jacket beyond the design level and into the nonlinear post-yield regime. A primary objective in establishing this procedure was that initial member sizing and interaction ratio (IR) checks be conducted using familiar procedures (e.g., API RP2A-WSD [10]. Within the framework of the proposed design procedure, members are first sized in the conventional manner (e.g., by working stress or LRFD procedures). A nonlinear static pushover analysis is then performed to establish the initial design’s ultimate capacity. It is desirable that the proposed design should yield a reliability that meets the target/desired reliability for the jacket. Both, the ultimate-level and the design-level wave loads, are derived with this goal in mind while employing various assumptions regarding the nature of the loads, response, and ultimate capacity of the structure. The initial assumptions are, if necessary, altered iteratively. By way of illustration of the proposed procedure, a jacket platform is adequately designed after a few member-sizing cycles. During these iterative design cycles, critical member sections are adjusted to ensure that the reliability is close to the target level; and the various assumptions made (in deriving load levels and that serve as the basis for load/capacity estimates) are modified and/or verified.