Average Conditional Exceedance Rate Research Articles

Temperature gradient estimation of long-span concrete box girders using average conditional exceedance rate function

An accurate assessment of temperature gradients in box girders is crucial for design and maintenance of long-span bridges. Although the current bridge specifications have provided temperature gradient patterns, these existing specifications are insufficient to accurately describe temperature gradients of bridges in service period. In this article, a novel methodology for determining an efficient positive temperature gradient pattern considering condition dependent and whole design service life is proposed. Firstly, statistical analysis and curve fitting are performed by using the long-term temperature data collected through structural health monitoring system, which indicates that temperature gradient patterns can be described as exponential functions. Secondly, the representative values of temperature difference have been estimated using average conditional exceedance rate (ACER) functions, which can use short-term data and consider conditional dependencies to predict long-term extreme values. Finally, the temperature gradient patterns of box girder of bridges in the whole service life have been estimated. Compared with the gradient patterns in current Chinese specification, the proposed temperature gradient pattern demonstrates better applicability in a long-span continuous concrete box-girder bridge. This result is expected to provide a research reference for accurately assessment of temperature gradients in box girders, which is crucial for design and maintenance of long-span bridges.

Short-term extreme response estimation methodology for marine umbilical cables with two configuration types

This study investigates the critical engineering problem of the short-term extreme responses of marine umbilical cables, which are essential components in offshore oil and gas operations. Umbilical cables play a pivotal role in connecting subsea systems to surface platforms, necessitating a safe design to withstand external loads. This study focused on two primary umbilical cable configuration types: deep-water catenary and shallow-water lazy wave. For each configuration type, 100 3-h dynamic numerical simulations were performed, with maximum values fitted by using the Gumbel distribution, and the most probable maximum (MPM) values were set as benchmark values. The average conditional exceedance rate (ACER) method and uncertainty-incorporated ACER method were applied to study the short-term extreme values of umbilical cable responses based on limited sample data. The predicted results have been compared with the MPM values, and the accuracy and uncertainty of different efficient extreme-value analysis methods are discussed. This study provides a comprehensive methodological framework for the reliability analysis and safety design of umbilical cables in marine engineering.

Prediction of ultimate tensions in mooring lines for a floating offshore wind turbine considering extreme gusts

The design of mooring line parameter for a floating offshore wind turbine (FOWT) should consider the ultimate limit state. Typhoons should be considered as a threatening condition for mooring design, and the characteristics of transient changing wind should be studied. Currently, few extreme value predictions consider gust features, and extreme mooring tensions may be underestimated in practical FOWT design. We conducted the simulations of the 5 MW wind turbine from the National Renewable Energy Laboratory (NREL) in the environmental conditions of extreme gusts, waves, and currents. Extreme gusts were found to cause dramatic increases in mooring tensions under 100-year typhoon conditions. The average conditional exceedance rate (ACER) method is used to predict extreme mooring tensions. The impacts of simulation duration and sample size on the prediction results are then discussed. The results show that in extreme gust conditions, the tail data of the average conditional exceedance rate of mooring tension presents a different extrapolation trend from stable wind conditions. Short-term predicted values in gust conditions are 14–20% larger than those in stable wind conditions. The research shows the necessity of considering threatening gust conditions in the ultimate limit state design of mooring system of FOWT.

Estimation of Return Levels with Long Return Periods for Extreme Sea Levels by the Average Conditional Exceedance Rate Method

Estimation of so-called return levels for environmental extremes is of importance for risk assessment. A particular challenge is to find estimates corresponding to long return periods, as uncertainties in the form of confidence intervals became too wide for practical use when applying conventional methodology where large portions of data are not used. A recently proposed technique, the Average Conditional Exceedance Rate (ACER), makes effective use of all available data. For risk analysis related to nuclear infrastructure, usually located along a coastline, extreme sea levels are of concern. We demonstrate, for measurements of the sea level along the Swedish coast at locations close to nuclear power plants, that the methodology results in considerably shorter confidence intervals compared to conventional approaches.

Extreme state prediction of long-span bridges using extended ACER method

An accurate prediction of the future service state of long-span bridges is crucial for the structural reliability evaluation, maintenance planning, and further life-cycle cost analysis. By extending the average conditional exceedance rate (ACER) statistical model and applying input–output data collected through a structural health monitoring (SHM) system, this paper proposes a novel methodology for predicting the future service state of long-span bridges. The advantages lie in the consideration of the main excitation load as the structural input and the strain response of the bridge as the output. Therefore, a mapping relationship between the extreme excitation load and extreme strain could be established, and the future service state of long-span bridges could be predicted. The proposed method comprises three steps: (1) extraction of the ambient temperature-induced strain and vehicle-induced strain from the measured strain series through the SHM system using the baseline estimation and denoising with sparsity (BEADS) method, (2) establishing statistical models of the extreme values of different excitations (input) and structural strains (output) using a cascade of conditioning approximations and the ACER to obtain the tail trend of the data and extrapolating it, and (3) establishing a functional relationship between the input and output extreme values based on the same conditions of the regression period at the target prediction level, after which the future service state of long-span bridges can be predicted. The proposed method is applied to a case study of the Jinchao Bridge in Guangdong Province, China, and the results are expected to provide a scientific reference for the design of new bridges and in the maintenance of existing ones in service.

Extreme Value Prediction of Traffic Loads Using the Average Conditional Exceedance Rate Method

An efficient prediction of the extreme value of traffic loads is crucial for the structural design, reliability evaluation, maintenance planning, and further life-cycle cost analysis of bridges. In this work, a novel method is proposed for predicting the appropriate extreme traffic load distribution. Specifically, the average conditional exceedance rate (ACER) statistical model is estimated from the historical traffic loads which was collected through a weigh-in-motion system installed in toll stations. The basic idea of the ACER approach lies in the introduction of a cascade of conditioning approximations and the average exceedance rate to capture the dependence effects and obtain the data tail, the trend features of which are fitted with a similar Gumbel distribution function and extrapolated to the concerned level. An illustration case dealing with traffic loads using the ACER strategy is presented, the extreme value and confidence interval (CI) in any return period can be predicted by application of this approach. Furthermore, the peaks-over-threshold (POT) method based on the asymptotic extreme theory is also applied to illustrate the advantages of the ACER method. The ACER method has advantages in analyzing extreme traffic loads, with good robustness and the ability to handle extreme value prediction for different sampling strategies, it also can produce more accurate confidence intervals and predicts consistent extreme values. The study results are expected to help accurately determine traffic loads and ensure safety in bridge engineering.

Oil tanker under ice loadings

As a result of global warming, the area of the polar pack ice is diminishing, making merchant travel more practical. Even if Arctic ice thickness reduced in the summer, fractured ice is still presenting operational risks to the future navigation. The intricate process of ship-ice interaction includes stochastic ice loading on the vessel hull. In order to properly construct a vessel, the severe bow forces that arise must be accurately anticipated using statistical extrapolation techniques. This study examines the severe bow forces that an oil tanker encounters when sailing in the Arctic Ocean. Two stages are taken in the analysis. Then, using the FEM program ANSYS/LS-DYNA, the oil tanker bow force distribution is estimated. Second, in order to estimate the bow force levels connected with extended return periods, the average conditional exceedance rate approach is used to anticipate severe bow forces. The vessel’s itinerary was planned to take advantage of the weaker ice. As a result, the Arctic Ocean passage took a meandering route rather than a linear one. As a result, the ship route data that was investigated was inaccurate with regard to the ice thickness data encountered by a vessel yet skewed with regard to the ice thickness distribution in the region. This research intends to demonstrate the effective application of an exact reliability approach to an oil tanker with severe bow forces on a particular route.

A comparison study of power performance and extreme load effects of large 10‐MW offshore wind turbines

AbstractThe utilisation of offshore wind turbines has rapidly increased in the last decade, which has resulted in a steady increase in wind turbine sizes. The global average offshore wind turbine size has increased from 1.5 MW to 6 MW in the last two decades. The research community has started to investigate huge 10 to 15 MW offshore wind turbines in recent years, resulting in the study of very innovative floating wind turbines using various substructure technologies. With this backdrop, this paper will investigate and thoroughly compare the power performance of extreme load effects of a large offshore 10 MW turbine installed on the monopile, spar, and semisubmersible substructures. This is performed by using the average conditional exceedance rate (ACER) and Gumbel methods to predict the extreme responses under the operating conditions of 8, 12, and 16 m/s mean wind speed, representing the below‐rated, rated, and above‐rated regions, respectively. The results show that the power performance and extreme loads experienced depends significantly on the operating regions. The mean power generation between the three different types of offshore wind turbines (OWTs) are closely in the whole operating range, which standard deviations differ significantly. Large standard deviations of power generation appear in the spar turbine under the below‐rated condition. Further, it was observed that the spar wind turbine generally experiences larger extreme loads due to larger platform pitch motion. In addition, the ACER method shows a better prediction for the 1, 2 and 5‐year extreme responses than the Gumbel method, which is due to the relatively poor data fitting of the Gumbel method at the upper tail. The study is believed to consolidate and close the knowledge gap in understanding wind turbine responses across the most common offshore substructure technologies and provide a basis for design and deployment of OWTs.

Offloading operation bivariate extreme response statistics for FPSO vessel

The Floating Production Storage and Offloading unit (FPSO) is an offshore unit producing and storing crude oil prior to tanker transport. An important design concern is an accurate prediction of risky dynamic hawser tensions during FPSO offloading operations. Bivariate extreme hawser tension contours are important for selecting proper design values. This paper employed the AQWA hydrodynamic software to analyze vessel hydrodynamic wave loads dynamic response, acting on FPSO vessels under realistic sea state conditions. This paper presents an efficient method for estimating FPSO bivariate response statistics based on numerical simulations validated by various experiments. The bivariate Average Conditional Exceedance Rate (ACER2D) method offers an accurate bivariate extreme value probability distribution and return period contours estimation, utilizing available data efficiently. The two-dimensional probability contours, corresponding to low probability return periods, are easily obtained by the ACER2D method. The performance of the presented method has shown that the ACER2D method provides an efficient and accurate prediction of extreme return period contours. The suggested approach may be used for FPSO vessel design, minimizing potential FPSO hawser damage. Bivariate contours yield bivariate design points, as opposed to a pair of uncoupled univariate design points with the same return period as currently adopted in the industry.

Uncertainty analysis of extreme mooring loads associated with environmental contours and peak tension distributions

This paper aims to assess the uncertainty on the extreme mooring loads of floating system considering short-term variability. Two environmental contour approaches based on the inverse First and Second Order Reliability Methods are employed to identify critical sea states that may give rise to extreme loads. The uncertainty related to the construction of environmental contours is addressed including significant differences due to marginal distribution fitting, parameter estimation methods and joint models. Three measured datasets are analysed using a known conditional joint distribution and proposed mixed copula model. 3-h time domain numerical simulation for each sea state is conducted and the characteristic extreme responses of mooring lines subjected to design loads are assessed. The uncertainties due to various statistical models including the average conditional exceedance rate method as well as global maxima, peak-over-threshold method combined with Gumbel distribution, Generalized Extreme Value distribution, Generalized Pareto distribution and 3-parameter Weibull distribution are investigated and quantified. It is observed that marginal distributions, joint models and parameters estimation methods have apparent effect on design loads estimation, and the extreme tensions of the semi-submersible platform shows significant difference using various probabilistic models. The results indicate that those epistemic uncertainties should be account for in the reliability analysis or safety factor calibration for mooring systems.

Characterisation of extreme load responses of a 10-MW floating semi-submersible type wind turbine

The global average size of offshore wind turbines has increased steadily from 1.5 MW to 6 MW from 2000 to 2020. With this backdrop, the research community has recently looked at huge 10–15 MW class floating offshore wind turbines (FOWTs). The larger rotor, nacelle structure and tower have more significant structural flexibility. The larger structural flexibility, controller dynamics, aerodynamics, hydrodynamics, and various environmental conditions result in complex structural responses. The structural load effects of a very large FOWT could be more severe than that of the lower MW classes. Accurate quantification of the extreme dynamic responses of FOWT systems is essential in the design of the Ultimate Limit State (ULS) due to the fully-coupled interaction between the FOWT system and environmental conditions. Motivated by this, extreme responses of the 10 MW semi-submersible type FOWT are investigated using the average conditional exceedance rate (ACER) and Gumbel methods. Three operating conditions representing below-rated (U = 8 m/s), rated (U = 12 m/s) and above-rated (U = 16 m/s) regions were considered. The aim is to guide future research on large FOWTs by indicating the expected ULS loads.

Parametric study on the short-term extreme mooring tension of nylon rope for a point absorber

A series of 1:40 model tests are carried out to study the dynamic responses of a point absorber moored by three taut nylon ropes under irregular wave conditions. The experimental results are applied to calibrate a numerical model, and then the calibrated numerical model is applied to study the influence of pretension, mooring axial stiffness, current velocity and tidal range on extreme mooring tension under head sea wave conditions. Both the global maximum method and the average conditional exceedance rate method are applied to study extreme mooring tension based on fifty 3-h fully coupled analyses. The nonlinear strain-tension curve is used in numerical simulations to consider the material non-linearities of nylon rope. To discuss the influence of axial stiffness on extreme mooring tension, nonlinear strain-tension curves of a worked rope and a new rope are studied. The numerical simulations under three current profiles are conducted to study the influence of current velocity on extreme mooring tension. It is found that the influence of axial stiffness and current velocity on extreme mooring tension is significant, and the influence of current velocity on extreme mooring tension reduces with the increase of mooring pretension.

Dynamic response of monopile-supported wind turbines considering non-Gaussian characteristics of wind inflow

Available wind turbine design standards usually assume that the inflow wind field is a smooth Gaussian process, but the in-situ measured data show that the inflow wind presents a certain degree of non-Gaussian characteristics. This study investigates the dynamic response of the supporting structure of the wind turbine under both Gaussian and non-Gaussian wind fields. The Mises stress at the tower base and the mudline of the monopile are considered. Through the global maxima method and the average conditional exceedance rate method, the extreme value response of the turbine under a given mean recurrence interval is obtained. The results indicate that by taking the non-Gaussian characteristics of wind fields into account, the short-term extreme values are generally larger than those under Gaussian wind fields. For the long-term extreme values of the stress at the two critical points, the influence of kurtosis is significantly greater than the skewness. Meanwhile, the long-term stress extreme value also increases with the increase of kurtosis. The non-Gaussian characteristic of the wind field has a particular influence on the safe operation of the wind turbine and should be considered when designing wind turbines.

A novel design approach for estimation of extreme load responses of a 10-MW floating semi-submersible type wind turbine

Offshore structures are constructed to withstand extreme wind and wave-induced loads, so studying these extreme loads is vital as it allows offshore structures, e.g., wind turbines, to be designed and operated with minimal disruption. A novel statistical model that is precise and meticulous will facilitate these extreme load values to be estimated accurately. Bivariate average conditional exceedance rate (ACER2D) method was utilized in this paper. This multivariate statistical analysis is more appropriate than a univariate statistical analysis for complete structures, e.g., wind turbines, since it can extrapolate the extreme values with better accuracy. This paper uses this ACER2D method to explore a novel approach to estimating the extreme load responses of a 10-MW semi-submersible type floating wind turbine (FWT). Two cases are considered to understand the feasibility of the ACER2D on the extreme load responses. The first case analyses the blade root flap wise bending moment, while the second one analyses the tower bottom fore-aft bending moment. Based on the performance of the proposed novel method, the ACER2D method can offer better robust and precise bivariate predictions of the bending moments of the FWT.

Bivariate statistics of floating offshore wind turbine dynamic response under operational conditions

FOWT (Floating offshore wind turbines) belong to the modern offshore wind energy industry generating green renewable energy. Accurate extreme loads and response prediction during power generation is an important design concern. More accurate and reliable estimations of extreme responses are significant for the offshore wind industry as it advances the design, manufacturing and deployment of large FOWTs in the coming decade. In this study, the OpenFAST code was used to model offshore wind turbine mooring line tension force and blade bending moment due to environmental loads, acting on a site-specific FOWT under realistic local environmental conditions. This paper presents an efficient Monte Carlo based method to study bivariate extreme dynamic response statistics. The ACER2D (bivariate average conditional exceedance rate) method is briefly discussed. The ACER2D method enables robust estimation of bivariate statistics, efficiently utilizing available data. Large return period 2D (two-dimensional) probability contours were obtained using the ACER2D method. Based on the studied performance of the presented methodology, it was seen that ACER2D provides accurate and efficient predictions of extreme return period contours.The described approach may be utilized at the design stage, defining optimal FOWT design values to minimize potential structural damage due to extreme environmental loads. It should be noted that the bivariate design point is less conservative than the classic univariate one; therefore, this study advocates a design method leading to lower structural production costs.

Extreme Value Estimation of Beaufort Sea Ice Dynamics Driven by Global Wind Effects

The purpose of the present study is to investigate the extreme values of the ice drift speed, which are also considered in the light of the magnitude of the simultaneous wind speed. The relationship between wind speed and ice drift speed is studied. The long-term ice drift data is collected by using local subsurface measurements based on acoustic Doppler current profilers (ADCP) in the Beaufort Sea during the period of 2006–2017. Upward-looking sonars (ULS) are deployed in order to observe the ice thickness as well as to identify events that correspond to open water conditions. The relationship between the ice drift speed and the wind speed is also investigated. It is found that the magnitude of the average ice drift speed is approximately 2.5% of the wind speed during the winter season. Estimation of the extreme values of the ice drift speed is studied by application of the average conditional exceedance rate (ACER) method. It is found that the extreme ice drift speed during the ice melt season (i.e. the summer season) is approximately 20%–30% higher than that during the ice growth season (i.e. the winter season). The extreme ice drift speed can be effectively estimated based on the 2.5% wind speed. Moreover, the extreme ice drift speed can be obtained based on the extreme values of 2.5% of the wind speed based on multiplying with an amplification factor which varies in the range from 1.7 to 2.0 during the growth season, corresponding to increasing return periods of 10, 25, 50 and 100 years.

Offshore renewable energy site correlated wind-wave statistics

Offshore engineering often requires estimation of extreme wind speeds and wave heights at offshore in-situ locations. This paper presents practical approach to study extreme wind speed and wave height statistics, based on available in-situ hourly wind speed and wave height maxima. The wind and wave data, studied in this paper, was obtained from numerical hind cast model, locally applied to the offshore the area that covers SEM-REV (European wind and wave energy research site) location, for the time period 2001–2010 years.To obtain accurate local wind and wave data set, accurate wave and wind measurements from in-situ monitoring tools (meteorological stations and buoys) as well as remote satellite sensing data (ENVISAT and TOPEX satellite records) were plugged into atmospheric wind and wave model.The novel bivariate correction technique based on the Average Conditional Exceedance Rate (ACER) method has been presented in brief detail. The bivariate correction method produced quite accurate extreme value predictions, efficiently utilizing available wind speeds and wave heights data set.In some practical situations it would be useful to improve accuracy of some statistical predictions, using information supplied by another synchronous highly correlated random process that has been measured for a longer time than the process of interest. In this paper the novel technique of improving correlated extreme wind speed and wave height predictions has been presented.

Assessment of methods for short-term analysis of riser collision probability

Reliability- and performance-based design of a riser cluster requires an accurate estimation of the extreme values of the stochastic relative distance between the risers during a given time duration. This study presents a comprehensive assessment of six methods for estimating the collision probability between two risers with limited simulation length. A pair of steep-wave risers in tandem arrangement subjected to combined current and wave loads is modeled. The wake effect generated by the upstream riser acting on the downstream riser is considered.Firstly, the critical locations at which collisions during a short duration are likely to occur are identified. After obtaining nonlinear riser responses, 3-hour short-term extreme relative motions are calculated, which are used for the collision probability estimation. Several methods for the extreme value analysis, including the Gumbel probability paper method, the general extreme value method and the average conditional exceedance rate method are presented. This paper also proposes two methods which offer reliable and satisfactory results for the extreme value analysis of highly skewed processes.

A Probabilistic Framework for the Fatigue Damage Assessment of Ships Navigating through Level Ice Fields

For ships navigating in ice-covered waters, fatigue damage due to ice loads is an important issue. The purpose of this paper is to provide ship researchers and engineers with a simulation-based procedure for a probabilistic fatigue damage assessment of ships moving through a level ice field. A novel procedure for fatigue damage assessment using numerical simulations is developed, and a hypothetical scenario with the Xuelong 2 icebreaker is used to illustrate the procedure. Long-duration time-domain simulations are performed to generate samples of the ice-load peaks due to ship-ice interactions. Based on the average conditional exceedance rate (ACER) method, the extreme value statistics of the line load peaks are predicted, and subsequently, the fatigue stresses caused by ice loads are estimated by means of beam theory. Several analytical models are applied to describe the probability distribution of the stress amplitudes, and the fatigue damage is calculated based on S-N curves and the Palmgren-Miner formula. Furthermore, a quantification of the effects of uncertainties related to discretization errors (mesh size, reference period), ship-model properties, choice of boundary conditions, and S-N curves is performed.

Estimation of characteristic extreme response for mooring system in a complex ocean environment

As vital key parts of offshore floating structures, mooring systems should be able to withstand harsh environmental conditions. This study aims to assess the design loads of mooring lines subjected to random loads using various statistical models. A benchmark of extreme values is established using the global maxima method, and is based upon a Weibull distribution model for the maxima of 150 3-h time series generated by a given design sea condition with different random seeds. To reduce the computational cost, a peak-over-threshold (POT) method is combined with an asymptotic approach. Different variations are investigated, and a better choice for the number of individual top peaks from single time domain simulations is determined from a statistical error analysis. The average conditional exceedance rate (ACER) method and environmental contour (EC) approach are also applied and compared. The effects of various load combinations are considered, and a 3-D EC surface is established based on the Nataf transformation model. A simplified long-term extreme response analysis is conducted by accounting for the POT-based variabilities, so as to provide a more reliable design load estimation. Numerical results are presented and discussed for the tension estimation of a semi-submersible platform considering a long-term coupled analysis.