Long-term performance assessment and design of offshore structures

doi:10.1016/j.compstruc.2015.02.029

Computers & Structures

Volume 154, 1 July 2015, Pages 101-115

https://doi.org/10.1016/j.compstruc.2015.02.029 Get rights and content

Highlights

•
A copula approach is proposed to assess the long term performance of offshore structures under environmental changes.
•
A discretized subcopula approach is presented to identify the most critical sea state parameter values in a dynamic analysis.
•
Advantages of the copula approach over traditional models are revealed for multivariate ocean environmental parameters.
•
The copula approach is found to be more efficient than traditional methods for long term performance assessment.

Abstract

The design of an offshore structure is highly dependent on the operating environmental parameters, where a realistic statistical model of the latter is essential to produce a representative estimate of the performance and failure probability. Establishing an accurate model of the offshore environment can be a challenging task. The use of simple probabilistic models may lead to biased results in the stochastic structural analysis since the environmental impact to an existing offshore structure is associated with a wide range of inter-dependent factors. In this paper, the specification of long-term design loads for offshore structures considering multiple environmental factors is investigated where the dependency between several commonly used sea state parameters are instituted through a copula-based multivariate probabilistic model. Several copula functions, capable of modeling both linear and non-linear dependence structures, are considered. The developed multivariate model based on copula concept is compared with the available approaches in the literature using actual environmental data. The modeled sea state parameters are then utilized to characterize the sea load for the reliability analysis of a real jacket structure where the prediction of the long term load is derived in a discretized form. The applicability of this approach in a high dimensional multivariate problem is also discussed.

Introduction

Designing an offshore platform in an uncertain marine environment is a challenge which requires extensive engineering analysis and decisions. While addressing different load cases on offshore structures, designers are usually required to estimate the environmental conditions at the ocean site, and usually a multivariate analysis is performed. The safety of the structure must be ensured at least over the design life of the structure, which is associated with many years of exposure. Normally, the design code requires an operation period of 50 or 100 years for the designed structure [13]. However, the long term assessment of offshore structures considering the stochastic nature of several environmental loads such as wind and wave loads encountered by the structure can be quite complicated. The consideration of only one parameter in the load extrapolation may not lead to realistic predictions of the response of the structure. The presence of several significant parameters that characterize a complex offshore environment requires suitable multivariate models to predict the long term performance of structures.

Besides the marginal distribution of the individual parameters, such as wave heights and wave periods, the dependency structure between various ocean parameters affects the response statistics and eventually the estimation of the structural reliability. If the actual dependency is nonlinear, then the models commonly used may only offer quite coarse approximations [25], [55]. To remedy this problem, a number of approaches have been developed in the context of multivariate analysis in wave climate studies and other areas [26], [20], [27]. However, a criterion for selecting the most appropriate model choice is still lacking data, and the numerical analysis for the long term reliability and performance assessment is demanding. The application of a direct integration method with environmental parameters simulated from the constructed multivariate model is often not feasible. Approaches to answer these two challenges include the use of efficient numerical methods and model test [1], [5], reduction in simulation efforts by selecting the critical sea states [41], use of environmental contour and inverse first order reliability method (IFORM) [49], [28], and use of bootstrap methods in deriving the confidence interval from the structural analysis [15]. These studies also assessed various types of structures with regards to long term performance, such as jacket structures [18], jackup rigs [39] as well as floating structures [56]. It was recognized that the long term assessment remains one of the most difficult tasks, and the statistical modeling of the ocean parameters remains challenging due to their usually complicated relationships between the parameters.

The nonlinear dependency between parameters needs to be addressed, especially in the context of efficient numerical processing when applied to large structures. This is addressed herein through the development of a copula-based multivariate model for ocean parameters, and an associated numerically efficient simulation approach to derive a long term design load for offshore structures. The paper is organized as follows. Section 2 presents the basic framework for the long term safety assessment of offshore structures. Related literature on multivariate statistical models and copula theory is discussed in Section 3. In Section 4, an example of measured data from a buoy at the southern coast of Alaska is analyzed to demonstrate the approach. Specifically, the data are preconditioned to treat the time-dependent dependencies between the environmental variables. The copula model is established in Section 5 and compared against alternative models based on the collected, preconditioned data. To facilitate efficient numerical simulation, a discretized form of the copula model is developed in Section 6. The derivation of a long-term design load is demonstrated through a jacket structure. Section 7 discusses the extension to higher dimensional problems. The concluding remarks of this paper are summarized in Section 8.

Section snippets

Estimation of long term design value

The long term safety of an offshore structure is characterized by the probability that the load level exceeds the capacity of the structure. This requires the long term probability distribution of the load, which can be obtained numerically using direct integration. This yields the exceedance probability $P_{E}$ corresponding to a load level l accounting for the variability of the load related parameters θ, $P_{E} = \Pr [L > l] = \int_{θ} \Pr [L > l | θ] f (θ) d θ$ where f(θ) represents the joint distribution of the random variables

Conditional joint distribution

Prior to structural analysis, the collected environmental data need to be studied so as to identify a robust statistical model f(θ) to be used in Eq. (2). The challenge in some situations is that the recorded environmental data are limited and time-variant, exhibiting strong non-stationarity in time [58]. An added complication in multivariate analysis is when there are nonlinear dependencies between the ocean parameters [19], [33], [32].

Among the probabilistic models available in the

Data description and pre-treatment

In order to show the advantage of the copula above the other models in a real case application, a comparative study is performed based on ocean data from Wave Information Studies [53]. The data were collected at a site off the south coast of Alaska (52.00°N, 172.00°E; Buoy No. 82442) which has a water depth of 150 m. The hourly measured data set spans 26 years (1985/1/1 01:00 −2011/1/1 01:00). The parameters in this data set include the significant wave height $H_{S}$ (m), peak wave period $T_{P}$ (s),

Data analysis

Based on the preconditioned data sets ( $H_{S}, T_{P}$ ) and ( $H_{S}, V_{W}$ ) from Section 4, the three approaches for multivariate modeling described in Section 3 are compared. This requires a model-specific estimation of the respective model parameters.

For the conditional joint distribution model, application of the maximum likelihood method requires an efficient algorithm in view of the numerous parameters to be determined. For this reason, a regression analysis is used to estimate the values of the parameters.

Structural analysis

The joint distribution provides the basic information for characterizing the environmental load, which will then be used in Eq. (2), where the environmental parameter changes over the complete domain need to be taken care of. This makes the integration a formidable task and several approaches have been investigated in the literature to make this process efficient [9], [5]. One popular approach is the environmental contour method but the variability of the environmental parameters considered and

Extension to higher dimensions

Conceptually, the copula-based concept can be extended to n-dimensional problems in a straightforward manner. The procedure for calculating the exceedance probability $P_{E}$ according to Eq. (16) remains unchanged except using a higher dimensional copula. The proposed discretization steps remain conceptually the same, but n-dimensional hypercubic subcopulas are involved. Fig. 13 illustrates the discretization process for a three-dimensional case, for example, corresponding to the triplet

Conclusion

In this research, copulas were utilized to model the ocean parameters in a multivariate setting. The conditional probability distribution approach and the Nataf approach were compared with the copula approach, specifically for bivariate data ( $H_{S}, T_{P}$ ) and ( $H_{S}, V_{W}$ ). It was found that the copula model is more flexible and able to describe nonlinear statistical dependencies between ocean parameters. The copula model was established for example ocean data after preconditioning to obtain piecewise

References (61)

P. Agarwal et al.
Simulation of offshore wind turbine response for long-term extreme load prediction
Eng Struct
(2009)
G.S. Baarholm et al.
Combining contours of significant wave height and peak period with platform response distributions for predicting design response
Mar Struct
(2010)
C. De Michele et al.
A multivariate model of sea storms using copulas
Coast Eng
(2007)
O. Ditlevsen
Stochastic model for joint wave and wind loads on offshore structures
Struct Safety
(2002)
S. Dong et al.
Bivariate maximum entropy distribution of significant wave height and peak period
Ocean Eng
(2013)
K. Farnes et al.
Extreme dynamic, nonlinear response of fixed platforms using a complete long-term approach
Appl Ocean Res
(1993)
J.A. Ferreira et al.
Modelling bivariate distributions of significant wave height and mean wave period
Appl Ocean Res
(2002)
E. Fontaine et al.
Reliability analysis and response based design of a moored FPSO in West Africa
Struct Safety
(2013)
C. Guedes Soares et al.
Modelling uncertainty in long-term predictions of significant wave height
Ocean Eng
(2001)
P. Jonathan et al.
Statistical modeling of extreme ocean environments for marine design: a review
Ocean Eng
(2013)

P. Jonathan et al.

Joint modeling of wave spectral parameters for extreme sea states

Ocean Eng

(2010)

R. Lebrun et al.

A generalization of the Nataf transformation to distributions with elliptical copula

Probab Eng Mech

(2009)

Y.J. Lu et al.

Prediction of most probable extreme values for jackup dynamic analysis

Mar Struct

(2002)

B. Renard et al.

Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology

Adv Water Res

(2007)

A. Repko et al.

Bivariate description of offshore wave conditions with physics-based extreme value statistics

Appl Ocean Res

(2004)

L.V.S. Sagrilo et al.

On the long-term response of marine structures

Appl Ocean Res

(2011)

F. Silva-González et al.

Development of environmental contours using Nataf distribution model

Ocean Eng

(2013)

X.S. Tang et al.

Impact of copula selection on geotechnical reliability under incomplete probability information

Comp Geotech

(2013)

H.T. Wist et al.

Statistical properties of successive wave heights and successive wave periods

Appl Ocean Res

(2004)

S. Zachary et al.

Multivariate extrapolation in the offshore environment

Appl Ocean Res

(1998)

J. Zhang et al.

Geotechnical reliability analysis with limited data: consideration of model selection uncertainty

Eng Geol

(2014)

H. Akaike

Information theory and an extension of the maximum likelihood principle

S. Antoniou et al.

Advantages and limitations of adaptive and non-adaptive force-based pushover procedures

J Earthq Eng

(2004)

B. Asgarian et al.

Inelastic postbuckling and cyclic behavior of tubular braces

J Offshore Mech Arctic Eng-Trans ASME

(2005)

J.A. Battjes

Long term wave height distributions at seven stations around the British Isles

Deutsche Hydrographische Zeitschrift

(1972)

Bitner-Gregersen EM. Joint probabilistic description for combined seas. In: Proceedings of 24th international...

T. Burton et al.

Wind energy handbook

(2001)

P.W. Cheng et al.

Reliability-based design methods to determine the extreme response distribution of offshore wind turbines

Wind Energy

(2003)

U. Cherubini et al.

Copula methods in finance

(2004)

DNV. Environmental conditions and environmental loads. Recommended Practice, DNV-RP-C205;...

Cited by (76)

Structural integrity of glass fiber reinforced nanocomposites under hydrothermal aging for offshore structure applications
2024, Applied Ocean Research
Glass fiber composites are widely used in offshore structures for marine application due to their exceptional strength-to-weight ratio, corrosion resistance, and durability. As offshore structures are exposed to harsh environmental conditions, including saltwater, fluctuating temperatures, and hydrothermal influences, understanding the effects of aging on structural integrity on glass fiber composites becomes very important. In this study glass fiber-reinforced epoxy nanocomposites with 1 % and 2 % nano Al₂O₃ reinforcement were produced using the vacuum-assisted resin transfer molding. These composites were subjected to a three-month aging process in artificial seawater at a temperature of 70 °C. Mechanical properties were assessed through Tensile and Flexural Tests, while thermal properties were analyzed via TGA, DTA, and DSC analysis. To examine the structural characteristics, Fourier Transform Infrared (FT-IR) spectrophotometry was utilized, and SEM analysis was conducted. Wear properties were evaluated through dry sliding wear tests. Water absorption properties were determined in a precisely controlled seawater bath. The findings reveal that the incorporation of 1 % nano Al₂O₃ effectively diminishes the water absorption rate, thereby safeguarding the mechanical, thermal, and structural properties within a hydrothermal environment.
A time-varying copula approach for describing seasonality in multivariate ocean data
2024, Marine Structures
Characterizing multivariate ocean variables is quite critical for reliability design and risk assessment of marine structures. A robust, precise, and practical multivariate statistic model is necessary for comprehending ocean characteristics. As the time-varying characteristics exist in the ocean data, it is unreasonable to employ a simple constant statistical model to characterize all the multivariate data at one time. Therefore, in this paper, a time-varying copula approach is developed for modeling time-varying multivariate ocean data. Considering climate variations, a time-varying formula for return period and environment contour is also derived. The developed approach is demonstrated based on a site-specific ocean dataset collected from a buoy on the US coast. The climate effects associated with the multivariate ocean variables are characterized. The developed time-varying copula approach is also compared to the conventional copula and the conditional model in estimating the return period. The results showed that the time-varying model is helpful to explore the most critical environmental conditions for marine structures.
Probability density function modelling and credible region construction for multivariate, asymmetric, and multimodal distributions of geotechnical data
2024, Structural Safety
Geotechnical data are typically Multivariate, Uncertain, and Irregular (MUI), so the probability distribution of geotechnical data is Multivariate, Asymmetric, and Multimodal (MAM). Probability Density Function (PDF) modelling and Credible Region (CR) construction are two key issues for a MAM distribution. There are two fundamental difficulties in characterizing a MAM distribution. The first is on joint PDF modelling as many traditional approaches collapse for a MAM distribution. Copula theory has attracted special attention for this purpose but very few works attempted to tackle the critical problem of probabilistic prediction on target variables using available information of remaining variables based on the copula-based joint PDF. The second is on CR construction of a MAM distribution as it cannot find a unique CR of a MAM distribution given an exceedance probability only. There is still a lack of a unified approach for CR construction for a MAM distribution of geotechnical data. Aiming to resolve these two fundamental difficulties, we propose the BAyeSIan Copula-based Highest density region/contour (BASIC-H) for providing a systematic framework of PDF modelling and CR construction of a MAM distribution. This framework contains Stage-PDF and Stage-CR. Stage-PDF fuses the copula theory and Bayesian inference to develop optimal, robust, and hyper-robust predictions on the posterior distribution and posterior predictive distribution. Stage-CR adopts the constraint for the CR that the probability density of every point inside the CR is at least as large as the probability density of any point outside, which is the same as the idea of the HDR (Highest Density Region). The Monte Carlo Simulation (MCS), based on the developed optimal, robust, and hyper-robust posterior distributions and posterior predictive distributions, is performed for estimation of the probability density boundary, which is a key parameter for constructing the HDR. Examples using simulated data and Quaternary clay data are presented to illustrate the capabilities of the BASIC-H in PDF modelling and CR construction of MAM distributions of geotechnical data.
Multivariate probability analysis of wind-wave actions on offshore wind turbine via copula-based analysis
2023, Ocean Engineering
Floating structures in service encounter extreme natural hazards, such as correlated extreme wind-wave loads. This study aims to provide realistic multivariate models of environmental parameters to accurately describe the statistical characteristics of metoceanic conditions, which are essential for the reliability-based design of marine structures. The multiload analysis method includes three major steps: (1) to identify the best-fit univariate marginal distributions of the wind-wave parameters. Mixed models composed of a set of single-mode parametric distributions were found to be more suitable for the measured variables. (2) To construct joint probability distributions of multiple variables using copula-based models, the performance of various models namely, trivariate metaelliptical copulas, Archimedean copulas, and vine copula models. It was observed that joint distributions can be best modelled using vine copula models with considerable flexibility. The final process involves establishing environmental surfaces and contours based on the inverse first-order reliability method. The most unfavourable combination of extreme design conditions can be defined on the environmental surface which is useful for evaluating the response characteristics of offshore wind turbines. These expressions provide a preliminary assessment of wind-wave loads on offshore structures.
A copula approach in the probabilistic evaluation of chloride ingress process for coastal concrete structures
2023, Structures
One of the most prevalent causes of reinforced concrete (RC) structural deterioration is chloride-induced corrosion. This paper is concerned with a novel approach to assess the chloride ingress process for coastal concrete structures under consideration of environmental effects. Firstly, the chloride diffusion process model for one-dimensional (1-D) and two-dimensional (2-D) concrete and the copula theory are introduced. Secondly, the climate data from the National Meteorological Center of China are investigated. Dependencies between temperature and humidity are described with a dedicated copula. Meanwhile, the results are analyzed regarding the geographical variations along the coastline. The critical environmental factors governing the diffusion process are identified and discussed. Finally, the feature of adopting the copula in modeling the environmental characteristics is highlighted. The work could significantly improve the durability design of coastal structures in China. A copula approach is developed to capture dependencies that are difficult to quantify from a physical perspective, including their uncertainties. Comparison to traditional methods shows the advantages clearly.
Impacts of climate change on seasonal extreme waves in the Northwest Atlantic using a Spatial Neural Gas clustering method
2023, Journal of Ocean Engineering and Science
Having estimates of wave climate parameters and extreme values play important roles for a variety of different societal activities, such as coastal management, design of inshore and offshore structures, marine transport, coastal recreational activities, fisheries, etc. This study investigates the efficiency of a state-of-the-art spatial neutral gas clustering method in the classification of wind/wave data and the evaluation of extreme values of significant wave heights (Hs), mean wave direction (MWD) and mean wave periods (T0) for two 39-year time periods; from 1979 to 2017 for the present climate, and from 2060 to 2098, for a future climate change scenario in the Northwest Atlantic. These data were constructed by application of a numerical model, WAVEWATCHIII™ (hereafter, WW3), to simulate the wave climate for the study area for both present and future climates. Data from the model was extracted for the wave climate, in terms of the wave parameters, specifically Hs, MWD and T0, which were analyzed and compared for winter and summer seasons, for present and future climates. In order to estimate extreme values in the study area, a Natural Gas (hereafter, NG) clustering method was applied, separate clusters were identified, and corresponding centroid points were determined. To analyze data at each centroid point, time series of wave parameters were extracted, and using standard stochastic models, such as Gumbel, exponential and Weibull distribution functions, the extreme values for 50 and 100-year return periods were estimated. Thus, the impacts of climate change on wave regimes and extreme values can be specified.

View all citing articles on Scopus

View full text

Long-term performance assessment and design of offshore structures

Highlights

Abstract

Introduction

Section snippets

Estimation of long term design value

Conditional joint distribution

Data description and pre-treatment

Data analysis

Structural analysis

Extension to higher dimensions

Conclusion

Eng Struct

Mar Struct

Coast Eng

Struct Safety

Ocean Eng

Appl Ocean Res

Appl Ocean Res

Struct Safety

Ocean Eng

Ocean Eng

Ocean Eng

Probab Eng Mech

Mar Struct

Adv Water Res

Appl Ocean Res

Appl Ocean Res

Ocean Eng

Comp Geotech

Appl Ocean Res

Appl Ocean Res

Eng Geol

Information theory and an extension of the maximum likelihood principle

Advantages and limitations of adaptive and non-adaptive force-based pushover procedures

J Earthq Eng

Inelastic postbuckling and cyclic behavior of tubular braces

J Offshore Mech Arctic Eng-Trans ASME

Long term wave height distributions at seven stations around the British Isles

Deutsche Hydrographische Zeitschrift

Wind energy handbook

Reliability-based design methods to determine the extreme response distribution of offshore wind turbines

Wind Energy

Copula methods in finance