Random Wave Loading Research Articles

Fatigue reliability analysis of floating offshore wind turbines under the random environmental conditions based on surrogate model

Fatigue reliability analysis is essential for ensuring the safe operation of floating offshore wind turbines (FOWTs) under random wind and wave loads. Traditionally, fatigue assessments are computationally expensive due to the need for numerous numerical simulations. To reduce computational costs, a fatigue reliability analysis method is proposed in the present study by implementing the surrogate model, C-vine copula, and Monte Carlo simulation. The multivariate distribution of environmental conditions is modeled using the C-vine copula and marginal mixed distribution models, while short-term fatigue damages are estimated by the surrogate model. Finally, Monte Carlo simulation is employed to assess the fatigue reliability. The proposed method is applied to evaluate fatigue reliability at three critical locations on a FOWT. Results show that both the back propagation neural network (BPNN) and the Kriging model can accurately predict short-term fatigue damage at various locations. However, the BPNN-based surrogate model is recommended for its lower computationally cost. Furthermore, the proposed method not only assesses the probability of fatigue failure at individual locations but also evaluates system-level fatigue reliability by accounting for correlation between fatigue damage at different locations.

Damage Probability Evaluation of Pontoon-type Floating Offshore Wind Turbines Subjected to Both Random Wind and Wave Loads

Damage Probability Evaluation of Pontoon-type Floating Offshore Wind Turbines Subjected to Both Random Wind and Wave Loads

Vibration improvement of offshore wind turbines under multiple hazards

The slenderness ratio, particularly pronounced in offshore wind turbines (OWTs) with values exceeding five, renders them highly susceptible to dynamic sensitivity when exposed to lateral loads, setting them apart from conventional structures. The simultaneous interaction of wind and wave forces often results in the generation of extreme vibrations, ultimately jeopardizing the structural integrity of offshore wind turbines. This study is dedicated to assessing the effectiveness of distributed tuned mass dampers (d-TMDs) in mitigating responses in OWTs when subjected to the concurrent action of wind and wave forces. The finite element model (FEM) for the OWT, accounting for its multi-degree of freedom (MDOF) nature, is meticulously constructed using ANSYS software. The analysis encompasses uncontrolled offshore wind turbines (NC), those equipped with single tuned mass dampers (STMD), and variants featuring d-TMDs. These structures are exposed to random wind and wave loading conditions, mirroring real-world scenarios and necessitating the deployment of control schemes to counteract the adverse vibrations induced. Consequently, wind and wave spectra are generated using the Kaimal spectrum and Pierson and Moskowitz spectrum, respectively, with drag wave forces calculated through Morison's equation. Moreover, the study takes into account the impact of soil-structure interaction (SSI), incorporating both rotational and lateral springs. The results, comprising displacement and acceleration responses at the pinnacle of the OWT, facilitate a comprehensive comparison between the responses of the NC, STMD, and d-TMD configurations. In single hazard analysis, it is evident that TMDs exhibit greater efficacy in mitigating wind-induced responses in offshore wind turbines compared to wave-induced responses. Furthermore, d-TMD schemes demonstrate superior performance in enhancing the response of flexible base offshore wind turbines as opposed to their fixed base counterparts.

Prediction of Long-Term Offshore Structural Responses Based on Nonlinear Wave Modeling

Wind-generated random wave loads are the dominant loads to consider for maintaining the reliability of fixed offshore structures. Based on probabilistic techniques, the inherent randomness of the wave loading can be used to predict extreme offshore structural response, which is Gaussian in nature. However, researchers have found that the hydrodynamic component and structural dynamics substantially impact the frequency spectrum, leading to a non-Gaussian stochastic offshore structural response. A finite-memory non-linear system (FMNSNL) has been proven to be an efficient approach to evaluate the non-Gaussian stochastic offshore structural response compared to the conventional method, Monte Carlo time simulation. However, the analysis has been conducted based on short-term distribution only. The most satisfactory analysis is based on long-term distribution. Hence, further investigation in this paper will evaluate the long-term probability distribution of extreme offshore structural responses. As a result, a 100-year extreme offshore structural response prediction achieves 80% to 96% accuracy compared to the Monte Carlo time simulation. The probability distribution has been evaluated using the Gumbel distribution function throughout this investigation. Still, there is a little deviation at the tail end of the distribution between the simulated response values and the fitted line. A different distribution function, such as the Generalised Extreme Value (GEV) distribution, is advised for future work.

The vibration mitigation of jacket offshore platform based on inerter nonlinear energy sink

The application of the traditional passive vibration control system is limited by the demand for large mass. To ameliorate this situation, the inerter nonlinear energy sink (NES) is introduced and applied, as the substitute for the traditional passive vibration control system, to vibration mitigation of jacket offshore platform under random wave loading, since it has the clear advantage of obtaining apparent vibration control effect through low amounts of added mass. For one thing, the equation of jacket offshore platform including inerter NES is developed considering wave loads. For another, the optimal parameters of inerter NES are obtained through Particle Swarm Optimization (PSO) using numerical simulations. Both analytical and numerical results strongly support that the inerter NES contributes greatly to vibration suppression, compared with traditionally tuned mass dampers (TMD). To explore more practical benefits, further comparison between the vibration mitigation of inerter NES and the optimal TMD system, considering different masses and stiffness, is made right after, which verifies the effectiveness and robustness of inerter NES. Based on the above study and results, it proves valid to conclude that the inerter NES system allows practical application of vibration mitigation for marine structures.

Tension Leg Rectangular Fish Cage Motion Analysis in Regular and Random Waves

This paper uses an analytical method to examine the motion of a Tension Leg Fish Cage (TLFC) in regular and random waves. TLFC is a conceptual design of a fish cage based on the Tension Leg Platform (TLP) working principle that is usually used in deep water offshore oil and gas exploration. The idea of providing a safe environment to combine ecotourism and fish farming in a single platform led us to perform an analytical calculation to assess the possibility of using the TLP concept in fish farming. A preliminary conceptual design of TLFC using an HDPE floater with steel cable tendon is presented. The analytical calculation of the response amplitude operator for surge and heave motion is presented using linear airy wave theory with head seas encountering angle. This paper also presents the calculation of TLFC surge and heave motion under random wave loads. The random wave spectra used in this paper are JONSWAP and ISSC spectra. The result shows that the surge and heave motion response of TLFC is relatively small and, therefore, can be analyzed further with more detailed consideration. It is admitted that HDPE is a brittle material that cannot sustain any long period of constant tension. Hence the optimum tendon-floater connection for the structure is subject to further research.

Nonlinear dynamic response of sea-crossing bridges to 3D correlated wind and wave loads

Long span sea-crossing bridges are often slender and sensitive to wind and wave loads. Nonlinear dynamic response analysis of the bridges under three-dimensional (3D) correlated wind and wave loads is performed in this study in consideration of both geometric and aerodynamic nonlinearities. An optimized C-vine copula is first used to construct a 3D joint probability distribution and environmental contour of mean wind speed, significant wave height and peak wave period. Multi-point fluctuating wind loads with Davenport coherence function and random wave loads with pile group effect are then determined using wind and wave spectra respectively. The nonlinear wind-wave-bridge system considering geometric and aerodynamic nonlinearities is solved by the Newmark-β method with the 3D correlated wind and wave parameters as an input. The proposed approach is finally applied to a real sea-crossing cable-stayed bridge with the measured wind and wave data. The results show that the nonlinear response of the bridge is higher than its linear response with the same input. The bridge response is significantly reduced if the 3D correlated wind and wave loads other than conventional uncorrelated wind and wave loads are considered.

Structural Reliability Analysis for the Construction Design of the High-Speed Ship with CFRP Material

A high-speed ship mostly experiences the excessive motions in seaway that influence wave loads act to ship’s hull extremely. For this reason, the structure of a high-speed ship must be designed more strength than a low-speed vessel. In this paper, the construction design of the high-speed ship with material of CFRP are evaluated consider to the vertical bending moment under various wave excitation conditions. The eight design variations of the midship section are proposed to be evaluated against the uncertainty load stress due to the vertical motions of ship in random wave. The diffraction theory is adopted to solve the random wave loads due to various wave condition of heading angles, heights, and periods in which the maximum vertical bending moments of the rigid ship are obtained. Structural reliability analysis is applied for assessing structural safety and reliability of the ship’s structure. The structural strength of the construction design which are required for the reliability analysis have been developed based on permissible stress of BKI regulations. Safety levels associated with each mode of failure of all construction designs are determined and compared. Finally, the construction design is selected with the safety index 1.07.

Wave vibration control of jacket platform by tuned liquid dampers

The studies on the applications of tuned mass and liquid column dampers for wave vibration control of offshore structures are notable. Though, the same is not the case for tuned liquid dampers (TLD). However, TLDs are a natural candidate for vibration control of flexible structure by utilizing the sloshing motion of fluid. The present study explores the effectiveness of TLD to mitigate the wave induced vibration effect of offshore jacket platform. In doing so, the jacket platform is modelled considering soil pile interaction effect and the TLD is represented by a spring mass system with due consideration to sloshing energy of water. The performance of TLD to control the wave induced vibration is studied for regular wave load, obtained by Stokes' fifth order theory and also for random wave load, generated by using the Pierson–Moskowitz wave spectrum. The dynamic response analyses are carried out without and with TLD for varying mass ratio, depth ratio and position of placement to study the effect of different parameters on the performance of TLD system. The results of numerical study in general show that TLD is potential for wave vibration mitigation of offshore jacket platform.

A dual response surface-based efficient fragility analysis approach of offshore structures under random wave load

This paper presents an efficient fragility analysis approach for offshore structures subjected to random wave load considering parameter uncertainty. Fragility analysis of structures under random dynamic load is generally accomplished by the direct Monte Carlo simulation (MCS), which requires extensive computational time. Hence, in the present study, a new cumulative distribution function matching-based fragility analysis approach is proposed in the framework of dual response surface method to reduce this computational burden. The proposed approach does not require MCS during failure probability computations once the two response surfaces of mean and standard deviation of response are obtained. Thereby, a substantial amount of computational time is saved. The proposed approach is generic in nature and can be applied to any offshore structure, with different probability distributions of system parameters and higher uncertainty levels, as well. The record-to-record variation of random wave force time-histories (that occurs even for the same set up of hazard parameters) can be easily considered by the proposed approach. The accuracy of the proposed approach is maintained by applying the moving least-squares method, in place of the conventional least-squares method, which is often reported to be a source of error. Two illustrative examples (one simple benchmark problem and another practical steel offshore platform structure) are presented to demonstrate the efficiency of the proposed fragility analysis approach. The results indicate that the present moving least-squares method yields more accurate solutions than the conventional least-squares method. Also, the computational efficiency by the proposed approach over the usual MCS-based approach can be clearly envisaged from the numerical studies.

An Efficient Monte-Carlo Simulation for the Dynamic Reliability Analysis of Jacket Platforms Subjected to Random Wave Loads

The growing demand for the application of jacket platforms in deep water requires more attention on the assessment of structural reliability. This paper is devoted to the dynamic reliability analysis of jacket platforms subjected to random wave loads with the Monte-Carlo simulation (MCS), in which a sample size of the order of magnitude of 104 to 105 for repeated time–history analyses is required for small failure probability problems, and a duration time up to three hours needs to be considered in the time–history analyses for a specific sea condition. To tackle the difficulty involved in the MCS, the explicit time-domain method (ETDM) is used for the required time–history analyses of jacket platforms, in which truncated explicit expressions of critical responses with regards to the contributing loading terms are first established and then used for numerous repeated sample analyses. The use of ETDM greatly enhances the computational efficiency of MCS, making it feasible for the dynamic reliability analysis of jacket platforms under random wave loads. A jacket platform with 11,688 degrees of freedom was analyzed for the evaluation of dynamic reliability under a given sea condition, indicating the accuracy and efficiency of the present approach and its feasibility to practical structures.

PORO-FSSI-FOAM model for seafloor liquefaction around a pipeline under combined random wave and current loading

In this study, unlike most previous investigations have limited to the regular wave conditions or combined wave and current conditions, a numerical model for seabed response around a pipeline in a trenched layer due to random waves is established. Three different wave spectra including the JONSWAP spectrum, Bretchneider–Mitsuyasu spectrum and Pierson–Moscowitz spectrum are considered in the present model for the simulation of random waves. Numerical examples indicate that the irregular wave-induced pore-water pressure can randomly amplify the upward gradient of the pore-water pressure in the porous seabed, making the backfill sand layer more likely to be liquefied at a deeper depth. It is observed that the upper width of the trench layer becomes larger once the seabed liquefaction occurs, which can effectively prevent the seabed liquefied surface from penetrating into the bottom of the pipeline by increasing the backfill thickness to twice of the pipe diameter. The superimposition of the irregular waves on the following current has more significant effect on the maximum-development of the seabed liquefaction depth, which is particularly obvious when the sand-bed is in the random wave system by using the JONSWAP spectrum.

Time-Domain Structure Analysis of a Typical Semisubmersible Drilling Rig

Ye, Q.; Jin, W.-L., and Bai, Y., 2020. Time-domain structure analysis of a typical semisubmersible drilling rig. In: Liu, X. and Zhao, L. (eds.), Today's Modern Coastal Society: Technical and Sociological Aspects of Coastal Research. Journal of Coastal Research, Special Issue No. 111, pp. 118–123. Coconut Creek (Florida), ISSN 0749-0208.This paper evaluates time-domain structure analysis approaches of a semisubmersible drilling rig using a nonlinear finite element method. Hydrodynamic random wave loads are calculated by WVTDUT, which was developed by a research group from the Dalian University of Technology. Time-domain structure analysis of a semisubmersible platform is very time consuming; simplified time-domain analysis approaches are therefore proposed to improve efficiency using equivalent time series. Validity of the approach is tested by a concrete example and simulation results are discussed in detail. The work of this paper can lead to a better understanding of structure behavior of a typical semisubmersible platform under characteristic wave loads. Performing structure analyses in time domain increases the accuracy and reliability of structure performance and the present study may be a benchmark study on time-domain structure analysis of a semisubmersible drilling rig.

Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads

This paper is devoted to the random vibration analysis of jacket platforms under wave loads using the explicit time-domain approach. The Morison equation is first used to obtain the nonlinear random wave loads, which are discretized into random loading vectors at a series of time instants. The Newmark-β integration scheme is then employed to construct the explicit expressions for dynamic responses of jacket platforms in terms of the random vectors at different time instants. On this basis, Monte Carlo simulation can further be conducted at high efficiency, which not only provides the statistical moments of the random responses, but also gives the mean peak values of responses. Compared with the traditional power spectrum method, nonlinear wave loads can be readily taken into consideration in the present approach rather than using the equivalent linearized Morison equation. Compared with the traditional Monte Carlo simulation, the response statistics can be obtained through the direct use of the explicit expressions of dynamic responses rather than repeatedly solving the equation of motion. An engineering example is analyzed to illustrate the accuracy and efficiency of the present approach.

Experimental modelling of a top-tensioned riser for vibration-based damage detection

Damage incidents in subsea risers may lead to catastrophic economic, environmental and human safety consequences. Therefore, early detection of damage is of paramount importance. Vibration-based damage detection methods have been extensively studied in the past for damage detection in a vast variety of structural types, however, their application to risers has hardly been explored to date. In the limited existing literature of vibration-based damage detection in risers, the proposed methods have mostly been verified by numerical studies or by experimental models which lacked realistic representations of ambient excitations and similarity of the model to a full-scale structure. This paper presents, for the first time, experimental modelling of a top-tensioned riser at a laboratory scale for vibration-based damage detection studies, in which the similarity of the experimental model to a full-scale structure, the multifaceted effects of damage and the dynamic ambience are explicitly addressed. An experimental riser model is built and subjected to random wave loading in a flume according to the JONSWAP spectrum to simulate the ambient excitations realistically. The experimental model consists of a tensioned rod made of acetal plastic and several small lumped steel masses attached to the rod such that they reduce the natural frequencies of the model to the range of wave frequencies that can be generated in the flume. An analysis is conducted to account for the similarity between the experimental model and a full-scale structure with the priority given to the modal characteristics of the structures. Corrosion is considered as the cause of damage and it is simulated non-destructively on the experimental model by partial removal of the attached lumped mass at the assumed damage location and reduction of applied tension load. The amount of removed mass and reduced tension load are calculated such that the simulated damage on the experimental model is equivalent to an actual cross-sectional area loss due to corrosion damage in the full-scale structure. An application of a vibration-based damage detection method is demonstrated using experimental data obtained for several different damage scenarios. An auto-regressive (AR) model is fitted to the acceleration response of the riser and coefficients of the AR model are used as the damage sensitive features (DSFs). Damage detection is achieved by conducting outlier analysis on the DSFs.

An Analytical Procedure to Predict Transverse Vibration Response of Jack-Up Riser under the Random Wave Load

Marine riser is a key equipment in offshore drilling operation, and failure of the riser can lead to drilling moratorium; in severe cases, it may cause oil and gas leaks. In this paper, the time-dependent boundary conditions of the riser and the randomness of wave load are considered to improve the calculation efficiency and accuracy of the dynamic response of the jack-up riser. Based on the Euler–Bernoulli beam theory, an analytical method to determine the response of the jack-up riser subjected to the random wave load was established by the Mindlin–Goodman method in the frequency domain, and an experiment was carried out to verify it. The research shows that transverse dynamic response is the main component of the transverse response of the riser, and the method proposed is feasible to calculate the transverse response of the riser.

Coherence and cross-spectral density matrix analysis of random wind and wave in deep water

From the collected records of simultaneously measured wind and wave data during FETCH experiment, the sample and mean power spectral density and coherence functions of the fluctuating wind velocity and wave height processes are calculated. Based on the calculated mean coherence function and interaction mechanism of wind and wave, a parametric model and simple parameter estimate method are proposed to fit the coherence of the fluctuating wind velocity and wave height processes. The model is an explicit function of the main characteristic parameters of wind and wave, hence it can be used to model other empirical coherences of the random wind and wave processes in deep water. Combining the theoretical spectrum models fitting the calculated mean power spectral density functions of the fluctuating wind velocity and wave height processes and proposed coherence model for modeling the processes, the theoretical cross-spectrum density matrix of the fluctuating wind velocity and wave height processes is established. Samples of the fluctuating wind velocity and wave height processes are simulated to illustrate the influence of coherence on the random wind and wave loads.

Frequency Domain Response of Jacket Platforms under Random Wave Loads

This article presents a procedure that simplifies an offshore jacket platform as a non-uniform cantilever beam subjected to an axial force. A Ritz method combined with a pseudo-excitation method is then used to analyze the responses of the jacket platform under random wave loads with the associated power spectral densities, variances and higher spectral moments. The theoretical basis and pertinent governing equations are derived. The proposed procedure not only eases the process of determining the pseudo wave loads, but also requires only the rudimentary structural details that are typically available at the preliminary design stage. Additionally, the merit of the proposed procedure is that the process does not require one to compute the normal modes, which saves time and is particularly convenient for the dynamic-response analysis of a complex structure (such as an offshore platform). An illustrative example based on a three-deck jacket platform is presented to demonstrate the procedure used to obtain the power spectral densities, variances and second spectral moments of jacket-top displacement and the bending moment of the jacket at the mud line. The results obtained are compared with those obtained using a Finite Element Mothed (FEM) model. Based on the findings of the study and good agreement shown in the comparison of results, it is concluded that the proposed method is effective, simple and convenient, and can be a useful tool for the preliminary design analysis of offshore platforms.

Dynamic analysis of an offshore wind turbine under random wind and wave excitation with soil-structure interaction and blade tower coupling

This study investigates the dynamic response of a 5 MW offshore wind turbine with monopile foundation subjected to wind and wave actions. The work includes dynamic interaction between the monopile and the underlying soil subjected to realistic offshore random wind and wave loading modeled using Von karman spectrum and Pierson Moskowitz spectrum respectively. The study also incorporates the effect of blade tower coupling in the analysis. The offshore wind turbine tower is modeled herein as a multi-degree of freedom system (MDOF) and it comprises of a rotor blade system, a nacelle, and a flexible tower. The mass of the rotor, blade, and nacelle are lumped at the top of the tower for simplicity. Separately, the effect of the rotation of blades has also been incorporated in the work. The rotational effect of the blades is taken into account considering shape filters using von Karman spectrum. The soil-structure interaction effect at the foundation level is modeled using equivalent spring-dashpot model for embedded foundations. The results are studied in time as well as frequency domain for both wind and wave loading. It has been observed that soil structure interaction effect greatly alters the response of the offshore wind turbine structure not only in the parked condition but also in operational conditions when blade tower coupling is also included. The effect of blade tower coupling and SSI on the response of the structure are observed more coherently in the case of wave induced loading.

Efficient time simulation method for predicting the 100-year extreme responses of an offshore platform

ABSTRACTThe most reliable technique for predicting the statistical properties of the response of an offshore structure to random wave loading is the conventional time simulation method (CTS). However, this study is concerned to reduce the computational demand of this method due to long simulation needed for stable results. To this end, a more efficient version of the time simulation technique (ETS) has been introduced which divides the simulated response extreme values into several groups based on the magnitude of the extreme values of their associated surface elevation or linear response records. The method has proved to be very efficient for both low and high-intensity sea states. In this study, the 100-year extreme responses from ETS and CTS methods have been compared to examine the accuracy of the ETS technique. Overall, the ETS technique was found to be many times more efficient than the conventional method.