Vortex-induced Vibration Prediction Research Articles

Machine learning models for predicting VIV amplitude of streamlined steel box girders

The vortex-induced vibrations (VIVs) can cause severe consequences for long-span bridges, including structural fatigue, human-body comfort and vehicle safety, and become significant issues in terms of the wind-resistance. Currently, estimations of VIV amplitudes are typically based on wind tunnel tests, field monitoring, computational fluid dynamics and theoretical models. In this paper, a machine learning (ML) approach is developed for rapidly estimating the VIV amplitude of a streamlined steel box girder during preliminary structural design. The VIV amplitude forecasting models are constructed using four well-established and widely used ML algorithms, e.g., support vector machine (SVM), random forest (RF), gradient boosting decision tree (GBDT), and artificial neural network (ANN). These four models take geometric and dynamic features as inputs, and output the VIV amplitude. The hyper-parameters are optimized to attain acceptable accuracy. To address the low interpretability of complex ML models, this paper introduces the Shapley additive explanations (SHAP) method to explain the VIV prediction pattern. The results indicate that the constructed ML models with optimal hyper-parameters show excellent performance for predicting the VIV amplitude in a validated and accurate manner. The SHAP explanation supports these results and offers valuable additional insights.

Simulation and prediction of vortex-induced vibration of a long suspension bridge using SHM-based digital twin technology

Although wind tunnel tests have already become a design basis for improving the stability of long-span bridges under the action of wind loads, vortex-induced vibration (VIV) events of in-service long-span bridges have still been frequently reported in recent years. The reasons behind this could be attributed to the limitations and uncertainties involved in wind tunnel tests as well as the changes and degradations of in-service bridges. In consideration that most long-span bridges have now been equipped with long-term structural health monitoring (SHM) systems and that digital twins could provide a new solution for simulating and predicting the reality, this study aims at developing a digital twin for VIV of a long suspension bridge to simulate and predict its VIV. The design document-based finite element (FE) model of the bridge is first updated using the measured dynamic characteristics. The numerical model for VIV of the bridge is then established using the vortex-induced force (VIF) model established based on wind tunnel test results. The numerical model together with the VIF model are finally updated against the measured vortex-induced responses (VIR) to produce a digital twin for VIV of the bridge. The relationships between the parameters in the VIF model and wind characteristics are further investigated to enable the digital twin to predict future VIV events. The accuracy of the digital twin for predicting the future VIV and the influence of the VIF parameters obtained from wind tunnel tests on the prediction accuracy both are confirmed through comparisons between the predicted and measured results.

Establishment and application of a digital twin for vortex-induced vibration of a bridge deck section

ABSTRACT Wind tunnel tests or computational fluid dynamics (CFD) simulations of the aeroelastic model of a bridge deck section are currently used to make sure that significant vortex-induced vibration (VIV) of a long-span bridge will not occur after the bridge is put into operation. However, significant VIV still occurred in several long-span bridges in operation, indicating that the currently used wind tunnel tests and CFD simulations have some drawbacks or uncertainties. This study aims at establishing a digital twin by interacting CFD simulation with wind tunnel test for accurately and efficiently predicting the VIV response of a bridge deck. The measurement information of VIV of the deck section is collected from the wind tunnel test and fused with the CFD simulation. The optimisation for reducing uncertainties existing in wind tunnel test and CFD simulation is then carried out to make the CFD simulation as a digital twin. The digital twin is finally used to investigate the blockage effect of wind tunnel test and give an accurate and efficient prediction of VIV of the bridge deck. The flat closed-box steel deck section used in the Xiangshan Harbor cable-stayed bridge is selected as a case study. The results from the case study show that the digital twin can be established and used for an accurate and efficient prediction of VIV of the bridge deck section.

Applying Bayesian optimization to predict parameters in a time-domain model for cross-flow vortex-induced vibrations

As the demand for harvesting offshore energy increases worldwide, the need for slender structures, such as marine risers and power cables, will increase. The dominating loads for deep water applications will primarily be caused by current-structure interactions, where vortex-induced vibrations (VIV) are known to be a challenging response type to handle correctly during design. Semi-empirical time-domain models are promising for VIV prediction, but uncertainties related to simplifications in the hydrodynamic load model and empirical parameters lead to over-conservative designs, where the parameters are estimated from model tests within a relatively low Reynolds number range. The aim of this paper is to present an efficient tool to estimate empirical hydrodynamic parameters directly from test data. To illustrate the method, the hydrodynamic parameters were estimated from pure cross-flow VIV model tests in a steady current with Reynolds numbers in the range of 40,000-120,000. The parameters were updated sequentially by using a Bayesian optimization framework, with the aim of minimizing an objective function that incorporates the response errors between time-domain VIV simulations and model test data. It is shown that three empirical parameters can be obtained simultaneously, resulting in small response errors but the optimal parameters were overly sensitive to variations in the flow velocity. The optimal parameters were used to reconstruct the drag amplification related to cross-flow VIV and in forced motion simulations to illustrate how the parameters in the load model would map into the traditional formulation in terms of the added mass and excitation coefficient.

Numerical simulations of 2-DOF vortex-induced vibration of a circular cylinder in two and three dimensions: A comparison study

Finding a reliable and efficient numerical method is of great importance for the safety design of a offshore riser whose model can be simplified as vortex-induced vibration (VIV) of an elastically-mounted circular cylinder. In the current study, two-degree-of-freedom (2-DOF) VIV responses of a circular cylinder with a small mass ratio m*=2.6 and small mass damping parameter (m*+1)ζ=0.013 is numerically investigated by two- and three-dimensional method. The simulations by using the URANS (Unsteady Reynolds Averaged Navier-Stokes) in combination with the SST (Shear Stress Transport) k−ω turbulence model are performed at subcritical Reynolds numbers (Re ranges from 1×103 to 1.5×104). From the overall results, both the 2D and 3D simulations can obtain relatively accurate statistical results including VIV response amplitudes and frequency values. The main differences between the 2D and 3D simulations lie on the three-dimensional effects that exist in the supper upper branch and the flow transition condition. However, the 2D numerical simulations can save hundreds of times of the computational resources compared with a 3D simulation, hence is more suitable for engineering VIV prediction under such conditions. The comparison of simulation and experimental results in this study provides research support for the selection of appropriate simulation methods (2D or 3D) for 2-DOF VIV of an offshore riser in research and engineering.

Aspects of vortex-induced in-line vibration at low Reynolds numbers: Simulation and prediction by a reduced-order model

The purpose of this study is to develop a reduced-order model (ROM) for the prediction of vortex-induced vibration of an elastically mounted circular cylinder constrained to oscillate purely in-line with a uniform free stream. The fluid force in the streamwise direction was modeled by an extended version of Morison’s equation that comprises an inviscid inertial component opposing the cylinder acceleration, a viscous drag component proportional to the square of the relative velocity of the free stream and the oscillating cylinder, and a wake drag component representing the excitation from vortex shedding. A van der Pol equation was employed to model the oscillating wake drag component. The coupling between the oscillating wake and the oscillating cylinder was accomplished by forcing the wake oscillator with a term proportional to either the acceleration or the velocity of the cylinder. The ROM parameters were tuned against data from numerical solutions of the full system of non-linear equations governing the fluid and cylinder motions for a cylinder with a mass ratio of 10 and a Reynolds number of 180. The results showed that acceleration forcing can predict well the amplitude response when the ROM is properly tuned, whereas velocity forcing leads to underestimation of the amplitude response. In addition, acceleration forcing can predict satisfactorily the magnitude of the total streamwise force and of the wake drag. However, the trend in the frequency response was not well predicted by acceleration forcing, which was predicted more satisfactorily by velocity forcing. Both acceleration and velocity forcing predicted satisfactorily the phase lag between the wake drag and the cylinder displacement. Predictions with the calibrated ROM at different mass ratios captured well the amplitude response as a function of the reduced velocity, including the narrowing of the range where relatively high amplitudes occur, as in the full numerical simulations. Linear stability analysis based on the ROM equations indicated that the interaction between the fluid and the vibrating cylinder has the characteristics of nonlinear resonance, where the selection of the common frequency of the system is sensitive to nonlinearities, which cannot be faithfully captured by the van der Pol wake oscillator.

Modelling of vortex-induced force and prediction of vortex-induced vibration of a bridge deck using method of multiple scales

With the increase of span length, long-span bridges become more flexible and susceptible to vortex-induced vibrations (VIV). Several models for vortex-induced force (VIF) and various methods for predicting VIV have been developed accordingly but without consensus. This paper uses the method of multiple scales, from a different angle of view, to analyze the general polynomial model for VIF and present a concise polynomial model for VIF and a simple method for predicting VIV of a bridge deck. The aeroelastic vibration of a deck section is simulated by the computational fluid dynamics (CFD) and the results are used to verify the concise polynomial model of VIF. The forced vibration of a deck section is also simulated by CFD to yield the simple method for predicting VIV together with the frequency response equation and the critical equation of VIV derived by the method of multiple scales. The results show that the even and cross terms of aerodynamic damping and stiffness in the general polynomial VIF model are small compared with the odd terms and can be thus omitted. The lock-in region and the amplitude of VIV of the deck section can be accurately predicted by the proposed simple method.

Coupling effect of time-varying axial tension and combined unsteady flow on vortex-induced vibration of flexible risers

The surge and heave motions of the floating platform have a non-negligible effect on vortex-induced vibration (VIV) of marine risers, which generates time-varying axial tension of risers, i.e., parametric excitation, and unsteady flow and complicates the prediction of VIV. A semi-empirical model is improved to simulate the VIV of flexible risers with parametric excitation under combined unsteady flow. Both the flow velocity and the stiffness matrix are updated with time. Fifty-five cases are simulated to investigate the separate and coupling effects of parametric excitation and combined unsteady flow on VIV. The phenomena such as sum and difference frequencies, Mathieu-type resonance, intermittent vibration and frequency fluctuation are observed. The effects of parameters such as excitation amplitude dT, excitation frequency fp, combined ratio r and oscillation period P on VIV are discussed in detail. Some interesting conclusions are drawn: VIV may be significantly suppressed when transition-low-frequency parametric excitation and short-period combined unsteady flow act together. Larger r makes the effect of combined unsteady flow more significant. VIV is mainly dominated by the parametric excitation when fp is twice the natural frequency of the riser corresponding to the dominant mode.

Machine learning-based deep data mining and prediction of vortex-induced vibration of circular cylinders

By means of numerical, experimental and field measurements, an unprecedented amount of data regarding vortex-induced vibration (VIV) of circular cylinders has become accessible recently. In this study, machine learning (ML) models are developed to predict the transverse VIV amplitude Y* and amplitude-velocity relations. First of all, an ML database is established by aggregating reliable, published data. Then, three ML techniques are developed, including support vector regression with particle swarm optimization (PSO + SVR), extreme learning machine (ELM), and improved ELM combined with preprocessed least squares QR decomposition (PLSQR + ELM). Three crucial parameters, mass damping ratio α, Reynolds number (Re) and mass ratio m*, are extracted by the partial least square (PLS) method to characterize VIV. The results show that the prediction accuracy of all algorithms is acceptable in the absence of noise, with the ELM-type being the highest. When noise is taken into account, PLSQR + ELM is the most efficient and robust. A new linear relation between the VIV amplitude Y* and log10(α/Re) is proposed, which is demonstrated to be better than published ones.

Vortex-induced vibration prediction of an inclined flexible cylinder based on machine learning methods

Vortex-induced vibration (VIV) is a main cause of fatigue damage to slender flexible structures in offshore engineering, e.g., marine risers, mooring lines, submarine cables and pipelines. In this paper, attempts have been made to predict the VIV response of an inclined flexible cylinder commonly encountered in practice using different machine learning methods. Three different machine learning algorithms (i.e., BP neural network, support vector machine and Gaussian process regression) are employed to establish the prediction models. The data in our previous experimental tests (Xu et al., 2018) are adopted to establish the data set of the present research. The numbers of data samples for constructing the displacement and frequency prediction models in each direction are 10,500 and 500, respectively. The inclination angle, incoming flow velocity, axial tension and the position along the cylinder span are used as the input variables and the output variables are the root mean square values of the in-line and cross-flow displacements and the dominant oscillation frequencies. Compared to the previous studies, the effect of the axial tension and the large inclination cases are considered to establish more comprehensive prediction models. The results show that all the three methods can predict the displacement and frequency responses in the cross-flow and in-line directions with acceptable accuracy. After a detailed comparative analysis of the three machine learning methods, it is found that the BP neural network models tend to result in a certain degree of overfitting and some response characteristics predicted by the GPR models are not consistent with the conclusions from our previous experimental studies. Within the parameter space of the present research, the support vector machine is considered to be the most suitable method for predicting the VIV of the inclined flexible cylinder.

Axial-transverse coupled vortex-induced vibration characteristics of composite riser under gas-liquid two-phase internal flow

In this paper, the dynamic behavior of axial (AX) and transverse coupled vortex-induced vibration (VIV) of composite riser under gas-liquid two-phase internal flow is studied. Firstly, based on Hamilton's principle, considering the structural characteristics of composite materials, gas-liquid two-phase internal flow, AX and transverse nonlinear coupling vibration and nonlinear external excitation, a more realistic VIV prediction model of composite riser is proposed. Compared with the existing experimental results, the validity of the model in this paper is verified, and it is found that the VIV prediction of the riser is more accurate when considering the AX and transverse coupling effects. Then, the effects of current velocity, liquid phase velocity, gas volume fraction and fiber orientation angle on the coupled VIV characteristics of gas-liquid mixed transport composite riser are studied. The results show that with the increase of current velocity, gas volume fraction and liquid phase velocity, the in-line (IL) vibration of the riser changes modally before the cross-flow (CF), but the fiber orientation angle has the opposite effect on this phenomenon. At the same time, when the two directions are in two different vibration modes, the vibration frequency in IL direction is obviously larger than that in CF direction. In addition, the riser AX vibration is almost unaffected by the parameters, but its vibration frequency is much larger than the other two directions, and the vibration center has shifted. We also find that the specific liquid phase velocity value will cause the chaotic vibration of the riser in the CF and IL directions, and the vibration displacements of the composite riser are almost equal in both directions.

Flow Past of a Drilling Riser System with Auxiliary Lines in Laminar Flow

Vortex-Induced Vibration (VIV) has emerged as a crucial problem that may arise during a drilling operation, which could result in riser failure. Engineers focus on drilling riser's flow characteristics and controls with the intention of improving the drilling environment. Auxiliary lines or control rods are usually placed around the main drilling riser to suppress the VIV. However, the issue related to the flow past drilling riser system with auxiliaries has yet to be resolved. The flow characteristics around a riser system with auxiliaries were analysed in this research. The simulations were conducted using Computational Fluid Dynamics (CFD) software, Altair AcuSolve. This work focuses on the influence of various gap ratios (G/D) and diameter ratios (d/D) on the vortex interaction. A main cylinder with six auxiliary lines was modelled with G/D of 0 to 2.0 and d/D of 0.10 to 0.60 to simulate the riser system. The simulations were carried out at Reynold Number of 200 in the laminar flow regime. The results revealed that the hydrodynamic forces decreased when d/D and G/D increased. The vortex shedding was significantly reduced for auxiliary lines with G/D between 0.3 and 1.4. The numerical simulation results indicated that the vortex interaction in the wake region was, and the hydrodynamic forces were reduced due to the auxiliary lines configurations. The findings of this study are intended to contribute a new CFD simulation result for a better prediction of VIV on a drilling riser with auxiliary lines.

Wave Effects on Vortex-Induced Vibrations of a Top-Tensioned Riser

Abstract Offshore drilling risers and many production risers are top-tensioned risers (TTRs), connecting the vessel and seabed via joints. External loads such as currents, waves, and vessel motions introduce cyclic loads and motions on riser sections and associated components, such as universal joint, flex joints, and well head at the bottom, which may shorten the service life due to accumulated fatigue damage. Dynamic responses under combined currents and waves are more complicated than vortex-induced vibrations (VIVs) caused by pure currents, and it is not fully understood. Several model test campaigns on TTR have been carried out at SINTEF Ocean (former MARINTEK) during the past decades. Currents, waves, and vessel motions were modeled, and the riser model responses were measured. In this study, selected cases from such model tests are analyzed, and used to validate a semi-empirical time domain VIV prediction tool—VIVANA-TD. A better understanding of the dynamic responses of TTR under combined currents and waves has been achieved. By comparing the results from numerical simulation using VIVANA-TD and model test measurements, validity and limitation of the time domain tool have been investigated. Important features that need to be considered are discussed. The experience gained from the present study establishes a good basis for VIV and wave load prediction of full-scale TTRs under combined currents and waves where the uncertainty of combined wave and VIV prediction is further reduced.

Test Study on Vortex-Induced Vibration of Deep-Sea Riser under Bidirectional Shear Flow

A model test was carried out to reveal the vortex-induced vibration characteristics of a deep-sea riser under bidirectional shear flow. Bandpass filtering and modal analysis were used to process the test strain data, and the amplitude and frequency response characteristics of the vortex-induced vibration of the riser in the bidirectional shear flow field were obtained. The results of the test data analysis show that the dominant frequency of the vortex-induced vibration of the riser model under bidirectional shear flow is locked in the natural frequency of the riser and does not increase with the increase in flow velocity, that the average resistance coefficient of the riser model has little change under different flow velocities because of the distribution characteristics of the “bidirectional shear” flow field, that there is an extreme value of the shear force in the middle of the riser model, and that the Strouhal number in the transverse direction of the vortex-induced vibration under bidirectional shear flow is less than the recommended value of the current vortex-induced vibration prediction software. The obtained results provide basic data for the prediction of vortex-induced vibration and research into the fatigue analysis method of a riser under an internal wave flow field.

Data-driven prediction and study of vortex induced vibrations by leveraging hydrodynamic coefficient databases learned from sparse sensors

Semi-empirical models are currently the state-of-the-art industry tool for flexible cylinder vortex induced vibrations (VIV) fatigue prediction. Accurate prediction of the structural response relies entirely on the accuracy of the acquired hydrodynamic coefficient database. The construction of systematic hydrodynamic coefficient databases from rigid cylinder forced vibration experiments can be time-consuming for simple cases and intractable for multi-parametric cases. An alternative approach has been implemented in this work to improve the flexible cylinder VIV prediction by machine-learning optimal parametric hydrodynamic databases using physical experimental measurements. The methodology is applied to a straight riser in uniform flow and extended to non-straight riser configurations and non-uniform incoming flow profiles. Moreover, database inference is extended to using direct sparse sensor measurements along the structure. Specifically, a 19-dimensional parametric hydrodynamic coefficient database is obtained for: (i) straight riser in uniform flow (using sparse strain measurements), (ii) straight riser in sheared flow, and (iii) catenary riser in uniform flow with a 60 deg incidence angle between the catenary plane and the incoming flow stream. The predicted amplitude and frequency responses, using the extracted databases, are compared with observed experimental results.

Numerical prediction of vortex-induced vibrations of a long flexible riser with an axially varying tension based on a wake oscillator model

A numerical study based on the wake oscillator model has been conducted to determine the vortex-induced vibration (VIV) responses of a flexible riser with an axial time-varying tension. Three different types of flows, viz., linear shear, exponential shear, and real stepped flows, have been considered. The coupling equations of a structural oscillator and a wake oscillator have been solved using a standard central finite difference method of the second order. The VIV response characteristics including the structural displacement, structural frequency, displacement envelope, and displacement evolution for three different flow profiles have been systematically compared. Subsequently, for each flow profile, the effect of the different tension models on the VIV characteristics has been investigated. The numerical results indicated that, both the VIV displacement and VIV frequency in real stepped flow had diverse characteristics from those in linear shear flow. Compared with the corresponding VIV characteristics in real stepped flow, the VIV displacement in exponential shear flow was similar, however, the VIV frequency in exponential shear flow was disparate. The VIV displacement with the constant tension model had larger values than that with the real tension model.

Machine-learning-based prediction of vortex-induced vibration in long-span bridges using limited information

Long-span bridges are susceptible to wind-induced vibration due to their high flexibility, low-frequency dominance, and light damping capacity. Vortex-induced vibrations (VIVs), which usually occur under in-service conditions, can result in discomfort to users and detrimental effects on the fatigue capacity of structural elements; therefore, accurate VIV assessments are essential in ensuring the vibrational serviceability of bridges. Despite the research efforts of data-driven VIV prediction, the robustness and general applicability of the proposed methods remains challenging, in that each method requires different conditions for the datasets in order to develop machine-learning (ML) models. Furthermore, collecting sufficient VIV datasets (anomaly state) from various operational conditions is impractical, time-consuming, and even impossible in some situations compared with non-VIV datasets (normal state). This imbalance in the dataset could degrade the model performance. To address this issue, this paper focuses on developing a general framework for introducing ML algorithms to predict VIVs with a limited amount of information. To properly replicate the practical cases, two different scenarios are assumed along with the amount of VIV data: (1) no VIV data are available, or (2) only a small number of VIV data can be obtained. A variety of ML-assisted methods are introduced for each scenario to predict VIVs in order to demonstrate the versatility of the proposed framework. The effectiveness and applicability of the proposed framework are demonstrated using actual monitoring data. Different methods are prepared to provide further insight into the ML algorithms used for VIV prediction. The proposed framework in this paper is expected to advance our knowledge and understanding of the application of ML algorithms to bridge systems, which are essential in enhancing resilience against wind hazards.

Dual-frequency vortex-induced vibrations of long flexible stepped cylinders

Flexible structures within a non-uniform inflow may undergo complex vortex-induced vibrations (VIV) containing multiple frequencies and vibration modes. Therefore, the critical question arises on whether and how a flexible cylinder's structural response and fluid forces undergoing multi-frequency vibrations resemble or differ from mono-frequency vibrations. Therefore, we experimentally studied the problem of dual-frequency VIV of a stepped flexible cylinder, viz., a large-aspect ratio flexible cylinder consisting of two segments with different diameters and rigid cylinder forced vibration experiments. The results show that the maximum in-line (IL) and cross-flow (CF) displacements and the frequency ratio of the stepped cylinder separated by individual frequency resemble those of a uniform cylinder vibrating in the uniform flow at a single frequency. In addition, it is found that forced vibration results from rigid cylinders undergoing multi-frequency IL and CF motion can improve the prediction of the multi-frequency flexible cylinder VIV, provided the amplitudes and phases, as well as the true reduced velocity Vr for each of the dual frequencies match, especially when Vr∈[4,8].

Internal flow effect on the cross-flow vortex-induced vibration of marine risers with different support methods

The present work investigates the effect of internal flow on the vortex-induced vibration (VIV) characteristics of a marine riser under different boundary conditions. A numerical model of the riser structure is established by considering the complex flow fields. The developed model is solved by the finite element theory and Newmark method, and it is verified by the experimental data. The effects of internal flow velocity and density on the vortex-induced dynamic responses with different support methods are studied. The results demonstrate that among different support methods, internal flow effect (IFE) has the greatest influence on the vortex-induced response of the riser with hinged-cantilevered support. In the case of hinged-cantilevered support method, the increment of the internal flow velocity and internal flow density has a negative influence on the vortex-induced vibration of the riser. In the case of fixed at both ends support method, the vibration amplitude and mode of riser decrease with the increment of flow density in riser. For the hinged-hinged support condition, the increment of the internal flow velocity slightly increases the amplitude of the riser and the vibration amplitude of riser decreases with the increase of density. This research may provide an efficient method for the VIV prediction, optimization design and operation control of the marine risers in practical applications.

Heave Motion Induced Vortex-Induced Vibrations of a Full-Scale Steel Lazy Wave Riser

Abstract Deepwater steel lazy wave risers (SLWR) subject to vessel motion will be exposed to time-varying oscillatory flow, vortices could be generated and the cyclic vortex-shedding force causes the structure vibrate, such fluid–structure interaction is called vortex-induced vibrations (VIV). To investigate VIV on a riser with nonlinear structures under vessel motion and oscillatory flows, time-domain approaches are needed. In this study, a time-domain approach is used to simulate a full-scale SLWR. Two cases with simplified riser top motions are simulated numerically. By using default input parameters to the time-domain approach, the key oscillatory flow induced VIV response characteristics such as response frequency, curvature, and displacements are examined and discussed. More accurate VIV prediction could be achieved by using realistic hydrodynamic inputs into the time domain model.