Multiple tuned mass damper based vibration mitigation of offshore wind turbine considering soil–structure interaction

The dynamics of jacket supported offshore wind turbine (OWT) in earthquake environment is one of the progressing focuses in the renewable energy field. Soil–structure interaction (SSI) is a fundamental principle to analyze stability and safety of the structure. This study focuses on the performance of the multiple tuned mass damper (MTMD) in minimizing the dynamic responses of the structures objected to seismic loads combined with static wind and wave loads. Response surface methodology (RSM) has been applied to design the MTMD parameters. The analyses have been performed under two different boundary conditions: fixed base (without SSI) and flexible base (with SSI). Two vibration modes of the structure have been suppressed by multi-mode vibration control principle in both cases. The effectiveness of the MTMD in reducing the dynamic response of the structure is presented. The dynamic SSI plays an important role in the seismic behavior of the jacket supported OWT, especially resting on the soft soil deposit. Finally, it shows that excluding the SSI effect could be the reason of overestimating the MTMD performance.


Introduction
As many countries aim to raise the production of renewable energy, wind energy has been obtained global popularity by employing offshore wind turbines (OWTs). Some researchers emphasized the study of the OWTs because of their plenty of resources (Jonkman, 2009). OWT structures in hostile environments are generally illuminated by the wind and wave loads (Hu et al., 2016), as well as the most destructive earthquake loads. It is important to study the impact of earthquake loads on the OWT structure to derive effective vibration reduction systems. Many inquisitions have been practiced in order to explore the dynamic response of the OWT to the strong interaction of aerodynamic and hydrodynamic loads (Tang et al., 2015;Zhao et al., 2016). Many researchers concern the behaviors of OWTs under seismic load conditions (Prowell et al., 2009;Valamanesh and Myers, 2014).
OWTs linked with jacket foundation subjected to complex environmental conditions have been established recently at large water depths. The dynamic interaction between the OWT and soil may lead to reduction or increase in response, depending on the characteristics of the soil-structure, the earthquake intensity and the geological media around the foundation (Stejska and Valášek, 1996). Many pioneer investigations on the offshore structure have been done by taking SSI effects into account (Zhao and Maißer, 2006;Abhinav and Shaha, 2015;Korzani and Aghakouchak, 2015).
Cone models to represent the soil, have been developed successfully for practical engineering applications over the last decade (Mohasseb and Abdollahi, 2009). It can be used conveniently for sites with general layering and embedment conditions, adopting all degrees of freedom. Moreover, this model can be employed both in force-based method as response spectrum and time history analyses and in displacement-based method such as push-over analysis. Cone models provide sufficient computational accuracy by considering the infinite soil medium and wave propagation with simple hypotheses. This model assumes underlying soil as homogeneous half space which allows the model to go under sway and rocking motions. This model follows three assumptions to solve the problem of interest, Hook's law using Young's modulus of elasticity, dynamic equilibrium and the basic equation of motion (Simos et al., 2001;Wolf and Deeks, 2004). The results in this investigation are accurate and exhibit a process which unites all engineering assertions for this research.
To reduce the vibration of slender structures, vibration control technologies have been developed rapidly. In order to alleviate the response of structure to different loads, many devices have been proposed (Patil and Jangid, 2005;Ou et al., 2007;Lackner and Rotea, 2011). Passive vibration control might be considered as one of the most suitable and feasible strategies for vibration control in offshore platforms. The effectiveness of tuned mass damper (TMD) defined as the combination of a mass, a spring and a viscous damper has been studied in mitigating the dynamic response of structures over the last few decades. The performance of TMD considering SSI has been explored through the several researchers (Xu and Kwok, 1992;Wu et al., 1999). The SSI effect is difficult to calculate precisely, thus the detuning of TMD would be inevitable. Multiple tuned mass dampers (MTMDs) have been proved to be more efficient than a single TMD in the dynamic response control of structures. The MTMDs with distributed natural frequencies have been proposed by several researchers previously (Han and Li, 2008;Moon, 2010). The efficiency of MTMD has been also evaluated with the consideration of SSI (Wang and Lin, 2005).
Investigations on vibration control have carried out for the monopile wind turbine with/without floating platforms due to wind and wave loads considering SSI effect with TMD (Carswell, 2015) and tuned liquid column damper (TLCD) (Colwell and Basu, 2009;Roderick, 2012). A physical model of floating wind turbine platforms for dynamic response in a wave basin has been done by Jaksic et al. (2015). Watson et al. (2016) also conduct some physical experiments on a wind turbine with SSI using TLCD. MTMD is rarely applied to the jacket supported OWT to reduce the seismic response with SSI. In order to achieve the attribute contributions from the TMDs, different optimization techniques have been introduced to optimize TMD parameters by several ways (Bekdaş and Nigdeli, 2011). Response surface methodology (RSM) applied in the optimization field is one of the best mathematical approaches. The effective use of RSM for structures has been pointed by Mohammed et al. (2012) and Khan et al. (2016). The RSM is one of the new approaches to optimize damping parameters for vibration control of the jacket supported OWT associated with SSI.
The present research reveals the influence of SSI on the jacket supported OWT with the MTMD system to mitigate the seismic responses to static wind and wave loads. TMDs are placed at the locations with the maximum mode shape amplitudes of the structure. Central composite design (CCD) based on the RSM and multi-objective optimization desirability function are proposed. Consequently, the strategy capable of optimizing the parameters of MTMD, which can increase the efficiency of the MTMD system is presented. Different soil types are used by changing the shear wave velocity of the soil to evaluate the SSI effects. The purpose of the study is to examine tower displacements, frequency response function (FRF), root mean square (RMS) of the tower displacement, shear and moment. The investigation has been carried out for uncontrolled and controlled structures with fixed and flexible bases under different ground motions. Finally, it shows that the RSM based design of MTMD for vibration control of structure under earthquakes is more applicable to large shear wave velocity than to less shear wave velocity of the soil model.

Structural model
The governing equation of motion for structure with TMDs at the top and the base of the tower is achieved considering the equilibrium of forces as: where M S , K S and C S are mass, stiffness and damping matrices of the structure of order , in which P and d are the degrees of freedom (DOF) for the structure and MTMD, respectively. , and are unknown relative nodal displacement, velocity, and acceleration vectors, respectively. The earthquake ground acceleration is depicted by and r is the vector of influence coefficients. Stiffness (K d ) and damping C d parameters of the TMDs ( ) are computed based on the modal frequencies. For the MTMD, the mass matrix is of order as: where and are the mass matrices of the structure and the MTMD, respectively. The concise stiffness matrix corresponding to the sway degree of freedom has been performed as the dynamic DOF. The damping matrix is not bluntly known, but is adopted by using the same Rayleigh's damping ratio in all modes. α and β are damping constants with units of s -1 and s. and are expressed corresponding to the degree of freedom of TMDs. Stiffness K S and damping C S of the MTMD are shown as follows: (P+d)×(P+d) ; (3) . (4) The coupled differential Eq. (1) is thus derived by using Newmark-β integration method (Here, β=0.25, γ=0.5) to evaluate dynamic responses of the structure with TMDs (Newmark, 1959). In which, 5% damping ratio is considered.
The current exploration has been carried out resorting the standard jacket foundation, supported 5 MW OWT, designed by the National Renewable Energy Laboratory (NREL) . Then, the finite element model (FEM) of OWT, accomplished by using the Open-Sees, is shown in Fig. 1. Vemula et al. (2010) introduce a model of this support structure and Song et al. (2013) apply this model in the offshore code collaboration continuation (OC4) project with water depth of 50 m and water density of 1025 kg/m 3 . The hydrodynamic loads estimated by the FAST (NREL, 2016) fare applied to jacket nodes as nodal forces and moments based on the environmental condition. The jacket support structure (655.83×10 3 kg) consists of 64 nodes and 112 force beam-column elements, which are subjected to the wave nodal loads. The 68 m long tower (230×10 3 kg) is fabricated with the combination of 9 force beam-column elements, including the rotor nacelle assembly (RNA), lumped mass (350×10 3 kg) at the top of it. The transition piece (TP) (666×10 3 kg) among the baseline turbine and the jacket structure is represented by a rigid body. TP is considered as a density filling a rectangular body (9.6 m×9.6 m×4 m). The mass density, Young's & shear modulus and Poisson's ratio of the TP are 1807 kg/m 3 , 2.1×10 11 kg/m 2 , 8.08×10 10 kg/m 2 and 0.18, respectively. In case of tower and jacket elements, Young's (2.1×10 11 N/m 2 ) and shear (8.08×10 10 N/m 2 ) modulus, mass density (7850 kg/m 3 ) and Poisson's ratio (0.3) are identical. More details of the geometric parameters of the reference jacket support structure and tower is listed in Song et al. (2013).
To justify the OpenSees FEM, the FAST analysis is implemented. Fig. 1 illustrates the mode shapes of the structure and the corresponding modal natural frequencies are shown in Table 1. Since the model parameters are taken to establish the FEM of the structure (Song et al., 2013), the natural frequencies of the structure are compared with those of the FAST model. The results of the present study show the harmonic trend of the natural frequencies between the FAST and OpenSees. In another word, the OpenSees model is validated. Moreover, the gravitational load is also checked for the OpenSees FEM. The static analysis result shows that all the reaction forces of the structure are 18.657 MN at fixed supports without giving any other load, as the structure has been subjected to the same magnitude of 18.657 MN for gravity load.

Damper design
It is obvious that the first two vibration modes typically m di = μM S generate the major contribution to the dynamic responses of the structure. Around 80% structural mass of the entire structure is dominated by the first two modes. The main purpose of this study is to reduce vibration by installing TMDs based on the first two modal parameters of the uncontrolled structure. The total mass of TMDs is considered as 5% of the structural mass after investigating 1% to 8% of the structural mass, which shows the more effective result. The mass of each TMD ( where μ is the mass ratio and M S is the mass of the structure) is distributed based on the modal participation factor. The first and the second TMDs are located on the top and the base of the tower for controlling first and second mode, respectively. To gain the potential performance of MTMD system, multi-objective optimization tool, called response surface methodology (RSM), is used here.
CCD based on RSM is applied to obtain the optimum frequency ratio and damping ratio for each damper. Due to the interaction effect of the frequency ratio and the damping ratio, frequency response amplitude of each mode and peak displacement of tower top and base under El Centro earthquake is counted as a structural response. The objective function is as follows: where indicates the maximum magnitude of the frequency response function (FRF) for each modal frequency and is the peak displacement response either top or base of the tower. To implement the RSM based optimization, the required analysis point is chosen randomly in the range of frequency and damping ratio based on the previous study (Nigdeli and Bekdaş, 2017). By combining the chosen frequency ratio (α) and damping ratio (ξ), the damper is designed and a structural analysis is done to evaluate the structural response corresponding to it.
The equation developed by the design matrix involving the quadratic term is to estimate the structural responses of the structure with MTMD. According to the multiple linear regressions, the variable coefficient is formulated ( , where r is the predicted response, P is the product of the design matrix and c is the corresponding coefficient).The corresponding coefficient vector is the pseudo inverse of P. The experimental response is described by . From the coefficients, it is possible to distinguish the response of various models based on the nature of different factors. Based on the CCD, the quadratic models have been derived and the magnitude of coefficients can be regarded as the contribution of several factors to the responses. The quadratic models are displayed as: In Eq. (7), S i and S F are the input variables that influence the predicted response r. The damper frequency ratio influence largely on the structural response under the seismic excitation. Table 2 shows R 2 for frequency response and peak displacement response for each damper, as well as the quadratic models. As can be seen from Table 2, R 2 is close to one (except for the second mode frequency response amplitude) indicating the good relationship between model result and data. Fig. 2 shows the three-dimensional structural response surface plot along with the two factors of MTMD under the El Centro earthquake. It can be seen from this figure that the response changes with the different combination of the factors. From this response surface plot, it can be conclude that the frequency ratio is the necessary factor compared to the damping ratio for designing MTMD.
Desirability function based on RSM is employed to optimize the MTMD performances. Four responses are compared with each other on the basis of the frequency ratio and damping ratio of the MTMD. The optimization analysis is carried out by using Minitab software tools (Minitab Inc., 2013). Mosaruf HUSSAN et al. China Ocean Eng., 2017, Vol. 31, No. 4, P. 476-486 A goal set up is used to find out the enrich optimization result from response and factors. In this study, 'Minimize' is set as a goal to evaluate the result with scores of lower, target and upper for all the responses separately. Although the importance of each objective can be different, it is assumed that the importance of the peak displacement at the top and the base of the tower is the same as the frequency response of the first mode and the second mode to optimize the final effective design parameter of the dampers in this study. The equal weight of 1 is imposed to all the responses under such assumption, as represents the shape of the responses for its intimate desirability function. The composite desirability function provides the ideal decision. Here, the composite desirability is equal to 1 in the MTMD parameter due to the first mode frequency amplitude and the peak displacement value on top of the tower. As a result of the second mode frequency amplitude and peak displacement value, installed at the base of the tower, 0.9041 is obtained from MTMD parameter, which is close to 1 as desired. It is noted that such settings are favorable as all part of the structure act as a whole.
The final optimal frequency and the damping ratio for TMD 1 are 1.0518 and 0.1114, with 0.9018 and 0.1114 for TMD 2 , respectively. By using optimal frequency ratio and damping ratio, damping and stiffness of those TMDs can be expressed as: (8) where K di and C di are stiffness and damping coefficients, m di is the mass of damper, α dopti and ξ dopti are RSM optimized frequency ratio and damping ratio of the damper, and ω si is the natural frequency of jacket supported structure. Here, i indicates the position of the damper. The predicted frequency response amplitude for the first and the second mode are 4.5068 dB and 2.3632 dB with the isolate desirability of 1.0 and 0.95382, respectively, as is opposed to the analyzed responses of 5.00 dB and 2.512 dB for the MTMD parameter. On the other side, the predicted peak displacement values of top and base of the tower are 0.2494 m and 0.0762 m with the individual desirability of 1.0 and 0.8570, respectively, whereas the analyzed responses of 0.2477 m and 0.0721 m.

SSI model
The sub-structure methodology is applied to adopt the SSI model. The infinite soil medium beneath the jacket substructure is assumed as a homogeneous half-space Wolf, 1993a, 1993b). It is replaced by a simplified 5DOFs system discrete model based on the concept of Voigt viscoelastic cone model. This model based on one-dimensional wave propagation theory is used for modeling the underlying soil with sufficient accuracy (Wolf, 1994). Four degrees of freedom are considered for sway and rocking motions in x and y directions, as well as the torsional degree of freedom in z direction. A set of frequency-independent springs and dashpots is used to simulate the inertial interaction between the structure and soil (Ghaffar-Zadeh and Chapel, 1983). The soil model in this study is shown in Fig. 3.
The response of the soil-structure system mainly depends on the size of a structure, its dynamic characteristics, the soil profile and the nature of excitation. The parameters of the soil foundation model, i.e. the coefficients of spring stiffness, viscous damping and added mass are as follows: where, V is the shear wave velocity for sway and torsional motions and the dilatational wave velocity for the rocking motions. ρ is the specific mass of the soil and u 0 is depended on soil's property (Wolf, 1994). A f and I f represent the area of foundation and the area of moment of inertia in the axes of rotation. , , , and are augmenting elements related to material damping of soil. ζ 0 and ω 0 are soil damping ratio and fundamental frequency of the soil-structure system, respectively. Four SSI models are developed in this study based on the different shear wave velocities such as V s =2000, 1000, 600, 300 m/s, which represent the site conditions of the jacket supported OWT structure. Specific mass of clay soil (1900 kg/m 3 ), damping ratio (0.05), Pois- son's ratio (0.47) are the same for all SSI clay soil model profiles. The site soil profile classification system of Building Seismic Safety Council (BSSC, 2003) is used in this study.

Natural frequency
The characterization of the dynamic model is evaluated by a modal analysis. The dynamic model result of fixed base and flexible base soil structures are analyzed to assess the fundamental periods of OWT. Normally the natural frequency decreases as the shear wave velocity attenuates and converges against the fixed base natural frequencies for stronger soil. Natural frequencies of uncontrolled and controlled structures with MTMD including the SSI effects of four different soil models are shown in Table 3.
It can be found from Table 3 that the first natural frequency varies about 5% between flexible base (V s =300 m/s) and fixed base. The reduction of the first natural frequencies is smaller than 2% for soil model of V s =600 m/s soil model and smaller than 1% for the rest of other two flexible base SSI models. The variation (<11%<4%<2%<1%) of the second mode frequency for flexible base with V s =300 m/s, V s =600 m/s, V s =1000 m/s, and V s =2000 m/s follows a detrimental trend with respect to the fixed base natural frequency. After installing MTMD based on the optimization parameter, the effects with/without SSI are studied. The maximum natural frequencies of the first mode and the second mode increase for the soil model of 300 m/s with respect to the uncontrolled structure. Although the obvious distinction of natural frequency can be found with SSI, the effects of SSI on the OWT in the purpose of vibration control cannot be distinguished. The other outcomes, i.e. shear forces and moment responses, frequency response curves and displacement responses with only seismic loads and seismic loads with operational loads, can implicitly exhibit the attribute of SSI for vibration reduction. Further discussion will be performed regarding the analyzed results.

Earthquake response
The OpenSees FEM model is used for the static analys-is with the external maximum nodal wind and wave loads first. The wind and wave loads have been enumerated by FAST, which is originated from NREL. Maximum wind and wave loads are applied on the tower nodes and the jacket nodes. The dynamic earthquake analysis from the previous static analysis case is performed. To examine the effectiveness of the RSM based MTMD system with SSI, the structure is simulated under the El Centro (1940) NS, Kobe (1995) and Tabas (1978) ground accelerations with operational loads. Several earthquakes are introduced to the simulations, as various earthquakes contain distinctive features.
As the aim of this research is to reduce the seismic vibration of the OWT by using the MTMD control strategy at different soil site conditions, validation of every model associated with/without SSI during earthquake is the prerequisite. Therefore, acceleration responses at the top node during earthquakes under three selected ground motions with SSI effects are plotted in Fig. 4. From Fig. 4 it can be observed that the fundamental modes are the governing modes for the OWT, as indicates every distinctive model considered is validated. It can be seen from Fig. 4 that the maximum response amplitudes increase with the consecutive reducing of shear wave velocities of the soil model compared to the uncontrolled fixed base structure. After implementing the MTMD systems, the maximum acceleration response amplitudes decrease by 67%, 42%, 52% and 77%, 68%, 75% of the first and the second modes under three distinctive earthquakes, respectively, with respect to the uncontrolled V s =300 m/s SSI model. It also can be found that a reasonable amount of vibration reduction of MTMD system with the influence of the other three types of SSI model. It should be noted that the results for the flexible base with V s =2000 m/s SSI model are nearly close to the fixed base condition. This means that the gradual decreasing of shear wave velocities of soil beneath the structures causes the largest vibration of the OWT. Hence, the soil with V s =300 m/s shows the most desperate results than those of other models. It may imply that the MTMD strategy is feasible to mitigate the vibration of the multi-mode fundamental frequencies of the fixed base, as well as flexible base structure accompanied with the influence of SSI, under the three distinctive earthquakes.

Displacement
In Fig. 5 the displacement response occurring at the tower top node is plotted. The comparison of tower displacement responses between uncontrolled and controlled structures not only for seismic loads but also seismic loads with operational loads is also shown in Fig. 5. The graphs in Fig. 5 can be described in two cases, (a) structural responses of uncontrolled and controlled OWT subjected to earthquakes with SSI and (b) structural responses of uncontrolled and controlled OWT subjected to operational loads with SSI.
Corresponding to the first case, the displacement of the tower simply needs to agree with the synopsis shown in Fig. 4. The maximum displacement response occurs for the structures assorted the soil with lowest shear wave velocity under earthquakes alone or earthquakes with operational loads.  According to Fig. 5, the vibration mitigation rate with only El Centro is about 33% in case of V s =300 m/s which is the largest mitigation rate compared with other soil models (V s ≥ 600 m/s and without SSI). The mitigation rate at the top is about 35% and it is same for all shear wave velocities subjected to Tabas earthquake. By applying the controlling strategy, it only able to reduce 15% vibration of the structure under Kobe earthquake. It is also remarkable that MT-MD efficiently reduces the high amplitude displacement response occurred during the primary period of the analysis and reacts rapidly to these initial vibration excitations for all the flexible base soil models. It is significant for the vibration suppression during earthquake.
The performance of MTMD is negligible during earthquakes with operational loads. The maximum mitigation of vibration can be found about 7% for V s ≥600 m/s soil model and 4% with V s =300 m/s soil model for El Centro earthquake. For the other two earthquakes, the efficiencies of vibration reduction are also small. It is intended that the combination of all the operational load responses has been shifted upward from the initial response position of the structure for all the distinctive SSI models. The initial response of V s =300 m/s soil model is more destructive than other soil models (V s ≥600 m/s and without SSI) during earthquakes with operational loads. More investigations should be carried out to examine the responses for all loads, which will be more effective in the case of the OWT structure, especially in a soft soil case.
The root means square (RMS) value (S RMS = , where S RMS is the root mean square value, n is the total number of sampling points and S n is input vector or matrix) on response displacements during earthquake with operational loads is used to check the efficiency of MTMD with SSI. The RMS values of response displacements with and without MTMD of the structure, including the effect of SSI at the top node of the tower, are shown in Fig. 6. From Fig. 6, it is observed that the MTMD is more suitable for El Centro and Tabas earthquakes rather than Kobe. This might be the different characteristics of the seismic excitations with SSI. It can be conclude that by taking the SSI effects into account, the MTMD is effective to mitigate the vibration of the structure subjected to seismic loads, as well asseismic loads associated with the operational loads.

Shear and moment
Scheme of shear force and moment responses of the tower nodes are shown in Figs. 7 and 8, respectively. Here, operational loads have been taken into account during earthquake. The tower nodes are mentioned by using sequent counting from 1 (tower base) to 10 (tower top) in Fig. 7. The performance of MTMD in decreasing shear responses of the tower at different soil boundary conditions is presented in Fig. 7. The maximum shear force changes randomly from top to base of the tower with SSI. Unfortunately, the presented control approach is not so effective to minimize the shear force of the tower for the case of induced by the three selected ground motions. As the characteristics of ground motion are 300 m/s different from one earthquake to another, the results about shear forces show distinctive manner. From Fig. 7, it can be found that the mitigation shear force values for the type of El Centro earthquake are around 14% and 11% on the tower top and base with uncontrolled flexible base (V s >600 m/s) structure due to the MTMD system. The shear force rises more than 100% and 200% of top and base of the tower, respectively, for V s =300 m/s soil model with respect to the fixed base uncontrolled OWT under three selected ground motions. These figures also indicate that for V s >600 m/s, effect of the SSI is negligible on the increases of shear force response with the fixed base uncontrolled OWT, as the structure behaves like a fixed base system.
As the tower is similar to cantilever structure, the moment of the tower top is zero. The major amount of moment can be found at the tower base. The dominating manner in the case of reducing of the tower base moment is found during the El Centro earthquake than those during other two earthquakes. From Fig. 8 it can be observed that the decrement moment values are around 10% and 4% during El Centro and Kobe earthquakes on the tower base successively with the uncontrolled flexible base V s >600 m/s struc- ture. During Tabas earthquake, the effect of MTMD system is negligible. In addition, soil types of 600 m/s and 300 m/s are slightly influenced by the proposed controlled approach. The results agree with the same scheme, as the soft soil condition could be the reason of the undesirable and most destructive failure of the OWT.

Conclusions
The vibration reduction of the jacket supported OWT during earthquakes is investigated in this study. The MT-MD is applied to decrease the multi-mode responses. The SSI is depicted by the Voigt viscoelastic cone model. The RSM based optimal design parameters are exhibited. The  entire analytical and numerical process is evaluated with and without the MTMD system under flexible and fixed bases of the OWT structure. The conclusions are as follows: (1) The MTMD optimally designed by the RSM is proved to control the vibration of the fixed base OWT. Based on the FRF, the peak responses of several multimode fundamental frequencies of the structures can be remitted during three selected earthquakes.
(2) The effectiveness of the MTMD decreases as the soil medium becomes softer. Soil models of V s >600 m/s behave like a fixed base structure. The present vibration control strategy is effective for the structures on the soil models with shear wave velocities more than or equal to 600 m/s.
(3) As the vibration for V s =300 m/s soil model is compared with the other flexible base as well as the fixed base models, the performance of MTMD is less efficient to control the vibration of this structural model.
Excluding SSI is no longer adequate to guarantee the structural safety for the gigantic jacket supported OWT structure. The detrimental effects of SSI should be carefully monitored for the design of structures and control devices. Further research is needed to improve the presented control approach for more soft flexible base structure.