Robust Requirements and Design Optimization for Offshore...

7
Journal of Ocean and Wind Energy (ISSN 2310-3604) http://www.isope.org/publications/publications.htm Copyright © by The International Society of Offshore and Polar Engineers Vol. 2, No. 3, August 2015, pp. 146–152; http://dx.doi.org/10.17736/jowe.2015.mmr08 Robust Requirements and Design Optimization for Offshore Wind Turbine Structure Utilizing Approximate Model Technology Hezhen Yang Department of Civil and Environmental Engineering, National University of Singapore Singapore Yun Zhu State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering Shanghai Jiao Tong University, Shanghai, China We discuss the robust design optimization (RDO) of the support structures of offshore wind turbines to decrease costs and variations considering uncertainties. First, an approximate model derived with design of experiment (DOE) methodology is introduced to replace the time-consuming computational dynamic response analysis of finite element (FE) models for reducing computational costs. Then, a deterministic optimization (DO) without considering the uncertainties is introduced for comparison. The results suggest the feasibility and efficiency of the whole framework of the RDO method, which can be a reference for the design of other offshore support structures. INTRODUCTION The support structure is the main body of an integrated offshore wind turbine. It takes the majority of the total weight and bears various kinds of loads from the complex marine environment. With fast development of modern ocean engineering structures, the generating capacity and quantity of offshore wind turbines are growing continuously. To keep up with the pace of construction of larger wind farms in deeper water, support structures will encounter a major contradiction. On the one hand, minimization of the structure weight is an effective way to economize demands because the smaller size of the components can reduce costs in the manufacturing, transportation, and installation processes (Chew et al., 2014). On the other hand, the safety of the structure needs to be guaranteed to avoid catastrophic accidents and extremely huge maintenance expenses. Additionally, increasing the size of the structure is a commonly used method. Thus, design optimization for support structures of offshore wind turbines is proposed here as a way of gaining the cheapest cost plan without losing a specific safety requirement. Modern offshore engineering is paying more and more attention to the support structures of offshore wind turbines in recent years. Above all, dynamic analysis with finite element (FE) models of the structure in the time domain is necessary to gain accurate responses, because of the tall flexible tower, highly nonlinear loads, and complex interactions between components. Manenti and Petrini (2010) built a FE model of a monopile-type support structure for offshore wind turbines. They used this model to study the dynamic behaviors with coupled winds and waves. Meanwhile, by using coupled aero-hydro-servo-elastic simulation to model the dynamic responses, Chew et al. (2013) optimized a bottom-fixed offshore wind turbine with jacket-type substructure. Further, they Received September 11, 2014; updated and further revised manuscript received by the editors June 11, 2015. The original version (prior to the final updated and revised manuscript) was presented at the Twenty-fourth International Ocean and Polar Engineering Conference (ISOPE-2014), Busan, Korea, June 15–20, 2014. KEY WORDS: Robust design optimization, uncertainty, approximate model, design of experiment, reliability analysis. ultimately saved up to 55% of the structural mass. However, these deterministic optimization (DO) studies did not take uncertainties into consideration. Then, Yang and Zheng (2011) made a reliability analysis for steel catenary risers considering uncertain factors, and they used a metamodel, including a Kriging model, in a dynamic optimization process to save the computational iterative cost. Furthermore, Yang et al. (2015) presented an integrated optimization framework using the reliability-based design optimization (RBDO) method with a three-tripod-type support structure of an offshore wind turbine. Additionally, they compared the advantages of the RBDO method with those of the DO method. However, it should be recognized that the RDO method has not been used for support structures of offshore wind turbines yet. So, this research needs to explore a feasible way to design a robust support structure for reference. In this study, a framework of robust design optimization (RDO) (Doltsinis and Kang, 2003) with an approximate model is proposed for the design of support structures of offshore wind turbines. A numerical case of a three-tripod-type support structure of a 5 MW offshore wind turbine is built for formal optimization. The case separately uses the DO and RDO methods, and the results are compared for discussion. THEORY AND METHOD Robust Design Optimization (RDO) Methodology The conventional deterministic optimization (DO) method (Tap- peta et al., 2006) is used to search for a set of design variables that can minimize the objective and satisfy the constraints at the same time. It can be expressed as follows: E x = 6x 1 1x 2 10001x n 7 R n min f4 E x5 s.t. g i 4 E x5 01 i = 110001m x L j x j x U j 1 j = 110001n (1) where E x is a design variable vector with n dimensions; f4 E x5 is the objective function; g i 4 E x5 are the equality or inequality constraint

Transcript of Robust Requirements and Design Optimization for Offshore...

Page 1: Robust Requirements and Design Optimization for Offshore ...legacy.isope.org/publications/jowe/jowe-02-3/jowe-02-3-p146-mmr08-Yang.pdfto be guaranteed to avoid catastrophic accidents

Journal of Ocean and Wind Energy (ISSN 2310-3604) http://www.isope.org/publications/publications.htmCopyright © by The International Society of Offshore and Polar EngineersVol. 2, No. 3, August 2015, pp. 146–152; http://dx.doi.org/10.17736/jowe.2015.mmr08

Robust Requirements and Design Optimization for Offshore Wind Turbine StructureUtilizing Approximate Model Technology

Hezhen YangDepartment of Civil and Environmental Engineering, National University of Singapore

Singapore

Yun ZhuState Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering

Shanghai Jiao Tong University, Shanghai, China

We discuss the robust design optimization (RDO) of the support structures of offshore wind turbines to decrease costs andvariations considering uncertainties. First, an approximate model derived with design of experiment (DOE) methodologyis introduced to replace the time-consuming computational dynamic response analysis of finite element (FE) models forreducing computational costs. Then, a deterministic optimization (DO) without considering the uncertainties is introduced forcomparison. The results suggest the feasibility and efficiency of the whole framework of the RDO method, which can be areference for the design of other offshore support structures.

INTRODUCTION

The support structure is the main body of an integrated offshorewind turbine. It takes the majority of the total weight and bearsvarious kinds of loads from the complex marine environment.With fast development of modern ocean engineering structures,the generating capacity and quantity of offshore wind turbines aregrowing continuously. To keep up with the pace of constructionof larger wind farms in deeper water, support structures willencounter a major contradiction. On the one hand, minimization ofthe structure weight is an effective way to economize demandsbecause the smaller size of the components can reduce costs in themanufacturing, transportation, and installation processes (Chewet al., 2014). On the other hand, the safety of the structure needsto be guaranteed to avoid catastrophic accidents and extremelyhuge maintenance expenses. Additionally, increasing the size of thestructure is a commonly used method. Thus, design optimizationfor support structures of offshore wind turbines is proposed here asa way of gaining the cheapest cost plan without losing a specificsafety requirement.

Modern offshore engineering is paying more and more attentionto the support structures of offshore wind turbines in recent years.Above all, dynamic analysis with finite element (FE) models ofthe structure in the time domain is necessary to gain accurateresponses, because of the tall flexible tower, highly nonlinear loads,and complex interactions between components. Manenti and Petrini(2010) built a FE model of a monopile-type support structurefor offshore wind turbines. They used this model to study thedynamic behaviors with coupled winds and waves. Meanwhile, byusing coupled aero-hydro-servo-elastic simulation to model thedynamic responses, Chew et al. (2013) optimized a bottom-fixedoffshore wind turbine with jacket-type substructure. Further, they

Received September 11, 2014; updated and further revised manuscriptreceived by the editors June 11, 2015. The original version (prior to thefinal updated and revised manuscript) was presented at the Twenty-fourthInternational Ocean and Polar Engineering Conference (ISOPE-2014),Busan, Korea, June 15–20, 2014.

KEY WORDS: Robust design optimization, uncertainty, approximatemodel, design of experiment, reliability analysis.

ultimately saved up to 55% of the structural mass. However, thesedeterministic optimization (DO) studies did not take uncertaintiesinto consideration. Then, Yang and Zheng (2011) made a reliabilityanalysis for steel catenary risers considering uncertain factors, andthey used a metamodel, including a Kriging model, in a dynamicoptimization process to save the computational iterative cost.Furthermore, Yang et al. (2015) presented an integrated optimizationframework using the reliability-based design optimization (RBDO)method with a three-tripod-type support structure of an offshorewind turbine. Additionally, they compared the advantages of theRBDO method with those of the DO method. However, it shouldbe recognized that the RDO method has not been used for supportstructures of offshore wind turbines yet. So, this research needsto explore a feasible way to design a robust support structure forreference.

In this study, a framework of robust design optimization (RDO)(Doltsinis and Kang, 2003) with an approximate model is proposedfor the design of support structures of offshore wind turbines. Anumerical case of a three-tripod-type support structure of a 5 MWoffshore wind turbine is built for formal optimization. The caseseparately uses the DO and RDO methods, and the results arecompared for discussion.

THEORY AND METHOD

Robust Design Optimization (RDO) Methodology

The conventional deterministic optimization (DO) method (Tap-peta et al., 2006) is used to search for a set of design variables thatcan minimize the objective and satisfy the constraints at the sametime. It can be expressed as follows:

Ex = 6x11 x21 0 0 0 1 xn7 ∈Rn

min f 4Ex5

s.t. gi4Ex5≥ 01 i = 11 0 0 0 1m

xLj ≤ xj ≤ xUj1 j = 11 0 0 0 1 n (1)

where Ex is a design variable vector with n dimensions; f 4Ex5 is theobjective function; gi4Ex5 are the equality or inequality constraint

Page 2: Robust Requirements and Design Optimization for Offshore ...legacy.isope.org/publications/jowe/jowe-02-3/jowe-02-3-p146-mmr08-Yang.pdfto be guaranteed to avoid catastrophic accidents

Journal of Ocean and Wind Energy, Vol. 2, No. 3, August 2015, pp. 146–152 147

functions with total number of m; xLj and xUjare the j-th lower

and upper boundaries, respectively, of the j-th design variable xj .Compared with the DO method, the RDO method is more

practical because of two advantages:(1) It takes unavoidable uncertainties of manufacturing errors,

material properties, and so on into consideration.(2) It takes robustness requirements into consideration. A robust

system requires insensitive responses under the disturbance ofuncertainties.

With all the advantages above, the RDO method can be simplydescribed as follows:

Ex = 6x11 x21 0 0 0 1 xn7 ∈Rn

min F =w1 �2f +w2 �2

f

s.t. P4gi4�4xj51�4xj55≤ 05≤ Pfi1 i = 11 0 0 0 1m

xLj ≤ xj ≤ xUj1 j = 11 0 0 0 1 n (2)

where f is the objective function from Eq. 1, �f and �f are themean value and standard deviation of f , respectively, and thusF is a multi-objective function that aims to render f minimizedand robust. w1 and w2 are the weight coefficients of F , whichobey the rules as follows: w1 +w2 = 1. �4xj5 and �4xj5 are themean value and standard deviation of the j-th design variable,respectively; P4gi4�4xj51�4xj55≤ 05 means the failure probabilityof the i-th constraint equation; and Pfi

is the i-th maximumallowable probability of failure.

FE Model and Approximate Model for Support Structures

The three-tripod-type support structure of the 5 MW offshorewind turbine that is going to be optimized is presented here inFig. 1. The goal of optimization is to minimize the total weight(or volume) and enhance the structural robustness against theuncertainties in order to obtain lower and steadier costs. Thus,some of the sizes of the structural components will be taken asdesign variables. The entire structure is seen as a multibody flexiblesystem with a huge height, so the responses of maximum bendingstiffness of the structure and displacement at the tower top will beconsidered as constraints.

Considering the fast-changing ocean environment (Vorpahl et al.,2012), the highly nonlinear loads (such as wind turbine force at

Fig. 1 Sketch of the three-tripod-type support structure for theoffshore wind turbine

Fig. 2 Finite element (FE) model of tripod support structure

the tower top, wind forces at the tower body, wave and currentforces under the water surface, and so on), and the numerousstructural components, the finite element (FE) model (seen inFig. 2) combined with dynamic analysis in the time domain isbuilt here to obtain accurate structural responses. Historically, windturbines were analyzed with 10 min load cases to ensure samplingenough variability from the stationary loading process, but currentstandards for offshore wind turbines have recognized the need forbetter estimates and recommend at least 60 min of simulation timeper load case, i.e., 6 × 10 min or 1 × 60 min in IEC (2009). Thus,one total run of such analysis will take at least one hour, which isobviously a time-consuming task.

The iterative process of optimization and reliability analysisusing the Monte Carlo method will call for tens of thousands ofsuch runs, so it is necessary to shorten the time of every single run.That is what our approximate (meta-) model does.

Approximate model technology uses regression analysis tosimulate and simplify the functional relationships between the inputs(such as design variables Ex) and the outputs (such as responses),while still retaining a relatively high accuracy (Muskulus andSchafhirt, 2014). The Kriging model (Kaymaz, 2005) is one suchapproximate model and can be described as follows:

y4x5= f T 4x5�+Z4x5 (3)

where x is the input; y4x5 is the output; f T 4x5 is a polynomialfunction of x, which provides a global approximation; and � is thevector of regression coefficient. Z4x5 is a random process that hasthe following properties:

E6Z4x57= 0

E6Z4x5Z4�57= �2R4�1�1x5 (4)

where �2 is the variance of Z4x5; R4�1�1x5 is the covariancefunction between points x and �; � is the parameter of thecorrelation model; and Z4x5 introduced here provides a localapproximation of simulation to modify the local errors. Also, it isobvious that the Kriging model is most accurate at x = 0, whichcan be seen from Eq. 4.

NUMERICAL CASE OF THE SUPPORT STRUCTUREOF THE OFFSHORE WIND TURBINE

As mentioned before, the support structure of the offshore windturbine is so complex that FE technology is used here again for

Page 3: Robust Requirements and Design Optimization for Offshore ...legacy.isope.org/publications/jowe/jowe-02-3/jowe-02-3-p146-mmr08-Yang.pdfto be guaranteed to avoid catastrophic accidents

148 Robust Requirements and Design Optimization for Offshore Wind Turbine Structure Utilizing Approximate Model Technology

Item Value

Cm 1.74Cd 1.01Water depth 24 mWave height 9.75 mWave cycle 10.01 sWave length 200.41 mCurrent speed 1.25 m/s

Table 1 Ocean conditions with 100-years-return period in AtlanticRegion 2; Cm, inertia coefficient; Cd , drag coefficient

building the model, which can be seen in Fig. 2, with the followingsimplification: ignore large-deformation, power-control effects fromthe turbine and vibrations to the support structure.

Dynamic Analysis

The loads performing on the support structure can be divided intothree main kinds: wave and current forces, wind turbine workingforces, and wind forces on the tower body. Other kinds of loads,such as seismic forces, typhoons, sea-ice forces, and so on, are notwithin our consideration. Due to the severe and rapidly changingsea environment, these loads are considerably stochastic and highlynonlinear.

Wave and current forces are calculated by Airy wave theory.The ocean conditions with 100-years-return period in AtlanticRegion 2 (ABS, 2011) are presented in Table 1. Wind turbineworking forces are calculated by General Dynamic Wake theory(Krothapalli et al., 1998) with the National Renewable EnergyLaboratory (NREL) 5 MW wind turbine model installed at the topof the tower, referring to Fig. 3 (Tu and Vorpahl, 2014). Windforce distribution on the tower body is calculated according toapproximate formulas in IEC specifications (IEC, 2009).

The selected responses are the maximum bending stress of thestructure 4M5, the displacement at the top of tower 4U5 and thewhole volume of the structure 4V 5. The extreme load cases andsafety factors are all according to IEC 61400-3 (IEC, 2009). Inorder to gain the M , we first calculate all the bending stresses ofthe whole structural elements, and then choose the largest one. Theformer two responses are taken as probabilistic constraints, and thelast response is seen as the objective.

Parameter Sensitivity Analysis

The support structure of the offshore wind turbine in Fig. 2 ismade up of many components. Optimization of all the sizes ofevery component will be a costly and unrealistic task. Sensitivity

Fig. 3 Model of NREL 5 MW wind turbine

Initial Upper and lowerPar. Description value (m) bounds (m)

T1 Wall thickness of center 0007 60005100097column underwater

T2 Wall thickness of 0007 60004100107top bracing

T3 Wall thickness of 0005 60003100077middle bracing

T4 Wall thickness of 0002 60001100037bottom bracing

T5 Wall thickness of leg 0002 60001100037D1 Bracing diameter 108 610312037D2 Leg diameter 201 610612067

Table 2 Parameters awaiting selection as design variables

Fig. 4 Pareto plot of the parameters of the support structure

analysis of the parameters with the help of DOE technology canfind out those variables that make the greatest contributions to thevariation of responses. By keeping these main geometric parametersas design variables and ignoring the secondary parameters, theefficiency of the optimization will be greatly improved.

Table 2 shows the initial values and the lower and upper boundsof parameters awaiting selection.

After analysis by the optimization of Latin hypercubes (OLH)design method (Stocki, 2005), the sensitivities of these parametersto the responses can be seen in Fig. 4. In this Pareto plot, they-axis represents the contribution (sensitivity) of each parameter tothe responses. The more sensitive one parameter is, the higher thevalue of contribution one parameter will get; parameters with thefewest contributions will be deleted from the design variables forreducing the optimization costs. So, as shown by the plot, fourparameters are considered to be the main design variables foroptimization. They are T1, T5, D1, and D2.

Robust Design Optimization (RDO) of the Support Structure ofthe Offshore Wind Turbine

The flowchart of the RDO method is presented in Fig. 5. Herewe use dynamic loads (wind, turbine, wave, and current forceswithin 60 seconds) for response analysis via FE model. Beforeoptimum iterative procedure, sensitivity analysis of parameters isintroduced to improve the efficiency of iteration.

The RDO problem for the support structure of the offshorewind turbine with final design variables T1, T5, D1, and D2 can bedescribed as follows:

min F =w1

s1�2

V +w2

s2�2V

Page 4: Robust Requirements and Design Optimization for Offshore ...legacy.isope.org/publications/jowe/jowe-02-3/jowe-02-3-p146-mmr08-Yang.pdfto be guaranteed to avoid catastrophic accidents

Journal of Ocean and Wind Energy, Vol. 2, No. 3, August 2015, pp. 146–152 149

Fig. 5 Flowchart of DO/RDO method for the support structure ofthe offshore wind turbine

s.t. P4gU 4T11 T51D11D21E1�5≤ 05≤ Pf 1

P4gM 4T11 T51D11D21E1�5≤ 05≤ Pf 2

T L1 ≤ T1 ≤ T U

1 3 T L5 ≤ T5 ≤ T U

5

DL1 ≤D1 ≤DU

1 3 DL2 ≤D2 ≤DU

2 (5)

where E is Young’s modulus; � is the density of steel; w1 andw2 are the weight coefficients; s1 and s2 are the scale factors;gU 4T11 T51D11D21E1�5 and gM 4T11 T51D11D21E1�5 are, respec-tively, the constraints functions for U and M ; and Pf 1 and Pf 2 arethe given possibilities of failure.

In the model of the support structure of the offshore wind turbine,w1 and w2 are all specified as 0.5, and s1 and s2 are all definedas 1. To gain a high reliability, Pf 1 and Pf 2 are all specified as0.02. The constraints functions are that U and M should not belower than 1.4 meters and 315 MPa, respectively.

The considered uncertainties in the design are given in Table 3.The cross-validation charts of the displacement at tower top,the maximum bending stress, and the volume are presentedin Fig. 6.

The accuracy assessment of the Kriging model is shown inTable 4, whereas the root-mean-square error (RMSE) is followedin Eq. 6:

RMSE =

∑ni=1 4yi − yi5

2

n(6)

where yi is the i-th accurate value of response calculated using theFE model; yi is the i-th predicted value of response calculated usingthe Kriging model; and n is the total number of the sampling points.

Upper andDistribution lower Initial Coefficient of

Par. type bounds (m) value variation

T1 Normal 60005100097 0.07 m 0.03T5 Normal 60001100037 0.02 m 0.03D1 Normal 610312037 1.8 m 0.03D2 Normal 610612067 2.1 m 0.03� Normal 7850 kg/m3 0.05E Normal 201 × 1011 N/m2 0.05

Table 3 Uncertainties in the RDO of the support structure of theoffshore wind turbine

Fig. 6 Cross validation for displacement at tower top (top), themaximum bending stress (middle), and structural volume (bottom)

Here the number of sampling points used for the construction ofthe model and the validation are respectively 200 and 150 in thedesign space. It can be seen that the approximate model is preciseenough to replace the FE model.

Page 5: Robust Requirements and Design Optimization for Offshore ...legacy.isope.org/publications/jowe/jowe-02-3/jowe-02-3-p146-mmr08-Yang.pdfto be guaranteed to avoid catastrophic accidents

150 Robust Requirements and Design Optimization for Offshore Wind Turbine Structure Utilizing Approximate Model Technology

Displacement Maximum StructuralResponses at tower top bending stress volume

RMSE 0.30681% 0.4803% 0.02745%

Table 4 Accuracy assessment of the Kriging model

Initial RDOPar. values DO Solution Solution

T1 (m) 7 × 10−2 50093 × 10−2 5 × 10−2

T5 (m) 2 × 10−2 10600 × 10−2 3 × 10−2

D1 (m) 1.8 10300 1.569D2 (m) 2.1 20431 2.210�V 52.687 41.278 45.225�V – 2.322 1.602�U – 1.386 1.311�U – 10462 × 10−2 10256 × 10−2

Failure probability of U – ≈ 32% 00001%�M (MPa) – 275.447 182.187�M (MPa) – 15.905 25.905Failure probability of M – ≈ 5% 0001%Iteration steps – 91 7850

Table 5 DO and RDO solutions for the support structure of theoffshore wind turbine

RESULTS AND REMARKS

The results of RDO and DO are summarized in Table 5. It canbe seen that the initial value of the volume of the support structureis cut down by 21.65% with the DO method and by 14.16% withthe RDO method.

The simulation results of volume of DO and RDO are achievedby using the Monte Carlo method with 50,000 samples. Aftertransforming the non-normal data into normal data (Tang and Than,1999) and fitting these data into curves, the probability densityfunctions of U , M , and V are shown instructively in Fig. 7 forcomparison. In terms of the objective V , the probability densityfunction (PDF) of the RDO method is sharper than that of theDO method, which means that the value is more insensitive tothe design variables. Although the RDO method sacrifices partialperformance of volume by obtaining a relatively more conservativemean value, this design point is preferable to the initial point andis close to the DO one. In the aspect of the constraints U and M ,the RDO method pushes the mean values away from the boundaryto keep the structure more reliable. It should be noted, however,that the standard deviation of M with the RDO method is greaterthan that with the DO method. All described above supports theadvantages of the RDO method mentioned in the Introduction.

Figure 8 shows the iterative histories of tripod-type supportstructure volume in DO and RDO. For DO, only the exteriorpenalty (EP) algorithm (Joghataie and Takalloozadeh, 2009) isused, because of its simplicity. For RDO, a combination of theEP algorithm and adaptive simulated annealing (ASA) algorithmis used. Figure 8 shows that the EP algorithm is calculated for ageneral sense of optimized direction in the first 1,000 iterationsteps. The ASA algorithm works in global design space, as isseen from the degree of dispersion in the rest of the nearly 6,000iteration steps. The computational expense of RDO is obviouslymuch greater (nearly eight times) than that of DO in this case.Thus, decreasing the time of each step is really important in RDO.

Fig. 7 Probability density function (PDF) of V (top), U (middle),and M (bottom)

CONCLUSIONS

A practical methodology concerning uncertainties and minimizingthe objective sensitivity with RDO is proposed in this study. The

Page 6: Robust Requirements and Design Optimization for Offshore ...legacy.isope.org/publications/jowe/jowe-02-3/jowe-02-3-p146-mmr08-Yang.pdfto be guaranteed to avoid catastrophic accidents

Journal of Ocean and Wind Energy, Vol. 2, No. 3, August 2015, pp. 146–152 151

Fig. 8 Steps of DO (upper) and RDO (lower) iterative histories

support structure of an offshore wind turbine is the main body tobear the loads of winds, waves, and currents with its huge towerand legs. The key problem is to balance safety and costs under theuncertainty of its components’ parameters. Also, the sensitivity ofthe objective volume should be minimized to control costs within asmall fluctuation. Then a tripod-type support structure of offshorewind turbines is modeled for optimization. Design of experiment(DOE) technology is used here to generate sampling data, fromwhich responses are calculated by dynamic analysis in the timedomain with a finite element (FE) model. Sensitivity analysis helpsto measure the contributions of design variables to the responsesand decreases the number of design variables in the optimizationprocess. To improve the computational efficiency, an approximationmodel based on these sampling data is introduced for optimumiterative and reliability procedures instead of the FE model. Withthe comparison of DO and RDO, the conclusions can be as follows:

(1) The failure probability of deterministic constraints cannot beaccepted if appropriate safety factors are not introduced. Althoughthe objective of RDO is a little more conservative than that of DO,its reliability is higher and satisfies the given value. Thus, the RDOmethod improves the safety of the structure.

(2) The standard deviation of the objective is less in RDOthan in DO, which means the costs of the support structure are

more stable under the disturbance of uncertain factors after RDO.Additionally, with the selection of weight coefficients, a flexiblescheme between optimality and robustness can be achieved.

(3) The approximate model that replaces the FE model in thenumerical case cuts down the computational costs considerably andremains high in accuracy. Therefore, the approximation technologycan promote the efficiency of the optimization procedure whensolving complex systems and excitations.

All the conclusions mentioned above prove that the proposedRDO is a valid and universal method to be extended for moregeneral behaviors of other types of large offshore structuresconsidering uncertainties.

ACKNOWLEDGEMENTS

This work was financially supported by the National NaturalScience Foundation of China (Grants 51379005 and 51009093).

REFERENCES

ABS (2011). Final Report: Design Standards for Offshore WindFarms, American Bureau of Shipping, Houston, TX, USA,182 pp.

Chew, KH, Muskulus, M, Zwick, D, Ng, EYK, and Tai, K (2013).“Structural Optimization and Parametric Study of Offshore WindTurbine Jacket Substructure,” Proc 23rd Int Offshore Polar EngConf, Anchorage, AK, USA, ISOPE, 1, 203–210.

Chew, KH, Ng, EYK, Tai, K, Muskulus, M, and Zwick, D (2014).“Offshore Wind Turbine Jacket Substructure: A Comparison StudyBetween Four-Legged and Three-Legged Designs,” J OceanWind Energy, ISOPE, 1(2), 74–81.

Doltsinis, I, and Kang, Z (2003). “Robust Design of StructuresUsing Optimization Methods,” Comput Methods Appl Mech Eng,193(23–26), 2221–2237.http://dx.doi.org/10.1016/j.cma.2003.12.055.

IEC (2009). Wind Turbines, Part 3: Design Requirements forOffshore Wind Turbines, IEC 61400-3 Offshore Wind TurbineDesign Standard, International Electrotechnical Commission,Geneva, Switzerland.

Joghataie, A, and Takalloozadeh, M (2009). “Improving PenaltyFunctions for Structural Optimization,” Scientia Iranica, 16(4A),308–320.

Kaymaz, I (2005). “Application of Kriging Method to StructuralReliability Problems,” Struct Saf, 27(2), 133–151.http://dx.doi.org/10.1016/j.strusafe.2004.09.001.

Krothapalli, KR, Prasad, JVR, and Peters, DA (1998). “A General-ized Dynamic Wake Model with Wake Distortion Effects,” Proc54th Annu Forum Amer Helicopter Soc, Washington, DC, USA,AHS, 1, 527–533.

Manenti, S, and Petrini, F (2010). “Dynamic Analysis of anOffshore Wind Turbine: Wind–Waves Nonlinear Interaction,”Proc 12th Int Conf Eng Sci Constr Oper Challenging Environ,Honolulu, HI, USA, ASCE, 2014–2026.http://dx.doi.org/10.1061/41096(366)184.

Muskulus, M, and Schafhirt, S (2014). “Design Optimization ofWind Turbine Support Structures: A Review,” J Ocean WindEnergy, ISOPE, 1(1), 12–22.

Stocki, R (2005). “A Method to Improve Design Reliability UsingOptimal Latin Hypercube Sampling,” J Comput Assisted MechEng Sci, 12, 393–411.

Page 7: Robust Requirements and Design Optimization for Offshore ...legacy.isope.org/publications/jowe/jowe-02-3/jowe-02-3-p146-mmr08-Yang.pdfto be guaranteed to avoid catastrophic accidents

152 Robust Requirements and Design Optimization for Offshore Wind Turbine Structure Utilizing Approximate Model Technology

Tang, LG, and Than, SE (1999). “Computing Process CapabilityIndices for Non-Normal Data: A Review and ComparativeStudy,” Qual Reliab Eng Int, 15(5), 339–353.http://dx.doi.org/10.1002/(SICI)1099-1638(199909/10)15:5<339::AID-QRE259>3.0.CO;2-A.

Tappeta, RV, Rao, G, and Mianowski, P (2006). “Practical Implemen-tation of Robust Design Optimization,” Proc 11th AIAA/ISSMOMultidiscip Anal Optim Conf, Portsmouth, VA, USA, AIAA, 2,876–889. http://dx.doi.org/10.2514/6.2006-6980.

Tu, Y, and Vorpahl, F (2014). “Influence of Superelement SupportStructure Modeling on the Loads on an Offshore Wind Turbinewith a Jacket Support Structure,” J Ocean Wind Energy, ISOPE,1(3), 153–160.

Vorpahl, F, Schwarze, H, Fischer, T, Seidel, M, and Jonkman, J(2012). “Offshore Wind Turbine Environment, Loads, Simulation,and Design,” WIREs Energy Environ, 2(5), 548–570.http://dx.doi.org/10.1002/wene.52.

Yang, HZ, and Zheng, WQ (2011). “Metamodel Approach forReliability-Based Design Optimization of a Steel Catenary Riser,”Int J Mar Sci Technol, 16(2), 202–213.http://dx.doi.org/10.1007/s00773-011-0121-6.

Yang, HZ, Zhu, Y, Lu, Q, and Zhang, J (2015). “Dynamic Reliability-Based Design Optimization of the Tripod Sub-Structure ofOffshore Wind Turbines,” Renewable Energy, 78(1), 16–25.http://dx.doi.org/10.1016/j.renene.2014.12.061.

The Proceedings of The Twenty-fifth (2015) International

OCEAN AND POLAR ENGINEERING CONFERENCE Kona, Hawaii, USA, June 21−26, 2015

ISBN 978−1−880653−89−0 ISSN 1098−6189 Indexed by Engineering Index, EI Compendex, Scopus and others.

VOLUME I FRONTIER ENERGY RESOURCES TECHNOLOGY

EOR & Drilling OCEAN MINING & GAS HYDRATES SYMPOSIUM: OMS-2015 (OMGH-2015)

Gas Hydrates, Manganese Nodules & Crusts, Massive Sulphide, Deep Ocean Mining and Environment

OFFSHORE WIND AND OCEAN AND ENVIRONMENT Wind Turbines – Foundations, Support Structures, Floating Turbines, Analysis & Testing, Wind & Wave Loading, Aerodynamics & Blades, Installation & Maintenance, Ocean and Wind Resources, Hybrid Installation, Tidal & Current Energy, OWC, OTEC

ENVIRONMENT SCIENCE AND ENGINEERING Carbon Capture Sequestration (CCS), Environ Impact & Monitoring

OFFSHORE MECHANICS AND OCEAN TECHNOLOGY Rules And Codes, Subsea, Installation, Decommissioning & Installation, Jackup & Fixed Structures, TLP, SPAR & Mooring, Offshore Systems, VLFS & Floating Structures, FLNG & FPSO

ARCTIC SCIENCE & TECHNOLOGY Arctic Environment, Arctic Mechanics, Arctic Test Methods, Arctic Operations, Arctic Operations, Arctic Ship Technology, Arctic Structures

VOLUME III HYDRODYNAMICS

HYDRODYNAMICS Resistance, Drift & Wind Forces, Hydroelasticity, Whipping, Stability & Roll Motion, Fluid-Structure Interactions, Dynamic Positioning Control, NWT, CFD, Shallow Water, MetOcean, Multi-structures, Reliability, Comparative Study

TSUNAMI AND SAFETY SYMPOSIUM Generation to Inundation, Tsunami Power, Monitoring & Warning

SLOSHING & SHIP DYNAMICS AND DESIGN Coupled Sloshing and Ship Dynamics, Liquefaction, Damping, Fluid-Structure Interactions, Design

FLOW-INDUCED VIBRATIONS Single Body, Multi-Bodies, Vortex Suppression

COASTAL HYDRODYNAMICS Storm Surge, Waves, Lagrangian Particle Methods, Beach & Estuary, Structures, Port Development

VOLUME II SUBSEA, PIPELINES, RISERS AND UMBILICALS

Pipeline Design, Pipeline Analysis, Installation & Commission, Riser Design, SCR & TTRs, Flow Assurance, Lateral Buckling & Walking, Flexibles & Umbilicals, Integrity Management, Test Experiments, Robotics & Control,

UNDERSEA VEHICLE, COMMUNICATION & CONTROL Acoustics & Imaging, ROV Design & Navigation, Navigation & Control, Oil Spill Tracking & Control

GEOTECHNICAL ENGINEERING Computational Geomechanics, Geohazards, Soil Properties, Soil Dynamics, Ground Improvement, Soil-Structure Interactions, Suction Piles, Offshore Pile Foundation, Anchors, Site Characterization

VOLUME IV HIGH-PERFORMANCE MATERIALS (HPM) Material Reliability in Petrochemicals, Advanced Materials & Offshore Structures, Fatigue & Fracture, Advances in Welding Technology

ARCTIC MATERIALS Materials Challenges in Arctic, Steel Testing & Characteristics, Steel Properties & Applications

HIGH MANGANESE STEEL SYMPOSIUM Phase Transform & Mechanical Properties, Cryogenic Properties & Welding

ASSET INTEGRITY Structural Integrity, Carbon-Based Maintenance, Corrosion Management, Marine Integrity, Pipeline & Riser Integrity

STRAIN-BASED DESIGN Keynote, Strain Capacity & Demand, Pipeline Material Properties, Strain-Based Design and Assessment, Full-Scale Testing, Pipeline Collapse & Fatigue

RISK, RELIABILITY & STRENGTH Slamming & Hydroelasticity, Product Reliability, Risk Analysis, Collision & Impact, System Design

ADVANCED SHIP TECHNOLOGY Green Ship, Hull Form Optimization, Ship Powering, Ship Hydrodynamics, Hydrodynamic Loading, Shipbuilding Simulation, Ultimate Strength, Structures & Strength, Transport & Navigation, Design and Analyses