Usanifu salama wa offshore wind turbines hauhusiani tu na kubainisha highest wind speed au largest wave. Direction ambayo wind inatoka, kama wave iko fully aligned na wind au la, na angle ambayo loads hizi zinaathiri legs na braces za jacket support system pia zinaweza kubadilisha distribution ya structural forces. Directional effect hii ni muhimu zaidi katika three-legged jacket systems kuliko circular-section na approximately axisymmetric monopile structures, kwa sababu stiffness na internal force paths za jacket si sawa katika directions zote.

Study inalinganisha 50-year extreme-load response ya 25 MW-class offshore wind turbine inayokaa juu ya three-legged jacket foundation kwa three different environmental-condition selection methods: traditional na aligned IFORM, D-IFORM inayozingatia wind-wave misalignment katika fixed wind direction, na DiREC inayosolve both absolute wind direction na wind-wave misalignment sector by sector.

Kwa IFORM only two, kwa D-IFORM ten, na kwa DiREC 372 time-domain simulations zilifanywa. Aerodynamic loads zilitengenezwa kwa OpenFAST 3.1 na TurbSim; jacket, wave, current na foundation behavior zilimodeliwa ndani ya Sesam. Kila load case ilitathminiwa katika 10-minute analysis interval baada ya kuondoa first 20-second numerical transient. Structural adequacy ilichunguzwa under NORSOK N-004 kwa combined axial-force-bending checks za tubular members na local punching checks za tubular joints.

Highest member utilization factor ilikuwa 0,214 katika IFORM, 0,211 katika D-IFORM na 0,201 katika DiREC. Kwa hiyo DiREC ilipunguza highest utilization ratio kwenye single member kwa approximately %6,1 compared with IFORM. Lakini decrease hii haimaanishi directional resolution iliifanya structure kwa ujumla kuwa less loaded. Katika DiREC results, high-utilization members ziliunda broader na flatter ranked envelope; different direction na misalignment combinations zilifanya multiple members kuwa critical kwa levels zinazokaribiana.

Opposite trend ilionekana katika local tubular joints. Highest joint utilization factor ilihesabiwa 0,170 katika IFORM, 0,173 katika D-IFORM na 0,197 katika DiREC. DiREC value ni approximately %15,9 higher than IFORM. Result hii inaonyesha kwamba absolute wind direction na wind-wave misalignment zikiresolvewa kwa detail zaidi, local force transfer kati ya brace na chord members inaweza kuwa more critical hata kama global structural response haiongezeki.

Leading DiREC load cases zilijikusanya especially katika 315° direction sector, na near-governing cases pia zilipatikana katika 195° sector. Most critical joint case; chini ya 315° wind direction, +20° wind-wave misalignment, 10,88 m significant wave height, 11,70 s peak period na -8° yaw misalignment, ilitoa 0,197 utilization factor katika JT28 joint. Hii inaonyesha highest structural demand haitokei kila mara katika direction yenye largest wave height.

Global base shear na overturning moment zilipungua kutoka IFORM kwenda D-IFORM na DiREC. Highest base shear zilikuwa respectively 11,62 MN, 11,38 MN na 10,59 MN; highest overturning moment 388,85 MN·m, 380,01 MN·m na 356,61 MN·m. Kwa upande mwingine, local joint demand iliongezeka katika DiREC. Kwa hiyo kuangalia base shear au overturning moment pekee kunaweza kukosa jinsi directional loads zinavyoredistribute force paths ndani ya jacket.

All reported utilization factors ziko clearly below limit 1,0. Investigated structure inaonekana adequate kwa ultimate limit state katika analyses hizi. Main contribution ya study si kugundua unsafe design; ni kuonyesha kwamba more detailed directional environmental modeling inaweza kubadilisha governing member, governing joint na critical load direction.

Tatizo kuu la utafiti ni nini?

Offshore wind turbines katika operating life yao hukabiliwa na combination ya wind, wave, current, turbulence, gravity na soil-foundation interaction. Ultimate limit state, yaani ULS assessment, huchunguza kama structure inaweza kupoteza load-carrying capacity chini ya low-probability lakini high-severity environmental conditions.

Kuchunguza every hourly wind-wave state katika maisha ya decades kwa separate time-domain simulation kunaleta very high computational cost. Environmental contour methods zinajaribu kutatua tatizo hili kwa kuchagua limited set ya critical metocean conditions zinazowakilisha specified return period.

Basic assumption ni kwamba selected environmental states zina-envelop sufficiently long-term extreme structural response. Lakini assumption hii huwa complex pale structural response inapohusiana si tu na scalar magnitudes kama wind speed na wave height bali pia na load direction.

Research question inaweza kusummarizewa kama:

Wind na wave directions zinapowakilishwa kwa detail zaidi, most critical members, tubular joints na global loads za 25 MW-class three-legged jacket structure zinabadilikaje?

Kwa nini 25 MW-class ni muhimu?

Rated power na rotor diameter za offshore wind turbines zinapoongezeka, aerodynamic loads, support-structure dimensions na structural load paths pia hubadilika. Turbine iliyotumika katika study:

• Iko katika 25 MW rated-power class.
• Ina 310 m rotor diameter.
• Hub height ni 185 m.
• Inatumia 148 m-high tapered tower.
• Rotor-nacelle assembly mass ni 1.556,81 tonnes.
• Transition-piece mass ni 526 tonnes.
• Ina cut-in wind speed 3 m/s, rated 10,87 m/s na cut-out 25 m/s.

Haijasemwa kwamba turbine ya scale hii ni actual commercial-site machine. Model inategemea 25 MW reference-turbine design iliyotengenezwa ndani ya CRC1463 project.

Kwa nini three-legged jacket ni direction-sensitive?

Jacket systems ni lattice structures zenye vertical au inclined main legs, braces zinazounganisha legs hizi na tubular joints. Investigated jacket ina:

• Three main legs,
• Three levels of X-bracing,
• Total jacket height 78,2 m,
• Three piles embedded approximately 65 m into soil,
• Piles zenye 4,3 m outer diameter na 40 mm wall thickness

.

Ingawa three-legged arrangement imewekwa kwa 120° intervals, haina continuous rotational symmetry. Environmental load direction ikibadilika:

• One leg inaweza kubaki directly on load side.
• Two legs zinaweza carry load together.
• Specific braces zinaweza kwenda tension, others compression.
• Brace-chord force combination katika joints inaweza kubadilika.
• Shares za horizontal force na moment zinazohamishwa kwa piles zinaweza redistribute.

Kwa hiyo same wind na wave magnitudes zikiletwa kutoka different directions hazitarajiwi kutoa same utilization factor.

Directional difference kati ya monopile na jacket

Monopile ni single large-diameter cylindrical foundation na global horizontal stiffness yake mara nyingi ni less direction-sensitive. Wind-wave misalignment inaweza kuathiri global monopile response, lakini load-transfer geometry haigawanywi kwenye individual members na joints nyingi kama katika jacket.

Katika jacket structure, direction change inaamua si total base force pekee bali pia force itapita kwenye brace gani, leg gani na tubular joint gani. High directional sensitivity iliyoonekana katika local joints inaendana na geometric difference hii.

Environmental contour method inafanya nini?

Environmental contour hufafanua combinations za wind, wave na other environmental variables zinazolingana na specified return period. Lengo ni kuchagua limited set ya structurally meaningful conditions badala ya kusimulate entire environmental time series.

Two-variable hierarchical conditional model kwa ujumla huandikwa:

\[ f_{X,Y}(x,y)=f_X(x)\,f_{Y|X}(y|x) \]

ambapo:

• f_X(x): Marginal probability density ya first environmental variable,
• f_Y|X(y|x): Conditional density ya second variable given first,
• f_X,Y(x,y): Joint density.

Copula-based alternative representation ni:

\[ f_{X,Y}(x,y)=f_X(x)f_Y(y)c\left(F_X(x),F_Y(y)\right) \]

. Copula function inalenga kutenganisha marginal distributions na dependence structure kati ya variables. Hata hivyo, katika high-dimensional problems zenye limited tail data, selection ya copula family huleta additional model uncertainty.

Special problem ya circular variables

Wind na wave directions si linear variables. 0° na 360° zinawakilisha same direction. Kwa hiyo kutumia ordinary linear distributions directly kwa directional data kunaweza kuleta problems kwenye boundary region.

Katika literature section ya study, directional distribution inaonyeshwa kwa mixture ya von Mises components kama:

\[ f_{\theta}(\theta)=\sum_{i=1}^{n}\omega_i f_i(\theta) \]

\[ f_i(\theta)= \frac{\exp\left[\kappa_i\cos(\theta-\mu_i)\right]} {2\pi I_0(\kappa_i)} \]

• ω_i: Weight ya mixture component,
• μ_i: Mean direction,
• κ_i: Concentration parameter inayoonyesha jinsi directions zinavyocluster around mean,
• I₀: Modified Bessel function of first kind, order zero.

Relations hizi si main distribution iliyotumika directly katika DiREC calculation; zimewasilishwa kueleza theoretical background ya directional environmental contour methods.

IFORM approach

Inverse First-Order Reliability Method hubadilisha environmental variables kwenda standard normal probability space na kutengeneza contour inayolingana na specified reliability au return period. Method inatumika widely katika offshore standards.

IFORM application katika study hii ni simple design case:

• Absolute wind direction fixed at 0°.
• Wave direction assumed fully aligned with wind direction.
• 50-year mean wind speed at 10 m height set to 50 m/s.
• 50-year significant wave height ni 12,53 m.
• Maximum wave height given as 23,31 m.
• Peak period ni 12,54 s.
• Two simulations performed kwa yaw misalignment values -8° na +8°.

IFORM imetumika kama aligned na fixed-direction baseline comparison method.

D-IFORM approach

Direct IFORM ni model-independent approach inayolenga kubainisha extremes kwa projecting normalized observations onto different direction vectors bila kujenga explicit multivariate joint distribution.

Normalized multidimensional observation vector Y hu-projectiwa onto unit direction vector u kama:

\[ R_u=u\cdot Y \]

. Projected sample katika kila direction huwa univariate extreme-value problem. Method description inaeleza kwamba tail values hizi zinaweza kukadiriwa kwa peaks-over-threshold approach na generalized Pareto distribution.

Katika applied D-IFORM load cases:

• Absolute wind direction again fixed at 0°.
• Wind-wave misalignments selected as 0°, ±30° na ±90°.
• Kwa kila misalignment -8° na +8° yaw cases used.
• Total ten simulations performed.

Magnitude ya misalignment angle ilipoongezeka, selected wave height na peak period zilipungua. Lakini +30° na -30°, licha ya kuwa na same environmental magnitudes, si lazima zitoe same structural result kwa sababu zinaathiri jacket geometry kutoka different directions.

DiREC approach

Directionally Resolved Environmental Contour ni sector-based method iliyotengenezwa na authors wa study. DiREC inaresolve both absolute wind direction na wave misalignment relative to wind separately.

Main steps ni:

1. Wind na wave records zina-pairiwa katika 3-hour blocks.
2. Katika kila block mean significant wave height na circular mean wave direction zina-pairiwa na highest hourly wind speed na direction yake.
3. First directional filter applied relative to center ya specified wind sector.
4. Simultaneously observed waves filtered again according to targeted wind-wave misalignment.
5. Univariate extreme-value distribution built kwa kila sector na misalignment interval.
6. 50-year significant wave height na associated peak period obtained.
7. Values hizi combined na sector's 50-year wind speed na transferred to structural simulation.

Directional range iliyotumika katika DiREC

Kulingana na empirical distribution katika study, approximately %60 ya simultaneous wind-wave events hubaki within ±30° misalignment. At high wind speeds distribution inaconcentrate zaidi around small misalignment angles, wakati at low wind speeds remote swell inapanua distribution.

Kwa hiyo DiREC analysis ilifanywa katika:

\[ -30^\circ\leq\varphi\leq+30^\circ,\qquad \Delta\varphi=2^\circ \]

range.

• φ: Deviation ya wave direction relative to wind direction,
• Δφ: 2° directional increment.

Absolute wind-sector centers zilizochunguzwa ni 195°, 225°, 255°, 285°, 315° na 345°. Hizi zinawakilisha 180°-360° geographic region ambako strongest wind na wave conditions kwenye site zinaconcentrate.

Two-stage directional filter

Katika first stage, simultaneous states within ±15° ya kila wind-sector center zilichaguliwa. Katika second stage, separate wave-sector filter ilitumika around target wave direction.

Kwa mfano, wind-sector center ikiwa 195° na target misalignment +2°, target wave direction ni:

\[ \theta_W=195^\circ+2^\circ=197^\circ \]

. Kati ya events zilizopita first filter, waves around 197° zinachaguliwa kuunda sample ya misalignment state hii.

Kwa nini wave-sector width ni muhimu?

Study ilijaribu half-widths ±5°, ±10° na ±15° kwa wave direction. Very narrow ±5° filter:

• Iliacha fewer than 20 observations katika some misalignment ranges.
• Ilitengeneza unstable na discontinuous directional curves.
• Ilifanya reliable estimation ya extreme-value parameters kuwa difficult.

±10° na ±15° results zilikuwa closer na smoother. Researchers walichagua ±10° half-width kwa sababu ilihifadhi directional resolution as much as possible huku ikitoa sufficient sample count.

At least 20 independent observations zilihitajika kwa kila directional sample; intervals below this count zilitolewa.

Three-parameter Weibull model

Sector-based 50-year values katika DiREC zilikadiriwa kwa three-parameter Weibull distribution:

\[ F(h)= \begin{cases} 0, & h<\gamma \\ 1-\exp\left[-\left(\dfrac{h-\gamma}{\alpha}\right)^\beta\right], & h\geq\gamma \end{cases} \]

• h: Significant wave height,
• α: Scale parameter,
• β: Shape parameter,
• γ: Location parameter.

Parameters zilikadiriwa kwa maximum likelihood; distribution ika-invertiwa kwa non-exceedance probability corresponding to daily maximum statistic ili kupata 50-year return value.

Katika stage hii wind na wave extremes zilitathminiwa kama separate marginal variables. DiREC haijengi joint multivariate distribution ya wind na wave.

Basic DiREC environmental conditions by sector

Table pia inaonyesha sector-conditioned wind speeds katika DiREC ni clearly lower kuliko unconditional 50 m/s value katika IFORM. Sehemu ya lower global loads katika DiREC inahusiana na different environmental characterization hii.

Je, highest wave ilitokea kila mara katika exact alignment?

Hapana. 2°-resolution tables katika Appendix A zinaonyesha highest sector-conditioned wave height ilitokea nje ya φ=0° katika most sectors:

Values hizi zinaonyesha highest wave conditions zinaweza kuunda plateau over roughly ±10°-15° na katika some sectors broader small-misalignment region badala ya narrow “exact alignment point”.

Hata hivyo, 225° sector yenye highest wave haikutoa highest structural utilization factor. Structural demand inategemea wave magnitude pamoja na jacket orientation, wind direction, wave direction, yaw sign na local load path.

Site na metocean data basis

Turbine ilidhaniwa kuwa located katika German North Sea. Site conditions:

• 48,2 m water depth,
• 0,266 m/s normal current at mean sea level,
• 1,35 m/s extreme current at mean sea level,
• 100 mm marine growth between -2 m and 40 m,
• 50 mm marine growth in deeper regions,
• 1.325 kg/m³ marine-growth density,
• 1.025 kg/m³ seawater density

.

Environmental records zilitolewa kutoka CoastDat-2 reanalysis/hindcast dataset na kuungwa mkono na FINO-1 research-platform measurements. Text inarejea 68-year observation period katika directional-distribution assessment.

Soil model

FINO-1 soil profile iliwakilishwa kwa 18 layers. Layers nyingi ni sand varying from loose to very dense, na sand-silt mixture katika some depths.

Depending on layer:

• Submerged unit weight 7,5–11 kN/m³,
• Internal friction angle 15°–45°

.

Pile-soil interaction ilimodeliwa kwa:

• p-y for lateral behavior,
• t-z for axial friction,
• q-z for pile tip

relationships.

Kwa sababu soil behavior ni nonlinear, equivalent stiffness matrices linearized at representative load levels ziliundwa na kutumika kama springs katika pile heads. Matrices zinajumuisha si linear translational stiffnesses pekee bali pia cross terms kati ya translation na rotation components.

Site orientation ya jacket

Jacket iliorientiwa na one leg facing dominant north-northwest wave direction katika site. Other two legs zinabaki upande wa nyuma wa load.

Choice hii ilijustifyiwa na prior design studies zinazoonyesha orientation yenye two legs simultaneously on load side inaweza kutengeneza higher demand katika rear leg, na having single leg face wave inaweza kupunguza required pile embedment na total pile mass.

Calculation ya aerodynamic loads

Aerodynamic load time series kwenye rotor, nacelle na tower zilitengenezwa kwa OpenFAST 3.1. Turbulent wind fields ziliundwa ndani ya TurbSim kwa Kaimal spectrum.

Katika extreme turbulent wind state consistent with IEC design framework:

\[ \psi_{\mathrm{yaw}}=\pm8^\circ \]

yaw misalignments zilizingatiwa.

Force na moment time series kutoka OpenFAST zilihamishwa kama external loads kwenda Sesam jacket model katika tower-transition-piece interface node.

Hydrodynamic loads

Wave na current loads zilihesabiwa ndani ya Sesam kwa Morison equation. Irregular wave field iliwakilishwa na JONSWAP spectrum.

Hydrodynamic calculation ilizingatia pamoja:

• Wave kinematics,
• Current,
• Diameter na mass effect ya marine growth,
• Added-mass effect ya internal water katika flooded members,
• Soil na pile-head flexibility

.

“Fully coupled” analysis inaelewekaje?

Study inaeleza workflow kama fully coupled aero-hydro-servo-elastic assessment. Method description inasema aerodynamic loads zilitengenezwa katika OpenFAST na kuhamishwa kwenda Sesam jacket model; hydrodynamic na foundation loads zilisolvewa katika Sesam.

PDF haielezi kwa detail bidirectional iterative software coupling ambapo Sesam jacket deformations zinarudishwa kwenye OpenFAST rotor model ndani ya same time step. Kwa hiyo, katika reproducing method, ingekuwa useful ku-document kama “fully coupled” inamaanisha one-way load transfer kati ya software au inajumuisha additional feedback mechanism.

Time-domain simulations

Kwa kila simulation, first 20 seconds ziliondolewa ili suppress numerical startup transients. Kisha 10-minute steady segment ilitathminiwa.

Number ya load cases by method:

Comparison hii inalinganisha si different probabilistic methods pekee bali pia substantially different directional sampling densities. Study inaeleza hili wazi.

Ultimate limit state na utilization factor

Structural-code checks zilifanywa according to NORSOK N-004. Utilization factor ilitafsiriwa kama:

• UF < 1,0: adequate,
• UF = 1,0: design resistance reached,
• UF > 1,0: inadequate

.

UF ya 0,20 haimaanishi member inafanya kazi kwa “%20 stress” pekee kwa kila maana. Utilization factor ni code ratio inayochanganya axial force, bending, buckling na relevant design resistances katika interaction equation.

Tension na biaxial bending check

Kwa tubular members under tension, interaction iliyotolewa katika PDF ni:

\[ UF_t= \left(\frac{N_{Sd,t}}{N_{t,Rd}}\right)^{1{,}75} + \frac{\sqrt{M_{y,Sd}^2+M_{z,Sd}^2}}{M_{Rd}} \leq1{,}0 \]

• N_Sd,t: Design tensile force,
• N_t,Rd: Design tensile resistance,
• M_y,Sd, M_z,Sd: Design bending moments about local axes,
• M_Rd: Design bending resistance.

Compression, buckling na biaxial bending check

Kwa members in compression, larger ya two complementary checks ilichukuliwa kama governing:

\[ UF_c=\max(UF_{c,1},UF_{c,2})\leq1{,}0 \]

\[ UF_{c,1}= \frac{N_{Sd,c}}{N_{c,Rd}} + \frac{1}{M_{Rd}} \left[ \left( \frac{C_{my}M_{y,Sd}} {1-N_{Sd,c}/N_{Ey}} \right)^2 + \left( \frac{C_{mz}M_{z,Sd}} {1-N_{Sd,c}/N_{Ez}} \right)^2 \right]^{1/2} \leq1{,}0 \]

\[ UF_{c,2}= \frac{N_{Sd,c}}{N_{cl,Rd}} + \frac{\sqrt{M_{y,Sd}^2+M_{z,Sd}^2}} {M_{Rd}} \leq1{,}0 \]

• N_Sd,c: Design compression force,
• N_c,Rd: Overall compression resistance,
• N_cl,Rd: Local buckling resistance,
• N_Ey, N_Ez: Euler buckling forces about two local axes,
• C_my, C_mz: Reduction factors depending on moment distribution and boundary conditions.

Tubular-joint punching check

Joint utilization relation iliyotolewa kwa local transfer ya brace forces into chord tube ni:

\[ UF_{\mathrm{joint}}= \frac{N_{Sd}}{N_{Rd}} + \left(\frac{M_{y,Sd}}{M_{y,Rd}}\right)^2 + \frac{M_{z,Sd}}{M_{z,Rd}} \leq1{,}0 \]

.

Equation 12 imeprintiwa hivi katika PDF: ratio ya y moment imesquarewa, wakati square sign haionekani kwenye z moment ratio. Formula haijabadilishwa kimya kimya katika explanation hii. Researchers wanaotaka reproduce NORSOK implementation wanapaswa kulinganisha notation hii na original relation katika relevant standard.

Results za member checks

IFORM na D-IFORM zilitengeneza same governing member na location. Nonzero misalignments katika D-IFORM zilibadilisha second- na lower-ranked member checks lakini hazikubadilisha absolute maximum.

Maximum member utilization katika DiREC ni:

• Approximately %6,1 lower than IFORM,
• Approximately %4,7 lower than D-IFORM

.

Kwa upande mwingine, first ten member results katika DiREC zilibaki closer to one another. Ranked-utilization curve katika Figure 10(a) inapungua more gradually kwa DiREC. Hii ina maana kuna many directionally different near-governing states badala ya one overwhelmingly governing state.

Near-governing member states katika DiREC

Distribution ya first five results across four different wind sectors inaonyesha critical member demand haiwezi kuelezwa only na highest-wave sector.

Results za tubular-joint checks

D-IFORM iliongeza highest joint UF kwa approximately %1,8 compared with IFORM na ikabadilisha governing joint. Ingawa absolute wind direction ilibaki fixed, -30° wave misalignment ilifanya brace-chord force transfer kuwa critical katika different joint.

DiREC joint utilization 0,197 ni:

• Approximately %15,9 higher than IFORM,
• Approximately %13,9 higher than D-IFORM

.

Leading joint states katika DiREC

Katika Figure 10(b), DiREC curve inabaki above IFORM na D-IFORM curves katika much of ranking. Kwa hiyo directional detail haikuongeza single maximum joint value pekee bali pia broadened envelope ya near-governing local joints.

Kwa nini joints ni more sensitive kuliko members?

Member utilization factor inaonyesha relation ya axial force na bending along element kwa capacity ya member hiyo. Joint check inategemea local transfer ya forces na moments kutoka brace kwenda chord wall.

Direction ikibadilika, hata kama total force ndani ya jacket inabaki similar:

• Braces carrying tension na compression zinaweza swap.
• Entry angle ya brace force into chord inaweza kubadilika.
• In-plane na out-of-plane bending components zinaweza redistribute.
• Local punching demand katika particular tubular joint inaweza kuongezeka.

Increase ya local joint utilization wakati global loads zinapungua katika DiREC inaelezwa na load-path mechanism hii.

Effect ya yaw sign

All governing member cases zilihusishwa na -8° yaw misalignment. Most leading DiREC joint cases pia zilitokea kwa -8° yaw sign.

Ingawa +8° na -8° zina same absolute misalignment magnitude, structural response si symmetric. Possible reasons ni:

• Direction ya rotor aerodynamic thrust,
• Rotor na nacelle geometry,
• Nonlinear force transfer kati ya tower na jacket,
• Phase na directional combination ya wave na aerodynamic loads,
• Lack of continuous rotational symmetry katika three-legged jacket

.

Global base shear

Resultant ya horizontal reactions katika mudline ilihesabiwa kama:

\[ V(t)=\sqrt{F_x(t)^2+F_y(t)^2} \]

ambapo:

• F_x(t), F_y(t): Time-varying horizontal reaction components,
• V(t): Instantaneous base shear.

Overturning moment

Resultant ya moments about two horizontal axes ilihesabiwa kama:

\[ M_{OT}(t)=\sqrt{M_x(t)^2+M_y(t)^2} \]

.

Kulingana na table values:

• D-IFORM base shear ni approximately %2,1 lower than IFORM.
• DiREC base shear ni approximately %8,9 lower than IFORM.
• D-IFORM overturning moment ni approximately %2,3 lower than IFORM.
• DiREC overturning moment ni approximately %8,3 lower than IFORM.

Percentages hizi ni comparisons zilizohesabiwa kutoka table values.

Important limit ya DiREC global-response result

Kwa IFORM na D-IFORM, global time series zilitathminiwa across all load cases. Kwa DiREC, global response time series zilitolewa kwa structurally highest-ranked subset katika ULS checks.

Kwa hiyo values 10,59 MN na 356,61 MN·m zinapaswa kutafsiriwa si kama absolute global maxima across all 372 DiREC load cases, bali kama maxima za structurally selected governing subset.

Shape ya time series

Figure 15 inaonyesha high-response interval ya base shear. IFORM, D-IFORM na DiREC curves zina:

• Similar peak times,
• Similar fluctuation pattern,
• Comparable frequency content

.

IFORM na D-IFORM largely overlap, huku DiREC ikiwa na slightly lower amplitude katika most peaks. Study inahitimisha kwamba method selection katika example hii inabadilisha peak magnitude na local force distribution zaidi kuliko fundamental dynamic character ya global time series.

Detailed interpretation ya figures

Figure 1: D-IFORM projection logic

Normalized two-dimensional observations zina-projectiwa onto direction vectors kwa different angles. Same observation inapata different projection distance depending on vector direction. Hivyo states ambazo ni extreme katika particular environmental-variable combination zinajitokeza katika one-dimensional tail sample.

Figure 2: DiREC algorithm

Two polar plots zinaonyesha jinsi wave height na wind speed simultaneous with wave zinavyochaguliwa ndani ya directional sectors. Distribution plots chini zinaonyesha fitting ya univariate extreme-value distribution kwa sector samples na obtaining 50-year values.

Figure 3: 25 MW turbine na jacket geometry

Schematic inaonyesha 148 m tower, 78,2 m jacket na 65 m pile embedment pamoja. Wind load inaathiri rotor-tower region, wave na current loads zinaathiri submerged jacket members.

Figure 4: Jacket orientation

Plan view ya three legs inaonyesha one leg imewekwa facing dominant wave direction. Locations Leg 1, Leg 2 na Leg 3 zinatoa geometric reference kwa later directional-response results.

Figure 5: Wind-wave misalignment distribution

Histogram ina highest frequency katika small misalignment angles. Wind speed inapoongezeka, distribution inaconcentrate zaidi around 0°. Inset map inaonyesha North Sea site location.

Figure 6: Effect ya sector half-width

Six polar plots zinalinganisha ±5°, ±10° na ±15° filter results. ±5° curves ni more irregular na partially discontinuous. Kwa sababu ±10° na ±15° curves ni largely similar, ±10° ilichaguliwa kwa balance kati ya resolution na data quantity.

Figure 7: Coupled load environment

Left section inaonyesha aerodynamic na gravity loads kwenye rotor na tower, right section wave, current, gravity na pile-head springs kwenye jacket. Red interface node ni location ambako OpenFAST loads zilihamishwa kwenda Sesam model.

Figure 8: Soil-pile linearization

Nonlinear soil-response curve inawakilishwa na slope ya equivalent line around representative load level. Resulting linear springs zinatumika kwenye three pile heads.

Figure 9: Member identifiers

Positions za many jacket elements kutoka BM3 hadi BM57 zimewekwa relative to water level na seabed. Governing members kama BM39, BM42, BM26 na BM51 ziko kwenye different faces na bracing systems za jacket.

Figure 10: Ranked utilization factors

Katika member plot, DiREC iko lower at first rank lakini inabaki above au close to IFORM na D-IFORM katika subsequent ranks. Katika joint plot, DiREC inaunda highest curve kupitia most ranks. Plots hizi zinaonyesha wazi difference kati ya “single maximum” na “broad critical envelope.”

Figure 11: Joint identifiers

Tubular joints JT5–JT30 zimewekwa along jacket height. Governing JT28, JT23 na JT27 zimeunganishwa na different legs na bracing systems.

Figure 12: Comparison ya member na joint maxima

Kutoka IFORM kwenda DiREC blue member bar inapungua huku orange joint bar ikiongezeka. Graph inasummarize opposite effects za directional resolution kwenye global member maximum na local joint maximum.

Figure 13: Polar distribution ya critical states

Angular axis inaonyesha absolute wind direction, radial axis utilization factor, color wind-wave misalignment. Points hazijasambazwa evenly katika all directions; zinacluster especially around 315° na 195°.

Figure 14: Global loads

Base-shear na overturning-moment bars zinapungua kwa order IFORM, D-IFORM, DiREC. Ikiangaliwa peke yake graph hii inaweza kuonyesha DiREC inatoa lower demand, lakini inapaswa kutafsiriwa pamoja na local-joint increase katika Figure 12.

Figure 15: Base-shear time history

Distinct peaks zinatokea at approximately same times kwa all three methods. DiREC curve ina slightly lower peak amplitude, huku overall temporal shape ya signal ikiwa similar.

Nguvu za utafiti

• Large 25 MW-class three-legged jacket system isiyo na continuous rotational symmetry ilichunguzwa.
• IFORM, D-IFORM na DiREC zililinganishwa kwenye same turbine na support model.
• Absolute wind direction na wind-wave misalignment zilitathminiwa kama separate variables.
• DiREC iliscani -30° hadi +30° kwa 2° resolution.
• Six different absolute wind sectors zilitumika.
• Directional distribution ilitathminiwa kwenye 68-year metocean data basis.
• Effect ya wave-sector width kwenye sample count na curve smoothness ililinganishwa.
• Minimum 20 independent observations condition ilitumika.
• Aerodynamic, hydrodynamic, marine-growth na foundation-flexibility effects zilizingatiwa katika same analysis chain.
• Si global base loads pekee bali pia member- na joint-level code checks zilifanywa.
• 372 DiREC load cases zilitoa broad directional-response envelope.
• Negative na positive yaw signs zilisimulatewa separately.
• Opposite trends za member maximum na joint maximum zilionyeshwa wazi.
• Appendix inatoa wave-height na peak-period values kwa 2° increments kwa all sectors.

Mapungufu ya utafiti

• Study ni preprint ambayo haijapitia peer review.
• Results zinahusu one 25 MW reference turbine na one three-legged jacket geometry.
• Only a specific German North Sea site ilitathminiwa.
• Analysis ni limited to 50-year return period na DLC 6.1 ultimate-limit-state condition.
• Normal operation, fault states outside parked condition na other design load cases hazikuchunguzwa.
• Fatigue damage au long-term cycle accumulation haikuhesabiwa.
• Actual occurrence probabilities za DiREC sectors hazikujumuishwa kama weights katika final structural ranking.
• DiREC haijengi joint multivariate tail distribution ya wind na wave.
• Only six wind sectors kati ya 180°-360° ziliingizwa katika structural DiREC analysis.
• DiREC misalignment ililimitiwa ±30°; rarer larger misalignments hazikujumuishwa katika structural scan.
• Some directional intervals zilitolewa kutokana na insufficient sample katika narrow sectors.
• Superiority ya three-parameter Weibull model over other extreme-value distributions haikulinganishwa kwa comprehensive model-selection metrics.
• Confidence intervals za distribution parameters na 50-year return values hazikuripotiwa.
• Propagation ya metocean-data na model uncertainty kwenda structural UF results haikutolewa.
• Kwa sababu IFORM, D-IFORM na DiREC zina very different numbers of load cases, method effect na sampling-density effect haziwezi kutenganishwa fully.
• No statistical distribution across multiple independent turbulence au wave seeds reported kwa each load case.
• Soil behavior ni nonlinear; ililinearizewa katika representative load levels katika time-domain analysis.
• No probabilistic sensitivity analysis kwa pile-soil parameter uncertainty.
• Structural model haijavalidatewa dhidi ya measured response data ya actual 25 MW site turbine.
• Bidirectional dynamic feedback kati ya OpenFAST na Sesam haijadocumentiwa kwa detail.
• DiREC global base loads zilitolewa si kutoka all 372 cases bali structurally high-ranked subset.
• All utilization factors ziko karibu 0,20 au below; lighter au capacity-near optimized jacket inaweza kuonyesha different directional sensitivity.
• Equation 12 ina asymmetric notation katika exponent display ya moment terms.
• Author-specific CRediT contribution statement, conflict-of-interest na open-data-access statement hazipo katika PDF.

Study inaunga mkono nini?

• Katika three-legged jacket structures, absolute load direction inaweza kubadilisha ranking ya critical members na joints.
• Wind-wave misalignment inaweza kubadilisha local force transfer hata kwa same absolute wind direction.
• IFORM na D-IFORM zilitengeneza similar governing member maximum katika example hii.
• D-IFORM ilireorder secondary critical members na governing joint kwa sababu ya nonzero misalignments.
• DiREC ilitoa lower single member maximum lakini broader near-governing member envelope.
• DiREC iliongeza local tubular-joint demand kwa approximately %15,9 relative to IFORM.
• Most critical DiREC states ziliconcentrate katika 315° na 195° sectors.
• Largest structural demand haikulingana kila mara na highest sector-conditioned wave height.
• -8° yaw sign ilitengeneza more critical member cases kuliko equal-magnitude +8°.
• Global base loads zinaweza kupungua kwa directional detail huku local joint loads zikiongezeka.
• Assessment inayotegemea only base shear na overturning moment inaweza kukosa local directional effects.
• Simplified methods zinaweza kutoa value moja kwa global preliminary design, wakati directionally detailed methods zinatoa different value kwa local-joint verification.

Study haithibitishi nini?

• Haijathibitishwa kwamba DiREC daima inatoa higher joint demand katika all offshore structures.
• Haijaonyeshwa kwamba IFORM ni safe au overly conservative katika all jacket designs.
• 0,197 utilization factor haiwezi kugeneralizewa kwa all 25 MW jackets.
• Haijaonyeshwa kwamba 315° direction itakuwa governing katika other sites au jacket geometries.
• Haijathibitishwa kwamba -8° yaw ni always more critical than +8° kwa all turbines.
• Haiwezi kuhitimishwa kwamba highest wave height ni structurally unimportant.
• Haijaonyeshwa kwamba DiREC inachukua nafasi ya full long-term reliability analysis.
• Kwa sababu sector probabilities hazitumiki, DiREC ranking haiwezi kutafsiriwa directly kama total failure probability.
• Measured safety ya structure under real-sea 50-year conditions haijathibitishwa.
• Study haitoi direct result kuhusu fatigue life au damage accumulation.
• Lower DiREC base shear haimaanishi entire structure ni safer.
• Lower member maximum haionyeshi local joints zinakabiliwa na lower demand.
• Study haihesabu economically optimal jacket orientation au minimum steel weight.

Possible implication kwa offshore-wind design

Study inapendekeza simplified na detailed environmental methods zinaweza kutumika complementarily katika preliminary na detailed design stages.

Simplified IFORM na D-IFORM cases zinaweza kutoa conservative envelope kwa:

• Global base shear,
• Overturning moment,
• Initial foundation sizing,
• Rapid design comparison

.

High-direction-resolution methods kama DiREC zinaweza kuwa more informative kwa:

• Identifying critical tubular joints,
• Evaluating brace-chord force paths,
• Locating local thickening au can/stub regions,
• Optimizing jacket orientation,
• Adding near-critical load cases to design set

.

Future work inapaswa kuinclude sector occurrence probabilities katika structural ranking, kuchunguza different load cases na operating conditions, kutest method kwenye other jacket geometries, na ku-extend directional effect kwenye fatigue damage.

Mbinu na Matokeo ya Utafiti

Technical summary ya research design

Technical comparison ya environmental methods

Summary ya member na joint results

Summary ya global results

Core technical finding

Directional resolution haikubadilisha all response metrics katika same direction:

• Global base loads: Zilipungua katika DiREC.
• Highest member utilization: Ilipungua slightly katika DiREC.
• Near-governing member envelope: Ilipanuka katika DiREC.
• Local joint utilization: Iliongezeka clearly katika DiREC.
• Location ya critical elements: Ilireorderiwa according to direction na misalignment combination.

Kwa hiyo value inayopatikana from directional analysis si larger au smaller total load pekee. Main contribution ni kubainisha load inapita wapi ndani ya jacket na joints zipi zinaweza govern design.

Safety interpretation

All reported member na joint utilization factors ziko below 1,0 limit. Hata highest value 0,214 iko far from capacity limit. Structure inapita NORSOK ULS checks under investigated model na load cases.

Hata hivyo, low utilization factors hazimaanishi directional method si muhimu. Katika lighter au capacity-near optimized jacket, same percentage redistribution inaweza kubadilisha design decision au need ya local thickening.

Maelezo ya Chanzo na Mbinu

Full original title: Long-Term Extreme Response Analysis of 25 MW Offshore Wind Turbine Considering Wind-Wave Directional Effects

Authors and order: Mastaneh Moattari; Boso Schmidt; Chen Zhu; Elyas Ghafoori.

Equal contribution or co-first authorship: Hakuna equal-contribution au co-first-authorship statement katika PDF.

Corresponding author: Mastaneh Moattari.

Corresponding-author email: moattari@stahl.uni-hannover.de

Other author emails given in PDF: B.Schmidt@ibmb.tu-bs.de; C.Zhu@ibmb.tu-bs.de; ghafoori@stahl.uni-hannover.de

Institutional affiliations

1. Mastaneh Moattari and Elyas Ghafoori: Leibniz University Hannover, Institute for Steel Construction, ForWind, Hannover, Germany.
2. Boso Schmidt and Chen Zhu: Technical University of Braunschweig, Institute of Building Materials, Concrete Construction and Fire Safety, Braunschweig, Germany.

Source type: Preprint research article including numerical structural analysis, extreme-value statistics na environmental-contour comparison.

Research areas: Offshore wind turbines, jacket support structures, environmental contours, wind-wave directional misalignment, structural reliability, ultimate limit state na tubular joints.

Page count: 37.

Publication platform: SSRN.

SSRN posting date: 15 June 2026.

DOI: 10.2139/ssrn.6945781

Official link:SSRN study record

DOI link:DOI record

Peer-review status: Study haijapitia peer review. Every page ya PDF ina warning “Preprint not peer reviewed”.

Journal status: A record associated with same title on SSRN states study was submitted to Marine Structures journal. Hata hivyo, completion ya peer review, acceptance au journal publication haijathibitishwa.

Verified peer-reviewed journal information: Hakuna volume, issue, article number au official peer-reviewed publication date kwa current version.

Original journal publisher: Kwa kuwa peer-reviewed journal publication haijathibitishwa, haijabainishwa kwa current version. Current publication platform ya scientific text ni SSRN.

Funding and acknowledgments

Study iliungwa mkono na German Research Foundation Deutsche Forschungsgemeinschaft under Collaborative Research Center CRC 1463, “Integrated Design and Operation Methodology for Offshore Megastructures”, project number 434502799.

Researchers pia walitumia central computing cluster operated by Leibniz University IT Services. Funding record ya cluster ni INST 187/742-1 FUGG.

Author contributions

PDF haina CRediT contribution statement inayobainisha individually conceptualization, software, data processing, structural modeling, analysis, visualization au writing tasks za authors. Kwa hiyo individual author roles hazijainferiwa.

Conflict of interest

Uploaded PDF haina explicit conflict-of-interest statement. Absence ya statement haijatafsiriwa kama independent verification kwamba no conflict exists.

Data and code access

PDF inaeleza CoastDat-2, ERA5, FINO-1, CRC1463 design data, OpenFAST, TurbSim na Sesam sources. Hata hivyo, haitoi open repository link ya study-specific processed directional dataset, MATLAB DiREC code, Sesam model, OpenFAST input files au full time series za 372 simulations.

Article preparation method

Makala hii ya Kituruki iliandaliwa kwa kuchunguza title na author information, abstract, introduction, environmental-contour theory, D-IFORM projection scheme, DiREC algorithm, three-parameter Weibull equation, 25 MW turbine na jacket geometry, site na soil tables, wind-wave misalignment histogram, polar plots za six direction sectors, OpenFAST–Sesam analysis scheme, soil linearization, NORSOK utilization equations, member na joint tables, ranked utilization curves, global-load graphs, conclusions, limitations na all sector tables katika Appendix A ya uploaded 37-page preprint.

Scientific content inategemea only methods, data na results zilizowasilishwa katika uploaded PDF. External sources zilitumika only kuverify bibliographically title, author order, institution, DOI, SSRN posting date, platform na current publication status. Hakuna new structural result au metocean finding kutoka outside PDF iliyoongezwa.

Main methodological limit

Most important direct result ya study ni kwamba more detailed directional environmental characterization haiongezi uniformly global extreme loads; badala yake inaredistribute critical demand across different members, joints na directional states. DiREC ilipunguza maximum member utilization huku ikiongeza maximum local joint utilization.

Result hii inahusu single 25 MW reference turbine na single three-legged jacket model. DiREC kutoinclude directly sector occurrence probabilities katika structural ranking, global DiREC comparison kutegemea only selected high-ranked subset, na results kutovalidatewa kwa experimental field measurements vinapaswa kuzingatiwa kabla ya generalization.

Study ni preprint ambayo haijapitia peer review. Findings zinaonyesha directional environmental analyses zinaweza kuwa valuable especially kwa local-joint design katika next-generation jacket-supported turbines; hazithibitishi kwamba particular design standard, environmental-contour method au jacket orientation ni definitively superior katika all projects.