A reliability-constrained optimisation framework for offshore wind turbine support structures

Figures & data

Figure 1. Different OWT support structures and foundation concepts (Kirkwood, Haigh, and Bhattacharya 2014).

Figure 2. Flowchart of Reliability-Constrained Design optimisation framework.

Figure 3. Reference model geometry and dimensions.

Table 1. NREL 5 MW baseline wind turbine (Jm. Jonkman et al. 2009).

Item	Value
Rating	5 MW
Rotor orientation	Upwind
Control	Variable speed, collective pitch
Drivetrain	High speed, multiple stages, gearbox
Rotor diameter	126 m
Hub height	90 m
Cut-in, rated, cut-out wind speed	3, 11.4, 25 m/s
Cut-in, rated rotor speed	6.9, 12.1 rpm
Rated tip speed	80 m/s
Overhang, shaft tilt, precone	5 m, 5°^, 2.5°
Rotor diameter	126 m
Tower base diameter	6 m
Tower base thickness	0.027 m
Tower top diameter	3.87 m
Tower top thickness	0.19

Table 2. Wave load assumption and values.

Item	Description
Monopole Inertia Coefficient, Cm	1.6 (DNV GL 2016)
Monopile Drag Coefficient, CD	1.0 (DNV GL 2016)
Water Density, ${\rho }_{\mathrm{water}}$	1025 Kg/m^3
Horizontal Velocity of Water Particles, $u\left(z,t\right)$	The linear/Airy wave theory (Chakrabarti 2005)
Acceleration of Water Particles, $\dot{u}\left(z,t\right)$	The linear/Airy wave theory (Chakrabarti 2005)

Figure 4. Applied loads on OWT support structure.

Table 3. Wind turbine aerodynamic loads, (Jm. Jonkman et al. 2009).

Load Case	Tilting moment (kN.m)	Thrust force (kN)
ULC	38567	781
FLC	3687	197

Table 4. Design load cases, (IEC 2005).

Load case	Wind	Wave	Load safety factor
Ultimate: DLC 6.1b/2.1	EWM: $V_{g50}$	RWH: $1.32\times H_{s50},T_{s50}$	– 1.0
(Parked)		ECM: $V_{c,\mathrm{ex}}$
Fatigue: DLC 6.1b/2.1	NTM: $V_{\mathrm{ave}}$	NSS: $H_{\mathrm{ave}},T_{\mathrm{ave}}$	Normal N 1.1/1.35
(Parked)		No Current

Figure 5. NREL 5MW wind turbine and OC3 platform geometry.

Figure 6. Isometric view of geometry and applied loads.

Table 5. Sand properties in different levels (Jung et al. 2015).

Sand Type	Young’s Modulus (MPa)	The angle of friction (deg)	Friction coefficient	Yield stress (kPa)
Loose	30	33	0.40	59.2
Medium	50	35	0.43	58.5
Dense	80	38.5	0.48	57

Table 6. Support structure material properties.

Item	Steel	Grout
Young Modulus, E (GPa)	210	70
Density (kg/m^3)	8500	2740
Poisson’s ratio	0.38	0.19
Tensile Strength (MPa)	–	10
Yield Strength (MPa)	355	–

Figure 7. Final generated mesh.

Table 7. Mesh sensitivity.

Description	Element size of Steel part	Number of Elements	Max Von Mises (MPa)
Mesh #1	4 m	1780	25.4
Mesh #2	2 m	7584	23.1
Mesh #3	1 m	37356	23.0
Mesh #4	0.5 m	235180	23.0

Table 8. Deformation in the reference model and current model.

Load case	Deformation
Mass/Thrust	Current model	Reference model	%Diff
2MN + Weight	1.676 m	1.644 m	+1.94%

Figure 8. Design variables of OWT support structure.

Figure 9. Illustration of typical excitation ranges of a modern OWT (Kallehave et al. 2015).

Table 9. Settings of GA.

Parameter name	Value
Number of initial samples	200
Number of samples per iteration	50
Convergence stability criteria	1.5%
Maximum number of iterations	25
Crossover probability	0.9
Mutation probability	0.01

Table 10. Design Variables (Jm. Jonkman et al. 2009).

Stochastic variables	Ultimate load case		Fatigue load case		CoV	Distribution type
	Mean value	Standard deviation	Mean value	Standard deviation
Wind Thrust (kN)	781	78.1	197	19.7	0.1	Normal
Torsional Moment (kN.m)	38,567	3856.7	3686	368.6	0.1	Normal
Tilting Moment (kN.m)	7876	787.6	3483	348.3	0.1	Normal
Steel Young’s Modulus (GPa)	210	21	210	21	0.1	Normal
RNA Mass (Tonne)	350	35	350	35	0.1	Normal

Figure 10. FEA DO analysis results for design candidate 1, (a) Von Mises equivalent stress, (b) Buckling deformation, (c) mudline displacement, (d) Total deformation, (e) 1st mode frequency and displacement, (f) Fatigue minimum safety factor.

Table 11. Deterministic optimisation results.

	Variable	Name	Unit	Lower bound	Initial design	Optimised design (Candidate 1)	Optimised design (Candidate 2)	Upper bound
Design Variables	Monopile base diameter	X1	[m]	5	6	6.10	6.10	7
	Monopile top diameter	X2	[m]	5	6	5.34	5.28	7
	Tower base diameter	X3	[m]	5	6	5.28	5.28	7
	Tower top diameter	X4	[m]	3	3.87	3.28	3.38	4.5
	Tower base thickness	X5	[mm]	20	27	30	31	40
	Tower Int1 thickness	X6	[mm]	20	25	26	26	40
	Tower Int2 thickness	X7	[mm]	15	22	21	22	35
	Tower top thickness	X8	[mm]	10	19	17	17	30
	Monopile substructure base thickness	X9	[mm]	45	60	46	45	70
	Monopile substructure top thickness	X10	[mm]	45	60	45	45	70
	Monopile foundation base thickness	X11	[mm]	40	60	45	46	70
	Monopile foundation top thickness	X12	[mm]	45	60	46	45	70
	Transition piece thickness	X13	[mm]	25	30	33.54	33.43	40
Objective function Constraints	1st Natural frequency		[Hz]	0.21	0.285	0.231	0.223	0.328
	Maximum equivalent Stress (Von Mises)		[MPa]	–	185	287	299	323
	Pile head deflection		[m]	–	0.057	0.079	0.08	0.1
	Pile head rotation		[°]	–	0.26	0.34	0.34	0.4
	Buckling load multiplier		–	1.4	2.35	1.68	1.56	–
	Minimum fatigue safety ratio		–	1.15	1.54	1.19	1.21	–
Mass Saving	Support Structure mass		[Tonnes]	–	924.5	741.4 (−19.7%)	739.1 (−19.95%)	–

Figure 11. Global sensitivity analysis.

Figure 12. Cumulative density function and probability density function of design candidate 1 for (a) Fatigue minimum safety factor; (b) Equivalent stress maximum; (c) First natural frequency; (d) Buckling load multiplier; (e) Total deflection.

Table 12. Reliability-Constrained analysis result.

Reliability-Constrained Candidate Designs Comparison
	Initial Design		Candidate Design 1		Candidate Design 2
	Pf	β	Pf	β	Pf	β
Ultimate Limit State
Max Stress Capacity	1.3E-06	4.71	3.0E-5	4.01	3.5E-5	3.99
Buckling Capacity	≈0	7.01	4.1E-5	3.94	5.3E-5	3.88
Maximum Deflection	≈0	7.61	6.0E-8	5.28	9.0E-8	5.21
Resonance Capacity	2.1E-08	5.48	5.9E-5	3.85	2.1E-4	3.53
Fatigue Limit State
Min Safety Factor	8.0E-06	4.32	6.1E-05	3.84	7.9E-5	3.81

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