Executing FloatingSE by hand is sufficient to explore some simple one-off or comparison analyses between a few runs. OpenMDAO provides extensive optimization capability, which can give yield richer and more insightful analyses.
In WISDEM, via OpenMDAO, any input parameter can be designated a design variable. The design variables used in this study focused on the geometric specification of the floating substructure and mooring subsystem. Slightly different design variables and bounds were used for spar, semisubmersible, and TLP optimizations. The complete listing of the design variables for each optimization configuration is shown in tbl_designvar. Note that the integer design variables were only used in the global optimization with the genetic algorithm, not the local search with the simplex algorithm.
Variable Name Units Type Bounds Main col section height main_section_heightFloat array (ns) 0.1–50 Main col outer diameter main_outer_diameterFloat array (ns + 1) 2.1–40 Main col wall thickness main_wall_thicknessFloat array (ns + 1) 0.001–0.5 Main col freeboard main_freeboardFloat scalar 0–50 Main col stiffener web height main_stiffener_web_heightFloat array (ns) 0.01–1 Main col stiffener web thickness main_stiffener_web_thicknessFloat array (ns) 0.001–0.5 Main col stiffener flange width main_stiffener_flange_widthFloat array (ns) 0.01–5 Main col stiffener flange thickness main_stiffener_flange_thicknessFloat array (ns) 0.001–0.5 Main col stiffener spacing main_stiffener_spacingFloat array (ns) 0.1–100 Main col permanent ballast height main_permanent_ballast_heightFloat scalar 0.1–50 Main col buoyancy tank diameter main_buoyancy_tank_diameterFloat scalar 0–50 Main col buoyancy tank height main_buoyancy_tank_heightFloat scalar 0–20 Main col buoyancy tank location (fraction) main_buoyancy_tank_locationFloat scalar 0–1 Number of offset cols number_of_offset_columnsInteger scalar 3-5 Offset col section height offset_section_heightFloat array (ns) 0.1–50 Offset col outer diameter offset_outer_diameterFloat array (ns + 1) 1.1–40 Offset col wall thickness offset_wall_thicknessFloat array (ns + 1) 0.001–0.5 Offset col freeboard offset_freeboardFloat scalar 2–15 Offset col stiffener web height offset_stiffener_web_heightFloat array (ns) 0.01–1 Offset col stiffener web thickness offset_stiffener_web_thicknessFloat array (ns) 0.001–0.5 Offset col stiffener flange width offset_stiffener_flange_widthFloat array (ns) 0.01–5 Offset col stiffener flange thickness offset_stiffener_flange_thicknessFloat array (ns) 0.001–0.5 Offset col stiffener spacing offset_stiffener_spacingFloat array (ns) 0.01–100 Offset col permanent ballast height offset_permanent_ballast_heightFloat scalar 0.1–50 Offset col buoyancy tank diameter offset_buoyancy_tank_diameterFloat scalar 0–50 Offset col buoyancy tank height offset_buoyancy_tank_heightFloat scalar 0–20 Offset col buoyancy tank location (fraction) main_buoyancy_tank_locationFloat scalar 0–1 Radius to offset col radius_to_offset_columnFloat scalar 5–100 Pontoon outer diameter pontoon_outer_diameterFloat scalar 0.1–10 Pontoon wall thickness pontoon_wall_thicknessFloat scalar 0.01–1 Lower main-offset pontoons lower_attachment_pontoons_intInteger scalar 0–1 Upper main-offset pontoons upper_attachment_pontoons_intInteger scalar 0–1 Cross main-offset pontoons cross_attachment_pontoons_intInteger scalar 0–1 Lower offset ring pontoons lower_ring_pontoons_intInteger scalar 0–1 Upper offset ring pontoons upper_ring_pontoons_intInteger scalar 0–1 Outer V-pontoons outer_cross_pontoons_intInteger scalar 0–1 Main col pontoon attach lower (fraction) main_pontoon_attach_lowerFloat scalar 0–0.5 Main col pontoon attach upper (fraction) main_pontoon_attach_upperFloat scalar 0.5–1 Fairlead (fraction) fairlead_locationFloat scalar 0–1 Fairlead offset from col fairlead_offset_from_shellFloat scalar 5–30 Fairlead pontoon diameter fairlead_support_outer_diameterFloat scalar 0.1–10 Fairlead pontoon wall thickness fairlead_support_outer_thicknessFloat scalar 0.001–1 Number of mooring connections number_of_mooring_connectionsInteger scalar 3–5 Mooring lines per connection mooring_lines_per_connectionInteger scalar 1–3 Mooring diameter mooring_diameterFloat scalar 0.05–2 Mooring line length mooring_line_lengthFloat scalar 0–3000 Anchor distance anchor_radiusFloat scalar 0–5000
Due to the many design variables, permutations of settings, and applied physics, there are many constraints that must be applied for an optimization to close. The constraints capture both physical limitations, such as column buckling, but also inject industry standards, guidelines, and lessons learned from engineering experience into the optimization. As described in the Introduction, this is a critically important element in building a MDAO framework for conceptual design that yields feasible results worth interrogating further with higher-fidelity tools. The constraints used in the substructure design optimization and sensitivity studies are listed in tbl_constraints. Where appropriate, some of the constraint values differ from one type of substructure to another. Some additional explanation is provided for a handful of constraints in the subsections below.
Lower Variable Upper Comments Tower / Main / Offset Columns Eurocode global buckling 1.0 Eurocode shell buckling 1.0 Eurocode stress limit 1.0 Manufacturability 0.5 Taper ratio limit 120.0 Weld-ability Diameter:thickness ratio limit Main / Offset Columns Draft ratio 1.0 Ratio of draft to max value API 2U general buckling- axial loads 1.0 API 2U local buckling- axial loads 1.0 API 2U general buckling- external loads 1.0 API 2U local buckling- external loads 1.0 Wave height:freeboard ratio 1.0 Maximum wave height relative to freeboard 1.0 Stiffener flange compactness 1.0 Stiffener web compactness Stiffener flange spacing ratio 1.0 Stiffener spacing relative to flange width Stiffener radius ratio 0.50 Stiffener height relative to diameter Offset Columns Semi only 0.0 Heel freeboard margin Height required to stay above waterline at max heel 0.0 Heel draft margin Draft required to stay submerged at max heel Pontoons Semi only Eurocode stress limit 1.0 Tower -0.01 Hub height error 0.01 Mooring 0.0 Axial stress limit 1.0 Line length limit 1.0 Loss of tension or catenary hang Heel moment ratio 1.0 Ratio of overturning moment to restoring moment Surge force ratio 1.0 Ratio of surge force to restoring force Geometry 1.0 Main-offset spacing Minimum spacing between main and offset columns 0.0 Nacelle transition buffer Tower diameter limit at nacelle junction -1.0 Tower transition buffer 1.0 Diameter consistency at freeboard point Stability 0.10 Metacentric height Not applied to TLPs 1.0 Wave-Eigenmode boundary (upper) Natural frequencies below wave frequency range Wave-Eigenmode boundary (lower) 1.0 Natural frequencies above wave frequency range 0.0 Water ballast height limit 1.0 0.0 Water ballast mass Neutral buoyancy
Words tbl_geomconvar
Variable Type Description max_draftFloat scalar Maximum allowable draft for the substructure
Manufacturing steel frustum shells requires rolling steel plates into shape and welding along a seam to close the section. To accommodate traditional rolling and welding practices, both the diameter taper over the course of a section and the wall thickness ratio relative to the diameter are capped. Similarly, to facilitate welding the semisubmersible pontoons to the columns, constraints regarding the radio of diameters between the two are enforced. These limits are determined by user parameters in tbl_manconvar and constraints,
Variable Type Description min_taper_ratioFloat scalar For manufacturability of rolling steel min_diameter_thickness_ratioFloat scalar For weld-ability connection_ratio_maxFloat scalar For welding pontoons to columns
The stress and buckling code compliance constraints are formulated as utilization ratios (ratio of actual to maximum values), with a safety factor, which must be less than one. The safety factor parameters are listed in tbl_safetyvar.
Variable Type Description gamma_fFloat scalar Safety factor on gamma_bFloat scalar Safety factor on buckling gamma_mFloat scalar Safety factor on materials gamma_nFloat scalar Safety factor on consequence of failure gamma_fatigueFloat scalar Not currently used
As described above, surge and pitch stability are enforced through similar approaches. The total force and moment acting on the turbine are compared to the restoring forces and moments applied by the mooring system, buoyancy, or other sources at the maximum allowable point of displacement. These constraints are formulated as ratios with the user specifying the maximum allowable limits via the variables in tbl_moorcon.
Variable Type Units Description max_offsetFloat scalar m Max surge/sway offset operational_heelFloat scalar deg Max heel (pitching) angle in operating conditions max_survival_heelFloat scalar deg Max heel (pitching) angle in parked conditions
Different anaylses will emphasize different metrics, requiring different objective functions. Under the default assumption that the user wishes to minimize cost and adhere to stability constraints, the objective function would be total substructure cost (variable name, total_cost) or mass (variable name, total_mass).
Example of optimized spar.
Example of optimized semi.
Example of optimized TLP.