Integrating Seakeeping Analysis into the Design of Floating Systems
Figure 5: Estimated Pareto Frontier and Selected Hull Shapes After 2,000 Designs
0.12
1,972
0.11
Highest payload
0.10 0.09 0.08 5.6 5.8 6.0 Displacement/payload ratio
6.2
Δ
mpayload
6.4 6.6
Good compromise design
1,739
1,918
1,608 1,550
1,588
Best seakeeping performance
Design 1972
mpayload
Pd
= 8940t = 0.1098
variables are computationally too expensive. We distinguish between single- and multi-objective optimisation problems. Single objective problems are solved with the Nelder–Mead simplex algorithm if only small modifications to a proven initial design are expected, and genetic algorithms are applied if a broader exploration of the design space is called for.7
In multi-objective cases we develop the Pareto
frontier of non-dominated (optimal) designs with a version of Deb’s epsilon multi-objective evolutionary algorithm (MOEA technique).8
Non-dominated designs can only be improved in one objective fi by encumbering deterioration in at least one other objective fj. The ideal case would be a design that minimises all objective functions fi at the same time. However, this so-called ideal solution, F(0), is hypothetical
in most practical applications because it is commonly not part of the feasible domain and therefore cannot be reached.
Optimisation Example
Definition of an optimisation task starts with the implementation of the hull generation rules. Here we optimise a semi-submersible with four quadratic columns and two pontoons with rectangular cross-section. The structure is double-symmetric to the x=0 and y=0 planes. Figure 4 explains the main form parameters used to model one quarter of the platform. All designs have a fixed volumetric displacement of ∆=51,250 cubic metres.
Free Variables
Free variables define the characteristics the optimisation process is allowed to change. In most cases we can achieve a wide range of hull shapes with fewer than a dozen variables. Often it is beneficial to set up ratios of form parameters as free variables. Table 1 summarises the eight free variables selected for the semi-submersible optimisation.
Objectives
Two objectives are to be minimised: ratio of total displacement to payload on deck and motion response for a target area of operation in the north-east Atlantic. The computation of response amplitude operators (RAOs) of the vessel for forces and motions in waves is performed by the linear 3D diffraction–radiation programme WAMIT®.9
Two-parameter Pierson–Moskowitz spectra are used
88
Pd
Design 1918
mpayload
= 8790t = 0.0995
Design 1588
mpayload
Pd
= 7825t = 0.0959
combined with long-term wave statistics for the Marsden Square 182 in the north-east Atlantic.10
Expected downtime probability is a statistical estimate of the vessel performance in a real ocean environment. Its absolute values are of minor importance and should be exploited with great care. However, the expected downtime probability represents an elaborate measure suitable for comparing different designs. More details can be found in articles by Birk.1,11
In the example presented below we minimise the expected downtime due to accelerations at a point off-centre of the structure and 30m above the waterline (x=y=z=30m). Operation is halted if acceleration exceeds 5% of gravitational acceleration.
Constraints
The following constraints have been recognised for optimisation:
• the metacentric height GM at working draft has to be least 1.2m; • the metacentric height GMsurvival at survival draft has to be least 0.6m; • the height of pontoons has to be <20m;
• the gap between pontoons has to be ≥50m to allow work-over barges to move under the deck;
• the maximum beam overall has to be <150m; • the column’s outer edges have to be ≥0.75m from the pontoon edges to facilitate welding; and
• the ballast in survival condition has to be positive otherwise the semi-submersible could not be de-ballasted to survival draft.
If one or more of the constraints are violated, the design is marked as unfeasible.
Optimisation Results
The optimisation algorithm starts by creating 400 designs for the initial population. Over the course of the next 1,000 designs the Pareto frontier is pushed towards the hypothetical ideal solution, improving both deck load capacity and seakeeping
EXPLORATION & PRODUCTION – VOLUME 8 ISSUE 1
Expected downtime Pd
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