Surrogate based optimization approach
The idea behind surrogate-based optimization is to replace the expensive simulation with pre-trained statistical models to be able to accurately emulate the objective function.
The workflow of SBO is shown below. First, a surrogate model is built with sufficient accuracy, then the optimum is found by optimizing the objective function by evaluating the surrogate model, rather than using expensive simulations.
A surrogate model is used to map input data to output data when the actual relationship between the two is unknown. It acts as a curve-fit between the input and output and can hence make predictions without the need for expensive simulations.
A single surrogate evaluation is much faster than the original time-consuming computer simulation and hence is easier to perform many output evaluations. This allows us to explore the landscape of the objective function, substantially speeding up the optimization process.
The optimization is a constrained single-objective optimization routine that seeks to find the best combination of decision variables to minimize the material cost, Cm, of the mooring lines. The material cost is determined by multiplying the unit cost of each line, pm, times the length of the unstretched line.
The minimization of the material cost of the mooring lines should not affect the performance and stability requirements of the FOWT. In order to achieve the required wind turbine performance and to maintain the stability of the platform and wind turbine, certain performance criteria have been evaluated, as explained below.
The critical steady-state offset for FOWTs is the offset in pitch, ROTY. A large offset in pitch compromises the efficiency of the wind turbine by causing the rotor to be at an angle relative to the inflow, thus also introducing complicated loading to the turbine (Wayman, 2006). If the pitch offset is too large, it may cause the turbine to capsize, which is not desirable. Pitch has been limited to have a maximum value of 10 deg, as it is speculated that a pitch larger than this will substantially decrease the efficiency of the turbine (Wayman, 2006).
The translational motion along the x-axis is called the surge motion, Ux, and is another important criterion that is to be considered. Surge motion is constrained to not cause excessive motions of the platform, so as to not damage the power cable that is used to connect the turbines to the grid.
Another critical performance criteria which the structure has to be evaluated for is the motion of the wind turbine nacelle (tower top acceleration), q. Large motions of the nacelle could cause degradation of turbine performance and damage to the equipment in extreme wave conditions (Sclavounos et al., 2008), hence it is desirable to limit the acceleration as much as possible.
Lastly, the static plus the dynamic line tension, T, in each of the mooring lines should not exceed the breaking load of the mooring lines. Hence, maximum tensions at the anchor and fairlead for each line have been limited to be less than the line breaking load, as well as less than that obtained for the reference turbine.
Each of the performance criteria under consideration has been compared to the values obtained from the simulation of the reference turbine
Mooring cost is directly dependent on the length of the mooring line installed and hence the shortest length of the mooring line is desired in order to reduce the cost. The shortest length of the mooring line may not satisfy all the design criteria defined above. It is essential to add the constraints to limit the search space to feasible solutions, so as to accurately represent real engineering limitations on the decision variables. The constraints added to the design criteria are tabulated below.
| Tower top acceleration, qrms,ref | Surge, Ux,max,ref | Pitch, ROTYmax,ref |
|---|---|---|
| 0.279 m/s2 | 24 m | 0.207 rad |