Response surface is a high dimensional polynomial that represents a relation between set of inputs and outputs. It generates a synthetic data and can be used as a surrogate model. By using response surface equations, the chosen design space can be explored with a lower computational cost.
Response surface needed to be calibrated using the input output relations from the simulations. Instead of running simulations for all possible values of design parameters in a given range, examining responses at properly selected points using Design of Experiments (DoE) is adequate and computationally cost effective.

This study will represent the application of response surface methodology to calculate load outputs of NREL 5MW wind turbine for different blade geometries. Blade geometry is defined by chord and twist distribution and thickness-to-chord (t/c) ratio of airfoils. Chord and twist values at 19 points along the span are varied 5% from the baseline and the t/c of 6 different airfoils are varied 3% from the baseline. The inflow conditions are defined by the turbulence intensity percentage, power law coefficient, surface roughness and mean wind speed. There are 48 design parameters total defining our design space.

Screening process will be implemented first, in order to decrease the number of design parameters. Screening eliminates unimportant design parameters for the design objective to reduce design space. The selection of unimportant parameters are done by the sensitivity analysis. This is implemented by observing the change in the response while all values of relevant design parameters are swept in their respective ranges. Usage of DOE decreases the computational cost. JMP Statistical Analysis Software will be used for DOE creation, sensitivity analysis and response surface equation calculation and FAST code will be used to calculate loads for different blade geometries and inflow conditions. A two-level resolution IV fractional factorial design will be used in the DOE methodology for screening purposes. Here, main effects are not confounded with other effects but some two-factor interactions are confounded with other two-factor interactions. FAST simulations are run for each DOE points and loads are recorded. Important parameter subset will be chosen by using the Pareto principle, 80% of the change in the output is due to the 20% of the inputs.

After eliminating the unimportant parameters, response surface will be fitted to outputs for a small number of design parameters. Central composite design will be used this time as DOE method since three distinct values for each factor are needed to fit a quadratic function. For important parameters' configuration, DOE will be used and for the eliminated design parameters baseline values will be used since their effects on the loads are low. Again FAST simulations will be run and loads will be recorded and using these input output relations a response surface will be fitted. The quality of the fit will be checked by comparing the values of the actual and the predicted and calculating the residual values and their distribution. Since DOE points are used to fit the response surface, the prediction of the model for these points should be very close to the actual values. But for the points beside the ones at DOE but still in the defined design space, the response surface should still be working. For this purpose model representation error will be checked at random points other than DOE points.

Finally response surface equations will be calculated. And instead of running time consuming simulations, the defined design space can be investigated by using this equation only for corresponding load output for a chosen blade geometry and inflow conditions.