DSD with categorial Factor

[#1]

Hello Everyone,

I am a masters student currently finishing my thesis. The objective of the thesis is to increase vertical axis wind turbine efficiency by adding winglets and optimizing the winglets design parameters to maximize efficiency (using DOE).

The design parameters of these winglets consist of 7 continuous parameters, and 1 categorial parameter (2-level).

I am lost on how to proceed after finishing the 22 runs of DSD (I still have few runs to finish but I am planning ahead because I am running out of time). I've read that augmenting the design is a good approach to fit an RSM, but can someone help me on that? Especially that I have a categorial factor I am not sure how to fit a RSM with this factor (should there be 2 equations each for a level of this categorial factor, or combined in 1 equation?)

Thank you so much for your help!

[#2]

Except it's not empirical, it's theoretical.

[#3]

@statman You’re absolutely right that CFD itself is a theoretical model based on the governing physics rather than direct experimental observation.

However, in my case the computational model has been validated against experimental data from the literature before running the DSD study. So while the underlying solver is theoretical, its predictive behavior has been benchmarked to ensure physical accuracy.

The DOE is then used to "empirically" explore and approximate how that validated model responds to changes in design and operating variables - essentially treating the CFD results as "data" for building a response surface (RSM) and identifying key interactions and optima.

So while the underlying physics is theoretical, the design-space exploration and statistical modeling remain empirical within that verified framework.

[#4]

Understood and I don't mean to be argumentative, but the simulation models don't know how to simulate real noise.  When I think of empirical data, I think of real physical experiments being conducted with actual noise in the study (BTW, this means any noise you have identified, varies during the study).  Since this is not what you are doing, you can';t really call it empirical.

This from AI:

To say something is an empirical model means that the model is based primarily on observations, measurements, or experimental data, rather than on first-principles theory (e.g., fundamental physics or mathematical derivation from basic laws).

[#5]

You’re absolutely right, simulation models don’t include real experimental noise, and in that strict sense, they’re not empirical data.

I appreciate the clarification!