topic Re: DSD with categorial Factor in Discussions

DSD with categorial Factor

Mohnasre — Fri, 07 Nov 2025 06:29:12 GMT

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!

Re: DSD with categorial Factor

Victor_G — Fri, 07 Nov 2025 08:09:12 GMT

Hi @Mohnasre,

Welcome in the Community !

You can read the documentation linked to Augment Designs platform.
The process to augment a design is quite straightforward:

Based on the modeling of the responses in your original design, identify key important factors that appear in effect terms of the models.
Open the Augment Designs platform, specify the key factors you want to keep in the design augmentation and the responses, and choose an augmentation method. I would recommend at this stage to check the option Group new runs into separate block, as it will introduce a block effect for the second round of experiments that you can use to check if your average response didn't change between the two stages of the design (original vs. augmented) as well as to track any variance difference between the two stages:

If your goal is to augment the initial DSD to fit a Response Surface Model (RSM) on the identified important factors, you can choose Augment, as it will allow you to specify the assumed model you want to be able to fit thanks to the augmented design:

Note that in my screenshot I kept all factors from the original 22-runs DSD, which makes the number of runs to add quite high (48 in total, including the 22 original runs, so 26 new runs to add). In your situation, you may augment the design with less factors, depending on the importance and significance of these factors based on the analysis of your original DSD.

Concerning your second question, a categorical factor will appear in the model as a "If Then" rule, like in this example:

In this example, "Hydrolyze" and "Pre-Soak" are two 2-levels categorical factors. Depending on the level set in the experiment, it will have a positive or negative effect on the response. For example, taking the example of the main effect linked to factor "Hydrolyze" (first Match function appearing in the equation), if the experiment is set at level L1, then the response will increase on average by 0,3794[...]. If the experiment is set at level L2, the response will decrease on average by -0,3794[...].

Note that categorical factors with 2 levels will have the same absolute value for the coefficients of these level, but opposite signs. If you have several levels for a categorical factor, these levels coefficients are linked by the equation: L1 + L2 + L3 + ... = 0.

Hope this answer will help you,

Re: DSD with categorial Factor

Mohnasre — Fri, 07 Nov 2025 08:16:14 GMT

Hello @Victor_G

Thank you for your response!

I am planning to use I-optimal augmentation strategy after the DSD, but I can't afford to run 24 extra runs. I was hoping that I would need 10 extra runs max. Is that possible?

Re: DSD with categorial Factor

Victor_G — Fri, 07 Nov 2025 08:42:15 GMT

Yes there may be several options possible, but the runs you couldn't afford to build your model will increase the uncertainty and lack of precision of your RSM model.

An option consists in creating a Bayesian I-Optimal model, where the estimability of some terms are set to "If Possible" instead of "Necessary". To do this, left-click on the estimability of the effects you want to change, and set it to "If Possible":

This will have the effect to reduce the required number of runs, but you may end up not able to include these "If Possible" terms in the model, as the creation of new runs will enforce the estimation of "Necessary" effects before the "If Possible" terms. So you have to carefully choose and evaluate the trade-off between the reduction of runs and the assumed model you want to fit.

Another option could have been to do a space filling augmentation, but the presence of your categorical factor will prevent you from this option.

Finally, I would encourage you to wait to have all your results and spend some time on the analysis. Some factors and terms may not be significant and practically important in the evaluation of your responses, so it may simplify the assumed model you want to use in the augmentation phase, by removing non important terms and respecting the principles of Effect Heredity, Effect Sparsity and Effect Hierarchy.

Hope this answer will give you some ideas for later,

Re: DSD with categorial Factor

statman — Fri, 07 Nov 2025 14:40:49 GMT

Just curious, are you actually making physical samples and multiple turbines, or are you using simulation software to run your tests?

Re: DSD with categorial Factor

Mohnasre — Fri, 07 Nov 2025 18:18:22 GMT

Thank you so much @Victor_G !!

Last thing, are there any videos (workshops or courses) that you recommend watching for DSD and augmentation?

I appreciate your help!

Re: DSD with categorial Factor

Mohnasre — Fri, 07 Nov 2025 18:19:43 GMT

Hello @statman ,

No I am just doing numerical simulations. At first we planned to make experiments as well, but due to lack of time, we are only doing numerical simulations (CFD) on ANSYS.

Re: DSD with categorial Factor

statman — Fri, 07 Nov 2025 20:22:16 GMT

Then why are you doing fractional factorials? Do you have limited computing power? Realize the models already exist for those programs. At best, you may uncover what models they are using, but if their models are inappropriate for your situation, then the results will be similarly poor. For example, if you have a tractor you'd like to learn about and it isn't in their model, you will find the factor to be insignificant. Not very useful for discovery work.

You should read:

Bradley Jones (2016) 21st century screening experiments: What, why, and how, Quality Engineering, 28:1, 98-106, DOI: 10.1080/08982112.2015.1100462.

Bradley Jones (2016) Rejoinder, Quality Engineering, 28:1, 122-126, DOI: 10.1080/08982112.2015.1100468

Jones, B., & Nachtsheim, C. J. (2011). A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects. Journal of Quality Technology, 43(1), 1–15. https://doi.org/10.1080/00224065.2011.1191784

Jones, B., & Nachtsheim, C. J. (2013). Definitive Screening Designs with Added Two-Level Categorical Factors^*. Journal of Quality Technology, 45(2), 121–129. https://doi.org/10.1080/00224065.2013.11917921

In addition, Brad has some Powerpoint presentations you find by doing a search.

Re: DSD with categorial Factor

Mohnasre — Fri, 07 Nov 2025 20:26:54 GMT

@statman

Yes I have limited time and computing power.

The objective is to find the optimum design for the winglets using DOE. But due to the many design parameters, I thought of doing a screening design first to check the most influential parameters, and then optimize them by augmenting the DSD.

Each run is a 3D CFD simulation, which can take up to 3 days depending on number of elements in the mesh. So I can't afford making a full factorial design with 8 parameters, it would take me forever to finish this. That is why a screening design is the best approach for my case.

Re: DSD with categorial Factor

Mohnasre — Fri, 07 Nov 2025 20:36:23 GMT

Just to make things clearer, I’m not trying to discover the built-in CFD equations in ANSYS Fluent. The Navier–Stokes model and turbulence framework are, of course, fixed.

My goal is to use a statistical design (initially a Definitive Screening Design) to explore how geometry and design variables — such as tip speed ratio, cant angle, tip twist, and number of winglets — influence the power coefficient (Cp) of a vertical-axis wind turbine within that physical model.

In other words, I’m not questioning Fluent’s internal physics; I’m using DOE to build an empirical response surface that quantifies how these design inputs interact and where the optimum performance region lies to maximize Cp.

Since each simulation run is computationally expensive, a screening design like a DSD helps minimize the number of simulations while still capturing curvature and key interactions.

So, while I agree with your general warning, in this case DOE isn’t being used to uncover the solver’s equations, it’s being used to optimize design performance within that modeling framework.

I hope it's clearer now!

Thank you!

Re: DSD with categorial Factor

statman — Sat, 08 Nov 2025 18:25:40 GMT

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

Re: DSD with categorial Factor

Mohnasre — Sat, 08 Nov 2025 18:41:24 GMT

@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.

Re: DSD with categorial Factor

statman — Sun, 09 Nov 2025 17:54:17 GMT

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).

Re: DSD with categorial Factor

Mohnasre — Mon, 10 Nov 2025 04:21:39 GMT

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!