Is a D optimal Design useful in this case?

[#1]

I have the following problem for which an experimental design has to be created:

The stress at a certain point of a model is to be determined by FEA. This model is varied by setting three different parameters. These parameters are to be varied in such a way that the stress is minimized. The stress should be the target value. Angle, modulus and radius are the factors whose influence must be investigated.

Now comes the more complex part of defining the factors and levels:

Angle: 3 levels for different angles

Module: 9 different modules

Radius: for each combination of angle and module there is a different lower and upper limit between which each value can be assumed

My question now is how best to deal with the dependency of the radius? Should the radius simply be normalized between 0 and 1 in the doe and then converted when the radius is used in the experiment?

Would you assume discrete numerical factors oder categorical factors for angle and modulus in this case... that still confuses me.

According to my research so far, a D optimal design would be best to collect the data and then RSM to find the optimal parameter combination for the optimality criterion?

Are there better ways to solve the problem?

Thank you so much.

[#2]

I think the idea of using a normalized Radius factor makes sense.

i would not use Discrete Numeric unless you are restricted or forced to use specific values. The optimal design will choose the best levels based on the model and the number of runs you require.

D-optimality is best when you are primarily interested in testing effects, and I-optimality is best when you are primarily interested in predicting responses. I think you know that these factors are important, so there is no need for testing. I-optimality seems appropriate in this case. (RSM designs use different methods to achieve the same goal as I-optimal designs.)

[#3]

So if, for example, the angle can take on 3 certain values and the module 9 certain values, can I still use Categorial and not use Discrete Numeric?

What is then the difference between these two types of factors?

[#4]

The angle can vary continuously and has a continuous effect on the response. I would choose Continuous, not Categorical. You further define the range of the continuous factor and the terms of the model in which it is involved. JMP will determine the levels. If you have a continuous factor, but its levels are predetermined, use Discrete Numeric. JMP will choose the terms in the model to suit the given levels.

A categorical factor presents truly discrete levels, like species or alloy type. The levels do not exist on a continuum. Each level produces an individual effect on the response.

Continuous factors are generally preferred because they offer several advantages. Continuous factors are statistically more informative than categorical factors (smaller number of runs). Continuous factors are an opportunity for a more parsimonious linear model. You can extend the range of a continuous factor to illicit a larger effect and improve the power of tests and precision of the estimates.

[#5]

To add to Mark's comments (His comments on the considerations regarding continuous, discrete numeric and categorical are spot on).  I would treat the variables as continuous.

I would consider the following questions:  Is this experiment to be entirely run via simulation?  FEA is a simulation based on an already known algorithm (model).  Is the FEA providing data that represents reality in your actual situation?  Since the algorithm is already known to the folks that wrote the FEA simulation, the relationships of the factors you are investigating is already known. How the FEA model was arrived at may be unknown to you. Whether it represents your situation also is likely unknown.  If you are experimenting using the simulation, the only thing you will accomplish is to uncover the already known model.  You do not need to consider optimality criteria....just run full factorials. If, however, you are going to actually make experimental units that will be measured for the actual stresses, then you may be able to validate the FEA software or determine it is not useful in your application. Are you trying to pick a winner or understand the mechanism and develop a prediction equation that is useful?

If you are going to actually make experimental units to understand the impact of factors on stress, you could start your iterations with 2 levels designs using the extremes of angles, modulus and radius as well as noise and iterate.

[#6]

Hello @bjarne,

Adding to the great directions given on the previous answers, you can make factorial designs to start touching the response surface and start moving towards your objective, once you are believe you are close to your objective you could also be interested in building a surrogate model. For computer experiments there are several ways to do this, you use a space filling design, to fill your inference space using different approaches such as Latin Hypercube Sampling (LHS), JMP supports other sampling strategies as well (refer links bellow) and once you get the data you can try different fits and find the best one that suits your needs, you may start from least square regressions, then try more complex fits such as Gaussian fits,  Neural nets, etc.

for further information to better undestand how to perform computer simulation experiments, you could also be checking out the following links:

https://community.jmp.com/t5/Discovery-Summit-2014/A-Primer-on-Running-Deterministic-Computer-Simula...

https://community.jmp.com/t5/Discovery-Summit-Korea-2020/Case-Study-The-Use-of-Gaussian-Process-for-...

Please let me know if you need any futher information,