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# Don't Let Your DOE Be DOA

August 8, 2014 By: Patrick Cunningham

If you are attempting a RSO (Response Surface Optimization), chances are you are using a DOE (Design of Experiments) to generate the response surface data.   DOE is a method used to characterize the output  of a system due to changes in the input using a minimum number of samples. In the context of a finite element analysis, we use the DOE to pre-determine the design points that will be needed  to generate accurate and predictive response surfaces.

Using this approach has the following advantages over an iterative optimization:

• The number of design points required and the individual design point definitions are known prior to the optimization step of the analysis.
• Multiple design points can be solved simultaneously using parallel computing tools.
• The design point definitions are independent of the optimization goals.  As such, the DOE results can be used for multiple goals.
• RSO is less likely to fall into a local minimum because the entire design space can be sampled. Figure 1 illustrates the local minimum effect that many iterative optimization methods are vulnerable to. RSO can support multiple objectives and can identify both the global and local minimums.

In order for this process to run smoothly, you need to be certain that your finite element solution will complete for each design point defined in the DOE. Kicking off your DOE overnight and returning to find that several design points failed to solve can be very frustrating. The good news is that there are some preventive checks that you can do to keep your DOE from being DOA.

There are several things than can cause a design point solution to fail. They can include:

1) The parametric geometry failing to regenerate due to conflicts in the input parameter values.

2) A geometry change creating a conflict in your mesh controls resulting a meshing failure.

3) A nonlinear model failing to converge.

Reason #1 is typically the most common occurrence and can be avoided with a little effort prior to the kick off of the DOE.  The simplest method is to manually test the geometry generation using the CAD tool by setting the geometry parameters to the upper and lower extremes.  This can be time consuming if you have a significant number of variables to test.  It is also difficult to evaluate the parameter combinations.

My preferred way of evaluating the robustness of my parametric model is to use the DOE to regenerate the model but halt the process before the finite element solution. If your DOE tool requires an output variable in order to run, you can track the mass as that is usually determined based on the solid model geometry. You will likely need the mass output variable in any event for the optimization.

This is a quick and automated way to determine if I will encounter any model generation problems in my full DOE solution. If a design point fails, I can determine interactively if the failure occurred with the CAD geometry generation or with the finite element update. For CAD geometry errors I may adjust parameter ranges or add a parameter association.  For a finite element model update error, I will modify either the mesh, connections, or boundary condition settings accordingly.

Once I am satisfied with the model generation portion of the DOE, I can move on to the finite element solution.  If my model includes nonlinearities, I want to be as confident as possible that the design point solutions will converge. Unfortunately, there is no silver bullet here.  All you can do is pick a design point and run it, adjusting the analysis settings to make the convergence as robust as possible.

With an actual solution in hand, I then move on to the output variables. Output variables add little computational cost, but provide a limited description of the response because they are only a single value of a minimum or maximum quantity in a specified region of the model. I prefer to define many output variables, each zeroed in on specific regions of the finite element model. This can take some preparation time but will give you confidence that the extreme response is always recorded even if it moves from one region to another in different design points. It is always a good idea to include component and principal stresses in addition to Von Mises so that you can fully understand the stress state of each design point. Although you may not use all of the output variables in the optimization it is still handy to have the data available to evaluate the overall design.

Follow these simple steps and you too can experience a full and detailed table of design point solutions! Would anyone care to share their own tips and tricks for a successful DOE?