A question just came to my mind! I appreciate any helpful answers.
Consider a problem that there are a number of input variables (for example 5 variables), and we have one output parameter. The purpose is to develop a meta-model for the problem for example using a second order RSM method. The problem is highly nonlinear, therefore using quadratic (or linear, or cubic) equations to relate the input variables to the output parameter, results in significant errors (in the whole domain). But when we subdivide the design domain (i.e input variables space) to small regions and derive specific equations for each region, the issue is resolved and the output parameter can be predicted with acceptable accuracy.
Now, my question is how one should subdivide the design region? Is there any criteria to do it with minimum subdivision of the domain? In a 2D space this can be done easily by plotting graphs and observe the graph and the points. But how can the design (input) domain be subdivided when there are more design variables (e.g. 5 design variables)?
The problem is that not all your variables are significant in modeling ur response. A screening design also known as a factorial design ought to be carried out first on the input variables to determined those variables that are significant in predicting the dependent variables. This woukd have reduced the variables and there won't be need to subdivide the independent variables. After the scrrening of the variables using factorial or screening design, those factors that are significant can now be optimized using response surface methodology. Thanks i hope it helps.
Babatunde Olawoye
Thanks. But I mean when the problem is highly nonlinear. For example you can develop a cubic RSM in a small region (e.g. 5% or 10% of design space). But when you expand the region (for example considering 100% of the design space or 50% of it) the behavior is more complicated and you could not use a unique cubic RSM for the problem. But the cubic, or for example quadratic functions have good accuracy in small regions. Now the question is how to subdivide the whole design space to small regions where the behavior can be represented using simple cubic or quadratic functions. How to perform the subdivision effectively? I mean the number of sub-regions just be sufficient, not too much nor inadequate. And what criteria should be used to define each sub-region?
Not specific or standard yet in my concern. This needs several trial approaches.
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