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Feb 16, 2015 10:58 AM
(3463 views)

I am trying to come up with a split-plot design for a wind tunnel experiment I am going to perform. My experiment will consist of changing flap deflection angle and angle of attack on a NACA 0012 airfoil. The flap deflection angle is a hard to change parameter because I have multiple parts of different deflection angles rather than a mechanism to mechanically vary the flap deflection angle.

I believe that at higher angles of attack, the data will be nonlinear. I am concerned that doing a split plot design of minimal number of points will not capture the data completely. So before designing my wind tunnel experiment, I have used some nonlinear historical wind tunnel data, and I tried to design an experiment for that and fit the resulting points with a response surface. However, the data is not fully captured by the designed experiment. I believe this is due to the fact that a limited number of angle of attacks are being tested in the design (upper limit, lower limit, and center).

What would be the best way to design a Split-Plot RSM experiment in JMP that can capture nonlinear regions while keeping the number of whole plots to a minimum? Below is the script for my split-plot design:

DOE(

Custom Design,

{Add Response( Minimize, "CN", ., ., . ),

Add Response( Minimize, "Cm", ., ., . ),

Add Factor( Continuous, -1, 1, "AMT Deflection", 1 ),

Add Factor( Continuous, -1, 1, "Alpha", 0 ), Set Random Seed( 4827091 ),

Number of Starts( 500 ), Add Term( {1, 0} ), Add Term( {1, 1} ),

Add Term( {2, 1} ), Add Term( {1, 2} ), Add Term( {1, 1}, {2, 1} ),

Add Term( {2, 2} ), Set N Whole Plots( 4 ), Set Sample Size( 12 ),

Optimality Criterion( 2 ), Make Design, Make Table}

)

By digitizing the data in the attached historical data figure, I was able to use interpolation to get all the responses at each of the design points. I have also attached the model script. Comparing the model to the historical data, it can be seen in the CN plots, that the curves do not have comparable maximums. The response surface for CN only goes up to about 1 whereas the historical data actually goes to about 1.2.

I am just trying to figure out a way to come up with a systematic way to generate a split-plot rsm design with many levels on angle of attack and minimum levels on flap deflection angle.

Any help is greatly appreciated!

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Alex,

I am not sure what to tell you without being more involved with all of the domain knowledge but since you had the data I figured that you could try that approach and see what you thought. At the end of the day as the Springsteen song goes "sooner or later it all comes down to money" so depending on the "best" design is often the one that provides the amount of knowledge required for the project. Many times direction is what we can afford and when we exceed prediction but have the dials correct, that can be okay:)

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Re: Design of a Split-Plot Wind Tunnel Experiment

Perhaps treating your AMT Deflection factor as a discrete numeric (5 level) "hard to change" factor and the Alpha as a continuous two-level factor is an option?

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Re: Design of a Split-Plot Wind Tunnel Experiment

I tried a new design treating my AMT Deflection factor as continuous and alpha as discrete numeric with 7 levels. In this design, I created a response surface up to the 5th power in alpha to capture the nonlinearity in alpha. It does a better job of matching the historical data since my response surface equation has a higher power.

I don't know if this is a good way about getting a better response surface to the historical data. Your response made me think of making a discrete numeric for alpha.

Thanks Lou!

Alex

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Alex,

I am not sure what to tell you without being more involved with all of the domain knowledge but since you had the data I figured that you could try that approach and see what you thought. At the end of the day as the Springsteen song goes "sooner or later it all comes down to money" so depending on the "best" design is often the one that provides the amount of knowledge required for the project. Many times direction is what we can afford and when we exceed prediction but have the dials correct, that can be okay:)