Composite Design Response Surfaces: Difference between revisions
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=Using Response Surface Data= | |||
Once you download the .mat file associated with a response surface, you will see two variables: | |||
* <code>model</code> | |||
** matrix of size <math>N_{vars} \times N_{polynomial terms}</math> | |||
** number of columns is equal to the number of input variables <math> | |||
** number of rows is equal to the number of terms in the polynomial response surface | |||
** variable order is as follows: | |||
*** Mass flowrate <math>\dot{m}</math> | |||
*** Reaction rate <math>k(T)</math> | |||
*** Mixing length <math>L_{mix}</math> | |||
*** Measurement location 1 <math>z_1</math> | |||
*** Measurement location 2 <math>z_2</math> | |||
*** Measurement location 3 <math>z_3</math> | |||
* <code>response_surface</code> | |||
** cell object that results from Matlab's <code>regstats()</code> function | |||
** polynomial coefficients corresponding to each row of <math>model</code> object are contained in <code>response_surface.beta</code> | |||
** covariance matrix is stored in <code>response_surface.covb</code> | |||
** R-squared and adjusted R-squared values stored in <code>response_surface.rsquare</code> and <code>response_surface.adjrsquare</code>, respectively | |||
** mean square error is contained in <code>response_surface.mse</code> | |||
See the Matlab <code>regstats()</code> help page for more information: http://www.mathworks.com/help/toolbox/stats/regstats.html | |||
=Composite Design Response Surfaces= | =Composite Design Response Surfaces= | ||
Revision as of 21:40, 13 July 2011
Using Response Surface Data
Once you download the .mat file associated with a response surface, you will see two variables:
model- matrix of size $ N_{vars} \times N_{polynomial terms} $
- number of columns is equal to the number of input variables $ ** number of rows is equal to the number of terms in the polynomial response surface ** variable order is as follows: *** Mass flowrate <math>\dot{m} $
- Reaction rate $ k(T) $
- Mixing length $ L_{mix} $
- Measurement location 1 $ z_1 $
- Measurement location 2 $ z_2 $
- Measurement location 3 $ z_3 $
response_surface- cell object that results from Matlab's
regstats()function - polynomial coefficients corresponding to each row of <math>model object are contained in
response_surface.beta - covariance matrix is stored in
response_surface.covb - R-squared and adjusted R-squared values stored in
response_surface.rsquareandresponse_surface.adjrsquare, respectively - mean square error is contained in
response_surface.mse
- cell object that results from Matlab's
See the Matlab regstats() help page for more information: http://www.mathworks.com/help/toolbox/stats/regstats.html
Composite Design Response Surfaces
Yp at X1
Quadratic Response, 6 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x1_6dim_2deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 6. Number of terms in polynomial is 28. Degree of response surface is 2. MSE = 0.00080509 MSE DoF = 17 L-inf norm resid = 0.05454099 R^2 = 0.99052326 adjusted R^2 = 0.97547197 ---------------------------------------------------
Quadratic Response, 2 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x1_2dim_2deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 2. Number of terms in polynomial is 6. Degree of response surface is 2. MSE = 0.00037084 MSE DoF = 39 L-inf norm resid = 0.04927581 R^2 = 0.98998584 adjusted R^2 = 0.98870197 ---------------------------------------------------
Cubic Response Surface, 6 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x1_6dim_3deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 6. Number of terms in polynomial is 37. Degree of response surface is varied, deg is a matrix. Max degree = 3. MSE = 0.00000010 MSE DoF = 8 L-inf norm resid = 0.00069080 R^2 = 0.99999947 adjusted R^2 = 0.99999709 ---------------------------------------------------
Yp at X2
Quadratic Response, 6 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x2_6dim_2deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 6. Number of terms in polynomial is 28. Degree of response surface is 2. MSE = 0.01492871 MSE DoF = 17 L-inf norm resid = 0.19955474 R^2 = 0.93864060 adjusted R^2 = 0.84118743 ---------------------------------------------------
Quadratic Response, 2 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x2_2dim_2deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 2. Number of terms in polynomial is 6. Degree of response surface is 2. MSE = 0.00690353 MSE DoF = 39 L-inf norm resid = 0.13735696 R^2 = 0.93490530 adjusted R^2 = 0.92655983 ---------------------------------------------------
Cubic Response Surface, 6 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x2_6dim_3deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 6. Number of terms in polynomial is 37. Degree of response surface is varied, deg is a matrix. Max degree = 3. MSE = 0.00000006 MSE DoF = 8 L-inf norm resid = 0.00020206 R^2 = 0.99999989 adjusted R^2 = 0.99999941 ---------------------------------------------------
Yp at X3
Quadratic Response, 6 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x3_6dim_2deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 6. Number of terms in polynomial is 28. Degree of response surface is 2. MSE = 0.03224452 MSE DoF = 17 L-inf norm resid = 0.30852831 R^2 = 0.88596596 adjusted R^2 = 0.70485306 ---------------------------------------------------
Quadratic Response, 2 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x3_2dim_2deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 2. Number of terms in polynomial is 6. Degree of response surface is 2. MSE = 0.01514132 MSE DoF = 39 L-inf norm resid = 0.20318228 R^2 = 0.87715488 adjusted R^2 = 0.86140551 ---------------------------------------------------
Cubic Response Surface, 6 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x3_6dim_3deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 6. Number of terms in polynomial is 37. Degree of response surface is varied, deg is a matrix. Max degree = 3. MSE = 0.00000005 MSE DoF = 8 L-inf norm resid = 0.00033261 R^2 = 0.99999992 adjusted R^2 = 0.99999957 ---------------------------------------------------
Yp at X Out
Quadratic Response, 6 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_out_6dim_2deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 6. Number of terms in polynomial is 28. Degree of response surface is 2. MSE = 0.03845480 MSE DoF = 17 L-inf norm resid = 0.34272386 R^2 = 0.86371957 adjusted R^2 = 0.64727417 ---------------------------------------------------
Quadratic Response, 2 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_out_2dim_2deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 2. Number of terms in polynomial is 6. Degree of response surface is 2. MSE = 0.01817059 MSE DoF = 39 L-inf norm resid = 0.23540351 R^2 = 0.85227039 adjusted R^2 = 0.83333069 ---------------------------------------------------
Cubic Response Surface, 6 Dimensions
Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_out_6dim_3deg.mat
The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
Some key statistics for this response surface are given below:
--------------------------------------------------- Response surface summary of information: Number of variables in response surface is 6. Number of terms in polynomial is 37. Degree of response surface is varied, deg is a matrix. Max degree = 3. MSE = 0.00000000 MSE DoF = 8 L-inf norm resid = 0.00000000 R^2 = 1.00000000 adjusted R^2 = 1.00000000 ---------------------------------------------------
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