Composite Design Response Surfaces
From charlesreid1
Contents
Using Response Surface Data
Once you download the .mat file associated with a response surface, you will see two variables:
model- matrix of size Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle N_{vars} \times N_{polynomial terms}}
- number of columns is equal to the number of input variables Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle N_{vars}}
- number of rows is equal to the number of terms in the polynomial response surface Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle N_{polynomial terms}}
- variable order is as follows:
- Mass flowrate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \dot{m}}
- Reaction rate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle k(T)}
- Mixing length Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle L_{mix}}
- Measurement location 1 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle z_1}
- Measurement location 2 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle z_2}
- Measurement location 3 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle z_3}
response_surface- cell object that results from Matlab's
regstats()function - polynomial coefficients corresponding to each row of
modelobject are contained inresponse_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
Example of how to use this information to compute the value of a response surface is here: EvaluateResponseSurface.m
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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