# Generate the meta-model 3D response surface data This function produces a data object for the three-dimensional graphical representations of the meta-model response surfaces for a set of factors (parameters), including the confidence interval for the surfaces. ```r response.surface.lsd( data, model, sa, gridSz = 25, defPos = 2, factor1 = 0, factor2 = 0, factor3 = 0 ) ``` ## Arguments - `data`: an object created by a previous call to `read.doe.lsd` which contains all the required experimental data for the analysis. - `model`: an object created by a previous call to `kriging.model.lsd` or `polynomial.model.lsd` which contains the meta-model estimated hyper-parameters. - `sa`: an object created by a previous call to `sobol.decomposition.lsd` which contains the estimated total and conditional variances for all the meta-model factors. - `gridSz`: integer: the number of divisions in the 3D wire frame grid. The default is 25. - `defPos`: 1, 2, 3: the position of the default/calibration configuration on the 3 plot sequence. The default is 2 (center position). - `factor1`: integer: the index of the first most-important factor: 0 = automatic selection (according to the Sobol index, the default); any other number = the selected factor index, according to DoE factor order. - `factor2`: integer: the index of the second most-important factor: 0 = automatic selection (according to the Sobol index, the default); any other number = the selected factor index, according to DoE factor order. - `factor3`: integer: the index of the third most-important factor: 0 = automatic selection (according to the Sobol index, the default); any other number = the selected factor index, according to DoE factor order. ## Details This function produces data for three different wire frame 3D plots. In the 3 plots, the x-y plan is defined by the 2 most-important factors (calculated or set by the user in `sobol.decomposition.lsd`) and the z axis represents the response variable chosen. The three different plots shows the response surface for three values of the third most-important factor: the minimum, the default/calibration and the maximum. The order the three response surfaces are shown is defined by `defPos`. The automatically set most-important factors can be overridden by any factors chosen by the user by the usage of the arguments `factor1`, `factor2` and `factor3`. This way, the response surfaces can be represented for a combination of any 3 factors (parameters) in the model. ## Returns The function returns an object/list of class `response` containing three similar objects, one for each 3D plot, each of them comprised of: - **calib**: the predicted meta-model response values on each point of the 3D grid. - **factor**: the predicted values for each individual factor. - **default**: the predicted values for the default/calibration configuration. ## Author(s) tools:::Rd_package_author("LSDsensitivity") ## Note See the note in LSDsensitivity-package for step-by-step instructions on how to perform the complete sensitivity analysis process using LSD and R. ## See Also `read.doe.lsd()`, `kriging.model.lsd()`, `polynomial.model.lsd()`, `sobol.decomposition.lsd()` ## Examples ```r # get the example directory name path <- system.file( "extdata/sobol", package = "LSDsensitivity" ) # Steps to use this function: # 1. define the variables you want to use in the analysis # 2. load data from a LSD simulation saved results using read.doe.lsd # 3. fit a Kriging (or polynomial) meta-model using kriging.model.lsd # 4. identify the most influential factors applying sobol.decomposition.lsd # 5. calculate the response surface for the selected factors using model.limits.lsd # 6. plot the response surface lsdVars <- c( "var1", "var2", "var3" ) # the definition of existing variables dataSet <- read.doe.lsd( path, # data files folder "Sim3", # data files base name (same as .lsd file) "var3", # variable name to perform the sensitivity analysis does = 2, # number of experiments (data + external validation) saveVars = lsdVars ) # LSD variables to keep in dataset model <- kriging.model.lsd( dataSet ) # estimate best Kriging meta-model SA <- sobol.decomposition.lsd( dataSet, model ) # find Sobol indexes resp <- response.surface.lsd( dataSet, # LSD experimental data set model, # estimated meta-model SA ) # Sobol sensitivity analysis results theta3d <- 310 # horizontal view angle phi3d <- 30 # vertical view angle grid3d <- 25 for( i in 1 : 3 ) { # do for each top factor # plot 3D grid charts zMat <- matrix( resp$calib[[ i ]]$mean, grid3d, grid3d, byrow = TRUE ) zlim <- range( zMat, na.rm = TRUE ) vt <- persp( resp$grid[[ 1 ]], resp$grid[[ 2 ]], zMat, col = "gray90", xlab = colnames( dataSet$doe )[ SA$topEffect[ 1 ] ], zlim = zlim, ylab = colnames( dataSet$doe )[ SA$topEffect[ 2 ] ], zlab = dataSet$saVarName, theta = theta3d, phi = phi3d, ticktype = "detailed" ) } ```

response.surface.lsd function