Prepare DOE

Tutorial

Design of experiments

Architecture

prepareDOE.R

UI and Server functions

source("modules/prepareDOE/generateDOE.R", local = TRUE)

prepareDOE.ui(id)

This function creates the panel Generate DOE and populates it by calling the generateDOE.ui() function

Parameters:

id (character) – namespace of the module

prepareDOE.server(input, output, session, settings)

This function builds a list-like object named output that contains all of the code needed to update the R objects in the app.

Parameters:

• input (list-like-object) – stores the widgets’ values.

• output (list-like-object) – stores the instructions to build R objects in the app.

• session (object) – environment that can be used to access information and functionality relating to the session.

• settings (list-like-object) – variables specified in settingsDOE.R

Main reactives:

calls generateDOE.server()

generateDOE.R

source("modules/shared/XinfosChange.R", local = TRUE) source("modules/prepareDOE/evaluateDOE.R", local = TRUE) source("modules/prepareDOE/visualizeDOE.R", local = TRUE)

UI and Server functions

generateDOE.ui(id)

This function populates the Generate DOE panel

Parameters:

id (character) – namespace of the module

Main reactives:

• Left column

  • nX: number of inputs

  • bounds: input definition/edition using XinfosChange.ui()

  • DOE.type: DOE method selection

  • nobs.UI: sample size selection

• Content

  • Previews the input definition with XinfosChange.ui.preview(ns("bounds"))

• Bottom

  • goDOE: button to generate DOE

  • prepare.gocheckDOE: button to evaluate DOE

  • download: button to export DOE

  • plotVisualize: calls visualizeDOE module, displays a pairplot to visualize the DOE points repartition. Appears after DOE generation

generateDOE.server(input, output, session, settings)

This function builds a list-like object named output that contains all of the code needed to update the R objects in the app.

Parameters:

• input (list-like-object) – stores the widgets’ values.

• output (list-like-object) – stores the instructions to build R objects in the app.

• session (object) – environment that can be used to access information and functionality relating to the session.

• settings (list-like-object) – variables specified in settingsDOE.R

Main reactives:

• DOE is the reactive expression that stores the point values and the DOE informations (e.g. bounds…)

• Xinfos: stores the bound definition

• initialXinfos: Xinfos generated by default

• var.num, var.cat: store the names of the variables (numerical and categorical)

• goDOE: button to generate the DOE, calls generateDOEXopt()

• output$scatter: generates the pairplot to visualize the DOE

• plotVisualize: calls visualizeDOE module, displays the pairplot

• output$download: generates a downloadable CSV file with DOE$Xopt variable

Main functions

sobolsequencecat(u, lvls, weights)

Generates a DOE using a Sobol sequence

Parameters:

• u (vector) – vector of observations (sobol sequence)

• lvls (vector) – vector of levels

• list (vector) – list of weights, could be a scalar if the levels share the same weight

Returns:

the DOE

Return type:

vector

generate.DOE.Xopt(nX, nobs, nobs.slide, DOEtype, Xinfos, names.num, names.cat)

Generates the design of experiment (DOE) using one of the following methods (DOEtype):

Methods for numerical variables

• LHS Maximin [1]

• LHS Discrepancy [2]

• LHS MaxProj (Optimal but slow) [3]

• Sobol Sequence (Fast but suboptimal exploration) [5]

Methods for mixed DOE (categorical and numerical variables)

• LHS for Categorical Inputs (Optimal but large sample size) [4]

• Mixed Sobol Sequence (Fast but suboptimal exploration) [5]

Parameters:

• nX (integer) – number of inputs

• nobs (integer) – number of observations

• nobs.slide (integer) – sample size for each category

• DOEtype (character) – method used to generate the DOE points

• Xinfos (data.table) – variable informations (name, type, lower bound, upper bound, number of levels, levels)

• names.num (vector) – names of numerical variables

• names.cat (vector) – names of categorical variables

Returns:

the generated DOE

Return type:

data.table

Secondary functions

check.input.size(input, min.value)

Compares the value of input and min.value, input must not be less than min.value.

Parameters:

• input (integer) – number of inputs

• min.value (integer) – minimum inputs allowed

Returns:

FALSE if input is strictly less than min.value, TRUE otherwise

Return type:

logical

evaluateDOE.R

UI and Server functions

evaluateDOE.ui(id)

This function builds the modal window, it is displayed by clicking on Evaluate DOE

Parameters:

id (character) – namespace of the module

Main reactives:

• check: button that calls compute.checkDOE()

• plot: displays plot.checkDOE()

• plotLHS: displays plot.checkDOE.LHS()

evaluateDOE.server(input, output, session, DOE, settings)

This function builds a list-like object named output that contains all of the code needed to update the R objects in the app.

Parameters:

• input (list-like-object) – stores the widgets’ values.

• output (list-like-object) – stores the instructions to build R objects in the app.

• session (object) – environment that can be used to access information and functionality relating to the session.

• DOE (object) – stores the informations related to the DOE

• settings (list-like-object) – variables specified in settingsDOE.R

Main reactives:

• checkDOE is the reactive expression that stores the list of DOEs generated by function compute.checkDOE()

• Xinfos: used to define the bounds

• initialXinfos: Xinfos generated by default

• output$plot: generates the plot using the plot.checkDOE() function

• output$plotLHS: generates the plot using the plot.checkDOE.LHS() function

Main functions

get.listDOE(Xopt, lb, ub, ntestMC, callback)

Creates a list with different DOE types.

The DOE types are the following:

• Faure, Halton and Sobol are low discrepency sequences

• MC is a random Monte Carlo sample

• DOE is the user’s

Parameters:

• Xopt (data.table) – DOE points generated

• lb (numeric) – lower bound

• ub (numeric) – upper bound

• ntestMC (numeric) – number of MC DOE for comparison

• callback (function) – function used to report progress

Returns:

list of DOEs

Return type:

list

Plot functions

plot.checkDOE(listDOE)

Three boxplots are displayed in order to compare the DOE types according to three criterions:

• Maximin [1]

• Discrepancy [2]

• MaxProj [3]

The DOE types are the following:

• Faure, Halton and Sobol are low discrepency sequences

• MC is a random Monte Carlo sample

• DOE is the user’s

Parameters:

listDOE (list) – list of DOEs, generated by get.listDOE()

plot.checkDOE.LHS(listDOE)

Diplays a boxplot to compare the chi2 distance between the different DOE types and the LHS for each variable. It shows how far the points are from a LHS position, and gives an insight about the quality of the repartition.

Parameters:

listDOE (list) – list of DOEs

Secondary functions

compute.checkDOE(Xopt, Xinfos, ntestMC, all.numeric)

Checks if the all the values are numeric since no evaluation method is available for a DOE with categorical variables. If it is true, calls the function get.listDOE() to create a list of DOEs in order to compare them.

Parameters:

• Xopt (data.table) – DOE points generated

• Xinfos (data.table) – variable information (name, type, lower bound, upper bound, number of levels, levels)

• ntestMC (numeric) – number of MC DOE for comparison

• all.numeric (logical) – TRUE if all the variables are numeric, FALSE otherwise

Returns:

list of DOEs

Return type:

list

visualizeDOE.R

UI and Server functions

visualizeDOEUI(id)

Displays the pairplot and two pickerInputs for the numeric variables, and the levels of categorical variables.

Parameters:

id (character) – namespace of the module

Main reactives:

• numericSelection: numeric variable selection

• categoricalSelection: categorical variable selection

• numSelectionClosed: informs whether the numericSelection picker is loaded or hidden

• catSelectionClosed: informs whether the categoricalSelection picker is loaded or hidden

• pairPlot: displays the pairplot

visualizeDOEServer(id, data, numericVariables, categoricalVariables, mapNames)

Parameters:

• id (character) – namespace of the module

• data (data.table) – table containing the data

• numericVariables (vector) – contains the numeric variable names

• categoricalVariables (vector) – contains the categorical variable names

• mapNames (data.frame) – a data.frame with 3 columns (names, menu, visu), containing the different names of the variables. They can be different in the data table, the menus, or the plots

Main reactives:

• numericSelection: numeric variable selection

• categoricalSelection: categorical variable selection

• output$pairPlot: builds the pairplot

Plot functions

pairPlot(data, numericSelection, categoricalSelection, mapNames)

Creates a pairplot to visualize the DOE point repartition. The points are colorized by group of levels if categoricalSelection is not NULL.

Parameters:

• data (data.table) – table containing the data

• categoricalSelection (vector) – contains the numeric variable names selected by the user

• categoricalSelection – contains the categorical variable names selected by the user

• mapNames (data.frame) – a data.frame with 3 columns (names, menu, visu), containing the different names of the variables. They can be different in the data table, the menus, or the plots

Secondary functions

getJsPickerEvent(pickerID, shinyInputID)

Returns two javascript functions to trigger an event when the menu is loaded, and when it’s hidden.

Parameters:

• pickerID (character) – the picker on which to apply the functions

• shinyInputID (character) – the desired name for the event, will be used as an input in the shiny app

buildCategoricalSelection(data, categoricalVariables, mapNames, separator='|')

Creates a list of named lists. The sublists are named after the categorical variables, they contain their levels. As the pickerInput returns a vector with the selection, and in order to identify which level belong to which variable, the variables names and levels are concatenated using the separator (“|” by default).

Parameters:

• data (data.table) – table containing the data

• categoricalVariables (vector) – contains the categorical variable names

• mapNames (data.frame) – a data.frame with 3 columns (names, menu, visu), containing the different names of the variables. They can be different in the data table, the menus, or the plots

• separator (character) – character used to separate the variable name from the level (default = “|”)

buildCatLevelsList(categoricalSelection, separator='|')

Splits the elements of the selection by the separator (“|” by default) and builds a list of named lists. Each list contains the selected levels for each variable.

Parameters:

• categoricalSelection (vector) – contains the categorical variable names selected by the user

• separator (character) – character used to separate the variable name from the level (default = “|”)

References

[1] (1,2)

Enhanced Stochastic Evolutionnary (ESE) Algorithm For Latin Hypercube Sample (LHS) Optimization Via PhiP Criteria

R Jin, W. Chen and A. Sudjianto (2005) An efficient algorithm for constructing optimal design of computer experiments. Journal of Statistical Planning and Inference, 134:268-287.

R function documentation | R Package: DiceDesign

[2] (1,2)

Enhanced Stochastic Evolutionnary (ESE) Algorithm For Latin Hypercube Sample (LHS) Optimization Via L2-Discrepancy Criteria

Hickernell F.J. (1998) A generalized discrepancy and quadrature error bound. Mathematics of Computation, 67, 299-322.

Pleming J.B. and Manteufel R.D. (2005) Replicated Latin Hypercube Sampling, 46th Structures, Structural Dynamics & Materials Conference, 16-21 April 2005, Austin (Texas) – AIAA 2005-1819.

R function documentation | R Package: DiceDesign

[3] (1,2)

Maximum Projection Latin Hypercube Designs For Continuous Factors

V Roshan Joseph, Evren Gul, Shan Ba. (2015) Maximum projection designs for computer experiments, Biometrika, Volume 102, Issue 2, June 2015, Pages 371–380

R function documentation | R Package: MaxPro

[4]

Maximin-Distance (Sliced) Latin Hypercube Designs

Ba, S., Brenneman, W. A. and Myers, W. R. (2015), Optimal Sliced Latin Hypercube Designs, Technometrics.

R function documentation | R Package: SLHD

[5] (1,2)

Scrambled Sobol’s Low Discrepancy Sequences

Bratley P., Fox B.L. (1988); Algorithm 659: Implementing Sobol’s Quasirandom Sequence Generator, ACM Transactions on Mathematical Software 14, 88–100.

Joe S., Kuo F.Y. (1998); Remark on Algorithm 659: Implementing Sobol’s Quasirandom Sequence Generator.

R function documentation | R Package: fOptions