Menu Explore

Tutorials

Surrogate Exploration
Uncertainty Propagation
Sensitivity Analysis

Architecture

menuExplore.R

UI and Server functions

menuExplore.ui(id)

This function adds the menu “Explore” to the user interface.

Parameters:: id (character) – namespace of the module

Main reactives:

Exploration with Surrogate Model: tabPanel in the menu, calls exploreModel.ui() with id exploreModel
UQ & GSA with Surrogate Model: tabPanel in the menu, calls UQModel.ui() with id UQModel

menuExplore.server(input, output, session, DOE, ML, listmodels, use_simulator, window.dimension, settings)

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 point values and the DOE information (e.g. bounds…)
ML (object) – stores the quantitative exploration of the data
listmodels (list) – list of trained models
use_simulator (logical) – informs if the user uses a simulator linked to Lagun
window.dimension (object) – dimensions of the window
settings (list-like-object) – variables specified in settingsExploration.R

Main reactives:

Calls module exploreModel.server() with id exploreModel
simulations: Calls module UQModel.server() with id UQModel

Explore Model

exploreModel.R

source("modules/menuExplore/exploreModel/modelQualitativeExploration.R", local = TRUE) source("modules/menuExplore/exploreModel/modelQuantitativeExploration.R", local = TRUE) source("modules/menuExplore/exploreModel/modelManualExploration.R", local = TRUE)

UI and Server functions

exploreModel.ui(id)

This function creates the Exploration with Surrogate Model page with three panels:

Qualitative Exploration
Quantitative Exploration
Manual Exploration

Parameters:: id (character) – namespace of the module

Main reactives:

Calls modelQualitativeExploration.ui() with id modelQualitativeExploration
Calls modelQuantitativeExploration.ui() with id modelQuantitativeExploration
Calls modelManualExploration.ui() with id modelManualExploration

exploreModel.server(input, output, session, DOE, listmodels, window.dimension, settings)

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 point values and the DOE information (e.g. bounds…)
listmodels (list) – list of trained models
window.dimension (object) – dimensions of the window
settings (list-like-object) – variables specified in settingsExploration.R

Main reactives:

Calls modelQualitativeExploration.server() with id modelQualitativeExploration
Calls modelQuantitativeExploration.server() with id modelQuantitativeExploration
Calls modelManualExploration.server() with id modelManualExploration

modelQualitativeExploration.R

UI and Server functions

modelQualitativeExploration.ui(id)

This function populates the Qualitative Exploration panel, which mainly displays a parallel coordinate plot

Parameters:: id (character) – namespace of the module

Main reactives:

keepbounds: switch to keep bounds
choose.palette.num: color palette selection for numerical variables
choose.palette.cat: color palette selection for categorical variables
downloadpcp: button to export parallel plot
chooseX: input variable selection
chooseY: output variable selection
chooseHistParcoords: variable selection for which a histogram will be displayed
chooseBoundsParcoords: bound selection for variables
Loadsampling: button to load a sampling from file
bounds: button to refine sampling
SMCsettings: button to perform inverse sampling
parcoords: displays parallel plot
dataView: displays data as a table

modelQualitativeExploration.server(input, output, session, DOE, listmodels, window.dimension, settings)

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 point values and the DOE information (e.g. bounds…)
listmodels (list) – list of trained models
window.dimension (object) – dimensions of the window
settings (list-like-object) – variables specified in settingsExploration.R

Main reactives:

choicesX: input variable list
selectedX: selected input variables
choicesY: output variable list
selectedY: selected output variables
choicesHistParcoords: list of variables for which to display a histogram
choicesBoundsParcoords: list of variables for which to update bounds
parcoordsData: data generated by getParcoordsData() or getParcoordsDataFromFile()
selectedParCoords: data.frame filtered out by user selection
dataPCP: object that contains the data and every information for the plot
output$parcoords: renders parallel plot
output$brushed: builds data table with filtered out by user selection
output$download: downloadable CSV file containing brushed data
output$downloadpcp: Downloadable html of parallelPlot
output$dataView: displays brushed data table

Main functions

getParcoordsData(DOE, nobs, predfunc, Xinfos, Yinfos, callback)

Generates input data using sampleInputs() and computes output data for the parallel plot using the selected metamodel

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
nobs (numeric) – number of observations expected
predfunc (function) – computes prediction with the selected metamodels
Xinfos (object) – input variable information
Yinfos (object) – output variable information
callback (function) – reports progress

getParcoordsDataFromFile(DOE, PCPsample, predfunc, Yinfos, callback)

Same as getParcoordsData() but gets the input data from a file

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
PCPsample (data.frame) – input sample
predfunc (function) – computes prediction with the selected metamodel
Yinfos (object) – output variable information
callback (function) – reports progress

Secondary functions

sampleInputs(DOE, nobs, Xinfos)

Generates a sample of data

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
nobs (numeric) – number of observations expected
Xinfos (object) – input variable information

unrestricted(N, range)

Generates a random composition with a uniform distribution [3]

Parameters:

N (numeric) – number of datasets to be simulated
range (matrix) – number of parts

logpost_vec(sample, nu_t, constraint)

Computes log-posterior, performs a smoothing of the indicator function [3]

Parameters:

sample (vector) – sample
nu_t (numeric) – smoothing parameter
constraint (function) – constraint function

Gibbs_vec(x, q, d, nu_t, lpdent = lpdent, N, constraint)

Computes Gibbs sampling, performs a random disturbance on the sample [3]

Parameters:

x (vector) – sample
q (numeric) – variance of the gaussian that disturbs each dimension
d (numeric) – dimension index to disturb
nu_t (numeric) – smoothing parameter
lpdent (function) – logpost_vec() function before diturbance, in order to compare after the disturbance. It helps decide whether to accept the disturbance or not.
N (numeric) – sample size
constraint (function) – constraint function

adapt_seq_vec(nu, nu0, t, N, term=term, Wt, constraint)

Performs adaptive specification of the constraint parameter. It chooses the next smoothing parameter by keeping a value of the Effective Samle Size (ESS) higher or equal to 1/2. [3]

Parameters:

nu (numeric) – smoothing parameter
nu0 (numeric) – previous smoothing parameter
t (numeric)
N (numeric) – sample size
term (numeric) – evaluated sample constraint
Wt (numeric) – weights of the particles
constraint (function) – constraint function

get.constraintfunction(dfparcoords, DOE, Xinfos, predfunc)

Returns constraint function

Parameters:

dfparcoords (data.frame) – contains data for the parallel plot
DOE (object) – stores the point values and the DOE information (e.g. bounds…)
Xinfos (object) – input variable information
predfunc (function) – computes prediction with the selected metamodels

get.lowerupper(dfparcoords, DOE, Xinfos)

Returns lower and upper bounds

Parameters:

dfparcoords (data.frame) – contains data for the parallel plot
DOE (object) – stores the point values and the DOE information (e.g. bounds…)
Xinfos (object) – input variable information

SCMC_withcallback(dfparcoords, DOE, Xinfos, predfunc, nsampleSMC, iterSMC, callback)

Computes inverse sampling [3]

Parameters:

dfparcoords (data.frame) – contains data for the parallel plot
DOE (object) – stores the point values and the DOE information (e.g. bounds…)
Xinfos (object) – input variable information
predfunc (function) – computes prediction with the selected metamodel
nsampleSMC (numeric) – number of observations
iterSMC (numeric) – number of iterations
callback (function) – reports progress

callback(i)__

Reports progress of a task. Calls R Shiny incProgress

Parameters:: i (numeric) – i^th iteration

modelQuantitativeExploration.R

source("modules/shared/dynamicSelect.R", local = TRUE) source("modules/shared/dynamicSelect.R", local = TRUE) source("modules/menuExplore/exploreModel/modelQualitativeExploration.R", local = TRUE)

UI and Server functions

modelQuantitativeExploration.ui(id)

This function populates the Quantitative Exploration panel with three tabs

Parameters:: id (character) – namespace of the module

Main reactives:

Regression plot - One by One
Regression plot using one or two input variables against one output variable. The values of the unused input variables is set by the user with the sliders. This way, we see the effect of the choosen input(s) on the output with specific values for the other inputs.
- chooseX1: input variable 1 selection
- chooseX2: input variable 2 selection
- chooseY: output variable selection
- chooseVisu: plot type selection
- sliders: slider to choose the value of the unselected input variables
- plotExplo: displays plot
Regression plot with smoothing - All in One
Same as the first regression plot but the mean over all possible values is used for the other inputs instead of a specific value.
- chooseYsmooth: output variable selection
- chooseXsmooth: input variable selection
- ui.treillis: lattice’s number of rows and columns / lattice navigation
- ui.smooth: displays plot
Regression plot with smoothing - All in One (Summary)
Compares all the inputs in the same coordinate system with quantiles. It allows to visualize how the output reacts with every input.
- chooseYsmoothsummary: output variable selection
- chooseXsmoothsummary: input variable selection
- ui.smooth.summary: displays plot

modelQuantitativeExploration.server(input, output, session, DOE, listmodels, window.dimension, settings)

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 point values and the DOE information (e.g. bounds…)
listmodels (list) – list of trained models
window.dimension (object) – dimensions of the window
settings (list-like-object) – variables specified in settingsExploration.R

Main reactives:

Regression plot - One by One
- choicesX1: contains input variables names
- choicesX2: contains input variables names
- choicesY: contains output variables names
- choicesVisu: contains plot types
- output$sliders: displays sliders for value selection
- remainingX: contains the unselected input variable names and values
- output$plotExplo: displays plot
Regression plot with smoothing - All in One
- chooseXsmooth: contains input variables names
- chooseYsmooth: contains output variables names
- goPrevious, goNext, goUp, goDown: buttons for lattice navigation
- output$ui.treillis: displays lattice
- output$plot.smooth: displays plot
Regression plot with smoothing - All in One (Summary)
- xnamesmooth.summary: input variable selection
- ynamesmooth.summary: output variable selection
- output$plot.smooth.summary: displays plot

Plot functions

plotExplo(DOE, predfun, yname, xname1, xname2, remainingX, ncontours, ftemp, visuname)

Plots either a regression plot, a contour plot, or a 3D suface plot

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
predfun (function) – selected metamodel predict function
yname (character) – output variable name
xname1 (character) – input variable name 1
xname2 (character) – input variable name 2
remainingX (list) – not selected input variable names and values
ncontours (numeric) – maximum number of contour levels
ftemp (numeric) – factor by which to shrink the range (see getShrinkedRange())
visuname (character) – type of plot (contour, 3D surface…)

Secondary functions

getShrinkedRange(data, rangeFactor)

Shrinks the range by +/- range * rangeFactor

Parameters:

data (vector) – data
rangeFactor (numeric) – factor by which the range should be shrinked

callback(i)__

Reports progress of a task. Calls R Shiny incProgress

Parameters:: i (numeric) – i^th iteration

modelManualExploration.R

UI and Server functions

modelManualExploration.ui(id)

This function populates the Manual Exploration panel

Parameters:: id (character) – namespace of the module

Main reactives:

choice: radio buttons to choose whether to import a file with new data, or enter the data manually in the UI
proceed: button proceed with the choice
compute: button to compute predictions
download: button to export the predictions
content: table to display the data

modelManualExploration.server(input, output, session, DOE, listmodels)

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 point values and the DOE information (e.g. bounds…)
listmodels (list) – list of trained models

Main reactives:

dataAdd: contains the new data
input$save: gets new data from input
input$file$datapath: gets new data from file
input$compute: computes prediction for the new data
output$content: renders new data and predictions as a table
output$download: builds a CSV file to download data

Main functions

get.newData.from.input(DOE, input, Yinfos)

Reads and shapes data from input file

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
input (list-like-object) – stores the widgets’ values.
Yinfos (object) – output variable information

computeYpredForDataAdd(DOE, predfun, Xvalues, Yinfos)

Computes output prediction for new data

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
predfun (function) – selected metamodel predict function
Xvalues (matrix) – input variable values
Yinfos (object) – output variable information

UQ Model

UQModel.R

source("modules/menuExplore/UQModel/uncertaintyDefinition.R", local = TRUE) source("modules/menuExplore/UQModel/uncertaintyPropagation.R", local = TRUE) source("modules/menuExplore/UQModel/sensitivityAnalysis.R", local = TRUE)

UI and Server functions

UQModel.ui(id)

This function creates the UQ & GSA with Surrogate Model page with three panels:

Step 1: Uncertainty Definition
Step 2: Uncertainty Propagation
Step 3: Sensitivity Analysis

Parameters:: id (character) – namespace of the module

Main reactives:

Calls uncertaintyDefinition.ui() with id uncertaintyDefinition
Calls uncertaintyPropagation.ui() with id uncertaintyPropagation
Calls sensitivityAnalysis.ui() with id sensitivityAnalysis

UQModel.server(input, output, session, DOE, ML, listmodels, use_simulator, window.dimension, settings)

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 point values and the DOE information (e.g. bounds…)
ML (object) – quantitative exploration measures
listmodels (list) – list of trained models
use_simulator (logical) – informs if the user uses a simulator linked to Lagun
window.dimension (object) – dimensions of the window
settings (list-like-object) – variables specified in settingsExploration.R

Main reactives:

Calls uncertaintyDefinition.server() with id uncertaintyDefinition
Calls uncertaintyPropagation.server() with id uncertaintyPropagation
Calls sensitivityAnalysis.server() with id sensitivityAnalysis

uncertaintyDefinition.R

source("modules/menuExplore/UQModel/UQparamsChange.R", local = TRUE)

UI and Server functions

uncertaintyDefinition.ui(id)

This function populates the Step 1: Uncertainty Definition panel

Parameters:: id (character) – namespace of the module

Main reactives:

Calls UQparamsChange.ui() to allow uncertainty definition modification
Calls UQparamsChange.ui.preview() to display uncertainty definition as a table

uncertaintyDefinition.server(input, output, session, DOE)

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 point values and the DOE information (e.g. bounds…)

Main reactives:

initialUQparams: default parameters, obtained by calling initialize.UQparams()
UQparams: calls module UQparamsChange.server() with id UQParams

Main functions

initialize.UQparams(Xinfos)

Initializes Uncertainty Quantification parameters according to the input data type

Parameters:: Xinfos (object) – input variable information

uncertaintyPropagation.R

source("modules/shared/dynamicSelect.R", local = TRUE)

UI and Server functions

uncertaintyPropagation.ui(id)

This function populates the Step 2: Uncertainty Propagation panel with two tabs:

Global Propagation
Probability Estimation

Parameters:: id (character) – namespace of the module

Main reactives:

Global Propagation
- go: button to propagate uncertainties
- nsample: input to specifiy sample size
- download: button to export UQ propagation
- chooseVisu: plot type selection (“Probability Distribution Function” or “Cumulative Distribution Function”)
- plot: displays selected plot
- table: displays data as a table
Probability Estimation
- signYUQproba: operator selection for threshold comparison
- threshYUQproba: input to specifiy threshold
- nsampleUQproba: input to specifiy sample size
- goUQproba: button to compute probability
- dobootproba: checkbox to resample data
- naddproba: input to specifiy number of additional simulations in order to refine model for output values satisfying the defined constraint
- generate: button to generate additional simulations
- downloadproba: button to export additional simulations
- plotproba: displays probability estimation plot
- preview: displays proposed additional simulations as a table

uncertaintyPropagation.server(input, output, session, DOE, listmodels, use_simulator, UQparams, settings)

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 point values and the DOE information (e.g. bounds…)
listmodels (list) – list of trained models
use_simulator (logical) – informs if the user uses a simulator linked to Lagun
UQparams (list) – list of Uncertainty Quantification parameters
settings (list-like-object) – variables specified in settingsExploration.R

Main reactives:

Global Propagation
- UQres: contains uncertainty quantification propagation data
- output$plot: displays distribution function
- output$table: displays UQres table
- output$download: downloadable CSV file containing UQres
Probability Estimation
- UQproba: contains uncertainty quantification probability data
- output$plotproba: displays probability estimation plot
- simulations$Xadd: contains computed additional simulations
- output$tableproba: additional simulation table
- output$preview: displays additional simulation table
- output$downloadproba: downloadable CSV file containing additional simulations

Main functions

getUQData(DOE, predfun, nsample, UQparams, Yinfos, callback)

Generates a UQ sample and predicts its output

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
predfun (function) – prediction function of the selected metamodel
nsample (numeric) – number of observations
UQparams (list) – list of Uncertainty Quantification parameters
Yinfos (object) – output variable information
callback (function) – reports progress

getUQStats(DOE, UQsample, Yinfos)

Computes descriptive statistics on a UQ sample

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
UQsample (data.frame) – Uncertainty Quantification sample
Yinfos (object) – output variable information

getUQDataProba(DOE, predfun, nrep, nsample, UQparams, id, sname, tname, callback)

Generates a UQ sample and predicts its output. Returns the mean, columnwise, of the data greater or lower than the threshold according to sname and tname

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
predfun (function) – predict function of the selected metamodel
nrep (numeric) – number of repetition
nsample (numeric) – number of observations
UQsample (data.frame) – Uncertainty Quantification sample
id (character) – output index
sname (character) – comparison operator
tname (numeric) – threshold
callback (function) – reports progress

computeAdditionalSimulationsUQ(DOE, nadd, ntest, yname, tname, models, Yinfos, callback)

Generates additional input points for extra simulations, in order to improve the quality of the model. This points can be used if the user is able to compute extra simulations.

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
nadd (numeric) – number of points to add
ntest (numeric) – number of points to test for model improvement
yname (character) – output variable name
tname (character) – target variable name
models (list) – list of the trained models
Yinfos (object) – output variable information
callback (function) – reports progress

Plot functions

plotUQ(DOE, idy, UQsample, typevisu)

Plots either the probability density function or the cumulative probability density function according to typevisu

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
idy (list) – output indices
UQsample (data.frame) – Uncertainty Quantification sample
typevisu (character) – type of plot

plotUQproba(yname, sname, tname, UQproba)

Plots a boxplot to show the probability estimation

Parameters:

yname (character) – output name
sname (character) – comparison operator
tname (numeric) – threshold
UQproba (list) – Uncertainty Quantification probability

Secondary functions

callback(a)__

Reports progress of a task. Calls R Shiny incProgress

Parameters:: i (numeric) – a^th iteration

callback2(r)

Reports progress of the resampling task. Calls R Shiny incProgress

Parameters:: i (numeric) – r^th iteration

sensitivityAnalysis.R

source("modules/menuImport/exploreDOE/quantitativeExploration.R", local = TRUE) source("modules/shared/dynamicSelect.R", local = TRUE)

UI and Server functions

sensitivityAnalysis.ui(id)

This function populates the Step 3: Sensitivity Analysis panel with three tabs:

First & Total Sobol Indices
Higher-Order Sobol Indices
Optimization Indices

Parameters:: id (character) – namespace of the module

Main reactives:

First & Total Sobol Indices
- ui.sobol: populates tab
- download: button to export GSA results
- plotGSAcomplete: displays heatmaps
Higher-Order Sobol Indices
- ui.sobolhigh: populates tab
- dthighorder: displays high-order data as a table
Optimization Indices
- ui.optim: populates tab

sensitivityAnalysis.server(input, output, session, DOE, ML, listmodels, UQparams, window.dimension, settings)

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 point values and the DOE information (e.g. bounds…)
ML (object) – stores the quantitative exploration of the data
listmodels (list) – list of trained models
use_simulator (logical) – informs if a simulator is connected to Lagun
UQparams (list) – list of Uncertainty Quantification parameters
window.dimension (object) – dimensions of the window
settings (list-like-object) – variables specified in settingsExploration.R

Main reactives:

First & Total Sobol Indices
- output$ui.sobol:
  goGSA: button to compute
  
  resamplesobol: checkbox to resample data
  
  chooseY: output variable selection
  
  plotGSA: displays plot
- output$plotGSA: builds first order and total indices plot
- output$plotGSAcomplete: builds heatmaps
- output$download: downloadable CSV file containing sensitivity analysis data
Higher-Order Sobol Indices
- output$ui.sobolhigh:
  selecthighorder: second-order interaction selection
  
  goGSAhighorder: button to compute second-order interactions
  
  resamplesobolhighorder: checkbox to resample data
  
  chooseYhighorder: output variable selection
  
  plotGSAhighorder: displays plot
- output$dthighorder: displays high-order data as a table
- output$plotGSAhighorder: builds high-order plot
Optimization Indices
- output$ui.optim:
  chooseYOptim: output variable selection
  
  GSAsign: comparison operator selection
  
  goGSAoptim: button to compute optimization indices
  
  GSAquantile: slider to select percentage (quantile)
  
  plotGSAOptim: displays optimization plot
- output$plotGSAOptim: builds optimization plot

Main functions

computeGSAres(DOE, UQparams, predfun, nrep, nsample, Yinfos, Ylevel_target, callback)

Computes the Monte Carlo estimation of the Sobol indices for both first-order and total indices. [1] Returns a list with the indices along with their median.

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
UQparams (list) – Uncertainty Quantification parameters
predfun (function) – predict function of the selected metamodel
nrep (numeric) – number of repetitions
nsample (numeric) – UQ sample size
Yinfos (object) – output variable information
Ylevel_target (character) – categorical output class for sensitivity analysis
callback (function) – reports progress

computeShapleyres(DOE, UQparams, predfun, nrep, nsample, Yinfos, Ylevel_target, permutations, callback)

Computes the estimation of Shapley effects using only N model evaluations via nearest neighbour search. [2] Returns a list with the indices along with their median.

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
UQparams (list) – Uncertainty Quantification parameters
predfun (function) – predict function of the selected metamodel
nrep (numeric) – number of repetitions
nsample (numeric) – UQ sample size
Yinfos (object) – output variable information
Ylevel_target (character) – categorical output class for sensitivity analysis
permutations (logical) – informs whether random permutations are used to estimate Shapley effects
callback (function) – reports progress

detectGSAgaps(S1, S1med, ST, STmed, th, Yinfos)

Computes for all inputs and outputs the gap delta between the total and first order Sobol indices (delta = ST - S1) to detect interactions. Interactions are significant if delta is greater than the threshold th for at least half of the repetitions of Sobol index computations. If no interaction is significant, the two inputs with the highest delta are returned for each output.

Parameters:

S1 (matrix) – Sobol first-order indices
S1med (matrix) – S1 median
ST (matrix) – Sobol total indices
STmed (matrix) – ST median
th (numeric) – threshold by which a gap is indicative (0.05 is used)
Yinfos (object) – output variable information

computeGSAres.highorder(DOE, UQparams, predfun, nrep, nsample, Yinfos, list.indices, Ylevel_target, callback)

Computes high-order sobol indices

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
UQparams (list) – Uncertainty Quantification parameters
predfun (function) – predict function of the selected metamodel
nrep (numeric) – number of repetitions
nsample (numeric) – UQ sample size
Yinfos (object) – output variable information
list.indices (list) – list of input variable indices to compute second order Sobol indices for each output
Ylevel_target (character) – categorical output class for sensitivity analysis
callback (function) – reports progress

computeGSAOptimres(DOE, UQparams, predfun, ynamemenu, GSAquantile, GSAsign, nrep, nsample, Yinfos, callback)

Computes optimization indices

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
UQparams (list) – Uncertainty Quantification parameters
predfun (function) – predict function of the selected metamodel
ynamemenu (character) – predicted variable name processed for menus
GSAquantile (numeric) – quantile
GSAsign (character) – optimization type (minimize or maximize)
nrep (numeric) – number of repetitions
nsample (numeric) – UQ sample size
Yinfos (object) – output variable information
callback (function) – reports progress

Plot functions

plotGSA(DOE, ynamemenu, S1, ST, nsample, Yinfos)

Plots the GSA boxplot for a specific output. The sensitivity index dispersion is shown for each input, and both Sobol Indices (first and total).

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
ynamemenu (character) – predicted variable name processed for menus
S1 (matrix) – Sobol first-order indices
S1 – Sobol total indices
nsample (numeric) – sample size
Yinfos (object) – output variable information

plotGSAOptim(DOE, S1, ynamemenu, nsample)

Plots the GSA optimization boxplot for a specific output. The sensitivity index dispersion is shown for each input.

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
S1 (matrix) – Sobol first-order indices
ynamemenu (character) – predicted variable name processed for menus
nsample (numeric) – sample size

plotGSAhighorder(DOE, ynamemenu, S2, idS2, nsample, Yinfos, adapt.visu)

Plots the second-order Sobol indices for a specific output as a grouped boxplot.

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
ynamemenu (character) – predicted variable name processed for menus
S2 (matrix) – Sobol higher-order indices
idS2 (matrix) – input variables indices for which second-order Sobol indices are computed
nsample (numeric) – sample size
Yinfos (object) – output variable information
adapt.visu (logical) – adapt plot to window

plotGSAcomplete(DOE, S1med, STmed, Yinfos)

Plots two heatmaps: one for first-order indices, the other one for total indices Shows the effect of the inputs.

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
S1med (matrix) – Sobol first-order indices median
STmed (matrix) – Sobol total indices median
Yinfos (object) – output variable information

plotShapley(DOE, ynamemenu, S, nsample, Yinfos)

Plots Shapley effects for a specific output as a boxplot.

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
ynamemenu (character) – predicted variable name processed for menus
S (vector) – estimations of the Sobol sensitivity indices
nsample (numeric) – sample size
Yinfos (object) – output variable information

plotShapleycomplete(DOE, Smed, Yinfos)

Plots a heatmap of the Shapley effects to show the effect of the inputs.

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
Smed (vector) – medians of the estimations of the Sobol sensitivity indices
Yinfos (object) – output variable information

Secondary functions

getDataframeGSAres(DOE, GSAres, Yinfos)

Binds the medians of the estimations of the Sobol first-order indices and the estimations of the Sobol total sensitivity indices

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
GSAres (list) – list of matrices, returned by computeGSAres()
Yinfos (object) – output variable information

getDataframeShapleyres(DOE, Shapleyres, Yinfos)

Returns the medians of the estimations of the Sobol sensitivity indices

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
GSAres (list) – list of matrices, returned by computeShapleyres()
Yinfos (object) – output variable information

subsets(set, size=length(set), type='leq')

Creates a subset from an existing set, according to the expected size

Parameters:

set (list) – set to extract a subset from
size (numeric) – expected size of the subset (default=length(set))
type (character) – comparison operator (default=”leq”)

callback(r)__

Reports progress of a task. Calls R Shiny incProgress

Parameters:: i (numeric) – r^th iteration

UQparamsChange.R

UI and Server functions

UQparamsChange.ui(id)

This function helps populating uncertaintyDefinition.ui() modal window, it allows to change uncertainty definition

Parameters:: id (character) – namespace of the module

Main reactives:

change: button to open modal window and change uncertainty definition
separator: radio buttons to choose value delimiter
decimal: radio buttons to choose decimal separator
file: input to upload a file
warning.file: displays the possible errors after checking the file
reset: button to reset values
unifReset: button to reset all distribution types to uniform

UQparamsChange.ui.preview(id)

This function helps populating uncertaintyDefinition.ui(), it displays uncertainty definition as a table

Parameters:: id (character) – namespace of the module

Main reactives:

download: button to export uncertainty definition data
preview: displays uncertainty definition data as a table

UQparams.row.ui(i, ns, input, UQparams, Xinfos, error.msg)

Builds UI for UQParams definition / modification

Parameters:

i (integer) – input variable number
ns (character) – namespaced ID
input (list-like-object) – stores the widgets’ values.
UQparams (list) – Uncertainty Quantification parameters
Xinfos (object) – input variable information
error.msg (object) – error messages

Main reactives:

name: text input for the variable name
typeDistr: distribution type selection
P1Distr, P2Distr, P3Distr, P4Distr: numeric inputs according to the distribution type
level: text input for levels if the variable is categorical
levelproba: weights for the levels

UQparamsChange.server(input, output, session, initialUQparams, DOE, verbose=FALSE)

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.
initialUQparams (list) – default uncertainty quantification parameters
DOE (object) – stores the point values and the DOE information (e.g. bounds…)
verbose (logical) – option to provide additional details during the process (default=FALSE)

Main reactives:

output$warning.file: text output to display potential errors after checking the input file
output$footer:
- save: button to save and close the modal window
- close: button to cancel uncertainty definition modification
output$preview: displays UQ parameters as a table
output$download: downloadable CSV file containing UQ parameters

Main functions

setAllEstimated(Xinfos)

Sets distribution to estimated for each variable.

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

get.UQparams(ind, line, DOE, decimal)

Get parameters stored in line

Parameters:

ind (character) – variable index for which to get parameters
line (vector) – line containing parameters
DOE (object) – stores the point values and the DOE information (e.g. bounds…)
decimal (character) – decimal separator

check.UQparams.file(nX, Xinfos, lines, decimal)

Checks validity of input file

Parameters:

nX (numeric) – number of inputs
Xinfos (object) – input variable information
lines (vector) – lines read from file
decimal (character) – decimal separator

get.UQparams.from.file(DOE, datapath, separator, decimal)

Get parameters stored in file using get.UQparams() for each line

Parameters:

DOE (object) – stores the point values and the DOE information (e.g. bounds…)
datapath (character) – path to data file
separator (character) – delimiter used to separate values in the file
decimal (character) – decimal separator

get.UQparams.from.input(input, Xinfos)

Get parameters entered by the user

Parameters:

input (vector) – input manually entered in the UI
Xinfos (object) – input variable information

UQparams.check(UQparams.temp)

Check parameters entered by the user

Parameters:: UQparams.temp (vector) – input manually entered in the UI

UQparams.normalize(UQparams.temp)

Normalizes the weights of the cateogorical inputs.

Divides each weight by the sum of the weights

Parameters:: UQparams.temp (vector) – input manually entered in the UI

get.UQparams.df(UQparams, Xinfos, ncolumns)

Turns the list of parameters into a data.frame with the right column names and row names

Parameters:

UQparams (list) – Uncertainty Quantification parameters
Xinfos (object) – input variable information
ncolumns (numeric) – number of columns

get.UQparams.download(UQparams, Xinfos, separator, decimal)

Shapes UQParams to properly write them into a file

Parameters:

UQparams (list) – Uncertainty Quantification parameters
Xinfos (object) – input variable information
separator (character) – delimiter used to separate values in the file
decimal (character) – decimal separator

distributionfitting.R

source("modules/menuExplore/UQModel/testfunctions.R", local = TRUE)

UI and Server functions

distributionfitting.ui(id)

This function adds the tab Distribution Fitting to the Uncertainty Definition panel.

It contains itself three more tabs:

Data to Fit Marginals
Distribution Fitting (marginals)
Select Distributions (marginals)

Parameters:: id (character) – namespace of the module

distributionfitting.server(input, output, session, UQparams, listCopulas, DOE)

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 related to the session.
UQparams (list) – list of Uncertainty Quantification parameters
listCopulas (list) – list of copulas
DOE (object) – stores the point values and the DOE informations (e.g. bounds…)

Main reactives:

data.to.fit.marginals: contains data to fit marginals
data.to.fit.copulas: contains data to fit copula
TempEstimDist: contains temporary estimated distribution
FinalEstimDist: contains final estimted distribution
CopulaType: contains the type of copula
output$plotDhist: plots distribution histogram
output$plotFDhist: plots distribution fit histogram
output$plotFDqqplot: plots distribution fit QQ-Plot
output$tableTests: displays the results of GOF tests, see computeGOF

Main functions

ComputeGOF(nameTest, sample, distr, fit, resample)

Computes Goodness-of-Fit with three possible tests :

Kolmogorov - Smirnov
Anderson - Darling
Cramer - Von Mises

Parameters:

nameTest (character) – test to compute
sample (vector) – vector of data
distr (character) – distribution to test
fit (list) – estimated parameters
resample (logical) – informs whether to resample the data or not

testfunctions.R

Main functions

ad.test.one(x, distr, fit)

Performs Anderson-Darling test

Parameters:

x (vector) – data
distr (character) – distribution to test
fit (list) – estimated parameters

ad.test.rep(x, distr, fit, nrep=4999)

Performs Anderson-Darling test with resampling

Parameters:

x (vector) – data
distr (character) – distribution to test
fit (list) – estimated parameters
nrep (numeric) – number of repetitions (default=4999)

cvm.test.one(x, distr, fit)

Performs Cramer-Von Mises test

Parameters:

x (vector) – data
distr (character) – distribution to test
fit (list) – estimated parameters

cvm.test.rep(x, distr, fit, nrep=4999)

Performs Cramer-Von Mises test with resampling

Parameters:

x (vector) – data
distr (character) – distribution to test
fit (list) – estimated parameters
nrep (numeric) – number of repetitions (default=4999)

ks.test.one(x, distr, fit)

Performs Kolmogorov-Smirnov test

Parameters:

x (vector) – data
distr (character) – distribution to test
fit (list) – estimated parameters

ks.test.rep(x, distr, fit, nrep=4999)

Performs Kolmogorov-Smirnov test with resampling

Parameters:

x (vector) – data
distr (character) – distribution to test
fit (list) – estimated parameters
nrep (numeric) – number of repetitions (default=4999)

Secondary functions

closed.form.estimators(distr, x)

Computes estimated parameters

Parameters:

distr (character) – distribution to test
x (vector) – data

UQparamsDependence.R

UI and Server functions

UQparamsDependence.ui(id, label)

Creates a modal window to change the inputs’ dependence definition.

Parameters:

id (character) – namespace of the module
label (character) – action button label

UQparamsDependence.server(input, output, session, initiallistCopulas, fitdistUQparams, DOE)

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 related to the session.
initiallistCopulas (list) – initial list of copulas
fitdistUQparams (object) – UQ parameters for distribution fitting
DOE (object) – stores the point values and the DOE informations (e.g. bounds…)

Main reactives:

listCopulas: list of copulas
Xnum: contains the numerical inputs
output$copulaInputs.dynui: UI to specify the groups and copula definition
output$group.dynui: UI to specify the independent inputs belonging to each group
output$paramcopula.dynui: UI to specify the copula parameters

Menu Explore

Tutorials

Architecture

menuExplore.R

UI and Server functions

Explore Model

exploreModel.R

UI and Server functions

modelQualitativeExploration.R

UI and Server functions

Main functions

Secondary functions

modelQuantitativeExploration.R

UI and Server functions

Plot functions

Secondary functions

modelManualExploration.R

UI and Server functions

Main functions

UQ Model

UQModel.R

UI and Server functions

uncertaintyDefinition.R

UI and Server functions

Main functions

uncertaintyPropagation.R

UI and Server functions

Main functions

Plot functions

Secondary functions

sensitivityAnalysis.R

UI and Server functions

Main functions

Plot functions

Secondary functions

UQparamsChange.R

UI and Server functions

Main functions

distributionfitting.R

UI and Server functions

Main functions

testfunctions.R

Main functions

Secondary functions

UQparamsDependence.R

UI and Server functions

References