sampling

Randomly samples variables according to their distributions

Topics

uncertainty_quantification, sampling

Specification

• Alias: nond_sampling

• Arguments: None

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Optional		samples	Number of samples for sampling-based methods
Optional		seed	Seed of the random number generator
Optional		fixed_seed	Reuses the same seed value for multiple random sampling sets
Optional		sample_type	Selection of sampling strategy
Optional		refinement_samples	Performs an incremental Latin Hypercube Sampling (LHS) study
Optional		d_optimal	Generate a D-optimal sampling design
Optional		variance_based_decomp	Activates global sensitivity analysis based on decomposition of response variance into contributions from variables
Optional		backfill	Ensures that the samples of discrete variables with finite support are unique
Optional		principal_components	Activates principal components analysis of the response matrix of N samples * L responses.
Optional		wilks	Number of samples for random sampling using Wilks statistics
Optional		std_regression_coeffs	Output Standardized Regression Coefficients and R^2 for samples
Optional		tolerance_intervals	Computes the double sided tolerance interval equivalent normal distribuion.
Optional		final_moments	Output moments of the specified type and include them within the set of final statistics.
Optional		response_levels	Values at which to estimate desired statistics for each response
Optional		probability_levels	Specify probability levels at which to estimate the corresponding response value
Optional		reliability_levels	Specify reliability levels at which the response values will be estimated
Optional		gen_reliability_levels	Specify generalized relability levels at which to estimate the corresponding response value
Optional		distribution	Selection of cumulative or complementary cumulative functions
Optional		rng	Selection of a random number generator
Optional		model_pointer	Identifier for model block to be used by a method

Description

This method generates parameter values by drawing samples from the specified uncertain variable probability distributions. The computational model is executed over all generated parameter values to compute the responses for which statistics are computed. The statistics support sensitivity analysis and uncertainty quantification.

Default Behavior

By default, sampling methods operate on aleatory and epistemic uncertain variables. The types of variables can be restricted or expanded (to include design or state variables) through use of the active keyword in the variables block in the Dakota input file. If continuous design and/or state variables are designated as active, the sampling algorithm will treat them as parameters with uniform probability distributions between their upper and lower bounds. Refer to Variable Support for additional information on supported variable types, with and without correlation.

The following keywords change how the samples are selected:

• sample_type

• fixed_seed

• rng

• samples

• seed

• variance_based_decomp

Expected Outputs

As a default, Dakota provides correlation analyses when running LHS. Correlation tables are printed with the simple, partial, and rank correlations between inputs and outputs. These can be useful to get a quick sense of how correlated the inputs are to each other, and how correlated various outputs are to inputs. variance_based_decomp is used to request more sensitivity information, with additional cost.

Additional statistics can be computed from the samples using the following keywords:

• response_levels

• reliability_levels

• probability_levels

• gen_reliability_levels

response_levels computes statistics at the specified response value. The other three allow the specification of the statistic value, and will estimate the corresponding response value.

distribution is used to specify whether the statistic values are from cumulative or complementary cumulative functions.

Expected HDF5 Output

If Dakota was built with HDF5 support and run with the hdf5 keyword, this method writes the following results to HDF5:

• When variance_based_decomp is enabled

  • Variance-Based Decomposition (Sobol’ Indices)

• For aleatory UQ studies

  • Probability Density

  • Level Mappings

  • Sampling Moments

  • Correlations

• For epistemic UQ studies

  • Extreme Responses

  • Correlations

Usage Tips

sampling is a robust approach to doing sensitivity analysis and uncertainty quantification that can be applied to any problem. It requires more simulations than newer, advanced methods. Thus, an alternative may be preferable if the simulation is computationally expensive.

Active Variables: By default sampling generates samples only for the uncertain variables, and treats any design or state variables as constants. However, if active all is specified sampling will be performed over all variables, including uncertain, design, and state. In this case, the sampling algorithm will treat any continuous design or continuous state variables as parameters with uniform probability distributions between their upper and lower bounds.

This is similar to the behavior of the design of experiments methods, since they will also generate samples over all continuous design, uncertain, and state variables in the variables specification. However, the design of experiments methods will treat all variables as being uniformly distributed between their upper and lower bounds, whereas the sampling method will sample the uncertain variables within their specified probability distributions. The other active options can enable sample over other subsets of variables.

Examples

# tested on Dakota 6.0 on 140501

environment
  tabular_data
    tabular_data_file = 'Sampling_basic.dat'

method
  sampling
    sample_type lhs
    samples = 20

model
  single

variables
  active uncertain
  uniform_uncertain = 2
    descriptors  =   'input1'     'input2'
    lower_bounds =  -2.0     -2.0
    upper_bounds =   2.0      2.0
  continuous_state = 1
    descriptors =   'constant1'
    initial_state = 100

interface
  analysis_drivers 'text_book'
    fork

responses
  response_functions = 1
  no_gradients
  no_hessians

This example illustrates a basic sampling Dakota input file.

• LHS is used instead of purely random sampling.

• The default random number generator is used.

• Without a seed specified, this will not be reproducable

• In the variables block, two types of variables are used

• Only the uncertain variables are varied, this is the default behavior, and is also specified by the active keyword, w/ the uncertain option

FAQ

Q: Do I need to keep the LHS* and S4 files? A: No