Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

ProbabilityofFailure (POF) darts is a novel method for estimating the probability of failure based on random spherepacking.
This keyword is related to the topics:
Alias: nond_pof_darts
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required  build_samples  Number of initial model evaluations used in build phase  
Optional  seed  Seed of the random number generator  
Optional  lipschitz  Select the type of Lipschitz estimation (global or local)  
Optional  samples_on_emulator  Number of samples at which to evaluate an emulator (surrogate)  
Optional  response_levels  Values at which to estimate desired statistics for each response  
Optional  distribution  Selection of cumulative or complementary cumulative functions  
Optional  probability_levels  Specify probability levels at which to estimate the corresponding response value  
Optional  gen_reliability_levels  Specify generalized relability levels at which to estimate the corresponding response value  
Optional  rng  Selection of a random number generator  
Optional  model_pointer  Identifier for model block to be used by a method 
pof_darts
is a novel method for estimating the probability of failure based on random spherepacking. Random spheres are sampled from the domain with the constraint that each new sphere center has to be outside prior disks. The radius of each sphere is chosen such that the entire sphere lie either in the failure or the nonfailure region. This radius depends of the function evaluation at the disk center, the failure threshold and an estimate of the function gradient at the disk center.
We utilize a global surrogate for evaluating the gradient and hence only one function evaluation is required for each sphere.
After exhausting the sampling budget specified by samples
, which is the number of spheres per failure threshold, the domain is decomposed into two regions. These regions correspond to failure and nonfailure, each represented by the union of the spheres of each type. The volume of the union of failure spheres gives a lower bound on the required estimate of the probability of failure, while the volume of the union of the nonfailure spheres subtracted from the volume of the domain gives an upper estimate. We currently report the average of both estimates.
pof_darts
handles multiple response functions and allows each to have multiple failure thresholds. For each failure threshold, pof_darts
will insert a number of spheres specified by the userinput parameter samples
.
However, estimating the probability of failure for each failure threshold would utilize the total number of disks sampled for all failure thresholds. For each failure threshold, the sphere radii changes to generate the right spatial decomposition.