Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Local reliability method
This keyword is related to the topics:
Alias: nond_local_reliability
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  mpp_search  Specify which MPP search option to use  
Optional  response_levels  Values at which to estimate desired statistics for each response  
Optional  reliability_levels  Specify reliability levels at which the response values will be estimated  
Optional  max_iterations  Stopping criterion based on number of iterations  
Optional  convergence_tolerance  Stopping criterion based on convergence of the objective function or statistics  
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  model_pointer  Identifier for model block to be used by a method 
Local reliability methods compute approximate response function distribution statistics based on specified uncertain variable probability distributions. Each of the local reliability methods can compute forward and inverse mappings involving response, probability, reliability, and generalized reliability levels.
The forward reliability analysis algorithm of computing reliabilities/probabilities for specified response levels is called the Reliability Index Approach (RIA), and the inverse reliability analysis algorithm of computing response levels for specified probability levels is called the Performance Measure Approach (PMA).
The different RIA/PMA algorithm options are specified using the mpp_search
specification which selects among different limit state approximations that can be used to reduce computational expense during the MPP searches.
The Mean Value method (MV, also known as MVFOSM in [41]) is the simplest, leastexpensive method in that it estimates the response means, response standard deviations, and all CDF/CCDF forward/inverse mappings from a single evaluation of response functions and gradients at the uncertain variable means. This approximation can have acceptable accuracy when the response functions are nearly linear and their distributions are approximately Gaussian, but can have poor accuracy in other situations.
All other reliability methods perform an internal nonlinear optimization to compute a most probable point (MPP) of failure. A sign convention and the distance of the MPP from the origin in the transformed standard normal space ("uspace") define the reliability index, as explained in the section on Reliability Methods in the Uncertainty Quantification chapter of the Users Manual [5]. Also refer to variable_support for additional information on supported variable types for transformations to standard normal space. The reliability can then be converted to a probability using either first or secondorder integration, may then be refined using importance sampling, and finally may be converted to a generalized reliability index.
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