mpp_search
Specify which MPP search option to use
Topics
uncertainty_quantification, reliability_methods
Specification
Alias: None
Arguments: None
Default: No MPP search (MV method)
Child Keywords:
Required/Optional 
Description of Group 
Dakota Keyword 
Dakota Keyword Description 

Required (Choose One) 
MPP Approximation 
Form Taylor series approximation in “xspace” at variable means 

Form Taylor series approximation in “uspace” at variable means 

Xspace Taylor series approximation with iterative updates 

Uspace Taylor series approximation with iterative updates 

Predict MPP using Twopoint Adaptive Nonlinear Approximation in “xspace” 

Predict MPP using Twopoint Adaptive Nonlinear Approximation in “uspace” 

MPP search for local reliability based on QMEA multipoint approximation in uspace 

MPP search for local reliability based on QMEA multipoint approximation in xspace 

Perform MPP search on original response functions (use no approximation) 

Optional (Choose One) 
Optimization Solver 
Uses a sequential quadratic programming method for underlying optimization 

Uses a nonlinear interior point method for underlying optimization 

Optional 
Integration approach 
Description
The x_taylor_mean
MPP search option performs a
single Taylor series approximation in the space of the original
uncertain variables (“xspace”) centered at the uncertain variable
means, searches for the MPP for each response/probability level using
this approximation, and performs a validation response evaluation at
each predicted MPP. This option is commonly known as the Advanced
Mean Value (AMV) method. The u_taylor_mean
option is identical to
the x_taylor_mean
option, except that the approximation is
performed in uspace. The x_taylor_mpp
approach starts with an
xspace Taylor series at the uncertain variable means, but iteratively
updates the Taylor series approximation at each MPP prediction until
the MPP converges. This option is commonly known as the AMV+ method.
The u_taylor_mpp
option is identical to the x_taylor_mpp
option,
except that all approximations are performed in uspace. The order of
the Taylorseries approximation is determined by the corresponding
responses
specification and may be first or secondorder. If
secondorder (methods named \(AMV^2\) and \(AMV^2+\) in
[EB06]), the series may employ
analytic, finite difference, or quasi Hessians (BFGS or SR1).
The x_two_point
MPP search option uses an xspace Taylor series
approximation at the uncertain variable means for the initial MPP
prediction, then utilizes the Twopoint Adaptive Nonlinear
Approximation (TANA) outlined in [XG98]
for all subsequent MPP predictions. The u_two_point
approach is
identical to x_two_point
, but all the approximations are performed
in uspace. The x_taylor_mpp
and u_taylor_mpp
, x_two_point
and u_two_point
approaches utilize the max_iterations
and
convergence_tolerance
method independent controls to control the
convergence of the MPP iterations (the maximum number of MPP
iterations per level is limited by max_iterations
, and the MPP
iterations are considered converged when
\(\parallel {\bf u}^{(k+1)}  {\bf u}^{(k)} \parallel_2\) <
convergence_tolerance
). And, finally, the .no_approx
option
performs the MPP search on the original response functions without
the use of any approximations. The optimization algorithm used to
perform these MPP searches can be selected to be either sequential
quadratic programming (uses the npsol_sqp
optimizer) or nonlinear
interior point (uses the optpp_q_newton
optimizer) algorithms
using the sqp
or nip
keywords.
In addition to the MPP search specifications, one may select among
different integration approaches for computing probabilities at the
MPP by using the integration
keyword followed by either
first_order
or second_order
. Secondorder integration employs the
formulation of [HR88]
(the approach of [Bre84] and the correction
of [Hon99] are also implemented, but are not active).
Combining the no_approx
option of the MPP search with first and
secondorder integrations results in the traditional first and
secondorder reliability methods (FORM and SORM). These integration
approximations may be subsequently refined using importance sampling.
The refinement
specification allows the seletion of basic
importance sampling ( import
), adaptive importance sampling (
adapt_import
), or multimodal adaptive importance sampling (
mm_adapt_import
), along with the specification of number of samples
( samples
) and random seed ( seed
). Additional details
on these methods are available in [EGC04]
and [EB06] and in the main Uncertainty Quantification Capabilities section.