G(x) = Z(x)T b (3-3)
where x is the vector of input random variables. With the polynomial approximation
G(x), the probability of failure can then be calculated inexpensively by Monte Carlo
simulation or FORM/SORM. Since the RSA is constructed in random variable space, this
approach is called stochastic response surface approach.
Stochastic RSA can be applied in difference ways. One approach is to construct
local RSA around the Most Probable Point (MPP), the region that contributes most to the
probability of failure of the structure. The statistical design of experiment (DOE) of this
approach is iteratively performed to approach the MPP. Another approach is to construct
global response surfaces over the entire range of the random variables, where the mean
value of the random variables is usually chosen as the center of DOE. The selection of
RSA approach depends on the limit state function of the problem. Global RSA is simpler
and efficient to use than local RSA for problems with limit state function that can be well
approximated globally.
Analysis Response Surface (ARS) Approximation for Reliability-Based Design
Optimization
In reliability-based design optimization (RBDO), the SRS approach needs to
construct response surfaces to limit state functions at each point encountered in the
optimization process, which requires a fairly large number of limit state function
evaluation and RS construction. The local SRS approach is more computationally
expensive than the global SRS approach due to multiple iterations involved in the RSA
construction.
This dissertation (see also Qu et al., 2000) developed an analysis response surface
(ARS) approach in the unified system space (x, d) to reduce the cost of RBDO, where x