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