  Reliability-based design optimization (RBDO) aims at determination of the
optimal design in the presence of uncertainty. The available Single-Loop
approaches for RBDO are based on the First-Order Reliability Method (FORM) for
the computation of the probability of failure, along with different
approximations in order to avoid the expensive inner loop aiming at finding the
Most Probable Point (MPP). However, the use of FORM in RBDO may not lead to
sufficient accuracy depending on the degree of nonlinearity of the limit-state
function. This is demonstrated for an extensively studied reliability-based
design for vehicle crashworthiness problem solved in this paper, where all RBDO
methods based on FORM strongly violates the probabilistic constraints. The
Response Surface Single Loop (RSSL) method for RBDO is proposed based on the
higher order probability computation for quadratic models previously presented
by the authors. The RSSL-method bypasses the concept of an MPP and has high
accuracy and efficiency. The method can solve problems with both constant and
varying standard deviation of design variables and is particularly well suited
for typical industrial applications where general quadratic response surface
models can be used. If the quadratic response surface models of the
deterministic constraints are valid in the whole region of interest, the method
becomes a true single loop method with accuracy higher than traditional SORM.
In other cases, quadratic response surface models are fitted to the
deterministic constraints around the deterministic solution and the RBDO
problem is solved using the proposed single loop method.
