Error Measure for Reliability Studies Using Reduced Variable Set

A reduction in the number of random variables carried in a structural-reliability analysis can be achieved by an orthogonal transformation of the basic random vector to a vector of independent standard normal variables, followed by a reduction procedure similar to that employed in modal analysis in structural dynamics. This paper investigates the error introduced by this reduction in the representation of random fields through orthogonal-series expansions. It is found that the error in the second-moment representation of a random field is bounded by the reduction error, which is easily computed, when the correlation length of the random field is short; this often is the case in stochastic finite-element analysis.