The ISPUD strategy (Bourgund and Bucher 1986) is to center the sampling density at the failure surface in the region of highest probability density. For this purpose, a searching procedure analogous to FORM (First Order Reliability Method (FORM)) is applied.

Figure 5.3: Parabola Example: Anthill Plots of Subsequent Adaptive Sampling Runs

The sampling density h _Y has a mean vector defined by the design point transformed back to original space. Distribution types, variances and correlations are taken over from the definitions of the original random parameters.

(5–22)

(5–23)

Figure 5.4: Parabola Example: Anthill Plot of Importance Sampling Using the Design Point shows the ISPUD sampling for the same example of a parabola, as it is introduced in Adaptive Sampling (ADSAP).

As for FORM, the success of the optimization step is crucial also for this method. At present, the gradient-based NLPQL algorithm is used, so the limit state function has to be sufficiently smooth, continuous, with a unique design point. If the design point can be determined correctly, ISPUD can overcome inaccuracies due to the linearization, which is typical for FORM.

Figure 5.4: Parabola Example: Anthill Plot of Importance Sampling Using the Design Point