Adaptive importance sampling for risk analysis of complex infrastructure systems

Complex civil infrastructure systems are typically exposed to random loadings and have a large number of possible failure modes, which often exhibit spatially and temporally variable consequences. Monte Carlo (level III) reliability methods are attractive because of their flexibility and robustness, yet computational expense may be prohibitive, in which case variance reduction methods are required. In the importance sampling methodology presented here, the joint probability distribution of the loading variables is sampled according to the contribution that a given region in the joint space makes to risk, rather than according to probability of failure, which is the conventional importance sampling criterion in structural reliability analysis. Results from simulations are used to intermittently update the importance sampling density function based on the evaluations of the (initially unknown) risk function. The methodology is demonstrated on a propped cantilever beam system and then on a real coastal dike infrastructure system in the UK. The case study demonstrates that risk can be a complex function of loadings, the resistance and interactions of system components and the spatially variable damage associated with different modes of system failure. The methodology is applicable in general to Monte Carlo risk analysis of systems, but it is likely to be most beneficial where consequences of failure are a nonlinear function of load and where system simulation requires significant computational resources.