Power Grid Reliability Estimation via Adaptive Importance Sampling

Quantile Estimation with Adaptive Importance Sampling

AN ADAPTIVE IMPORTANCE SAMPLING-BASED ALGORITHM USING THE FIRST-ORDER METHOD FOR STRUCTURAL RELIABILITY

Monte Carlo simulation (MCS) is a useful tool for computation of probability of failure in reliability analysis. However, the large number of samples, often required for acceptable accuracy, makes it time-consuming. Importance sampling is a method on the basis of MCS which has been proposed to reduce the computational time of MCS. In this paper, a new adaptive importance sampling-based algorith...

Faster Coordinate Descent via Adaptive Importance Sampling

Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive, we mean that our selection rules are based on the dual residual or the primal-dual gap estimates and can change at each iteration. We theoretically character...

Adaptive Importance Sampling via Stochastic Convex Programming

We show that the variance of the Monte Carlo estimator that is importance sampled from an exponential family is a convex function of the natural parameter of the distribution. With this insight, we propose an adaptive importance sampling algorithm that simultaneously improves the choice of sampling distribution while accumulating a Monte Carlo estimate. Exploiting convexity, we prove that the m...

Model Bank State Estimation for Power Grids Using Importance Sampling

Power grid operators decide where and how much power to generate based on the current topology and demands of the network. The topology can change as safety devices trigger (connecting or disconnecting parts of the network) or as lines go down. Often, the operator cannot observe these events directly, but instead has contemporary measurements and historical information about a subset of the lin...