Optimal Hit-Based Splitting Technique for Rare-Event Simulation and Its Application to Power Grid Blackout Simulation
Date Issued
2011
Date
2011
Author(s)
Wang, Sing-Po
Abstract
Rare-event probability estimation is a crucial issue in areas such as reliability, telecommunications and aircraft management. When an event rarely occurs, naive Monte Carlo simulation becomes unreasonably demanding for computing power and often results in an unreliable probability estimate, i.e., an estimate with a large variance. Level splitting simulation has emerged as a promising technique to reduce the variance of a probability estimate by creating separate copies (splits) of the simulation whenever it gets close to a rare event. This technique allocates simulation runs to levels of event progressively approaching a final rare event. However, determination of a good number of simulation runs at each stage can be challenging. An optimal splitting technique called the Optimal Splitting Technique for Rare Events (OSTRE) provides an asymptotically optimal allocation solution of simulation runs. A splitting simulation characterized by allocating simulation runs may fail to obtain a probability estimate because the probability of an event occurring at a given level is too low, and the number of simulation runs allocated to that level is not enough to observe it. In this research, we propose a hit-based splitting method that allocates a number of hits, instead of the number of simulation runs, to each stage. The number of hits is the number of event occurrences at each stage. Regardless of the number of simulation runs required, the allocated number of hits has to be reached before advancing to the next level of splitting simulation. We derive an asymptotically optimal allocation of hits to each stage of splitting simulation, referred to as Optimal Hit-based Splitting Simulation. Experiments indicate that the proposed method performs as well as OSTRE under most conditions. In addition to the allocation problem, choice of levels is also a critical issue in level splitting simulation. Based on the proposed hit-based splitting simulation method, we have developed an algorithm capable of obtaining optimal levels by effectively estimating the initial probability for some events to occur at each stage of progression. Results indicate that the choice of optimal levels is effective. Furthermore, we apply our technique to an IEEE-bus electric network and demonstrate our approach is just as effective as conventional techniques in detecting the most vulnerable link in the electric grid, i.e., the link with the highest probability leading to a blackout event.
Subjects
rare event
multilevel splitting
hit-based splitting
power grid
blackout
Type
thesis
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