Characterization and prediction of rare and extreme events that correspond to large excursions is of
central importance in several applications. Important examples can be found in natural phenomena
such as climate, weather, oceanography and engineering systems such as structures, power grids, etc.
Accurate characterization and reliable prediction of these events allows for realistic balancing of
risks and costs in complex and expensive infrastructure. Two important challenges related to these
rare and extreme events are i) limited availability of data that correspond to these rare and extreme
events, leads to difficulty in quantifying tail properties for the relevant distribution and ii)
determining the statistics of level crossings and durations of temporally or spatially correlated
processes. The aim of this MS is to present research that address these two general problems. Approaches based on, but not restricted to, data, dynamics, or a combination of both will be discussed.
16:30
- NEW - Characterizing the distribution of cascading power network failures
Jake Roth | Argonne National Laboratory | United States
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Author:
Jake Roth | Argonne National Laboratory | United States
In power grid planning, operating points are set so that power generation can safely satisfy projected power demand until the next setpoint. Between setpoints (~10 minutes), the grid is subject to parametric uncertainty in demand and generation levels. These variations can cause the grid's autonomous feedback systems to initiate fault-protection mechanisms that may de-energize infrastructure components and spread throughout the network. In severe cases, these sequences of actions may result in the loss of power in significant portions of the grid. Such cascading failures are rare and difficult to study empirically, and in this talk, we discuss one approach for characterizing the distribution of cascade severity due to parametric uncertainty in demand and generation. Specifically, using a stochastically perturbed, first-principles dynamical model of the power grid, we explore how the magnitude of our initial uncertainty can impact the failure-severity distribution via simulation. To do so efficiently, we utilize results from large deviation theory in combination with simulation tools developed for studying chemical reactions.
17:00
Estimation of Failure Probabilities via Local MCMC Subset Approximations
Kenan Sehic | Technical University of Denmark | Denmark
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Authors:
Kenan Sehic | Technical University of Denmark | Denmark
Mirza Karamehmedovic | Technical University of Denmark | Denmark
Youssef Marzouk | Massachusetts Institute of Technology | United States
Classical Monte Carlo methods for estimating small failure probabilities have high computational demands. Therefore, an adaptive simulation approach called subset simulation, was proposed which expresses the failure probability as a product of larger intermediate conditional failure probabilities, shifts the sampling focus to smaller probability regions and increases efficiency. The conditional probabilities are found via a Markov Chain Monte Carlo (MCMC) approach. An MCMC chain typically requires many steps to converge within an acceptable error and is limited by the computational cost of the likelihood. Therefore, we here build on the work of P. Conrad et al. (2015) and introduce local approximations of a limit state function within Metropolis-Hastings kernels for the subset simulation approach. The ideas are based on deterministic approximation theory, optimization, and experimental design. To increase the overall efficiency of local MCMC approximations in high-dimension cases, we employ partial least squares regression (PLS). Using local approximations in subset simulations, we can reduce the number of expensive numerical evaluations by 85% in low-dimensional cases and by 60% in high-dimensional cases.
17:30
Extreme Event Quantification for Rogue Waves in Deep Sea
Tobias Grafke | University of Warwick | United Kingdom
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Author:
Tobias Grafke | University of Warwick | United Kingdom
A central problem in uncertainty quantification is how to characterize
the impact that our incomplete knowledge about models has on the
predictions we make from them. This question naturally lends itself to a
probabilistic formulation, by making the unknown model parameters random
with given statistics. Here this approach is used in concert with tools
from large deviation theory (LDT) and optimal control to estimate the
probability that some observables in a dynamical system go above a large
threshold after some time, given the prior statistical information about
the system's parameters and its initial conditions. We use this approach
to quantify the likelihood of extreme surface elevation events for deep
sea waves, so-called rogue waves, and compare the results to
experimental measurements. We show that our approach offers a unified
description of rogue wave events in the one-dimensional case, covering a
vast range of paramters. In particular, this includes both the
predominantly linear regime as well as the highly nonlinear regime as
limiting cases, and is able to predict the experimental data regardless
of the strength of the nonlinearity.
18:00
Extreme values of LIDAR wind speed
Charlotte Haley | Argonne National Laboratory | United States
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Authors:
Charlotte Haley | Argonne National Laboratory | United States
Vishwas Rao | Argonne National Laboratory | United States
Mihai Anitescu | Argonne National Laboratory and University of Chicago | United States
Extremes of wind speed cause structural damage to buildings and wind turbine structures, and can be
relatively unpredictable in the presence of complex orography. Boundary layer fluid models are known
to systematically underpredict the extremes of wind speed. In this study we examine a model for
vertical wind speed that accounts for the nonstationary diurnal fluctuations of wind speed due to
convection and gravity wave impacts at the top of the boundary layer, and hierarchically we model
the extremes of the process using a two-state Markov chain constructed by observing whether the
process exceeds a given threshold. Using Markov Chain Monte Carlo techniques, we can tune the model
to reproduce the level crossings observed using data collected by lidar instruments, and produce
additional realizations of the threshold crossing process. Additionally we can model the durations
of the exceedancees above the threshold.