A probabilistic framework for the reduced-order modeling of rare events in water waves and mechanical systems
Abstract
Summary This project is focused on the development, application, and demonstration of new theories and computational methods that will creatively combine elements of dynamical systems theory and probabilistic analysis towards the quantification and prediction of extreme events occurring in complex systems. Systems exhibiting rare events range from climate dynamics and the formation of freak water waves in the ocean to mechanical systems subjected to stochastic loads and critical events in power grids, just to mention a few. For many systems of practical interest like those it has now been well established that rare transitions occur frequently enough so that it is essential to study them more carefully and develop a framework specifically designed to describe and predict them. Here we are interested to address two specific topics related to rare events in complex dynamical systems: i) perform short-term prediction in the future given that we are able to measure specific quantities about the current system’s state (Rare Event Prediction Problem); and ii) quantify the probability of occurrence of a rare event for a given energetic regime of the system (Rare Event Quantification Problem). The first topic is important for a wide range of applications for which we need to know in advance when and where there is high likelihood for the occurrence of a rare response in the near future (e.g. unusually high water wave elevations in naval operations, predictive control and suppression of instabilities in power grids, etc.). The second topic is particularly important for the formulation of probabilistic design criteria in engineering systems. In order to perform reliable design with reasonable cost it is essential to know what rare events we should expect and with what probability (e.g. what is the maximum structural load for a ship moving in a wave field with given spectrum or what is the probability of a critical event in a power grid for a given energy consumption). The developed methods will combine information theory, reducedorder adaptive filtering/predictive schemes, and stochastic dynamical systems theory. A successful implementation of the proposed research plan will introduce a new paradigm for the analysis, quantification, and prediction of strongly transient and nonlinear dynamical responses in complex systems. In addition, by linking information-theoretic techniques to adaptive reduced order probabilistic models our research will catalyze new domains of numerical/mathematical analysis and it will extend the reach of more conventional mathematics-assisted modeling beyond some of its current limits
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512381
Entities
People
- Danforth Apollo Nicholas
Organizations
- Massachusetts Institute of Technology
- Office of Naval Research
- United States Navy