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Generalised Interval Probability and its Applications in Engineering
Uncertainty in engineering analysis is composed of two components. One is the inherent randomness because of fluctuation and perturbation as aleatory uncertainty, and the other is epistemic uncertainty due to lack of perfect knowledge about the system. Imprecise probability provides a compact way to quantify and differentiate the two components, where the probability measures randomness and the interval range quantifies the imprecision associated with the probability. Several forms of imprecise probability have been proposed such as Dempster-Shafer theory, coherent lower prevision, p-box, possibility theory, fuzzy probability, and random set. To simplify the computation for engineering analysis, we introduced generalized interval probability where the interval bounds take the form of directed or modal interval instead of classical set-based interval. Interval calculation is based on the more intuitive Kaucher interval arithmetic. Generalized interval probability has been applied in studying stochastic dynamics, hidden Markov model, Kalman filter, random set sampling, and molecular dynamics simulation.
Professor Yan Wang, Ph.D. is a Professor of Mechanical Engineering at Georgia Institute of Technology. He is interested in multiscale systems engineering, modeling and simulation, and uncertainty quantification, and has published over 90 archived journal papers and 80 peer-reviewed conference papers. He recently edited the first book of its kind on uncertainty quantification in multiscale materials modeling
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