7,003 research outputs found
Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response
A fundamental issue when predicting structural response by using mathematical models is how to treat both modeling and excitation uncertainty. A general framework for this is presented which uses probability as a multi-valued
conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The
fundamental probability models that represent the structure’s uncertain behavior are specified by the choice of a stochastic
system model class: a set of input-output probability models for the structure and a prior probability distribution over this set
that quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic
structural model by stochastic embedding utilizing Jaynes’ Principle of Maximum Information Entropy. Robust predictive
analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if
structural response data is available, by its posterior probability from Bayes’ Theorem for the model class. Additional robustness
to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates
weighted by the prior or posterior probability of the model class, the latter being computed from Bayes’ Theorem. This higherlevel application of Bayes’ Theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more
complex model classes that extract more information from the data. Robust predictive analyses involve integrals over highdimensional spaces that usually must be evaluated numerically. Published applications have used Laplace's method of
asymptotic approximation or Markov Chain Monte Carlo algorithms
Statistical analysis of Hasegawa - Wakatani turbulence
Resistive drift wave turbulence is a multipurpose paradigm that can be used
to understand transport at the edge of fusion devices. The Hasegawa-Wakatani
model captures the essential physics of drift turbulence while retaining the
simplicity needed to gain a qualitative understanding of this process. We
provide a theoretical interpretation of numerically generated probability
density functions (PDFs) of intermittent events in Hasegawa-Wakatani turbulence
with enforced equipartition of energy in large scale zonal flows and small
scale drift turbulence. We find that for a wide range of adiabatic index values
the stochastic component representing the small scale turbulent eddies of the
flow, obtained from the ARIMA model, exhibits super-diffusive statistics,
consistent with intermittent transport. The PDFs of large events (above one
standard deviation) are well approximated by the Laplace distribution, while
small events often exhibit a Gaussian character. Furthermore there exist a
strong influence of zonal flows for example, via shearing and then viscous
dissipation maintaining a sub-diffusive character of the fluxes
Minimizing value-at-risk in the single-machine total weighted tardiness problem
The vast majority of the machine scheduling literature focuses on deterministic
problems, in which all data is known with certainty a priori. This may be a reasonable assumption when the variability in the problem parameters is low. However, as variability in the parameters increases incorporating this uncertainty explicitly into a scheduling model is essential to mitigate the resulting adverse effects. In this paper, we consider the celebrated single-machine total weighted tardiness (TWT) problem in the presence of uncertain problem parameters. We impose a probabilistic constraint on the random TWT and introduce a risk-averse stochastic programming model. In particular, the objective of the proposed model is to find a non-preemptive static job processing sequence that minimizes the value-at-risk (VaR) measure on the random
TWT at a specified confidence level. Furthermore, we develop a lower bound on the optimal VaR that may also benefit alternate solution approaches in the future. In this study, we implement a tabu-search heuristic to obtain reasonably good feasible solutions and present results to demonstrate the effect of the risk parameter and the value of the proposed model with respect to a corresponding risk-neutral approach
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