图书馆订阅: Guest
Begell Digital Portal Begell 数字图书馆 电子图书 期刊 参考文献及会议录 研究收集
国际不确定性的量化期刊
影响因子: 4.911 5年影响因子: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN 打印: 2152-5080
ISSN 在线: 2152-5099

Open Access

国际不确定性的量化期刊

DOI: 10.1615/Int.J.UncertaintyQuantification.2012003641
pages 271-288

PRIOR AND POSTERIOR ROBUST STOCHASTIC PREDICTIONS FOR DYNAMICAL SYSTEMS USING PROBABILITY LOGIC

James L. Beck
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
Alexandros Taflanidis
Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame 156 Fitzpatrick Hall, Notre Dame, IN 46556

ABSTRACT

An overview is given of a powerful unifying probabilistic framework for treating modeling uncertainty, along with input uncertainty, when using dynamic models to predict the response of a system during its design or operation. This framework uses probability as a multivalued conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The fundamental probability models that represent the system's uncertain behavior are specified by the choice of a stochastic system model class: a set of input–output probability models for the system and a prior probability distribution over this set that quantifies the relative plausibility of each model. A model class can be constructed from a parametrized deterministic system model by stochastic embedding which utilizes 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 response data are 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 higher-level 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 high-dimensional spaces that usually must be evaluated numerically by Laplace's method of asymptotic approximation or by Markov chain Monte Carlo methods. These computational tools are demonstrated in an illustrative example involving the vertical dynamic response of a car being driven along a rough road.


Articles with similar content:

A BAYES NETWORK APPROACH TO UNCERTAINTY QUANTIFICATION IN HIERARCHICALLY DEVELOPED COMPUTATIONAL MODELS
International Journal for Uncertainty Quantification, Vol.2, 2012, issue 2
Sankaran Mahadevan, Thomas L. Paez, Angel Urbina
A MIXED UNCERTAINTY QUANTIFICATION APPROACH USING EVIDENCE THEORY AND STOCHASTIC EXPANSIONS
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 1
Tyler Winter, Serhat Hosder, Harsheel Shah
ORTHOGONAL BASES FOR POLYNOMIAL REGRESSION WITH DERIVATIVE INFORMATION IN UNCERTAINTY QUANTIFICATION
International Journal for Uncertainty Quantification, Vol.1, 2011, issue 4
Oleg Roderick, Mihai Anitescu, Fred Hickernell, Yiou Li
ASSESSMENT OF COLLOCATION AND GALERKIN APPROACHES TO LINEAR DIFFUSION EQUATIONS WITH RANDOM DATA
International Journal for Uncertainty Quantification, Vol.1, 2011, issue 1
Raymond S. Tuminaro, Eric T. Phipps, Christopher W. Miller, Howard C. Elman
PHYSICS-BASED COVARIANCE MODELS FOR GAUSSIAN PROCESSES WITH MULTIPLE OUTPUTS
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 1
Mihai Anitescu, Emil M. Constantinescu