000004541 001__ 4541
000004541 005__ 20141118192704.0
000004541 0177_ $$2doi$$a10.3850/978-981-07-2219-7_P262

000004541 0247_ $$210.3850/978-981-07-2219-7_P262
$$adoi
000004541 04107 $$aeng
000004541 046__ $$k2012-05-23
000004541 100__ $$aXu, X. Frank
000004541 24500 $$aConvolved Orthogonal Expansions on Dynamics and Random Media Problems

000004541 24630 $$n5.$$pProceedings of the 5th Asian-Pacific Symposium on Structural Reliability and its Applications
000004541 260__ $$bResearch Publishing, No:83 Genting Lane, #08-01, Genting Building, 349568 SINGAPORE
000004541 506__ $$arestricted
000004541 520__ $$2eng$$aConventional probabilistic and reliability methods have been prevalently formulated with a random variable representation of uncertainties for both inputs and outputs through physical, chemical, or biochemical systems. Due to exponential increase of random dimensions in nonlinear propagation of uncertainties, the rv-based probabilistic methods are by nature subjected to the curse-of-dimensionality issue. In (Xu, 2011; Xu and Stefanou, submitted), by constructing an orthogonal functional space about an underlying random process, a novel random field/process based convolved orthogonal expansion (COE) method is proposed, which opens a new direction to break the curse-of-dimensionality in stochastic computation. 
 To model nonlinear systems, an n-th order convolved orthogonal expansion (COE) is formulated as 
 u(t,ϑ)=∑<sub>n=0</sub>∑<sub>i=0</sub>u<sub>i</sub><sup>(n)</sup>(t)∅<sub>i</sub><sup>(n)</sup>(t,ϑ) 
∅<sub>i</sub><sup>(n)</sup>(t,ϑ)=g*g*...*g*∅<sub>i</sub>=g<sup>*n</sup>*∅<sub>i</sub>
 where g(t,t') is a given kernel, typically a Green's function. The COE method is applied to temporal and spatial uncertainty problems, both of which involve nonlinear propagation of a random process/field input.

000004541 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000004541 653__ $$aOrthogonal expansion, Random process, Random field, Random variable, Convolved.

000004541 7112_ $$a5th Asian-Pacific Symposium on Structural Reliability and its Applications$$cSingapore (SG)$$d2012-05-23 / 2012-05-25$$gAPSSRA2012
000004541 720__ $$aXu, X. Frank
000004541 8560_ $$ffischerc@itam.cas.cz
000004541 8564_ $$s504763$$uhttps://invenio.itam.cas.cz/record/4541/files/P262.pdf$$yOriginal version of the author's contribution as presented on CD, .
000004541 962__ $$r4180
000004541 980__ $$aPAPER