TY - CHAP

T1 - Identification of Properties of Stochastic Elastoplastic Systems

AU - Rosić, Bojana V.

AU - Matthies, Hermann G.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - This paper presents the parameter identification in a Bayesian setting for the elastoplastic problem, mathematically speaking the variational inequality of a second kind. The inverse problem is formulated in a probabilistic manner in which unknown quantities are embedded in a form of the probability distributions reflecting their uncertainty. With the help of the stochastic functional analysis the update procedure is introduced as a direct, purely algebraic way of computing the posterior, which is comparatively inexpensive to evaluate. Such formulation involves the process of solving the convex minimisation problem in a stochastic setting for which the extension of classical optimization algorithm in predictor-corrector form as the solution procedure is proposed. A validation study of identification procedure is done through a series of virtual experiments taking into account the influence of the measurement error and the order of approximation on the posterior estimate.

AB - This paper presents the parameter identification in a Bayesian setting for the elastoplastic problem, mathematically speaking the variational inequality of a second kind. The inverse problem is formulated in a probabilistic manner in which unknown quantities are embedded in a form of the probability distributions reflecting their uncertainty. With the help of the stochastic functional analysis the update procedure is introduced as a direct, purely algebraic way of computing the posterior, which is comparatively inexpensive to evaluate. Such formulation involves the process of solving the convex minimisation problem in a stochastic setting for which the extension of classical optimization algorithm in predictor-corrector form as the solution procedure is proposed. A validation study of identification procedure is done through a series of virtual experiments taking into account the influence of the measurement error and the order of approximation on the posterior estimate.

KW - Linear Bayesian update

KW - Stochastic convex minimisation

KW - Stochastic elastoplasticity

KW - Stochastic Galerkin method

UR - http://www.scopus.com/inward/record.url?scp=84963620256&partnerID=8YFLogxK

U2 - 10.1007/978-94-007-5134-7_14

DO - 10.1007/978-94-007-5134-7_14

M3 - Chapter

AN - SCOPUS:84963620256

SN - 978-94-007-5133-0

VL - 2

T3 - Computational Methods in Applied Sciences

SP - 237

EP - 253

BT - Computational Methods in Stochastic Dynamics

PB - Springer

CY - Dordrecht

ER -