TY - GEN
T1 - Reliability analysis of linear dynamical systems with uncertain structural parameters subject to discrete white noise excitation
AU - Valdebenito, Marcos A.
AU - Jensen, Héctor A.
AU - Schüeller, Gerhart I.
AU - Labarca, Alejandro A.
PY - 2012
Y1 - 2012
N2 - The estimation of first excursion probabilities for dynamical systems remains as one of the most challenging problems of computational stochastic mechanics. Hence, this contribution introduces an approach for estimating first excursion probabilities for a particular class of problems, i.e. linear dynamical systems involving uncertain structural parameters subject to discrete white noise excitation. The proposed approach is based on Importance Sampling. The Importance Sampling density (ISD) function related with uncertainty in stochastic loading is selected based on the work reported in [1]. In addition, a novel ISD function associated with uncertainty in structural parameters is introduced. This novel ISD function is defined such that it is proportional to the probability density function of the uncertain structural parameters and also to a parameter related with the probability of excursion at specific time instants. The application of the proposed approach is illustrated by means of a simple structural model involving two uncertain structural parameters and a stochastic excitation comprising a large number of random variables. The efficiency and accuracy of the proposed approach is analyzed in terms of failure probability estimators, the associated coefficient of variation and the number of samples required. Results obtained indicate that the proposed approach is accurate and also numerically efficient.
AB - The estimation of first excursion probabilities for dynamical systems remains as one of the most challenging problems of computational stochastic mechanics. Hence, this contribution introduces an approach for estimating first excursion probabilities for a particular class of problems, i.e. linear dynamical systems involving uncertain structural parameters subject to discrete white noise excitation. The proposed approach is based on Importance Sampling. The Importance Sampling density (ISD) function related with uncertainty in stochastic loading is selected based on the work reported in [1]. In addition, a novel ISD function associated with uncertainty in structural parameters is introduced. This novel ISD function is defined such that it is proportional to the probability density function of the uncertain structural parameters and also to a parameter related with the probability of excursion at specific time instants. The application of the proposed approach is illustrated by means of a simple structural model involving two uncertain structural parameters and a stochastic excitation comprising a large number of random variables. The efficiency and accuracy of the proposed approach is analyzed in terms of failure probability estimators, the associated coefficient of variation and the number of samples required. Results obtained indicate that the proposed approach is accurate and also numerically efficient.
KW - First passage problem
KW - Importance sampling
KW - Reliability analysis
KW - Stochastic excitation
KW - Uncertain structural parameters
UR - http://www.scopus.com/inward/record.url?scp=84871631977&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84871631977
SN - 9783950353709
T3 - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
SP - 2168
EP - 2178
BT - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
T2 - 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
Y2 - 10 September 2012 through 14 September 2012
ER -