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Structural and Multidisciplinary Optimization

, Volume 58, Issue 3, pp 1051–1065 | Cite as

Time-variant reliability-based design optimization using sequential kriging modeling

  • Mingyang Li
  • Guangxing Bai
  • Zequn Wang
RESEARCH PAPER

Abstract

This paper presents a sequential Kriging modeling approach (SKM) for time-variant reliability-based design optimization (tRBDO) involving stochastic processes. To handle the temporal uncertainty, time-variant limit state functions are transformed into time-independent domain by converting the stochastic processes and time parameter to random variables. Kriging surrogate models are then built and enhanced by a design-driven adaptive sampling scheme to accurately identify potential instantaneous failure events. By generating random realizations of stochastic processes, the time-variant probability of failure is evaluated by the surrogate models in Monte Carlo simulation (MCS). In tRBDO, the first-order score function is employed to estimate the sensitivity of time-variant reliability with respect to design variables. Three case studies are introduced to demonstrate the efficiency and accuracy of the proposed approach.

Keywords

Time-variant reliability analysis Design optimization Stochastic processes Simulation-based Kriging surrogate model 

Abbreviations

X

Random variables

d

Design variables

Y(t)

Stochastic processes

YG(t

Gaussian stochastic process

YNG(t)

Non-Gaussian stochastic process

G(.)

Original limit state function

g(.)

Transformed time-independent limit state function

gK(.)

Surrogate Kriging model

t

Time parameter

[0, T]

Time interval

cost(.)

Cost function

R

Reliability

Rt

Reliability target

CCLt

User-defined cumulative confidence level target

Φ(.)

Standard Gaussian cumulative distribution function

fx(.)

Probability density function

Pf

Probability of system failure

W

Input random variables [X, Y, t’] of Kriging model

D

Training data set

Cov(.,.)

Covariance matrix

R

Correlation matrix

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering-Engineering MechanicsMichigan Technological UniversityHoughtonUSA
  2. 2.Department of Industrial EngineeringWichita State UniversityWichitaUSA

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