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


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.


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



Random variables


Design variables


Stochastic processes


Gaussian stochastic process


Non-Gaussian stochastic process


Original limit state function


Transformed time-independent limit state function


Surrogate Kriging model


Time parameter

[0, T]

Time interval


Cost function




Reliability target


User-defined cumulative confidence level target


Standard Gaussian cumulative distribution function


Probability density function


Probability of system failure


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


Training data set


Covariance matrix


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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