Nonlinear Dynamics

, Volume 95, Issue 2, pp 1693–1711 | Cite as

Estimation of time-variant system reliability of nonlinear randomly excited systems based on the Girsanov transformation with state-dependent controls

  • Oindrila Kanjilal
  • C. S. ManoharEmail author
Original Paper


The problem of time-variant system reliability analysis of nonlinear dynamical systems subjected to random excitations is considered. The governing equations are formulated as a set of Ito’s stochastic differential equations. Subsequently, a Monte Carlo simulation strategy, which incorporates Girsanov’s transformation- based variance reduction step, is developed. The novel element of the work lies in the formulation of state-dependent Girsanov’s control forces for estimating the system reliability. The study considers failure modes arranged in series, parallel, or composite configurations. Illustrative examples include studies on a 5-dof Duffing’s system and an inelastic frame subjected to multi-support, non-stationary, Gaussian excitations. The numerical results demonstrate significant variance reduction achieved in estimating low probabilities of failure.


Time-variant system reliability Monte Carlo simulation Importance sampling Girsanov’s transformation 

Supplementary material

11071_2018_4655_MOESM1_ESM.pdf (191 kb)
Supplementary material 1 (pdf 191 KB)


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of ScienceBengaluruIndia

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