Koopman operator for time-dependent reliability analysis

by   Navaneeth N., et al.

Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work, we propose a Koopman operator based approach for time-dependent reliability analysis of nonlinear dynamical systems. Since the Koopman representations can transform any nonlinear dynamical system into a linear dynamical system, the time evolution of dynamical systems can be obtained by Koopman operators seamlessly regardless of the nonlinear or chaotic behavior. Despite the fact that the Koopman theory has been in vogue a long time back, identifying intrinsic coordinates is a challenging task; to address this, we propose an end-to-end deep learning architecture that learns the Koopman observables and then use it for time marching the dynamical response. Unlike purely data-driven approaches, the proposed approach is robust even in the presence of uncertainties; this renders the proposed approach suitable for time-dependent reliability analysis. We propose two architectures; one suitable for time-dependent reliability analysis when the system is subjected to random initial condition and the other suitable when the underlying system have uncertainties in system parameters. The proposed approach is robust and generalizes to unseen environment (out-of-distribution prediction). Efficacy of the proposed approached is illustrated using three numerical examples. Results obtained indicate supremacy of the proposed approach as compared to purely data-driven auto-regressive neural network and long-short term memory network.


Assessment of DeepONet for reliability analysis of stochastic nonlinear dynamical systems

Time dependent reliability analysis and uncertainty quantification of st...

MAntRA: A framework for model agnostic reliability analysis

We propose a novel model agnostic data-driven reliability analysis frame...

Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems

Accurately learning the temporal behavior of dynamical systems requires ...

Data-driven Influence Based Clustering of Dynamical Systems

Community detection is a challenging and relevant problem in various dis...

Data-driven learning of non-autonomous systems

We present a numerical framework for recovering unknown non-autonomous d...

dynoNet: a neural network architecture for learning dynamical systems

This paper introduces a network architecture, called dynoNet, utilizing ...

Machine Learning the Tangent Space of Dynamical Instabilities from Data

For a large class of dynamical systems, the optimally time-dependent (OT...

Please sign up or login with your details

Forgot password? Click here to reset