Time-Dependent Reliability Analysis of Random Vibration Based on Deep Neural Operator Surrogate Model

A deep neural operator (DNO) is a neural network representing mapping relationships between function spaces, rendering it highly valuable in investigating dynamical systems, vibrations, and other time-dependent systems. The DeepONet, a deep neural operator framework, is founded upon the universal operator approximation theorem. It has demonstrated its effectiveness in science and engineering, particularly in addressing ordinary and partial differential equation issues. This study investigates the time-dependent reliability within the context of random vibrations by employing the DeepONet framework. First, the Karhunen-Loève Expansion (KLE) is utilized to transform the excitation of the stochastic process system into expansion terms encompassing random variables, eigenvalues, and eigenfunctions. Then, a random vibration surrogate model is established to address time-dependent reliability by leveraging the capabilities of DeepONet. Finally, the Monte Carlo simulation is adopted to calculate the time-dependent reliability at a specified threshold. The effectiveness and generalizability of the proposed method regarding time-dependent reliability matters have been empirically verified through a case study on the Duffing oscillator.