Hyperparameter-optimized multi-fidelity deep neural network model associated with subset simulation for structural reliability analysis

The present study proposes a two-stage Bi-Fidelity Deep Neural Network surrogate model to quantify the uncertainty of structural analysis using low-fidelity data samples added to the model to predict high-fidelity responses. This multi-fidelity surrogate model efficiently reduces the high computational cost for highly non-linear and high dimensional structural reliability problems. The framework is demonstrated using three different representative examples. First, it demonstrates the multi-fidelity model's accuracy for approximating a high non-linear 20-dimensional standard benchmark function that is hard to approximate with other methods and compared with another multi-fidelity neural network framework. In the other examples, the multi-fidelity framework is associated with Subset Simulation to efficiently estimate rare events considering a benchmark case study including high-dimensional scenarios, and the third example considers finite element model case studies. The proposed framework is also compared with a multi-fidelity Co-Kriging method. The results show that the proposed multi-fidelity framework, with its optimized hyperparameters using Bayesian Optimization, is an excellent strategy for reducing the number of samples used to construct the performance function's surrogate model. Moreover, the proposed framework can provide an accurate failure probability estimation with a lower computational cost in high non-linear, high dimensional, and rare events.