Executive Summary : | "Physical and engineering dynamical systems with stochasticity in parameters and excitation, such as structures under earthquake or wind excitation, require uncertainty quantification using a probabilistic framework. Reduced order model (ROM) is an economic alternative, with recent variants developed for various applications. ROM has two phases: offline or training phase and online. In the offline phase, response snapshots are computed on training points, and a singular value decomposition is performed to identify a dominant subspace. The ROM is invoked in the online phase for economical estimation of response at any desired system parameter and excitation. To achieve robustness, various training schemes have been reported, including an error estimator at a training point and an interpolation scheme among the training points. However, the discretization of random excitation leads to a considerable number of random variables, leading to the curse of dimensionality in interpolation schemes. This proposal aims to address this issue by harnessing the growing development in machine learning to achieve high dimensional interpolation, particularly through a neural network.
The proposed methodology involves using a data compression technic like principal component analysis or auto encoder on the excitation, followed by a supervised learning scheme to train a neural network as the interpolant in the online phase. The development of error estimators and bounds of the ROM will be essential for efficient training. Structures under earthquake excitation will be chosen as numerical examples to test the accuracy and computational efficiency of the developed methodology." |