Application Of Polynomial Chaos Expansions And Uncertainty In Earthquake Engineering

Uncertainty quantification is important and has become indispensable in dynamic structural systems.The framework of uncertainty quantification aims to evaluate their effects on structural responses.In this context,surrogate model technology provides effective tools for uncertainty quantification,which extremely reduces the computational costs and efforts.This master study aims to explore the polynomial chaos expansion(PCE)surrogate models and apply them in dynamic structural systems with uncertainties.To this end,the typical polynomial chaos expansions(PCE)are firstly explored and applied in sensitivity analysis of 120 single-degree-of-degree(SDOF)shape memory alloy(SMA)based structures.The SMA uncertainty parameters are sampled by Markov Chain Monte Carlo(MCMC)algorithm.Furthermore,the first-four order linear moment(LM)method was introduced to help get the distribution of SMA parameters.The PCE surrogate models are then constructed for peak accelerations and displacements about each SDOF structures.The widely-used Sobol indices are calculated to evaluate the sensitivity of SMA uncertainty parameters just by post-processing the coefficients of PCE.In this way,the sensitivity is evaluated and the computational cost is almost limited to train the PCEs,which demonstrates PCE is a promising technology in structural engineering or earthquake engineering.However,the typical PCE is not effective and efficient for replicating dynamic history of strong nonlinear system.Therefore,the state-of-the-art polynomial chaos nonlinear autoregressive with exogenous input form(PC-NARX)model was explored.A generalized Bouc-Wen model with degradation was designed to evaluate the effectiveness of PC-NARX model.The uncertainties mainly originate from the Bouc-Wen structural parameters and the ground motion.The results were then compared with typical analysis.The comparisons show PC-NARX model has far superior performance than typical PCE.Therefore,PC-NARX presents a great tool for dynamic analysis for strong nonlinear system.Finally,a potential approach was proposed to overcome existing issue of PC-NARX model for multi-degree-of-freedom(MDOF)systems.The approach was applied to a two-degree-of-freedom(2-DOF)benchmark to examine its effectiveness.The dynamic history obtained by the proposed method is demonstrated better than that obtained by typical PC-NARX model.In summary,the master study aims to explore the application of surrogate models on uncertainty in structural dynamic systems.I believe that the work has made meaningful contributions to the knowledge of earthquake engineering or structural dynamics.