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Das, Sourav

University of British Columbia

This thesis presents the reliability analysis and probabilistic design of a one-storey moment-resisting frame coupled with a nonlinear energy sink (NES) with negative stiffness and sliding friction and a shape memory alloy (SMA)-based damped outrigger structure when the structures are subjected to earthquake excitation. Initially, the reliability-based design optimization (RBDO) of the above structures is carried out to estimate the tuning parameters of NES and SMA so that the proposed systems produce effective performances when exposed to uncertain environments. To do that, the probability of failure of the structure is estimated using an outcrossing rate approach based on a stationary assumption. To reduce the computational time, a surrogate model is used in the RBDO analysis. To overcome stationary assumption, the next work is devoted to formulate an efficient reliability analysis method using surrogate model-based probability density evolution method (PDEM). The PDEM is used to estimate the probability density function (PDF) of the structural responses. The partial differential equations (PDE) in PDEM are solved using the finite difference method coupled with total variation diminishing, in which a set of representative points of random parameters are generated using the generalized F-discrepancy scheme. To obtain satisfactory accuracy of the numerical solution, representative points are needed, which becomes computationally expensive for complex structures. To reduce the computation burden, the stochastic spectral embedding (SSE) surrogate model is used, which approximates the original response surface. The SSE is a class of supervised machine learning algorithm where it is trained by few observations and enables output prediction as spectral representation. In general, PDE in PDEM are solved using a finite difference scheme in which the accuracy of the numerical solution depends on the number of temporal and spatial discretizations, making them computationally inefficient for high-fidelity models. With this in view, the last work is devoted to forming a physics-informed neural network (PINN) based PDEM, for solving the PDE. This method does not need any interpolation or coordinate transformation, which is often seen in any numerical scheme, thus the computational budget is reduced. Lastly, time-dependent reliability analysis of the above structures is performed using the proposed PINN-based PDEM.

Text

2023-06-01

Attribution 4.0 International

http://hdl.handle.net/2429/84769

Civil Engineering

University of British Columbia

UBCO

http://creativecommons.org/licenses/by/4.0/