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Dissertation Defence: Surrogate Assisted Reliability Analysis and Probabilistic Design of Structures under Uncertainty
May 17, 2023 at 11:00 am - 3:00 pm
Sourav Das, supervised by Dr. Solomon Tesfamariam, will defend their dissertation titled “Surrogate Assisted Reliability Analysis and Probabilistic Design of Structures under Uncertainty” in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering.
An abstract for Sourav’ dissertation is included below.
Examinations are open to all members of the campus community as well as the general public.
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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. NES is a passive vibration absorber that consists of a mass attached to a nonlinear spring. In this proposed absorber, the elastic springs are arranged in such a manner that the elastic spring produces nonlinear force due to geometry, called negative stiffness. The sliding friction is introduced to protect the NES system from instability, such as distortions of hinged springs in the negative stiffness region. The other application, i.e., outrigger structure, is considered. Outriggers have been proven to be an efficient system to reduce the dynamic responses of core-tube high-rise buildings by utilizing the axial stiffness of the peripheral columns. However, outer columns and outriggers are subjected to excessive lateral force demands. To reduce the demand, the damped outrigger is used, where dampers are installed between the perimeter columns and outriggers. To improve the performance and enhance the residual deformation, in this thesis, the use of shape memory alloy (SMA) springs is introduced to dissipate energy. The SMA dissipates energy through a hysteretic phase transformation of its microstructure triggered by cyclic loading.
Initially, the reliability-based design optimization 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. For a one-storey steel moment-resistant frame, shake table tests were carried out to show the effectiveness of the NES, and the results were used to validate numerical models. Sensitivity analysis is carried out to demonstrate the performance envelops of the proposed control strategy. Reliable performance of the proposed controller, through tuning parameters of the proposed NES and SMA, are determined through the RBDO framework. To reduce computational time, a surrogate model is used in the RBDO analysis.
To overcome the drawbacks in outcrossing rate method i.e., the stationary assumption, the works are devoted to formulate an efficient reliability analysis method using surrogate model based probability density evolution method (PDEM). The PDEM is used to estimate the structural response’s probability density function (PDF). The PDEM is derived based on the principle of probability conservation, where generalized density evolution equations (GDEEs) are decoupled from the physical system. The GDEEs 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. This is achieved by minimizing the residual using domain decomposition technique. The performance of the proposed SSE-based PDEM is compared with Monte Carlo simulation.
In general, GDEEs 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), a novel deep learning method based PDEM, for solving the GDEEs. PINN utilizes physical information in the form of differential equations to enhance the performance of the neural networks. This method does not need any interpolation or coordinate transformation, which is often seen in any numerical scheme, thus the computational budget is reduced. The numerical examples are utilized to show the accuracy of the proposed method by comparing results with the Fokker–Planck–Kolmogorov equation and Monte Carlo simulation. Lastly, time-dependent reliability analysis of the proposed structure, i.e., the NES system and SMA-based outrigger structure, is performed using the proposed PINN-based PDEM when these structures deteriorate with time.