Thesis Defense: Hwanpyo Kim “Simulation of non-Gaussian/non-stationary stochastic processes: beyond second-order orthogonality”
THE DEPARTMENT OF CIVIL ENGINEERING
ADVISOR MICHAEL SHIELDS, ASST. PROFESSOR
ANNOUNCE THE THESIS DEFENSE OF
Tuesday, April 24, 2018
“Simulation of non-Gaussian/non-stationary stochastic processes: beyond second-order orthogonality”
The theory of stochastic processes and their generations are indispensable to characterize wind fluctuations, ocean waves, and earthquake excitations among other quantities in engineering. To computationally analyze and simulate these stochastic systems, practical realization of samples of stochastic processes is essential. The object of this thesis is to introduce new state-of-the-art methodologies for the generation of stochastic processes with non-Gaussianity/non-stationarity possessing higher-order properties than the second-order orthogonality.
A new type of Iterative Translation Approximation Method (ITAM) using the Karhunen-Loève expansion was developed for simulating non-Gaussian and non-stationary processes utilizing translation process theory. The proposed methodology enhances the accuracy of simulated processes in matching a prescribed autocorrelation, maintains the computational efficiency, and resolves limitations caused by utilizing evolutionary power spectra for non-stationary processes.
A new generalized stochastic expansion, the bispectral representation method (BSRM), expanded from the traditional spectral representation method is introduced to simulate skewed nonlinear stochastic processes. With new orthogonal increments to satisfy the conditions of the Cramér spectral representation up to third order orthogonality, the BSRM generates samples that match both the power spectrum and bispectrum of the process by modeling complex nonlinear wave interactions.
A model of phase angle distributions to characterize phase coupling in higher-order stochastic processes is presented. Relationships between the trigonometric moments of circular distributions of phase differences and higher-order cumulant spectra are derived. The prescribed properties are shown to accurately model quadratic and cubic phase couplings in simple stochastic processes and can easily be extended to general n-wave couplings.
Lastly, as applications of the prescribed methods, wind pressure and turbulent wind velocity time histories are generated with SRM, ITAM, and BSRM and applied to two different nonlinear dynamic structural systems. For structures having material and geometrical nonlinearities, performance of an elastic perfectly-plastic structure and the buffeting response of a long-span bridge with coupled aerodynamic forces are examined. The structures are investigated to observe the effect of higher-order properties of the excitations on the response when compared to conventional second-order Gaussian and non-Gaussian excitations.