Dimension Reduction Representation Research Articles

Time-domain dimension-reduction representation for stochastic ground motion utilizing filtered white noise

A method is proposed for characterizing and simulating both stationary and fully non-stationary stochastic ground motions. This method is based on discrete filtered white noise models, including single and double filtered, with the latter is introduced to suppress low-frequency components. Specifically, the proposed method expresses seismic ground motion as a linear combination of products involving orthogonal random variables and deterministic functions. Further, by defining high-dimensional orthogonal random variables as orthogonal functions of extremely low dimensional elementary random variables, efficient dimension-reduction (DR) of primitive ground motion process can be achieved. To illustrate this concept, three distinct categories of random orthogonal functions involving only one or two elementary random variables are examined, employing filtered white noise models to simulate ground motion acceleration processes, thereby demonstrating the accuracy and efficiency of the proposed method. Simultaneously, recommendations for employing the proposed method in simulations are provided based on an analysis of the impacts of various parameters on random ground motion processes. Case studies demonstrate the accuracy and robustness of the proposed method compared to Monte Carlo (MC) methods. Furthermore, case studies on fully non-stationary ground motion highlight the practical applicability of the proposed method in engineering.

Dimension-Reduction Representation of Multivariate Mainshock-Aftershock Ground Motions Based on Measured Records

ABSTRACT This study proposes an integrated dimension-reduction representation strategy for simulating multivariate mainshock-aftershock stochastic ground motions based on measured motion records. The strategy includes a parameter identification method for modeling evolutionary power spectrum density (EPSD) of mainshock-aftershocks, a coherence function describing the spectrum correlation between mainshock and aftershock, and the EPSD function matrix establishment for mainshock-aftershock field combining with complex spatial coherence function. Furthermore, the dimension-reduction representation for simulating the ground motions considering the sequence and spatial variability simultaneously is presented with merely two elementary random variables. Numerical results effectively demonstrate the accuracy, efficiency, and engineering applicability of the proposed method.

Global reliability evaluation of a high-pier long-span continuous RC rigid frame bridge subjected to multi-point and multi-component stochastic ground motions

High-pier long-span continuous RC rigid frame bridges would be more vulnerable to seismic spatial variability and multi-component nature due to their large geometric dimension. However, research on seismic performance of these bridges subjected to multi-point and multi-component ground motions is sparse. In this study, the unified expression of spectral decomposition integrating spectral representation method and proper orthogonal decomposition based on coherency function matrix is derived. Then the dimension-reduction representation is developed for sample realization of multi-point and multi-component non-stationary stochastic ground motions with merely three elementary random variables, which bypasses the challenges of high-dimensional randomness degree and huge computation expense faced by the Monte Carlo simulation scheme. Thereafter the accurate seismic response analysis of a high-pier long-span bridge is numerically scrutinized combining with the probability density evolution method to further expound the effectiveness of the dimension-reduction model. Finally, a heuristic global reliability evaluation strategy employing relative displacement angle of bridge pier segments as criterion is proposed inspired by the idea of equivalent extreme-value event. Benefiting from this, both the refined reliability evaluation of bridge members and the structural global reliability can be accomplished, providing the possibilities of quantitative seismic performance assessment and earthquake resistance optimization design from an overall perspective.

Analysis of stochastic errors and Gaussianity of random vector process simulated by dimension-reduction representation method

The simulation of random vector process is of great importance, particularly for the nonlinear dynamic analysis and reliability evaluation of large-scale structures. Combining the probability density evolution method, which provides an efficient way to perform the structural dynamic reliability analysis, reducing the randomness degree of the simulation method becomes a new challenge task. In order to address this issue, dimension-reduction representation methods for simulating stationary vector processes were proposed recently. However, the features regarding the stochastic error of power spectral density functions and the Gaussianity of vector processes generated by the dimension-reduction representation methods remain unclear. In this paper, the analytical stochastic errors of power spectral density functions for dimension-reduction representation methods will be given, and be proved through the numerical example. Moreover, the Gaussianity of the generated vector processes will be discussed from the view of the first four statistical moments.

Dimension-reduction representation of stochastic ground motion fields based on wavenumber-frequency spectrum for engineering purposes

It is of great necessity to achieve the efficient and accurate representation of ground motion fields considering the spatial variation of which possess paramount importance to the seismic safety and reliability evaluation of lifeline systems. To circumvent the difficulties caused by the decomposition of cross power spectral density (PSD) matrix and the interpolation between discretized spatial points in the spectral representation method (SRM) for uni-dimensional multi-variate (1D-nV) stochastic vector process (regarded as discrete stochastic field), a wavenumber-frequency SRM (WSRM) for simulating multi-dimensional uni-variate (mD-1V) spatial-temporal stochastic field (regarded as continuous stochastic field) has been developed for years. In this paper, an updated WSRM (UWSRM), which can reduce the number of elementary random variables, is proposed for simulating the 2D-1V stochastic ground motion fields. Compared with the conventional WSRM (CWSRM) which belongs to the Monte Carlo simulation schemes, merely two elementary random variables are required to realize the precise modeling of ground motion fields. For the sake of facilitating the calculation, the UWSRM embedded in the Fast Fourier Transform (FFT) technique is applied to simulate the stochastic ground motion fields. Numerical results including the comparison of the accuracy and efficiency with the CWSRM verify the effectiveness of the UWSRM. Moreover, to illustrate the application prospect of the UWSRM, the refined random seismic response analysis of a buried pipeline network is implemented by combining with the probability density evolution method (PDEM). The analysis results preliminarily demonstrate the applicability of the UWSRM in lifeline systems.

Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods.