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

Abstract 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.

[1]  Masanobu Shinozuka,et al.  Stochastic wave representation of seismic ground motion. I, F-K spectra , 1990 .

[2]  Yongbo Peng,et al.  A stochastic harmonic function representation for non-stationary stochastic processes , 2017 .

[3]  Y. Peng,et al.  Random function based spectral representation of stationary and non-stationary stochastic processes , 2016 .

[4]  Masanobu Shinozuka,et al.  Simulation of Nonstationary Stochastic Processes by Spectral Representation , 2007 .

[5]  H. L. Wong,et al.  Response of a rigid foundation to a spatially random ground motion , 1986 .

[6]  L. G. Jaeger,et al.  Dynamics of structures , 1990 .

[7]  Brett A. Benowitz,et al.  Simulation of wind velocity time histories on long span structures modeled as non-Gaussian stochastic waves , 2020, Probabilistic Engineering Mechanics.

[8]  Haifan Xiang,et al.  SIMULATION OF STOCHASTIC WIND VELOCITY FIELD ON LONG-SPAN BRIDGES , 2001 .

[9]  Ahsan Kareem,et al.  Simulation of Multivariate Nonstationary Random Processes by FFT , 1991 .

[10]  Ahsan Kareem,et al.  Simulation of Multivariate Nonstationary Random Processes: Hybrid DFT and Digital Filtering Approach , 1997 .

[11]  Michael J. O'Rouke,et al.  Response of buried pipelines subject to earthquake effects , 1999 .

[12]  Jianbing Chen,et al.  Stochastic Dynamics of Structures , 2009 .

[13]  Zheng Gang.  Shaking Table Test of Soil-pipe Dynamic Interaction under Non-uniform Earthquake Wave Excitation , 2008 .

[14]  A. Zerva,et al.  Spatial variation of seismic ground motions: An overview , 2002 .

[15]  Pol D. Spanos,et al.  Karhunen-Loéve Expansion of Stochastic Processes with a Modified Exponential Covariance Kernel , 2007 .

[16]  Zhangjun Liu,et al.  Spectral representation-based dimension reduction for simulating multivariate non-stationary ground motions , 2018, Soil Dynamics and Earthquake Engineering.

[17]  Hanlong Liu,et al.  An improved approximation for the spectral representation method in the simulation of spatially varying ground motions , 2012 .

[18]  Aspasia Zerva,et al.  Seismic ground motion simulations from a class of spatial variability models , 1992 .

[19]  Jie Li,et al.  Nonlinear stochastic seismic analysis of buried pipeline systems , 2015 .

[20]  Wei Liu,et al.  Stochastic Seismic Response of Pipelines with Corrosion , 2008 .

[21]  Yongbo Peng,et al.  Dimension reduction of Karhunen-Loeve expansion for simulation of stochastic processes , 2017 .

[22]  Jianbing Chen,et al.  Strategy for selecting representative points via tangent spheres in the probability density evolution method , 2008 .

[23]  M. Shinozuka,et al.  Simulation of Seismic Ground Motion Using Stochastic Waves , 1989 .

[24]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[25]  Ahsan Kareem,et al.  Simulation of Multivariate Nonstationary Random Processes: Hybrid Stochastic Wave and Proper Orthogonal Decomposition Approach , 2017 .

[26]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[27]  Yongbo Peng,et al.  Nonlinear stochastic optimal control strategy of hysteretic structures , 2011 .

[28]  K. Fang,et al.  Number-theoretic methods in statistics , 1993 .

[29]  Howard H. M. Hwang,et al.  Probabilistic seismic analysis of a steel frame structure , 1993 .

[30]  Yu Huang,et al.  PDEM-based stochastic seismic response analysis of sites with spatially variable soil properties , 2019, Soil Dynamics and Earthquake Engineering.

[31]  M. Di Paola,et al.  Digital simulation of multivariate earthquake ground motions , 2000 .

[32]  Guoqing Huang,et al.  New formulation of Cholesky decomposition and applications in stochastic simulation , 2013 .

[33]  Michał Kleiber,et al.  The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation , 1993 .

[34]  G W Clough,et al.  Finite Element Analyses of Retaining Wall Behavior , 1971 .

[35]  R. Ghanem,et al.  Polynomial Chaos in Stochastic Finite Elements , 1990 .

[36]  George Deodatis,et al.  Non-stationary stochastic vector processes: seismic ground motion applications , 1996 .

[37]  M. Shinozuka,et al.  Digital simulation of random processes and its applications , 1972 .

[38]  Xin Li,et al.  A modified method for simulating non-stationary multi-point earthquake ground motion , 2010 .

[39]  Pol D. Spanos,et al.  Simulation of Homogeneous Fluctuating Wind Field in Two Spatial Dimensions via a Joint Wave Number–Frequency Power Spectrum , 2018, Journal of Engineering Mechanics.

[40]  Jianbing Chen,et al.  The Number Theoretical Method in Response Analysis of Nonlinear Stochastic Structures , 2007 .

[41]  Ahmet S. Cakmak,et al.  Simulation of earthquake ground motions using autoregressive moving average (ARMA) models , 1981 .

[42]  Weiling Sun,et al.  Stochastic Harmonic Function Representation of Stochastic Processes , 2013 .

[43]  G. Deodatis.  Simulation of Ergodic Multivariate Stochastic Processes , 1996 .

[44]  Masanobu Shinozuka,et al.  Stochastic wave models for stationary and homogeneous seismic ground motion , 1991 .

[45]  Pol D. Spanos,et al.  Nonstationary Stochastic Response Determination of Nonlinear Systems: A Wiener Path Integral Formalism , 2014 .

[46]  George Deodatis,et al.  Simulation of wind velocities on long span structures: A novel stochastic wave based model , 2015 .

[47]  De-Cheng Feng,et al.  Stochastic dynamic response analysis and reliability assessment of non-linear structures under fully non-stationary ground motions , 2019, Structural Safety.

[48]  Zhangjun Liu,et al.  Probability density evolution analysis of stochastic nonlinear structure under non-stationary ground motions , 2019, Structure and Infrastructure Engineering.

[49]  Aspasia Zerva,et al.  Spatial incoherence effects on seismic ground strains , 1992 .

[50]  Jianbing Chen,et al.  Stochastic modeling of engineering dynamic excitations for stochastic dynamics of structures , 2012 .