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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2017, Vol. 11 Issue (4) : 470-479     https://doi.org/10.1007/s11709-017-0440-8
RESEARCH ARTICLE |
An efficient stochastic dynamic analysis of soil media using radial basis function artificial neural network
P. ZAKIAN()
Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran 14115–397, Iran
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Abstract

Since a lot of engineering problems are along with uncertain parameters, stochastic methods are of great importance for incorporating random nature of a system property or random nature of a system input. In this study, the stochastic dynamic analysis of soil mass is performed by finite element method in the frequency domain. Two methods are used for stochastic analysis of soil media which are spectral decomposition and Monte Carlo methods. Shear modulus of soil is considered as a random field and the seismic excitation is also imposed as a random process. In this research, artificial neural network is proposed and added to Monte Carlo method for sake of reducing computational effort of the random analysis. Then, the effects of the proposed artificial neural network are illustrated on decreasing computational time of Monte Carlo simulations in comparison with standard Monte Carlo and spectral decomposition methods. Numerical verifications are provided to indicate capabilities, accuracy and efficiency of the proposed strategy compared to the other techniques.

Keywords stochastic analysis      random seismic excitation      finite element method      artificial neural network      frequency domain analysis      Monte Carlo simulation     
Corresponding Authors: P. ZAKIAN   
Online First Date: 25 July 2017    Issue Date: 10 November 2017
 Cite this article:   
P. ZAKIAN. An efficient stochastic dynamic analysis of soil media using radial basis function artificial neural network[J]. Front. Struct. Civ. Eng., 2017, 11(4): 470-479.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-017-0440-8
http://journal.hep.com.cn/fsce/EN/Y2017/V11/I4/470
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P. ZAKIAN
Fig.1  Radial basis function neural network.
Fig.2  Spectral density function of the seismic excitation.
Fig.3  Schematic of the soil Medium.
Fig.4  The shear modulus distribution over soil depth.
Fig.5  Mean spectral density function of soil response with SFEM.
Fig.6  Standard deviation spectral density function of soil response with SFEM.
Fig.7  Mean spectral density function of soil response with MC and MC-ANN procedures.
Fig.8  Standard deviation spectral density function of soil response with MC and MC-ANN procedures
Fig.9  Error of mean of spectral density function of soil response
Fig.10  Error of standard deviation of spectral density function of soil response
Fig.11  Convergence curve of radial basis ANN training.
ProcessSFEM with KL order=20 and PC order=1ANN TrainingMC via ANNMC
Time (sec)1165591584343
Tab.1  Elapsed Time for the three procedures.
aCoefficients of polynomial chaos
bCorrelation length
bBias
cCoefficient of polynomial chaos in compact form
cCentral input vector for ANN
CResponse vector in frequency domain
diag [.]Diagonal terms of a matrix
dEuclidean distance
E[.]Expected value
F0Scale factor
FForce vector in frequency domain
f(s)Radial basis function
GShear modulus of soil
G*Complex shear modulus
HTransfer function
KeElement stiffness matrix: mean part
KeElement stiffness matrix
Kstiffness matrix: mean part
Kstiffness matrix in frequency domain
leLength of an element
mNumber of KL terms
MeElement mass matrix
MMass matrix
mIInfluence vector
NNumber of elements
PNumber of PC terms
RααAutocorrelation function
REpicentral distance
rpolynomial chaos in compact form
sEarthquake duration
SSpectral density function
tlStrong motion duration
TaMean period of the earthquake excitation
uHorizontal displacement
u¨g?max?Maximum ground acceleration
wWeights of the second layer for ANN
xInput vector for ANN
  
φEigenfunction
λEigenvalue
Δu¨gCorrelation factor
δGScale of fluctuation
σGStandard deviation of shear modulus
ρSoil mass density
ψ0Shape function for non-stationary effect
ΓPolynomial chaos
ωSolution to the transcendental equations
ωComponent frequency
ωgFrequency of the ground
ξgDamping ratio of ground
ξRandom variable
θMember of random space
αGFluctuation part of shear modulus
βFrictional damping
.Mean value
  
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