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Artificial neural network model for ground vibration amplitudes prediction due to light railway traffic in urban areas

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Abstract

The growth of density and circulation speed of railway transportation systems in urban areas increases the importance of the research issues of the produced environmental impacts. This study presents a field data analysis, obtained during monitoring campaigns of ground vibration, due to light railway traffic in urban areas, based on the artificial neural network (ANN) approach, using quantitative and qualitative predictors. Different ANN-based models, using those predictors, were evaluated/trained and validated. Using several criteria, including those that measures the possibility of ANN overfitting (RR2) and complexity (AIC), the best ANN model was successfully obtained for Lisbon area. This model, with 16 input elements (quantitative and qualitative predictors), 2 neurons on the hidden layer with a hyperbolic tangent sigmoid transfer function, and 1 neuron on the output layer considering a linear transfer function, has 0.9720 for the coefficient of determination and 0.5293 for the sum squared error.

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Abbreviations

AIC:

Akaike information criteria

ANOVA:

Analysis of variance

ANN:

Artificial neural network

FFT:

Fast Fourier transform

FTA:

Federal Transit Administration

FRA:

Federal Railroad Administration

ISO:

International Organization for Standardization

LFSS:

Sum of the squared lack-of-fit error

MSE:

Mean squared error

PESS:

Sum of the squared pure error

SBIC:

Schwarz–Bayesian information criteria

SSE:

Sum of the squared error

SST:

Total sum of squares

A :

Ground vibration peak amplitude

B :

Building type (qualitative predictor)

Cn :

Category of a qualitative variable

C :

Coefficient of determination matrix between pairs of distinct columns of matrix X

c :

Vibration propagation velocity

E :

Energy

f :

Wave frequency

f(s):

Transfer function

G :

Dominant geology (qualitative predictor)

hls:

Hidden layer size

D :

Distance

Kn :

Indicator variables

PVS:

Peak velocity sum

Q :

Quality factor

R2:

Coefficient of determination

\(R_{\text{Max}}^{2}\) :

Maximum coefficient of determination

RR2 :

Ratio of coefficients of determination

s :

Input of the transfer function

T :

Rail track type (qualitative predictor)

\(\varvec{t}\left( {\varvec{\gamma}^{h} \varvec{x} +\varvec{\theta}^{h} } \right)\) :

Vector of transfer functions associated to two neurons of the hidden layer

V :

Train circulation speed

X :

Input matrix

x :

Vector of the input variable

xi :

Input variable

Y :

Output vector

Yi :

Sum of a predicted mean response

α :

Damping factor

∆E :

Dissipated energy

γ :

Parameter (or weight)

\(\varvec{\gamma}^{O}\) :

Weights between the hidden layer and the output layer

\(\gamma_{ij}\) :

Adjustable parameters

\(\varvec{\gamma}^{h}\) :

Weights between the inputs and the hidden layer

\(\theta^{O}\) :

Bias of the output vector

\(\varvec{\theta}^{h}\) :

Bias vector for the hidden layer

θj :

Bias

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Authors and Affiliations

  1. DECivil/CERENA, Técnico Lisboa, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001, Lisbon, Portugal

    G. Paneiro, F. O. Durão, M. Costa e Silva & P. Falcão Neves

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  1. G. Paneiro
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  2. F. O. Durão
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  3. M. Costa e Silva
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  4. P. Falcão Neves
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Correspondence to G. Paneiro.

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Paneiro, G., Durão, F.O., Costa e Silva, M. et al. Artificial neural network model for ground vibration amplitudes prediction due to light railway traffic in urban areas. Neural Comput & Applic 29, 1045–1057 (2018). https://doi.org/10.1007/s00521-016-2625-9

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