PSI - Issue 17

Ahmed Belmokre et al. / Procedia Structural Integrity 17 (2019) 698–703 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Recently, machine learning techniques have become more common for time series data analysis (Salazar et al. 2015). Some of the techniques are the artificial neural networks, the support vector machines or the random forests. These models, also called “black box”, are able to deal with nonlinear problems with high accuracy and relatively low computational cost. In this paper, we present a comparison methodology applied to a case study for predicting seepage flow rates using two novel techniques: Random Forest Regression (RFR) (Breiman 2001) and Support Vector Regression machine (SVR) (Vapnik 1995) models. We apply our methodology to the Beni Haroun roller compact concrete dam. Water temperature, water level variation and time effect are the inputs to the model. The accuracy of each model is assessed by comparing their results with the recorded data. Finally, we estimate the importance of each variable in seepage mechanism.

Nomenclature ρ

density (kg/m 3 )

k g μ

permeability coefficient acceleration of gravity (m/s -2 ) water viscosity (cm 2 /s) hydraulic conductivity (m/s)

K T

temperature (°C) number of trees

N tree m try

number of variables randomly sampled to split each node

OOB out of bag errOOB out of bag error Φ kernel function α, α *

lagrangian multipliers number of observations

N X i Y i

measured value predicted value

2. METHODOLOGY

2.1. Mechanisms of seepage in concrete dam The flow of an incompressible fluid through a rigid solid is governed by the Darcy ’s law presented in equation number (1) where is the intrinsic permeability of the porous medium, is the fluid dynamic viscosity, is the pressure, is the density of the water, and is the acceleration of gravity. Darcy’s law can be s olved with numerical schemes in any domain. Nevertheless, those methods are computationally demanding, which represents an embarrassment for dam’s engineers. In order to overcome these problems, learning machine models are an alternative .

( ) . k p g     

  − 

(1)





2.2. Random forest regression method

Random forest was proposed in 2001 by Leo Breiman. It is a machine learning technique. This algorithm combines the concepts of random subspaces and bagging. The random forest regression (RFR) algorithm performs by learning on multiple decision trees driven on different subsets of data (Breiman 2001). Two important parameters of the random forest algorithm are the number of trees to grow, N tree , and the number of variables randomly sampled to split each node, m try . Both are used to calibrate the model. N tree should not be too small in order to ensure that every input gets