Prediction of Concrete Carbonation Depth Based on Support Vector Regression

RUAN Xiang RUAN Xiang Department of Geotechnical Engineering

School of Civil Engineering Shenzhen Gongkan Geotechnical Engineering Co. Tongji University LTD

Shanghai 200092, China Shenzhen 518026, China Email: iamarnold@163.com Email: iamarnold@163.com

Abstract—Concrete carbonation depth forecasting is significant to avoid the cracking of concrete. In the study, support vector regression (SVR) which is the regression model of support vector machine (SVM) is proposed to forecast concrete carbonation depth. Water cement ratio, cement consumption and service time have an important influence on concrete carbonation depth, so they are important features in concrete carbonation depth forecasting. Real case data from historical concrete carbonation depth are used in the paper. The experimental results indicate that the proposed SVR model has higher forecasting accuracy than artificial neural network.

Keywords : concrete carbonation depth; forecasting method; support vector regression; forecasting accuracy

І. INTRODUCTION Carbonation will decrease the strength of concrete.

Concrete carbonation depth forecasting is significant to avoid the cracking of concrete. At present, artificial neural network has been proposed to forecast concrete carbonation depth[1]. Artificial neural network (ANN) adopts itself to reproduce the desired output when presented along with input data sets[2]. However, training a neural network requires a number of iterations and a large number of training iterations may make ANN overtraining, which may affect the predicting capabilities of the model. This study explores the potential of another machine learning approach called support vector machine (SVM) in forecasting concrete carbonation depth. The performance of SVM was found to be better due to its use of the structural risk minimization principle in formulating cost functions[3]. This advantage leads to a unique optimal and global solution as compared to conventional neural network models[4,5]. Therefore, the regression model of support vector machine is proposed to forecast concrete carbonation depth,and real case data from historical concrete carbonation depth are used in the paper.

ІІ. SUPPOERT VECTOR REGRESSION Support vector machine was proposed by Vapnik. Suppose that we are given a training set l

iii yx )},{( , where

ix is the input vector, iy is the output value and l

denotes the number of samples. The goal is to find a function )(xf whose deviation from each target iy is for all training data, the SVM regression function is:

bxwxf +⋅= )()( ϕ (1)

where )(xϕ denotes the high-dimensional feature space, w denotes the weight vector and b denotes the bias term.

Flatness in the case of Eq.(1) can be ensured by

minimizing the norm 2w , leading to the following

convex optimization problem: Two positive slack variables ξ and ∗ξ are introduced to represent the distance from actual values to the corresponding boundary values of the ε -tube. Then, Eq.(2) is transformed into the following constrained form:

min ∑=

++l

iiiCw

1

*2 )(21 ξξ (2)

s.t. ⎩⎨⎧

≥+≤−+⋅≥+≤−⋅−

0)(0)(

**iii

iii

ybxwbxwy

ξξεϕξξεϕ

In the above formulation, positive slack variables ξ

and ∗ξ are introduced to cope with otherwise infeasible constraint of the optimization problem, whereas the constant C denotes a cost function measuring the empirical risk. Loss function represents the fact that there is no loss for deviations smaller than ε and that larger deviations will be linearly penalized:

⎩⎨⎧

−≤

=otherwiseif

Lεξ

εξξ

||||0

)( (3)

where iα and ∗iα are the Lagrange multipliers.

2009 Third International Symposium on Intelligent Information Technology Application

978-0-7695-3859-4/09 $26.00 © 2009 IEEE

DOI 10.1109/IITA.2009.469

172

2009 Third International Symposium on Intelligent Information Technology Application

978-0-7695-3859-4/09 $26.00 © 2009 IEEE

DOI 10.1109/IITA.2009.469

172

The SVM for function fitting obtained by using the above-mentioned maximization function is then given by

bxxKxf i

l

iii +−=∑

=

),()()(1

*αα (4)

Only parts of iα and ∗iα have non-zero values. These

errors of data points on non-zero coefficients are referred to as the support vectors. ),( ji xxK is called the kernel function, In this SVM model, the Gaussian radial basis kernel function (RBF) is used.

ІІІ. CONCRETE CARBONATION DEPTH SVM FORECASTING MODEL

Water cement ratio, cement consumption and service time have an important influence on concrete carbonation depth, so they are important features in concrete carbonation depth forecasting. Thus, water cement ratio, cement consumption and service time are the inputs of the SVM model, concrete carbonation depth is the output of the SVM model. Then, the SVM forecasting of concrete carbonation depth is shown in Fig.1.

The experimental data should be normalized to improve generalization capability of SVM. For a time series },,,{ 1 nj vvvV = , which is normalized as

},,,{ 1'

nj vvvV ′′′= , where )(max

1 i

n

i

jj

v

vv

=

=′ .

Figure 1. Concrete carbonation depth forecasting model

TABLE І. THE TRAINING DATA OF CONCRETE CARBONATION DEPTH

Number Water cement ratio Cement consumption/(kg/m3) Service time/(year) Carbonation

depth/(mm) 1 0.40 450 10 3.86

2 0.40 450 15 4.73

3 0.40 400 5 3.06

4 0.40 400 10 4.32

5 0.40 400 15 5.29

6 0.45 400 5 4.18

7 0.45 400 10 5.92

8 0.45 400 15 7.24

9 0.45 350 5 4.75

10 0.45 350 10 6.72

11 0.45 350 15 8.22

12 0.50 350 5 6.03

……

42 0.50 325 15 11.21

43 0.60 275 30 26.49

44 0.65 250 30 33.32

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TABLE ІІ. THE TESTING DATA OF CONCRETE CARBONATION DEPTH

Number Water cement ratio Cement consumption/(kg/m3) Service time/(year) Carbonation

depth/(mm) 1 0.55 300 20 16.94

2 0.60 275 20 21.64

3 0.50 325 25 14.47

4 0.55 300 25 18.94

5 0.45 350 30 11.64

6 0.50 325 30 15.86

TABLE ІІІ. FORECASTING RESULTS OF SVM AND RBFNN

1 2 3 4 5 610

12

14

16

18

20

22

conc

rete

car

bona

tion

dept

h/m

m

Actual

SVMANN

Figure 2. Comparison of concrete carbonation depth forecasting between SVM and ANN

ІV. EXPERIMENTAL TESTING The historical concrete carbonation depth data are used

as our research data. In order to improve operation speed and generalization capability of forecasting model, the primary data should be normalized before training sample sets are constructed. The real date are divided into two data

sets: the training data sets and the testing data sets, which are shown in Tab.1,Tab.2 respectively.

Mean absolute percentage error is used to evaluate the forecasting accuracy. As shown in Tab.3 and Fig.2, the forecasting results of SVM and RBFNN are compared, which indicates that SVM has more excellent performance than RBFNN in forecasting concrete carbonation depth.

Number Actual value/(mm)

ANN(RBFNN) SVM Forecasting value/(mm) Error/% Forecasting

value/(mm) Error/%

1 16.94 16.9612 4.89 17.8205 5.20

2 21.64 21.6457 0.16 20.6201 4.72

3 14.47 14.6025 11.26 14.8311 2.49

4 18.94 19.1433 8.40 17.8205 5.91

5 11.64 16.4504 14.71 14.8311 6.49

6 15.86 11.9979 13.30 11.7340 0.82

MAPE/% 8.79 4.27

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V. CONCLUSION In the study, the regression model of support vector

machine is applied to forecast concrete carbonation depth. The real data are used to study the forecasting results of concrete carbonation depth. In concrete carbonation depth forecasting, the experimental results indicate that SVM has higher forecasting accuracy than artificial neural network.

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detection of structural damage”, Computers&Structure, 1992, vol.42,no.4,pp.649-659.

[2] S.F. Fang, M.P. Wang, W.H. Qi, and F. Zheng, “Hybrid genetic algorithms and support vector regression in forecasting atmospheric corrosion of metallic materials”, Computational Materials Science, 2008, vol.44,pp. 647-655.

[3] V.T. Tran, B.S. Yang, and A.C.C. Tan, “Multi-step ahead direct prediction for the machine condition prognosis using regression trees and neuro-fuzzy systems”, Expert Systems with Applications, 2009,vol.36,pp. 9378-9387.

[4] W.W. He, Z.Z. Wang, and H. Jiang “Model optimizing and feature selecting for support vector regression in time series forecasting”,Neurocomputing, 2008, vol.72,pp. 600-611.

[5] S.C. Huang, “Integrating nonlinear graph based dimensionality reduction schemes with SVMs for credit rating forecasting”, Expert Systems with Applications,2009,vol.36,pp. 7515-7518.

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