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USE OF NEURAL NETWORKS FOR THE EVALUATION OF

CONCRETE CORE STRENGTHS

S Tapkin

Civil Eng. Department

Anadolu University

Eskisehir, Turkey

cstapkin@anadolu.edu.tr

M Tuncan

Civil Eng. Department

Anadolu University

Eskişehir, Turkey

mtuncan@anadolu.edu.tr

K Ramyar

Civil Eng. Department

Ege University

Izmir, Turkey

kambiz.ramyar@ege.edu.tr

Abstract- This paper examines a method to evaluate

concrete core strengths by using artificial neural

networks. Eight different concrete mixtures were

prepared by using two different aggregates of four

different maximum sizes. Beam specimens were cast

by prepared mixtures. Cores with different diameters

and length-to-diameter ratios were drilled from beam

specimens. Compressive strength tests were carried

out on core specimens at different ages. The

parameters influencing the strength of cores were

used as input for neural network architecture and the

core strengths were evaluated. The outputs of the

proposed network were examined by root mean

squared errors (RMSE). The proposed architecture

gave reliable estimates of the concrete core strength.

The RMSE values were found to be highly reliable.

Conclusively, the results revealed that the feed

forward back propagation neural networks can

perform to obtain reasonable evaluation of core

strengths.

Keywords: Neural networks, Back propagation,

Compressive strength, Core strength

1. INTRODUCTION

The strength is one of the most important

properties of concrete [1-4]. The quality control of

concrete in structures is generally carried out on

standard test specimens [5,6]. However, it is

difficult to assess the actual strength of concrete in

structures since the compaction and curing received

by the in-situ concrete and those received by the

standard specimens are quite different [7]. This

becomes more pronounced for larger members [8].

On the other hand, it is sometimes necessary to

know the strength of concrete in a structure [9].

Although it is expensive, the core test is one the

O Arioz

Civil Eng. Department

Anadolu University

Eskişehir, Turkey

oarioz@anadolu.edu.tr

A Tuncan

Civil Eng. Department

Anadolu University

Eskişehir, Turkey

atuncan@anadolu.edu.tr

most reliable methods to determine the strength of

concrete in structures [2]. However, the results of

the core tests should be carefully interpreted since

the strength of cores is influenced by a number of

factors such as diameter, length-to-diameter (l/d)

ratio, and the moisture conditions of the cores

[2,3,11-16]. Moreover, the maximum size of the

aggregate in concrete mixture plays an important

role for the evaluation of the test results [3,17]. This

is strongly emphasized in recently published

Turkish Standard, TS EN 12504-1 [18].

In the present study, the effects of core

diameter, l/d ratio as well as the type and maximum

size of the aggregate and the age of the concrete on

the core strengths were examined by means of

neural networks.

2. HISTORY OF ARTIFICIAL NEURAL

NETWORKS

The progressing development of

neurobiology has enabled scientists to develop

mathematical models of neurons for the simulation

of neural behaviour. In the early 1940s, one of the

first abstract models of a neuron was introduced by

McCulloch and Pitts [19]. Hebb proposed a

learning law explaining how a network of neurons

learned [20]. Minsky and Rosenblatt followed this

notion through the next two decades [21, 22]. Later,

Minsky and Papert pointed out theoretical

limitations of single-layer neural network models

[23]. Research on artificial neural networks failed

into an indefinable era for nearly two decades due

to this pessimistic projection. In spite of the

negative atmosphere, some researchers still

continued with their research and produced

valuable results. For example, Anderson and

Grossberg did important studies on psychological

models and Kohonen developed associative

memory models [24-26]. In the early 1980s, the

neural network approach was resurrected. Hopfield

introduced the idea of energy minimization in

physics into neural networks [27]. His influential

paper endowed this technology with renewed

momentum. Feldman and Ballard made the term

“connectionist” popular [28]. Sometimes,

connectionism is also referred to as subsymbolic

process, which have become the study of cognitive

and artificial intelligence systems inspired by neural

networks [29]. Unlike symbolic artificial

intelligence, connectionism emphasized the

capability of learning and discovering

representations. Insidiously, connectionism has

become a common ground between traditional

artificial intelligence and neural network research.

In the middle 1980s, Rumelhart and McClelland

generated great impacts on computer, cognitive and

biological sciences [30]. Notably, the

backpropagation learning algorithm developed by

Rumelhart, Hinton and Williams offers a powerful

solution to training a multilayer neural network and

shattered the curse imposed on perceptrons [31].

However, it should be noted that the idea of

backpropagation had been developed by Werbos

and Parker independently [32, 33]. The symbolic

approach which has long dominated the field of

artificial intelligence was recently challenged by the

neural network approach. There have been

speculations about whether one approach should

substitute for another or whether the two

approaches should coexist and combine. More

evidence favours the integration alternative in

which the low-level pattern recognition capability

offered by the neural network approach and the

high-level cognitive reasoning ability provided by

the symbolic approach complement each other. The

optimal architecture of future intelligent systems

may well involve their integration in one way or

another.

3. DATA SET FOR TRAINING AND TESTING

OF THE NEURAL NETWORK

In this study, the core strengths were

analyzed by feed forward back propagation neural

networks. The reason of utilizing feed forward back

propagation was that they were used widely in

almost every study concerning neural network

applications. In this study, there are two hidden

layers in the present architecture opposed to the

other studies which have only one hidden layer in

their architectures [34-41]. The training process

time does not differ too much with two layered

architecture and this gives a more flexible approach

to the solution. The gradient descent algorithm was

used in the training process.

There are several studies on the application of

neural networks to predict the compressive strength

of concrete through input parameters such as type

and dosage of the cement, water-cement ratio,

fineness modulus of sand, sand-aggregate ratio,

slump, type and dosage of admixtures, etc. [34-41].

The use of test results in the neural network

approaches is a fairly new concept. In a recent

study by Hola and Schabowicz, non-destructive

assessment of concrete strength using artificial

intelligence has been presented [42]. The core test

results have not been utilised yet in a neural

network approach. In this study, type and maximum

size of the aggregate used in concrete mixture,

diameter, length-to-diameter ratio and the age of the

concrete cores were used as input parameters for

the estimation of concrete core strength by means

of artificial intelligence. Both the architecture of

two hidden layers and the gradient descent

algorithm has been utilised.

In this study, the neural network toolbox of

MATLAB was used. The reason of using this

software was to provide quick and reliable results.

Two main data sets were analysed. One of them

was for cores removed from crushed limestone

aggregate-containing concrete. The other one was

for cores drilled from natural aggregate containing

concrete. Table 1 presents designations, mix

proportions and some properties of the concrete

mixtures.

The cores with 144, 94, 69 and 46 mm in

diameter were obtained and cut to six different l/d

ratios which were selected as 2, 1.75, 1.5, 1.25, 1,

and 0.75. The cores were tested at the ages of 7, 28,

and 90 days and the compressive strength values

were calculated by taking the average of at least six

specimens.

Table 1.Constituents and some properties of concrete mixtures

Mixture

Mix Proportions (kg/m

3

) Some Properties

Coarse

Aggregate

Fine

Aggregate

Cement

Water

w/c

Type of

Aggregate

Maximum

Aggregate

Size

(mm)

MIX-A 696 1043 356 215

0.6

Crushed

Limestone

10

MIX-B 729 1094 331 200 15

MIX-C 1034 846 315 190 22

MIX-D 1128 752 315 190 30

MIX-E 507 1259 356 195

0.55

Natural

Aggregate

10

MIX-F 833 994 331 181 15

MIX-G 1158 706 315 173 22

MIX-H 1300 565 315 173 30

4. CONSTRUCTION OF NEURAL NETWORK

MODEL

The problem can be defined as a nonlinear

input-output relation between the influencing

factors (core diameter, l/d ratio, maximum

aggregate size and age of concrete) and

compressive strength values at 7, 28 and 90 days.

Fig.2 illustrates the architecture of the neural

network applied in the present study. There are four

nodes in the input layer corresponding to above

mentioned four factors and one in the output layer

corresponding compressive strength. Lots of trials

were carried out for the determination of hidden

neuron number of the two hidden layers. This

procedure was performed for cores drilled from

both crushed limestone aggregate and natural

aggregate-containing concretes. Different optimum

hidden neuron numbers were obtained for different

cases. In this study, the neurons of neighbouring

layers were fully connected.

Each batch of data was divided into two sets,

one for the network learning called training set, and

the other for testing the network called testing set.

Each set was composed of 144 pairs of input and

output vectors. Each input pair was calculated by

taking the average of at least six specimens. An

input vector consisted of four components and an

output vector had only one component.

In general, the network parameters; number of

training samples for each concrete core sample

property was 144, number of input layer neurons

was 4, number of hidden layer neurons ranged

between 5 to 50, number of output layer neurons

was 1, type of back-propagation learning rule was

gradient descent algorithm, activation functions

were logarithmic sigmoid, learning rate was 0.3 and

number of epochs varied from training to training.

Actually, the number of training samples was more

than 144 and different combinations of the number

of hidden neurons and activation functions for the

training of the neural network architecture were

used to have the optimum number of hidden

neurons.

The network was tested with 144 pairs. It was

found out that logarithmic sigmoid activation

function served our purpose very well. Therefore,

logarithmic sigmoid activation function was used

throughout the analyses.

Fig.2. Neural network architecture

Fig.3. Sample training performed through the analyses

Core

diameter

Core

l/d ratio

Maximum

aggregate size

Concrete

age

Core

compressive

strength

Hidden la

y

ers

Input layer

Output layer

Fig.3 shows a typical sample training session

performed in this study. As the data set was

representative of the test data, the learning process

terminated after approximately 200 epochs. As

analyses proceeded, it was seen that the epoch number

rose to maximum 600. The testing set was employed

to evaluate the confidence in the performance of the

trained network. One hundred and forty four testing

vectors of the batch of data were used to test the

neural network model. The training was conducted on

by the 10 and 15 mm maximum aggregate sizes and

the testing was carried out by the 22 and 30 mm

maximum aggregate sizes.

The target outputs of the output neurode are

supposed as the actual compressive strength obtained

from the results of the core tests. The training data set

was normalised before the analyses and the predictive

capabilities of the feed forward back-propagation

neural network were examined. The basis of this

discussion was to demonstrate the prediction

performance of these models by comparing their

levels of prediction rather than to illustrate how well

the models predict a given set of data. The prediction

performances were compared with the Root Mean

Squared Error (RMSE) values. The lesser the Root

Mean Squared Error, the better the estimates were.

RMSE values can be obtained by the following

standard formula:

N

X

X

R

MSE

N

j

j

1

2

_

(Eq.1)

where;

N

= number of observations,

X

J

= predicted values, and

_

X

= Observed values

In other word, the correspondence of the data set

has been ensured. The behaviour of all of the system,

rather data set can be monitored by this way.

Therefore, it is much easier to decide the number of

hidden neurons that can be utilised in the hidden

layers. This is solely done on a root mean squared

error minimisation basis. This means that when the

value of the root mean squared error for the whole set

of data is minimum, the optimum number of hidden

neurons is determined. Many trials were carried out to

determine the optimum number of hidden neurons. It

was found that the optimum number of hidden

neurons was 40 and 35 for cores obtained from

crushed aggregate-containing and natural aggregate-

containing concrete, respectively. After obtaining the

number of hidden neurons, some further analyses

were also carried out to determine the optimum

learning rate. Fig.4 shows the RMSE values for

different hidden neuron numbers. It can be seen that

the smallest RMSE value was obtained by 40 hidden

neurons. The learning rates were found to be 0.3 and

0.5 for cores drilled from crushed limestone and

natural aggregate-bearing concretes, respectively.

5. CONSISTENCY BETWEEN NEURAL

NETWORK MODELLING AND

EXPERIMENTS

When the simulation results for the optimum

hidden neuron numbers were further analyzed, it can

be seen that the modelling results are reasonably good

for such a big data set. RMSE values of 0.0708 and

0.1006 are fairly representative for crushed limestone

and natural aggregate-bearing cores, respectively. It is

not surprising to observe some fluctuations in the root

mean squared errors due to the nature of the back

propagation algorithm. However, it was observed that

the modelling results were very close to the real

compressive strength test results.

As the data set is extremely big, the analyses

gave fairly reasonable results and show the behaviour

of the whole system. As the data sets are composed of

mainly four elements acting together as a whole unit,

there were no means to show the effect of each of

these parameters on concrete strength individually.

Therefore, the above given root mean squared values

show the most correct and realistic representation of

the analysis results.

According to Fig.4, the RMSE values range

between 0.07 and 0.13. There was a regular pattern of

spread in the RMSE values as the graph was

analyzed. Since the minimum RMSE value was

important, the optimum hidden neuron number for

cores drilled from crushed aggregate-containing

concrete was forty. Further analyses were carried on

the forty hidden neuron neural network architecture

and it was found out that the optimum learning rate

was 0.3. Similar analyses were carried out on results

obtained from natural aggregate-bearing concrete and

the optimum hidden neuron number was found to be

thirty five. Further analyses were carried on the thirty

five hidden neurons network architecture (Fig.3). It

was found out that the optimum learning rate was 0.5.

This type of error presentation is more realistic

and meaningful. In this way, a more visual insight to

the whole data set’s performance can be obtained. A

new point of view to the neural network training and

testing can be drawn by the help of the RMSE and

learning rate graphs.

RMSE vs HN Number

0.1072

0.1313

0.0708

0.1242

0.1267

0.0938

0.06

0.08

0.10

0.12

0.14

25 30 35 40 45 50

Hidden Neuron

RMSE

Fig.4. RMSE values vs. hidden neuron number for crushed

aggregate-containing cores

RMSE vs LR Value

0.2289

0.1095

0.0708

0.1211

0.083

0.1072

0.05

0.10

0.15

0.20

0.25

0.1 0.2 0.3 0.4 0.5 0.6

LR Value

RMSE

Fig.5. Different learning rate values for forty hidden

neurons for crushed aggregate-containing cores

RMSE vs HN Number

0.1247

0.1006

0.1383

0.1189

0.1224

0.1459

0.09

0.11

0.13

0.15

25 30 35 40 45 50

Hidden Neuron Number

RMSE

Fig.6. RMSE values vs. hidden neuron number for natural

aggregate-containing cores

RMSE vs LR Value

0.1011

0.1008

0.1048

0.1007

0.1006

0.1012

0.100

0.102

0.104

0.106

0.1 0.2 0.3 0.4 0.5 0.6

LR Value

RMSE

Fig.7. Different learning rate values for forty hidden

neurons for crushed aggregate-containing cores

6. CONCLUSIONS

The core strength test results were analyzed by

means of multi layer feed forward back propagation neural

network model. In this analysis, gradient descent algorithm

and two hidden layers were employed. The following

conclusions can be drawn from this study;

1. The results obtained from the analyses show that the

prediction of the compressive strength of concrete core

specimens by artificial neural networks particularly by

the gradient descent algorithm and two hidden layers

architecture was a viable method. This was mainly

evidenced by the calculated RMSEs for the gradient

descent network. Moreover, by the differences between

the RMSEs enabled to determine the optimum hidden

neuron numbers and the learning rates that make easier

estimations of the core strengths.

2. The average compressive strengths of concrete cores

determined by the artificial neural networks and by

destructive tests during the investigation were very

similar to each other. It was highly significant that the

calculated RMSEs were definitely low therefore it

indicates that the estimations were representative of the

real results.

3. The responsible person on the site can neurally identify

the compressive strength of similar concretes

incorporated in building structures without needing to

determine correlations or to fit hypothetical scaling

curves. Required optimum hidden neuron number and

learning rate values for better predictions can be

obtained by means of RMSE values. A neural network

model can be constructed to provide a quick and

dependable mean of predicting the core strengths. This

model may convert the strength of non standard core to

that of a standard core recommended by relevant

standards and specifications. Neural networks will be

useful to civil engineers especially dealing with material

engineering to evaluate core strength and will provide a

sound basis for these and similar types of analyses.

7. ACKNOWLEDGEMENTS

The authors would like to acknowledge the

financial and technical supports supplied by Scientific

Research Projects (03 02 23) Commission of Anadolu

University, Turkey. The authors also thank to Research

Assistant Kadir Kilinc for his great efforts for the

preparation of the manuscript.

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