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Compressive Strength Prediction of High Strength Concrete using

Regression and ANN Models.

S Mandal1, Shilpa M2, R Rajeshwari3

Department of Civil Engineering

PES University, Bengaluru -560085 [email protected], [email protected], [email protected]

Abstract: High strength concrete (HSC) is one of the most popular terminologies used in the concrete

technology, which is known for benefits like high workable, durable and high ultimate strength. The

estimation of the compressive strength (CS) using experimental method is too expensive and time

consuming procedure and small error will lead to repetition of the work, to overcome this, alternative

methods are used for prediction of the CS of HSC. In the present study, the experimental data on the

strength of HSC of various mix designs are collected from authenticated journal papers, which are

used to predict the CS using regression analysis (MLR- multi-linear regression) and artificial neural

network (ANN) models. The collected data set are divided into two groups, one for training and other

for testing. The input parameters used in regression and ANN models are cement content,

superplasticizer, coarse aggregate, fly ash, fine aggregate, silica fume, blast furnace slag, water-

cement ratio and the CS of HSC at 28 days is the output parameter. The models are developed using

training dataset and the developed model is validated using testing dataset. The comparison is made

between the CS obtained from the MLR and ANN models. The ANN model yields better correlation

between predicted and actual values of the CS (test correlation for MLR-45.48% and ANN-95.03%)

and the percentage of error also reduces as compared to that of MLR. From this investigation, it is

observed that the ANN model can be used to predict the CS of HSC.

Keywords: High strength concrete, artificial neural network, Multi-linear regression.

1. Introduction

Concrete is an excellent building material which carries the compressive stresses from large

infrastructure because of this advantage concrete is used for the construction. Concrete is classified as

different types based on their strength and performance. The concrete which has properties like high

durable, workable and high ultimate-strength is called as HSC. The production of HSC depends upon

the good selection and mix proportioning of the ingredient to achieve a high strength of concrete. The

use of HSC in construction increases the service life of the structure and suffers less damage which

would reduce overall cost.

In construction the estimation of the CS has received a large amount of interest because, the CS is one

of the important mechanical properties of concrete. On specific topic several investigations are carried

to estimate the CS of HSC with the addition of different types of admixtures. The comparison was

made by considering the properties like CS, consumption of cement and economic validation. HSC

saves the consumption of cement about 50% and which results in less usage of raw materials and

reduction in overall costs (Alves et. al 2003). The performance of HSC is studied by variation of

dosage of silicafume (SF) and water-cement ratio (w/c). SF effects negatively on the CS as compared

to w/c ratio (Behnood and Ziari 2007). HSC gives the high workability and concrete strength without

using the special ingredient except good quality of material and proportions of concrete (Rashid et. al

2008). The CS variation at different temperatures ranges are carried out. The study indicates that the

CS decreases with increase in temperatures and structure may damage by fire (Husem 2005). Partial

replacement of cement with other admixture increases the strength of concrete as compared to mixture

made by 100% port land cement (Ibrahim et. al 2013).

The estimation of the CS by experimental method is too expensive and time consuming procedure and

small error will lead to repetition of the work, to overcome this, an alternative method is used for

prediction of the CS of HSC. Many attempts are made to develop the suitable mathematical models

which have ability of find the strength of concrete at various ages and conditions. Sometimes

mathematical model like regression analysis shows poor agreement with experimental data. To deal

these drawbacks, a different method of modelling known as ANN is used. ANN is a soft computation

method based on the structure and functionality of biological neuron in similar way how human brain

works. The massages and information that flow through neural network, depends on the structure of

ANN because ANN has the ability to learn on the basis of data provided for the input and output

variables, and ANN method is trained and tested.

The present study involves the estimation of the strength of HSC. For this requirement, a total of 106

experimental data on HSC is extracted from authenticated journal papers; these data set are divided

into two groups, 70% of data are taken for training and remaining 30% data are taken for testing the

models. Finally the performances in estimating the CS of HSC using MLR and ANN are compared.

2. Modelling techniques

2.1 Multi-linear Regression Model

The linear regression model is a general form of regression models, the linear estimator functions are

used to model the data, and output parameters are determined from the data. Some times for the

regression analysis include more than one input variables which would lead to the formation of

“multiple linear regression” function. MLR evaluates the correlation between two or more input

variables by ?tting a linear equation between them and involves summarization of data as well as

investigation of relationship between variables. Mathematically, a MLR model can be expressed as

given below:

y = a? + a? x? +a? x?+… (1)

Where, y is the dependent variable, x?, x? … etc. are the independent input variables to the model,

and a?, a? , a?,… are partial regression coefficients.

2.2 Artificial Neural Networks

The artificial neuron mimics the characteristics of the biological neuron that is human brain structure

and it basically consists of inputs; each input represents the output of another neuron. The input used

to solve the problem is multiplied with corresponding weights and these weighted inputs are summed

with bias value. The summation of the inputs are processed in the hidden layer using transfer

functions like linear, tan-sigmoid and log-sigmoid transfer functions etc. The processed information

by transfer function sends along the output layer as required result. The arrangement of neurons into

layers and the connection pattern between other layers is known as network architecture.

Figure 1: Structure of an Artificial Neuron Model.

Figure 1 shows the structure of an Artificial Neuron Model. Feed forward network (FFN) is generally

used back propagation for training network where the error obtained at the output layer is moved back

to the input and hidden layers for updating weights and decreases the errors to get the best output

from ANN. The main aim of the FFN process is to reduce the overall error between the observed and

estimated values by adjusting the weights, and these weights are combined and processed through an

activation function and released to the output layer.

3. Data

For the present study, experimental data on HSC are obtained from various authenticated journals

(Alves et. al 2003; Behnood and Ziari 2007; Husem 2005; Ibrahim et. al 2013; Elahia et. al 2010;

Prasad et. al 2009; Biskri et. al 2017; Kumar et. al 2017; Hassan et. al 2000;Ouda 2015;Rashida et. al

2008). A total of 106 datasets collected and the data consists of input and output parameters. The

input parameters include cement content, coarse aggregates, fine aggregates, blast furnace slag, silica

fume, fly-ash content, super plasticizer and water-cement ratio. Output parameter is the 28 days CS of

HSC. All collected data are converted into desirable units. Further, these data sets are normalized

using Eq. 2.

( )

( ) ( )

(2)

Where, is the normalized value, is the actual value, is ( ) the maximum value, ( ) is

the minimum value.

Table 1: Range of experimental variables

Variables Range

Cement(kg/m3) 135 – 91O

Coarse aggregate(kg/m3) 814.54 – 1547.06

Fine aggregate(kg/m3) 241.93 – 1164

Fly ash(kg/m3) 0 – 27M

Silica fume(kg/m3) 0 – 91

Blast furnace slag(kg/m3) 0 – 34M

Super plasticizers(kg/m3) 0 – 32.2

W/C(kg/m3) 0.21 – 1.23

Compressive strength(MPaF 55 – 88.9M

Total numbers of data sets collected are 106 and the data is divided into two sets: one is for testing

and another for training purpose. Data considered for training consist of varying values covering

maximum to minimum range. 70% of the data are taken for training purpose, therefore 75 data sets

are used for training the network. 30% of the data are taken for testing purpose; hence 31 data sets are

used for testingK

4. Methodology used for Model Development

4.1 MLR model

The MLR model constructed in the current study has eight input parameters namely cement content,

superplasticizer (SP), coarse aggregate (CA), fly ash(F),fine aggregate(FA), , silica fume(SF), blast

furnace slag(BFS) and w/c to get the 28 days CS as output parameter. Initially, the 75 train data set

containing both the input and output parameters are used to get the regression coefficients for each

variable and obtained CCtrain, thereafter remaining data are utilized to estimate the CS and obtained

CCtest. The estimated and observed CS of testing data sets are compared based on the correlation

between them and performance of MLR in predicting the CS of HSC is assessed based the CC value

of testing data set.

4.2 ANN model

Here, the ANN model with the 8- input nodes, 6-hidden nodes and one output node is developed to

estimate the CS of HSC. The input information is passed along the input layer no computation are

happens in this layer but it pass the information to the next layer called hidden layer in hidden layer

inputs are multiplied by weights and the bias value is added to the each input nodes. These weighted

inputs are processed by the transfer function of the ANN model, finally the processed information are

received from output layer. The ANN model works on the basis of the Levenberg-Marquardt (LM)

algorithm.

5. Results and Discussion

Regression (MLR) and ANN approaches have been used to predict the CS of HSC. The capability of

these models was assessed using statistical measures like Correlation Coefficient (CC), Root Mean

Square Error (RMSE) and Scatter Index (SI), which are defined as,

?( )( ) ??( ) ( )

(3)

??( )

(4)

??? (5)

Where and is the observed and predicted CS of HSC respectively. n is the number of data set

used. ? and is the average observed and predicted CS of HSC respectively.

5.1 Regression Analysis:

The MLR model is trained using normalized training data set. After training the model, the MLR

coefficients are used to predict the CS of test data set. Both train and test data sets are shown in

Figures 2 and 3.

Eq. 6 is developed using training data:

Y = – 0.5009 + (0.7885*x1) + (0.7421*x2) + (0.5846*x3) + (0.1693*x4) + (0.0115*x5) +

(0.6027*x6) – (0.1595*x7) – (0.1018*x8) (6)

Figure 2: Comparison between predicted and observed CS for training and testing by MLR

Figure 2 shows variation of the predicted and observed CS of trained and tested data set with the CC

of 0.6757 and 0.4548. This shows that prediction of CS by MLR is poor, as could be observed, when

data are scattered and not along or near by the (y=mx) line. If the predicted data are mostly lying

along a nearby (y=mx) line, the prediction is fairly, accurate.

5.2 Artificial Neural Network:

The ANN model is trained and tested using LM algorithm for a given input and output parameter. The

network is trained for different number of hidden layer nodes; initially 3 hidden nodes are used to

model. Further numbers of hidden layer nodes are increased to arrive at better results. The results

obtained during training and testing processes showing the CC, RMSE and SI values are shown in

Table 2.

Table 2: Statistical results obtained for ANN model (8-X-1).

NETWORK CC RMSE SI

8-3-1 Training

Testing

0.8868

0.8843

11.1774

10.9854

0.2800

0.2759

8-4-1 Training

Testing

0.9220

0.9002

9.3633

10.1574

0.2311

0.2589

8-5-1 Training

Testing

0.9475

0.9293

7.7485

8.8217

0.1913

0.2248

8-6-1 Training

Testing

0.9589

0.9503

6.8668

7.1643

0.1695

0.1826

8-7-1 Training

Testing

0.9505

0.9413

7.5208

7.9991

0.1856

0.2039

8-8-1 Training

Testing

0.9524

0.9393

7.3698

8.2017

0.1819

0.2090

CCs between the observed output and predicted output are calculated using Eq. 3. RMSE and SI

between the observed output and predicted output are calculated using Eq. 4 and Eq. 5 respectively.

From Table 2, it is observed that CC obtained for the network 8-6-1 with 15 epochs has achieved the

best value. The CC value obtained for trained and tested data is 0.9589 and 0.9503 respectively. The

RMSE value is found to be 6.8668 and 7.1643 for training and testing respectively. The SI value is

found to be 0.1695 and 0.1826 for training and testing respectively. Hence the ANN model with

network 8-6-1(Figure 4) yields the best performance to predict the CS of HSC.

Figure 3: Correlation between predicted and observed CSs for training and testing by ANN (8-6-1).

Figure 3 shows the comparison between predicted and observed values of CS by ANN (8-6-1) with

CC of 0.9589 and 0.9503 for trained and tested data respectively.

Figure 4: Structures of ANN (8-6-1).

Once the network is trained, the weight and bias values are fixed for that model. The ANN structure

constructed for predicting the CS of HSC is shown in Figure.4. The structure consists of 8- input

nodes, 6-hidden layer nodes, and one output node.

5.3 Comparison between MLR and ANN models

Table 3 shows the comparison between CC values for regression (MLR) and ANN models. The test

data for CC of 45.48% by MLR shows that it gives poor correlation; whereas CC of 95.03% by ANN

shows that the ANN model predicts the CS of HSC with very good correlation.

Table 3: CCs for MLR and ANN Models

Model CC

MLR Training

Testing

0.6757

0.4548

ANN Training

Testing

0.9589

0.9503

6. Conclusion

Regression and ANN models have been trained and tested with about 70:30 of the total data sets.

Based on the present study, the following conclusions are drawn:

? The regression model yields CC of 0.6757and 0.4548 for training and testing data

respectively; this shows that estimation of the CS by MLR is poor.

? For better prediction of the CS of HSC, a soft computing model such as ANN is used and the

results are compared in terms of statistical measures such as CC, RMSE and SI.

? ANN model yields a good correlation between the input parameters and compressive strength

of HSC with 15 epochs. The statistical parameters obtained, CC- 0.9589 and 0.9503, RMSE –

6.86 and 7.18and SI- 0.16 and 0.18 for training and testing respectively, demonstrate that the

predicted output values are very close to the actual output values.

? With comparison to regression model, the performance of ANN models show good results in

terms of statistical measures like CC, RMSE and SI for the observed and predicted CS of

HSC. Therefore, the ANN model can be used to predict the CS of HSC.

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