Soft Computing and Regression Models for Compressive Strength of Blast
Furnace Slag and Super Plasticizer Mixed Concrete
Naresh Nischol Harry1 and Yeetendra Kumar Bind2
1&2
Department of Civil Engineering, SHUATS, Allahabad, U.P., India, yeetendra@gmail.com
Abstract
The aim of this research work is to explore the application and limitations of soft computing methods in
determining the compressive strength of mineral and chemical admixture mixed concrete. Concrete mix
design calculation was carried out as per IS 10262:2009 for blast furnace slag and super plasticizer
mixed concrete. The experimental investigation yielded seven set of variables viz. cement content, water
content, super plasticizer, coarse aggregate, fine aggregate, curing period and compressive strength.
Artificial Neural Network and Adaptive Neuro Fuzzy Inference System were employed to understand the
nonlinear pattern between concrete mix design data and corresponding compressive strength.
Compressive strength was satisfactorily modeled from ANN technique with given set of variables. Most of
the soft computing techniques are applied either on nominal mix or mineral admixture mixed concretes.
However, this study takes into account both mineral and chemical admixture mixed concrete. The
compressive strength was determined for curing period of 3, 7, 28, 56 and 91 days which gives deep
insight in to the compression behavior of concrete and subsequent performances of various models.
Studied available till date, usually take curing period of 7 and 28 days only. The limitations of models
were also explored in this study and it was found that same set of variables did not yield reasonable
results in ANFIS models, which indicates that, ANFIS are vulnerable for higher number of inputs. A
unique feature of the study was the employment of multivariate power equations in regression models.
Even with five different curing periods the coefficient of determination in ANN was above 0.8. It shows
that ANN can successfully replace the conventional destructive methods.
Keywords: Blast Furnace Slag (BFS), Super Plasticizer (SP), Artificial Neural Network (ANN), Adaptive
Neuro Fuzzy Inference System (ANFIS).
1. Introduction
A suitable value of compressive strength of concrete is the primary and most important requirement of
hardened concrete to ensure satisfactory performance under service load. However, binding capacity,
strength and workability of conventional concrete is often found below expectations. To overcome this
problem, use of admixtures in concrete are encouraged. Mineral admixtures increases the binding
capacity of concrete [1-4]. In addition, chemical admixtures are used to increase the workability of
concrete [5-6]. Hence, this study takes into account the use of Blast Furnace Slag (BFS) and Super
Plasticizer (SP) into concrete mix.
Variation in behavior of conventional concrete materials and admixture in different places, vagueness in
design parameters like workability, shrinkage of cement and shape of aggregate causes substantial
imprecision in the design strength even though quite a lot of care had taken in the calculation of design
mixes and subsequent preparation of laboratory samples. Casted cubes takes several days in curing. To
overcome above difficulties empirical methods and nondestructive testing methods have been developed
and practiced [7]. Soft computing methods can offer a ground to overcome the difficulties involved in
standard design mix process and save time involved in curing.
This research paper is prepared to examine the feasibility Artificial Neural Network (ANN) and Adaptive
Neuro Fuzzy Inference System (ANFIS) in determining the concrete compressive strength. Two
regression analysis were also carried out to compare the results of ANN and ANFIS models with the
regression models.
2. Artificial Neural Network
A large number of interconnected processing units (also called as neuron) working on the principle of
biological neuronal cell is called as Artificial Neural Network [8]. Function and structural aspects of
ANN is same as a bunch of biological neurons. ANN is advanced and standard tools to find solutions to a
wide variety of non-linear statistical data complications [9]. Interconnections among neurons are
established by weights. The ANNs are arranged in three or more layers (depending on number of hidden
layers). The very first layer is input layer, second layer is hidden layers and last layer is target layer. Each
layer of neurons has connections to all the neurons in next layer. Each neuron receives an input signals
from the previous neuron. Each of these connections has numeric weights associated with it. Figure 1
shows the simplest form of ANN.
x1
x2
wk1
bias
bk
Activation
Function
wk2
∑xiwki
xm
vk
Φ(.)
yk
wkm
Figure 1: simplest form of ANN
Where x1, x2, …,xm are input signals; wk1, wk2, …., wkm are synaptic weights of neuron k; uk is the linear
combiner output; bk is the bias ;φ (.) is the activation function; vk is the induced local field or activation
potential; and yk is the output signal [10].
Ongoing pair of equations represents gradual process in a neuronal model as depicted above.
𝑢𝑘 = ∑𝑚
𝑗=1 𝑤𝑗 𝑥𝑗
𝑣𝑘 = (𝑢𝑘 + 𝑏𝑘 )
𝑦𝑘 = 𝜑(𝑢𝑘 + 𝑏𝑘 )
or, 𝑦𝑘 = 𝜑(𝑣𝑘 )
(1)
(2)
(3)
(4)
There are categories of ANN depending on algorithm introduced to the above mentioned simplest form of
ANN to minimize error in the final output. One of the very popular and frequently used is back
propagation algorithm. We may understand the back propagation algorithm by the following set of
equations
The error signal ek(n) of neuron k at iteration n may be calculated by
𝑒𝑘 (𝑛) = 𝑑𝑘 (𝑛) − 𝑦𝑘 (𝑛)
(5)
The error energy of neuron j may be ½ ej2 (n). Thus total error energy for all neurons in the output layer
ξ(𝑛) =
1
2
∑𝑗 𝜖 𝑐 𝑒𝑘2 (𝑛)
(6)
Where set C includes all the neurons in the output layer of the network. Let N denote the total number of
patterns contained in the training set. The average squared error energy is obtained by summing 𝛏 (n) over
all n and then normalizing with respect to the size N
ξ𝑎𝑣𝑔 =
1
𝑁
∑𝑁
𝑛 = 1 ξ (𝑛)
(7)
The objective of learning process is to adjust the free parameters (like synaptic weights and bias levels) to
minimize 𝛏av. This process continues till minimum error is achieved. If network is trained (in repeated
cycles) with sufficient number of datasets then we can validate, the trained network to make predictions
for a new set of data that it is never been introduced during the previous phases [11].
3. Neurofuzzy Inference System
There are various categories of neurofuzzy system which is essentially an integration of ANN and Fuzzy
logic. However Adaptive Neuro-Fuzzy Inference System (ANFIS) which was originally proposed by
Jhang [12], is frequently used due to its simplicity and vast applicability. Fuzzy inference systems are
mainly composed of a rule base, a database and a decision making unit [13]. The steps of FIS consist of
fuzzification, allotment of membership grade, rule base development by employing if, then reasoning and
finally defuzzification i.e. fuzzy set into crisp set. This is how an input variable x is fuzzified to be a
partial member of the fuzzy set A by transforming it into a degree of membership of function µ A(x) of
interval (0, 1) [14]. A typical ANFIS structure containing zero order and first order Takagi-Sugeno-Kang
(TSK) model are shown below (Figure 2 & 3).
Figure 2: Sugeno method of fuzzy inference system
Figure 3: Architecture of ANFIS model in conjunction with Sugeno FIS
A typical rule in a Sugeno fuzzy model has the form, if input x = A1 and input y = B1, then output is given
as f1 = p1x + q1 y+ r1. For a zero-order Sugeno model, the output level f1 is a constant (p1= q1 =0).
Likewise, If input x = A2 and input y = B2, then output is given as f2 = p2x + q2 y+ r1. For a zero-order
Sugeno model, the output level f2 is a constant (p2= q2 =0). But if output f1, f2 are linear then we have first
order TSK fuzzy inference system. The output level fi of each rule is weighted by the firing strength wi of
the rule. For example, for an AND rule with input x = Ai and input y = Bi, the firing strength is
wi = And Method {µ Ai(x), µ Bi(y)}, i=1,2
(8)
Where, µ Ai (.) and µ Bi (.) are the membership functions for inputs 1 and 2. The final output of the
system is the weighted average of all rule outputs, computed as shown in Equation 1 below
Overall output = ∑𝑖 𝑤𝑖 𝑓𝑖 =
∑𝑖 𝑤𝑖 𝑓𝑖
∑𝑖 𝑤𝑖
(9)
4. Development of Concrete Mix Design Data
The concrete mix data used in this research paper was developed in laboratory by casting cubes of Blast
Furnace Slag (BFS) and Super Plasticizer (SP) mix concrete as per IS 10262:2009 guidelines. The
maximum water cement ratio was taken as 0.45. BFS and SP were used as partial replacement of cement
and water respectively. The BFS quantities were varied from 5% to 40% of cement. Similarity, SP
quantities were varied from 1% to 3% of water. The discussion on performance of optimum values of
these admixtures in concrete is avoided due to two reasons; first, several literatures are available,
highlighting the ideal proportions of these admixtures, and second, the discussion on this subject is
beyond the scope of this research work. Total 170 samples of cubes were casted to carry out compression
test. The compression testing machine was used to break the casted cubes of concrete for curing period of
3, 7, 28, 56, and 91 days. In this manner, seven variable data matrix was prepared from BFS and SP
mixed concrete. These variables were cement content (CC), water content (w), coarse aggregate (CA),
fine aggregate (FA), BFS, SP and curing period (CP). These seven variable were taken as input in both
soft computing methods. The concrete compressive strength (CCS) obtained from compression test was
taken as target parameter in both methods.
A typical representation of above discussed variables is given in Table 1. Serial no. 1 – 6 in this table
illustrates the ranges of each components of concrete in Kilograms in one m3 mixture of concrete. Serial
no. 7 (curing periods) and 8 (Concrete Compressive Strength) are in days and MPa respectively. 145
datasets were used to develop the soft computing and regression models and remaining 25 datasets were
reserved to validate the models.
Table1: Range of input and target parameters
Sr. No
Input Parameters
Minimum
Maximum
(Kg in a m3 of mix.)
1
2
3
4
5
6
7
8
Cement Content (CC)
Blast Furnace Slag (BFS)
Water content (w)
Super Plasticizer (SP)
Coarse Aggregate (CA)
Fine Aggregate (FA)
Curing Period (CP)
Concrete Compressive Strength (CCS)
133.00
50.00
126.60
2.00
811.00
605.00
3.00
18.28
(Kg in a m3 of mix.)
475.00
282.80
214.00
32.20
1134.30
992.60
91.00
82.60
5. ANN attribute and architecture
As discussed in previous articles back-propagation neural network (BPNN) was employed for all kind of
operations. Training in BPNN is carried out through the minimization of the defined error function using
the gradient descent approach [15]. There exist many ways to improve the rate of convergence one of
them is normalization, therefore datasets were normalized using following equation [16-18].
𝑈𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 =
𝑈𝑎𝑐𝑡𝑢𝑎𝑙 −𝑈𝑚𝑖𝑛
𝑈𝑚𝑎𝑥 −𝑈𝑚𝑖𝑛
(10)
The ANN toolbox in MATLAB (R2010a) computer added software was utilized to perform the necessary
computation in which learning rate (LR) and momentum term kept constant whereas connection weights
kept adjustable for all the models. ANN network architecture with a hidden layer (ten number of neurons
in hidden layer) is shown in Figure 4. It describes the way the network was treated from given set of input
and target parameters.
CC
w
BFS
SP
N1
N2
N3
CCS
CA
N10
FA
CP
Figure 4: ANN network architecture
6. ANFIS attributes
Subtractive clustering was used with hybrid optimization to generate ANFIS models. Hybrid optimization
is a combination of least-squares and back propagation gradient descent method. Training was carried out
for fifty iterations only since more iterations results over-fitting in training output and FIS out.
7. Results and Discussion
The best validation performance was obtained at MSE of 0.0043939 at second number of cycle (Figure
5). Optimum weights and biases obtained on second cycle is shown in Table 2, in which N1, N2, N3,---------N10 represents neurons in hidden layer.
Figure 5: MSE plot from ANN model
Table 2: Optimized weights and biases from ANN model
Hidde
n
Layer
Weights
Input layer to Nodes
Node
No.
CC
BFS
W
SP
CA
FA
CP
Nodes
to
Output
layer
CCS
N1
N2
0.55158
-0.34945
0.77204
-0.55945
0.40521
-2.0313
0.16512
0.90273
1.0503
1.6044
1.1198
0.60476
-4.6116
0.96781
-2.2239
-0.58882
Biases
Nodes
and
Output
layer
Bias
Values
-4.9573
1.7794
N3
N4
N5
N6
N7
N8
N9
0.18092
0.030191
1.9851
0.4017
1.1411
-1.2918
1.4252
0.090958
0.4172
-0.35992
-1.3128
-0.70451
-0.73591
0.86012
1.2185
0.5842
1.6609
2.8817
0.06933
-1.0171
2.6637
1.2971
0.06204
0.68516
-0.97579
1.2501
-0.52544
-0.23507
1.1028
-2.0139
1.7595
-0.96765
0.51052
0.64201
0.31671
1.4507
-1.2295
-0.47434
0.63426
-0.37993
-2.3347
0.95476
-0.301
-0.046788
-0.67697
0.22499
0.34757
0.88525
-0.32786
-0.79023
-2.0145
-0.62492
-0.7741
1.1814
-0.67259
2.1659
1.1204
1.4876
-0.41815
-0.080173
0.82499
-1.8846
1.7105
N10
-0.89714
0.52447
-0.90076
1.495
1.1027
0.85925
0.38834
1.645
-1.2236
CCS
-
-
-
-
-
-
-
-
-0.99538
Figure 6 shows continuously decreasing trend of mean squared error in ANFIS model. Error was
decreased to a value of 0.0182393 which is higher compared to ANN. This indicates improper training
and it may yield in poor predictability. Total sixteen number of fuzzy rules were developed after
minimization of error (Figure 7). These rule bases in the form of generalized bell shaped membership
function can be observed in this figure.
Figure 6: Training error in concrete ANFIS model
Figure 7 Rule bases in concrete ANFIS model
Predicted Compressive Strength
(MPa)
Figure 8a & b shows coefficient of determination obtained from ANN and ANFIS models respectively.
The R2 was 0.8275 for ANN model. Contrary to ANN models, the performance of ANFIS model got
declined giving R2 = 0.4886. The higher performance of ANN model may be attributed to higher number
of inputs. However, same could be the cause of underperformance of ANFIS, that is, it don’t work well
with higher number of inputs. However, poor predictability also depends on several other factors also like
reliability of input and validation data, optimization of fuzzy rule bases and training parameters etc.
90
80
y = 0,8351x + 8,1811
R² = 0,8275
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
Actual Compressive Strength (MPa)
Predicted Compressive Strength
(MPa)
Figure 8a ANN Prediction for BFS & SP Mixed Concrete
90
80
y = 0,738x + 12,919
R² = 0,4886
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
Actual Compressive Strength (MPa)
Figure 8b ANFIS Prediction for BFS & SP Mixed Concrete
Concrete compressive strength (CCS) of BFS and SP mixed concrete was selected as dependent variable
in multiple linear regression (MLR) and multiple nonlinear regression (MNR) analysis. Dependent
variables were same as input in case of soft computing models. The SPSS 20 statistical software was used
for developing regression models. The multiple linear equation obtained from MLR analysis is gives as
CCS = 0.696+ (0.439cc) + (0.296BFS) - (0.636w) - (0.375SP) - (0.378CA) - (0.434FA) + (0.499CP)
(11)
The values of gradients and intercept obtained from regression analysis are shown in above equation. The
R2 obtained from compressive strength yielded by this multiple linear equation and actual compressive
strength was 0.5885 (Figure 9a). Multivariate power equation was adopted for MNR analysis. Same set of
independent and dependent variable yielded following multivariate power function
CCS = 2.032895cc 0.864565 BFS 0.476152 w – 72.328 SP – 0.06611CA -0.1991FA -0.048406CP 0.215445
(12)
Predicted Copressive Stength
(MPa)
This MNR model yielded R2 = 0.7354 (Figure 9b) which is higher than R2 obtained from MLR analysis. It
shows that multivariate power equation can model concrete compressive strength better than multiple
linear equation. Overall it can be observed that soft computing method may satisfactorily model concrete
compressive strength by offering favorable conditions to them.
90
80
70
60
50
40
30
20
10
0
y = 0,6454x + 19,977
R² = 0,5885
0
10
20
30
40
50
60
70
80
90
Actual compressive Strength (MPa)
Predicted Compressive
Strength (MPa)
Figure 9a MLR Prediction for BFS & SP Mixed Concrete
90
80
70
60
50
40
30
20
10
0
y = 0,7488x + 13,321
R² = 0,7354
0
10
20
30
40
50
60
70
80
Actual Compressive Strength (MPa)
Figure 9b MNR Prediction for BFS & SP Mixed Concrete
90
8. Conclusions
The study was carried out to test the ability of soft computing methods in determining concrete
compressive strength. Based on obtained results it was concluded that higher number of inputs minimized
the training error considerably in ANN modeling. Hence, ANN models with seven input variables gave
good performance evaluation measure. Contrary to ANN model, performance of ANFIS was severely
affected due to higher number of inputs. Hence, ANFIS model can be further examined when number of
inputs are less. Another important conclusion drawn from regression analysis is that multivariate power
regression equations have far greater ability to work with higher number of data matrix and they can be
used to understand the relative performance of soft computing techniques. However, multiple linear
regression was not found suitable for modeling compressive strength.
9. References
11.1. Journal Article
1.
2.
3.
4.
Jagadeesh, P., Kumar, P., S., and Prakash, S., S., B., “Influence of quarry dust on compressive strength of concrete”,
Indian Journal of Science and Technology. (2016), 9 (22): 1-6.
Sudha, C., Ravichandran, P. T., Krishnan , K. D., Rajkumar, P. R. K., and Anand, A., “Study on mechanical
properties of high performance concrete using M-Sand”, Indian Journal of Science and Technology. (2016), 9 (5): 1-6.
Huang, C., Lin, S., Chang, C. and Chen, H., “Mix proportions and mechanical properties of concrete containing very
high volume of class F fly ash”, Construction and Building Materials, Elsevier. (2013), 46: 71 – 78.
Nath, P. and Sarker, P., “Effect of Fly Ash on the Durability Properties of High Strength Concrete”, Procedia
Engineering, Elsevier. (2011), 14: 1149–1156.
11.2. Conference Proceedings
5.
Elsageer, M., E., Millard, S., G. and Barnett, S., J., “Strength development in concrete containing coal fly ash under
different curing temperature conditions”, Proceedings of World of Coal Ash (WOCA) conference, Lexington, KY,
USA, (2009) May 4-7.
11.3. Journal Article
6.
7.
8.
9.
Jatale, A., Tiwari, K., and Khandelwal, S., “Effects On Compressive Strength When Cement Is Partially Replaced By
Fly-Ash”, IOSR Journal of Mechanical and Civil Engineering. (2013), 5 (4): 34-43.
Arundas P H., and Dewangan, U. K., “Compressive strength of concrete based on ultrasonic and impact echo test”,
Indian Journal of Science and Technology, (2016), 9 (29): 1-7.
Goh A.T.C., “Probabilistic neural network for evaluating seismic liquefaction potential”, Canadian Geotechnical
Journal, (2002), 39: 219-232.
Hanna A.M., Ural D., and Saygili G., “Neural network model for liquefaction potential in soil deposits using Turkey
and Taiwan earthquake data”, Soil Dynamics and Earthquake Engineering, (2007), 27: 521– 540.
11.4. Book
10. Haykin, S., “Neural Networks.” 2nd Ed., Prentice Hall, New Delhi, India. (2006).
11.5. Journal Article
11. Rao K.S., Satyam D.N., “ Liquefaction studies for seismic microzonation of Delhi region”, Current Science, (2007),
92(5): 646-654.
12. Jang, J.–S. R., “ ANFIS: Adaptive-network-based fuzzy inference system”, IEEE Transactions on Systems, Man, and
Cybernetics, (1993), 23 (3): 665-685.
13. Habibagahi G., “Post construction settlement of rockfill dams analyzed via adaptive network based fuzzy inference
system”, Journal of Computers and Geotechnics, (2002), 29: 211-233.
14. Shahin M.A., Maier H.R., and Jaksa M.B., “Settlement prediction of shallow foundation on granular soils using Bspline neurofuzzy models”, Journal of Computers and Geotechnics, (2003), 29: 211-233.
15. Chua, C.G. and Goh. A.T.C., “A hybrid Bayesian back-propagation neural network approach to multivariate
modeling”, International Journal of Numerical and Analytical Methods in Geomechanics, John Wiley & Son, (2003),
27: 651-667.
16. Rafiq, M.Y., Bugmann, G. and Easterbrook, D.J., “Neural network design for engineering applications”, Computer
Structure, (2001), 79: 1541-1552.
17. Kayadelen, C., “Estimation of effective stress parameter of unsaturated soils by using artificial neural networks”,
International Journal of Numerical and Analytical Methods in Geomechanics, John Wiley & Son, (2008), 32(9): 10871106.
18. Gunaydım,O., “ Estimation of soil compaction parameters by using statistical analyses and artificial neural networks”,
Environmental Geology, (2009), 57: 203-215.
Authors
Naresh Nischol Harry, Assistant Professor, Department of Civil Engineering, Sam
Higginbottom University of Agriculture, Science and Technology, Prayagraj, Uttar
Pradesh, India.
Yeetendra Kumar Bind, Assistant Professor, Department of Civil Engineering,
Sam Higginbottom University of Agriculture, Science and Technology, Prayagraj,
Uttar Pradesh, India.
.