ESTIMATING THE COMPRESSIVE STRENGTH OF PORTLAND CEMENT USING
ARTIFICIAL NEURAL NETWORK AND FUZZY LOGIC
A Thesis
Presented to the faculty of the Department of Mechanical Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Mechanical Engineering
by
Henok Hunduma
SPRING
2013
©2013
Henok Hunduma
ALL RIGHTS RESERVED
ii
ESTIMATING THE COMPRESSIVE STRENGTH OF PORTLAND CEMENT USING
ARTIFICIAL NEURAL NETWORK AND FUZZY LOGIC
A Thesis
by
Henok Hunduma
Approved by:
, Committee Chair
Akihiko Kumagai
, Second Reader
Ilhan Tuzcu
__________________________
Date
iii
Student: Henok Hunduma
I certify that this student has met the requirements for format contained in the University
format manual, and that this and thesis is suitable for shelving in the Library and credit is
to be awarded for the thesis.
_____________________________, Graduate Coordinator
Akihiko Kumagai
Department of Mechanical Engineering
iv
____________________
Date
Abstract of
of
ESTIMATING THE COMPRESSIVE STRENGTH OF PORTLAND CEMENT USING
ARTIFICIAL NEURAL NETWORK AND FUZZY LOGIC
by
Henok Hunduma
The purpose of this thesis is to develop Artificial Intelligence Models to predict
the 28-days compressive strength of Portland cement (CCS). Two models, Artificial
Neural Network and Fuzzy Logic were created using 4 input parameters of Portland
cement that comprise both the physical and chemical characteristics. C3S, C2S, Alkali,
and Cement fineness, were used as input variables to predict one outcome of compressive
strength. Early strength prediction in the production process instead of waiting 28 days
for the test to be completed could significantly improve the quality of the cement and
reduce the cost associated with the waiting period.
Data collected from literature was applied to predict the compressive strength of
Portland cement. A rectangular mold of cement and water was created and kept in a
temperature of 20℃ with 90% relative humidity for 24 hours. The cured sample was then
stored in a water bath for 27 days and 6 identical bars were tested. The original data had
v
twenty input parameters of cement with one output of compressive strength. The four
most significant input parameters were selected for this particular revision. Out of the 150
generated points 100 were used to train the models while 50 data points were applied in
the testing of the system.
The average percentage errors achieved were 4.2% and 5.8 % for the fuzzy logic
model and ANN model respectively. The results indicated that Artificial Intelligence (AI)
could be a useful tool for the prediction of cement strength, and through the application
of fuzzy logic algorithms, a more user friendly and more explicit model than the ANN
could be produced within successful low error margins.
_____________________________, Committee Chair
Akihiko Kumagai
_____________________________
Date
vi
Acknowledgements
I would like to thank all of my prodigious professors at CSUS that helped me
come this far with my education. It has been an awesome aspiration and unlimited
learning experience to be a part of the Department of Mechanical Engineering at CSUS. I
personally would like to thank Dr. Akihiko Kumagai, the graduate coordinator for his
constructive assistance in organizing and consulting with my thesis. My special thanks
and gratitude also goes out to my family particularly my mother, brother and sister who
had helped me significantly throughout my life to reach my ultimate goals.
vii
TABLE OF CONTENTS
Page
Acknowledgements ........................................................................................................... vii
List of Figures ..................................................................................................................... x
List Of Tables ................................................................................................................... xii
1.
INTRODUCTION ....................................................................................................... 1
1.1. Compressive Strength .............................................................................................. 2
1.2. Tricalcium Silicate (C3S) ......................................................................................... 3
1.3. Dicalcium Silicate (C2S).......................................................................................... 5
1.5. Cement Fineness ...................................................................................................... 9
1.6. Surface Views ........................................................................................................ 10
2.
3.
ARTIFICIAL INTELLIGENCE ............................................................................... 16
2.1.
Fuzzy Logic Model Construction ....................................................................... 16
2.2.
Membership Functions ....................................................................................... 23
2.3.
FIS Editor ........................................................................................................... 27
2.4.
Rule Viewer........................................................................................................ 28
2.5.
Results for Fuzzy Logic Model .......................................................................... 29
MODEL CONSTRUCTION OF ANN ..................................................................... 35
3.1.
Artificial Neuron Network ................................................................................. 35
viii
4.
3.2.
Training of ANN Model ..................................................................................... 37
3.3.
Artificial Neural Network Results ..................................................................... 40
CONCLUSIONS ....................................................................................................... 44
APPENDIX A: Training Data Used in Modeling............................................................. 45
APPENDIX B: Testing Data Used for Modeling ............................................................. 48
APPENDIX C: MatLab Structure Syntax......................................................................... 50
REFERENCES ................................................................................................................. 53
ix
List of Figures
Figures
Page
1. Effects of C3S on CCS .................................................................................................... 4
2. Effects of C2S on CCS .................................................................................................... 6
3. Effects of Alkali on CCS ................................................................................................ 8
4. Effects of Cement Fineness on CCS ............................................................................. 10
5. Effects of C3S and C2S on CCS .................................................................................... 11
6. Effects of C3S and Alkali on CCS ................................................................................ 12
7. Effects of C3S and Cement Fineness on CCS ............................................................... 13
8. Effects of Alkali and C2S on CCS ................................................................................ 13
9. Effects of C2S and Cement Fineness on CCS ............................................................... 14
10. Effects of Alkali and Cement Fineness on CCS ......................................................... 15
11. Graphical Representation of Input - Output System ................................................... 17
12. Training Data Sets....................................................................................................... 18
13. Training and Testing Data .......................................................................................... 19
14. FIS Model Structure .................................................................................................... 20
15. Membership Function for C3S .................................................................................... 23
16. Membership Functions of C2S .................................................................................... 24
17. Membership Function of Alkali .................................................................................. 25
18. Membership Function of Cement Fineness ................................................................ 26
19. FIS Editor .................................................................................................................... 27
20. Rule Viewer ................................................................................................................ 28
x
21. Training FIS against Testing Data .............................................................................. 29
22. Predicted Value against Actual Value ........................................................................ 30
23. Results of Membership Function ................................................................................ 31
24. Error Signals ............................................................................................................... 32
25. Feed Forward Networks .............................................................................................. 35
26. Neural Network Training ............................................................................................ 38
27. Actual and Predicted Values for CCS ......................................................................... 40
28. Training and Testing Error.......................................................................................... 41
xi
List Of Tables
Tables
Page
1. Actual and Predicted Data and Error of Membership Function ................................. 35
2. Actual and Predicted Data and Error of ANN ............................................................. 44
xii
1
1. INTRODUCTION
Portland cement has been widely used for more than eighteen decades and the
basics of the production process remained unchanged. The availability, relative cost and
minimal labor requirements makes it the most desired concrete around the world matched
with other construction techniques. The characteristic strength of cement is defined as the
compressive strength of a sample that has been aged for 28 days. Portland cement
chemical and physical parameters such as Tricalcium Silicate, Dicalcium Silicate, Alkali,
Cement fineness and particle size distribution are features all effective in producing a
single cement compressive strength (CCS).
Prediction of concrete strength has been an active area of research with several
attempts and analysis implemented to obtain a suitable mathematical model that is
capable of predicting strength of cement at various ages with suitable accuracy. Earlier
prediction studies included Regression Analysis and Extrapolation method. In this study
the techniques of Artificial Intelligence had been investigated in order to improve the
precision of the prediction by using the tools in the MatLab environment of Artificial
Intelligence Systems.
This first chapter defines cement compressive strength, and the four input
variables used for the prediction methods and their roles in the production of cement
associated with the output (compressive strength).
2
1.1. Compressive Strength
One of the most important physical characteristic of Portland cement is its
compressive strength. Tensile and flexural strength values are measured but are not as
reliable as those of compressive strength measurements. Compressive strength test is
carried out in a lab prior for use. Strength test are not done on neat cement paste because
of difficulties of excessive shrinkage and subsequent cracking of neat cement. Strength of
cement is found in specific proportion around cement mortar and the samples have to be
specially prepared for this reason. Testing of samples is carried out at the end of 3, 7 and
28 days of the production process.
3
1.2. Tricalcium Silicate (C3S)
This is the most abundant chemical in Portland cement, and mostly responsible
for strength by forming C-S-H gel upon hydration. Higher amounts of C3S would
produce higher heat of hydration that accounts for increase on cement compressive
strength. The effects of C3S on cement compressive strength is shown in Figure 1. The
illustration shows that compressive strength of Portland cement increases meaningfully as
the percentage amount of C3S increases.
4
Figure 1. Effects of C3S on CCS
5
1.3. Dicalcium Silicate (C2S)
Dicalcium Silicate is an essential ingredient in Portland cement that is responsible
for the development of late compressive strength beyond one week. C2S hardens quickly
and small percentage amounts of C2S results in high early strength but also high heat
generation as the concrete sets. Figure: 2 shows the effects of C2S on compressive strength.
It is observed that at very low percentage amount of Dicalcium Silicate (less than 5%),
CCS increases exceedingly. However, between 5%-10% of an amount of C2S, we can
observe the strength to fluctuate until it reaches the highest level of compressive strength
above 10% remaining at a constant level.
6
Figure 2. Effects of C2S on CCS
1.4. Alkali (Na2O)
The alkali content of cement is reflected in the amounts of potassium oxide and
sodium oxide. Large amounts can cause certain difficulties in regulating set times of
cement. Low alkali cements, when used with calcium chloride in concrete can cause
7
discoloration in trowelled flatwork surfaces. Addition of alkalis increases the rate of
hydration at early ages increasing early strength and reduction in ultimate strength.
Figure: 3 shows the effects of Alkali on CCS. It is clearly visible on the diagram that
compressive strength of Portland cement increases at very low levels of Alkali and
remains at a constant low level at Alkali contents of .95% and above.
8
Figure 3. Effects of Alkali on CCS
9
1.5. Cement Fineness
Greater cement fineness increases surface available for hydration, causing greater
early strength and more rapid generation of heat. Coarser cement will result in higher
ultimate strengths and lower early strength gain. Blaine air permeability test is used for
measuring cement fineness based on the fact that the rate at which air can pass through a
porous bed of particles under a given pressure gradient is a function of the surface area of
the powder. The measured value (Blaine fineness) has an average range from 3000 -5000
cm2/g. Figure: 4 shows that the compressive strength of Portland cement increases as the
surface area of the cement powder is increasing.
10
Figure 4. Effects of Cement Fineness on CCS
1.6. Surface Views
The overall effects of paired input parameters against the one output will be
shown on the next surface plots, Figure 5- Figure 10.
11
Figure 5. Effects of C3S and C2S on CCS
12
Figure 6. Effects of C3S and Alkali on CCS
13
Figure 7. Effects of C3S and Cement Fineness on CCS
Figure 8. Effects of Alkali and C2S on CCS
14
Figure 9. Effects of C2S and Cement Fineness on CCS
15
Figure 10. Effects of Alkali and Cement Fineness on CCS
16
2. ARTIFICIAL INTELLIGENCE
Artificial intelligence is the intelligence of machines and the branch of computer
science that aims to create it. John McCarthy, who coined the term in 1955, defines it as
the science and engineering of making intelligent machines (Anderson, 1992). Neural
networks and fuzzy systems represent two distinct methodologies that deal with
uncertainty.
Neural networks approach the modeling representation by using precise inputs
and outputs, which are used to train a generic model which has sufficient degrees of
freedom to formulate a good approximation of the complex relationship between the
inputs and outputs. Neural network and fuzzy logic technologies has unique capabilities
that are useful in information processing and accomplish the same results in different
ways.
2.1. Fuzzy Logic Model Construction
Fuzzy systems consist of an input layer, an output layer, and some additional
layers between them. Fuzzy inference system (FIS) interprets the values in the input
vector and, based on some sets of rules, assigns values to the output vector. ANFIS is
used to construct a set of fuzzy rules with appropriate membership functions to generate a
stimulated input-output pair.
17
The following Figure 10 shows the graphical representation of input-output
system using one example of the input system (C3S) and an outcome of compressive
strength.
Input
C3 S
Output
Fuzzy Engine
CCS
Figure 11. Graphical Representation of Input - Output System
Fuzzy Logic Toolbox in MatLab is used to train the data. Back-propagation and
least square methods were combined in Hybrid learning algorithms. FIS partitioning was
generated using sub clustering on the data prior to training the data. The training data set
is used to train a fuzzy system by adjusting the membership function parameters that best
model the data, and appears in Figure 11 in the center of the plot as a set of circles. The
horizontal axis is marked data set index. This index indicates the row from which that
input data value was obtained.
18
Figure 12. Training Data Sets
19
Figure 13. Training and Testing Data
20
The (4 x 3) FIS model structure created is shown in the next Figure 13. The input
parameters are represented by the four block nodes in the first layer. The three white
nodes connected to the input layer represent the membership functions selected for each
input.
Figure 14. FIS Model Structure
21
The generalized Bell membership functions were used in this research and are
specified by the following three parameters a, b and c:
F(x: a, b, c) =
1
𝑥−𝑐 2𝑏
|
𝑎
1+|
Eqn. 2.1
The parameter ‘a’ determines the width, and ‘c’ adjusts the center of the
corresponding membership function. The parameter ‘b’ controls the slopes at the border
points. A total of 81 rules were created by using the 4 inputs and 3 membership functions
(34). Rules are shown by the blue nodes on Figure 13. The 81 rules format is expressed
by “If” and “Then” format. An example of such rules is,
If in 1mfl AND in 2mfm AND 3mfn AND 4mfp THEN outmfk.
Eqn. 2.2
Where 1mf, 2mf, 3mf and 4mf represents the antecedents of the four input
membership functions used, and outmf is the consequent output membership function.
The constraints are specified by l, m, n, and p and their pattern changes as the rule
number k increases:
(l = 1-3, m = 1-3, n = 1-3, p = 1-3)
Eqn. 2.3
The incoming signals are multiplied by each node, and the product Pk is called the
firing strength of the rule k (k = 1-81):
Pk = Ml1 x Mm2 x Mn3 x Mp4
Eqn. 2.4
Where, Ml1, Mm2, Mn3 and Mp4 are the four input membership functions.
22
Rk is the normalized firing strength which is the ratio of the firing strength of kth
rule to the sum of all rules’ firing strength and is represented as follows:
𝑃𝑘
Rk = ∑81
𝑘=1 𝑃𝑘
Eqn. 2.5
The output of the fourth layer in figure 2.4 is denoted by Qk:
Qk = RkMk
Eqn.2.6
The last node in figure 2.4 represents the output of the inference system. The
results of all the 81 rules generated are superimposed into a single fuzzy set and are
obtained by adding the outputs of all the nodes from the third layer in the diagram.
O = ∑81
𝑘=1 𝑄𝑘
Eqn. 2.7
Defuzzification methods are applied at the end to convert the fuzzy set into a
single number.
23
2.2. Membership Functions
The Bell type membership functions used for the inputs are shown in the
succeeding four diagrams.
Figure 15. Membership Function for C3S
24
Figure 16. Membership Functions of C2S
25
Figure 17. Membership Function of Alkali
26
Figure 18. Membership Function of Cement Fineness
27
2.3. FIS Editor
The FIS Editor used for the Sugeno type fuzzy inference system is shown in the
following figure 18.
Figure 19. FIS Editor
28
2.4. Rule Viewer
The generated rules for the fuzzy logic engine to predict compressive strength are
shown on Figure 20. The first four columns represent the input parameters and the last
column represents the output of cement compressive strength.
Figure 20. Rule Viewer
29
2.5. Results for Fuzzy Logic Model
The predicted cement compressive strength data is tested against the actual
data. Figure 20 exhibits the obtained results, the blue represent the testing data
and the red dot denotes the trained fuzzy inference system results.
Figure 21. Training FIS against Testing Data
30
It could be observed in the next Figure 22 that the model estimation followed the
actual value of the data on most of the points. Only small deviation from the actual values
for compressive strength can be perceived.
70
60
50
40
CCS
(MPa
30
)
Predicted CCS(Mpa)
Actual CCS(Mpa)
20
10
0
1
6
11 16 21 26
31 36 41 46
TEST POINTS
Figure 22. Predicted Value against Actual Value

31
The next plot shown in Figure 23 illustrate the results of the membership
functions.
Figure 23. Results of Membership Function
32
The plot of the error signals is shown in the following Figure 24. The plots
display the root-mean-square error. The plot in blue represents error1, the error for the
training data. The plot in green represents error2, the error for testing data
Figure 24. Error Signals
33
TABLE 1: Actual and Predicted Data and Error of Membership Function
Actual Value (Mpa) Predicted Value (Mpa)
55.6
54.6
51.7
53
47.6
55.1
54
54.3
56.6
51
55.8
52.9
57
54.2
51.8
55.9
54.2
56.4
49.7
53.7
55
58.4
56.5
49.4
53.9
54.1
50.2
53.8
55.7
52.7
55.1
54.1
53.2
53.9
50.7
53.4
52.8
53.4
52
49.6
54.7
54
50.6
53.6
49.8
52.8
55
52.4
55.7
52.8
50.6
50.2
52.8
55.1
52.6
52.5
58
52.7
58.2
53.8
53.14
52.9
58.3
55
47.6
52.7
55.2
54.3
53.4
50.4
Predicted Error (%)
1.6
2.2
12.8
0.6
9.5
4.9
4.7
7
3.8
6.9
5.9
12.1
0.4
6.2
5
1.6
1.2
4.7
1.1
3.9
1.1
5.2
5.2
4.3
4.8
0.5
4
0.08
8.9
7.5
0.3
5.6
8.8
1.5
5
34
52.5
54.5
53.8
54.6
52.2
49.9
52.7
53.7
52.3
52.9
54
49.5
55
52.4
53.1
Average Error
55.4
55.6
54.7
51.7
52.5
55.5
54.2
53.8
51.4
52
51.8
54.2
53.9
50.8
49.3
4.9
2
1.7
5.7
0.6
9.7
2.5
0.3
1.3
1.4
3.7
8.1
1.7
2.7
6.4
4.20%
35
3. MODEL CONSTRUCTION OF ANN
3.1. Artificial Neuron Network
The number of hidden layers and neurons are usually determined via a trial and
error procedure. Different size neurons were tested in the input layer and in all of the
hidden layers. Various learning algorithms and types of training functions were tested.
The feed-forward back-propagation neural network containing an input, hidden and
output layer is shown in Figure 25.
Figure 25. Feed Forward Networks
36
In the feed forward network, the data of input parameters were normalized before
being fed into the layer using the following generalized equation:
.8
Xi = 𝑑𝑚𝑎𝑥− 𝑑𝑚𝑖𝑛 (𝑑𝑖 − 𝑑𝑚𝑖𝑛) + 0.1
Eqn. 3.1
Where Xi is the input value, 𝑑𝑚𝑎𝑥 is the maximum raw data, 𝑑𝑚𝑖𝑛 is the
minimum raw data and 𝑑𝑖 is the ith raw data.
Once the normalized data has been calculated, the input to the jth neuron is
obtained as follows:
Iyj = ∑𝑀
𝑖=1 𝑊𝑥𝑦𝑖𝑗Xi
Eqn. 3.2
Where Iyj is the input to the jth neuron on the hidden layer, 𝑊𝑥𝑦𝑖𝑗 is the adaptive
weight connection and M is the size of neurons in the input layer.
The output on the hidden layer Yj is calculated by using the activation function
(sigmoid function):
1
Yj = 1+𝑒 −𝑆(𝐼𝑦𝑗)
Eqn. 3.3
Where S represents the slope of the sigmoid function.
The outputs from input and hidden layers were added to get the results for the
output layer Iz:
𝑁
Iz = ∑𝑀
𝑖=1 𝑊𝑥𝑧𝑖𝑘𝑋𝑖 + ∑𝑖=1 𝑊𝑦𝑧𝑗𝑘𝑌𝑗
Eqn. 3.4
Where M and N are the number of layer neurons in the input and output layers
respectively. 𝑊𝑥𝑧𝑖𝑘 are weights from the input to the output layers, and 𝑊𝑦𝑧𝑗𝑘 are
weights from the hidden to the output layers.
The actual output is calculated by:
37
Zk = f (Izk)
Eqn. 3.5
The standard form of the training rule on the neuron of output layer is calculated
by:
σzk = f\(Izk)(Tk - Zk)
Eqn. 3.6
Where Tk is the target value of the kth training vector and f\ is the derivative of the
sigmoid function.
3.2. Training of ANN Model
The training procedure was carried out by presenting the network with the set of
data in a patterned format. Each training pattern includes an input set of 4 input
parameters, and a corresponding output set representing the compressive strength. The
structure of the Neural Network training is shown in the following Figure 25.
38
Figure 26. Neural Network Training
39
The network is presented with the variables in the input vector of the first training
pattern followed by computations through the nodes in the hidden layers and prediction
of the fitting output. The error between the predicted output and target value is calculated
and stored. All calculated results will be shown in the next result’s section of Chapter 3.
The increase in iterations resulted in best pattern recognition; however as the training
iterations increased, most other data points were left out. The iteration was reduced and
new network weights and biases were tested and calculated to minimize the error
associated with the testing data.
40
3.3. Artificial Neural Network Results
The results of the actual and predicted values are shown in Figure 27.
70
60
50
CCS(Mpa) 40
Predicted Value
30
Actual Value
20
10
0
1
6
11
16
21
26
31
36
41
46
Test Points
Figure 27. Actual and Predicted Values for CCS
The observation shows only a slight deviation between the prediction and actual
values of compressive strength of Portland cement. The following Figure 28 show the
training and testing error platform in the feed forward network.
41
Figure 28. Training and Testing Error
The blue represents the training data used to adjust the weights in the neural
network. The validation data in green is used to minimize overfitting verifying that any
increase in accuracy of the training data actually yields an increase in accuracy over a
data that has not been shown to the network before. The test data shown in red is used
only for testing the final solution in order to confirm the actual estimating power of the
network.
42
TABLE 2: Actual and Predicted Data and Error of ANN
Actual CCS (Mpa)
52.2
52.4
52.8
52.5
52.8
52.5
56.9
57.5
55.1
55.3
53.6
55.3
53.2
51.9
54.1
56.1
55.8
52.7
53.7
51.2
53.3
54.6
51.4
49.4
55.1
51
55.6
51.7
47.6
54
56.6
55.8
57
51.8
54.2
Predicted CCS (Mpa)
53.4
52.9
57.9
54.9
53.2
52.8
53.6
53.7
54.1
53.2
54.4
51.8
51.2
52.4
53.2
49.6
53.4
52.7
52.8
53
51.6
53
47.3
53.1
51.5
53.4
51.7
51.3
58.7
54.4
46
52.8
53.9
54.6
51.1
Predicted Error (%)
2
0.8
8.8
4.1
0.6
0.5
5.7
6.6
1.7
3.6
1.3
6
3.4
0.8
1.5
11.3
4.1
0
1.5
3.1
2.9
2.7
7.1
6.4
6.2
4.1
6.7
0.6
19.3
0.6
18.4
5.2
5.3
4.8
5.3
43
55.1
51
55.6
51.7
47.6
54
56.6
55.8
57
51.8
54.2
49.7
55
56.5
53.9
50.2
55.7
55.1
53.2
50.7
52.8
52
54.7
50.6
49.8
55
Average Error
51.5
53.4
51.7
51.3
58.7
54.4
46
52.8
53.9
54.6
51.1
53.7
52.4
49.8
52.5
52.9
55.3
53.2
51.4
38.6
52.2
52.1
51.6
52.8
55.2
49.4
6.2
4.1
6.7
0.6
19.3
0.6
18.4
5.2
5.3
4.8
5.3
6.9
4.5
11.6
2.4
4.6
0.6
3.3
3.1
21
1
0.1
5.3
3.8
9.3
9.7
5.8 %
44
4. CONCLUSIONS
Prediction of 28-day compressive strength of Portland cement was performed
using artificial intelligence techniques of ANN and fuzzy logic. Four Portland cement
chemical and physical variables were applied for the estimation process. The two
different artificial intelligence models studied proved that more efficient and rapid
cement production could be accomplished using the proposed intelligence techniques.
The fuzzy model yielded slightly lower error than the ANN model, and the clever rule
creation approach of its explicit nature may grant its use by experts for various prediction
purposes.
As a recommendation for future work the fuzzy logic model generated in this
research can be subjected to analysis for observation of the effects of several other input
parameters that may have direct effect on the 28-day CCS. Such a study would provide
an intelligent methodology and visual inspection tool for potential users in cement plants.
It is also advised that further study could be adapted to monitor and control the
production process and predict the expected life of machines used by using artificial
intelligence.
45
APPENDIX A: Training Data Used in Modeling
C3S (%)
61.2
59.9
58.7
54
62.4
58.5
59.8
54.7
62.1
56.5
64.1
62.5
63.5
64.4
60.7
60.9
62.8
61.4
63.4
61.6
63.1
58.9
64.5
58.8
60
60.7
61.5
59.2
60.7
60
61.7
61.2
59.3
59
61.2
63.5
59.9
C2S (%)
8.7
10.6
9.2
12.6
7.9
10.7
8.8
13.1
9.1
11
7.7
11.4
7.6
8.9
10
12.1
8.5
9.9
8.2
13.8
7.8
10
7.7
11.5
10
12.4
9
12.1
10.6
13.1
10
10.2
13.8
9.6
10
7.6
11
Alkali (%)
1.1
1.1
1
1.1
1
1.1
1.1
1
0.8
1.1
1.1
1.1
1.1
1.1
0.9
1.1
1.1
1.1
0.9
1.1
0.9
1.1
1
1.1
1.1
1
1.1
1.1
0.9
0.9
0.9
1.1
1.1
1.1
1.1
0.9
0.9
Cement Fineness (cm2/g)
3580
3520
3360
3480
3580
3560
3590
3420
3620
3610
3470
3630
3680
3520
3580
3900
3510
3580
3590
3580
3650
3570
3830
3490
3720
3660
3690
3770
3380
3680
4000
3550
3580
3390
3740
3530
3670
CCS (Mpa)
52.2
52.4
52.8
52.5
52.8
52.5
56.9
57.5
55.1
55.3
53.6
55.3
53.2
51.9
54.1
56.1
55.8
52.7
53.7
51.2
53.3
54.6
51.4
49.4
55.1
51
55.6
51.7
47.6
54
56.6
55.8
57
51.8
54.2
49.7
55
46
62.2
60.4
59.6
56.5
63.1
60.6
63
51.7
63.5
58.1
63.5
60
61.7
61.3
57.2
54.7
60.2
60
59.1
64.3
62.9
61
64
58
64
67.1
56.4
57.1
64
59.4
65.1
55.8
62.5
61.7
62.9
60.4
58.7
61.6
60.7
10.2
10.2
11.2
13.3
11.2
10.1
13.2
15.5
9.9
15.1
8.8
10.9
12.5
12.3
12.3
14.2
8.9
10.5
9.5
11.3
10.4
9.4
8.2
14
7.9
8.4
13.1
12.3
8.2
12.7
7.7
15.3
9.3
8.5
7.8
9.5
10.4
9.7
9.9
1
0.9
1
1
1
1
1
0.9
1.1
0.9
1.1
1
0.9
1
1.1
0.9
1
0.9
1
1
0.9
1
0.9
1
0.9
1.1
1
1
1
1
1
0.8
1
0.9
1
0.8
1
0.9
0.8
3800
3620
3650
3750
3640
3700
4060
3540
3570
3990
3450
3330
3850
3620
3770
3760
3540
3660
3540
3770
3160
3740
3430
3640
4050
3560
3540
3650
3650
3930
3590
3770
3630
3680
3530
3720
4100
3650
3770
56.5
53.9
50.2
55.7
55.1
53.2
50.7
52.8
52
54.7
50.6
49.8
55
55.7
50.6
52.8
52.6
58
58.2
53.14
58.3
47.6
55.2
53.4
52.5
54.5
53.8
54.6
52.2
49.9
52.7
53.7
52.3
52.9
54
49.5
55
52.4
53.1
47
64.1
64.8
65.3
61.6
61.11
68.3
51.7
65.6
62.1
60.4
63.2
61.3
64.5
59.7
68.3
67.6
59.5
57.5
64.6
61.3
61.1
60
65.1
63.6
12.5
7.1
8.3
10.4
9.8
7
17.7
7.4
11.3
11.6
10.2
12.2
13.1
10.4
7
5.8
8.5
8.9
9.9
8.1
8.8
9.2
7.6
8.7
1
1
1
0.99
1.1
0.8
0.9
1
0.9
1
1.1
1
1
1.1
0.9
0.9
0.9
0.9
1
0.8
1
1.1
0.9
1.1
3560
3710
3840
3651
4100
3120
4080
3690
3120
3850
3560
4060
3570
3610
3400
4030
3520
3890
4050
3630
3680
3560
3600
3530
53.9
51.9
53.9
50.8
54.5
50.4
55.4
58.4
54.8
51.8
51.3
54.7
54.1
54.5
51.5
52.1
51.7
54.2
53.8
51.5
48.9
53.2
54.7
54.3
48
APPENDIX B: Testing Data Used for Modeling
C3S (%)
61.7
61.3
57.2
54.7
60.2
60
59.1
64.3
62.9
61
64
58
64
67.1
56.4
57.1
64
59.4
65.1
55.8
62.5
61.7
62.9
60.4
58.7
61.6
60.7
64.1
64.8
65.3
61.6
61.11
68.3
51.7
65.6
62.1
60.4
C2S (%)
12.5
12.3
12.3
14.2
8.9
10.5
9.5
11.3
10.4
9.4
8.2
14
7.9
8.4
13.1
12.3
8.2
12.7
7.7
15.3
9.3
8.5
7.8
9.5
10.4
9.7
9.9
12.5
7.1
8.3
10.4
9.8
7
17.7
7.4
11.3
11.6
Alkali (%)
0.9
1
1.1
0.9
1
0.9
1
1
0.9
1
0.9
1
0.9
1.1
1
1
1
1
1
0.8
1
0.9
1
0.8
1
0.9
0.8
1
1
1
0.99
1.1
0.8
0.9
1
0.9
1
Cement Fineness (cm2/g)
3850
3620
3770
3760
3540
3660
3540
3770
3160
3740
3430
3640
4050
3560
3540
3650
3650
3930
3590
3770
3630
3680
3530
3720
4100
3650
3770
3560
3710
3840
3651
4100
3120
4080
3690
3120
3850
CCS (Mpa)
55.6
51.7
47.6
54
56.6
55.8
57
51.8
54.2
49.7
55
56.5
53.9
50.2
55.7
55.1
53.2
50.7
52.8
52
54.7
50.6
49.8
55
55.7
50.6
52.8
52.6
58
58.2
53.14
58.3
47.6
55.2
53.4
52.5
54.5
49
63.2
61.3
64.5
59.7
68.3
67.6
59.5
57.5
64.6
61.3
61.1
60
65.1
10.2
12.2
13.1
10.4
7
5.8
8.5
8.9
9.9
8.1
8.8
9.2
7.6
1.1
1
1
1.1
0.9
0.9
0.9
0.9
1
0.8
1
1.1
0.9
3560
4060
3570
3610
3400
4030
3520
3890
4050
3630
3680
3560
3600
53.8
54.6
52.2
49.9
52.7
53.7
52.3
52.9
54
49.5
55
52.4
53.1
50
APPENDIX C: MatLab Structure Syntax
getfis(a)
Name
Type
= Trained FIS
= sugeno
NumInputs = 4
InLabels =
C3S
C2S
Alkali
Cement Fineness
NumOutputs = 1
OutLabels =
CCS
NumRules = 81
AndMethod = prod
OrMethod = probor
ImpMethod = prod
AggMethod = sum
DefuzzMethod = wtaver
ans =
Trained FIS
51
>> showfis(a)
1. Name
Trained FIS
2. Type
sugeno
3. Inputs/Outputs [4 1]
4. NumInputMFs
[3 3 3 3]
5. NumOutputMFs
81
6. NumRules
81
7. AndMethod
prod
8. OrMethod
probor
9. ImpMethod
prod
10. AggMethod
sum
11. DefuzzMethod
12. InLabels
wtaver
C 3S
13.
C2 S
14.
Alkali
15.
Cement Fineness
16. OutLabels
CCS
17. InRange
[51.7 68.3]
18.
[5.8 17.7]
19.
[0.8 1.1]
20.
[3120 4100]
21. OutRange
[47.6 58.4]
52
22. InMFLabels
23.
in1mf1
in1mf2
24. OutMFLabels
25.
out1mf2
26. InMFTypes
27.
out1mf1
gbellmf
gbellmf
28. OutMFTypes
29.
constant
30. InMFParams
31.
constant
[4.15 2.5 51.7 0]
[245 2.5 4100 0]
name: 'Trained FIS'
type: 'sugeno'
and Method: 'prod'
orMethod: 'probor'
defuzzMethod: 'wtaver'
impMethod: 'prod'
aggMethod: 'sum'
input: [1x4 struct]
output: [1x1 struct]
rule: [1x81 struct]
53
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