TH 3582
TH 3582
TH 3582
MASTER OF TECHNOLOGY
IN
CIVIL ENGINEERING
(TRANSPORTATION ENGINEERING)
BY
MEENAKSHI SINGH
(Roll No. 211071)
Dr. S. N. SACHDEVA
&
Kurukshetra
•^^^*^«K'e^
National Institute of Technology
Kurukshetra
CERTIFICATE
I hereby certify that the work presented in this dissertation entitled PREDICTION OF
STRENGTH AND ABRASION RESISTANCE OF CONCRETE USING FUZZY
LOGIC APPROACH which is being submitted to National Institute of Technology,
Kurukshetra in partial fulfilment of the requirements for the award of the Degree of
Master of Technology in Civil Engineering (Transportation Engineering), is an
authentic record of my own work carried out during the period from Dec. 2012 to June
2013 under the supervision and guidance of Dr. S. N. Sachdeva Professor, and Dr.
Paratibha Aggarwal Associate Professor, Civil Engineering Department, National
Institute of Technology, Kurukshetra.
The matter presented in this dissertation has not been submitted by me for the award of
any other degree of this Institute or any other Institute.
This is to certify that the above statement made by the candidate is correct to the best of
my knowledge.
9<= ,^^V^
Dated: ^l ^1 -lo)] (Dr. S. N. Sachdeva) (Dr. Pratibha Aggarwal)
Professor Professor
Civil Engineering Deptt. Civil Engineering Deptt.
NIT, Kurukshetra NIT, Kurukshetra
ACKNOWLEDGEMENTS
I am thankful to all staff members, my batch mates and to every individual who
assisted me in completing the dissertation work.
Last, but not the least, I wish to express my gratitude to my family members for
motivating me to take up this M Tech course.
(MEENAKSHI SINGH)
Roll No. 211071
TABLE OF CONTENTS
Page
DISSERTATION TOPIC i
CERTIFICATE ii
ACKNOWLEDGEMENT iii
CHAPTER
1. INTRODUCTION 1-7
1.4 LIMITATIONS 6
3. METHODOLOGY 20-31
3.1 INTRODUCTION 21
OUTPUTS 28
3.8.5 DEFUZZIFICATION 29
4.4 DATABASE 34
4.4.2 COEFFICIENTS 36
V 1 <.
4.6.1 COMPRESSIVE STRENGTH MODELS 44
5. CONCLUSIONS 60-62
5.1 CONCLUSIONS 61
REFERENCES 63-66
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LIST OF TABLES
4.1 The input and output parameters used in the fuzzy logic models 37
for compressive strength
4.2 The input and output parameters used in the ftizzy logic models 40
for depth of wear
4.3 Ranges ofparameters used for analysis 42
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LIST OF FIGURES
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4.15 Comparison between compressive strength predicted by model 52
FL2 and actual values
4.16 Comparison between compressive strength predicted by model 53
FL3 and actual values
4.17 Comparison between compressive strength predicted by model 53
FLl,FL2andFL3
4.18 Comparison between depth of wear predicted by model FL4 and 54
actual values
4.19 Comparison between depth of wear predicted by model FL5 and 55
actual values
4.20 Comparison between depth of wear predicted by model FL6 and 55
actual values
4.21 Comparison between depth of wear predicted by model FL4, 56
FL5 and FL6
IX I X
INTRODUCTION
CHAPTER-1
INTRODUCTION
\-
T"T<
INTRODUCTION
CHAPTER-1
INTRODUCTION
Concrete is the second largest material consumed by human beings after food and water
as per WHO. Concrete is a product obtained artificially by hardening of the mixture of
cement, sand, gravel and water in predetermined proportions. When these ingredients
are mixed, they form a plastic mass which can be poured in suitable moulds, called
forms, and sets into hard solid mass. The hardening is caused by chemical action
between water and the cement due to which concrete gains strength with age. The
chemical reaction of cement and water, in the mix, is relatively slow and requires time
and favourable temperature for its completion. This time is known as setting time. The
strength, durability and other characteristics of concrete depend upon the properties of
its ingredients, proportion of the mix, and the method of compaction and other controls
during placing, compaction and curing.
Admixtures are almost always used in modem practice and thus become an essential
component of modem concrete. Admixtures are defined as materials other than
aggregate (fine and coarse), water, fibre and cement, which are added into concrete
batch immediately before or during mixing. The widespread use of admixture is mainly
due to the many benefits made possible by their application. For instance, chemical
admixtures can modify the setting and hardening characteristic of cement paste by
influencing the rate of cement hydration. Water-reducing admixture can plasticize fi-esh
concrete mixtures by reducing surface tension of water, air-entraining admixtures can
improve the durability of concrete, and mineral admixtures such as pozzolans can
reduce thermal cracking.
Concrete being most widely used construction material is used in many different
structures such as dam, pavement, building frame or bridge. Its worldwide production
exceeds that of steel by a factor of 10 in tonnage and by more than a factor of 30 in
volume. The present consumption of concrete is over 10 billion tons a year, that is, each
person on earth consumes more than 1.7 ton of concrete per year. It is more than 10
times the consumption by weight of steel. Concrete possess a high compressive strength
and is usually more economical than steel and is non-corrosive which can be made with
locally available materials. Hence concrete is used widely in all present-day
constructions.
Cement concrete pavements are considered to be the highest pavement types which
withstand heavy traffic even under adverse subgrade and climatic conditions. The
cement concrete pavement maintains a very high recognition among the engineers and
road users alike due to excellent riding surface and pleasing appearance. Further, the
engineers have inherent confidence in the cement concrete materials for its use in any
construction project. Concrete can support heavy loads, such as truck traffic, with less
deformation than asphalt. Although, initial cost of concrete is more, its maintenance
cost is generally lower and negligible. In addition, concrete usually has a useful life of
twice that of asphalt. Concrete commonly serves 20-30 years without needing any
major repair, while asphalt typically lasts only 8 to 12 years, before resurfacing or
significant repair is required.
yT^TTX
INTRODUCTION
The concept of fiizzy logic was conceived by Lotfi Zadeh, a professor at the University
of California in Berkley. He presented it not as a control methodology, but as a way of
processing data by allowing an element to have partial membership of a set. He
explained that human reasoning process does not require precise, numerical information
input, and yet is capable of performing complex tasks such as natural language
understanding and difficult decision-making. Fuzzy logic provides a simple way to
arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy or
missing input information. Fuzzy logic's approach helps how a person would make
decision with imprecise and incomplete information. Fuzzy logic approach has the
following advantages:
1. In practice, most of the things encountered in life are imprecise. Fuzzy logic is
inherently robust since it does not require precise, noise-firee inputs and
degrades gradually when system components fail like if a feedback sensor quits
or is destroyed.
2. Fuzzy logic is flexible. With any given system, it is easy to manage and add
more functionality on top of it, without starting again fi-om scratch. Since the
3. Fuzzy logic is not limited to a few feedback inputs and one or two outputs. Any
sensor data that provides some indication of a system's actions and reactions is
sufficient. This allows the sensor to be inexpensive and imprecise thus keeping
the overall system cost and complexity low.
4. Because of the rule-based operations, system can be easily designed for any
reasonable number of inputs and outputs. Defining the rule base becomes
complex if number of inputs and outputs becomes large. It would be better to
break the system into smaller parts and use several smaller fiizzy logic modules
distributed on the system, each with more limited responsibilities.
5. Fuzzy logic can model non-linear functions of arbitrary complexity. One can
create a fiizzy system to match any set of input-output data. Fuzzy logic can
model or control non-linear systems that would be difficult or impossible to
model mathematically. This opens doors for control systems that would
normally be deemed unfeasible for automation. This process is made
particularly easy by adaptive techniques like Adaptive Neuro-Fuzzy Inference
system (ANFIS).
6. It can store the knowledge database using the knowledge of experts. In direct
contrasts to neural networks, which requires training data and generate opaque,
impenetrable models, fiizzy logic lets one rely on the experience of people who
already understand the system.
1.4 LIMITATIONS
• Fuzzy logic cannot solve problems that have no known solution; it requires the
knowledge of an expert. It is particularly useful when there is an expert who can
solve the problem, but there is no mathematical model to follow. If no one
knows who to solve the problem, then it follows that no rules can be devised
and fuzzy logic principles cannot be applied.
• Fuzzy logic algorithms do not have the ability to learn membership functions or
rules during or after problem solving.
The research work aims to predict the compressive strength and abrasion depth of wear
on concrete by using fuzzy logic approach. Humans have a remarkable capability to
reason and make decisions in an environment of uncertainty, imprecision,
incompleteness of information, and partiality of knowledge, truth and class
membership. The principal objective of fuzzy logic is formalization/mechanization of
this capability.
In the present study a fuzzy logic prediction model for compressive strength and depth
of wear on concrete is developed. Experimental data were gathered from the sources
available in literature. The model has five input parameters such as cement, fine
aggregate, coarse aggregate, water cement ratio and superplastisizer. The main
objectives of the research work are:
a) To develop various fiizzy logic models for predicting compressive strength and
depth of wear.
r^ ^7
INTRODUCTION
b) To analyse results obtained from various frizzy logic models based on the
experimental data.
The study had been taken up to predict the strength and abrasion resistance of concrete
using frizzy logic model. Strength and abrasion resistance can be obtained according to
fuzzy logic model test results without any experimental study. Fuzzy logic system has
strong potential for predicting compressive strength and depth of wear. Successful
prediction by the model indicates that frizzy logic could be a usefril modelling tool for
engineers and research scientists in the area of cement and concrete.
? 1 !
LITERATURE REVIEW
CHAPTER-2
LITERATURE REVIEW
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LITERATURE REVIEW
CHAPTER-2
LITERATURE REVIEW
Several applications of Artificial Neural Networks and Fuzzy Logic to civil engineering
problems have been reported. But modelling on the basis of fuzzy logic for
compressive strength can be found in some of the literatures, but depth of wear
(abrasion resistance) has not yet been reported in the literature.
Garzon-Roca et al. (2013), used Artificial Neural Networks and Fuzzy Logic to
determine the compressive strength of a masonry structure composed of clay bricks and
cement mortar, by using only two parameters: the compressive strength of the mortar
and that of the bricks with a data of 96 laboratory tests. These mathematical techniques
were an alternative to the complex analytical formulas dependent on a large number of
parameters and to empirical formulas, which, even though simple, often gave
unrealistic values. The results of applying the Artificial Neural Network proved to be
highly satisfactory, with mean values of the real/estimated compressive strength ratio
close to 1 and relatively low standard deviation. It was also possible to obtainfi-omthis
model an expression that allowed the compressive strength of a masonry structure to be
calculated directly, without the need to program an Artificial Neural Network. The
application of Fuzzy Logic was also shown to give good results, with a mean value of
the real/estimated compressive strength ratio of 1.09 and standard deviation at 0.3. This
technique also showed that in general the compressive strength of a masonry structure
increases when the compressive strength of the bricks and mortar is raised and normally
lies somewhere between these two values. The results obtained were compared to the
calculation methods proposed by other authors and comparisons showed that the
different proposals did not closely agree with the experimental results, with an average
discrepancy of around 20% with the real value, which demonstrates the suitability of
applying tools such as Neural Networks and Fuzzy Logic, which has been shown to
achieve good agreement with experimental results.
LITERATURE REVIEW
Dantas et al. (2013), developed Artificial Neural Networks (ANNs) models for
predicting the compressive strength, at the age of 3, 7, 28 and 91 days, of concretes
containing Construction and Demolition Waste (CDW). The experimental results used
to construct the models were gathered from literature. A total of 1178 data was used for
modeling ANN, 77.76% in the training phase, and 22.24% in the testing phase. To
construct the model, 17 input parameters were used to achieve one output parameter,
referred to as the compressive strength of concrete containing CDW. ANN analysis
indicated a good correlation between the input parameters and the response variable,
which were 3, 7, 28 and 91 days compressive strength of concrete containing CDW.
The statistical parameters R^ was 0.928 and 0.971, for ANN training and testing,
respectively, and the frequency of results with errors less than 7.5% and greater than
20%, for ANN testing, demonstrate that the output values were very close to the
experimental values. The results obtained in both, the fraining and testing phases
strongly showed the potential use of ANN to predict 3, 7, 28 and 91 days compressive
sfrength of concretes containing CDW.
Duan et al. (2013), showed the possible applicability of artificial neural networks
(ANNs) to predict the compressive strength of recycled aggregate concrete. ANN
model was constructed, trained and tested using 146 available sets of data obtained
from 16 different published literature sources. The ANN model developed used 14
input parameters that included: the mass of water, cement, sand, natural coarse
aggregate, recycled coarse aggregate used in the mix designs, water to cement ratio of
concrete, fineness modulus of sand, water absorption of the aggregates, saturated
surface-dried (SSD) density, maximum size, and impurity content of recycled coarse
aggregate, the replacement ratio of recycled coarse aggregate by volume, and the
coefficient of different concrete specimen. The ANN model, run in a Matlab platform,
was used to predict the compressive strength of the recycled aggregate concrete. The
artificial neural networks method was assessed to see whether it can be used to predict
the compressive strength of RAC. It could be seen that:
(1) The maximum size of aggregates, water absorption values and SSD specific density
could generally reflect the properties of RA.
y 10
LITERATURE REVIEW
(2) Artificial neural networks had fairly high accuracy on predicting the strength of
RAC.
ii. In all mixtures, the specimens with the Si02/Al203 ratio equal to 2.99 had the
highest strength. On the other hand the highest strength was achieved equals
58.9 MPa for the mixture of fine fly ash to fine rice husk bark ash of 70:30.
iii. Fuzzy logic could be an alternative approach for the evaluation of the effect of
seeded mixture of FA and RHBA on compressive strength values of
geopolymer specimens.
11
LITERATURE REVIEW
iv. Considering R^ values showed that FL model were capable to predict suitable
results for compressive strength values of geopolymer specimens.
Atici et al. (2011), applied multiple regression analysis and an artificial neural network
in estimating the compressive strength of concrete that contains various amounts of
blast furnace slag and fly ash, based on the properties of the additives (blast furnace
slag and fly ash in this case) and values obtained by non-destructive testing rebound
number and ultrasonic pulse velocity for 28 different concrete mixtures (Mcontroi and
M1-M27) at different curing times (3, 7, 28, 90, and 180 days). The results obtained
using the two methods were then compared and discussed. The results reveal that
although multiple regression analysis was more accurate than artificial neural network
in predicting the compressive strength using values obtained from non-destructive
testing, the artificial neural network models performed better than multiple regression
analysis models. The application of an artificial neural network to the prediction of the
compressive strength in admixture concrete of various curing times shows great
potential in terms of inverse problems, and it was suitable for calculating nonlinear
fiinctional relationships, for which classical methods could not be applied.
12
LITERATURE REVIEW
Sobhani et al. (2010), utilized various nonlinear regression, artificial neural network,
and ANFIS models to predict the 28-days compressive strength of no-slump concrete
(28-CSNSC). Totally 96 no-slump concrete (NSC) mixtures were made, cured and
tested to obtain the 28-CSNSC records. Of these data, 79 data were randomly selected
as training sets and the remaining 17 data were used for testing of models.
i. The neural network and ANFIS models could predict the 28- CSNSC with
satisfactory performance owing to their distributed and parallel computing
nature.
iii. All of the proposed ANFIS models exhibited acceptable performance. Of these
models, ANM4 with Gaussian membership fiinctions in its layers presented the
best prediction performance.
iv. The regression was familiar method in modelling of engineering systems for its
closed-form representation. Unfortunately, in the case of inadequate data, the
regression models failed to be reliable and hence, advanced models like neural
network and ANFIS models were preferred. Nevertheless, the regression model
1-2, developed based on the partial second order polynomial, presented a
relatively good performance.
V. In general, the regression model 1-2 was proposed for preliminary mix design
of no-slump concrete and clearly in the case of higher accuracy requirements,
e.g. in the mix design optimization, the neural network and ANFIS models were
recommended.
Saridemir et al. (2009), used artificial neural networks and fiizzy logic systems for the
prediction of 3, 7, 28, 60 and 90 days compressive strength values of mortars
containing metakaolin. In the model developed in artificial neural networks system, a
n r-:
LITERATURE REVIEW
Tanyildizi et al. (2009), devised a fuzzy logic prediction model for compressive and
splitting tensile strength of lightweight concrete made with scoria aggregate and fly ash
after exposed to high temperature. Cement dosages (400 and 500 kg/m^) were used in
the study. The mixes incorporating 0%, 10%, 20% and 30% fly ash were prepared.
After being heated to temperatures of 200, 400 and 800 °C, respectively, the
compressive and splitting tensile strength of lightweight concrete was tested. The
obtained results with fuzzy logic were compared with the experimental methods and
found remarkably close to each other. The compressive and splitting tensile strength
using fuzzy logic was estimated with a small error (7.88% and 6.48%). For the
performance evaluation, multiple linear regression models were applied. The R^ values,
calculated by the difference between calculated and measured values, were found (0.82
and 0.57). Although results obtained by multiple linear regression analyses were not
successfiil, the results obtained by fuzzy logic model could be said to be better than
regression model. Thus, the study suggested an alternative approach of compressive
1-4 ' \
LITERATURE REVIEW
Saridemir et al. (2009), developed artificial neural networks and fiizzy logic models
for prediction of long-term effects of ground granulated blast furnace slag on
compressive strength of concrete under wet curing conditions. For purpose of
constructing these models, 44 different mixes with 284 experimental data were
gathered fi-om the literature. The data used in the artificial neural networks and fuzzy
logic models were arranged in a format of five input parameters that cover the age of
specimen, quantity of portland cement, ground granulated blast furnace slag, water and
aggregate, and output parameter as 3, 7, 14, 28, 63, 90, 119, 180 and 365-day
compressive strength. In the models of the training and testing results has shown that
artificial neural networks and fuzzy logic systems has strong potential for prediction of
long-term effects of ground granulated blast furnace slag on compressive strength of
concrete.
Ozcan et al. (2009), developed artificial neural network (ANN) and fuzzy logic (FL)
model to predict the compressive strength of silica fume concrete. A data set of a
laboratory work, in which a total of 48 concretes were produced, was utilized in the
ANNs and FL model. The concrete mixture parameters were four different water-
cement ratios, three different cement dosages and three partial silica fume replacement
ratios. Compressive strength of moist cured specimens was measured at five different
ages. The obtained results with the experimental methods were compared with ANN
and FL results. The results showed that ANN and FL could be alternative approaches
for the predicting of compressive strength of silica fume concrete. The following
conclusions were drawn from investigation:
15 ^-.
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LITERATURE REVIEW
ii. ANN and FL could be an alternative approach for the evaluation of the effect of
cementitious material on the compressive strength either in long or short term.
There is an optimum replacement ratio of silica fume existed, this value could
be predicted using ANN and FL models.
iii. ANN and FL were efficient for predicting the compressive strength of silica
fume concrete. Comparison between ANN and FL in terms of R^ showed that
ANN provided better results than the FL results.
Saridemir et aL (2009), developed the models in artificial neural networks (ANN) for
predicting compressive strength of concretes containing metakaolin and silica fiime at
the age of 1, 3, 7, 28, 56, 90 and 180 days. For purpose of building these models,
training and testing using the available experimental results for 195 specimens
produced with 33 different mixture proportions were gathered from the technical
literature. The data used in the multilayer feed forward neural networks models were
arranged in a format of eight input parameters that cover the age of specimen, cement,
metakaolin (MK), silica fume (SF), water, sand, aggregate and superplasticizer.
According to these input parameters, in the multilayer feed forward neural networks
models were predicted the compressive strength values of concretes containing
metakaolin and silica fume. The training and testing results in the neural network
models showed that neural networks has strong potential for predicting 1, 3, 7, 28, 56,
90 and 180 days compressive strength values of concretes containing metakaolin and
silica fume.
16 i ^-.
LnER.\TURE RE\aEW
any experimental tests using the artificial neural network and fuzzy logic models. It has
been observed that training and testing results were similar to the experimental results.
• As the amount of waste rubber used in mortar replacing sand increased, the hardened
flexural strength values decreased. Flexural strength values decreased in coarse rubber
mortars compared to the fine rubber ones.
• As a result of the increase in the amount of waste rubber used replacing sand, the
compressive strength of waste rubber mortar decreased excessively. These values
decrease in recycled coarse rubber mortars compared to the recycled fine rubber ones.
• In order to predict the flexural strength and compressive strength values of the waste
rubber mortars without attempting any experiments, models were constructed by ANN
and FL method. The models were trained with input and output data. Using only the
input data in trained models, flexural strength and compressive strength values of
hardened concrete were found. The values were very closer to the experimental results
obtainedfi-omboth methods.
• As a result, it was shown that, flexural strength and compressive strength values of the
waste rubber mortars could be predicted in ANN and FL models in a quite short period
of time with small error rates.
Topcu et al. (2008), studied the strength development of different mineral admixtures,
which were preparedfi-omtrasses, zeolite (clinoptilolite), fly ash and ground granulated
blast furnace slag was investigated. According to the experimental results, the early age
compressive strength of blended cements reduced with increasing replacement ratios.
However, when compared with the reference CEM 142.5 cement, at the ages of 28 and
180 days, zeolite (clinoptilolite), blast furnace slag and fly ash replacements increased
the compressive strengths depending on the pozzolanic reaction between Ca(0H)2 and
mineral additive.
When compressive strength results were considered, the optimum replacement ratio
was determined to be 20 and 30% for all pozzolan blended cement mixes. Furthermore,
to predict the strength development of differervt blended cement mortars ANN and FL
system models were constructed with the experimental results.
V~r-
17
LITERATURE REVIEW
As a result, it was shown that compressive strength values of the different blended
cement mortars could be predicted in ANN and FL models in a relatively short period
of time with tiny error rates. A comparison based on strength development and cost per
unit strength indicated that the addition of pozzolans to cement was the most
economical and environmental effective production method in the cement industry.
Akkurt et al. (2004), created a flizzy logic prediction model for the 28-day
compressive strength of cement mortar under standard curing conditions. Data collected
from a cement plant were used in the model construction and testing. The input
variables of alkali, Blaine, SO3, and C3S and the output variable of 28-day cement
strength were fuzzified by the use of artificial neural networks (ANNs), and triangular
membership fimctions were employed for the fuzzy subsets. The Mamdani fixzzy rules
relating the input variables to the output variable were created by the ANN model and
were laid out in the If-Then format. Product (prod) inference operator and the centre of
gravity (COG; centroid) defiizzification methods were employed. The prediction of 50
sets of the 28-day cement strength data by the developed fuzzy model was observed to
be quite satisfactory. The average percentage error levels in the fuzzy model were
successfully low (2.69%). The model was compared with the ANN model for its error
levels and ease of application. The results indicated that through the application of
fuzzy logic algorithm, a more user fiiendly and more explicit model than the ANNs
could be produced within successfully low error margins.
Akkurt et al. (2003) developed a three-layer GA-ANN model for the prediction of 28-
day cement strength. Input parameters used in the model creation process included the
chemical composition of cement, surface area, particle size distribution, and C3S and
silicate moduli. The model was created for a local cement plant process control data.
The training and testing data were separated from the complete original data set by the
use of genetic algorithms (GAs). A GA- artificial neural network (ANN) model based
on the training data of the cement strength was created. Testing of the model was also
done within low average error levels (2.24%). The model was subjected to sensitivity
analysis to predict the response of the system to different values of the factors affecting
the strength. The plots obtained after sensitivity analysis indicated that increasing the
> " ^ ^ la I ^
LITERATURE REVIEW
amount of C3S, SO3 and surface area led to increased strength within the Umits of the
model. C2S decreased the strength whereas C3A decreased or increased the strength
depending on the SO3 level. Because of the limited data range used for training, the
prediction results were good only within the same range. The satisfactory prediction of
the observed cement strength by the model indicated that ANNs could be a useful tool
for understanding such systems. Consequently, the model could be utilized by plant
operators to optimally choose strength as a function of measured cement properties.
1. From the above literature review, it is observed that most of the research work
already carried out has emphasized on the artificial neural networks models for
predicting the compressive strength, tensile strength and flexural strength.
2. Few studies have been conducted that use only fuzzy logic models to predict
compressive strength.
3. Also, most of the research work has been carried out to predict compressive
strength, but modelling on the basis of fuzzy logic approach to predict depth of
wear (abrasion resistance) has not been yet reported.
Thus, the present study is carried out to address these gaps and provide the base for
better understanding and improved usage of fuzzy logic approach.
19
METHODOLOGY
CHAPTER-3
METHODOLOGY
;--sa —T-x~.
> 20 : V
METHODOLOGY
CHAPTER-3
METHODOLOGY
3.1 INTRODUCTION
Fuzzy Logic was initiated in 1965 by Lotfi A. Zadeh, professor for computer science at
the University of California in Berkeley. Basically, Fuzzy Logic (FL) is a multi-valued
logic that allows intermediate values to be defined between conventional evaluations
like true/false, yes/no, high/low, etc. Notions like rather tall or very fast can be
formulated mathematically and processed by computers, in order to apply a more
human-like way of thinking in the programming of computers.
The term "fuzzy" was introduced by Zadeh in his paper on fuzzy sets, where a new
mathematical discipline, fuzzy logic, based on the theory of fuzzy sets, was presented.
The proposed logic was aimed at supporting of presentation and consideration of
inexact or imprecise concepts by fuzzy sets. The imprecision is to be understood as
grouping of set members into classes, the boundaries of which are not sharply defined.
It was expected that the theory of fuzzy sets should become a novel methodology
suitable enough to help formulate and solve complex problems in engineering and
science that are difficult to handle using "precise" crisp logic, such as binary logic,
where the variables can be either true or false. The theory of fuzzy sets allows the
concept of partial belongingness of an object or a variable in a fuzzy set and, therefore,
allows a gradual transition from a full membership to a totally non-membership.
Thereby, in fuzzy logic an object or a variable within a domain may partially belong to
several fuzzy sets in the same domain simultaneously and, thus, it provides a
framework for a multi-valued logic. This is essential for capturing the vagueness in a
natural linguistic description of any system. Moreover, the underlying fuzzy logic
incorporates a variety of rules with the premises containing fiizzy propositions
generally defined using linguistic terms, such as low and high (temperature, pressure,
flow, frequency, voltage, etc.), old, older, very old (person, engine, sensor, measured
value, etc.). The related linguistic rules are of the IF-THEN art.
N "r21
METHODOLOGY
The membership function is the key idea introduced in fuzzy set theory to measure the
degree to which the fuzzy set elements meet the specific properties, i.e. to measure the
degree of belongingness of an element in a specific fuzzy set. Consequently, the
propositions used need not be true or false, but can be to any degree partially true.
Using a membership ftinction //, we can define a fuzzy set F on a universe of discourse
t/as
//FW:U^[0,1]
which is nothing but a mapping from the universe of discourse U into the unit interval
[0, 1] and /^F {x) represents the extent (degree/grade) to which x belongs to fuzzy set F.
The concept of membership functions allows any element within the xmiverse of
discourse to have partial membership to a specific fuzzy set and also to have partial
membership to other fuzzy sets. In order to demonstrate the idea of membership
functions, two examples are given, one each for a crisp set and a fuzzy set.
Let C be a crisp set and x be any element of the set C such that x e X, where X is the
universe of discourse (domain), then the degree of membership of x in crisp set C will
be 1 and 0 respectively if the element x belongs to C completely (full member) or it
does not belong to it at all. Mathematically, this is stated as
/ x_(l; if XGC
^cV^J-|0; if x^C
Let us now consider that F be a fuzzy set and x be any element of the fuzzy set F such
that
xzX, where X is the universe of discourse (domain), then the degree of membership of
X in fiizzy set F will be 1 and 0 respectively if the element x belongs to F completely
(full member) or it does not belong to it at all. However, if x belongs to F partially, then
the degree of membership of x in fuzzy set F can have any intermediate value, such as
0.5, 0.9, etc., within 0 and 1. Mathematically, this is stated as
.^T'z^'n fl
METHODOLOGY
1, if X e F (completely)
/"r(-v) (0,1), if A-e/-"(partially)
0, if-X'^ F (totally non-member)
Figure 3.1(a) shows an example of two crisp sets, "short" and "tall", where it is shown
that even if the height of a person is 1.7999 m then that person definitely belongs to the
"short" category only. This is because the crisp set "short" includes heights up to 1.8 m.
In contrast, if the height of the same person had been just 1.8011 m, as per the same
Figure 3.1(a), then the person would belong to the category "tall", as in this case the
height is 0.0001 m greater than 1.801 m and that categorizes the person into the crisp
set "tall". This is obviously quite impractical. Similarly, Figure 3.1(b) shows the
example of two fuzzy sets, "short" and "tall", where it is shown that if the height of a
person is less than or equal to 1.5 m, then the person belongs to the category "short",
whereas if the height is say 1.8 m then the person belongs to the category "short" with a
degree of membership 0.5 and at the same time the person is considered as "tall" with a
degree of membership equal to 0.5.
The simplest membership functions (MFs) are formed using straight lines. Triangular
MF (trimf) is the simplest and described by the three points forming a triangle. The
?T-irTl
METHODOLOGY
trapezoidal MF, (trapmf) has a flat top. The two MFs are shown in figure 3.2 (a) and
figure 3.2(b) respectively.
Fuzzy logic toolbox also provides two MFs built on the Gaussian distribution curve: a
simple Gaussian curve (gaussmf) and a two-sided composite of two different Gaussian
curves (gauss2mf). Another MF, the generalized bell function (gbellmf), is specified by
three parameters. Gaussian and bell shaped MFs are very popular because they are
smooth, differentiable and non-zero at all points in the universe of discourse.
. J i —^->-«_^
PL, i .
an- OM
\
o
u OS
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; Vt
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i 4 1
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fc
S
(c) Gaussian MF
Figure 3.2 Fuzzy Membership Functions
In fiizzy logic operations, unlike Boolean logic operations, the results are not crisp.
Fuzzy logical reasoning is a superset of standard Boolean logic. In other words, if we
keep the fijzzy values at their extremes of 1 (completely true), and 0 (completely false),
standard logical operations will hold. The output of fuzzy logic operations exhibit a
distribution described by the membership function. The operations are analogous to
Boolean union (OR) and intersection (AND) and are described by min-max logic. The
24 jX
METHODOLOGY
fuzzy output of the union of a set of fuzzy variables is the maximum* membership
function value of any of the variables. The fuzzy output of the intersection of a set of
fuzzy variables is the minimum membership function value of any of the variables. The
complement operation (equivalent to NOT) is the complement of 1, i.e., 1 minus the
membership function value.
The IF-THEN rule statements are used to formulate the conditional statements that
comprise fuzzy logic. A single fuzzy IF-THEN rule assumes the form
Where ai, a2 and bi are linguistic values defined by fuzzy sets on the ranges xi, X2 and
yi, respectively. The IF part of the rule 'xi is "ai" AND xi is "a2" ' is called the
antecedent, while the THEN part of the rule 'yi is "bi" ' is called the consequent.
Fuzzy inference systems (FISs) are also known as fuzzy rule-based systems, fiizzy
model, fuzzy expert system, and fuzzy associative memory. This is a major unit of a
fuzzy logic system. The decision-making is an important part in the entire system. The
FIS formulates suitable rules and based upon the rules the decision is made. This is
mainly based on the concepts of the fiizzy set theory, fuzzy IF-THEN rules, and fuzzy
reasoning. FIS uses "IF-THEN" statements, and the connectors present in the rule
statement are "OR" or "AND" to make the necessary decision rules. The basic FIS can
take either fuzzy inputs or crisp inputs, but the outputs it produces are almost always
fiizzy sets.
^ I 25 1 5
METHODOLOGY
Knowledge base
'
Database Rule base '' output
Fuzzificalion Defuzzification
interface interface
,
'•
The working of FIS is as follows. The crisp input is converted in to fiizzy by using
fuzzification method. After fuzzification the rule base is formed. The rule base and the
database are jointly referred to as the knowledge base. Defuzzification is used to
convert fuzzy value to the real world value which is the output.
y , 26 1
METHODOLOGY
The most important two types of fuzzy inference method are Mamdani's fuzzy
inference method, which is the most commonly seen inference method. This method
was introduced by Mamdani and Assihan (1975). Another well-known inference
method is the so-called Sugeno or Takagi-Sugeno-Kang method of fuzzy inference
process. This method was introduced by Sugeno (1985). This method is also called as
TS method. The main difference between the two methods lies in the consequent of
fuzzy rules. Mamdani fuzzy systems use fuzzy sets as rule consequent whereas TS
fuzzy systems employ linear functions of input variables as rule consequent.
Mamdani's fuzzy inference method is the most commonly seen fuzzy methodology.
Mamdani's method was among the first control systems built using fuzzy set theory. It
was proposed by Mamdani (1975) as an attempt to control a steam engine and boiler
combination by synthesizing a set of linguistic control rules obtained fi-om experienced
human operators. Mamdani's effort was based on Zadeh's (1973) paper on fuzzy
algorithms for complex systems and decision processes.
Mamdani type inference, as defined it for the Fuzzy Logic Toolbox, expects the output
membership functions to be fuzzy sets. After the aggregation process, there is a fuzzy
set for each output variable that needs defuzzification. It is possible, and in many cases
much more efficient, to use a single spike as the output membership functions rather
than a distributed fuzzy set. This is sometimes known as a singleton output membership
function, and it can be thought of as a pre-deflizzified fuzzy set. It enhances the
efficiency of the defuzzification process because it greatly simplifies the computation
required by the more general Mamdani method, which finds the centroid of a two-
dimensional function. Rather than integrating across the two-dimensional function to
find the centroid, the weighted average of a few data points.
The FIS for mamdani model can be broadly divided into five major steps:
27
METHODOLOGY
The first step is to take the inputs and determine the degree to which they belong to
each of the appropriate fiizzy sets with the help of their MFs. In the fiizzy logic toolbox,
the input is always a crisp numerical value limited to the universe of discourse of the
input variables. The output of its fuzzification is degree of membership corresponding
to this numerical value defined by the qualifying linguistic set. The crisp inputs are
fuzzified for all other fuzzy sets defining that variable. For example, variable
temperature may be defined by fuzzy sets: hot, normal and cold.
Normally, there are multiple inputs, that is antecedents, mentioned on the left IF part of
the rule. The fiizzy logic operators that describe the relation between different inputs
are then applied in order to combine them and obtain the result of the left part of the
rule. The inputs to a fuzzy operator are two or more membership values (degrees) fi-om
the fuzzified input variables. The result is the degree of matching or the degree of
support for that rule and its value is between 0 and 1. This degree of matching is
determined for each rule describing the system.
In fiizzy logic toolbox, two built-in AND methods: min (minimum) and prod (product)
and two built-in OR methods: max (maximum), and the probabilistic OR method,
probor, are supported.
The degree of matching obtained for the left IF part of each rule by applying the fuzzy
operators to the inputs i.e. antecedents, is used to evaluate the conclusion or inference
by mapping it on to the THEN part of each rule. The mapping can be implemented
using two methods: Clipping and Scaling. The two methods map the matching degree
28
. METHODOLOGY
of the inputs to obtain the conclusion by modifying the MF of the consequent, i.e.
outputs, differently. Both functions are supported by the fuzzy logic toolbox.
The clipping method used in the mamdani approach cuts or clips off part of the MF of
the consequent corresponding to degree higher than that obtained by matching the IF
part of the rule. The method can be implemented using the min (minimum) function.
The scaling method scales down the MF of the consequent in proportion to the
matching degree obtained from the IF part of the rule. The method can be implemented
using the product function. In this method the shape of the output MF represented by
the THEN part of the rule is not changed but its highest degree is scaled by equating it
to the degree of matching obtained from the IF part of the rule. Mapping of degree of
matching is implemented for each rule in the rule-base defining the behaviour of the
system. Further, every rule has a weight (a number between 0 and 1), that is the
importance attached to the rule depending on the problem at hand. This weight value is
multiplied to the matching degree obtainedfi-omthe antecedents.
Since decisions are based on all the rules in the rule-base the fuzzy output obtained
from each rule must be combined in order to compute the final composite output fuzzy
set. This process is called 'Composition' or 'Aggregation'. Aggregation is carried out
for each output variable. The output of the aggregation process is one fuzzy set for each
output variable. The aggregation method is commutative and the order in which the
rules are executed is not important. Three built-in composition methods are supported
in fuzzy logic toolbox: max (maximum), probor (probabilistic OR), and sum (simply
the sum of each rule's output set).
3.8.5 Defuzzification
The input for the defuzzification process is a fuzzy set (the aggregate output fuzzy set)
and the output obtained is also aggregated fuzzy output. But generally, it is required
that the output be a single crisp number. As the aggregated fuzzy set encompasses a
range of output values, it must be defuzzified in order to resolve to a single crisp output
Tn^-X':.
METHODOLOGY
value from the set. Perhaps, the most popular deftizzification method is the centroid
method, which returns the centre of area under the curve. There are five built-in
methods supported in fuzzy logic toolbox: centroid, bisector, middle of maximum (the
average of the maximum value of the output set), largest of maximum and smallest of
maximum.
The Sugeno frizzy model was proposed by Takagi, Sugeno, and Kang in an effort to
formalize a system approach to generating frizzy rules from an input-output data set.
Sugeno frizzy model is also known as Sugeno-Takagi model. In sugeno-type systems,
output variables are described as linear frinctions or constants and simplifies the
computation required. Though, it enhances the efficiency of the defrizzification process,
the output cannot be expressed in linguistic terms. A typical frizzy rule in a Sugeno
frizzy model has the format
where AB are frizzy sets in the antecedent; Z = y(x, y) is a crisp frmction in the
consequent. Usually X^, ;;) is a polynomial in the input variables x and y, but it can be
any other frinctions that can appropriately describe the output of the output of the
system within the frizzy region specified by the antecedent of the rule. Wheny(x, y) is a
first-order polynomial, we have ihe.first-orderSugeno frizzy model.
- It is computationally efficient.
./ ' 30 \
METHODOLOGY
- It is intuitive.
^- _ 31
RESULTS AND ANALYSIS
CHAPTER-4
32 ' \
.i
RESULTS AND ANALYSIS
CHAPTER-4
The compressive strength of concrete is calculated by the failure load divided with the
cross sectional area resisting the load and reported in mega pascals (MPa) in SI units.
Concrete's compressive strength requirements can vary from 17 MPa for residential
concrete to 28 MPa and higher in commercial structures. Compressive strength results
are primarily used to determine that the concrete mixture as delivered on site meets the
requirements of the specified strength in the job specification.
Abrasion (wear) resistance is the ability of a surface to resist being worn away or to
maintain its original appearance when rubbed with another object. Abrasion of concrete
y j 33 ;_ \
RESULTS AND ANALYSIS
occurs due to sciaping, rubbing, skidding or sliding of objects on its surface. This form
of wear is observed in pavements, floors, or other surfaces on which friction forces are
applied due to relative motion between the surfaces and moving objects. Abrasion
resistance of concrete is influenced by number of factors such as compressive strength,
surface finish, aggregate properties, types of hardeners and curing. The abrasion
resistance of concrete also depends on the compressive strength of concrete, therefore
types of aggregates and their properties also have effect on the abrasion resistance. The
depth of wear increased with increase in abrasion time and decreased with the increase
in age of curing. For all concrete mixtures the depth of wear decreased with the
increase in curing time indicating better abrasion resistance.
Abrasion testing was performed on the specimens of size 65x65x60 mm under standard
conditions for the experimental data that was taken from literature. Abrasion was
determined from the difference in values of thickness measured before and after the
abrasion test. The depth of wear was predicted by fuzzy logic models with triangular
MF, trapezoidal MF and Gaussian MF, respectively. Predicted depth of wear results of
concrete mixtures from frizzy logic models along experimental values are shown in
Table 4.2
4.4 DATABASE
The success of the fuzzy logic model to predict the compressive strength and depth of
wear depends upon the magnitude of the data. A database of about 72 mixes for
compressive strength model and 42 mixes for depth of wear model was retrieved from
literatures to predict the results using frizzy logic technique. A database of 114 mixes
from the literature was retrieved having mixture composition with comparable physical
and chemical properties. The exclusion of one or more of concrete properties in some
studies and the ambiguity of mixtures proportions and testing methods in others was
responsible for setting the criteria for identification of data. Results were obtained for
both the models from three fuzzy logic models one with triangular MF, second with
trapezoidal MF and third with Gaussian MF. The predicted results obtained from
various models were compared with the experimental results.
The input parameter cement has been shown with both triangular as well as trapezoidal
MF, fine aggi^egate and coarse aggregate has been shown with only triangular MF,
\
RESULTS AND ANALYSIS
water cement ratio and superplasticizer has been shown with trapezoidal MF and output
parameters compressive strength and depth of wear were shown with Gaussian MF in
figure 4.1.
^ .1
(c) Fine aggregate with triangular MF (d) Coarse aggregate with triangular MF
IHWtvtrUHfSf
(g) Compressive strength with Gaussian MF (h) Depth of wear with Gaussian MF
Figure 4.1 some of the parameters are shown using various membership functions
^T^nx
RESULTS AND ANALYSIS
The ranges of various parameters for both compressive strength and depth of wear
model for all the data sets are shown in Table 4.3. The major input variables used in
compressive strength and depth of wear models are:
• Cement content
• Superplasticizer dosage
4.4.2 Coefficients
Correlation coefficient, mean absolute error and root mean squared error (RMSE)
obtained using fuzzy logic approach is shown in Table 4.4. Mean absolute error is the
same as root mean square except using absolute difference instead of squared
difference and is calculated in a similar way as root mean square error.
1 ^
RMSE =
M A7 X Z " " ^ ^ * ^ ^ ' ~ predicted)^
Six different models with varying membership functions such as triangular MF,
trapezoidal MF and Gaussian MF were considered in terms of predicting the
compressive strength and depth of wear of concrete. Three models FLl, FL2 and FL3
with triangular MF, trapezoidal MF and Gaussian MF respectively were used to predict
compressive strength and another three models FL4, FL5 and FL6 with triangular MF,
trapezoidal MF and Gaussian MF, respectively were used to predict depth of wear.
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RESULTS AND ANALYSIS
In the study, 72 experimental data from literature were used in the process of Mamdani
type FIS model in fuzzy logic system model. Five properties cement content, fine
aggregate, coarse aggregate, water cement ratio and superplasticizer dosage, were used
as the input and compressive strength were used as the output.
A fuzzy rule is a simple IF-THEN rule with a condition and a conclusion. After getting
the membership values of the inputs, they are evaluated using IF-THEN rules. In the
rule AND or min operation is specified and 72 rules were created in all three fuzzy
models for compressive strength. The rules were evaluated in model FLl, FL2 and FL3
in such a manner to generate the respective output as shown on the right in the figure
4.1, figure 4.2 andfigure4.3 respectively.
PWpMfl.: ,g,
*** 1501.5:601«85.S:0.49;7.5) *"»*• m rigM down up
44
RESULTS AND ANALYSIS
45
RESULTS AND ANALYSIS
The surface diagram represents the results based on the prediction of various models
i.e. fuzzy logic models FLl, FL2 and FL3 shows the effect of two factors at a time on
each surface plot of the compressive strength in figure 4.4, figure 4.5 and figure 4.6
respectively.
CaiENT
700
CEMENT
46
RESULTS AND ANALYSIS
CEWENT
In the study, 42 experimental data from literature were used in the process of Mamdani
type FIS model in fuzzy logic system model. Five properties cement content, fine
aggregate, coarse aggregate, water cement ratio and superplasticizer dosage, were used
as the input and depth of wear were used as the output.
47
RESULTS AND ANALYSIS
48
RESULTS AND ANALYSIS
23
IZ3
A 3-D surface from input variables and the output of the model which helps to Simulate
and analyze fuzzy inference systems was generated. Based on the results of prediction
from the fuzzy logic model FL4, FL5 and FL6 shows the effect of two factors at a time
on each surface plot of the depth of wear in figure 4.10, figure 4.11 and figure 4.12
respectively.
49
RESULTS A N D ANALYSIS
FincAggregate CB«IMT
700
FincAggregate CEhCNT
50
RESULTS AND ANALYSIS
700
FineAggregate CEMENT
Table 4.4 provides the correlation coefficient, root mean squared error (RMSE) and
mean absolute error (MAE) obtained with the data to predict compressive strength. To
compare the performance of models, graphs between actual and predicted compressive
strength are plotted. The performance of fiizzy logic model FLl, FL2 and FL3 are
shown in figure 4.13,figure4.14 andfigure4.15 respectively. Results suggest that most
of the points are lying near the line of perfect agreement, which suggest that fuzzy logic
can effectively be used to predict the compressive strength of concrete. A correlation
coefficient of 0.935, 0.933 and 0.887 was achieved in FLl (triangular KlF), FL2
(trapezoidal MF) and FL3 (Gaussian MF) respectively. Considering the correlation
coefficient along with root mean squared error (RMSE) and mean absolute error
(MAE), it can be concluded that fuzzy logic model with trapezoidal MF (FL2) is the
most acceptable model to predict the compressive strength of concrete.
51
RESULTS AND ANALYSIS
Triangular MF
70
JZ
tie Line of perfect
c
a> 60 agreement
i_
«••
** 50
^j^^'^'
5!
S 40
21
gSO triangular MF
o
w
•D 20
I 10 0 20 40 60 80 100
•a- 0 experimental compressive strength
Fig 4.14 Comparison between compressive strength predicted by Model FLl and
actual values
Trapezoidal MF
80
to 70
c Line of perfect
9
•» 60 aggrement
irt
01
50
>
M
in
<0
*m
40
a Trapezoidal IVIF
£ 30
o
u 20
tS 10
•o
01 0
>-
a 20 40 60 80 100
experimental compressive strength
Fig 4.15 Comparison between compressive strength predicted by Model FL2 and
actual values
52
RESULTS AND ANALYSIS
Gaussian MF
70
c
9>
60 Line of perfect
4i< 50 aggrement
V
> 40
l/t
Vt
S! 30
a. Gaussian MF
E 20
o
u
"O 10
V
C n
"O
JV 0 20 40 50 80 100
experimental compressive strength
Fig 4.16 Comparison between compressive strength predicted by Model FL3 and
actual values
80
triangular
trapezoidal
gaussian
10
Fig 4.17 Comparison between compressive strength predicted by Models FLl, FL2
andFL3
53
RESULTS AND ANALYSIS
Table 4,4 provides the correlation coefficient, root mean squared error (RMSE) and
mean absolute error (MAE) obtained on predicting depth of wear. To compare the
performance of models, graphs between actual and predicted depth of wear are plotted.
The performance of fuzzy logic model FL4, FL5 and FL6 are shown in figure 4.17,
figure 4.18 and figure 4.19 respectively. Results suggest that most of the points are
lying near the line of perfect agreement, which suggest that fuzzy logic csn effectively
be used to predict the depth of wear on concrete. A correlation coefficient of 0.899,
0.895 and 0.892 was achieved in FL4 (triangular MF), FL5 (trapezoidal MF) and FL6
(Gaussian MF), respectively. Considering the correlation coefficient along with root
mean squared error (RMSE) and mean absolute error (MAE), it can be concluded that
fuzzy logic model with Gaussian MF (FL6) is the most acceptable model to predict the
depth of wear of concrete.
Triangular MF
3 -
•S 1.5 ^
•o
« • Triangular MF
« 1-
T3
Of
Q.0.5 -
0 - 1
() 1 2 3 4
experimental depth of wear
Fig 4.18 Comparison between depth of wear predicted by Model FL4 and actual
values
54
RESULTS AND ANALYSIS
Trapezoidal MF
Line of perfect
aggrement
r
•O 0.5
Trapezoidal MF
1 2 3
experimental depth of wear
Fig 4.19 Comparison between depth of wear predicted by Model FL5 and actual
values
Gaussian MF
re
I 2.5 • Line of
perfect
I-
I: • Gaussian MF
1 2 3
experimental depth of wear
Fig 4.20 Comparison between depth of wear predicted by Model FL6 and actual
values
mns
RESULTS AND ANALYSIS
2.5
15 2 :^^^SS^
*Sl.5 •triangular
•trapezoidal
T3 1
-gaussian
0.5
I I I I I ( I I I I r I I 1 I I' t t I 1 I I I I I I I t ( I 1 I ( I I I I I I I I I
Fig 4.21 Comparison between depth of wear predicted by Models FL4, FL5 and
FL6
The Matlab Fuzzy Logic Toolbox was used to find a mamdani fuzzy inference system
that could be used to determine the compressive strength and depth of wear of concrete.
This tool provides a membership function, the if-then rules and provides the
relationships between a series of inputs and the output. The developed fuzzy logic-
based model was applied to predict 28-day compressive strength and depth of wear. To
have an objective comparison of the performance of the models, the error measures of
the root mean square error (RMSE) and the mean absolute error (MAE) were computed
for each model, and these are summarized in table 4.4. The acceptance/rejection of the
model developed are determined by its ability to predict the strength and wear.
Statistical methods are commonly used in the development of empirical relationships
between various interacting factors. This is often complex and circuitous, particularly
for nonlinear relationships. Also, to formulate the statistical model, the unportant
parameters must be known. Fuzzy logic can be effective for analyzing a system
containing a number of variables, to establish patterns and characteristics not
56
RESULTS AND ANALYSIS
previously known. Summary of steps followed by the fuzzy logic prediction models are
as follows:
The FIS Editor helps to create five input variables that is cement, fine aggregate, coarse
aggregate, water cement ratio and superplasticizer dosage and output variable as
compressive strength. The Fuzzy Logic Toolbox does not limit the number of inputs.
For model FLl, the FIS editor window is shown below.
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CuimriltiWStritiglh
cmwivvmut
Typt
tt*im
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S!ra<W>*CMprtwtVt tlTM^h rwwr: 5 MMM, 1 MlHt, M i 72 n«H
The Membership Function Editor is used to define the shapes of all the membership
functions associated with each variable. Triangular, trapezoidal and Gaussian shapes of
membership fimctions were selected for model FLl, FL2 and FL3 respectively. Model
FLl with triangular MF is shown below.
pMeiT<witibfanctionfaaoKCompfcgi>»etfceBOthresirft aEiyt
He Edil V M W
£~«
ImMwrhbto'CTHCTr
Cbw {
ITrrrz
RESULTS AND ANALYSIS
The Membership Function Editor is the tool that lets you display and edits all of the
membership functions associated with all of the input and output variables for the entire
fuzzy inference system.
The Rule Editor is for editing the list of rules that defines the behaviour of the system.
Based on the descriptions of the input and output variables defined with the FIS Editor,
the Rule Editor allows you to construct the IF-THEN rule statements automatically, by
clicking on and selecting one item in each input variable box, one item in each output
box, and one connection item. Rules may be changed, deleted, or added, by clicking on
the appropriate button. For model FLl, the rule editor window is shown below.
1070^
ItlO
^iL •roni
Cfc— _ J
The Rule Viewer displays a roadmap of the whole fiizzy inference process. Each
column of plots (yellow) shows how the input variable is used in the rules and column
of plots (blue) shows how the output variable is used in the rules. In the lower right
there is a text field into which you can enter specific input values. You can also adjust
these input values by clicking anywhere on any of the plots for each input. Fuzzy
inference process takes place and a new calculation is performed to generate the output
as shown below.
58
RESULTS AND ANALYSIS
-~1
The Surface Viewer is used to display the dependency of one of the outputs on any one
or two of the inputs that is, it generates and plots an output surface map for the system.
The effect of two factors at a time on each surface plot of the compressive strength is
shown below.
auEKT » ytm^r- FA
59
CONCLUSION
CHAPTER-5
CONCLUSIONS
CONCLUSION
CHAPTERS
CONCLUSIONS
5.1 CONCLUSIONS
In the present study, a fuzzy logic prediction model for compressive strength and
abrasion resistance has been developed. Input parameters used in model creation
process include cement content, fine aggregate content, coarse aggregate content, water
cement ratio and superplasticizer dosage. Results were obtained fi-om various fuzzy
logic models with different membership functions. Three models FLl, FL2 and FL3
with triangular MP, trapezoidal MP and Gaussian MP respectively were used to predict
compressive strength and other three models PL4, PL5 and PL6 with triangular MP,
trapezoidal MP and Gaussian MP respectively were used to predict depth of wear. Main
conclusions drawn from the study are as under.
1. The predicted results with fuzzy logic model were compared with the
experimental and found remarkably close to each other.
2. Modelling using fiizzy logic approach was carried out for the data fi-om
literature for compressive strength at 28-days. The correlation coefficients of the
model PLl, PL2 and PL3 were found to be 0.935, 0.933 and 0.887 respectively.
3. Modelling using fuzzy logic approach was carried out for the data from
literature for depth of wear. The correlation coefficients of the model PL4, PL5
and FL6 were found to be 0.899, 0.895 and 0.892 respectively.
4. In case of fiizzy logic prediction models for compressive strength, least mean
absolute error (MAE) and root mean squared error (RMSE) were found to be
10.656 and 12.563 in model PL2, whereas in case of fuzzy logic prediction
models for depth of wear, least mean absolute error and root mean squared error
were found to be 0.381 and 0.471 in model FL6.
5. Various fuzzy logic prediction models for compressive strength were compared
and based on correlation coefficient, RMSE and MAE, it can be concluded that
r%xT"<:
CONCLUSION
fuzzy logic model with trapezoidal MF (FL2) is the most acceptable model to
predict the compressive strength of concrete.
6. Various fuzzy logic prediction models for depth of wear were compared and
based on correlation coefficient, RMSE and MAE, it can be concluded that
fuzzy logic model with Gaussian MP (FL6) is the most acceptable model to
predict the depth of wear of concrete. .
7. The fuzzy logic approach can be used as a usefiil tool for reducing the duration
of the project execution in huge civil projects.
1. The study can be carried out for various fuzzy logic models with other
membership functions.
2. Fuzzy logic model can be developed with more input variables to study their
effect on the prediction of strength and wear.
3. Fuzzy logic prediction model for more properties of the concrete can be
developed.
S i 1 if
I 0/ I V
REFERENCES
REFERENCES
63
REFERENCES
REFERENCES
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17. R. Siddique, "Effect of fine aggregate replacement with Class F fly ash on the
abrasion resistance of concrete", Cement and Concrete Research 33 (2003)
1877-1881
./ , 65
REFERENCES
21. S. Akkurt, G. Tayfur, S. Can, "Fuzzy logic model for the prediction of cement
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