ApplyingAdaptiveNeuralFuzzyInferenceSystemtoImprove ...downloads.hindawi.com/journals/ace/2018/2451915.pdfgreased to adherence between the sample and mold after casting.After2-3daysofcasting,thespecimensareslightly

Research ArticleApplying Adaptive Neural Fuzzy Inference System to ImproveConcrete Strength Estimation in Ultrasonic Pulse Velocity Tests

Loan T Q Ngo Yu-Ren Wang and Yi-Ming Chen

Department of Civil Engineering National Kaohsiung University of Science and Technology Kaohsiung Taiwan

Correspondence should be addressed to Yu-Ren Wang yrwangkuasedutw

Received 20 March 2018 Revised 23 July 2018 Accepted 7 August 2018 Published 20 September 2018

Academic Editor Arnaud Perrot

Copyright copy 2018 LoanTQ Ngo et alis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

When inspecting the property of material nondestructive testing methods are more preferable than destructive testing since theydo not damage the test sample Nondestructive testing methods however might not yield the same accurate results in examiningthe property of material when compared with destructive testing To improve the result of nondestructive testing methods thisresearch applies artificial neural networks and adaptive neural fuzzy inference system in predicting the concrete strength es-timation using nondestructive testing method the ultrasonic pulse velocity test In this research data from a total of 312 cylinderconcrete samples were collected Ultrasonic pulse velocity test was applied to those 312 samples in the lab following the ASTMprocedure en the testing results of 312 samples were used to develop and validate two artificial intelligence prediction modelse research results show that artificial intelligence prediction models are more accurate than statistical regression models interms of the mean absolute percentage error

1 Introduction

Examining concrete compressive strength in existingstructure is one of the most important issues in the con-struction industry e compressive strength serves asone of the most essential factors in quality assurancefor concrete ere are nondestructive and destructivemethods to test the compressive strength of concreteNondestructive testing (NDT) methods will not only notdamage the concrete structure but they are also economicand feasible A common NDT method to inspect thecompressive strength of the concrete is ultrasonic pulsevelocity (UPV) testing UPV testing is mainly used tomeasure the pulse velocity of the concrete and then thecompressive strength of the concrete is interpolated UPVtesting can effectively evaluate the uniformity and relativequality of concrete structures Moreover UPV testing hasa lot of advantages like low cost easy to operate andconvenient to carry e disadvantage of the NDTmethodsin general is that they are qualitative and have an average of20 mean absolute percentage error (MAPE) whencompared with destructive methods [1] To enhance the

accuracy in estimating compressive strength a combina-tion of destructive and nondestructive methods has beenproposed in [2 3] A combination of UPV testing andrebound hammer test was employed in [2 3]

With the development of artificial ntelligence (AI)technology incorporating AI in enhancing the accuracy ofcompressive strength has become a new research approachCho and Pham [4] employ AI technology including supportvector machines artificial neural networks (ANNs) chi-squared automatic interaction detector and linear re-gression to predict the compressive strength of high per-formance concrete Adaptive neural fuzzy inference systems(ANFIS) is also an effective (AI) prediction method Vakh-shouri and Nejadi [5] have concluded that the ANFIS modelgave the best prediction of the compressive strength of self-compact concrete Comparing ANNs ANFIS and multiplelinear regression in estimating the compressive strength ofconcrete [6 7] state that ANNs and ANFIS are suitableprediction models Based on the reliability of ANNs andANFIS this research has chosen those two AI technologies inenhancing the prediction of concrete compressive strength inUPV testing

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 2451915 11 pageshttpsdoiorg10115520182451915

In concrete the actual compressive strength is theunconfined one or the self-compacted one [8] One of theNDT methods commonly used to measure the actualcompressive strength is UPV test UPV test is done basedon the principle of measuring the travelling time of anultrasonic pulse in concrete sample en the ultrasonicpulse velocity is obtained Based on the velocity in-formation the actual compressive strength of concretesample is evaluated It is shown in previous researches thatthe higher the ultrasonic pulse velocity the better thequality of concrete sample [9 10]

e compressive strength of concrete is predicted usinga constructed prediction model Since there are many waysto construct this prediction model Kademi [11] stated thatusing multiple linear regression to develop the model cannotgive an accurate prediction of compressive strength Arti-ficial neural network on the other hand is more suitable forestimating the property of concrete sample [12 13]

is research aims to improve the prediction of concretecompressive strength in UPV test with the help of ANNs andANFIS A linear and a nonlinear regression predictionmodels were developed en 312 test samples that un-derwent UPV testing from a local laboratory were collected252 out of the 312 test samples were randomly chosen to bethe training dataset e remaining 60 test samples wereused to evaluate the accuracy of the prediction modeldeveloped

e rest of this paper is organized as follows Section 2 isthe literature review the methodology of the research isdescribed in Section 3 the prediction results are discussed inSection 4 and the conclusion is discussed in Section 5

2 Literature Review

Since destructive testing is not preferable in some applica-tions nondestructive testing methods have attracted lots ofinterests in the field of concrete structure assessment NDTdoes not require much on sample preparation and its testingequipment is quite simple [14] erefore NDT can beapplied easily and economically to assess concrete structureproperties In addition due to the limitation of laboratoryequipment NDTmethods are preferable for the predictionprocess [15] Based on the relationship between strength andNDTparameters the strength of concrete will be evaluatede detail information of the empirical relationship betweenstrength and NDT parameters is provided by the NDTequipment manufacturers e information provided isdirectly related to the testing system used in NDTmethodsand it is not always suitable for all type of concrete Hencethe calibration of different types of concrete is necessary[16 17] UPV testing method is one of the most popularNDT methods that is successfully used to evaluate theproperty of concrete

Ultrasonic pulse velocity (UPV) test uses the propaga-tion of sound wave through material to measure the depth ofmaterial It also gives information on damages inside thematerial From the data measured by UPV test the materialstrength and low-strain elastic modulus can be calculated orpredicted [18ndash20] It has been shown in [21] that UPV of

concrete is inversely proportional to the volume of poresinside and develops with age of the concrete e UPV rateof change can be used to determine the setting of concreteand give inside information on the changes at the micro-structural level of concrete in early ages [22 23] e re-search in [24] found the effect of microstructural variationson UPV in mortar is is used to estimate the sand contentin mortar UPV testing is also used to detect damages insideconcrete effectively in [25 26] UPV testing has been shownto be the effective testing method for different types ofconcrete such as lightweight or asphalt concrete in [27ndash29]UPV testing measures the ultrasonic wave speed when itpenetrates through materials in order to predict the strengthof the materials find any changes in condition of the ma-terials internal flaws and other factors UPV techniquehowever is not always practical for all types of concretesamples Since there is sound wave related to the method itis not accurate for samples that have internal water-filledcracks and rough surfaces [30] To increase the accuracy ofthe testing for rough surfaces a coupling gel is applied inbetween the transducer of testing equipment and roughnesssamples to smoothen the contact layer Many studies havebeen conducted in detail to investigate the correlation be-tween UPV and concrete strength however not many lit-erature results on the correlation between parameters ofUPV and properties of concrete have been found[17 19 20 27] In addition there are many factors that affectthe one important parameter of UPV the ultrasonic pulsevelocity is leads to the derivation on the relationshipbetween UPV parameters and concrete properties unreliable[17] erefore the risk level in the evaluating process mustbe defined quantitatively Recently artificial intelligenttechnology has been employed into predicting the com-pressive strength of concrete In addition to using UPV testthe adaptive neuro fuzzy inference system (ANFIS) and theartificial neural network (ANN) are used to give moreprecise prediction on the compressive strength under var-ious conditions of the mix proportion of concrete [24 31] Itstates in [32 33 34] that inverse modelling of concretecompressive strength has been developed with statisticaltechniques or artificial intelligent techniques Among AItechniques ANNs is quite popular and user friendly for theprocess after the prediction model is established One ad-vantage of ANNs is that there is no requirement in definingthe explicit input-output relationship as in the conventionalregression In ANNs the neuron used is the informationprocessing system unit is system unit consists of con-nection links and summationactivation functions Eachneuron receives input and weights from neurons belongingto the previous layer of this neuron in the training process[34] e learning process in ANNs is adaptive ApplyingANNs does not require any prior knowledge of the func-tional relationship among the variables e distributedprocessing system of ANNs is a parallel one that consists ofone input and one output layer and one or more hiddenlayers connecting by neurons ere are different types ofANNs developed like the multilayer feed-forward neuralnetwork or the cascade-forward neural network [35] Ap-plying ANNs in predicting the compressive strength of

2 Advances in Civil Engineering

concrete has been studied by researchers and several authorshave applied ANNs in structural engineering [36 37]

Combining ANNs with the fuzzy inference systemANFIS is a hybrid neuro-fuzzy approach ANFIS has theadaptive learning algorithm and the reasoning ability whichis a well-known approach to model complex nonlinearsystem [38] Fuzzy inference system (FIS) is a linguistic rule-based system that can represent any system with high ac-curacy FIS is regarded as the universal approximator [39]e downside of FIS is lacking self-adaptability and self-learning ability when there is a change in the external en-vironment With that ANFIS takes the learning property ofneural network in combination with FIS to create an ap-proach for forecasting and regression [40] Author PJLAdeodato (2011) predicted the concrete compressivestrength by applying a sensor-based forecasting model usingANFIS e results showed that ANFIS gives lower error inprediction when compared with conventional back-propagation neural networks [41]

Prediction models take measured data as input variablesin their data-driven modelling e models learn throughthe training step from a collection of training patterns ispaper uses ANN and ANFIS as two different predictionmodels with the aim of predicting more accurate concretecompressive strength in UPV tests

3 Experiment Methodology

Two artificial intelligence models used to integrate datain this study are ANNs and ANFIS Using AI approachis expected to improve the performance of predicting theconcrete compressive strength when compared with theconventional approach e model development is shown inFigure 1 According to Khademi [42] the generalizationof the predictive models can be enhanced but their effec-tiveness needs further examination

In this study data were collected from both destructivetests and nondestructive tests using 28-day cylinder concretespecimens ey are stored in standard curing conditionsbefore conducting the tests e UPV measurements aretaken against all the cylinder concrete samples with a di-ameter of 12 cm and a height of 24 cm Before collecting thecylinder to the laboratory the mixture must be cleaned andgreased to adherence between the sample and mold aftercasting After 2-3 days of casting the specimens are slightlydemanded and carefully be transferred to store in air en-vironment in the laboratory room e process is shown inFigure 2

31 Destructive Concrete Compressive Strength Test In thisstudy the actual compressive strength of concrete is in-vestigated according to the Taiwan National CNS1232standard ldquoCompressive strength of cylindrical concretespecimensrdquo is the method that determines the compressivestrength of cylindrical concrete samples such as monolithicconcrete sample or core drilled cylindrical concrete samplee testing device HT-8391 hydraulic machine is able toproduce up to 200 tons of press force on the surface of theconcrete sample is procedure follows the study of [43]

First measure the diameter and height of the cylindricalconcrete sample en eliminate all the strange objects onthe surface of the test object and on the surface of thepressure machine as in Figure 3e test object will be placedconcentrically with the surface of the pressure machine ecompressive force will be increased from 150 kfgcm2

(0150MPa) to 350 kfgcm2 (035MPa) per second For thefirst half of the test the highest compressive force will bepredicted to increase the force until the test sample isbroken en the maximum compressive force for that testsample will be recorded

32 Ultrasonic Pulse Velocity Ultrasonic pulse velocity(UPV) in concrete is an important parameter in evaluatingconcretersquos properties [44] UPV testing measures the ultra-sonic wave speed when it penetrates through materials inorder to predict the strength of the materials find any changesin condition of the materials and find any internal flaws andthe travelling distance has a full report on the correlationbetween the compressive strength [45] UPV techniquehowever is not always practical for all types of concretesamples Since there is sound wave related to the method it isnot accurate for samples that have internal water-filled cracksand rough surfaces [46]e unconfined compressive strength(UCS) is the maximum longitudinal axial compressive stressof the sample [47]e relationship between pulse velocity andcompressive strength is also identified In [41] Yu LY andYong S (2008) propose an empirical equation on the re-lationship between the unconfined compressive strength andthe pulse velocity as follows

UCS aebV

(1)

where the properties of material will determine a and b andV is the speed of ultrasonic pulse

In this study the UPV test used follows the ASTM C597-16 the standard test method for pulse velocity throughconcretee instrument used forUPV test is a TICO concreteultrasonic detector developed by Proceq Company in ZurichSwitzerland As shown in Figure 4 the instrument can per-form the calculation and evaluation on functions of concreteuniformity column hole crack depth elastic modulus andconcrete strengthe ultrasonic pulse velocity test conductedin this study is described as follows the measurement wastaken four times for each of the cylindrical concrete samplewith a diameter of 12 cm and height of 24 cm as shown inFigure 5 For typical 3000 psi (210 kgfcm2) concrete for eachcubic meter the material properties are as follows 325 kgcementingmaterial (including 2275 kg cement 65 kg slag and325 kg fly ash) 180 kg water 940 kg sand 900 kg aggregateand 325 kg chemical admixture

e ultrasonic pulse velocity test was conducted for eachof 312 test samples First one transducer was placed againstone end of the test sample e other transducer was placedat the other end of the test sample e distance between thetwo transducers was measured as L After the excitationmeasurement the first Vaseline was applied between thetransducer and the concrete surface and the pressure wavewas received

Advances in Civil Engineering 3

UPV test equipment consists of three parts the ultrasonicpulser the receive amplifier and the time measurementdevice that indicates that the time of ultrasonic wave travelthrough themedium and the receiving transducer receives thesignal e measurement data are displayed and recorded inthe control host

To determine the velocity of ultrasonic pulse wave twoquantities are measured the transmission distance and theduration ultrasonic pulses transmittede ultrasonic velocity(v) was determined as follows

v l

t103 (2)

where l is the specimen length (peat-cement-sand brickwith length measured in millimetres (mm)) v is the ve-locity of ultrasound (ms) and t is the actual travelling time

through medium of the ultrasonic pulse measured inmicroseconds (micros)

33 General Linear Regression General linear regression(GLR) is used to estimate the correlation between input andoutput variables e correlation that GLR estimates isbetween one response variable which is a dependent vari-able and two or more predictors which are independentvariables [48] General linear regression has 2 categories

(i) Linear regression in the training data input themargin is maximized by using the best hyperplanethat is to define the hyperplane boundary as thetraining sample and its range is the shortest distancebetween +1 minus1 and the hyperplane

(ii) Nonlinear regression can use the nonlinear functionto classify when the linear classification cannot beused is type of data is transformed into a featurespace by transforming it into a high-dimensionfeature space through a nonlinear mapping func-tion Φ

e GLR form of a model uses a link function based onits distribution pattern which gives the relationship be-tween X as the predictor variable and y as the responsevariable [49]

e (X-y) relational model is shown in the followingequation

g(E(y)) X times β + Ο y sim F (3)

with selected link function g(middot) offset variable O the dis-tribution model F of y predictor X response variable y andregression coefficient β

34 Artificial Neural Networks Artificial neural networks(ANNs) are simulations of the human brain with the abilityof learning adapting and multivariate analyzing With theadvantages over traditional statistical methods ANNs have

Research data Prediction method Final model

e ultrasonic value of concertecylindrical specimen

+actual compressive strength of

concrete column

Model (linear nonlinear)

Simulation model(ANN ANFIS)

Comparison of predictionresults

Figure 1 Model development

Figure 2 Cylinder collection process by the laboratory

Figure 3 Concrete compressive strength test


the ability to do multiple regression analysis and give outcomplex interrelationships between dependentindependentvariables through simple process elements [49 50] eneuron used in ANNs is an information processing systemunit that consists of connecting link summation and ac-tivation function [51] As shown in Figure 6 for eachneuron it receives inputs and weights from neurons of theprevious layer in the training process en the weightedsum becomes an argument for the activation function inorder to form the output [52] Using mathematic modellinga neuron output is calculated by using (4) (5) and (6) il-lustrated as follows

u 1113944m

j1wjxj + b (4)

y f(u) (5)

f(u) 1 + eminusu

1minus eminusu (6)

where xj(j 1 2 m) is the input signal from the previouslayer wj(j 1 2 m) is the weight associated with xj m isthe number of inputs b is the bias and f(u) is the activationfunction

To develop the ANN model this paper used NeuroSolutions 70 software to construct a neural network model

speed of training and host of neural network architecturesBackpropagation network (BPN) was also adopted for theprediction of concrete compressive strength BPN super-vised the training process BPN used the gradient descent asthe algorithm to find out the minimum mean of the errorfunction in weight space

With the testing data of 312 testing samples from thedata testing laboratory 252 industrial samples were ran-domly chosen as the training models set for the prediction20 samples were extracted from 252 training group data andthey were set as the cross validation groupen the trainingprocess is used to find out the best prediction model Finally60 remained data of 312 samples were used to evaluate theaccuracy of the prediction model As shown in Figure 7 theinput layer in this study was the average ultrasonic pulsewave velocity e output was the compressive strength ofthe concrete

After setting the properties of the predictive model themodel was trained and tested to obtain the predictive valueof the model e result of the predictive model was judgedby the mean absolute error percentage (MAPE) as shown inFigure 8

e average velocity of the four ultrasonic waves ob-tained from each specimen was an independent variableecompressive strength of the concrete was used to carry onthe neural network analysis Various modes have been triedto different training times MAPE of the concrete strengthand actual strength predicted by the model under differentparameter settings is shown in Table 1

Bias b

Activationfunction

Outputy

Summingfunction

Inputs Weights

sum f (bull)

w1

w2

wm

x1

x2

xm

Figure 6 Model of network block [32]

Figure 4 Ultrasonic pulse velocity test and TICO ultrasonic pulse velocity

Receive amplifier

Ultrasonic Plulser

Oslash = 12cmL = 24cm

L e Specimen length

Figure 5 Model of schematic diagram of pulse velocity testingcircuit


35AdaptiveNeural Fuzzy Inference System Adaptive neurofuzzy inference system (ANFIS) is an adaptive network usedto find responses for complex problems In ANFIS super-vised learning is adopted ANFIS is comprised of a learningalgorithm multilayer and feed-forward networks that in-clude inputoutput variables and a fuzzy rule

e ANFIS multilayer contains 5 layers that work dif-ferently from each other nodes in the same layer work

similar to each other [53] Figure 9 shows the frameworkstructure of ANFIS with two input variables

e fuzzy rule is illustrated as follows

(i) Rule 1 if x is A1 y is B1 then j f1 p1 x + q1 y + r1(ii) Rule 2 if x is A2 y is B2 then j f2 p2 x + q2 y + r2

where A1 A2 B1 B2 and C1 C2 are the membershipfunctions of each input x and y as part of the premises p1 q1r1 and p2 q2 r2 are linear parameters in the consequent partof Takagi-Sugeno fuzzy inference model [53]

In this study the ANFIS modelling was performed inMATLAB to train and test data 252 experimental data wereused as the training group data (train data) of the neuron-based fuzzy inference system e best predictive model wasfound by the model training process 60 remained data wereused as the test data into the best prediction model tocalculate the average absolute error percentagee concretestrength predicted by the model was compared with thecompressive strength obtained from the destructive testen the verification of the established model with theactual strength of concrete cylindrical test was made edevelopment of the ANFIS model in MATLAB follows thebelow steps

Step 1 Import the training group and test group data usingimport instruction syntax as follows

Traindata xlsread(ldquotraindataxlsxrdquo)Testdata xlsread(ldquotestdataxlsxrdquo)

Step 2 Create the ANFIS prediction model is study at-tempts 32 different setups for the ANFIS prediction modelfour membership functions with eight different types isstudy uses the membership functions available in MATLABlike triangle trapezoid bell gauss bilateral Gaussian double

1234567891011121314151617

336332337309336346351374364370184288291283300298277

252253254255256257258259260261262263264265256267268

4057540425406039704095405040903975

400753890

3757540254005

400254060

397753895

287291296292165172170337333303305299153153284286262

398250394500400750401250356000357750351500398750400000397000395500394500352750358250407250403750381250

Number Average wavespeed

Concrete strength(kgfcm2)

252 training group data

Input Output



Input Output

60 testing group data

Figure 7 ANNs model data collection process

4005

40575

40425

4060

3970

4095

4050

4090

3975

40075

3890

37575

4025

4005

40025

4060

325

336

332

337

309

336

346

351

374

364

370

184

288

291

283

300

3234327743

3497252102

3417911436

351048794

3114835861

3689149015

3457499542

3664795062

3127353884

3245278274

3097138242

2058672991

3328012024

3234327743

3223638208

351048794

048

408

295

417

080

980

007

441

1638

1084

1629

1188

1556

1115

1391

1702

MAPE ()Predictedstrength (kgfcm2)

Compressivestrength (kgfcm2)

Average wavespeed

Figure 8 Predictor of absolute error percentage in invertedtransmitter ANNs


S-shaped double S-shaped and so on during the estab-lishment of the prediction model

Step 3 e model is set to be trained by the hybrid train FISmethod with zero error tolerance and an epoch of 5000

Step 4 When the training model is completed predictionvalue is exported using command syntax as follows

Out_value evalfis (testdata fis1)

A total of 32 ANFIS prediction models are establishedWith the prediction results obtained and the actual com-pression strength the absolute percentage of error of themodeland the prediction accuracy of the model can be calculated

4 Prediction Results

Among the 312 test samples collected in the lab 252 of themare randomly selected as the training dataset and 60 selectedas testing dataset e prediction accuracy is measured bythe mean absolute percentage error (MAPE) illustrated inthe following equation

MAPE 1n

1113944

n

i1

Ai minusPi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (7)

where Ai is the actual concrete sample compressive strengthand Pi is the predicted strength

In this research there are two different AI-based pre-diction models (a) the artificial neural network (ANN) and(b) the adaptive neural fuzzy inference system (ANFIS) Forthese models the actual compressive strength is setup as the

output variable is experiment includes a total of 312samples Among them 252 are sample data in the trainingdataset e prediction model was used as the training data ofthe model en 60 samples as the model of the test groupdata into the best predictionmodel after the completion of thetest with the actual compressive strength to do the accuracy ofthe model e model is tested with a different number ofstudies (epoch) e default value is set to 5000 incrementsuntil the convergence is complete and the error tolerance isexpected to be closer to the actual compressive strength

41 Prediction of ANNs Model Parameters e mean ab-solute percentage error (MAPE) of the concrete strength andactual strength predicted by the model under different pa-rameter settings is obtained as shown in Table 2 eminimum MAPE obtained are 1048 and 1046 for one-input and two-input network types respectively e mostaccurate prediction made using neuro network is as follows

(i) For one-input the network type recommended is 1-3-1 as one-inputmdashthree input layer processingunitsmdashone hidden layer processing unit that istrained 2000 timeseminimumMAPE strength ofconcrete is 1048 as the number of hidden layermanufacturing unit increases Once the number ofprocessing units exceeds a certain number thetraining time of the model will increase during thetraining and the average absolute error percentagewill not be improved

(ii) For two-input the network type recommended is 2-3-1 as two-inputmdashthree hidden layer processingunitsmdashone output layer processing unit that istrained 2000 times the best percentage of the averagepredicted concrete intensity is 1046 It can be seenthat as the number of hidden layer processing unitincreases the average absolute error percentageobtained by them can reach a smaller error value Ifthe number of hidden layer processing units exceedsa certain number it will increase the model in thetraining process During training time the averageabsolute error percentage will not be improved sothe best predictive model for this type of neuralnetwork is the network type 2-3-1

Table 1 Network model parameter setting

Network parameters of the project ExplanationInternet usage examples model Backpropagation neural network

Sample selection (exemplars)Training group 232 set of data

Cross validation group 20 set of dataTest group 60 set of data

e number (hidden layers) Layer 1 and layer 2Transfer Tanh AxonLearning rule Levenberg MarquaMaximum epochs e default value is 200 increased by the amount

Termination (1) e minimum tolerable range (MSE)(2) e maximum training period (epochs)

Cumulative weights update method Batch

Layer 1 Layer 2 Layer 3 Layer 4 Layer 5

X

X

X

Y

Y

Y

W2

W1 W1

W2

W1

W2

f

f2

f1

A1

A2

B1

B2

N

N

prod

prod

sum

sumsum

Figure 9 Structure of ANFIS model used in this study


Table 3 gives the result when inserting the remaining 60sets of data as the test group data of the model into the bestpredicted model of this research e MAPE is 1094 forone-input and 1087 for two-input e absolute error ratecan be reduced by increasing the model input for examplethe average ultrasonic velocity and the standard deviation

42 Prediction of Adaptive Neural Fuzzy Inference System(ANFIS) e MATLAB environment and command win-dow for ANFIS model development and process are setupwith four different numbers of attribution functions to eachinput (this research uses 2 3 4 and 5) and eight kinds ofattribution function types trimf trapmf gbellmf gaussmfgauss2mf pimf dsigmf and psigmf A total of 32 ANFISprediction models are established In order to observewhether there is a better predictive result this study attemptsthree things First is to increase the input of the model theaverage ultrasonic wave velocity and the standard deviationas inputs of the ANFIS predictive concrete strength modelSecond is to compare the different attributive function typesird is to compare the MAPE of the actual concretestrength and the strength predicted by the model Table 4shows the MAPE when examining the accuracy in pre-diction e average value of the ultrasonic wave is used asthe input variable of ANFIS Result shows that one-inputwith 5 attribution functions gives smallest MAPE of 937and 918 for two-input model

Similar to ANN model validation the same 60 test dataare used to validate the best ANFIS training model forvalidation purpose e obtained MAPE from these 60 testdata is shown in Table 5

43 Result Analysis e outputs that predict the estimatedconcrete compressive strength are compared directly withthe actual compressive strength obtainedemean absolutepercentage error MAPE of the linear and nonlinear re-gression are 1117 and 1766 respectively and the ac-curacy is not enough e best predictive model is based onthe adaptive neurocognitive fuzzy inference system and theaverage absolute error percentage MAPE is 986 e re-search results can provide valuable information when UPVtests are used to estimate concrete compressive strength It isalso proved that the accuracy of the prediction is higher

when using the artificial intelligence algorithme artificialintelligence method used to establish the prediction modeldoes improve the prediction accuracy of concrete com-pressive strength as shown in Table 6

Table 7 is the result of the prediction model establishedby different methods in this study e artificial intelli-gence method does improve the prediction accuracy ofconcrete compressive strength prediction model isstudy attempted to increase the input variable of the modelfor example the average velocity of the ultrasonic pulsevelocity and standard deviation As shown in Table 7by increasing the number of input variables from one totwo the prediction results from both ANN and ANFISmodels are slightly improved In order to understand thetype of model and parameter settings and the concretestrength prediction accuracy it is necessary to comparethe result using the linear regression and nonlinear re-gression e mean absolute percentage error MAPE ob-tained by linear regression and nonlinear regression are1117 and 1766 respectively And the ANN is 10940for one-input and 1087 for two-input e best pre-dictive model is based on the adaptive neurocognitiveinference system with the average absolute error percentageMAPE of 986

e results in Table 7 show that the model does improvethe prediction accuracy of concrete compressive strengthWhen attempting to increase the input of the model theresults show that the minimum error rate of the concrete isless than 1087 and 979 respectively for ANN andANFIS e results are better than the predictions of thesingle input which proves that the increase in the input ofthe model can reduce the absolute error percentage

5 Conclusions

To improve the result of nondestructive tests the averagevelocity of ultrasonic waves obtained from each specimenwas calculated Adaptive neurocognitive inference system(ANFIS) and the neural network (ANN) method are usedto predict the compressive strength of concrete Within 312test samples 252 test samples are randomly chosen to bethe train data in this study e remaining 60 test samplesare set as the test data to evaluate the prediction modelaccuracy

Table 2 Artificial neural network model training result

One-input (single entry) Two-input (double entry)Network type Hidden layer Number of training R2 MAPE () Network type Hidden layer Number of training R2 MAPE ()1-1-1 1 200 073 1479 2-1-1 1 200 073 12851-1-1 1 500 074 1137 2-1-1 1 500 074 10631-1-1 1 1000 074 1452 2-1-1 1 1000 074 12431-3-1 1 2000 073 1048 2-3-1 1 2000 075 10461-5-1 1 2000 075 1098 2-2-1 1 2000 074 10581-1-1 1 2000 074 1093 2-7-1 1 2000 073 10961-1-1 1 3000 074 1291 2-1-1 1 3000 074 10611-1-1 1 5000 074 1349 2-1-1 1 5000 073 14791-1-1 1 7500 074 1308 2-1-1 1 7500 074 12841-1-1 1 15000 074 1431 2-1-1 1 15000 075 13231-1-1 1 20000 074 1145 2-1-1 1 20000 074 1101


e results show that traditional concrete compressivestrength estimations have an average of over 20 meanabsolute percentage error when compared with the actualcompressive strength obtained by destructive tests eMAPE in predicting the compressive strength for linear andnonlinear regression models are 1117 and 1766 re-spectively Based on the result obtained the combined twodifferent artificial intelligence methods in establishinga predictive strength model becomes more reliable and the

prediction is more accurate When compared with thepredictions from the other two models with one-input(average ultrasonic pulse wave velocity) the best MAPEvalues of 1094 and 986 were obtained by the ANN testand ANFIS test respectively In addition the predictionresults from two-input (average ultrasonic pulse wave ve-locity and standard deviation) show that the minimum errorrates of the concrete are 1087 and 979 which imply thatthe results are better than the predictions of the one input

Table 5 Results of the test group data into the ANFIS

Attribution function Number of function Standard deviation Input typeMAPE ()

Training TestingGbellmf 5 1390 Single entry 937 986Trapmf 5 1395 Double entry 918 979

Table 6 Comparison of ANFIS ANN linear and nonlinear regression model prediction accuracy

Forecasting model Prediction formula and parameter setting Standard deviation Single entry (MAPE )Linear regression fc 03713Vminus 11628 1680 1117Nonlinear regression fc 08648 exp(00015V) 2313 1766

AIANN test Network type (1-3-1) 1642 1094

ANFIS test e number of functions 5 1390 986Function type Gbellmflowastfc is the compressive strength and V is the average wave speed

Table 7 ANN and ANFIS model prediction accuracy

Forecasting model Parameter setting Standard deviationMAPE ()

One-input Two-inputANN model Hidden layer 1634 1094 1087

ANFIS model e number of functions [5 5] 1995 986 979Function type (trapmf)

Table 3 Results of the test group data into the ANN

Network type Hidden layer R2 Standard deviation Input typeMAPE ()

Training Testing1-3-1 1 074 1642 Single entry 1048 10942-3-2 1 075 1634 Double entry 1046 1087

Table 4 Adaptive neuro-fuzzy inference system (ANFIS) model

Attribution functionMAPE () MAPE ()

One-input number of functions Two-input number of functions[2] [3] [4] [5] [2 2] [3 3] [4 4] [5 5]

Trimf 1004 980 966 980 998 994 1005 1046Trapmf 1026 1094 948 1000 1052 1094 1043 918Gbellmf 973 989 946 937 968 989 1040 956Gaussmf 976 1001 941 976 977 1085 1028 994Gauss2mf 978 1001 949 988 1018 1054 1026 1098Pimf 1048 1050 1050 1050 1073 1066 1031 1049Dsigmf 1015 997 946 969 1011 1056 1067 1058Psigmf 1015 991 946 943 1011 1057 1067 1056Trimf 1004 980 966 980 998 994 1005 1046Trapmf 1026 1094 948 1000 1052 1094 1043 918


For the collected sample the research results have shownthat the increase in the input of the model can reduce themean absolute percentage error

Data Availability

e research data are collected in collaboration with a localmaterial testing laboratory in Taiwan e testing samplebelongs to the local labrsquos customer e authors have signeda nondisclosure agreement to keep the raw data informationconfidential e authors can only mention certain amountof raw data according to the requirement of not publishingthe completed set of raw data but only the analytical data

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] Y R Wang W T Kuo S S Lu et al ldquoApplying supportvector machines in rebound hammer testrdquo Advanced Mate-rials Research vol 853 pp 600ndash604 2014

[2] B S Mohammed N J Azmi and M Abdullahi ldquoEvaluationof rubbercrete based on ultrasonic pulse velocity and reboundhammer testsrdquo Construction and Building Materials vol 25no 3 pp 1388ndash1397 2011

[3] R Pucinotti ldquoReinforced concrete structure non destructivein situ strength assessment of concreterdquo Construction andBuilding Materials vol 75 pp 331ndash341 2015

[4] J-S Chou and A-D Pham ldquoEnhanced artificial intelligencefor ensemble approach to predicting high performanceconcrete compressive strengthrdquo Construction and BuildingMaterials vol 49 pp 554ndash563 2013

[5] B Vakhshouri and S Nejadi ldquoPrediction of compressivestrength of self-compacting concrete by ANFIS modelsrdquoNeurocomputing vol 280 pp 13ndash22 2018

[6] F Khademi S M Jamal N Deshpande and S LondheldquoPredicting strength of recycled aggregate concrete usingartificial neural network adaptive neuro-fuzzy inferencesystem and multiple linear regressionrdquo International Journalof Sustainable Built Environment vol 5 no 2 pp 355ndash3692016

[7] K Behfarnia and F Khademi ldquoA comprehensive study on theconcrete compressive strength estimation using artificialneural network and adaptive neuro-fuzzy inference systemrdquoIran University of Science and Technology vol 7 no 1pp 71ndash80 2017

[8] S T Bhat and C W Lovell Use of Coal Combustion Residuesand Foundry Sands in Flowable Fill Publication FHWAINJHRP-9602 Joint Highway Research Project Indiana De-partment of Transportation and Purdue University WestLafayette IN USA 1996

[9] ACI-229R Controlled-Low Strength Materials AmericanConcrete Institute Farmington Hills MI USA 2005

[10] K Komlos S Popovics T Nurnbergerova B Babal andJ S Popovics ldquoUltrasonic pulse velocity test of concreteproperties as specified in various standardsrdquo Cement andConcrete Composites vol 18 no 5 pp 357ndash364 1996

[11] F Khademi and S M Jamal ldquoPredicting the 28 days com-pressive strength of concrete using artificial neural networkrdquoi-managerrsquos Journal on Civil Engineering vol 6 no 2 2016

[12] M Nikoo P Zarfam and M Nikoo ldquoDetermining dis-placement in concrete reinforcement building with usingevolutionary artificial neural networksrdquo World Applied Sci-ences Journal vol 16 no 12 pp 1699ndash1708 2012

[13] D Padmini K Ilamparuthi and K P Sudheer ldquoUltimatebearing capacity prediction of shallow foundations on co-hesionless soils using neuro fuzzy modelsrdquo Computers andGeotechnics vol 35 no 1 pp 33ndash46 2008

[14] S Kahraman ldquoEvaluation of simple methods for assessing theuniaxial compressive strength of rockrdquo International Journalof Rock Mechanics and Mining Science vol 38 no 7pp 981ndash994 2001

[15] H Y Qasrawi ldquoConcrete strength by combined non-destructive methods simply and reliably predictedrdquo Cementand Concrete Research vol 30 no 5 pp 739ndash746 2000

[16] M Nehdi H E Chabib and A Naggar ldquoPredicting per-formance of self-compacting concrete mixtures using artificialneural networksrdquo ACI Materials Journal vol 98 no 5pp 394ndash401 2001

[17] G Trtnink B Kavcic and G Turk ldquoPredicting of concretestrength using ultrasonic pulse velocity and artificial neuralnetworksrdquo Ultrasonics vol 49 no 1 pp 53ndash60 2009

[18] IT Yusuf Y A Jimoh and W A Salami ldquoAn appropriaterelationship between flexural strength and compressivestrength of palm kernel shell concreterdquo Alexandria Engi-neering Journal vol 55 no 2 pp 1553ndash1562 2016

[19] T R Naik V M Malhotra and J S PopovicsGe UltrasonicPulse Velocity Method Handbook on Non-Destructive Testingof Concrete CRC Press Boca Raton FL USA 2004

[20] American Concrete Institute (ACI 228) Non-Destructive TestMethods for Evaluation of Concrete in Structures ACI 2282R-98 Farmington Mills MI USA 1998

[21] SC Kou CS Poon and HW Wan ldquoProperties of concreteprepared with low-grade recycled aggregatesrdquo Constructionand Building Materials vol 36 pp 881ndash889 2012

[22] R Latif Al Mufti and AN Fried ldquoe early age non-destructive testing of concrete made with recycled concreteaggregaterdquo Construction and Building Materials vol 37pp 379ndash386 2012

[23] G Barluenga J Puentes and I Palomar ldquoEarly age mon-itoring of self-compacting concrete with mineral additionsrdquoConstruction and Building Materials vol 77 pp 66ndash732015

[24] M Molero I Segura M A G Izquierdo J V Fuente andJ J Anaya ldquoSandcement ratio evaluation on mortar usingneural networks and ultrasonic transmission inspectionrdquoUltrasonics vol 49 no 2 pp 231ndash237 2009

[25] S O Naffa M Goueygou B Piwakowski and F Buyle-BodinldquoDetection of chemical damage in concrete using ultrasoundrdquoUltrasonics vol 40 no 1ndash8 pp 247ndash251 2002

[26] M Ohtsu M Shigeishi and Y Sakata ldquoNon-destructiveevaluation of defects in concrete by quantitative acousticemission and ultrasonicsrdquo Ultrasonics vol 36 no 1ndash5pp 187ndash195 1998

[27] J A Bogas M G Gomes and A Gomes ldquoCompressivestrength evaluation of structural lightweight concrete by non-destructive ultrasonic pulse velocity methodrdquo Ultrasonicsvol 53 no 5 pp 962ndash972 2013

[28] R J Sztukiewicz ldquoApplication of ultrasonic methods in as-phalt concrete testingrdquo Ultrasonics vol 29 no 1 pp 5ndash121991

[29] M Colombo and R Felicetti ldquoNew NDT techniques for theassessment of fire-damaged concrete structuresrdquo Fire SafetyJournal vol 42 no 6-7 pp 461ndash472 2007


[30] BSI Method for Determination of Compressive Strength ofConcrete Cubes BS 1881 Part116 British Standards In-stitution London UK 1983

[31] T Catalina V Iordache and B Caracaleanu ldquoMultiple re-gression model for fast prediction of the heating energy de-mandrdquo Energy and Buildings vol 57 pp 302ndash312 2013

[32] S S K Kwok and E W M Lee ldquoA study of the importance ofoccupancy to building cooling load in prediction by intelligentapproachrdquo Energy Conversion andManagement vol 52 no 7pp 2555ndash2564 2011

[33] B Dong C Cao and S E Lee ldquoApplying support vectormachines to predict building energy consumption in tropicalregionrdquo Energy and Buildings vol 37 no 5 pp 545ndash5532005

[34] Y Wu H Wang B Zhang et al ldquoUsing radial basis functionnetworks for function approximation and classificationrdquoISRN Applied Mathematics vol 2012 Article ID 32419434 pages 2012

[35] J L Rogers ldquoSimulating structural analysis with neuralnetworkrdquo Journal of Computing in Civil Engineering vol 8no 2 pp 252ndash265 1994

[36] J Ghaboussi and A Joghataite ldquoActive control of structuresusing neural networksrdquo Journal of Engineering Mechanicsvol 121 no 4 pp 555ndash567 1995

[37] J Sobhani M Najimi A R Pourkhorshidi and T ParhizkarldquoPrediction of the compressive strength of no-slump concretea comparative study of regression neural network and ANFISmodelsrdquo Construction and Building Materials vol 24 no 5pp 709ndash718 2010

[38] Z Yuan L N Wang and X Ji ldquoPrediction of concretecompressive strength research on hybrid models geneticbased algorithms and ANFISrdquo Advances in EngineeringSoftware vol 67 pp 156ndash163 2014

[39] Q Zhou ldquoEstimation of compressive strength of hollowconcrete masonry prisms using artificial neural networks andadaptive neuro-fuzzy inference systemsrdquo Construction andBuilding Materials vol 125 pp 417ndash426 2016

[40] P J L Adeodato A L Arnaud G C VasconcelosR C L V Cunha and D S M P Monteiro ldquoEnsemblesimprove long term prediction accuracy over single networksrdquoInternational Journal of Forecasting vol 27 no 3 pp 661ndash671 2001

[41] F Khademi and K Behfarnia ldquoEvaluation of concretecompressive strength using artificial neural network andmultiple linear regression modelsrdquo Iran University of Scienceamp Technology vol 6 no 3 pp 423ndash432 2016

[42] W Shixiang ldquoANFIS applied to concrete compressionstrength prediction moderdquo Masterrsquos thesis National Kaoh-siung University of Applied Science and Technology of CivilEngineering and Disaster Prevention Technology Kaohsiung2012

[43] J H Bungey J H Millard and M G Grantham Testing ofConcrete In Structures Taylor amp Francis New York NY USA2006

[44] B Ahmadi-Nedushan ldquoPrediction of elastic modulus ofnormal and high strength concrete using ANFIS and optimalnonlinear regression modelsrdquo Construction and BuildingMaterials vol 36 pp 665ndash673 2012

[45] M G Hernandez M A G Izquierdo A Ibantildeez J J Anayaand L G Ullate ldquoPorosity estimation of concrete by ultra-sonic NDErdquo Ultrasonics vol 38 no 1ndash8 pp 531ndash533 2000

[46] SILVER SCHMIDT Electronic Concrete Test Hammer EnkayEnterprises Information httpwwwenkaymachineorgproceq6htm

[47] L Y Yu and S Yong ldquoe relationship between the com-pressive strength of concrete slabs and rebound hammerresearchrdquo Taiwan National Kaohsiung University of AppliedScience and Technology vol 37 no 2 2008

[48] J S Chou and D K Bui ldquoModeling heating and cooling loadsby artificial intelligence for energy-efficient building designrdquoEnergy and Buildings vol 82 pp 437ndash446 2014

[49] T M S Elhag and A H Boussabaine ldquoTender price esti-mation using artificial neural networks II modellingrdquoJournal of Financial Management of Property and Construc-tion vol 7 no 1 pp 49ndash64 2002

[50] T M S Elhag ldquoCost modeling neural networks vs regressiontechniquesrdquo in Proceedings of International Conference onConstruction Information Technology (INCITE) ConstructionIndustry Development Board Malaysia (CIDB) LangkawiMalaysia May 2004

[51] M B Jaksa and H R Maier ldquoFuture challenges for artificialneural network modeling in geotechnical engineeringrdquo inProceedings of 12th International Conference of InternationalAssociation for Computer Methods and Advances in Geo-mechanics (IACMAG) Goa India October 2008

[52] A A Shah S H Alsayed H Y Abbas and A Al-SalloumldquoPredicting residual strength of non-linear ultrasonicallyevaluated damaged concrete using artificial neural networkrdquoConstruction and Building Materials vol 29 pp 42ndash50 2012

[53] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Prentice-Hall International Inc Upper SaddleRiver NJ USA 2015


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Control Scienceand Engineering

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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


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Hindawi

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Submit your manuscripts atwwwhindawicom

In concrete the actual compressive strength is theunconfined one or the self-compacted one [8] One of theNDT methods commonly used to measure the actualcompressive strength is UPV test UPV test is done basedon the principle of measuring the travelling time of anultrasonic pulse in concrete sample en the ultrasonicpulse velocity is obtained Based on the velocity in-formation the actual compressive strength of concretesample is evaluated It is shown in previous researches thatthe higher the ultrasonic pulse velocity the better thequality of concrete sample [9 10]

e compressive strength of concrete is predicted usinga constructed prediction model Since there are many waysto construct this prediction model Kademi [11] stated thatusing multiple linear regression to develop the model cannotgive an accurate prediction of compressive strength Arti-ficial neural network on the other hand is more suitable forestimating the property of concrete sample [12 13]

is research aims to improve the prediction of concretecompressive strength in UPV test with the help of ANNs andANFIS A linear and a nonlinear regression predictionmodels were developed en 312 test samples that un-derwent UPV testing from a local laboratory were collected252 out of the 312 test samples were randomly chosen to bethe training dataset e remaining 60 test samples wereused to evaluate the accuracy of the prediction modeldeveloped

e rest of this paper is organized as follows Section 2 isthe literature review the methodology of the research isdescribed in Section 3 the prediction results are discussed inSection 4 and the conclusion is discussed in Section 5

2 Literature Review

Since destructive testing is not preferable in some applica-tions nondestructive testing methods have attracted lots ofinterests in the field of concrete structure assessment NDTdoes not require much on sample preparation and its testingequipment is quite simple [14] erefore NDT can beapplied easily and economically to assess concrete structureproperties In addition due to the limitation of laboratoryequipment NDTmethods are preferable for the predictionprocess [15] Based on the relationship between strength andNDTparameters the strength of concrete will be evaluatede detail information of the empirical relationship betweenstrength and NDT parameters is provided by the NDTequipment manufacturers e information provided isdirectly related to the testing system used in NDTmethodsand it is not always suitable for all type of concrete Hencethe calibration of different types of concrete is necessary[16 17] UPV testing method is one of the most popularNDT methods that is successfully used to evaluate theproperty of concrete

Ultrasonic pulse velocity (UPV) test uses the propaga-tion of sound wave through material to measure the depth ofmaterial It also gives information on damages inside thematerial From the data measured by UPV test the materialstrength and low-strain elastic modulus can be calculated orpredicted [18ndash20] It has been shown in [21] that UPV of

concrete is inversely proportional to the volume of poresinside and develops with age of the concrete e UPV rateof change can be used to determine the setting of concreteand give inside information on the changes at the micro-structural level of concrete in early ages [22 23] e re-search in [24] found the effect of microstructural variationson UPV in mortar is is used to estimate the sand contentin mortar UPV testing is also used to detect damages insideconcrete effectively in [25 26] UPV testing has been shownto be the effective testing method for different types ofconcrete such as lightweight or asphalt concrete in [27ndash29]UPV testing measures the ultrasonic wave speed when itpenetrates through materials in order to predict the strengthof the materials find any changes in condition of the ma-terials internal flaws and other factors UPV techniquehowever is not always practical for all types of concretesamples Since there is sound wave related to the method itis not accurate for samples that have internal water-filledcracks and rough surfaces [30] To increase the accuracy ofthe testing for rough surfaces a coupling gel is applied inbetween the transducer of testing equipment and roughnesssamples to smoothen the contact layer Many studies havebeen conducted in detail to investigate the correlation be-tween UPV and concrete strength however not many lit-erature results on the correlation between parameters ofUPV and properties of concrete have been found[17 19 20 27] In addition there are many factors that affectthe one important parameter of UPV the ultrasonic pulsevelocity is leads to the derivation on the relationshipbetween UPV parameters and concrete properties unreliable[17] erefore the risk level in the evaluating process mustbe defined quantitatively Recently artificial intelligenttechnology has been employed into predicting the com-pressive strength of concrete In addition to using UPV testthe adaptive neuro fuzzy inference system (ANFIS) and theartificial neural network (ANN) are used to give moreprecise prediction on the compressive strength under var-ious conditions of the mix proportion of concrete [24 31] Itstates in [32 33 34] that inverse modelling of concretecompressive strength has been developed with statisticaltechniques or artificial intelligent techniques Among AItechniques ANNs is quite popular and user friendly for theprocess after the prediction model is established One ad-vantage of ANNs is that there is no requirement in definingthe explicit input-output relationship as in the conventionalregression In ANNs the neuron used is the informationprocessing system unit is system unit consists of con-nection links and summationactivation functions Eachneuron receives input and weights from neurons belongingto the previous layer of this neuron in the training process[34] e learning process in ANNs is adaptive ApplyingANNs does not require any prior knowledge of the func-tional relationship among the variables e distributedprocessing system of ANNs is a parallel one that consists ofone input and one output layer and one or more hiddenlayers connecting by neurons ere are different types ofANNs developed like the multilayer feed-forward neuralnetwork or the cascade-forward neural network [35] Ap-plying ANNs in predicting the compressive strength of












UCS aebV

(1)







v l

t103 (2)














concrete column









u 1113944m

j1wjxj + b (4)

y f(u) (5)

f(u) 1 + eminusu

1minus eminusu (6)







Bias b

Activationfunction

Outputy

Summingfunction

Inputs Weights

sum f (bull)

w1

w2

wm

x1

x2

xm



Receive amplifier

Ultrasonic Plulser


L e Specimen length













1234567891011121314151617

336332337309336346351374364370184288291283300298277

252253254255256257258259260261262263264265256267268

4057540425406039704095405040903975

400753890

3757540254005

400254060

397753895

287291296292165172170337333303305299153153284286262

398250394500400750401250356000357750351500398750400000397000395500394500352750358250407250403750381250




Input Output



Input Output



4005

40575

40425

4060

3970

4095

4050

4090

3975

40075

3890

37575

4025

4005

40025

4060

325

336

332

337

309

336

346

351

374

364

370

184

288

291

283

300

3234327743

3497252102

3417911436

351048794

3114835861

3689149015

3457499542

3664795062

3127353884

3245278274

3097138242

2058672991

3328012024

3234327743

3223638208

351048794

048

408

295

417

080

980

007

441

1638

1084

1629

1188

1556

1115

1391

1702



Average wavespeed










MAPE 1n

1113944

n

i1

Ai minusPi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (7)















X

X

X

Y

Y

Y

W2

W1 W1

W2

W1

W2

f

f2

f1

A1

A2

B1

B2

N

N

prod

prod

sum

sumsum










5 Conclusions



























Data Availability




References


























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












UCS aebV

(1)







v l

t103 (2)














concrete column









u 1113944m

j1wjxj + b (4)

y f(u) (5)

f(u) 1 + eminusu

1minus eminusu (6)







Bias b

Activationfunction

Outputy

Summingfunction

Inputs Weights

sum f (bull)

w1

w2

wm

x1

x2

xm



Receive amplifier

Ultrasonic Plulser


L e Specimen length













1234567891011121314151617

336332337309336346351374364370184288291283300298277

252253254255256257258259260261262263264265256267268

4057540425406039704095405040903975

400753890

3757540254005

400254060

397753895

287291296292165172170337333303305299153153284286262

398250394500400750401250356000357750351500398750400000397000395500394500352750358250407250403750381250




Input Output



Input Output



4005

40575

40425

4060

3970

4095

4050

4090

3975

40075

3890

37575

4025

4005

40025

4060

325

336

332

337

309

336

346

351

374

364

370

184

288

291

283

300

3234327743

3497252102

3417911436

351048794

3114835861

3689149015

3457499542

3664795062

3127353884

3245278274

3097138242

2058672991

3328012024

3234327743

3223638208

351048794

048

408

295

417

080

980

007

441

1638

1084

1629

1188

1556

1115

1391

1702



Average wavespeed










MAPE 1n

1113944

n

i1

Ai minusPi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (7)















X

X

X

Y

Y

Y

W2

W1 W1

W2

W1

W2

f

f2

f1

A1

A2

B1

B2

N

N

prod

prod

sum

sumsum










5 Conclusions



























Data Availability




References


























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




v l

t103 (2)














concrete column









u 1113944m

j1wjxj + b (4)

y f(u) (5)

f(u) 1 + eminusu

1minus eminusu (6)







Bias b

Activationfunction

Outputy

Summingfunction

Inputs Weights

sum f (bull)

w1

w2

wm

x1

x2

xm



Receive amplifier

Ultrasonic Plulser


L e Specimen length













1234567891011121314151617

336332337309336346351374364370184288291283300298277

252253254255256257258259260261262263264265256267268

4057540425406039704095405040903975

400753890

3757540254005

400254060

397753895

287291296292165172170337333303305299153153284286262

398250394500400750401250356000357750351500398750400000397000395500394500352750358250407250403750381250




Input Output



Input Output



4005

40575

40425

4060

3970

4095

4050

4090

3975

40075

3890

37575

4025

4005

40025

4060

325

336

332

337

309

336

346

351

374

364

370

184

288

291

283

300

3234327743

3497252102

3417911436

351048794

3114835861

3689149015

3457499542

3664795062

3127353884

3245278274

3097138242

2058672991

3328012024

3234327743

3223638208

351048794

048

408

295

417

080

980

007

441

1638

1084

1629

1188

1556

1115

1391

1702



Average wavespeed










MAPE 1n

1113944

n

i1

Ai minusPi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (7)















X

X

X

Y

Y

Y

W2

W1 W1

W2

W1

W2

f

f2

f1

A1

A2

B1

B2

N

N

prod

prod

sum

sumsum










5 Conclusions



























Data Availability




References


























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



u 1113944m

j1wjxj + b (4)

y f(u) (5)

f(u) 1 + eminusu

1minus eminusu (6)







Bias b

Activationfunction

Outputy

Summingfunction

Inputs Weights

sum f (bull)

w1

w2

wm

x1

x2

xm



Receive amplifier

Ultrasonic Plulser


L e Specimen length













1234567891011121314151617

336332337309336346351374364370184288291283300298277

252253254255256257258259260261262263264265256267268

4057540425406039704095405040903975

400753890

3757540254005

400254060

397753895

287291296292165172170337333303305299153153284286262

398250394500400750401250356000357750351500398750400000397000395500394500352750358250407250403750381250




Input Output



Input Output



4005

40575

40425

4060

3970

4095

4050

4090

3975

40075

3890

37575

4025

4005

40025

4060

325

336

332

337

309

336

346

351

374

364

370

184

288

291

283

300

3234327743

3497252102

3417911436

351048794

3114835861

3689149015

3457499542

3664795062

3127353884

3245278274

3097138242

2058672991

3328012024

3234327743

3223638208

351048794

048

408

295

417

080

980

007

441

1638

1084

1629

1188

1556

1115

1391

1702



Average wavespeed










MAPE 1n

1113944

n

i1

Ai minusPi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (7)















X

X

X

Y

Y

Y

W2

W1 W1

W2

W1

W2

f

f2

f1

A1

A2

B1

B2

N

N

prod

prod

sum

sumsum










5 Conclusions



























Data Availability




References


























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












1234567891011121314151617

336332337309336346351374364370184288291283300298277

252253254255256257258259260261262263264265256267268

4057540425406039704095405040903975

400753890

3757540254005

400254060

397753895

287291296292165172170337333303305299153153284286262

398250394500400750401250356000357750351500398750400000397000395500394500352750358250407250403750381250




Input Output



Input Output



4005

40575

40425

4060

3970

4095

4050

4090

3975

40075

3890

37575

4025

4005

40025

4060

325

336

332

337

309

336

346

351

374

364

370

184

288

291

283

300

3234327743

3497252102

3417911436

351048794

3114835861

3689149015

3457499542

3664795062

3127353884

3245278274

3097138242

2058672991

3328012024

3234327743

3223638208

351048794

048

408

295

417

080

980

007

441

1638

1084

1629

1188

1556

1115

1391

1702



Average wavespeed










MAPE 1n

1113944

n

i1

Ai minusPi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (7)















X

X

X

Y

Y

Y

W2

W1 W1

W2

W1

W2

f

f2

f1

A1

A2

B1

B2

N

N

prod

prod

sum

sumsum










5 Conclusions



























Data Availability




References


























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









MAPE 1n

1113944

n

i1

Ai minusPi

Ai

11138681113868111386811138681113868111386811138681113868

11138681113868111386811138681113868111386811138681113868 (7)















X

X

X

Y

Y

Y

W2

W1 W1

W2

W1

W2

f

f2

f1

A1

A2

B1

B2

N

N

prod

prod

sum

sumsum










5 Conclusions



























Data Availability




References


























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









5 Conclusions



























Data Availability




References


























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
























Data Availability




References


























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Data Availability




References


























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

ApplyingAdaptiveNeuralFuzzyInferenceSystemtoImprove ...downloads.hindawi.com/journals/ace/2018/2451915.pdfgreased to adherence between the sample and mold after casting.After2-3daysofcasting,thespecimensareslightly