on the modeling of energy efficiency indices of agricultural tractor driving wheels applying...

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Journal of Terramechanics 56 (2014) 37–47

ofTerramechanics

Research Paper

On the modeling of energy efficiency indices of agriculturaltractor driving wheels applying adaptive neuro-fuzzy inference system

Hamid Taghavifar ⇑, Aref Mardani

Department of Mechanical Engineering of Agricultural Machinery, Faculty of Agriculture, Urmia University, Iran

Received 22 October 2013; received in revised form 11 August 2014; accepted 14 August 2014

Abstract

The objective is to assess the potential of adaptive neuro-fuzzy inference system (ANFIS) for the prediction of energy efficiency indicesof driving wheels (i.e. traction coefficient and tractive power efficiency). The output parameters were evaluated as affected by the tireparameters of wheel load at three different levels, velocity at three different levels and slippage at three different levels with three repli-cations forming a total of 81 data points. ANFIS with a hybrid method of the gradient descent and the least-squares method was appliedto find the optimal learning parameters using various membership functions (MFs). Statistical performance parameters of mean squareerror (MSE) and coefficient of determination, R2, were considered as the modeling evaluation criteria. The implementations divulged thatGaussian membership function (gaussmf) and Trapezoidal membership function (tramf) configurations were found to denote MSE of0.0166 and R2 of 0.98 for traction coefficient while MSE equal to 1.5676 and R2 equal to 0.97 for the tractive power efficiency wereobtained.� 2014 ISTVS. Published by Elsevier Ltd. All rights reserved.

Keywords: ANFIS; Energy efficiency; Traction coefficient; Tractive power efficiency

1. Introduction

Off-road vehicles especially agricultural wheeledmachines are of major sources of energy consumptiondue to their massive size and complex soil-wheel interactionthat forms stochastic tire deflection and soil deforma-tion [1]. As documented in literature, the soil-tire interfaceis responsible for approximately 20–55% of the losses oftractor power, a factor that drastically affects the amountof fuel used in drawbar – implement applications [2,3]. Inaddition, Gill and Vanden Burg [4] estimated a national

http://dx.doi.org/10.1016/j.jterra.2014.08.002

0022-4898/� 2014 ISTVS. Published by Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Address: Department of MechanicalEngineering of Agricultural Machinery, Faculty of Agriculture, UrmiaUniversity, Nazloo Road, Urmia 571531177, Iran. Tel.: +98 441 2770508;fax: +98 441 277 1926.

E-mail addresses: [email protected], [email protected] (H. Taghavifar).

annual fuel loss of 575 million liters due to the mismanage-ment of off-road vehicles at the soil-traction interfaces inagricultural applications alone. It is essential to take drasticmeasures in concern with the minimization of energy lossand maximization of energy efficiency of the off-road vehi-cles. Of the significant parameters administering the perfor-mance of driving wheels are tire parameters such as wheelload, velocity, slippage, and tire inflation pressure. For theagricultural tractors the term net traction, which is the sub-traction of gross traction created at the soil-tire interfaceand rolling resistance, is the most prominent objective tobe increased. However, net traction is affected by numeroussoil and tire parameters added with soil-interaction prod-ucts such as contact area, tire deflection, and soil sinkage.For a certain farmland, however, administration of tireparameters is more beneficial than those of terrain specifi-cations. In order to assess the influence of different appliedparameters on the overall tractive performance of driving


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38 H. Taghavifar, A. Mardani / Journal of Terramechanics 56 (2014) 37–47

wheels, indices such as traction coefficient and tractivepower efficiency are utilized. It is reported that the tractionproperties of agricultural tires are of special importancebecause the tractive efficiency varies in a wide range to amaximum of 75% [5]. This confirms the lowest energywaste of at least 25% in the optimal operating conditionwhich is more in the real term situation.

There are many studies dedicated to the investigation ofthe effect of tire parameters on tractive performance ofdriving wheels [5–11]. The attempts in these studies werefocused on experiments to get a better insight into thesoil-wheel interaction and then to propose mathematical-based models or to assess the previously introducedequations. However, these equations were afflicted tounavoidable simplifications due to the complexity of ana-lytical models. Furthermore, elastic–plastic characteristicof soil substance along with the stochastic behavior ofwheel dynamic should be added to the difficulties of pre-dicting by conventional models [1]. It is well-documentedthat soil-machine traction equations are an essential partof vehicle performance simulation [12]. Wismer and Luthattempted to predict the traction of off-road machines bydeveloping a number of mathematical equations. However,various artificial intelligence (AI) techniques are applied tosolve stochastic problems in different science and engineer-ing disciplines.

Roul et al. [13] considered a 5–9–1 artificial neural net-work (ANN) structure, with a back propagation learningalgorithm, to simulate draught requirements of differenttillage implements in a sandy clay loam soil under varyingoperating and soil conditions. Carman and Taner [3]applied a 1-4-6-2 ANN topology with a back propagationlearning algorithm to estimate the tractive performance ofa driven tire in a clay loam soil under varying operatingand soil conditions. The input parameter of the networkwas only travel reduction (slippage) where the outputparameters of the network were net traction ratio and trac-tive efficiency. There are studies documented in the litera-ture regarding the application of various artificialintelligence techniques for tractive performance of wheels[14–18].

To the best knowledge of authors, literature lacks theassessment of energy efficiency indices of driving wheels(i.e. traction coefficient and tractive power efficiency) asaffected by wheel load, slippage and forward velocityemploying artificial intelligence techniques, particularlyANFIS as a promising approach in this realm. In Ref.[3], the authors included only the travel reduction as theinput parameter of their study which detracted the reliabil-ity of the model since there are many influential parametersaffecting the tractive performance parameters of off-roadvehicles such as wheel load and velocity. In contradictoryto Ref. [3], the present study is aimed at inclusion of wheelload, slippage and forward velocity in the proposed modelfor introducing a more general model using a supervisedANFIS model rather than ANN technique owing to theinherent drawbacks of ANN.

2. Experimental data acquisitioning

A soil bin facility featuring 24 m length, 2 m width and1 m depth was adopted to carry out the considered exper-iments. The soil bin system consisted of a single-wheel tes-ter, a carriage device, control panel, and soil processingequipment. At both sides, a rail road was used to assistthe motioning of the carriage and the attached singlewheel-tester along the soil channel. To pull the carriagethrough the chain system an electromotor with the powerof 22 kW at the nominal rotational speed of 1457 rpmwas applied. A SV 220IS5 – 2 N O, 380V model of LGinverter (brand LS) for rotational speed of the enginewas applied that provided the speed control for the carriageusing the chain system. This facility assisted the forwardand reverse movements of the carriage hub.

An L-shape frame connected the wheel-tester and thecarriage. An induction motor of 5 kW, 3-phase, 1430 syn-c rev/min was applied to provide driving power for thewheel. The speed of the motor was primarily reduced bya gear box (7.5:1) then decreased by a gear reduction unit(4.5:1) and the latest reduction ratio was (33.75:1). The dif-ference between the velocity imposed to the single-wheeltester and the carriage velocity provided various slippagelevels. A general view of the soil bin facility and single-wheel tester is demonstrated in Fig. 1. The tire was directlydriven by the electromotor. An electric motor and an inver-ter were used to impose desired rotational speed for wheel.The difference between imposed rotational speed for wheel-tester and carriage speed provided preferred slippage levels.The utilized tire for experimentations was a 220/65R21driving tire. The inflation pressure was adjusted at 19 psi(131 kPa) suggested by the manufacturer. As appreciatedfrom Fig. 1, tester hub and the L-shape frame of carriageare linked through a four-bar mechanism each of whichare horizontally situated and accommodate a load cell forthe measurement of wheel tractive performance. The dataacquisition system for the test is placed on the carriage.Four load cells were positioned on four parallel arms tomeasure the horizontal forces to determine the net tractionforce and another load cell was located on a bolt power ofwheel to measure the vertical load on the wheel. The verti-cal load cell transmitted data to a separated digital indica-tor. Load cells sent data to a Bongshin digital indicatorBS722 model and from output digital indicator by RS232port to a data logger. In addition to synchronization, datawere sent by USB port to a computer and then were stored.The general experiment plan and soil properties and aregiven in Tables 1 and 2, respectively.

After the data were obtained, it was intended to com-pute the energy efficiency indices of driving wheels (i.e.traction coefficient and tractive power efficiency). Asdefined by [19] tractive power efficiency is obtained asfollowing:

gt ¼Output power

Inputpower¼ P � V

H � V 0

ð1Þ

Fig. 1. General depiction of the soil bin system setup for experimental phase of the study.

Table 1Summary of experiment conducted.

Independent Parameters Dependent parameter

Wheel load(kN)

Slippage(%)

Velocity(m/s)

2 8 0.83 12 1 Traction coefficient4 15 1.2 Tractive power efficiency

Table 2Soil constituents and its measured properties.

Item Value

Sand (%) 34.3Silt (%) 22.2Clay (%) 43.5Bulk density (kg/m3) 2360Frictional angle (�) 32Cone index (kPa) 700

H. Taghavifar, A. Mardani / Journal of Terramechanics 56 (2014) 37–47 39

Considering that:

vv0

¼ ð1� iÞ ð2Þ

And P = H � R:

gt ¼PHð1� iÞ ð3Þ

In addition, traction coefficient is obtained as:

lt ¼PW

ð4Þ

where P is the net traction (kN), R is rolling resistance(kN), W is wheel load (kN), i is slippage (%), V is actual

velocity (m/s), V0 is the theoretical velocity (m/s) and H

is gross traction (kN) defined as following:

H ¼Z A

0

cþ WA

tan u

� �dA ð5Þ

where A is the contact area (m2), c is the cohesion, W is thewheel load (kN) and u is the internal friction angle. c and uare defined in Table 2 which is in concern with the soilproperties. A (i.e. contact area) for each of treatments wereobtained by image processing technique. A white colorpowder was poured on the periphery of the wheel at soil-tire interface under each treatment and images were takensimultaneously. A Panasonic LUMIX DMC TZ25 camerawas used for taking the required images at a constant dis-tance while a 4 � 4 cm index was used for calibration inimage processing technique for determination of the areahaving the pixels of images. The images were taken inRGB environment where illumination is combined withcolor that a small change in color space can affect the colorof image significantly. Therefore, it is necessary to use aspace that color and illumination are separated. Using s(saturation) component in HSV color space and b compo-nent in LAB space, a preferred separation of tire track andbackground was achieved. First, the components were nor-malized in the range between 0 and 1 while m is intensityvalue for normalization. For improving the separation,the Gamma transform was applied as following.

X 1 ¼ ðsþ mÞ ð6ÞX 2 ¼ xa

1 ð7Þwhere a = 2 was found as an optimal degree for separa-tions. Furthermore, dilation was performed with structuralelements equivalent to ball. Otsu method, which is used to


automatically perform clustering-based image threshold-ing, or, the reduction of a graylevel image to a binaryimage, was applied to achieve the desired thresholding leveland the binary images were obtained. Structural elementclosing was also used for deletion of noise effects on theimages. Subsequently, connected components which hadpixels lower than a definite level were removed and the con-nected region was filled [1,8].

3. Adaptive neuro-fuzzy inference system

Adaptive neuro-fuzzy inference system (ANFIS) is amultilayer feed-forward network to map an input spaceto an output space by fusion of artificial neural networklearning algorithms and fuzzy inference system. To enablea system to manage cognitive indecisions in a method moresimilar to humans, neural networks have been fused withfuzzy logic, according to” neuro-fuzzy method” [20].

Although ANN is a powerful technique for modelingvarious real-world problems, it has its own shortcomings.If the input data are ambiguous or subject to a relativelyhigh uncertainty, a fuzzy system such as ANFIS may bea better option. Furthermore, adaptive-neuro fuzzy infer-ence system (ANFIS) which is the combination of artificialneural networks and fuzzy logic system inherits both theadvantageous of aforementioned techniques. Whereas ithas been reported that ANN is a promising tool for manycomplex modeling problems, it suffers from some draw-backs such as the case that the input data are less preciseand in such condition it is hard to deal with ANN imple-mentation. Therefore, a fuzzy system such as ANFISmay be a beneficial alternative.

Using a given input/output data set, ANFIS constructsa fuzzy inference system (FIS) whose membership functionparameters are tuned using either a back-propagation algo-rithm alone or in combination with a least squares type ofmethod. The corresponding parameters of MFs are chan-ged during the learning process and the adjustment of theseparameters is conducted through a gradient vector. Thegradient vector provides an evaluation measure for theassessments of ANFIS modeling performance. ANFISadopts two methods for principle parameters that definemembership functions, ANFIS practices gradient descentto tune the parameters. For consequent parameters thatdefine the coefficients of each output equations, ANFISuses the least-squares method to identify them. Thisapproach is referred as to hybrid learning method as itcombines gradient descent and the least-squares method.The architecture of an ANFIS model with three input vari-ables is depicted in Fig. 2. A typical rule set with twentyseven fuzzy IF–THEN rules for the first-order Sugenofuzzy model is the following:

� Rule 1: IF x = A1, y = B1 and z = C1 THEN f1 = p1

x + q1 y + r1z + s1


x + q2 y + r2 z + s2


x + q3 y + r3 z + s3


x + q4 y + r4 z + s4


x + q5 y + r5 z + s5


x + q6 y + r6 z + s6


x + q7 y + r7 z + s7


x + q8 y + r8z + s8


x + q9 y + r9z + s9


x + q10 y + r10z + s10


x + q11 y + r11z + s11


x + q12 y + r12z + s12


x + q13 y + r13z + s13


x + q14 y + r14z + s14


x + q15 y + r15z + s15


x + q16 y + r16z + s16


x + q17 y + r17z + s17


x + q18 y + r18z + s18


x + q19 y + r19z + s19


x + q20 y + r20z + s20


x + q21 y + r21 z + s21


x + q22 y + r22 z + s22


x + q23 y + r23 z + s23


x + q24 y + r24 z + s24


x + q25 y + r25 z + s25


x + q26 y + r26 z + s26


x + q27 y + r27 z + s27

Including input layer into considerations, ANFIS struc-ture includes six layers. The authors, to avoid paper overextension, describe the procedure briefly.

� First layer is the input layer which has n nodes where nis the representative of the system inputs number.

Fig. 2. Adaptive neuro-fuzzy inference system structure.


� Second layer is the fuzzification in which each node rep-resents a membership function. The node function of anode i can be expressed by:

O1i ¼ lAjðxÞ; j ¼ 1; 2; 3

O1i ¼ lBk

ðyÞ; k ¼ 1; 2; 3

O1i ¼ lCl

ðzÞ; l ¼ 1; 2; 3

ð8Þ

where x, y, and z are the inputs to node i, lAj(x),lBjðyÞ

and lClðzÞ are the membership function of the linguistic

variables Ai, Bj, and Ck, respectively.� Third layer provides the strength of the rule by means of

multiplication operator in each node.

O2i ¼ wi ¼ lAjðxÞlBkðyÞlCl

ðzÞ; j; k; l ¼ 1; 2; 3 ð9Þ

� Fourth layer is the normalization layer which normal-izes the firing strength of the rules according to the fol-lowing equation where w is the normalized firingstrengths of the rules:

w1¼ wiw1þw2þw3þw4þw5þw6þw7þw8þw9

; i¼1;2;3;4;5;6;7;8;9


; i¼10;11;12;13;14;15;16;17;18


; i¼19;20;21;22;23;24;25;26;27

ð10Þ

� Fifth layer consists adaptive nodes each of which com-putes a linear function whose coefficients referred to asconsequent parameters are adapted by using the errorfunction of the feed-forward neural network [21].

j¼ 1;2;3

wif i ¼ wiðpj;k;lxþ qj;k;lyþ rj;k;lzþ sj;k;lÞ k ¼ 1;2;3

l¼ 1;2;3

ð11Þ

� Sixth layer has a single node which is fixed the summa-tion of the inputs of the nodes in fifth layer. The output fis computed as follows:

f ¼ w1 f 1 þ w2 f 2 þ w3 f 3 ð12ÞANFIS relates the gradient descent methodology to

describe the optimal conditions for tuning the member-ship functions to map input variables to output variables.The main ideology of ANFIS is based on the back-prop-agation gradient descent methodology that quantifieserror signals repetitively from the output layer backwardto the input nodes. However, a hybrid method of the gra-dient descent and the least-squares method was used tofind optimal learning parameters. There are two pathsof forward and backward. In the forward pass, the nodeoutputs go forward until layer 5 and the linear parametersare identified by the least-squares method, while the pre-mise parameters are kept constant in the current cyclethrough the training set. In the backward pass, the errorsignals propagate backward and the non-linear parame-ters are updated by the gradient descent method, whilethe linear parameters are held constant. There were a totalof 81 data points available for three input parameters andtwo output parameters. Therefore, two different ANFISmodels with various MFs were developed to find the bestANFIS models for prediction of the objective parameters.Data were split and shuffled into 80% training and 20%testing portions to avoid the overfitting drawback. Thebelonging of a factor to a fuzzy set is accompanied withmembership functions. The membership function definesthe quality of mapping each point of the input space toa relevant degree of membership varying between 0 and1. The primary amounts for membership functions as well

Table 3The characteristics of the best structure of developed ANFIS architectures; TC: traction coefficient and TPE: tractive power efficiency. The boldfacedvalues show the outperforming models.

Item Type of MF Number of MF MSE for TC R2 for TC MSE for TPE R2 for TPE

Input Output Input Iteration

ANFIS1 dsigmf Linear 3,3,3 50 0.0587 0.94 4.3421 0.93ANFIS2 Gbellmf Linear 3,3,3 50 0.0166 0.98 3.8754 0.94ANFIS3 Pimf Linear 3,3,3 50 0.0428 0.97 3.9746 0.93ANFIS4 Trimf Linear 4,4,4 50 0.0335 0.98 2.2333 0.96ANFIS5 Tramf Linear 3,3,3 50 0.0423 0.97 1.5676 0.97

ANFIS6 Gaussmf Linear 3,4,5 50 0.0243 0.97 3.2148 0.95

Fig. 3. The prototype membership functions of traction coefficient input variables; (a) wheel load (kN), (b) velocity (m/s) and (c) slippage (%).


as number of them is dependent on research stipulation.Various membership functions of (l) Built-in member-ship function composed of difference between twosigmoidal membership functions (dsigmf), (2) generalizedbell-shaped built-in membership function (gbellmf), (3)

P-shaped built-in membership function (pimf), (4)triangular-shaped built-in membership function (trimf),(5) Trapezoidal-shaped built-in membership function(tramf), (6) Gaussian curve built-in membership func-tion (gaussmf), and (7) Sigmoidally shaped built-in

Fig. 4. The prototype membership functions of tractive power efficiency input variables; (a) wheel load (kN), (b) velocity (m/s) and (c) slippage (%).


membership function (sigmf) were adopted in the model-ing implementations. Fuzzy membership functions cantake various forms; however, straight-line functions areadvantageous due to theirs considerable simplicity. Owingto superior accuracy, the uniformly triangular member-ship functions were selected for three input variablesand the output variable. Furthermore, tri-angular func-tions with equal base widths are the simplest possibleand are preferred for practical applications.

In modeling disciplines, it is absolutely essential toassess the performance of developed models by various sta-tistical criterions. The mean square error (MSE) and thecoefficient of determination (R2) are introduced for analysisof model quality as described below, respectively.

MSE ¼ 1

n

Xn

i¼1

Y predicted � Y actual

� �2 ð13Þ

R2 ¼Pn

i¼1ðY predicted � Y actualÞ2Pni¼1ðY predicted � Y meanÞ2

ð14Þ

Where Yactual and Ypredicted are measured and predicted val-ues of the developed models, respectively.

4. Results and discussion

Two different models were considered for the two objec-tive parameters while various MFs were tested to discoverthe highest quality solution for the representations. The

Fig. 5. ANFIS rule viewer and rules of the traction coefficient and the tractive power efficiency models.

Fig. 6. 3D surface curves of traction coefficient as affected by interactions of input parameters; (a) interaction between velocity and wheel load, (b)interaction between velocity and slippage, (c) interaction between wheel load and slippage and (d) 2D plot of traction coefficient vs. slippage at wheel loadof 3 kN.


Fig. 7. 3D surface curves of tractive power efficiency as affected by interactions of input parameters; (a) interaction between velocity and wheel load, (b)interaction between velocity and slippage and (c) interaction between wheel load and slippage.


results for the corresponding objective parameters of trac-tion coefficient and tractive power efficiency are detailed inTable 3. It is noteworthy that the best outperformedANFIS models corresponding to each membership func-tion type are presented in Table 3 while the other represen-tations of different numbers of membership functions arenot included. As it can be appreciated from Table 3, Gauss-ian curve built-in membership function (gaussmf) andTrapezoidal-shaped built-in membership function (tramf)configurations were found to denote MSE of 0.0166 andR2 of 0.98 for traction coefficient where MSE equal to1.5676 and R2 equal to 0.97 for the tractive power efficiencywere obtained. Furthermore, it is deducible that the afore-mentioned ANFIS structures with the hybrid method ofthe gradient descent and the least-squares method for find-ing the optimal learning parameters have yielded the high-est quality solutions to the corresponding problems thanthose of other tested configurations (Table 3). The distribu-tions of the outperforming membership functions for trac-tion coefficient and tractive power efficiency as gaussmf andtramf functions are depicted in Figs. 3 and 4, respectively.The prototype membership functions in Figs. 3 and 4 aredepictions of disparate input variables. As shown in Figs. 3and 4, the membership functions in the y-axis are scaled inthe range between 0 and 1. That is, for the membershipfunctions at any amount of input parameter, a degree of

membership between 0 and 1 is assigned. The x-axis inFigs. 3 and 4 is the range of input parameters of slippage,wheel load and velocity. The belonging of a factor to afuzzy set is accompanied with membership functions. Amembership function (MF) is a curve defines how everypoint in the input is mapped to a membership valuebetween 0 and 1. The input space is sometimes referredto the universe of discourse, a visualized name for a simplenotion. Straight-line functions are beneficial due to theirsconsiderable simplicity where the uniformly triangularmembership functions were selected owing to superioraccuracy. The membership function defines the quality ofmapping each point of the input space to a relevant degreeof membership varying between 0 and 1 and Figs. 3 and 4define the tuned membership functions of each inputparameters mapped between 0 and 1. Fig. 5 shows theassessment of the applied rules in the ANFIS models fortraction coefficient and tractive power efficiency, respec-tively. The typified values of the objective parameters arealso depicted in Fig. 5 at the example averaged multitudesof different input parameters. The Rule Viewer interpretsthe entire fuzzy inference process at once. This shows theuse of the ANFIS system for calculating the output ofthe model for specific input values. On this basis, it is dem-onstrated that at wheel load of 3 kN, velocity of 1 m/s, slip-page of 11.5%, traction coefficient equal to 0.221 is

Fig. 8. The scatter plots of ANFIS predicted values vs. actual values; (a) traction coefficient and (b) tractive power efficiency (%).


obtained (Fig. 5). Additionally, Fig. 5 demonstrates that atthe same input values, the tractive efficiency equal to 26.5%is yielded. The input values in rule reviewer are typicallyaveraged and the corresponding output values are reportedthe averaged values of the input parameters. The red verti-cal lines in the input parameter section of Fig. 5 show theaverage value of each input parameter and the correspond-ing values for the output parameters can be observed inFig. 5. 3D surface curves of traction coefficient and tractivepower efficiency as two energy efficiency indices of drivingwheels that are affected by wheel load, velocity and slip-page are illustrated in Figs. 6 and 7, respectively. As appre-ciated from Fig. 6, traction coefficient increases withincreased wheel load, however, except for the speed isbetween 0.8–0.9 m/s. Additionally, it is perceived thatincrease of slippage led to increased traction coefficient(Fig. 6). This could be attributed to the increase of tangen-tial stress distributions under driving wheel by increment ofslippage multitudes. Moreover, tractive power efficiency

increases with increased wheel load velocity and slippage(Fig. 7). It is noteworthy that the increase trend is obtainedin the range of tested scenario. The obtained results showedthat 2.8 times greater tractive power efficiency is achieveddue to increase of wheel load from 2 to 4 kN. While wheelload had the greatest share, slippage had the lowest sharewith only 19% increase owing to the increment of slippagefrom 8% to 15%. Similar trends have been reported in lit-erature for the effect of wheel load, slippage and velocityon traction coefficient and tractive power efficiency [7,22–24]. The study carried out by Wismer and Luth [12], furtherconfirm the trends of traction coefficient and tractive effi-ciency with respect to slippage. Based on the theoreticalequations developed in Ref. [12], it is clear that tractioncoefficient increases with respect to the slippage exponen-tially. The trendlines of the 2D plot of traction coefficientwith respect to the slippage confirms this trend as presentedin Fig. 6d. Furthermore, it is clear that the tractive effi-ciency increases to a peak value against slippage and then


decreases depending on the wheel load. Hence, our resultsas demonstrated in Figs. 6 and 7 are further confirmed byRef. [12]. The fitting lines are given as y = ax + b for trac-tion coefficient and tractive power efficiency parameterswhere the determined value for a is closer to 1 for ANFISmodel and b is closer to 0 (Fig. 8). Coefficient of determi-nation values of 0.98 and 0.97 for traction coefficient andtractive power efficiency parameters were obtained, respec-tively. These satisfactory results confirm the promisingability of ANFIS-based modeling for prognostication ofenergy efficiency indices of driving wheels.

5. Concluding remarks

The objective was to assess the potential of ANFIS tech-nique for prognostication of energy efficiency indices (i.e.traction coefficient and tractive power efficiency) of drivingwheels. The data were obtained through a soil bin tire test-ing facility at three levels of wheel load, three levels of tireslippage and three levels of velocity with three replicationsforming a total of 81 data points. Various ANFISMFswere tested to discover the supervised ANFIS-based mod-els for the objective parameters. On the basis of statisticalperformance criteria of MSE and R2, it was found thatGaussian curve built-in membership function (gaussmf)and Trapezoidal-shaped built-in membership function(tramf) configurations were found to denote MSE of0.0166 and R2 of 0.98 for traction coefficient where MSEequal to 1.5676 and R2 equal to 0.97 for tractive power effi-ciency were achieved. It was discovered that the tractioncoefficient and tractive power efficiency increase withincreased slippage. Similar trend is valid for the influenceof wheel load on the objective parameters. Whereinincrease of velocity led to increment of tractive power effi-ciency, velocity had no significant effect on tractioncoefficient.

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