Research ArticleApplication of Soft Computing Techniques for theAnalysis of Tractive Properties of a Low-Power AgriculturalTractor under Various Soil Conditions

Katarzyna Pentos Krzysztof Pieczarka and Krzysztof Lejman

Wroclaw University of Environmental and Life Sciences ul J Chełmonskiego 37 51-630 Wrocław Poland

Correspondence should be addressed to Katarzyna Pentos katarzynapentosupwredupl

Received 27 May 2019 Accepted 17 December 2019 Published 10 January 2020

Guest Editor Murari Andrea

Copyright copy 2020 Katarzyna Pentos et alis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Considering the fuel consumption and soil compaction optimization of the performance of tractors is crucial for modernagricultural practices e tractive performance is inuenced by many factors making it dicult to be modeled In this work thetraction force and tractive eciency of a low-power tractor as aected by soil coecient vertical load horizontal deformationsoil compaction and soil moisture were studied e optimal work of a tractor is a compromise between the maximum tractionforce and the maximum tractive eciency Optimizing these factors is complex and requires accurate models To this end theperformances of soft computing approaches including neural networks genetic algorithms and adaptive network fuzzy inferencesystem were evaluated e optimal performance was realized by neural networks trained by backpropagation as well asbackpropagation combined with a genetic algorithm with a coecient of determination of 0955 for the traction force and 0954for the tractive eciency Based onmodels with the best accuracy a sensitivity analysis was performede results showed that thetraction performance is mainly inuenced by the soil type nevertheless the vertical load and soil moisture also exhibited arelatively strong inuence

1 Introduction

e mechanization of agricultural operations is essential formodern agricultural practices Most agricultural operationsare conducted using tractors that exert a high traction force(eg during tilling cultivation and seeding) or a lighttraction force (eg during harvesting and haymaking)Studies have found that 20ndash55 of the available tractorpower is lost because of the interaction between the tires andtopsoil [1] e traction performance of a tractor signi-cantly aects the fuel consumption and eld performanceresulting from soil compaction erefore optimizing theperformance is crucial for tillage management e pa-rameters signicantly inuencing the performance of drivewheels include the tire ination pressures wheel slip andvertical wheel loads [2ndash5]

A mathematical modeling of the soil-tire interactionprocess can help improve the tractor design and minimize

fuel consumption Such models can be based on empiricalsemiempirical or analytical methods [6] Analytical modelshave been developed for predicting traction parameters[7 8] However Tiwari et al emphasized some of the dif-culties limiting the widespread use of analytical modelsincluding the complex tire-soil interaction [6] Semiem-pirical models are based on the vertical deformation of thesoil and the shear deformation of the soil under a tractiondevice Rosca et al proposed using experimentally derivedparameters in semianalytical models to predict the tractionperformance of a driving tractor tire [9] Empirical modelsare simpler than analytical and semiempirical modelshowever their applicability is limited to cases in which theservice and experimental conditions used to develop themodel are similar

e complex soil-tire interaction and the limitations inimplementing the mathematical models described abovehave encouraged researchers to develop models based on

HindawiComplexityVolume 2020 Article ID 7607545 11 pageshttpsdoiorg10115520207607545

soft computing techniques Artificial neural networks(ANNs) have been employed for predicting draught re-quirement of tillage implements under sandy clay loam soilconditions [10] prognosticating the energy efficiency indicesof driven wheels [11] and modeling the relationship be-tween travel reduction-to-net traction ratio and tractiveefficiency [12] Although an ANN is a powerful tool forsolving stochastic and complex problems and can producehighly accurate prediction models more sophisticated(hybrid) soft computing techniques have also beenemployed [13] An ANN-genetic algorithm (GA) has beenused tomodel the power of agricultural tractors as a functionof the wheel load slip and speed [14] and to model thedynamic characteristics of a tractor on sloping terrain [15]Another hybrid method used for modeling complex rela-tionships in the agricultural field is the adaptive networkfuzzy inference system (ANFIS) which combines the ad-vantages of neural networks and fuzzy logic [16 17]

Most studies on topsoil-tire interactions were conductedfor high-power tractors (engine powergt 73 kW) Studiesconcerning low-power tractors (engine powerlt 15 kW) arelacking A high-power tractor is not always necessary Forexample in horticulture vineyards maintenance of greenspaces or in foothill areas on sloping terrain the use of bighigh-power tractors may be difficult Furthermore usinglow-power tractors is likely to reduce machinery costs anddecrease soil compaction as a result of low tractor weight[18] When high traction force is not required the use oflow-power tractors will result in lower fuel consumptionexhaust emissions reduction and reduction of environ-mental pollution

+e tractive properties of agricultural tractors need to beoptimized to minimize fuel consumption However theoptimization process requires an accurate objective func-tion Nevertheless based on measurement data it is rela-tively easy to develop an empirical model of soil-tireinteraction to be used as the objective function for an op-timization algorithm Considering the nonlinearity andcomplexity of a soil-tire interaction soft computing tech-niques can be used to develop highly accurate models

+e objective of this study was to develop ANN ANNtrained by GA ANN trained by backpropagation (BP) andGA and ANFIS models to estimate the traction force ortractive efficiency of a low-power tractor as a function of thesoil coefficient (which is indicative of soil texture as defined inequation (1)) vertical load horizontal deformation soilcompaction and soil moisture Additionally various mod-eling methodologies were compared to determine their ac-curacy in predicting the experimentally measured tractionforce or tractive efficiency An analysis on the importance ofpredictor variables was conducted with highly accuratemodels +e parameters that significantly affect the tractiveproperties and can be varied by the tractor operator to op-timize the traction force and tractive efficiency were found

2 Materials and Methods

21 Experimental Data Acquisition +e tests were con-ducted on the following types of soil sand fine sandy loam

sandy loam and silty clay loam To obtain a universal modelthat can be used for different soil types the soil texture wasdetermined according to the USDA Comprehensive SoilSurvey System [19] +e soil coefficient was calculated asfollows

Sc c1 + c2 + c3

100 (1)

where Sc is the soil coefficient [minus ] c1 is the proportion ofmedium silt in the test sample [] c2 is the proportion offine silt in the test sample [] and c3 is the proportion of clayin the test sample []

Based on equation (1) the values of Sc for sand finesandy loam sandy loam and silty clay loam were calculatedto be 008 021 033 and 068 respectively Table 1 lists thevalues of soil moisture corresponding to various soil typesfield capacity beginning of plant growth inhibition andstrong inhibition of plant growth

A soil bin testing facility (see Figure 1) was used in thelaboratory to provide a controlled environment for evalu-ating the interaction between the soil and the tire +etractive force was measured using a load cell with a mea-surement range of up to 1 kN and a precision of 1N

Low-power tractors are usually equipped with wheelshaving a rim diameter of 10 inches On this type of rim tireswith different overall widths can be mounted eg 400ndash10450ndash10 and 500ndash10 In the case of 500ndash10 tires the contactarea is the largest resulting in a low-unit pressure and lesssoil compaction +erefore this tire is particularly advan-tageous for soils of low compaction because the larger treadblocks are unlikely to penetrate a highly compact soilConversely in the case of highly compact soils a 400ndash10 tirewould be most beneficial as the narrow tread blocks will beable to extend deeper into the soil ensuring an optimumtraction force In this work experiments were conducted onsoils of both low and high compactions +erefore the drivetire Kenda 450ndash10 type K365 for small agricultural tractorswas used for the measurements Considering that tractortires must to some extent be universal the results obtainedfor Kenda 450ndash10 can be extended to other tires manu-factured for low-power tractors

During the measurement the peripheral speed of thewheel was constant and low (03 rads) +e decision to use alow speed value was caused by the need to eliminate theimpact of dynamic phenomena that could affect the resultswhen the tests were performed on soils with different tex-tures+e following five vertical load values were used in thiswork 375 490 638 785 and 932N+e values of the verticalload were chosen on the basis of technical documentationprovided by the manufacturers of the low-power tractors+e average vertical load recommended for low-powertractors is in the range of 800ndash900N+e aim of this researchwas to develop mathematical models of the relationshipsunder study which can subsequently be used for optimizingthe selected operating parameters in order to minimize soilcompaction +erefore the authors selected three values ofthe vertical load all of which were lower than that rec-ommended for low-power tractors +e influence of tireinflation pressure on the tractive properties was not a subject

2 Complexity

of this research +us all the measurements were conductedusing a constant pressure of 016MPa (as recommended bythe tire manufacturer)

For measuring the static-loaded radius the tire deflec-tion under certain vertical load and tire inflation pressureswas determined +e measurement method is detailed inFigure 2(a)

+e static loaded radius was calculated as follows

rs r minus e (2)

where rs is the static loaded radius r is the tire radius whenthe vertical load is equal to 0 and e is the tire deflection

Based on the static loaded radius values and wheel ro-tation angle the horizontal deformation can be calculated asfollows

j α middot rs middot π180

(3)

where j is the horizontal deformation α is the wheel rotationangle and rs is the static loaded radius (see Figure 2(b))

+e result of the measurements conducted using the soilbin testing facility (see Figure 1) was the traction force as afunction of the rotation angle of the wheel For eachcombination of the independent variables the traction forceincreases with an increase in the horizontal deformationConsequently the maximum traction force could not bedetermined +erefore the horizontal deformation thatproduced a wheel slip of 20 (the slip limit accepted in thecase of agricultural tractors) was determined analyticallyand the traction force corresponding to this horizontaldeformation was considered the maximum +e wheel slipdepends on both the horizontal and vertical deformationsHence the horizontal deformation that produces a wheelslip of 20 can be determined only for a certain value of thevertical deformation (affected by vertical load soil type soil

moisture and soil compaction) In this research the verticaldeformation was calculated as an arithmetic mean of themaximum values measured for each soil type+e horizontaldeformation corresponding to this vertical deformation andunder a slip of 20 is found to be 005m +erefore thetraction force measured for a horizontal deformation of005m was considered the maximum To determine therelationship between the traction force and the horizontaldeformation measurements were also taken for horizontaldeformations of 002 003 and 004m (corresponding toslips of 5 10 and 15 respectively)

+e tractive efficiency was calculated as follows

η 1113938

j

0 PT(j)dj

1113938j

0 PT(j)dj + G middot h (4)

where η is the tractive efficiency PT is the traction force (N) jis the horizontal deformation (m) G is the vertical load ofthe wheel (N) and h is the rut depth (m)

Table 2 lists the statistics of the experimental data+e 1600 datasets (the vectors of measured parameters)

obtained during the measurement process were randomlyseparated into training (80) and validation (20) setsTable 2 lists the minimum and maximum input and outputparameter values Prior to utilizing the dataset for modeldevelopment the data were normalized to a range of 0-1using the following equation

NV V minus Vmin

Vmax minus Vmin (5)

where NV is the input or output normalized vector V is theinput or output data Vmax is the maximum of the input oroutput data and Vmin is the minimum of the input or outputdata We followed the methods of Pentos and Pieczarka [20]

Table 1 Values of soil moisture ()

125 field water capacity Field water capacity Beginning of plant growth inhibition Strong inhibition of plant growthSand 1531 1225 1000 700Fine sandy loam 2438 1950 1600 1120Sandy loam 2563 2050 1800 1260Silty clay loam 3781 3025 2700 1890

GM

A

A

A ndash A

12

3 4

PT(t)α(t)

5

Figure 1 Schematic of a soil bin testing facility 1 linear potentiometer 2 wheel 3 box with soil 4 load cell 5 data agent

Complexity 3

22ArtificialNeuralNetworks AnANN is a highly simplifiedmodel of the biological structure of neurons in the humannervous system An ANN is considered an effective substitutefor the empirical and statistical process modeling techniquesand is widely used in agricultural applications In this work afeed-forward neural network namely multilayer perceptron(MLP) was used +e ability of an ANN strongly depends onits topology ie the number of hidden layers and the numberof neurons in these layers +e optimal topology and learningparameters are usually determined by a trial and error methodrequiring many simulations For this study an MLP with asingle hidden layer was chosen as the ANN architecture +einput layer was composed of five nodes (soil coefficient verticalload horizontal deformation soil compaction and soilmoisture) +e number of neurons in the hidden layer was setto a range of 10ndash40 and nonlinear sigmoid neurons wereimplemented in this layer+ere was one neuron in the output

layer producing the predicted value of the traction force ortractive efficiency For each ANN architecture 10 simulationswere performed and as a result 310 ANNs were trained foreach output parameter +e following were the three trainingmethods used for the simulations resilient backpropagationwith and without weight backtracking and a modified globallyconvergent algorithm+e resilient backpropagation algorithmis based on the traditional backpropagation however in thisalgorithm a separate learning rate ηk is used for each weight inthe network and can be changed during the training processContrary to the traditional backpropagation in resilientbackpropagation only the sign of the partial derivatives is usedto indicate the direction of weight updation +e weights weremodified using the following equation [21]

w(t+1)k w

(t)k minus η(t)

k middot signzE(t)

zw(t)k

⎛⎝ ⎞⎠ (6)

Table 2 Statistics of experimental data by the soil type

+e parameter Minimum Maximum Mean Standard deviationHorizontal deformation (m) 001 005 003 001Vertical load (N) 37500 93200 64400 19953

SandSoil compaction (kPa) 20104 57185 38645 12451Soil moisture () 700 1500 1100 291Traction force (N) 6581 59656 28491 11427Tractive efficiency () 504 8555 3361 1743

Fine sandy loamSoil compaction (kPa) 10269 49811 30085 12592Soil moisture () 1100 2400 1776 482Traction force (N) 9978 78763 33994 14015Tractive efficiency () 445 8571 3344 1739

Sandy loamSoil compaction (kPa) 9088 48630 28859 12584Soil moisture () 1300 2600 1950 472Traction force (N) 3609 68361 32627 13330Tractive efficiency () 099 6498 2797 1438

Silty clay loamSoil compaction (kPa) 9589 52083 30836 12813Soil moisture () 1900 3800 2850 681Traction force (N) 4883 77065 36224 15015Tractive efficiency () 205 7377 3180 1491

Nondeformed ground

G = 0 G gt 0

r

e

r s

(a)

j

α

rs

(b)

Figure 2 Method of static loaded radius measurement (a) and graphical representation of the parameters used for horizontal deformationcalculation (b)

4 Complexity

where wk is the kth connection weight and E is the errorfunction Weight backtracking implies weight update re-versal when the sign of the partial derivative changes [22]

Δw(t)k minus Δw(tminus 1)

k ifzE(tminus 1)

zw(t)k

middotzE(t)

zw(t)k

lt 0 (7)

+e modified globally convergent algorithm presentedby Anastasiadis et al is based on resilient backpropagationA new modification to the learning rate is proposed [23]

η(t)i minus

1113936nkkneiη

(t)k middot zE(t)zw

(t)k1113872 1113873 + δ

zE(t)zw(t)i

(8)

where (zE(t)zw(t)i )ne 0 and 0lt δ ltltinfin +is modification

improves the convergence speed and stability of the learningalgorithm

+e ldquoneuralnetrdquo package version 1442 for the R en-vironment (R Foundation for Statistical Computing (httpswwwr-projectorg)) was used for the simulations [24]

23 Artificial Neural Network Combined with GeneticAlgorithm A typical problem with the ANN trained by analgorithm based on backpropagation is the possibility offalling into a local minimum of the error function resultingin a slow convergence +erefore this technique needs to beimproved by hybridizing the ANNwith an optimization toolsuch as the GA +e GA suggested by Holland can be apragmatic alternative to conventional local search methods[25] In this study two hybridizations of the ANN combinedwith GA were used +e first one (ANN+GA) utilizes a GAto realize the optimal allocation for the given networkweights and biases starting from the random values +esecond one (ANN_BP+GA) uses one of the algorithmsbased on backpropagation (resilient backpropagation withand without weight backtracking and modified globallyconvergent algorithm) for initial ANN training +e GA isthen employed for the final optimization starting from theinitial chromosome population produced by the ANNtraining+e chromosome in this work is the vector of genesreal numbers representing the ANN weights and biases +efollowing operations are performed on chromosome pop-ulation during GA selection and genetic operations(crossover and mutation) During the selection the pop-ulation of the chromosomes is chosen based on the fitnessfunction for genetic operations In the selection procedurethe probability that an individual can become a parentshould be higher for higher fitness functions A crossoveroperation is when two individuals (parents) exchange geneswith each other A crossover is performed with probabilityPc which is usually high Mutation is a small random tweakin the chromosome that leads to a new individual It isperformed with probability Pm which is usually low +efunction of a mutation operation is to ensure a higherpopulation diversity consequently preventing the GA fromfalling into local extremes After reaching the maximumgeneration the GA converges to produce the best chro-mosome which represents an optimal or near-optimal so-lution In this work the population size was set to 100

chromosomes the crossover probability was set to 08 andthe mutation probability was set to 001 As a fitnessfunction the root mean square error (RMSE) of the ANNwas used for the validation dataset +e following were thethree selection methods used roulette wheel tournamentselection and fitness proportional selection with fitnesslinear scaling +e genetic operations were performed withlocal arithmetic crossover and uniform random mutationAn R package ldquoGArdquo version 302 for optimization with theGA was used for the simulations [26]

24 Adaptive Network Fuzzy Inference System +e ANFIS isa global search soft computing technique which combinesthe advantages of fuzzy logic and ANN It is based on thefirst-order TakagindashSugeno fuzzy inference system intro-duced by Jang [27] +is machine-learning technique gen-erates fuzzy rules from a given inputoutput dataset and canadjust the membership function parameters directly fromthe data during the training process +e membershipfunction parameters are adjusted using a combination ofgradient descent and the least squares method +e typicalfuzzy IF-THEN rules for the first-order TakagindashSugeno fuzzymodel are as follows

IF x1 A1 andx2 A3 THENf p11x1 + p

12x2 + r

1

IF x1 A2 andx2 A4 THENf p21x1 + p

22x2 + r

2

(9)

+e ANFIS architecture contains a five-layer feed-for-ward neural network Figure 3 shows the architecture used inthe present work

Layer 1 is the fuzzification layer Each node in this layerrepresents a membership function (MF) and defines themembership grades for each set of input +ere are varioustypes of MFs Because a normalized Gaussian function isused in this study the output of this layer is given by

O1n μAn(x) expminus x minus cn( 1113857

2

2σ2n1113888 1113889 (10)

where cn and σn are the parameters that make up a premiseset

Layer 2 is a multiplicative layer Each node uses amultiplication operator and calculates the firing strength ofthe rule as a product of the previous membership grades Forinstance for the first node this is given by

O21 w1 μA1 x1( 1113857μA4 x2( 1113857μA7 x3( 1113857μA10 x4( 1113857μA13 x5( 1113857

(11)

Layer 3 normalizes the firing strength of the rules

O3n wn wn

1113936jwj

(12)

Layer 4 consists adaptive nodes that compute a linearfunction in which the parameters pn and rn are adapted usingthe error function of the feed-forward neural network

O4n wn middot fn wn middot 1113944k

pnkxk + r

n⎛⎝ ⎞⎠ (13)

Complexity 5

of this research +us all the measurements were conductedusing a constant pressure of 016MPa (as recommended bythe tire manufacturer)

For measuring the static-loaded radius the tire deflec-tion under certain vertical load and tire inflation pressureswas determined +e measurement method is detailed inFigure 2(a)

+e static loaded radius was calculated as follows

rs r minus e (2)

where rs is the static loaded radius r is the tire radius whenthe vertical load is equal to 0 and e is the tire deflection

Based on the static loaded radius values and wheel ro-tation angle the horizontal deformation can be calculated asfollows

j α middot rs middot π180

(3)

where j is the horizontal deformation α is the wheel rotationangle and rs is the static loaded radius (see Figure 2(b))

+e result of the measurements conducted using the soilbin testing facility (see Figure 1) was the traction force as afunction of the rotation angle of the wheel For eachcombination of the independent variables the traction forceincreases with an increase in the horizontal deformationConsequently the maximum traction force could not bedetermined +erefore the horizontal deformation thatproduced a wheel slip of 20 (the slip limit accepted in thecase of agricultural tractors) was determined analyticallyand the traction force corresponding to this horizontaldeformation was considered the maximum +e wheel slipdepends on both the horizontal and vertical deformationsHence the horizontal deformation that produces a wheelslip of 20 can be determined only for a certain value of thevertical deformation (affected by vertical load soil type soil

moisture and soil compaction) In this research the verticaldeformation was calculated as an arithmetic mean of themaximum values measured for each soil type+e horizontaldeformation corresponding to this vertical deformation andunder a slip of 20 is found to be 005m +erefore thetraction force measured for a horizontal deformation of005m was considered the maximum To determine therelationship between the traction force and the horizontaldeformation measurements were also taken for horizontaldeformations of 002 003 and 004m (corresponding toslips of 5 10 and 15 respectively)

+e tractive efficiency was calculated as follows

η 1113938

j

0 PT(j)dj

1113938j

0 PT(j)dj + G middot h (4)

where η is the tractive efficiency PT is the traction force (N) jis the horizontal deformation (m) G is the vertical load ofthe wheel (N) and h is the rut depth (m)

Table 2 lists the statistics of the experimental data+e 1600 datasets (the vectors of measured parameters)

obtained during the measurement process were randomlyseparated into training (80) and validation (20) setsTable 2 lists the minimum and maximum input and outputparameter values Prior to utilizing the dataset for modeldevelopment the data were normalized to a range of 0-1using the following equation

NV V minus Vmin

Vmax minus Vmin (5)

where NV is the input or output normalized vector V is theinput or output data Vmax is the maximum of the input oroutput data and Vmin is the minimum of the input or outputdata We followed the methods of Pentos and Pieczarka [20]

Table 1 Values of soil moisture ()

125 field water capacity Field water capacity Beginning of plant growth inhibition Strong inhibition of plant growthSand 1531 1225 1000 700Fine sandy loam 2438 1950 1600 1120Sandy loam 2563 2050 1800 1260Silty clay loam 3781 3025 2700 1890

GM

A

A

A ndash A

12

3 4

PT(t)α(t)

5

Figure 1 Schematic of a soil bin testing facility 1 linear potentiometer 2 wheel 3 box with soil 4 load cell 5 data agent

Complexity 3

22ArtificialNeuralNetworks AnANN is a highly simplifiedmodel of the biological structure of neurons in the humannervous system An ANN is considered an effective substitutefor the empirical and statistical process modeling techniquesand is widely used in agricultural applications In this work afeed-forward neural network namely multilayer perceptron(MLP) was used +e ability of an ANN strongly depends onits topology ie the number of hidden layers and the numberof neurons in these layers +e optimal topology and learningparameters are usually determined by a trial and error methodrequiring many simulations For this study an MLP with asingle hidden layer was chosen as the ANN architecture +einput layer was composed of five nodes (soil coefficient verticalload horizontal deformation soil compaction and soilmoisture) +e number of neurons in the hidden layer was setto a range of 10ndash40 and nonlinear sigmoid neurons wereimplemented in this layer+ere was one neuron in the output

layer producing the predicted value of the traction force ortractive efficiency For each ANN architecture 10 simulationswere performed and as a result 310 ANNs were trained foreach output parameter +e following were the three trainingmethods used for the simulations resilient backpropagationwith and without weight backtracking and a modified globallyconvergent algorithm+e resilient backpropagation algorithmis based on the traditional backpropagation however in thisalgorithm a separate learning rate ηk is used for each weight inthe network and can be changed during the training processContrary to the traditional backpropagation in resilientbackpropagation only the sign of the partial derivatives is usedto indicate the direction of weight updation +e weights weremodified using the following equation [21]

w(t+1)k w

(t)k minus η(t)

k middot signzE(t)

zw(t)k

⎛⎝ ⎞⎠ (6)

Table 2 Statistics of experimental data by the soil type

+e parameter Minimum Maximum Mean Standard deviationHorizontal deformation (m) 001 005 003 001Vertical load (N) 37500 93200 64400 19953

SandSoil compaction (kPa) 20104 57185 38645 12451Soil moisture () 700 1500 1100 291Traction force (N) 6581 59656 28491 11427Tractive efficiency () 504 8555 3361 1743

Fine sandy loamSoil compaction (kPa) 10269 49811 30085 12592Soil moisture () 1100 2400 1776 482Traction force (N) 9978 78763 33994 14015Tractive efficiency () 445 8571 3344 1739

Sandy loamSoil compaction (kPa) 9088 48630 28859 12584Soil moisture () 1300 2600 1950 472Traction force (N) 3609 68361 32627 13330Tractive efficiency () 099 6498 2797 1438

Silty clay loamSoil compaction (kPa) 9589 52083 30836 12813Soil moisture () 1900 3800 2850 681Traction force (N) 4883 77065 36224 15015Tractive efficiency () 205 7377 3180 1491

Nondeformed ground

G = 0 G gt 0

r

e

r s

(a)

j

α

rs

(b)

Figure 2 Method of static loaded radius measurement (a) and graphical representation of the parameters used for horizontal deformationcalculation (b)

4 Complexity

where wk is the kth connection weight and E is the errorfunction Weight backtracking implies weight update re-versal when the sign of the partial derivative changes [22]

Δw(t)k minus Δw(tminus 1)

k ifzE(tminus 1)

zw(t)k

middotzE(t)

zw(t)k

lt 0 (7)

+e modified globally convergent algorithm presentedby Anastasiadis et al is based on resilient backpropagationA new modification to the learning rate is proposed [23]

η(t)i minus

1113936nkkneiη

(t)k middot zE(t)zw

(t)k1113872 1113873 + δ

zE(t)zw(t)i

(8)

where (zE(t)zw(t)i )ne 0 and 0lt δ ltltinfin +is modification

improves the convergence speed and stability of the learningalgorithm

+e ldquoneuralnetrdquo package version 1442 for the R en-vironment (R Foundation for Statistical Computing (httpswwwr-projectorg)) was used for the simulations [24]

23 Artificial Neural Network Combined with GeneticAlgorithm A typical problem with the ANN trained by analgorithm based on backpropagation is the possibility offalling into a local minimum of the error function resultingin a slow convergence +erefore this technique needs to beimproved by hybridizing the ANNwith an optimization toolsuch as the GA +e GA suggested by Holland can be apragmatic alternative to conventional local search methods[25] In this study two hybridizations of the ANN combinedwith GA were used +e first one (ANN+GA) utilizes a GAto realize the optimal allocation for the given networkweights and biases starting from the random values +esecond one (ANN_BP+GA) uses one of the algorithmsbased on backpropagation (resilient backpropagation withand without weight backtracking and modified globallyconvergent algorithm) for initial ANN training +e GA isthen employed for the final optimization starting from theinitial chromosome population produced by the ANNtraining+e chromosome in this work is the vector of genesreal numbers representing the ANN weights and biases +efollowing operations are performed on chromosome pop-ulation during GA selection and genetic operations(crossover and mutation) During the selection the pop-ulation of the chromosomes is chosen based on the fitnessfunction for genetic operations In the selection procedurethe probability that an individual can become a parentshould be higher for higher fitness functions A crossoveroperation is when two individuals (parents) exchange geneswith each other A crossover is performed with probabilityPc which is usually high Mutation is a small random tweakin the chromosome that leads to a new individual It isperformed with probability Pm which is usually low +efunction of a mutation operation is to ensure a higherpopulation diversity consequently preventing the GA fromfalling into local extremes After reaching the maximumgeneration the GA converges to produce the best chro-mosome which represents an optimal or near-optimal so-lution In this work the population size was set to 100

chromosomes the crossover probability was set to 08 andthe mutation probability was set to 001 As a fitnessfunction the root mean square error (RMSE) of the ANNwas used for the validation dataset +e following were thethree selection methods used roulette wheel tournamentselection and fitness proportional selection with fitnesslinear scaling +e genetic operations were performed withlocal arithmetic crossover and uniform random mutationAn R package ldquoGArdquo version 302 for optimization with theGA was used for the simulations [26]

24 Adaptive Network Fuzzy Inference System +e ANFIS isa global search soft computing technique which combinesthe advantages of fuzzy logic and ANN It is based on thefirst-order TakagindashSugeno fuzzy inference system intro-duced by Jang [27] +is machine-learning technique gen-erates fuzzy rules from a given inputoutput dataset and canadjust the membership function parameters directly fromthe data during the training process +e membershipfunction parameters are adjusted using a combination ofgradient descent and the least squares method +e typicalfuzzy IF-THEN rules for the first-order TakagindashSugeno fuzzymodel are as follows

IF x1 A1 andx2 A3 THENf p11x1 + p

12x2 + r

1

IF x1 A2 andx2 A4 THENf p21x1 + p

22x2 + r

2

(9)

+e ANFIS architecture contains a five-layer feed-for-ward neural network Figure 3 shows the architecture used inthe present work

Layer 1 is the fuzzification layer Each node in this layerrepresents a membership function (MF) and defines themembership grades for each set of input +ere are varioustypes of MFs Because a normalized Gaussian function isused in this study the output of this layer is given by

O1n μAn(x) expminus x minus cn( 1113857

2

2σ2n1113888 1113889 (10)

where cn and σn are the parameters that make up a premiseset

Layer 2 is a multiplicative layer Each node uses amultiplication operator and calculates the firing strength ofthe rule as a product of the previous membership grades Forinstance for the first node this is given by

O21 w1 μA1 x1( 1113857μA4 x2( 1113857μA7 x3( 1113857μA10 x4( 1113857μA13 x5( 1113857

(11)

Layer 3 normalizes the firing strength of the rules

O3n wn wn

1113936jwj

(12)

Layer 4 consists adaptive nodes that compute a linearfunction in which the parameters pn and rn are adapted usingthe error function of the feed-forward neural network

O4n wn middot fn wn middot 1113944k

pnkxk + r

n⎛⎝ ⎞⎠ (13)

Complexity 5

22ArtificialNeuralNetworks AnANN is a highly simplifiedmodel of the biological structure of neurons in the humannervous system An ANN is considered an effective substitutefor the empirical and statistical process modeling techniquesand is widely used in agricultural applications In this work afeed-forward neural network namely multilayer perceptron(MLP) was used +e ability of an ANN strongly depends onits topology ie the number of hidden layers and the numberof neurons in these layers +e optimal topology and learningparameters are usually determined by a trial and error methodrequiring many simulations For this study an MLP with asingle hidden layer was chosen as the ANN architecture +einput layer was composed of five nodes (soil coefficient verticalload horizontal deformation soil compaction and soilmoisture) +e number of neurons in the hidden layer was setto a range of 10ndash40 and nonlinear sigmoid neurons wereimplemented in this layer+ere was one neuron in the output

layer producing the predicted value of the traction force ortractive efficiency For each ANN architecture 10 simulationswere performed and as a result 310 ANNs were trained foreach output parameter +e following were the three trainingmethods used for the simulations resilient backpropagationwith and without weight backtracking and a modified globallyconvergent algorithm+e resilient backpropagation algorithmis based on the traditional backpropagation however in thisalgorithm a separate learning rate ηk is used for each weight inthe network and can be changed during the training processContrary to the traditional backpropagation in resilientbackpropagation only the sign of the partial derivatives is usedto indicate the direction of weight updation +e weights weremodified using the following equation [21]

w(t+1)k w

(t)k minus η(t)

k middot signzE(t)

zw(t)k

⎛⎝ ⎞⎠ (6)

Table 2 Statistics of experimental data by the soil type

+e parameter Minimum Maximum Mean Standard deviationHorizontal deformation (m) 001 005 003 001Vertical load (N) 37500 93200 64400 19953

SandSoil compaction (kPa) 20104 57185 38645 12451Soil moisture () 700 1500 1100 291Traction force (N) 6581 59656 28491 11427Tractive efficiency () 504 8555 3361 1743

Fine sandy loamSoil compaction (kPa) 10269 49811 30085 12592Soil moisture () 1100 2400 1776 482Traction force (N) 9978 78763 33994 14015Tractive efficiency () 445 8571 3344 1739

Sandy loamSoil compaction (kPa) 9088 48630 28859 12584Soil moisture () 1300 2600 1950 472Traction force (N) 3609 68361 32627 13330Tractive efficiency () 099 6498 2797 1438

Silty clay loamSoil compaction (kPa) 9589 52083 30836 12813Soil moisture () 1900 3800 2850 681Traction force (N) 4883 77065 36224 15015Tractive efficiency () 205 7377 3180 1491

Nondeformed ground

G = 0 G gt 0

r

e

r s

(a)

j

α

rs

(b)

Figure 2 Method of static loaded radius measurement (a) and graphical representation of the parameters used for horizontal deformationcalculation (b)

4 Complexity

where wk is the kth connection weight and E is the errorfunction Weight backtracking implies weight update re-versal when the sign of the partial derivative changes [22]

Δw(t)k minus Δw(tminus 1)

k ifzE(tminus 1)

zw(t)k

middotzE(t)

zw(t)k

lt 0 (7)

+e modified globally convergent algorithm presentedby Anastasiadis et al is based on resilient backpropagationA new modification to the learning rate is proposed [23]

η(t)i minus

1113936nkkneiη

(t)k middot zE(t)zw

(t)k1113872 1113873 + δ

zE(t)zw(t)i

(8)

where (zE(t)zw(t)i )ne 0 and 0lt δ ltltinfin +is modification

improves the convergence speed and stability of the learningalgorithm

+e ldquoneuralnetrdquo package version 1442 for the R en-vironment (R Foundation for Statistical Computing (httpswwwr-projectorg)) was used for the simulations [24]

23 Artificial Neural Network Combined with GeneticAlgorithm A typical problem with the ANN trained by analgorithm based on backpropagation is the possibility offalling into a local minimum of the error function resultingin a slow convergence +erefore this technique needs to beimproved by hybridizing the ANNwith an optimization toolsuch as the GA +e GA suggested by Holland can be apragmatic alternative to conventional local search methods[25] In this study two hybridizations of the ANN combinedwith GA were used +e first one (ANN+GA) utilizes a GAto realize the optimal allocation for the given networkweights and biases starting from the random values +esecond one (ANN_BP+GA) uses one of the algorithmsbased on backpropagation (resilient backpropagation withand without weight backtracking and modified globallyconvergent algorithm) for initial ANN training +e GA isthen employed for the final optimization starting from theinitial chromosome population produced by the ANNtraining+e chromosome in this work is the vector of genesreal numbers representing the ANN weights and biases +efollowing operations are performed on chromosome pop-ulation during GA selection and genetic operations(crossover and mutation) During the selection the pop-ulation of the chromosomes is chosen based on the fitnessfunction for genetic operations In the selection procedurethe probability that an individual can become a parentshould be higher for higher fitness functions A crossoveroperation is when two individuals (parents) exchange geneswith each other A crossover is performed with probabilityPc which is usually high Mutation is a small random tweakin the chromosome that leads to a new individual It isperformed with probability Pm which is usually low +efunction of a mutation operation is to ensure a higherpopulation diversity consequently preventing the GA fromfalling into local extremes After reaching the maximumgeneration the GA converges to produce the best chro-mosome which represents an optimal or near-optimal so-lution In this work the population size was set to 100

chromosomes the crossover probability was set to 08 andthe mutation probability was set to 001 As a fitnessfunction the root mean square error (RMSE) of the ANNwas used for the validation dataset +e following were thethree selection methods used roulette wheel tournamentselection and fitness proportional selection with fitnesslinear scaling +e genetic operations were performed withlocal arithmetic crossover and uniform random mutationAn R package ldquoGArdquo version 302 for optimization with theGA was used for the simulations [26]

24 Adaptive Network Fuzzy Inference System +e ANFIS isa global search soft computing technique which combinesthe advantages of fuzzy logic and ANN It is based on thefirst-order TakagindashSugeno fuzzy inference system intro-duced by Jang [27] +is machine-learning technique gen-erates fuzzy rules from a given inputoutput dataset and canadjust the membership function parameters directly fromthe data during the training process +e membershipfunction parameters are adjusted using a combination ofgradient descent and the least squares method +e typicalfuzzy IF-THEN rules for the first-order TakagindashSugeno fuzzymodel are as follows

IF x1 A1 andx2 A3 THENf p11x1 + p

12x2 + r

1

IF x1 A2 andx2 A4 THENf p21x1 + p

22x2 + r

2

(9)

+e ANFIS architecture contains a five-layer feed-for-ward neural network Figure 3 shows the architecture used inthe present work

Layer 1 is the fuzzification layer Each node in this layerrepresents a membership function (MF) and defines themembership grades for each set of input +ere are varioustypes of MFs Because a normalized Gaussian function isused in this study the output of this layer is given by

O1n μAn(x) expminus x minus cn( 1113857

2

2σ2n1113888 1113889 (10)

where cn and σn are the parameters that make up a premiseset

Layer 2 is a multiplicative layer Each node uses amultiplication operator and calculates the firing strength ofthe rule as a product of the previous membership grades Forinstance for the first node this is given by

O21 w1 μA1 x1( 1113857μA4 x2( 1113857μA7 x3( 1113857μA10 x4( 1113857μA13 x5( 1113857

(11)

Layer 3 normalizes the firing strength of the rules

O3n wn wn

1113936jwj

(12)

Layer 4 consists adaptive nodes that compute a linearfunction in which the parameters pn and rn are adapted usingthe error function of the feed-forward neural network

O4n wn middot fn wn middot 1113944k

pnkxk + r

n⎛⎝ ⎞⎠ (13)

Complexity 5

where wk is the kth connection weight and E is the errorfunction Weight backtracking implies weight update re-versal when the sign of the partial derivative changes [22]

Δw(t)k minus Δw(tminus 1)

k ifzE(tminus 1)

zw(t)k

middotzE(t)

zw(t)k

lt 0 (7)

+e modified globally convergent algorithm presentedby Anastasiadis et al is based on resilient backpropagationA new modification to the learning rate is proposed [23]

η(t)i minus

1113936nkkneiη

(t)k middot zE(t)zw

(t)k1113872 1113873 + δ

zE(t)zw(t)i

(8)

where (zE(t)zw(t)i )ne 0 and 0lt δ ltltinfin +is modification

improves the convergence speed and stability of the learningalgorithm

+e ldquoneuralnetrdquo package version 1442 for the R en-vironment (R Foundation for Statistical Computing (httpswwwr-projectorg)) was used for the simulations [24]

23 Artificial Neural Network Combined with GeneticAlgorithm A typical problem with the ANN trained by analgorithm based on backpropagation is the possibility offalling into a local minimum of the error function resultingin a slow convergence +erefore this technique needs to beimproved by hybridizing the ANNwith an optimization toolsuch as the GA +e GA suggested by Holland can be apragmatic alternative to conventional local search methods[25] In this study two hybridizations of the ANN combinedwith GA were used +e first one (ANN+GA) utilizes a GAto realize the optimal allocation for the given networkweights and biases starting from the random values +esecond one (ANN_BP+GA) uses one of the algorithmsbased on backpropagation (resilient backpropagation withand without weight backtracking and modified globallyconvergent algorithm) for initial ANN training +e GA isthen employed for the final optimization starting from theinitial chromosome population produced by the ANNtraining+e chromosome in this work is the vector of genesreal numbers representing the ANN weights and biases +efollowing operations are performed on chromosome pop-ulation during GA selection and genetic operations(crossover and mutation) During the selection the pop-ulation of the chromosomes is chosen based on the fitnessfunction for genetic operations In the selection procedurethe probability that an individual can become a parentshould be higher for higher fitness functions A crossoveroperation is when two individuals (parents) exchange geneswith each other A crossover is performed with probabilityPc which is usually high Mutation is a small random tweakin the chromosome that leads to a new individual It isperformed with probability Pm which is usually low +efunction of a mutation operation is to ensure a higherpopulation diversity consequently preventing the GA fromfalling into local extremes After reaching the maximumgeneration the GA converges to produce the best chro-mosome which represents an optimal or near-optimal so-lution In this work the population size was set to 100

chromosomes the crossover probability was set to 08 andthe mutation probability was set to 001 As a fitnessfunction the root mean square error (RMSE) of the ANNwas used for the validation dataset +e following were thethree selection methods used roulette wheel tournamentselection and fitness proportional selection with fitnesslinear scaling +e genetic operations were performed withlocal arithmetic crossover and uniform random mutationAn R package ldquoGArdquo version 302 for optimization with theGA was used for the simulations [26]

24 Adaptive Network Fuzzy Inference System +e ANFIS isa global search soft computing technique which combinesthe advantages of fuzzy logic and ANN It is based on thefirst-order TakagindashSugeno fuzzy inference system intro-duced by Jang [27] +is machine-learning technique gen-erates fuzzy rules from a given inputoutput dataset and canadjust the membership function parameters directly fromthe data during the training process +e membershipfunction parameters are adjusted using a combination ofgradient descent and the least squares method +e typicalfuzzy IF-THEN rules for the first-order TakagindashSugeno fuzzymodel are as follows

IF x1 A1 andx2 A3 THENf p11x1 + p

12x2 + r

1

IF x1 A2 andx2 A4 THENf p21x1 + p

22x2 + r

2

(9)

+e ANFIS architecture contains a five-layer feed-for-ward neural network Figure 3 shows the architecture used inthe present work

Layer 1 is the fuzzification layer Each node in this layerrepresents a membership function (MF) and defines themembership grades for each set of input +ere are varioustypes of MFs Because a normalized Gaussian function isused in this study the output of this layer is given by

O1n μAn(x) expminus x minus cn( 1113857

2

2σ2n1113888 1113889 (10)

where cn and σn are the parameters that make up a premiseset

Layer 2 is a multiplicative layer Each node uses amultiplication operator and calculates the firing strength ofthe rule as a product of the previous membership grades Forinstance for the first node this is given by

O21 w1 μA1 x1( 1113857μA4 x2( 1113857μA7 x3( 1113857μA10 x4( 1113857μA13 x5( 1113857

(11)

Layer 3 normalizes the firing strength of the rules

O3n wn wn

1113936jwj

(12)

Layer 4 consists adaptive nodes that compute a linearfunction in which the parameters pn and rn are adapted usingthe error function of the feed-forward neural network

O4n wn middot fn wn middot 1113944k

pnkxk + r

n⎛⎝ ⎞⎠ (13)

Complexity 5

Layer 5 has a single node and produces the output signalof the ANFIS which is the sum of the outputs of the nodesfrom layer 4

O51 1113944n

O4n (14)

+e package ldquoanfisrdquomdashAdaptive Neurofuzzy InferenceSystem in R version 0991 was used for the simulationsExcessive membership functions in the ANFIS model is notappropriate because many parameters need to be predicted+erefore the number of membership functions was set to 3and the number of iterations was set to 20

25 Comparison Criteria +e accuracy of the models werecompared in terms of the mean absolute error (MAE)RMSE and coefficient of determination (R2) which areexpressed as follows

MAE1n

1113944

n

i1Ypredicted minus Ymeasured

11138681113868111386811138681113868

11138681113868111386811138681113868

RMSE

1n

1113944n

i1Ypredicted minus Ymeasured1113872 1113873

2

11139741113972

R2

1113936 Ymeasured minus Ymean meas( 1113857 Ypredicted minus Ymean predict1113872 1113873

1113936 Ymeasured minus Ymean meas( 111385721113936 Ypredicted minus Ymean predict1113872 1113873

21113969

⎡⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎦

2

(15)

where Ypredicted and Ymean_predict are the absolute and averagepredicted values and Ymeasured and Ymean_meas are the ab-solute and average measured values respectively

+e MAE using the absolute values of the differencesbetween the measured and predicted values rates over- andunderestimations equally +e RMSE is an indicator of thedistribution of positive and negative errors of the estimated

values R2 estimates the strength of the relationship betweenthe output value calculated using a model and the expectedvalue +erefore the closer MAE and RMSE are to 0 and thecloser R2 is to 1 the better is the accuracy of the model inestimating the dependent variable

26 Sensitivity Analysis Based on the mathematical modelthe importance of the independent variables can be esti-mated Many methods have been proposed for modelsensitivity analysis +e relevance of the method depends onthe characteristics of the particular model In this researchthe partial derivatives method dedicated for a neural net-workmodel was used whereby the contribution of the inputvariables is determined based on the connection weights anda bias matrix [28] It is difficult to select an optimal ANNmodel architecture thus the contribution of the predictorvariables should be determined based on a group of ANNmodels [29] In the present research a group of twenty ANNmodels with the highest R2 values and the lowest MAE andRMSE values was selected As the final result for each de-pendent variable (traction force and tractive efficiency) thearithmetical mean of the results produced by the twentyANNs was calculated

3 Results and Discussion

31 Soft ComputingModels +e optimal solution accordingto energy savings is to have high values of both tractionforce and tractive efficiency Figure 4 shows the dependenceof the traction force and tractive efficiency on the verticalload and soil moisture measured on sand for a horizontaldeformation of 005m

As shown in Figure 4 the optimal traction force isproduced under a high vertical load whereas an optimaltractive efficiency can be achieved under a rather low verticalload +erefore achieving an optimal balance between the

x1Soil coefficient

x2Vertical load

π

π

π

π

π

N

N

N

N

N

ΣTraction force

ortraction efficiency

Layer 1 Layer 2 Layer 3 Layer 4 Layer 5

A1

A2

A3

A4

A5

A6

A7

A8

A9

A10

A11

A12

A13

A14

A15

x1x2x3x4x5

x1x2x3x4x5

x1x2x3x4x5

x1x2x3x4x5

x1x2x3x4x5

w5

w4

w3

w2

w1

w5

w4

w3

w2

w1

x4Soil compaction

x5Soil moisture

Horizontaldeformation

x3

Figure 3 Adaptive neurofuzzy inference system structure

6 Complexity

traction force and the tractive efficiency is very difficult andrequires accurate mathematical models of the tractiveproperties

Before the development of the models based on theANN linearly dependent predictor variables must be re-moved from the dataset +erefore Pearsonrsquos correlationcoefficients between the explanatory variables were calcu-lated A high positive correlation was observed only betweenthe soil coefficient and the soil moisture (r 0767) How-ever after analyzing the experimental procedures it wasevident that both soil coefficient and soil moisture must beconsidered as input variables and used for model devel-opment +e correlation coefficient is high because the soilmoisture range (Table 1) was determined depending on thesoil texture

Table 3 lists the statistical parameters namely R2 RMSEand MAE for the best configurations of the mentionedmodels +e calculations were performed using normalizeddata (equation (5))

In the case of the traction force model the best archi-tecture of the ANN was a network with 28 neurons in thehidden layer and this network was chosen for weightsoptimization by the GA +e best ANN architecture trainedby the GA starting from random values (ANN+GA) was anetwork with 14 neurons in the hidden layer+e best neuralnetwork for the tractive efficiency model had 26 neurons inthe hidden layer and the best ANN+GA model contained17 neurons in the hidden layer

Figures 5 and 6 show the measured and predictedtraction force and tractive efficiency values for all the pre-dictive models on the validation dataset +ese graphs showthe number of data points located very close to the diagonalline thus facilitating the assessment of the model accuracy

As listed in Table 3 and shown in Figures 5 and 6 forboth output model parameters among all the computationalmodels the ANN and ANN_BP+GA models exhibit thebest performance as indicated by high values of R2 (0954and 0955 for traction force and 0954 for tractive efficiency)and low values of MAE and RMSE for the validation dataset+e use of the GA for optimizing the weights and biasesadjusted by the BP algorithm produced slightly better ac-curacy in the case of the traction force model +e accuracyof the ANFIS model was lower than those of the ANN andANN_BP+GA models with R2 values below 09 Addi-tionally the computational time required for the calcula-tions during the ANFIS model development wassignificantly higher than that required in the case of modelsbased on MLP +e ANN+GA technique seems to be un-suitable exhibiting a low accuracy in estimating the tractionforce and tractive efficiency (R2 0820 and 0752 for thevalidation dataset respectively) Generally it can be statedthat in agriculture mathematical models (also based onmachine learning) with coefficient of determination (R2)exceeding 09 are useful for real life applications [30]

Neural networks and hybrid methods were also used byother researchers to model the behavior of agriculturaltractors +e ANFIS-based modeling was found to be apromising technique for prognosticating the traction coef-ficient and tractive power efficiency with R2 values of 098

and 097 respectively [17] and for prognosticating thedrawbar pull energy of tractor driving wheels with MSE andR2 values of 000236 and 0995 respectively [16] In the caseof ANN combined with a GA Taghavifar et al demonstratedthat this method drastically decreased the error and in-creased the performance of the model of power provided byagricultural tractors as affected by wheel load slip and speed[14] +ey obtained high values for the coefficient of de-termination for the ANN+GA model 09696 for thetraining dataset and 09672 for validation dataset

Comparing the current results with those presented byother researchers it is unclear which technique most ac-curately models the nonlinear and complex relationshipssuch as the ones investigated in this study Similar resultswere obtained by other researchers Johann et al comparedcomputational models based on ANN and ANFIS in esti-mating the soil moisture from the stochastic information ofthe horizontal and vertical forces acting on a no-till chiselopener using autoregressive error function parameters [31]+e ANN model (R2 079 and RMSE 127) outperformedthe ANFIS model (R2 069 and RMSE 162) in the testphase Citakoglu applied ANN and ANFIS for estimating thesolar radiation in Turkey using the calendar month numberand pertinent meteorological data and obtained a higheraccuracy when using the ANN (R2 0930 andRMSE 1650) in comparison with using the ANFIS(R2 0926 and RMSE 1691) [32] In contrast the ANFISwas found to be more suitable than the ANN for estimatingthe soil cation exchange capacity as affected by clay siltsand organic carbon and pH in arid rangeland ecosystemsand for estimating the oxidation parameters of Kilka oil[33 34] Based on relevant error (RE) values Ping and Feishowed that the accuracy of an ANN combined with a GA(RE 148) is better than that of a traditional ANN model(RE 391) for Guangdong port throughput forecasting[35] Similarly Srinivasulu and Jain found that the predictivecapability of an ANN combined with GA rainfall-runoffmodels is better than that trained using a BP algorithm [36]

32 Sensitivity Analysis A highly accurate mathematicalmodel can give additional information about the relation-ships under study A sensitivity analysis has been performedto determine the contribution of independent variables inblack box data mining models +e neural network trainedby backpropagation combined with a GA was found to bethe best model for the relationships analyzed in the presentresearch +is soft computing technique was used for de-veloping the models for the sensitivity analysis For eachdependent variable (traction force and tractive efficiency) agroup of twenty ANN models was developed Table 4 liststhe parameters of the models

+e results of the relative importance of the input pa-rameters for each model were determined as the arithmeticalmean of the results produced by the group of twenty ANNmodels +e results revealed that the traction force andtractive efficiency are most affected by the soil type (583 and745 respectively) +is is in agreement with the resultsreported by other authors [37 38] +e two additional

Complexity 7

700

600

500

400

300

200

100

1615

1413

1211

109

87

6

1000900

800700

600500

400300

Trac

tion

forc

e (

)

Soil moisture () Vertical load (N)

(a)

1615

1413

1211

109

87

6

1000900

800700

600500

400300

44

42

40

38

36

34

32

30

28

Trac

tive e

ffici

ency

()

Soil moisture () Vertical load (N)

(b)

Figure 4 3D surface curves of traction force (a) and tractive efficiency (b) as affected by the interactions of vertical load and soil moisture

Table 3 Error metrics of best model performances

ModelTrain Validation

MAE RMSE R2 MAE RMSE R2

Traction forceANN 0026 0037 0957 0029 0040 0954ANN+GA 0064 0084 0808 0063 0087 0820ANN_BP+GA 0026 0037 0958 0028 0040 0955ANFIS 0042 0061 0892 0045 0064 0888

Tractive efficiencyANN 0022 0030 0975 0024 0037 0954ANN+GA 0076 0102 0789 0068 0096 0752ANN_BP+GA 0022 0030 0975 0024 0037 0954ANFIS 0038 0061 0883 0040 0064 0872

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0954

(a)

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0820

(b)

Figure 5 Continued

8 Complexity

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0954

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(a)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0752

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(b)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0954

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(c)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0872

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(d)

Figure 6 Scatterplot of model-predicted values versus actual values of tractive efficiency (a) ANN (b) ANN+GA (c) ANN_BP+GA and(d) ANFIS

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0955

(c)

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0888

(d)

Figure 5 Scatterplot of model-predicted values versus actual values of traction force (a) ANN (b) ANN+GA (c) ANN_BP+GA and(d) ANFIS

Table 4 Statistics of neural model architectures used for sensitivity analysis

Dependentvariable

+e range of number of neuronsin hidden layer

+e range of R2 forvalidation dataset

+e range of MAE forvalidation dataset

+e range of RMSE forvalidation dataset

Tractionforce 16ndash40 0944ndash0955 0028ndash0032 0040ndash0045

Tractiveefficiency 16ndash38 0928ndash0954 0024ndash0032 0037ndash0047

Complexity 9

parameters that significantly influenced the traction forceand tractive efficiency are the vertical load (183 and 101respectively) and soil moisture (198 and 103 respec-tively) +e significant effects of these parameters on thetractive performance have been highlighted in other studiesas well [11 39] It is worth emphasizing that the verticalload is one of the more easily manageable parametersduring traction performance optimization Soil moisturecan also be varied in a certain range as the operator canadvance or delay agricultural operation depending on theweather condition +e influence of both horizontal de-formation and soil compaction on the traction perfor-mance is very low (does not exceed 4)

4 Conclusions

+e optimization of the traction performance of an agri-cultural tractor is essential considering fuel economy +edevelopment of highly accurate mathematical models thatdescribe the tractive properties is an integral part of theoptimization process In this work four soft computingtechniques were used for predicting the traction force andtractive efficiency of a low-power tractor as affected by the soiltype (expressed as soil coefficient) vertical load horizontaldeformation soil compaction and soil moisture Compari-sons of the error statistics revealed that the neural networkmodel trained by a traditional BP algorithm or by a com-bination of BP and GA performs better in estimating both thetraction force and tractive efficiency than an ANFIS model oran ANN trained by only a GA An ANN structure with 28neurons in the hidden layer produced the best model of thetraction force with an R2 value of 0954 amean absolute errorof 0029 and an RMSE of 0040 Similarly an ANN with 26neurons in the hidden layer was found to be the best structurefor the tractive efficiency model with R2 0954MAE 0024 and RMSE 0037 Using GA for optimizingthe weights and biases in the ANNmodel trained by BP led toa slight improvement in model accuracy Considering theresults presented by other authors it can be stated that thepotential usability of a certain technique depends strongly onthe data characteristics Moreover the behavior of eachmachine-learning algorithm is affected by its parameters+us for improving the optimization process differenttechniques should be employed and the model with thehighest accuracy should be chosen Considering the com-putational time required for ANFIS model development theneural network trained by the backpropagation algorithmseems to be the best soft computing technique+e results of asensitivity analysis conducted on a group of models with thehighest accuracy showed that the soil type is the parametermost affecting the traction performance of a low-powertractor A relatively strong influence was also found for thevertical load and soil moisture which can be varied by thetractor operator to optimize the traction performance

+e results of this research are expected to be useful insaving energy in agricultural production systems Howeverit should be noted that the application of the empiricalmodels obtained by the authors is limited to conditionssimilar to those present during the measurements

Data Availability

+e data samples used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

+e authors have no conflicts of interest to declare

References

[1] T Smerda and J Cupera ldquoTire inflation and its influence ondrawbar characteristics and performancemdashenergetic indica-tors of a tractor setrdquo Journal of Terramechanics vol 47 no 6pp 395ndash400 2010

[2] A Janulevicius and V Damanauskas ldquoHow to select airpressures in the tires of MFWD (mechanical front-wheeldrive) tractor to minimize fuel consumption for the case ofreasonable wheel sliprdquo Energy vol 90 pp 691ndash700 2015

[3] H Taghavifar A Mardani and H Karim-Maslak ldquoMulti-criteria optimization model to investigate the energy waste ofoff-road vehicles utilizing soil bin facilityrdquo Energy vol 73pp 762ndash770 2014

[4] J H Lee and K Gard ldquoVehicle-soil interaction testingmodeling calibration and validationrdquo Journal of Terra-mechanics vol 52 pp 9ndash21 2014

[5] F M Zoz and R D Grisso ldquoTraction and tractor perfor-mancerdquo in ASAE Distinguished Lecture Series Vol 27American Society of Agricultural Engineers Tractor DesignNo 27 St Joseph MI USA 2003

[6] V K Tiwari K P Pandey and P K Pranav ldquoA review ontraction prediction equationsrdquo Journal of Terramechanicsvol 47 no 3 pp 191ndash199 2010

[7] C W Fervers ldquoImproved FEM simulation model for tire-soilinteractionrdquo Journal of Terramechanics vol 41 no 2-3pp 87ndash100 2004

[8] H Nakashima and A Oida ldquoAlgorithm and implementationof soil-tire contact analysis code based on dynamic FE-DEmethodrdquo Journal of Terramechanics vol 41 no 2-3pp 127ndash137 2004

[9] R Rosca P Carlescu and I Tenu ldquoA semi-empirical tractionprediction model for an agricultural tyre based on the superellipse shape of the contact surfacerdquo Soil and Tillage Researchvol 141 pp 10ndash18 2014

[10] A K Roul H Raheman M S Pansare and R MachavaramldquoPredicting the draught requirement of tillage implements insandy clay loam soil using an artificial neural networkrdquoBiosystems Engineering vol 104 no 4 pp 476ndash485 2009

[11] H Taghavifar and A Mardani ldquoApplying a supervised ANN(artificial neural network) approach to the prognostication ofdriven wheel energy efficiency indicesrdquo Energy vol 68pp 651ndash657 2014

[12] K Ccedilarman and A Taner ldquoPrediction of tire tractive per-formance by using artificial neural networksrdquo Mathematicaland Computational Applications vol 17 no 3 pp 182ndash1922012

[13] S A Hoseinpour A Barati-Harooni P Nadali et al ldquoAc-curate model based on artificial intelligence for prediction ofcarbon dioxide solubility in aqueoustetra-n-butylammoniumbromide solutionsrdquo Journal of Chemometrics vol 32 no 2Article ID e2956 2018

[14] H Taghavifar A Mardani and A H Hosseinloo ldquoAppraisalof artificial neural network-genetic algorithm based model for

10 Complexity

prediction of the power provided by the agricultural tractorsrdquoEnergy vol 93 pp 1704ndash1710 2015

[15] Z X Zhu R Torisu J I Takeda E R Mao and Q ZhangldquoNeural network for estimating vehicle behaviour on slopingterrainrdquo Biosystems Engineering vol 91 no 4 pp 403ndash4112005

[16] H Taghavifar and A Mardani ldquoEvaluating the effect of tireparameters on required drawbar pull energy model usingadaptive neuro-fuzzy inference systemrdquo Energy vol 85pp 586ndash593 2015

[17] H Taghavifar and A Mardani ldquoOn the modeling of energyefficiency indices of agricultural tractor driving wheels ap-plying adaptive neuro-fuzzy inference systemrdquo Journal ofTerramechanics vol 56 pp 37ndash47 2014

[18] N H Abu-Hamdeh ldquo+e disturbance of topsoil using ul-trasonic wavesrdquo Soil and Tillage Research vol 75 no 1pp 87ndash92 2004

[19] N C Brady and R R WeilCe Nature and Properties of SoilsPearson Education International London UK 15th edition2008

[20] K Pentos and K Pieczarka ldquoApplying an artificial neuralnetwork approach to the analysis of tractive properties inchanging soil conditionsrdquo Soil and Tillage Research vol 165pp 113ndash120 2017

[21] G Frauke and S Fritsch ldquoNeuralnet training of neuralnetworksrdquo 2010 httpsjournalr-projectorgarchive2010RJ-2010-006RJ-2010-006pdf

[22] M Riedmiller ldquoAdvanced supervised learning in multi-layerperceptrons-from backpropagation to adaptive learning al-gorithmsrdquo Computer Standards amp Interfaces vol 16 no 3pp 265ndash278 1994

[23] A D Anastasiadis G D Magoulas andM N Vrahatis ldquoNewglobally convergent training scheme based on the resilientpropagation algorithmrdquo Neurocomputing vol 64 pp 253ndash270 2005

[24] S Fritsch F Guenther M NWright M Suling S M Mueller2019 httpscranr-projectorgwebpackagesneuralnetindexhtml

[25] J H Holland Adaptation in Natural and Artificial SystemsUniversity of Michigan Press Ann Arbor MI USA 1975

[26] L G A Scrucca ldquoA package for genetic algorithms in RrdquoJournal of Statistical Software vol 53 no 4 pp 1ndash37 2013

[27] J-S R Jang ldquoANFISmdashadaptive-network-based fuzzy infer-ence systemrdquo IEEE Transactions on Systems Man and Cy-bernetics vol 23 no 3 pp 665ndash685 1993

[28] Y Dimopoulos P Bourret and S Lek ldquoUse of some sensi-tivity criteria for choosing networks with good generalizationabilityrdquo Neural Processing Letters vol 2 no 6 pp 1ndash4 1995

[29] K Pentos ldquo+e methods of extracting the contribution ofvariables in artificial neural network modelsmdashcomparison ofinherent instabilityrdquo Computers and Electronics in Agricul-ture vol 127 pp 141ndash146 2016

[30] K Liakos P Busato D Moshou S Pearson and D BochtisldquoMachine learning in agriculture a reviewrdquo Sensors vol 18no 8 p 2674 2018

[31] A L Johann A G de Araujo H C Delalibera andA R Hirakawa ldquoSoil moisture modeling based on stochasticbehavior of forces on a no-till chisel openerrdquo Computers andElectronics in Agriculture vol 121 pp 420ndash428 2016

[32] H Citakoglu ldquoComparison of artificial intelligence tech-niques via empirical equations for prediction of solar radia-tionrdquo Computers and Electronics in Agriculture vol 118pp 28ndash37 2015

[33] H Ghorbani H Kashi N Hafezi Moghadas andS Emamgholizadeh ldquoEstimation of soil cation exchangecapacity using multiple regression artificial neural networksand adaptive neuro-fuzzy inference system models in Gole-stan province Iranrdquo Communications in Soil Science andPlant Analysis vol 46 no 6 pp 763ndash780 2015

[34] M Asnaashari R Farhoosh and R Farahmandfar ldquoPre-diction of oxidation parameters of purified Kilka fish oilincluding gallic acid and methyl gallate by adaptive neuro-fuzzy inference system (ANFIS) and artificial neural net-workrdquo Journal of the Science of Food and Agriculture vol 96no 13 pp 4594ndash4602 2016

[35] F F Ping and F X Fei ldquoMultivariant forecasting mode ofGuangdong Province port throughput with genetic algo-rithms and Back Propagation neural networkrdquo in Proceedingsfrom the 13th Cota International Conference of TransportationProfessionals vol 96 pp 1165ndash1174 Shenzhen ChinaAugust 2013

[36] S Srinivasulu and A Jain ldquoA comparative analysis of trainingmethods for artificial neural network rainfall-runoff modelsrdquoApplied Soft Computing vol 6 no 3 pp 295ndash306 2006

[37] E V McKyes Soil Cutting and Tillage Elsevier SciencePublishers BV Amsterdam Netherlands 1985

[38] F M Zoz Predicting Tractor Field Performance Vol 49085ASAE St Joseph MI USA 1970

[39] M I Lyasko ldquoHow to calculate the effect of soil conditions ontractive performancerdquo Journal of Terramechanics vol 47no 6 pp 423ndash445 2010

Complexity 11

traction force and the tractive efficiency is very difficult andrequires accurate mathematical models of the tractiveproperties

Before the development of the models based on theANN linearly dependent predictor variables must be re-moved from the dataset +erefore Pearsonrsquos correlationcoefficients between the explanatory variables were calcu-lated A high positive correlation was observed only betweenthe soil coefficient and the soil moisture (r 0767) How-ever after analyzing the experimental procedures it wasevident that both soil coefficient and soil moisture must beconsidered as input variables and used for model devel-opment +e correlation coefficient is high because the soilmoisture range (Table 1) was determined depending on thesoil texture

Table 3 lists the statistical parameters namely R2 RMSEand MAE for the best configurations of the mentionedmodels +e calculations were performed using normalizeddata (equation (5))

In the case of the traction force model the best archi-tecture of the ANN was a network with 28 neurons in thehidden layer and this network was chosen for weightsoptimization by the GA +e best ANN architecture trainedby the GA starting from random values (ANN+GA) was anetwork with 14 neurons in the hidden layer+e best neuralnetwork for the tractive efficiency model had 26 neurons inthe hidden layer and the best ANN+GA model contained17 neurons in the hidden layer

Figures 5 and 6 show the measured and predictedtraction force and tractive efficiency values for all the pre-dictive models on the validation dataset +ese graphs showthe number of data points located very close to the diagonalline thus facilitating the assessment of the model accuracy

As listed in Table 3 and shown in Figures 5 and 6 forboth output model parameters among all the computationalmodels the ANN and ANN_BP+GA models exhibit thebest performance as indicated by high values of R2 (0954and 0955 for traction force and 0954 for tractive efficiency)and low values of MAE and RMSE for the validation dataset+e use of the GA for optimizing the weights and biasesadjusted by the BP algorithm produced slightly better ac-curacy in the case of the traction force model +e accuracyof the ANFIS model was lower than those of the ANN andANN_BP+GA models with R2 values below 09 Addi-tionally the computational time required for the calcula-tions during the ANFIS model development wassignificantly higher than that required in the case of modelsbased on MLP +e ANN+GA technique seems to be un-suitable exhibiting a low accuracy in estimating the tractionforce and tractive efficiency (R2 0820 and 0752 for thevalidation dataset respectively) Generally it can be statedthat in agriculture mathematical models (also based onmachine learning) with coefficient of determination (R2)exceeding 09 are useful for real life applications [30]

Neural networks and hybrid methods were also used byother researchers to model the behavior of agriculturaltractors +e ANFIS-based modeling was found to be apromising technique for prognosticating the traction coef-ficient and tractive power efficiency with R2 values of 098

and 097 respectively [17] and for prognosticating thedrawbar pull energy of tractor driving wheels with MSE andR2 values of 000236 and 0995 respectively [16] In the caseof ANN combined with a GA Taghavifar et al demonstratedthat this method drastically decreased the error and in-creased the performance of the model of power provided byagricultural tractors as affected by wheel load slip and speed[14] +ey obtained high values for the coefficient of de-termination for the ANN+GA model 09696 for thetraining dataset and 09672 for validation dataset

Comparing the current results with those presented byother researchers it is unclear which technique most ac-curately models the nonlinear and complex relationshipssuch as the ones investigated in this study Similar resultswere obtained by other researchers Johann et al comparedcomputational models based on ANN and ANFIS in esti-mating the soil moisture from the stochastic information ofthe horizontal and vertical forces acting on a no-till chiselopener using autoregressive error function parameters [31]+e ANN model (R2 079 and RMSE 127) outperformedthe ANFIS model (R2 069 and RMSE 162) in the testphase Citakoglu applied ANN and ANFIS for estimating thesolar radiation in Turkey using the calendar month numberand pertinent meteorological data and obtained a higheraccuracy when using the ANN (R2 0930 andRMSE 1650) in comparison with using the ANFIS(R2 0926 and RMSE 1691) [32] In contrast the ANFISwas found to be more suitable than the ANN for estimatingthe soil cation exchange capacity as affected by clay siltsand organic carbon and pH in arid rangeland ecosystemsand for estimating the oxidation parameters of Kilka oil[33 34] Based on relevant error (RE) values Ping and Feishowed that the accuracy of an ANN combined with a GA(RE 148) is better than that of a traditional ANN model(RE 391) for Guangdong port throughput forecasting[35] Similarly Srinivasulu and Jain found that the predictivecapability of an ANN combined with GA rainfall-runoffmodels is better than that trained using a BP algorithm [36]

32 Sensitivity Analysis A highly accurate mathematicalmodel can give additional information about the relation-ships under study A sensitivity analysis has been performedto determine the contribution of independent variables inblack box data mining models +e neural network trainedby backpropagation combined with a GA was found to bethe best model for the relationships analyzed in the presentresearch +is soft computing technique was used for de-veloping the models for the sensitivity analysis For eachdependent variable (traction force and tractive efficiency) agroup of twenty ANN models was developed Table 4 liststhe parameters of the models

+e results of the relative importance of the input pa-rameters for each model were determined as the arithmeticalmean of the results produced by the group of twenty ANNmodels +e results revealed that the traction force andtractive efficiency are most affected by the soil type (583 and745 respectively) +is is in agreement with the resultsreported by other authors [37 38] +e two additional

Complexity 7

700

600

500

400

300

200

100

1615

1413

1211

109

87

6

1000900

800700

600500

400300

Trac

tion

forc

e (

)

Soil moisture () Vertical load (N)

(a)

1615

1413

1211

109

87

6

1000900

800700

600500

400300

44

42

40

38

36

34

32

30

28

Trac

tive e

ffici

ency

()

Soil moisture () Vertical load (N)

(b)

Figure 4 3D surface curves of traction force (a) and tractive efficiency (b) as affected by the interactions of vertical load and soil moisture

Table 3 Error metrics of best model performances

ModelTrain Validation

MAE RMSE R2 MAE RMSE R2

Traction forceANN 0026 0037 0957 0029 0040 0954ANN+GA 0064 0084 0808 0063 0087 0820ANN_BP+GA 0026 0037 0958 0028 0040 0955ANFIS 0042 0061 0892 0045 0064 0888

Tractive efficiencyANN 0022 0030 0975 0024 0037 0954ANN+GA 0076 0102 0789 0068 0096 0752ANN_BP+GA 0022 0030 0975 0024 0037 0954ANFIS 0038 0061 0883 0040 0064 0872

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0954

(a)

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0820

(b)

Figure 5 Continued

8 Complexity

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0954

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(a)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0752

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(b)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0954

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(c)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0872

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(d)

Figure 6 Scatterplot of model-predicted values versus actual values of tractive efficiency (a) ANN (b) ANN+GA (c) ANN_BP+GA and(d) ANFIS

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0955

(c)

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0888

(d)

Figure 5 Scatterplot of model-predicted values versus actual values of traction force (a) ANN (b) ANN+GA (c) ANN_BP+GA and(d) ANFIS

Table 4 Statistics of neural model architectures used for sensitivity analysis

Dependentvariable

+e range of number of neuronsin hidden layer

+e range of R2 forvalidation dataset

+e range of MAE forvalidation dataset

+e range of RMSE forvalidation dataset

Tractionforce 16ndash40 0944ndash0955 0028ndash0032 0040ndash0045

Tractiveefficiency 16ndash38 0928ndash0954 0024ndash0032 0037ndash0047

Complexity 9

parameters that significantly influenced the traction forceand tractive efficiency are the vertical load (183 and 101respectively) and soil moisture (198 and 103 respec-tively) +e significant effects of these parameters on thetractive performance have been highlighted in other studiesas well [11 39] It is worth emphasizing that the verticalload is one of the more easily manageable parametersduring traction performance optimization Soil moisturecan also be varied in a certain range as the operator canadvance or delay agricultural operation depending on theweather condition +e influence of both horizontal de-formation and soil compaction on the traction perfor-mance is very low (does not exceed 4)

4 Conclusions

+e optimization of the traction performance of an agri-cultural tractor is essential considering fuel economy +edevelopment of highly accurate mathematical models thatdescribe the tractive properties is an integral part of theoptimization process In this work four soft computingtechniques were used for predicting the traction force andtractive efficiency of a low-power tractor as affected by the soiltype (expressed as soil coefficient) vertical load horizontaldeformation soil compaction and soil moisture Compari-sons of the error statistics revealed that the neural networkmodel trained by a traditional BP algorithm or by a com-bination of BP and GA performs better in estimating both thetraction force and tractive efficiency than an ANFIS model oran ANN trained by only a GA An ANN structure with 28neurons in the hidden layer produced the best model of thetraction force with an R2 value of 0954 amean absolute errorof 0029 and an RMSE of 0040 Similarly an ANN with 26neurons in the hidden layer was found to be the best structurefor the tractive efficiency model with R2 0954MAE 0024 and RMSE 0037 Using GA for optimizingthe weights and biases in the ANNmodel trained by BP led toa slight improvement in model accuracy Considering theresults presented by other authors it can be stated that thepotential usability of a certain technique depends strongly onthe data characteristics Moreover the behavior of eachmachine-learning algorithm is affected by its parameters+us for improving the optimization process differenttechniques should be employed and the model with thehighest accuracy should be chosen Considering the com-putational time required for ANFIS model development theneural network trained by the backpropagation algorithmseems to be the best soft computing technique+e results of asensitivity analysis conducted on a group of models with thehighest accuracy showed that the soil type is the parametermost affecting the traction performance of a low-powertractor A relatively strong influence was also found for thevertical load and soil moisture which can be varied by thetractor operator to optimize the traction performance

+e results of this research are expected to be useful insaving energy in agricultural production systems Howeverit should be noted that the application of the empiricalmodels obtained by the authors is limited to conditionssimilar to those present during the measurements

Data Availability

+e data samples used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

+e authors have no conflicts of interest to declare

References

[1] T Smerda and J Cupera ldquoTire inflation and its influence ondrawbar characteristics and performancemdashenergetic indica-tors of a tractor setrdquo Journal of Terramechanics vol 47 no 6pp 395ndash400 2010

[2] A Janulevicius and V Damanauskas ldquoHow to select airpressures in the tires of MFWD (mechanical front-wheeldrive) tractor to minimize fuel consumption for the case ofreasonable wheel sliprdquo Energy vol 90 pp 691ndash700 2015

[3] H Taghavifar A Mardani and H Karim-Maslak ldquoMulti-criteria optimization model to investigate the energy waste ofoff-road vehicles utilizing soil bin facilityrdquo Energy vol 73pp 762ndash770 2014

[4] J H Lee and K Gard ldquoVehicle-soil interaction testingmodeling calibration and validationrdquo Journal of Terra-mechanics vol 52 pp 9ndash21 2014

[5] F M Zoz and R D Grisso ldquoTraction and tractor perfor-mancerdquo in ASAE Distinguished Lecture Series Vol 27American Society of Agricultural Engineers Tractor DesignNo 27 St Joseph MI USA 2003

[6] V K Tiwari K P Pandey and P K Pranav ldquoA review ontraction prediction equationsrdquo Journal of Terramechanicsvol 47 no 3 pp 191ndash199 2010

[7] C W Fervers ldquoImproved FEM simulation model for tire-soilinteractionrdquo Journal of Terramechanics vol 41 no 2-3pp 87ndash100 2004

[8] H Nakashima and A Oida ldquoAlgorithm and implementationof soil-tire contact analysis code based on dynamic FE-DEmethodrdquo Journal of Terramechanics vol 41 no 2-3pp 127ndash137 2004

[9] R Rosca P Carlescu and I Tenu ldquoA semi-empirical tractionprediction model for an agricultural tyre based on the superellipse shape of the contact surfacerdquo Soil and Tillage Researchvol 141 pp 10ndash18 2014

[10] A K Roul H Raheman M S Pansare and R MachavaramldquoPredicting the draught requirement of tillage implements insandy clay loam soil using an artificial neural networkrdquoBiosystems Engineering vol 104 no 4 pp 476ndash485 2009

[11] H Taghavifar and A Mardani ldquoApplying a supervised ANN(artificial neural network) approach to the prognostication ofdriven wheel energy efficiency indicesrdquo Energy vol 68pp 651ndash657 2014

[12] K Ccedilarman and A Taner ldquoPrediction of tire tractive per-formance by using artificial neural networksrdquo Mathematicaland Computational Applications vol 17 no 3 pp 182ndash1922012

[13] S A Hoseinpour A Barati-Harooni P Nadali et al ldquoAc-curate model based on artificial intelligence for prediction ofcarbon dioxide solubility in aqueoustetra-n-butylammoniumbromide solutionsrdquo Journal of Chemometrics vol 32 no 2Article ID e2956 2018

[14] H Taghavifar A Mardani and A H Hosseinloo ldquoAppraisalof artificial neural network-genetic algorithm based model for

10 Complexity

prediction of the power provided by the agricultural tractorsrdquoEnergy vol 93 pp 1704ndash1710 2015

[15] Z X Zhu R Torisu J I Takeda E R Mao and Q ZhangldquoNeural network for estimating vehicle behaviour on slopingterrainrdquo Biosystems Engineering vol 91 no 4 pp 403ndash4112005

[16] H Taghavifar and A Mardani ldquoEvaluating the effect of tireparameters on required drawbar pull energy model usingadaptive neuro-fuzzy inference systemrdquo Energy vol 85pp 586ndash593 2015

[17] H Taghavifar and A Mardani ldquoOn the modeling of energyefficiency indices of agricultural tractor driving wheels ap-plying adaptive neuro-fuzzy inference systemrdquo Journal ofTerramechanics vol 56 pp 37ndash47 2014

[18] N H Abu-Hamdeh ldquo+e disturbance of topsoil using ul-trasonic wavesrdquo Soil and Tillage Research vol 75 no 1pp 87ndash92 2004

[19] N C Brady and R R WeilCe Nature and Properties of SoilsPearson Education International London UK 15th edition2008

[20] K Pentos and K Pieczarka ldquoApplying an artificial neuralnetwork approach to the analysis of tractive properties inchanging soil conditionsrdquo Soil and Tillage Research vol 165pp 113ndash120 2017

[21] G Frauke and S Fritsch ldquoNeuralnet training of neuralnetworksrdquo 2010 httpsjournalr-projectorgarchive2010RJ-2010-006RJ-2010-006pdf

[22] M Riedmiller ldquoAdvanced supervised learning in multi-layerperceptrons-from backpropagation to adaptive learning al-gorithmsrdquo Computer Standards amp Interfaces vol 16 no 3pp 265ndash278 1994

[23] A D Anastasiadis G D Magoulas andM N Vrahatis ldquoNewglobally convergent training scheme based on the resilientpropagation algorithmrdquo Neurocomputing vol 64 pp 253ndash270 2005

[24] S Fritsch F Guenther M NWright M Suling S M Mueller2019 httpscranr-projectorgwebpackagesneuralnetindexhtml

[25] J H Holland Adaptation in Natural and Artificial SystemsUniversity of Michigan Press Ann Arbor MI USA 1975

[26] L G A Scrucca ldquoA package for genetic algorithms in RrdquoJournal of Statistical Software vol 53 no 4 pp 1ndash37 2013

[27] J-S R Jang ldquoANFISmdashadaptive-network-based fuzzy infer-ence systemrdquo IEEE Transactions on Systems Man and Cy-bernetics vol 23 no 3 pp 665ndash685 1993

[28] Y Dimopoulos P Bourret and S Lek ldquoUse of some sensi-tivity criteria for choosing networks with good generalizationabilityrdquo Neural Processing Letters vol 2 no 6 pp 1ndash4 1995

[29] K Pentos ldquo+e methods of extracting the contribution ofvariables in artificial neural network modelsmdashcomparison ofinherent instabilityrdquo Computers and Electronics in Agricul-ture vol 127 pp 141ndash146 2016

[30] K Liakos P Busato D Moshou S Pearson and D BochtisldquoMachine learning in agriculture a reviewrdquo Sensors vol 18no 8 p 2674 2018

[31] A L Johann A G de Araujo H C Delalibera andA R Hirakawa ldquoSoil moisture modeling based on stochasticbehavior of forces on a no-till chisel openerrdquo Computers andElectronics in Agriculture vol 121 pp 420ndash428 2016

[32] H Citakoglu ldquoComparison of artificial intelligence tech-niques via empirical equations for prediction of solar radia-tionrdquo Computers and Electronics in Agriculture vol 118pp 28ndash37 2015

[33] H Ghorbani H Kashi N Hafezi Moghadas andS Emamgholizadeh ldquoEstimation of soil cation exchangecapacity using multiple regression artificial neural networksand adaptive neuro-fuzzy inference system models in Gole-stan province Iranrdquo Communications in Soil Science andPlant Analysis vol 46 no 6 pp 763ndash780 2015

[34] M Asnaashari R Farhoosh and R Farahmandfar ldquoPre-diction of oxidation parameters of purified Kilka fish oilincluding gallic acid and methyl gallate by adaptive neuro-fuzzy inference system (ANFIS) and artificial neural net-workrdquo Journal of the Science of Food and Agriculture vol 96no 13 pp 4594ndash4602 2016

[35] F F Ping and F X Fei ldquoMultivariant forecasting mode ofGuangdong Province port throughput with genetic algo-rithms and Back Propagation neural networkrdquo in Proceedingsfrom the 13th Cota International Conference of TransportationProfessionals vol 96 pp 1165ndash1174 Shenzhen ChinaAugust 2013

[36] S Srinivasulu and A Jain ldquoA comparative analysis of trainingmethods for artificial neural network rainfall-runoff modelsrdquoApplied Soft Computing vol 6 no 3 pp 295ndash306 2006

[37] E V McKyes Soil Cutting and Tillage Elsevier SciencePublishers BV Amsterdam Netherlands 1985

[38] F M Zoz Predicting Tractor Field Performance Vol 49085ASAE St Joseph MI USA 1970

[39] M I Lyasko ldquoHow to calculate the effect of soil conditions ontractive performancerdquo Journal of Terramechanics vol 47no 6 pp 423ndash445 2010

Complexity 11

700

600

500

400

300

200

100

1615

1413

1211

109

87

6

1000900

800700

600500

400300

Trac

tion

forc

e (

)

Soil moisture () Vertical load (N)

(a)

1615

1413

1211

109

87

6

1000900

800700

600500

400300

44

42

40

38

36

34

32

30

28

Trac

tive e

ffici

ency

()

Soil moisture () Vertical load (N)

(b)

Figure 4 3D surface curves of traction force (a) and tractive efficiency (b) as affected by the interactions of vertical load and soil moisture

Table 3 Error metrics of best model performances

ModelTrain Validation

MAE RMSE R2 MAE RMSE R2

Traction forceANN 0026 0037 0957 0029 0040 0954ANN+GA 0064 0084 0808 0063 0087 0820ANN_BP+GA 0026 0037 0958 0028 0040 0955ANFIS 0042 0061 0892 0045 0064 0888

Tractive efficiencyANN 0022 0030 0975 0024 0037 0954ANN+GA 0076 0102 0789 0068 0096 0752ANN_BP+GA 0022 0030 0975 0024 0037 0954ANFIS 0038 0061 0883 0040 0064 0872

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0954

(a)

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0820

(b)

Figure 5 Continued

8 Complexity

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0954

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(a)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0752

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(b)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0954

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(c)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0872

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(d)

Figure 6 Scatterplot of model-predicted values versus actual values of tractive efficiency (a) ANN (b) ANN+GA (c) ANN_BP+GA and(d) ANFIS

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0955

(c)

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0888

(d)

Figure 5 Scatterplot of model-predicted values versus actual values of traction force (a) ANN (b) ANN+GA (c) ANN_BP+GA and(d) ANFIS

Table 4 Statistics of neural model architectures used for sensitivity analysis

Dependentvariable

+e range of number of neuronsin hidden layer

+e range of R2 forvalidation dataset

+e range of MAE forvalidation dataset

+e range of RMSE forvalidation dataset

Tractionforce 16ndash40 0944ndash0955 0028ndash0032 0040ndash0045

Tractiveefficiency 16ndash38 0928ndash0954 0024ndash0032 0037ndash0047

Complexity 9

parameters that significantly influenced the traction forceand tractive efficiency are the vertical load (183 and 101respectively) and soil moisture (198 and 103 respec-tively) +e significant effects of these parameters on thetractive performance have been highlighted in other studiesas well [11 39] It is worth emphasizing that the verticalload is one of the more easily manageable parametersduring traction performance optimization Soil moisturecan also be varied in a certain range as the operator canadvance or delay agricultural operation depending on theweather condition +e influence of both horizontal de-formation and soil compaction on the traction perfor-mance is very low (does not exceed 4)

4 Conclusions

+e optimization of the traction performance of an agri-cultural tractor is essential considering fuel economy +edevelopment of highly accurate mathematical models thatdescribe the tractive properties is an integral part of theoptimization process In this work four soft computingtechniques were used for predicting the traction force andtractive efficiency of a low-power tractor as affected by the soiltype (expressed as soil coefficient) vertical load horizontaldeformation soil compaction and soil moisture Compari-sons of the error statistics revealed that the neural networkmodel trained by a traditional BP algorithm or by a com-bination of BP and GA performs better in estimating both thetraction force and tractive efficiency than an ANFIS model oran ANN trained by only a GA An ANN structure with 28neurons in the hidden layer produced the best model of thetraction force with an R2 value of 0954 amean absolute errorof 0029 and an RMSE of 0040 Similarly an ANN with 26neurons in the hidden layer was found to be the best structurefor the tractive efficiency model with R2 0954MAE 0024 and RMSE 0037 Using GA for optimizingthe weights and biases in the ANNmodel trained by BP led toa slight improvement in model accuracy Considering theresults presented by other authors it can be stated that thepotential usability of a certain technique depends strongly onthe data characteristics Moreover the behavior of eachmachine-learning algorithm is affected by its parameters+us for improving the optimization process differenttechniques should be employed and the model with thehighest accuracy should be chosen Considering the com-putational time required for ANFIS model development theneural network trained by the backpropagation algorithmseems to be the best soft computing technique+e results of asensitivity analysis conducted on a group of models with thehighest accuracy showed that the soil type is the parametermost affecting the traction performance of a low-powertractor A relatively strong influence was also found for thevertical load and soil moisture which can be varied by thetractor operator to optimize the traction performance

+e results of this research are expected to be useful insaving energy in agricultural production systems Howeverit should be noted that the application of the empiricalmodels obtained by the authors is limited to conditionssimilar to those present during the measurements

Data Availability

+e data samples used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

+e authors have no conflicts of interest to declare

References

[1] T Smerda and J Cupera ldquoTire inflation and its influence ondrawbar characteristics and performancemdashenergetic indica-tors of a tractor setrdquo Journal of Terramechanics vol 47 no 6pp 395ndash400 2010

[2] A Janulevicius and V Damanauskas ldquoHow to select airpressures in the tires of MFWD (mechanical front-wheeldrive) tractor to minimize fuel consumption for the case ofreasonable wheel sliprdquo Energy vol 90 pp 691ndash700 2015

[3] H Taghavifar A Mardani and H Karim-Maslak ldquoMulti-criteria optimization model to investigate the energy waste ofoff-road vehicles utilizing soil bin facilityrdquo Energy vol 73pp 762ndash770 2014

[4] J H Lee and K Gard ldquoVehicle-soil interaction testingmodeling calibration and validationrdquo Journal of Terra-mechanics vol 52 pp 9ndash21 2014

[5] F M Zoz and R D Grisso ldquoTraction and tractor perfor-mancerdquo in ASAE Distinguished Lecture Series Vol 27American Society of Agricultural Engineers Tractor DesignNo 27 St Joseph MI USA 2003

[6] V K Tiwari K P Pandey and P K Pranav ldquoA review ontraction prediction equationsrdquo Journal of Terramechanicsvol 47 no 3 pp 191ndash199 2010

[7] C W Fervers ldquoImproved FEM simulation model for tire-soilinteractionrdquo Journal of Terramechanics vol 41 no 2-3pp 87ndash100 2004

[8] H Nakashima and A Oida ldquoAlgorithm and implementationof soil-tire contact analysis code based on dynamic FE-DEmethodrdquo Journal of Terramechanics vol 41 no 2-3pp 127ndash137 2004

[9] R Rosca P Carlescu and I Tenu ldquoA semi-empirical tractionprediction model for an agricultural tyre based on the superellipse shape of the contact surfacerdquo Soil and Tillage Researchvol 141 pp 10ndash18 2014

[10] A K Roul H Raheman M S Pansare and R MachavaramldquoPredicting the draught requirement of tillage implements insandy clay loam soil using an artificial neural networkrdquoBiosystems Engineering vol 104 no 4 pp 476ndash485 2009

[11] H Taghavifar and A Mardani ldquoApplying a supervised ANN(artificial neural network) approach to the prognostication ofdriven wheel energy efficiency indicesrdquo Energy vol 68pp 651ndash657 2014

[12] K Ccedilarman and A Taner ldquoPrediction of tire tractive per-formance by using artificial neural networksrdquo Mathematicaland Computational Applications vol 17 no 3 pp 182ndash1922012

[13] S A Hoseinpour A Barati-Harooni P Nadali et al ldquoAc-curate model based on artificial intelligence for prediction ofcarbon dioxide solubility in aqueoustetra-n-butylammoniumbromide solutionsrdquo Journal of Chemometrics vol 32 no 2Article ID e2956 2018

[14] H Taghavifar A Mardani and A H Hosseinloo ldquoAppraisalof artificial neural network-genetic algorithm based model for

10 Complexity

prediction of the power provided by the agricultural tractorsrdquoEnergy vol 93 pp 1704ndash1710 2015

[15] Z X Zhu R Torisu J I Takeda E R Mao and Q ZhangldquoNeural network for estimating vehicle behaviour on slopingterrainrdquo Biosystems Engineering vol 91 no 4 pp 403ndash4112005

[16] H Taghavifar and A Mardani ldquoEvaluating the effect of tireparameters on required drawbar pull energy model usingadaptive neuro-fuzzy inference systemrdquo Energy vol 85pp 586ndash593 2015

[17] H Taghavifar and A Mardani ldquoOn the modeling of energyefficiency indices of agricultural tractor driving wheels ap-plying adaptive neuro-fuzzy inference systemrdquo Journal ofTerramechanics vol 56 pp 37ndash47 2014

[18] N H Abu-Hamdeh ldquo+e disturbance of topsoil using ul-trasonic wavesrdquo Soil and Tillage Research vol 75 no 1pp 87ndash92 2004

[19] N C Brady and R R WeilCe Nature and Properties of SoilsPearson Education International London UK 15th edition2008

[20] K Pentos and K Pieczarka ldquoApplying an artificial neuralnetwork approach to the analysis of tractive properties inchanging soil conditionsrdquo Soil and Tillage Research vol 165pp 113ndash120 2017

[21] G Frauke and S Fritsch ldquoNeuralnet training of neuralnetworksrdquo 2010 httpsjournalr-projectorgarchive2010RJ-2010-006RJ-2010-006pdf

[22] M Riedmiller ldquoAdvanced supervised learning in multi-layerperceptrons-from backpropagation to adaptive learning al-gorithmsrdquo Computer Standards amp Interfaces vol 16 no 3pp 265ndash278 1994

[23] A D Anastasiadis G D Magoulas andM N Vrahatis ldquoNewglobally convergent training scheme based on the resilientpropagation algorithmrdquo Neurocomputing vol 64 pp 253ndash270 2005

[24] S Fritsch F Guenther M NWright M Suling S M Mueller2019 httpscranr-projectorgwebpackagesneuralnetindexhtml

[25] J H Holland Adaptation in Natural and Artificial SystemsUniversity of Michigan Press Ann Arbor MI USA 1975

[26] L G A Scrucca ldquoA package for genetic algorithms in RrdquoJournal of Statistical Software vol 53 no 4 pp 1ndash37 2013

[27] J-S R Jang ldquoANFISmdashadaptive-network-based fuzzy infer-ence systemrdquo IEEE Transactions on Systems Man and Cy-bernetics vol 23 no 3 pp 665ndash685 1993

[28] Y Dimopoulos P Bourret and S Lek ldquoUse of some sensi-tivity criteria for choosing networks with good generalizationabilityrdquo Neural Processing Letters vol 2 no 6 pp 1ndash4 1995

[29] K Pentos ldquo+e methods of extracting the contribution ofvariables in artificial neural network modelsmdashcomparison ofinherent instabilityrdquo Computers and Electronics in Agricul-ture vol 127 pp 141ndash146 2016

[30] K Liakos P Busato D Moshou S Pearson and D BochtisldquoMachine learning in agriculture a reviewrdquo Sensors vol 18no 8 p 2674 2018

[31] A L Johann A G de Araujo H C Delalibera andA R Hirakawa ldquoSoil moisture modeling based on stochasticbehavior of forces on a no-till chisel openerrdquo Computers andElectronics in Agriculture vol 121 pp 420ndash428 2016

[32] H Citakoglu ldquoComparison of artificial intelligence tech-niques via empirical equations for prediction of solar radia-tionrdquo Computers and Electronics in Agriculture vol 118pp 28ndash37 2015

[33] H Ghorbani H Kashi N Hafezi Moghadas andS Emamgholizadeh ldquoEstimation of soil cation exchangecapacity using multiple regression artificial neural networksand adaptive neuro-fuzzy inference system models in Gole-stan province Iranrdquo Communications in Soil Science andPlant Analysis vol 46 no 6 pp 763ndash780 2015

[34] M Asnaashari R Farhoosh and R Farahmandfar ldquoPre-diction of oxidation parameters of purified Kilka fish oilincluding gallic acid and methyl gallate by adaptive neuro-fuzzy inference system (ANFIS) and artificial neural net-workrdquo Journal of the Science of Food and Agriculture vol 96no 13 pp 4594ndash4602 2016

[35] F F Ping and F X Fei ldquoMultivariant forecasting mode ofGuangdong Province port throughput with genetic algo-rithms and Back Propagation neural networkrdquo in Proceedingsfrom the 13th Cota International Conference of TransportationProfessionals vol 96 pp 1165ndash1174 Shenzhen ChinaAugust 2013

[36] S Srinivasulu and A Jain ldquoA comparative analysis of trainingmethods for artificial neural network rainfall-runoff modelsrdquoApplied Soft Computing vol 6 no 3 pp 295ndash306 2006

[37] E V McKyes Soil Cutting and Tillage Elsevier SciencePublishers BV Amsterdam Netherlands 1985

[38] F M Zoz Predicting Tractor Field Performance Vol 49085ASAE St Joseph MI USA 1970

[39] M I Lyasko ldquoHow to calculate the effect of soil conditions ontractive performancerdquo Journal of Terramechanics vol 47no 6 pp 423ndash445 2010

Complexity 11

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0954

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(a)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0752

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(b)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0954

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(c)

0 10 20 30 40 50 60 70 80 90Tractive efficiency () ndash empirical values

R2 = 0872

0102030405060708090

Trac

tive e

ffici

ency

() ndash

pre

dict

ed v

alue

s

(d)

Figure 6 Scatterplot of model-predicted values versus actual values of tractive efficiency (a) ANN (b) ANN+GA (c) ANN_BP+GA and(d) ANFIS

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0955

(c)

0 100 200 300 400 500 600 700 800 900Traction force (N) ndash empirical values

0100200300400500600700800900

Trac

tion

forc

e (N

) ndash p

redi

cted

val

ues

R2 = 0888

(d)

Figure 5 Scatterplot of model-predicted values versus actual values of traction force (a) ANN (b) ANN+GA (c) ANN_BP+GA and(d) ANFIS

Table 4 Statistics of neural model architectures used for sensitivity analysis

Dependentvariable

+e range of number of neuronsin hidden layer

+e range of R2 forvalidation dataset

+e range of MAE forvalidation dataset

+e range of RMSE forvalidation dataset

Tractionforce 16ndash40 0944ndash0955 0028ndash0032 0040ndash0045

Tractiveefficiency 16ndash38 0928ndash0954 0024ndash0032 0037ndash0047

Complexity 9

parameters that significantly influenced the traction forceand tractive efficiency are the vertical load (183 and 101respectively) and soil moisture (198 and 103 respec-tively) +e significant effects of these parameters on thetractive performance have been highlighted in other studiesas well [11 39] It is worth emphasizing that the verticalload is one of the more easily manageable parametersduring traction performance optimization Soil moisturecan also be varied in a certain range as the operator canadvance or delay agricultural operation depending on theweather condition +e influence of both horizontal de-formation and soil compaction on the traction perfor-mance is very low (does not exceed 4)

4 Conclusions

+e optimization of the traction performance of an agri-cultural tractor is essential considering fuel economy +edevelopment of highly accurate mathematical models thatdescribe the tractive properties is an integral part of theoptimization process In this work four soft computingtechniques were used for predicting the traction force andtractive efficiency of a low-power tractor as affected by the soiltype (expressed as soil coefficient) vertical load horizontaldeformation soil compaction and soil moisture Compari-sons of the error statistics revealed that the neural networkmodel trained by a traditional BP algorithm or by a com-bination of BP and GA performs better in estimating both thetraction force and tractive efficiency than an ANFIS model oran ANN trained by only a GA An ANN structure with 28neurons in the hidden layer produced the best model of thetraction force with an R2 value of 0954 amean absolute errorof 0029 and an RMSE of 0040 Similarly an ANN with 26neurons in the hidden layer was found to be the best structurefor the tractive efficiency model with R2 0954MAE 0024 and RMSE 0037 Using GA for optimizingthe weights and biases in the ANNmodel trained by BP led toa slight improvement in model accuracy Considering theresults presented by other authors it can be stated that thepotential usability of a certain technique depends strongly onthe data characteristics Moreover the behavior of eachmachine-learning algorithm is affected by its parameters+us for improving the optimization process differenttechniques should be employed and the model with thehighest accuracy should be chosen Considering the com-putational time required for ANFIS model development theneural network trained by the backpropagation algorithmseems to be the best soft computing technique+e results of asensitivity analysis conducted on a group of models with thehighest accuracy showed that the soil type is the parametermost affecting the traction performance of a low-powertractor A relatively strong influence was also found for thevertical load and soil moisture which can be varied by thetractor operator to optimize the traction performance

+e results of this research are expected to be useful insaving energy in agricultural production systems Howeverit should be noted that the application of the empiricalmodels obtained by the authors is limited to conditionssimilar to those present during the measurements

Data Availability

+e data samples used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

+e authors have no conflicts of interest to declare

References

[1] T Smerda and J Cupera ldquoTire inflation and its influence ondrawbar characteristics and performancemdashenergetic indica-tors of a tractor setrdquo Journal of Terramechanics vol 47 no 6pp 395ndash400 2010

[2] A Janulevicius and V Damanauskas ldquoHow to select airpressures in the tires of MFWD (mechanical front-wheeldrive) tractor to minimize fuel consumption for the case ofreasonable wheel sliprdquo Energy vol 90 pp 691ndash700 2015

[3] H Taghavifar A Mardani and H Karim-Maslak ldquoMulti-criteria optimization model to investigate the energy waste ofoff-road vehicles utilizing soil bin facilityrdquo Energy vol 73pp 762ndash770 2014

[4] J H Lee and K Gard ldquoVehicle-soil interaction testingmodeling calibration and validationrdquo Journal of Terra-mechanics vol 52 pp 9ndash21 2014

[5] F M Zoz and R D Grisso ldquoTraction and tractor perfor-mancerdquo in ASAE Distinguished Lecture Series Vol 27American Society of Agricultural Engineers Tractor DesignNo 27 St Joseph MI USA 2003

[6] V K Tiwari K P Pandey and P K Pranav ldquoA review ontraction prediction equationsrdquo Journal of Terramechanicsvol 47 no 3 pp 191ndash199 2010

[7] C W Fervers ldquoImproved FEM simulation model for tire-soilinteractionrdquo Journal of Terramechanics vol 41 no 2-3pp 87ndash100 2004

[8] H Nakashima and A Oida ldquoAlgorithm and implementationof soil-tire contact analysis code based on dynamic FE-DEmethodrdquo Journal of Terramechanics vol 41 no 2-3pp 127ndash137 2004

[9] R Rosca P Carlescu and I Tenu ldquoA semi-empirical tractionprediction model for an agricultural tyre based on the superellipse shape of the contact surfacerdquo Soil and Tillage Researchvol 141 pp 10ndash18 2014

[10] A K Roul H Raheman M S Pansare and R MachavaramldquoPredicting the draught requirement of tillage implements insandy clay loam soil using an artificial neural networkrdquoBiosystems Engineering vol 104 no 4 pp 476ndash485 2009

[11] H Taghavifar and A Mardani ldquoApplying a supervised ANN(artificial neural network) approach to the prognostication ofdriven wheel energy efficiency indicesrdquo Energy vol 68pp 651ndash657 2014

[12] K Ccedilarman and A Taner ldquoPrediction of tire tractive per-formance by using artificial neural networksrdquo Mathematicaland Computational Applications vol 17 no 3 pp 182ndash1922012

[13] S A Hoseinpour A Barati-Harooni P Nadali et al ldquoAc-curate model based on artificial intelligence for prediction ofcarbon dioxide solubility in aqueoustetra-n-butylammoniumbromide solutionsrdquo Journal of Chemometrics vol 32 no 2Article ID e2956 2018

[14] H Taghavifar A Mardani and A H Hosseinloo ldquoAppraisalof artificial neural network-genetic algorithm based model for

10 Complexity

prediction of the power provided by the agricultural tractorsrdquoEnergy vol 93 pp 1704ndash1710 2015

[15] Z X Zhu R Torisu J I Takeda E R Mao and Q ZhangldquoNeural network for estimating vehicle behaviour on slopingterrainrdquo Biosystems Engineering vol 91 no 4 pp 403ndash4112005

[16] H Taghavifar and A Mardani ldquoEvaluating the effect of tireparameters on required drawbar pull energy model usingadaptive neuro-fuzzy inference systemrdquo Energy vol 85pp 586ndash593 2015

[17] H Taghavifar and A Mardani ldquoOn the modeling of energyefficiency indices of agricultural tractor driving wheels ap-plying adaptive neuro-fuzzy inference systemrdquo Journal ofTerramechanics vol 56 pp 37ndash47 2014

[18] N H Abu-Hamdeh ldquo+e disturbance of topsoil using ul-trasonic wavesrdquo Soil and Tillage Research vol 75 no 1pp 87ndash92 2004

[19] N C Brady and R R WeilCe Nature and Properties of SoilsPearson Education International London UK 15th edition2008

[20] K Pentos and K Pieczarka ldquoApplying an artificial neuralnetwork approach to the analysis of tractive properties inchanging soil conditionsrdquo Soil and Tillage Research vol 165pp 113ndash120 2017

[21] G Frauke and S Fritsch ldquoNeuralnet training of neuralnetworksrdquo 2010 httpsjournalr-projectorgarchive2010RJ-2010-006RJ-2010-006pdf

[22] M Riedmiller ldquoAdvanced supervised learning in multi-layerperceptrons-from backpropagation to adaptive learning al-gorithmsrdquo Computer Standards amp Interfaces vol 16 no 3pp 265ndash278 1994

[23] A D Anastasiadis G D Magoulas andM N Vrahatis ldquoNewglobally convergent training scheme based on the resilientpropagation algorithmrdquo Neurocomputing vol 64 pp 253ndash270 2005

[24] S Fritsch F Guenther M NWright M Suling S M Mueller2019 httpscranr-projectorgwebpackagesneuralnetindexhtml

[25] J H Holland Adaptation in Natural and Artificial SystemsUniversity of Michigan Press Ann Arbor MI USA 1975

[26] L G A Scrucca ldquoA package for genetic algorithms in RrdquoJournal of Statistical Software vol 53 no 4 pp 1ndash37 2013

[27] J-S R Jang ldquoANFISmdashadaptive-network-based fuzzy infer-ence systemrdquo IEEE Transactions on Systems Man and Cy-bernetics vol 23 no 3 pp 665ndash685 1993

[28] Y Dimopoulos P Bourret and S Lek ldquoUse of some sensi-tivity criteria for choosing networks with good generalizationabilityrdquo Neural Processing Letters vol 2 no 6 pp 1ndash4 1995

[29] K Pentos ldquo+e methods of extracting the contribution ofvariables in artificial neural network modelsmdashcomparison ofinherent instabilityrdquo Computers and Electronics in Agricul-ture vol 127 pp 141ndash146 2016

[30] K Liakos P Busato D Moshou S Pearson and D BochtisldquoMachine learning in agriculture a reviewrdquo Sensors vol 18no 8 p 2674 2018

[31] A L Johann A G de Araujo H C Delalibera andA R Hirakawa ldquoSoil moisture modeling based on stochasticbehavior of forces on a no-till chisel openerrdquo Computers andElectronics in Agriculture vol 121 pp 420ndash428 2016

[32] H Citakoglu ldquoComparison of artificial intelligence tech-niques via empirical equations for prediction of solar radia-tionrdquo Computers and Electronics in Agriculture vol 118pp 28ndash37 2015

[33] H Ghorbani H Kashi N Hafezi Moghadas andS Emamgholizadeh ldquoEstimation of soil cation exchangecapacity using multiple regression artificial neural networksand adaptive neuro-fuzzy inference system models in Gole-stan province Iranrdquo Communications in Soil Science andPlant Analysis vol 46 no 6 pp 763ndash780 2015

[34] M Asnaashari R Farhoosh and R Farahmandfar ldquoPre-diction of oxidation parameters of purified Kilka fish oilincluding gallic acid and methyl gallate by adaptive neuro-fuzzy inference system (ANFIS) and artificial neural net-workrdquo Journal of the Science of Food and Agriculture vol 96no 13 pp 4594ndash4602 2016

[35] F F Ping and F X Fei ldquoMultivariant forecasting mode ofGuangdong Province port throughput with genetic algo-rithms and Back Propagation neural networkrdquo in Proceedingsfrom the 13th Cota International Conference of TransportationProfessionals vol 96 pp 1165ndash1174 Shenzhen ChinaAugust 2013

[36] S Srinivasulu and A Jain ldquoA comparative analysis of trainingmethods for artificial neural network rainfall-runoff modelsrdquoApplied Soft Computing vol 6 no 3 pp 295ndash306 2006

[37] E V McKyes Soil Cutting and Tillage Elsevier SciencePublishers BV Amsterdam Netherlands 1985

[38] F M Zoz Predicting Tractor Field Performance Vol 49085ASAE St Joseph MI USA 1970

[39] M I Lyasko ldquoHow to calculate the effect of soil conditions ontractive performancerdquo Journal of Terramechanics vol 47no 6 pp 423ndash445 2010

Complexity 11

parameters that significantly influenced the traction forceand tractive efficiency are the vertical load (183 and 101respectively) and soil moisture (198 and 103 respec-tively) +e significant effects of these parameters on thetractive performance have been highlighted in other studiesas well [11 39] It is worth emphasizing that the verticalload is one of the more easily manageable parametersduring traction performance optimization Soil moisturecan also be varied in a certain range as the operator canadvance or delay agricultural operation depending on theweather condition +e influence of both horizontal de-formation and soil compaction on the traction perfor-mance is very low (does not exceed 4)

4 Conclusions

+e optimization of the traction performance of an agri-cultural tractor is essential considering fuel economy +edevelopment of highly accurate mathematical models thatdescribe the tractive properties is an integral part of theoptimization process In this work four soft computingtechniques were used for predicting the traction force andtractive efficiency of a low-power tractor as affected by the soiltype (expressed as soil coefficient) vertical load horizontaldeformation soil compaction and soil moisture Compari-sons of the error statistics revealed that the neural networkmodel trained by a traditional BP algorithm or by a com-bination of BP and GA performs better in estimating both thetraction force and tractive efficiency than an ANFIS model oran ANN trained by only a GA An ANN structure with 28neurons in the hidden layer produced the best model of thetraction force with an R2 value of 0954 amean absolute errorof 0029 and an RMSE of 0040 Similarly an ANN with 26neurons in the hidden layer was found to be the best structurefor the tractive efficiency model with R2 0954MAE 0024 and RMSE 0037 Using GA for optimizingthe weights and biases in the ANNmodel trained by BP led toa slight improvement in model accuracy Considering theresults presented by other authors it can be stated that thepotential usability of a certain technique depends strongly onthe data characteristics Moreover the behavior of eachmachine-learning algorithm is affected by its parameters+us for improving the optimization process differenttechniques should be employed and the model with thehighest accuracy should be chosen Considering the com-putational time required for ANFIS model development theneural network trained by the backpropagation algorithmseems to be the best soft computing technique+e results of asensitivity analysis conducted on a group of models with thehighest accuracy showed that the soil type is the parametermost affecting the traction performance of a low-powertractor A relatively strong influence was also found for thevertical load and soil moisture which can be varied by thetractor operator to optimize the traction performance

+e results of this research are expected to be useful insaving energy in agricultural production systems Howeverit should be noted that the application of the empiricalmodels obtained by the authors is limited to conditionssimilar to those present during the measurements

Data Availability

+e data samples used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

+e authors have no conflicts of interest to declare

References

[1] T Smerda and J Cupera ldquoTire inflation and its influence ondrawbar characteristics and performancemdashenergetic indica-tors of a tractor setrdquo Journal of Terramechanics vol 47 no 6pp 395ndash400 2010

[2] A Janulevicius and V Damanauskas ldquoHow to select airpressures in the tires of MFWD (mechanical front-wheeldrive) tractor to minimize fuel consumption for the case ofreasonable wheel sliprdquo Energy vol 90 pp 691ndash700 2015

[3] H Taghavifar A Mardani and H Karim-Maslak ldquoMulti-criteria optimization model to investigate the energy waste ofoff-road vehicles utilizing soil bin facilityrdquo Energy vol 73pp 762ndash770 2014

[4] J H Lee and K Gard ldquoVehicle-soil interaction testingmodeling calibration and validationrdquo Journal of Terra-mechanics vol 52 pp 9ndash21 2014

[5] F M Zoz and R D Grisso ldquoTraction and tractor perfor-mancerdquo in ASAE Distinguished Lecture Series Vol 27American Society of Agricultural Engineers Tractor DesignNo 27 St Joseph MI USA 2003

[6] V K Tiwari K P Pandey and P K Pranav ldquoA review ontraction prediction equationsrdquo Journal of Terramechanicsvol 47 no 3 pp 191ndash199 2010

[7] C W Fervers ldquoImproved FEM simulation model for tire-soilinteractionrdquo Journal of Terramechanics vol 41 no 2-3pp 87ndash100 2004

[8] H Nakashima and A Oida ldquoAlgorithm and implementationof soil-tire contact analysis code based on dynamic FE-DEmethodrdquo Journal of Terramechanics vol 41 no 2-3pp 127ndash137 2004

[9] R Rosca P Carlescu and I Tenu ldquoA semi-empirical tractionprediction model for an agricultural tyre based on the superellipse shape of the contact surfacerdquo Soil and Tillage Researchvol 141 pp 10ndash18 2014

[10] A K Roul H Raheman M S Pansare and R MachavaramldquoPredicting the draught requirement of tillage implements insandy clay loam soil using an artificial neural networkrdquoBiosystems Engineering vol 104 no 4 pp 476ndash485 2009

[11] H Taghavifar and A Mardani ldquoApplying a supervised ANN(artificial neural network) approach to the prognostication ofdriven wheel energy efficiency indicesrdquo Energy vol 68pp 651ndash657 2014

[12] K Ccedilarman and A Taner ldquoPrediction of tire tractive per-formance by using artificial neural networksrdquo Mathematicaland Computational Applications vol 17 no 3 pp 182ndash1922012

[13] S A Hoseinpour A Barati-Harooni P Nadali et al ldquoAc-curate model based on artificial intelligence for prediction ofcarbon dioxide solubility in aqueoustetra-n-butylammoniumbromide solutionsrdquo Journal of Chemometrics vol 32 no 2Article ID e2956 2018

[14] H Taghavifar A Mardani and A H Hosseinloo ldquoAppraisalof artificial neural network-genetic algorithm based model for

10 Complexity

prediction of the power provided by the agricultural tractorsrdquoEnergy vol 93 pp 1704ndash1710 2015

[15] Z X Zhu R Torisu J I Takeda E R Mao and Q ZhangldquoNeural network for estimating vehicle behaviour on slopingterrainrdquo Biosystems Engineering vol 91 no 4 pp 403ndash4112005

[16] H Taghavifar and A Mardani ldquoEvaluating the effect of tireparameters on required drawbar pull energy model usingadaptive neuro-fuzzy inference systemrdquo Energy vol 85pp 586ndash593 2015

[17] H Taghavifar and A Mardani ldquoOn the modeling of energyefficiency indices of agricultural tractor driving wheels ap-plying adaptive neuro-fuzzy inference systemrdquo Journal ofTerramechanics vol 56 pp 37ndash47 2014

[18] N H Abu-Hamdeh ldquo+e disturbance of topsoil using ul-trasonic wavesrdquo Soil and Tillage Research vol 75 no 1pp 87ndash92 2004

[19] N C Brady and R R WeilCe Nature and Properties of SoilsPearson Education International London UK 15th edition2008

[20] K Pentos and K Pieczarka ldquoApplying an artificial neuralnetwork approach to the analysis of tractive properties inchanging soil conditionsrdquo Soil and Tillage Research vol 165pp 113ndash120 2017

[21] G Frauke and S Fritsch ldquoNeuralnet training of neuralnetworksrdquo 2010 httpsjournalr-projectorgarchive2010RJ-2010-006RJ-2010-006pdf

[22] M Riedmiller ldquoAdvanced supervised learning in multi-layerperceptrons-from backpropagation to adaptive learning al-gorithmsrdquo Computer Standards amp Interfaces vol 16 no 3pp 265ndash278 1994

[23] A D Anastasiadis G D Magoulas andM N Vrahatis ldquoNewglobally convergent training scheme based on the resilientpropagation algorithmrdquo Neurocomputing vol 64 pp 253ndash270 2005

[24] S Fritsch F Guenther M NWright M Suling S M Mueller2019 httpscranr-projectorgwebpackagesneuralnetindexhtml

[25] J H Holland Adaptation in Natural and Artificial SystemsUniversity of Michigan Press Ann Arbor MI USA 1975

[26] L G A Scrucca ldquoA package for genetic algorithms in RrdquoJournal of Statistical Software vol 53 no 4 pp 1ndash37 2013

[27] J-S R Jang ldquoANFISmdashadaptive-network-based fuzzy infer-ence systemrdquo IEEE Transactions on Systems Man and Cy-bernetics vol 23 no 3 pp 665ndash685 1993

[28] Y Dimopoulos P Bourret and S Lek ldquoUse of some sensi-tivity criteria for choosing networks with good generalizationabilityrdquo Neural Processing Letters vol 2 no 6 pp 1ndash4 1995

[29] K Pentos ldquo+e methods of extracting the contribution ofvariables in artificial neural network modelsmdashcomparison ofinherent instabilityrdquo Computers and Electronics in Agricul-ture vol 127 pp 141ndash146 2016

[30] K Liakos P Busato D Moshou S Pearson and D BochtisldquoMachine learning in agriculture a reviewrdquo Sensors vol 18no 8 p 2674 2018

[31] A L Johann A G de Araujo H C Delalibera andA R Hirakawa ldquoSoil moisture modeling based on stochasticbehavior of forces on a no-till chisel openerrdquo Computers andElectronics in Agriculture vol 121 pp 420ndash428 2016

[32] H Citakoglu ldquoComparison of artificial intelligence tech-niques via empirical equations for prediction of solar radia-tionrdquo Computers and Electronics in Agriculture vol 118pp 28ndash37 2015

[33] H Ghorbani H Kashi N Hafezi Moghadas andS Emamgholizadeh ldquoEstimation of soil cation exchangecapacity using multiple regression artificial neural networksand adaptive neuro-fuzzy inference system models in Gole-stan province Iranrdquo Communications in Soil Science andPlant Analysis vol 46 no 6 pp 763ndash780 2015

[34] M Asnaashari R Farhoosh and R Farahmandfar ldquoPre-diction of oxidation parameters of purified Kilka fish oilincluding gallic acid and methyl gallate by adaptive neuro-fuzzy inference system (ANFIS) and artificial neural net-workrdquo Journal of the Science of Food and Agriculture vol 96no 13 pp 4594ndash4602 2016

[35] F F Ping and F X Fei ldquoMultivariant forecasting mode ofGuangdong Province port throughput with genetic algo-rithms and Back Propagation neural networkrdquo in Proceedingsfrom the 13th Cota International Conference of TransportationProfessionals vol 96 pp 1165ndash1174 Shenzhen ChinaAugust 2013

[36] S Srinivasulu and A Jain ldquoA comparative analysis of trainingmethods for artificial neural network rainfall-runoff modelsrdquoApplied Soft Computing vol 6 no 3 pp 295ndash306 2006

[37] E V McKyes Soil Cutting and Tillage Elsevier SciencePublishers BV Amsterdam Netherlands 1985

[38] F M Zoz Predicting Tractor Field Performance Vol 49085ASAE St Joseph MI USA 1970

[39] M I Lyasko ldquoHow to calculate the effect of soil conditions ontractive performancerdquo Journal of Terramechanics vol 47no 6 pp 423ndash445 2010

Complexity 11

prediction of the power provided by the agricultural tractorsrdquoEnergy vol 93 pp 1704ndash1710 2015

[15] Z X Zhu R Torisu J I Takeda E R Mao and Q ZhangldquoNeural network for estimating vehicle behaviour on slopingterrainrdquo Biosystems Engineering vol 91 no 4 pp 403ndash4112005

[16] H Taghavifar and A Mardani ldquoEvaluating the effect of tireparameters on required drawbar pull energy model usingadaptive neuro-fuzzy inference systemrdquo Energy vol 85pp 586ndash593 2015

[17] H Taghavifar and A Mardani ldquoOn the modeling of energyefficiency indices of agricultural tractor driving wheels ap-plying adaptive neuro-fuzzy inference systemrdquo Journal ofTerramechanics vol 56 pp 37ndash47 2014

[18] N H Abu-Hamdeh ldquo+e disturbance of topsoil using ul-trasonic wavesrdquo Soil and Tillage Research vol 75 no 1pp 87ndash92 2004

[19] N C Brady and R R WeilCe Nature and Properties of SoilsPearson Education International London UK 15th edition2008

[20] K Pentos and K Pieczarka ldquoApplying an artificial neuralnetwork approach to the analysis of tractive properties inchanging soil conditionsrdquo Soil and Tillage Research vol 165pp 113ndash120 2017

[21] G Frauke and S Fritsch ldquoNeuralnet training of neuralnetworksrdquo 2010 httpsjournalr-projectorgarchive2010RJ-2010-006RJ-2010-006pdf

[22] M Riedmiller ldquoAdvanced supervised learning in multi-layerperceptrons-from backpropagation to adaptive learning al-gorithmsrdquo Computer Standards amp Interfaces vol 16 no 3pp 265ndash278 1994

[23] A D Anastasiadis G D Magoulas andM N Vrahatis ldquoNewglobally convergent training scheme based on the resilientpropagation algorithmrdquo Neurocomputing vol 64 pp 253ndash270 2005

[24] S Fritsch F Guenther M NWright M Suling S M Mueller2019 httpscranr-projectorgwebpackagesneuralnetindexhtml

[25] J H Holland Adaptation in Natural and Artificial SystemsUniversity of Michigan Press Ann Arbor MI USA 1975

[26] L G A Scrucca ldquoA package for genetic algorithms in RrdquoJournal of Statistical Software vol 53 no 4 pp 1ndash37 2013

[27] J-S R Jang ldquoANFISmdashadaptive-network-based fuzzy infer-ence systemrdquo IEEE Transactions on Systems Man and Cy-bernetics vol 23 no 3 pp 665ndash685 1993

[28] Y Dimopoulos P Bourret and S Lek ldquoUse of some sensi-tivity criteria for choosing networks with good generalizationabilityrdquo Neural Processing Letters vol 2 no 6 pp 1ndash4 1995

[29] K Pentos ldquo+e methods of extracting the contribution ofvariables in artificial neural network modelsmdashcomparison ofinherent instabilityrdquo Computers and Electronics in Agricul-ture vol 127 pp 141ndash146 2016

[30] K Liakos P Busato D Moshou S Pearson and D BochtisldquoMachine learning in agriculture a reviewrdquo Sensors vol 18no 8 p 2674 2018

[31] A L Johann A G de Araujo H C Delalibera andA R Hirakawa ldquoSoil moisture modeling based on stochasticbehavior of forces on a no-till chisel openerrdquo Computers andElectronics in Agriculture vol 121 pp 420ndash428 2016

[32] H Citakoglu ldquoComparison of artificial intelligence tech-niques via empirical equations for prediction of solar radia-tionrdquo Computers and Electronics in Agriculture vol 118pp 28ndash37 2015

[33] H Ghorbani H Kashi N Hafezi Moghadas andS Emamgholizadeh ldquoEstimation of soil cation exchangecapacity using multiple regression artificial neural networksand adaptive neuro-fuzzy inference system models in Gole-stan province Iranrdquo Communications in Soil Science andPlant Analysis vol 46 no 6 pp 763ndash780 2015

[34] M Asnaashari R Farhoosh and R Farahmandfar ldquoPre-diction of oxidation parameters of purified Kilka fish oilincluding gallic acid and methyl gallate by adaptive neuro-fuzzy inference system (ANFIS) and artificial neural net-workrdquo Journal of the Science of Food and Agriculture vol 96no 13 pp 4594ndash4602 2016

[35] F F Ping and F X Fei ldquoMultivariant forecasting mode ofGuangdong Province port throughput with genetic algo-rithms and Back Propagation neural networkrdquo in Proceedingsfrom the 13th Cota International Conference of TransportationProfessionals vol 96 pp 1165ndash1174 Shenzhen ChinaAugust 2013

[36] S Srinivasulu and A Jain ldquoA comparative analysis of trainingmethods for artificial neural network rainfall-runoff modelsrdquoApplied Soft Computing vol 6 no 3 pp 295ndash306 2006

[37] E V McKyes Soil Cutting and Tillage Elsevier SciencePublishers BV Amsterdam Netherlands 1985

[38] F M Zoz Predicting Tractor Field Performance Vol 49085ASAE St Joseph MI USA 1970

[39] M I Lyasko ldquoHow to calculate the effect of soil conditions ontractive performancerdquo Journal of Terramechanics vol 47no 6 pp 423ndash445 2010

Complexity 11

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