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Energy 66 (2014) 569e576

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Energy

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A comparative trend in forecasting ability of artificial neural networksand regressive support vector machine methodologies for energydissipation modeling of off-road vehicles

Hamid Taghavifar*, Aref MardaniDepartment of Mechanical Engineering of Agricultural Machinery, Faculty of Agriculture, Urmia University, Nazloo Road, Urmia 57153 1177, Iran

a r t i c l e i n f o

Article history:Received 4 June 2013Received in revised form4 January 2014Accepted 6 January 2014Available online 28 January 2014

Keywords:Artificial neural networkEnergy lossMotion resistanceSoil binSupport vector regression

* Corresponding author. Tel.: þ 98 441 277 0508; fE-mail addresses: Hamid.Taghavifar@gmail.com

HamidTaghavifar@hotmail.com (H. Taghavifar).

0360-5442/$ e see front matter � 2014 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2014.01.022

a b s t r a c t

Machine dynamics and soil elasticeplastic characteristic sort out the soil-wheel interaction productionsas very complex problem to be estimated. Energy dissipation due to motion resistance, as the mostprominent performance index of towed wheels, is associated with soil properties and tire parameters.The objective of this study was to develop, for the first time, a model for prediction of energy loss in soilworking machines using the datasets obtained from soil bin facility and a single-wheel tester. A total of90 data points were derived from experimentations at five levels of wheel load (1, 2, 3, 4, and 5 kN), sixtire inflation pressure (50, 100, 150, 200, 250, and 300 kPa) and three forward velocities (0.7, 1.4 and 2 m/s). ANN (Artificial neural network) was used for modeling of obtained results compared to the forecastingability of SVR (support vector regression) technique. Several statistical criterions, (i.e. MAPE (mean ab-solute percentage error), MSE (mean square error), MRE (mean relative error) and coefficient of deter-mination (R2) were incorporated in the investigations. It was observed, on the basis of statisticalcriterions, that SVR-based generalized model outperformed ANN in modeling energy loss and exhibitedits applicability as a promising tool in this domain.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Off-road vehicles are considered as any type of vehicles that arecapable of trafficking and traversing on off paved, gravel surface ortrain roads. This paper offers an overview of the wasted energy dueto motion resistance force in run-off-road vehicles using SVR(support vector regression) technique comparing with the classicalANN (artificial neural network). There is a global concern regardingthe increment of energy loss trends in wheeled vehicles, particu-larly in the run-off-road conditionwhere traversing-resistive forcesincrease significantly due to the augmentedmotion resistance forcein soil-wheel interactions. As reported in literature, the CEC (Cali-fornia Energy Commission) carried out a research on light trucksand by applying the low-motion resistance tires. Results showedthat if all light truck tires in California were changed to low-rollingresistance tires, the energy savings could be about 1135623.53 m3/yof gasoline [1]. The motion resistance of a tire during the traversingis quantified on the basis that it is in the subject of hysteresis losses

ax: þ98 441 277 1926., ha.taghavifar@urmia.ac.ir,

All rights reserved.

of the rubber in repetitive deformation. In terrain running condi-tion, energy loss is increased due to both hysteresis losses in cyclicdeformation of the rubber and also soil deformation under thetraversing wheel. Mobility progression and enhanced fuel effi-ciency of off-road vehicles are contradictory technical problems tobe achieved simultaneously, since in order to improve vehiclemobility, it is usually required to have extra fuel available, and theoptimization of fuel consumption reduces the vehicle mobility [2].

Motion resistance, soil sinkage and skid are of the most prom-inent factors for the determination of the performance character-istics of a towed wheel, amongst which, motion resistance is themost fundamental performance parameter of the towed pneumaticwheel [3]. It is, however, well documented in literature that motionresistance is commonly influenced by tire parameters and systemparameters, including traditional design parameters of the tire suchas diameter, section width, section height, inflation pressure andload deflection relationship. It is believed that these parametershave varying degree of influence on tire soil interaction [4]. Tostudy the interaction between wheel and soil, the related tire pa-rameters of wheel are the basic inputs and must, therefore, bequantitatively and qualitatively defined.

Thus far, many attempts have been made to investigate theeffects of tire and system parameters as well as soil characteristics

H. Taghavifar, A. Mardani / Energy 66 (2014) 569e576570

on motion resistance mutually in field experiments and soil binprovision; nevertheless, literature is poor regarding studiesfocusing on loss of energy due to motion resistance of towedwheels in off-road condition. In Ref. [5], the effects of some tireparameters such as wheel load, velocity and tire inflation pressurewere investigated on the formation of rolling resistance thatconfirmed the effectiveness of tire inflation pressure and wheelload. However, it was reported that velocity has no significant ef-fect on rolling resistance. Similar results were obtained for theincrease of rolling resistance due to increase of wheel load in Ref.[6] using a soil bin testing facility and in Ref. [7] by field experi-ments using two tractors. Moreover, the insignificant effect of ve-locity on rolling resistance was approved in Ref. [8] and in sandysoil using a wheel-tester [9]. Furthermore, Elwaleed et al. [10]found that tire inflation pressure can either increase or decreasethe rolling resistance depending on being overinflated level orlower than the recommended level.

The problematic experimental data modeling is apropos tomany engineering applications [11]. In experimental data modelinga process of induction is used to build up a model of the process,from which it is expected to realize responses of the process.Traditional neural network approaches have drawbacks withgeneralization and development of models with over-learningshortcomings. The foundations of SVM (Support Vector Ma-chines) have been developed by Vapnik [12] and are gainingpopularity due to many attractive features, and promising empir-ical performance. SVMs can also be applied to regression problemsby the introduction of an alternative loss function [13].

The ANN and SVM methodologies are of prominent arrange-ments of artificial intelligence and have been expansively appliedfor experimental data representations where principal ideology ofdeveloping ANN and SVM approaches is to train these algorithmsby use of series of experimental data points. SVM and ANN tech-niques have been successfully applied for stochastic modeling ofenergy systems in recent years and have gained increasing popu-larity among researchers. For example, in Ref. [14], the authors useda hybrid algorithm of support vector regression, radial basis func-tion neural network, and dual extended Kalamn filter for short-term load prognostication and reported the fitting performanceof the developed model. Moreover, a model based on ANNs wasproposed to predict the maximum power of a high concentratorphotovoltaic module using easily measurable atmospheric param-eters with satisfactory performance of ANN [15]. In two separateinvestigations, performance of a VGCHP (vertical ground coupledheat pump) system for cooling and heating purposes was modeledusing SVR [16] and ANN [17] and discussed the promising appli-cability of artificial intelligence techniques in energy systemmodeling.

In the study documented here, SVR (support vector regression),a particular implementation of SVM, is investigated for its capa-bility to predict energy loss of run-off-road vehicles. More specif-ically, SVR is compared to a MLP (Multilayer Perceptron NeuralNetwork) model in order to cross-validate the superior model.

2. Data collection

Assessment of energy was based on direct measurement ofrolling resistance and quantifying the waste power as following:

P ¼ R� dxdt

¼ R� V (1)

Where P is Power, R is rolling resistance (N) and V is velocity (m/s).The loss of power is then used to calculate the loss of energy byknowing the time of wheel traversing as:

W ¼Z

Pdt (2)

Hence,

W ¼Z

RVdt (3)

Therefore the measurement of rolling resistance and forwardvelocity are required to quantify the energy loss during wheeltraversing.

Experimentations in soil-wheel interaction domain are usuallycarried out in field or in laboratories, known as soil bin facilities.The advantages of soil bin environment over field experiments aremainly attributed to the provided controlled condition of soil bin intraversing, loading, ground levelness, soil characteristic adjust-ments such as moisture content, compaction level, and soil type,and dynamic stability. Aiming this, experiments were conducted inthe soil bin facility of Urmia University, Iran utilizing a well-equipped single wheel-tester tool. The soil bin featured capaciousdimensions of 23 m length, 2 m width and 1 m depth which isappropriate for deletion of boundary condition during trials. Thesingle-wheel tester was mounted on the carriage which waspowered for traversing by a three-phase electromotor of 22.3 kN.Four S-shape load cells with the capacity of 200 kg were calibratedand then were horizontally positioned at proper places in parallelpattern between the carriage and single-wheel tester to measurethe rolling resistance of traversing wheel. The load cells wereinterfaced to data acquisition system integrated of a data logger,digital indicators and laptop computer. Data were transmitted tothe laptop with the frequency of about 30 Hz. The utilized was aGood year 9.5L-14, 6 radial ply agricultural tractor tire. The systemsetup is shown in Fig. 1.

The measured volume of soil bin was evaluated to be 46 m3 andconsequently was filled with soil texture of clay-loam to simulatethe real condition of farmlands of most regions in Urmia, Iran.Particular implements were employed to organize soil bedincluding leveler and harrow since it’s very important to have well-prepared soil inside soil bin for acquiring reliable and precise re-sults from this experiment. Soil constituents and its properties aredefined in Table 1.

3. Support vector regression

Support Vector Machine can also be used as a regressionmethod, maintaining all the main features that characterize themaximal margin of the algorithm. The SVR (Support VectorRegression) uses the same principles as the SVM for classification,with only a few minor differences. First of all, because output is areal number it becomes very difficult to predict the information athand, which has infinite possibilities. In the case of regression, amargin of tolerance ( 3) is set in approximation to the SVM whichwould have already requested from the problem. However, themain idea is always the same: tominimize error, individualizing thehyperplane which maximizes the margin, keeping in mind thatpart of the error is tolerated.

In the theorem of 3-SVR is consisted of training vectors {(x1, y1),.,(xi, yi), i ¼ 1, .,l} to train the function f(x) ¼ <w,x> þ b asminimizing the risk function of following.

R ¼ 12kwk2 þ C

Xli¼1

ðyi; hw; xiÞ (4)

Wherew controls the smoothness of themodel,<w,x> is a functionof the fitting input space to the feature space, b is bias, andðyi; hw; xiÞ is the chosen loss function. In order to solve the

Fig. 1. A general schematic of system setup including soil bin and single-wheel tester and data acquisitioning equipment.

H. Taghavifar, A. Mardani / Energy 66 (2014) 569e576 571

aforementioned model, however, it is necessary to deal with thefollowing optimization problem [24].

min

12kwk2 þ C

Xli¼1

�xi þ x*i

�!(5)

Subject to8><>:

yi � hw; xii � b � εþ xihw; xii þ b� yi � εþ x*ixi; x

*i � 0

9>=>; (6)

where xi and x*i are to fulfill the function constraints. The dual formof optimization difficulty is achieved by minimization of theLagrange function. Hence, the data points are fitted into the equa-tions as following.

jxjε:¼

�0 if jxj � ε

jxj � ε otherwise

�(7)

K�xi;xj

�¼ �fðxiÞf�xj��¼ exp�� 12s2

xi�xj2 ij¼ 1; :::;N (8)

f�x;ai;a

*i

�¼XNsv

i¼1

�ai � a*i

��K�xi; xj

��þ b (9)

Due to well-documented details about 3-SVR process forsimplicity, the interested reader can refer to [18].

Table 1Soil constituents and its measured properties.

Item Value

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

4. ANNs (Artificial neural networks)

The ANN modeling approach is a soft computing methodologythat endeavors mimicking the human biological nervous system byinterconnecting various artificial neurons. In other words, theability to solve problems by applying information obtained frompast experiences to new problems or case scenarios.

ANN is a soft computing technique to model complex andnonlinear problems after the existing relationship between inputeoutput data is deduced [19]. Contradictory to mathematical ap-proaches, the deduced relationship is not representational in theformat of equations, however, is stored in terms of connectionweights between neurons [20]. ANN models and their estimatingability rely on training experimental data followed by validatingand testing the model by independent data. Holding multiple inputvariables, while it has the ability to improve its performance withnew series of data, multiple output variables can be efficientlypredicted and modeled. Furthermore, Appropriate ANN topology issignificant to attain simple models. Each input to the artificialneural network is multiplied by the synaptic weight, addedtogether and dealt with an activation function while ANNs aretrained by frequently exploring the best relationship between theinput and output values creating a model after a sufficient numberof learning repetitions, or training known as epochs [21]. It isknown that the computational models using ANN of the type MLP(Multilayers Perceptron) are dependent on the network structure(topology, connections, neurons number) and their operationalparameters (learning rate, momentum, etc.). The form in which thenetwork architecture is defined affects significantly its perfor-mance that can be classified in: learning speed, generalization ca-pacity, fault tolerance and accuracy in the learning.

A back propagation network usually arranged into layers: aninput layer, the one or more hidden layer(s), and an output layer.The number of input neurons is equal to the number of indepen-dent variables while the output neuron(s) represent the dependentvariable(s). The number of hidden layer and neurons within eachlayer can vary depending on the size, complexity and nature of thedataset. A general configuration of developed network in this studyis depicted in Fig. 2.

Fig. 2. Architecture of developed multilayer feed-forward neural network for energy dissipation prediction.

H. Taghavifar, A. Mardani / Energy 66 (2014) 569e576572

4.1. Training algorithms and training, testing and validationportions

It is noteworthy that data were split into 75%, 15% and 10%portions for training, testing and cross-validating in the represen-tations. The most beneficial and convenient training algorithms forthe back-propagation algorithms which are mainly categorized intotwo sets [22] were applied in the study including a) the heuristictechniques by use of the standard steepest descent algorithm ofGradient Descent with Momentum and Adaptive Learning Rate(traingdx) and b) the numerical methods including Scaled Conju-gate Gradient (trainscg) and LevenbergeMarquardt (trainlm).traingdx can train any network as long as its weight, net input, andtransfer functions derivate. Back-propagation is used to calculatederivatives of performance with respect to the weight and biasvariables. trainlm is often the fastest back-propagation algorithm inpractice, and is highly recommended as a first-choice supervisedalgorithm. In the light of aforementioned justifications and docu-mented recommendations in literature, traingdx, trainscg, andtrainlm training algorithms were applied.

4.2. Normalization range

If the input variables are combined linearly, as in an MLP, then itis rarely strictly necessary to standardize the inputs, at least intheory. The reason is that any rescaling of an input vector can beeffectively undone by changing the corresponding weights andbiases, leaving you with the exact same outputs as you had before.However, there are a variety of practical reasons why standardizingthe inputs can make training faster and reduce the chances ofgetting stuck in local optima.

Xn ¼ Xr � Xr;min

Xr;max�Xr;min� ðXh � XlÞ þ Xl (10)

Where Xn denotes normalized input variable, Xr is raw input vari-able, and Xr,min and Xr,max denote minimum and maximum of inputvariable. Moreover, Xh and Xl are set to be 0 and 1. Since that thenormalization outputs would be in compliance with the logsigtransfer function.

4.3. Transfer functions

The transfer function translates the input signals to output sig-nals. In multilayered perceptron feed-forward networks Log-Sigmoid (logsig), Tan-Sigmoid (tansig) and Linear (pureline) trans-fer functions are the fundamental ones [23]. Logsig takes input sig-nals in the range of between �N and þN and forms outputsbetween 0 and 1. Moreover, tansig takes input signals inputs in therangeof between�N andþN and formsoutput signals between�1and 1. Pureline accommodates inputs from �N to þN and fallsoutputs between �N and þN. Logsig functionwas applied to be incompliancewith the normalization range of study between 0 and 1.

4.4. ANN topological considerations

In the case of ANN modeling implementations, extension ofhidden layers leads to the over-fitting drawback, computationalcomplexity, time-consuming pattern recognition, low generaliza-tion and necessity for availability of capacious memory. In this re-gard, ANN structure with one hidden layer was developed duringvariety of trials.

4.5. Performance analysis

In modeling disciplines, it is absolutely required to evaluate theperformance of developed representation by various statisticalcriterions. The MSE (mean square error), the coefficient of deter-mination (R2), the MAPE (mean absolute percentage error), theMRE (mean relative error) are introduced for analysis of modelquality as described below.

MSE ¼ 1n

Xni¼1

�Ypredicted � Yactual

�2(11)

R2 ¼Pn

i¼1

�Ypredicted � Yactual

�2Pn

i¼1

�Ypredicted � Ymean

�2 (12)

Fig. 3. MSE of training data for all of applied training algorithms with respect to increment of number of neurons in the hidden layer between 0 and 20 neurons.

H. Taghavifar, A. Mardani / Energy 66 (2014) 569e576 573

MAPE ¼ 1n

Xn ����Ypredicted � YactualY

���� (13)

i¼1 actual

MRE ¼ 1n

Xni¼1

�����Yactual � YpredictedYpredicted

����� (14)

where Yactual and Ypredicted are measured and predicted values ofenergy loss by the developed models.

Fig. 4. MSE of training data for all of applied training algorithms with respect to inc

5. Results and discussion

From Fig. 3, it is appreciated that increased number of neuronsin the hidden layer reduces the error of model except for that ofGradient Descent with Momentum and Adaptive Learning Ratetraining algorithm. Increment of neurons, however, is most bene-ficial for decrement of error for Scaled Conjugate Gradient andLevenbergeMarquardt algorithms. A more detailed observation ofFig. 4 indicates that neurons more than 15 for LevenbergeMar-quardt entail the drawback of over-fitting which reduces

rement of number of neurons in the hidden layer between 15 and 20 neurons.

Fig. 5. Regression result of neural network training for MSE of all epochs between 0 and 1000 for training and validation portions.

H. Taghavifar, A. Mardani / Energy 66 (2014) 569e576574

forecasting ability of the model and increases the error for thenumber of neurons more than 15. Fig. 5 shows the variation ofcross-validation and training algorithms against the 1000 epochs(i.e. iterations). This is true for feed-forward ANN with back prop-agation learning algorithm since there is error optimization by backpropagation algorithm. It is also deduced that increment of epochsleads to decrement of model error. In terms of performance criteria,the ANN representation with 3-15-1 structure trained by Leven-bergeMarquardt algorithm outperformed the two other algorithms

Table 2The comparison between SVR-linear SVR-polynomial techniques and the best ANNmodel.

Model MSE MAPE MRE R2

ANN 2.223 � 10�12 0.34583 0.53421 0.98SVR-linear 8.652 � 10�3 0.83441 0.95423 0.97SVR-polynomial 9.467 � 10�18 0.18356 0.26208 0.99

Fig. 6. Mapping between experimental and predicted value

of Gradient Descent with Momentum and Adaptive Learning Ratetraining algorithm and Scaled Conjugate Gradient where MSE,MAPE, MRE, and coefficient of determination with 2.223 � 10�12,0.34583, 0.53421, and 0.98. So this model was selected as the bestANN solution for predicting the energy dissipation of run-off-roadvehicles. ANN approach made it possible to model a complex andnonlinear problem with desired experimental data points and itcan be more practically applicable for promising simulation ofobjective problem. It is noteworthy that in our investigation weused soil bin data that were obtained under controlled conditionsand thus errors due to unevenness of the surface and untestedparameters were not significant.

Table 2 shows the comparison made between SVR-linear andSVR-polynomial techniques and the best ANN model. It can benoticed from Table 2 that the coefficient of determination for eachof the developed models is high. This confirms that there isreasonably fitting linear relation between the actual and predictedvalues. However, SVR-polynomial featured the highest coefficient

s by SVR-linear algorithm in the case of 68 data points.

Fig. 7. Mapping between experimental and predicted values by ANN algorithm in the case of 68 data points.

H. Taghavifar, A. Mardani / Energy 66 (2014) 569e576 575

of determination among the developed models. The performanceof the SVR-linear and ANN models are comparable and are worsethan that of SVR-polynomial. This is mainly attributed to thenonlinear relationship between the input parameters and outputvariables. The SVR-polynomial model gives the best performance(i.e. lowest MRE (%), MSE, AARE (%), and highest coefficient ofdetermination) among the developed models.

Figs. 6e8 illustrate the mapping between experimental andpredicted values by SVR-linear, ANN and SVR-polynomial models. Asupreme quality mapping of experimental and predicted relation-ship of SVR-polynomial model compared to ANN and SVR-linearmodels is appreciated from Figs. 6e8.

For SVR representations, the optimal values for C in the case oflinear and polynomial kernel functions were found to be 15 and 6.Moreover, the optimal values for ε parameter in the case of linearand polynomial kernel functions were obtained 0.2 and 0.1,

Fig. 8. Mapping between experimental and predicted values b

respectively. Furthermore, optimal coefficient g and parameter b

for polynomial functions were observed to be 0.5 and 2, respec-tively. Parameter C governs the compromise between errors of theε-SVR on training data and margin maximization, ε is influential onsupport vectors in the ε-SVR regression structures, b represents thelevel of polynomial kernel function and g is used for characteriza-tion of the polynomial kernel function. One substantial benefit ofSVRs is that while ANNs can suffer from multiple local minima, thesolution to an SVR converges to the global minima. Furthermore,the computational complexity of SVRs is independent of thedimensionality of the input space in contrast to that of ANN. ANNsutilize empirical risk minimization, while SVMs take advantage ofstructural risk minimization during the training stage. Additionally,the reason that SVRs often outperform ANNs is that while dealingwith a complex problem, SVMs are less disposed to the overfittingdrawback when compared to ANN.

y SVR-polynomial algorithm in the case of 68 data points.

H. Taghavifar, A. Mardani / Energy 66 (2014) 569e576576

6. Concluding remarks

The study was developed to model energy dissipation of run-off-road vehicles where the experimentations were carried out incontrolled condition of soil bin facility utilizing a well-equippedsingle-wheel tester. The input variables were five levels of wheelload (1, 2, 3, 4, and 5 kN), six tire inflation pressure (50, 100, 150,200, 250, and 300 kPa) and three forward velocities (0.7, 1.4 and2 m/s) forming a total 90 data points. Some state-of-the-artmethodologies such as SVR (support vector regression) includinglinear and polynomial functions and also ANN (artificial neuralnetworks) were applied to obtain a promising predicting tool. Onthe basis of some performance criteria, it was divulged that SVR-polynomial outperformed SVR-linear and ANN. It is advised to theresearchers to evaluate the findings of this study for other soiltextures to generalize the validity of the proposed model.

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