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Artificial Neural Network estimation of wheel rolling resistance in clay loam soil
Applied Soft Computing 13 (2013) 3544–3551
Contents lists available at SciVerse ScienceDirect
Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc
Artificial Neural Network estimation of wheel rolling resistance in clay loam soil Hamid Taghavifar a,∗ , Aref Mardani a , Haleh Karim-Maslak a , Hashem Kalbkhani b a b
Department of Mechanical Engineering of Agricultural Machinery, Faculty of Agriculture, Urmia University, Urmia, Iran Department of Electrical Engineering, Urmia University, Urmia, Iran
a r t i c l e
i n f o
Article history: Received 25 June 2012 Received in revised form 25 January 2013 Accepted 8 March 2013 Available online 24 April 2013 Keywords: Artificial Neural Networks Rolling resistance Soil bin Velocity Tire inflation pressure Vertical load
a b s t r a c t Despite of complex and nonlinear relationships imparting soil–wheel interactions, however, logical, nonrandomized, and manifold relations tackle to express and model the interactions which are valid for variety of conditions and are likely to be established whereas mathematical equations are restricted to present. A 3-10-1 feed-forward Artificial Neural Network (ANN) with back propagation (BP) learning algorithm was utilized to estimate the rolling resistance of wheel as affected by velocity, tire inflation pressure, and normal load acting on wheel inside the soil bin facility creating controlled condition for test run. The model represented mean squared error MSE of 0.0257 and predicted relative error values with less than 10% and high coefficient of determination (R2 ) equal to 0.9322 utilizing experimental output data obtained from single-wheel tester of soil bin facility. These rewarding outcomes signify the fitting exploit of ANN for prediction of rolling resistance as a practical model with high accuracy in clay loam soil. Derived data revealed rolling resistance is less affected by applicable velocities of tractors in farmlands nevertheless is much influenced by inflation pressure and vertical load. An approximate constant relationship existed between velocity and rolling resistance implying that rolling resistance is not function of velocity chiefly in lower ones. Increase of inflation pressure results in decrease of rolling resistance while increase of vertical load brings about increase of rolling resistance which was measured to be function of vertical load by polynomial with order of two model validated by conventional models such as Wismer and Luth model. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The current study intends to estimate wheel rolling resistance utilizing Artificial Neural Network (ANN). Traction performance is the most imperative characteristic of agricultural tractors. Total traction and rolling resistance should be subtracted in order to acquire net traction. Obviously rolling resistance is the principal attribute affecting traction performance. Moreover, rolling resistance is extremely influential on fuel consumption. Energy loss due to erroneous management of agricultural tires was reported to be about 575 million liters per year in USA [1]. This statistic spotlights the prerequisites on minimizing the rolling resistance to the lowest possible level. Rolling resistance is naturally negative force applied on wheel against with the forward direction of movement. In other words, it is a direct function
∗ Corresponding author at: Department of Mechanical Engineering of Agricultural Machinery, Faculty of Agriculture, Urmia University, Nazloo Road, Urmia 571531177, Iran. Tel.: +98 441 2770508; fax: +98 441 2771926. E-mail addresses: st [email protected], [email protected], [email protected] (H. Taghavifar). 1568-4946/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2013.03.017
of required energy to deform the soil under a wheel as well as tire deformation while initiating to roll. Tire deformation generates tire’s heating up and consequent energy loss whiles the latter component of rolling resistance (i.e. soil deformation) proceed further concern of soil compaction. Rolling resistance as a major soil–wheel interaction production has been investigated by various researchers. Bekkar [2] established the relations between wheel and soil while described amount of rolling resistance to be influenced by variety of parameters may be expressed by: R=
3W ((2n+2)/(2n+1)) (3 − n)
((2n+2)/(2n+1))
(n + 1)(KC + bKϕ )
(1/(2n+1)) ((n+1)/(2n+1)) d
(1) where KC and Kϕ have been yielded from pressure sinkage equation as follows: P=
K
C
b
+ Kϕ Z n
(2)
where P yields pressure-sinkage equation in kPa, W is vehicle weight in kN, n is sinkage exponent, b is the smaller dimension of the rectangular contact area in m, d is wheel diameter in m, Z is
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the sinkage in m, and KC and Kϕ are the soil condition parameters. The required energy to compact the soil beneath the wheel during movement for a definite distance equals with a resistive force against movement multiplied by the distance. This resistive force (i.e. rolling resistance) is suggested to be yielded as:
R = bw 0
Zmax
K
C
b
+ Kϕ Z n dz
(3)
where R is rolling resistance in kN and bw is wheel width in m and the other parameters are introduced above. Validity of equation above in order to predict rolling resistance based on soil deformation was offered by Wong [3] for wheel diameters more than 50 cm and sinkage levels less than 15% of wheel diameter. There are numerous parameters affecting rolling resistance of them wheel diameter, tire inflation pressure, multipass, soil texture, sinkage, wheel slip, normal load, and velocity can be included. In 1971, the effect of wheel speed on rolling resistance was verified by Pope at velocities of between 0.1 and 5.5 m/s and reported the reverse relation between speed and rolling resistance [4]. Elwaleed et al. [5] reported the effect of inflation pressure on motion resistance in their experiments. Way and Kishimoto [6] surveyed soil–wheel interaction and approved the influence of velocity on rolling resistance especially for high speeds. Zoz and Grisso [7] reported identical results in their experiments. McAllister [8] observed reduction in the rolling resistance of wheels determining the values of the coefficient of rolling resistance (CRR) for wheels. The results indicated that reductions in CRR can be produced by reducing inflation pressure and vertical load. Coutermarsh [9] claimed that in dry sand, the rolling resistance has linear relation with velocity until the tire starts to plane, and then it becomes stabilized or decreases. Soft computing technology is an interdisciplinary research approach which includes statistics, machine learning, Artificial Neural Network (ANN) and fuzzy data analysis in computational science to analyze data [10]. Hence, the methods of artificial intelligence have greatly been used in the different fields of the agricultural applications [10]. Of soft computing approaches, ANNs are used which are constituted from several elements known as neurons and is an idea of data processing inspired from human neural network. ANNs feature the capability of finding out the correlation between the input and output data [11] and has the ability to deal with manifold variables as well as linear and non-linear relationships [12]. ANNs have been carried out in the fields of pattern, recognition, modeling, and control in an effectively manner [13]. Roul et al. [14] successfully applied ANN representation predicting the draught requirement of tillage implements under varying operating and soil conditions. A neural network is adjusted for a definite task such as model distinguishing and data classification during a training process. Extensive aptitude of this approach for accurate estimations of complicated regressions contributes more advantage compared to classical statistical techniques. Each input to the ANN is multiplied by the synaptic weight, added together and dealt with an activation function while ANNs are trained by frequently exploring the best relationship between the input and output values creating a model after a sufficient number of learning repetitions, or training known as epochs [15]. After training, the neural representation has generalization capacity with new input values to predict, simulate and re-establish the condition identified as testing procedure. Tire movement progression on soil is necessarily sophisticated behavior encountering numerous variables. There have been three variables in the present research including forward velocity, vertical load applied on wheel, and tire inflation pressure. The experimental investigation was carried out in a soil bin facility. Moreover, soil resistance described with cone index (CI) is a complicated variable and is difficult to be repeated
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with the purpose of test replicates. Soil processing, however, is more complex to achieve the same soil condition for soil resistance parameter and regarding the dependence of conventional statistical methods to test repetitions, ANNs facilitates this predicament since it is free of dependence to a constant variable during repeated tests. This study was conducted developing the objectives of investigating the effect of velocity, tire inflation pressure, and vertical load on rolling resistance in a soil bin facility and utilizing ANNs to predict and model the inter-relations between each variable and the objective parameter with acceptable performance, high coefficient of determination, low MSE and simple topology.
2. Materials and methods 2.1. Data acquisition A long soil bin was built in 2010 in the Faculty of Agriculture, Urmia University, Iran. This soil bin has 23 m length, 2 m width and 1 m depth [16]. This long channel had the ability to hold a wheel carriage, a single-wheel tester, and different tillage tools to be moved altogether in the length of the soil bin. The facility to fill the channel with various soil textures and different moisture contents provided higher advantage in comparison with uncontrolled conditions. A three-phase electromotor of 30 hp was used to move a carriage through the length of soil bin by means of chain system along with the wheel-tester when the carriage had the ability to traverse at the speed of about 20 km/h. The output shaft of the electromotor was connected to the drive shaft of the chains that pull the carriage forward or reverse. An inverter providing variable frequencies was used to supply power of electromotor in order to reach varying velocities. Another advantage of this system is the facility of adjusting braking and starting acceleration of electromotor which results in decrease of inertia forces. Four S-shape load cells with the capacity of 200 kg were calibrated and then were placed at proper places horizontally in parallel pattern between carriage and single-wheel tester and these load cells were interfaced to data acquisition system included a data logger, enabled monitoring the data on a screen and simultaneously, the data were sent to a computer with frequencies of around 30 Hz. A single-wheel tester was assembled to the carriage system with four S-shape load cells to measure the rolling resistance alterations caused by motion of wheel in various treatments being tested. The utilized driven tire was Good year 9.5L-14, 6 radial ply agricultural tractor tire. The system set up is shown in Fig. 1 The measured volume of soil bin was assessed to be 46 m3 and consequently was filled with soil. To initiate the process, the electromotor generated power for the carriage movement based on adjusted velocity by an inverter by connection between the shafts of electromotor and chain system. An optic tachometer was used to measure the speed of carriage while an inverter could produce variety of velocities for the carriage. The movement of carriage by chain system generated traction of single-wheel tester in the soil bin and accordingly, load cells sent signals to the data acquisition system which were indicators of rolling resistance of wheel and eventually, data acquisition system enabled monitoring these data and also transferring them to the computer. Transmitted files were recorded as txt files and subsequently transferred to MATLAB software (version 7.6, 2008, Mathworks Company) for being processed. Summary of treatments being tested is shown in Table 1. The soil bin was filled with clay-loam soil to simulate the real condition of farms that exists in most of regions in Urmia, Iran. Particular equipments were employed to organize soil bed including leveler and harrow since it is exceedingly crucial to have wellprepared soil inside soil bin for acquiring reliable and precise results
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Table 1 Summary of input and output variables ranges. Input (Independent variables)
Parameter
Unit
Levels
1 2 3
Velocity Inflation pressure Wheel load
m/s kPa kgf
0.7 100 100
1.4 200 200
Output (dependent variables)
Parameter
Unit
1
Rolling resistance
N
Table 2 Soil constituents and its measured properties. Item
Value
Sand (%) Silt (%) Clay (%) Bulk density (kg/m3 ) Frictional angle (◦ ) Cone index (kPa)
34.3 22.2 43.5 2360 32 700
from this experiment. Additionally, they were used since soil condition should be reverted to previous state soil constituents and its properties are defined in Table 2. 2.2. Artificial Neural Network representation Soil–tool interactions demonstrate complex behaviors whilst the output data are dependent on various input data. The predictions of dependent parameters are being carried out with higher advantage compared with conventional statistical techniques [17]. The high capability of ANNs, nonlinear relations between input and output variables are possible to be estimated. A multilayer feedforward neural network is shown in Fig. 2 with back propagation (BP) algorithm. In this paper, a feed-forward Artificial Neural Network back-propagation algorithm was used. Since the experiments had three variables (velocity, tire inflation pressure and wheel load) and one output (rolling resistance), a neural network with one hidden layer could achieve acceptable performance. Increasing number of hidden layers may increase efficiency of system in terms of mean squared error (MSE), however, causes more computational complexity. Hence, MLP neural network with 3-N1 -1 architecture was considered. Determination of number of neurons in hidden layer (N1 ) is important step in MLP neural network design.
2.1 300 300
400
500
In order to determine the number of neurons in hidden layer, N1 was increased from 1 to 30. At the start of network training, initial weights and biases of neurons are chosen randomly. Therefore, for each number of hidden neurons (each network structure), network was trained for 100 times to overcome this problem. In each system training network was trained for 1000 epochs. Then, network with minimum value of MSE was considered for that structure. The size of obtained dataset was 13,000. 13,000 dataset numbers was due to the frequency of load cells (30 Hz) that could send 30 data per second. While the single-wheel tester was traversing, the wheel load was changing to be dynamic load which by frequency of load cells, overall amount of 13,000 datasets were obtained. Therefore, 13,000 different patterns were generated. These patterns were randomly divided into three different sets; i.e. training, validation, and testing. In training, validation, and testing step, 65%, 15%, and 20% of these patterns were used, respectively. Independent variables (i.e. inputs) were velocity, vertical load acting on wheel, and tire inflation pressure. The dependent variable (i.e. output) was rolling resistance. MATLAB software was utilized to make a representation for predicting the rolling resistance of wheel in a soil bin facility. It was noticed that the range of input variables were different. Hence, each of variables was normalized in the range of 0 to 1 by the following equation. Xn =
Xr − Xr,min Xr,max − Xr,min
(4)
where Xn denotes normalized input variable, Xr is raw input variable, and Xr,min and Xr,max denote minimum and maximum of raw input variable, respectively. Performance of system in each of training, validation, and testing steps is measured by mean squared error (MSE) which is calculated by: 1 (Yi,a − Yi,p )2 N N
MSE =
(5)
i=1
Fig. 1. System set up and components for laboratory testes.
Fig. 2. Architecture of developed multilayer feed-forward neural network for rolling resistance prediction.
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Table 3 Statistical properties of error of testing data samples. Minimum absolute error
Maximum absolute error
Mean
Standard deviation
0.0032
0.0784
0.0204
20.6431
Table 4 Statistical properties of training, validation, and testing samples. Partition
Source
Minimum
Maximum
Mean
Standard deviation
Training
Inflation pressure Velocity Vertical load Rolling resistance
100 0.7 82.10 −108.78
300 2.1 531.2 519.93
200.7 1.42 296.76 119.42
82.45 0.57 138.06 104.82
Validation
Inflation pressure Velocity Vertical load Rolling resistance
100 0.7 83.1 −78.4
300 2.1 532 506.66
201.01 1.42 295.54 121.24
82.13 0.58 138.80 107.75
Testing
Inflation pressure Velocity Vertical load Rolling resistance
100 0.7 81.9 −78.4
300 2.1 532.80 499.32
200.7 1.42 292.30 116.28
82.45 0.57 137.71 106.19
In order to develop the neural network representation, the method for training is to be decided. To evaluate the bestfitting representation, mean squared error (MSE) as index of network performance, was utilized. Five prominent training BP methods, Levenberg–Marquardt back-propagation as default algorithm in the software, Gradient descent back-propagation, BFGS quasi-Newton back-propagation, Resilient back-propagation, and Bayesian regulation back-propagation were used with the intention of achieving the lowest possible MSE. Training was conducted separately for each of the representations. Levenberg–Marquardt algorithm with Log-sigmoid transfer function provided the best results in training with the lowest MSE compared with the other methods being utilized in this study. The minimum MSE for different networks are presented in Table 3. It is seen minimum MSE is obtained for Levenberg–Marquardt BP algorithm with sigmoid transfer function for hidden layer. In Fig. 3, the MSE of training samples for different number of neurons in hidden layer with sigmoid transfer function and Levenberg–Marquardt BP algorithm is shown. As shown in Fig. 3a, MSE reduces considerably when N1 increases from 1 to 10 while it seems to be constant in the range of between 10 and 30. However more magnification of Fig. 3 between 10 and 30 numbers of neuron reveals that MSE decreases by increasing in number of neurons to be equal with 0.0256 which corresponds to the structure of 3-30-1 (Fig. 3b). Nevertheless, in order to have computationally efficient ANN and overcome overfitting of ANN, N1 equal to 10, which results in MSE of 0.0257, was selected as the optimal structure for the prediction. In Fig. 4, the MSE variations are shown for training and validation samples during number of epochs. In Table 4, statistical properties of MSE of testing set samples are presented. As seen in Table 4, the statistical properties of the training, testing, and validation sets are about the same under the
0.038
0.036
Mean Squared Error (MSE)
3. Results and discussion
a
0.034
0.032
0.03
0.028
0.026
0.024
0
5
10 15 20 25 Number of Neurons in the Hidden Layer (N1)
30
b 0.0257 0.0257
Mean Squared Error (MSE)
where Yi,a and Yi,p are ith output variables that obtained by experiment (actual) and neural network (predicted), respectively, and N is number of samples that used in each step. The index threshold of trained network was based on the accuracy of network based on test partition. Hence the closer value to zero was the criteria to decide which representation was better. The ANN is required to yield general solution than simply to learn the training data set.
0.0257
0.0257
0.0256
0.0256
0.0256 10
12
14 16 18 20 22 24 26 Number of Neurons in the Hidden Layer (N1)
28
30
Fig. 3. MSE of training and validation data for different number of epochs (a) between 0 and 30 and (b) between 10 and 30, respectively.
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18 16 14
MSE
12 10 8 6 4 2 0 0 10
1
2
10
10
3
10
Epoch
Fig. 4. Regression result of neural network training for MSE of all epochs (x-axis in log-scale).
effect of inflation pressure, velocity and vertical load. The range of input data for each of variables is shown for the partitions of training, test and validation, respectively. Also the minimum value and standard deviations for each of variables is inferable in Table 4. Representation accuracy of neural network for training is shown in Fig. 5 of R2 with 0.9322. As well, Representation accuracy of neural network test and validation are shown in Figs. 6 and 7 of R2 with 0.9064 and 0.9004, respectively. Coefficient of determination values for both network training and network test were obtained with acceptable accuracy. Other Transfer functions and BP training algorithms being utilized in ANN representations are presented in Table 5. The learning rate balances the level of descending the error after each epoch. The learning rate, LR, applies a larger or smaller portion of the respective adjustment to the old weight. If the factor is set to a large value, then the neural network may learn more quickly, however if there is a large changeability in the input
Fig. 5. Regression result of neural network training.
Fig. 6. Regression result of neural network test.
set then the network may not learn very well or at all. In real terms, setting the learning rate to a large value is inappropriate and counter-productive to learning. Usually, it is better to set the factor to a small value and edge it upward if the learning rate seems slow. Momentum operates as a low pass filter to settle sudden changes in the progress. Momentum basically allows a change to the weights to persist for a number of adjustment cycles. The magnitude of the persistence is controlled by the momentum factor. If the momentum factor is set to nonzero value, then increasingly greater persistence of previous adjustments is permitted in modifying the current adjustment. This can improve the learning rate in some situations, by helping to smooth out unusual conditions in the training set. The optimum values of learning rate and momentum of
Fig. 7. Regression result of neural network validation.
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Table 5 Transfer functions and BP training algorithms being utilized in ANN. Transfer function
Training algorithms
Topology
R2
MSE
Log-sigmoid transfer function Hyperbolic tangent sigmoid transfer function Hard-limit transfer function Normalized radial basis transfer function Triangular basis transfer function
lm (Levenberg–Marquardt backpropagation) gd (Gradient descent backpropagation) bfg (BFGS quasi-Newton backpropagation) rp (Resilient backpropagation) br (Bayesian regulation backpropagation)
3-10-1 3-14-1 3-17-1 3-16-1 3-17-1
0.9322 0.9237 0.8871 0.9037 0.8631
0.0257 0.3426 0.0898 0.3125 0.4916
Fig. 8. The effect of training rate and momentum values on learning ability of the ANN representation.
ANN used to predict the process was 0.3 and 0.6, respectively. Fig. 8 shows the effect of learning rate and momentum on the training MSE. The relation between each input variable and output parameter were separately extracted and plotted in Microsoft Office Excel 2007 in the condition of considering the other input variables to be constant. For example, in order to investigate the relation between velocity and rolling resistance (RR), two columns related to tire inflation pressure, and velocity were stabilized with the levels of 300 kPa and 1.4 m/s, respectively. The column related to velocity varied in the range of 0.7–2.1 m/s with scale of 0.05 m/s. After neural networks simulation, the outputs were returned to Microsoft Office Excel and were placed beside the column of velocity. Fig. 9 demonstrates the variation of rolling resistance with respect to velocity. Clearly, variation of rolling resistance in the range of tested velocities is negligible. It is perceived that the value of rolling resistance in the range of tested velocity in the soil bin is independent of velocity.
Fig. 9. Rolling resistance with respect to velocity.
Despite of reported results signifying increase of rolling resistance for speeds varying from 40 m/s to higher ones, rolling resistance has negligibly changed in this study when velocity increased from 0.7 to 2.1 m/s. In similar studies, Way and Kishimoto [6] reported an increasing linear relation between velocity and rolling resistance. This experiment was conducted for high velocities varying from 11 m/s and upper ones which are not frequently used as operational speeds of tractors in the farmlands. Unlikely, the results of this study is validated by the results reported by Zoz and Grisso [7] describing slight effect of velocity on rolling resistance in regular running velocities of tractors. The results reported by Coutermarsh [9] strengthens the results of present study while states in various inflation pressures, increase of velocity up to about 20 miles/h (8.9 m/s) does not seem to be effective although for higher speeds, rolling resistance commences to rise. Despite of reported results signifying increase of rolling resistance for speeds varying from 40 m/s to higher ones, rolling resistance has negligibly changed in this study when velocity varied from 0.7 to 2.1 m/s. Similar analysis comes factual when tire inflation pressure is considered as variable stabilizing the velocity and vertical load acting on wheel. The result of analysis is shown in Fig. 10 illustrating decrease of rolling resistance by increase of tire inflation pressure. Based on presented results, decrease of rolling resistance in higher inflation pressures is absolutely distinct while rapidly decreases in higher vertical loads. This phenomenon is possible to be interpreted regarding the important impact of tire deformation on rolling resistance since continuous tire deformation during rolling under high vertical loads require greater energy. Accordingly, increasing inflation pressure and decreasing tire deformation result in reduction of energy loss. A further input data to the network was vertical load as variable while the other input data were constant. Rolling resistance variation with respect to vertical load is demonstrated in Fig. 11 R2 value 0.9868 was obtained with high reliability as shown in Fig. 11.
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Fig. 12. Theoretical relation between vertical load and rolling resistance using Wismer and Luth suggested equation. Fig. 10. Rolling resistance with respect to tire inflation pressure.
It is noticeable that rolling resistance is approximately polynomial (with order of two) function of vertical load. Although the regression value in Fig. 11 suggests a linear relation between vertical load and rolling resistance but in contrast, it seems more reasonable to describe their relation as a quadratic equation while rolling resistance is function of vertical load. Of conventional predicting models, Wismer and Luth [18] equation can be exemplified based on wheel numerics as follows (Eq. (6)): R=
1.2 × W 2 + 0.04W CI · b · d
(6)
where W is vertical load in N, CI is cone index in kPa, b is width of tire in m, and d is wheel diameter in m. Fig. 12 demonstrates the relation between vertical load and rolling resistance using Eq. (4) where CI is 700 kPa, b is 0.2 m, and d is 0.7 m for the tested tire. Obviously, the results of current study expressing interrelation between vertical load and rolling resistance suggest an acceptable correlation. Reliability of this investigation is apparently validated by Eq. (6) and Fig. 12. The latest input variable to the network in order to investigate the impact of dynamic load on rolling resistance was a sinusoidal load with static load of 4 kN and dynamic load frequency of 1 Hz. This load with the equation of W(t) = 4000 + 500 sin ωt was created
Fig. 11. Rolling resistance with respect to vertical load.
as column of W(t) and was introduced to the network as variable (i.e. input data) while tire inflation pressure and vertical load were stable. The output data of trained neural network was obtained after plotting and conforming to sinusoidal equation of dynamic load as shown in Fig. 13. Accordingly, the fluctuations of both rolling resistance and dynamic load are in high concord while the variations of diagrams were acquired in sinusoidal form while RR was shifted to higher values to signify vertical load and RR relation. From the high harmony of these diagrams, it is inferred that dynamic load and rolling resistance have approximately linear relation. Application of ANN in the current study revealed that on the subject of conventional models, neither mathematical nor analytical models could express complex nonlinear relations between soil–tire parameters and in the cases being performed, the sophisticated models were incapable of being used extensively for all of soil–tire interaction conditions because of their restricted mathematical function shapes. Advantage of utilizing ANN in the present research was obtaining accurate simulation as well as precise estimation of wheel rolling resistance which is competent to be conducted for nonlinear relations existing in soil–tire interactions. The results generally confirm the reliability of the network in predicting the rolling resistance in a clay loam soil. However, more studies are required for other soils to make it a generalized ANN representation.
Fig. 13. Rolling resistance along with dynamic load.
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4. Conclusion
References
Single wheel-tester in a soil bin was utilized to investigate the influence of prominent parameters of velocity, inflation pressure, and vertical load on rolling resistance accurately. Experimentations were carried out at three levels of velocity (i.e. 0.7, 1.4, and 2.1 m/s), three levels of inflation pressure (i.e. 100, 200, and 300 kPa), five levels of vertical load (i.e. 1, 2, 3, 4, and 5 kN), and dynamic sinusoidal load with static load of 4 kN and dynamic load frequency of 1 Hz with the equation of W(t) = 4000 + 500 sin ωt. ANN representation was trained with BP feed-forward algorithm with trial and error method was developed, trained and tested for prediction of rolling resistance as affected by input variables. A 3-10-1 representation, consisted of three input data and one hidden layer with manifold nodes, represented relative error of predicted values with less than 10% which is in acceptable limit. ANN representation indicated following results:
[1] Wulfsohn, D., Tractive Characteristics of Radial Ply and Bias Ply Tires in a California Soil. M.S. Thesis, Dept. of Agr. Eng., University of California, Davis, 1987. [2] M.G. Bekkar, Off Road Locomotion. Research and Development in Terramechanics, The University of Michigan Press, Ann Arbor, Michigan, 1960. [3] J.Y. Wong, On the study of wheel–soil interaction, Journal of Terramechanics 21 (2) (1984) 117–131. [4] R.G. Pope, The effect of wheel speed on rolling resistance? Journal of Terramechanics 8 (1) (1971) 51–58. [5] A.K. Elwaleed, A. Yahya, M. Zohadie, D. Ahmad, A.F. Kheiralla, Effect of inflation pressure on motion resistance ratio of a high-lug agricultural tyre, Journal of Terramechanics 43 (2) (2006) 69–84. [6] T.R. Way, T. Kishimoto, Interface pressures of a tractor drive tyre on structured and loose soils? Biosystem Engineering 87 (3) (2004) 375–386. [7] F.M. Zoz, R.D. Grisso, Traction and Tractor Performance, ASAE Publication Number 913C0430, 2003. [8] M. McAllister, Reduction in the rolling resistance of tyres for trailed agricultural machinery, Journal of Agricultural Engineering Research 28 (2) (1983) 127–137. [9] B. Coutermarsh, Velocity effect of vehicle rolling resistance in sand, Journal of Terramechanics 44 (4) (2007) 275–291. [10] K. C¸arman, Prediction of soil compaction under pneumatic tires a using fuzzy logic approach, Journal of Terramechanics 45(4) (2008) 103–108. [11] G. Mittal, Zhang F S., Artificial neural network-based psychometric predictor, Biosystems Engineering 85 (3) (2003) 283–284. [12] Q. Zhang, S.X. Yang, G.S. Mittal, S. Yi, Prediction performance indices and optimal parameters of rough rice drying using neural networks, Biosystems Engineering 83 (3) (2002) 281–290. [13] S.S. Haykin, Neural Networks: A comprehensive Foundation, Prentice-Hall, Upper Saddle River, NJ, USA, 1999. [14] A.K. Roul, H. Raheman, M.S. Pansare, R. Machavaram, Predicting the draught requirement of tillage implements in sandy clay loam soil using an artificial neural network, Biosystems Engineering 104 (4) (2009) 476–485. [15] S. Jaiswal, E.R. Benson, J.C. Bernard, G.L. Van Wicklen, Neural network modelling and sensitivity analysis of a mechanical poultry catching system, Biosystems Engineering 92 (1) (2005) 59–68. [16] A. Mardani, K. Shahidi, A. Rahmani, B. Mashoofi, H. Karimmaslak, Studies on a long soil bin for soil–tool interaction, Cercet˘ari Agronomice în Moldova XLIII (2 142) (2010) 5–10. [17] Z.X. Zhang, R.L. Kushwaha, Application of neural networks to simulate soil tool interaction and soil behaviour, Canadian Agricultural Engineering 41 (2) (1999) 119–125. [18] R.D. Wismer, H.J. Luth, Off-road traction prediction for wheeled vehicles, Journal of Terramechanics 10 (2) (1973) 49–61.
1. A 3-10-1 ANN was effectively developed predicting the relation between rolling resistance as output data and each of predescribed input variables. 2. The rolling resistance has approximately constant relation with low velocities (0.7, 1.4, and 2.1 m/s) tested in this study which are in the range of practical speeds of tractors. 3. Increase of inflation pressure brings about reverse relation with rolling resistance particularly for higher values of vertical load. 4. Increases of vertical load results in increase of rolling resistance with polynomial order of two. 5. Dynamic load with sinusoidal function and rolling resistance have approximately linear relation indicating the increase of dynamic load induces increase or rolling resistance and reverse.
Contents lists available at SciVerse ScienceDirect
Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc
Artificial Neural Network estimation of wheel rolling resistance in clay loam soil Hamid Taghavifar a,∗ , Aref Mardani a , Haleh Karim-Maslak a , Hashem Kalbkhani b a b
Department of Mechanical Engineering of Agricultural Machinery, Faculty of Agriculture, Urmia University, Urmia, Iran Department of Electrical Engineering, Urmia University, Urmia, Iran
a r t i c l e
i n f o
Article history: Received 25 June 2012 Received in revised form 25 January 2013 Accepted 8 March 2013 Available online 24 April 2013 Keywords: Artificial Neural Networks Rolling resistance Soil bin Velocity Tire inflation pressure Vertical load
a b s t r a c t Despite of complex and nonlinear relationships imparting soil–wheel interactions, however, logical, nonrandomized, and manifold relations tackle to express and model the interactions which are valid for variety of conditions and are likely to be established whereas mathematical equations are restricted to present. A 3-10-1 feed-forward Artificial Neural Network (ANN) with back propagation (BP) learning algorithm was utilized to estimate the rolling resistance of wheel as affected by velocity, tire inflation pressure, and normal load acting on wheel inside the soil bin facility creating controlled condition for test run. The model represented mean squared error MSE of 0.0257 and predicted relative error values with less than 10% and high coefficient of determination (R2 ) equal to 0.9322 utilizing experimental output data obtained from single-wheel tester of soil bin facility. These rewarding outcomes signify the fitting exploit of ANN for prediction of rolling resistance as a practical model with high accuracy in clay loam soil. Derived data revealed rolling resistance is less affected by applicable velocities of tractors in farmlands nevertheless is much influenced by inflation pressure and vertical load. An approximate constant relationship existed between velocity and rolling resistance implying that rolling resistance is not function of velocity chiefly in lower ones. Increase of inflation pressure results in decrease of rolling resistance while increase of vertical load brings about increase of rolling resistance which was measured to be function of vertical load by polynomial with order of two model validated by conventional models such as Wismer and Luth model. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The current study intends to estimate wheel rolling resistance utilizing Artificial Neural Network (ANN). Traction performance is the most imperative characteristic of agricultural tractors. Total traction and rolling resistance should be subtracted in order to acquire net traction. Obviously rolling resistance is the principal attribute affecting traction performance. Moreover, rolling resistance is extremely influential on fuel consumption. Energy loss due to erroneous management of agricultural tires was reported to be about 575 million liters per year in USA [1]. This statistic spotlights the prerequisites on minimizing the rolling resistance to the lowest possible level. Rolling resistance is naturally negative force applied on wheel against with the forward direction of movement. In other words, it is a direct function
∗ Corresponding author at: Department of Mechanical Engineering of Agricultural Machinery, Faculty of Agriculture, Urmia University, Nazloo Road, Urmia 571531177, Iran. Tel.: +98 441 2770508; fax: +98 441 2771926. E-mail addresses: st [email protected], [email protected], [email protected] (H. Taghavifar). 1568-4946/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2013.03.017
of required energy to deform the soil under a wheel as well as tire deformation while initiating to roll. Tire deformation generates tire’s heating up and consequent energy loss whiles the latter component of rolling resistance (i.e. soil deformation) proceed further concern of soil compaction. Rolling resistance as a major soil–wheel interaction production has been investigated by various researchers. Bekkar [2] established the relations between wheel and soil while described amount of rolling resistance to be influenced by variety of parameters may be expressed by: R=
3W ((2n+2)/(2n+1)) (3 − n)
((2n+2)/(2n+1))
(n + 1)(KC + bKϕ )
(1/(2n+1)) ((n+1)/(2n+1)) d
(1) where KC and Kϕ have been yielded from pressure sinkage equation as follows: P=
K
C
b
+ Kϕ Z n
(2)
where P yields pressure-sinkage equation in kPa, W is vehicle weight in kN, n is sinkage exponent, b is the smaller dimension of the rectangular contact area in m, d is wheel diameter in m, Z is
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the sinkage in m, and KC and Kϕ are the soil condition parameters. The required energy to compact the soil beneath the wheel during movement for a definite distance equals with a resistive force against movement multiplied by the distance. This resistive force (i.e. rolling resistance) is suggested to be yielded as:
R = bw 0
Zmax
K
C
b
+ Kϕ Z n dz
(3)
where R is rolling resistance in kN and bw is wheel width in m and the other parameters are introduced above. Validity of equation above in order to predict rolling resistance based on soil deformation was offered by Wong [3] for wheel diameters more than 50 cm and sinkage levels less than 15% of wheel diameter. There are numerous parameters affecting rolling resistance of them wheel diameter, tire inflation pressure, multipass, soil texture, sinkage, wheel slip, normal load, and velocity can be included. In 1971, the effect of wheel speed on rolling resistance was verified by Pope at velocities of between 0.1 and 5.5 m/s and reported the reverse relation between speed and rolling resistance [4]. Elwaleed et al. [5] reported the effect of inflation pressure on motion resistance in their experiments. Way and Kishimoto [6] surveyed soil–wheel interaction and approved the influence of velocity on rolling resistance especially for high speeds. Zoz and Grisso [7] reported identical results in their experiments. McAllister [8] observed reduction in the rolling resistance of wheels determining the values of the coefficient of rolling resistance (CRR) for wheels. The results indicated that reductions in CRR can be produced by reducing inflation pressure and vertical load. Coutermarsh [9] claimed that in dry sand, the rolling resistance has linear relation with velocity until the tire starts to plane, and then it becomes stabilized or decreases. Soft computing technology is an interdisciplinary research approach which includes statistics, machine learning, Artificial Neural Network (ANN) and fuzzy data analysis in computational science to analyze data [10]. Hence, the methods of artificial intelligence have greatly been used in the different fields of the agricultural applications [10]. Of soft computing approaches, ANNs are used which are constituted from several elements known as neurons and is an idea of data processing inspired from human neural network. ANNs feature the capability of finding out the correlation between the input and output data [11] and has the ability to deal with manifold variables as well as linear and non-linear relationships [12]. ANNs have been carried out in the fields of pattern, recognition, modeling, and control in an effectively manner [13]. Roul et al. [14] successfully applied ANN representation predicting the draught requirement of tillage implements under varying operating and soil conditions. A neural network is adjusted for a definite task such as model distinguishing and data classification during a training process. Extensive aptitude of this approach for accurate estimations of complicated regressions contributes more advantage compared to classical statistical techniques. Each input to the ANN is multiplied by the synaptic weight, added together and dealt with an activation function while ANNs are trained by frequently exploring the best relationship between the input and output values creating a model after a sufficient number of learning repetitions, or training known as epochs [15]. After training, the neural representation has generalization capacity with new input values to predict, simulate and re-establish the condition identified as testing procedure. Tire movement progression on soil is necessarily sophisticated behavior encountering numerous variables. There have been three variables in the present research including forward velocity, vertical load applied on wheel, and tire inflation pressure. The experimental investigation was carried out in a soil bin facility. Moreover, soil resistance described with cone index (CI) is a complicated variable and is difficult to be repeated
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with the purpose of test replicates. Soil processing, however, is more complex to achieve the same soil condition for soil resistance parameter and regarding the dependence of conventional statistical methods to test repetitions, ANNs facilitates this predicament since it is free of dependence to a constant variable during repeated tests. This study was conducted developing the objectives of investigating the effect of velocity, tire inflation pressure, and vertical load on rolling resistance in a soil bin facility and utilizing ANNs to predict and model the inter-relations between each variable and the objective parameter with acceptable performance, high coefficient of determination, low MSE and simple topology.
2. Materials and methods 2.1. Data acquisition A long soil bin was built in 2010 in the Faculty of Agriculture, Urmia University, Iran. This soil bin has 23 m length, 2 m width and 1 m depth [16]. This long channel had the ability to hold a wheel carriage, a single-wheel tester, and different tillage tools to be moved altogether in the length of the soil bin. The facility to fill the channel with various soil textures and different moisture contents provided higher advantage in comparison with uncontrolled conditions. A three-phase electromotor of 30 hp was used to move a carriage through the length of soil bin by means of chain system along with the wheel-tester when the carriage had the ability to traverse at the speed of about 20 km/h. The output shaft of the electromotor was connected to the drive shaft of the chains that pull the carriage forward or reverse. An inverter providing variable frequencies was used to supply power of electromotor in order to reach varying velocities. Another advantage of this system is the facility of adjusting braking and starting acceleration of electromotor which results in decrease of inertia forces. Four S-shape load cells with the capacity of 200 kg were calibrated and then were placed at proper places horizontally in parallel pattern between carriage and single-wheel tester and these load cells were interfaced to data acquisition system included a data logger, enabled monitoring the data on a screen and simultaneously, the data were sent to a computer with frequencies of around 30 Hz. A single-wheel tester was assembled to the carriage system with four S-shape load cells to measure the rolling resistance alterations caused by motion of wheel in various treatments being tested. The utilized driven tire was Good year 9.5L-14, 6 radial ply agricultural tractor tire. The system set up is shown in Fig. 1 The measured volume of soil bin was assessed to be 46 m3 and consequently was filled with soil. To initiate the process, the electromotor generated power for the carriage movement based on adjusted velocity by an inverter by connection between the shafts of electromotor and chain system. An optic tachometer was used to measure the speed of carriage while an inverter could produce variety of velocities for the carriage. The movement of carriage by chain system generated traction of single-wheel tester in the soil bin and accordingly, load cells sent signals to the data acquisition system which were indicators of rolling resistance of wheel and eventually, data acquisition system enabled monitoring these data and also transferring them to the computer. Transmitted files were recorded as txt files and subsequently transferred to MATLAB software (version 7.6, 2008, Mathworks Company) for being processed. Summary of treatments being tested is shown in Table 1. The soil bin was filled with clay-loam soil to simulate the real condition of farms that exists in most of regions in Urmia, Iran. Particular equipments were employed to organize soil bed including leveler and harrow since it is exceedingly crucial to have wellprepared soil inside soil bin for acquiring reliable and precise results
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Table 1 Summary of input and output variables ranges. Input (Independent variables)
Parameter
Unit
Levels
1 2 3
Velocity Inflation pressure Wheel load
m/s kPa kgf
0.7 100 100
1.4 200 200
Output (dependent variables)
Parameter
Unit
1
Rolling resistance
N
Table 2 Soil constituents and its measured properties. Item
Value
Sand (%) Silt (%) Clay (%) Bulk density (kg/m3 ) Frictional angle (◦ ) Cone index (kPa)
34.3 22.2 43.5 2360 32 700
from this experiment. Additionally, they were used since soil condition should be reverted to previous state soil constituents and its properties are defined in Table 2. 2.2. Artificial Neural Network representation Soil–tool interactions demonstrate complex behaviors whilst the output data are dependent on various input data. The predictions of dependent parameters are being carried out with higher advantage compared with conventional statistical techniques [17]. The high capability of ANNs, nonlinear relations between input and output variables are possible to be estimated. A multilayer feedforward neural network is shown in Fig. 2 with back propagation (BP) algorithm. In this paper, a feed-forward Artificial Neural Network back-propagation algorithm was used. Since the experiments had three variables (velocity, tire inflation pressure and wheel load) and one output (rolling resistance), a neural network with one hidden layer could achieve acceptable performance. Increasing number of hidden layers may increase efficiency of system in terms of mean squared error (MSE), however, causes more computational complexity. Hence, MLP neural network with 3-N1 -1 architecture was considered. Determination of number of neurons in hidden layer (N1 ) is important step in MLP neural network design.
2.1 300 300
400
500
In order to determine the number of neurons in hidden layer, N1 was increased from 1 to 30. At the start of network training, initial weights and biases of neurons are chosen randomly. Therefore, for each number of hidden neurons (each network structure), network was trained for 100 times to overcome this problem. In each system training network was trained for 1000 epochs. Then, network with minimum value of MSE was considered for that structure. The size of obtained dataset was 13,000. 13,000 dataset numbers was due to the frequency of load cells (30 Hz) that could send 30 data per second. While the single-wheel tester was traversing, the wheel load was changing to be dynamic load which by frequency of load cells, overall amount of 13,000 datasets were obtained. Therefore, 13,000 different patterns were generated. These patterns were randomly divided into three different sets; i.e. training, validation, and testing. In training, validation, and testing step, 65%, 15%, and 20% of these patterns were used, respectively. Independent variables (i.e. inputs) were velocity, vertical load acting on wheel, and tire inflation pressure. The dependent variable (i.e. output) was rolling resistance. MATLAB software was utilized to make a representation for predicting the rolling resistance of wheel in a soil bin facility. It was noticed that the range of input variables were different. Hence, each of variables was normalized in the range of 0 to 1 by the following equation. Xn =
Xr − Xr,min Xr,max − Xr,min
(4)
where Xn denotes normalized input variable, Xr is raw input variable, and Xr,min and Xr,max denote minimum and maximum of raw input variable, respectively. Performance of system in each of training, validation, and testing steps is measured by mean squared error (MSE) which is calculated by: 1 (Yi,a − Yi,p )2 N N
MSE =
(5)
i=1
Fig. 1. System set up and components for laboratory testes.
Fig. 2. Architecture of developed multilayer feed-forward neural network for rolling resistance prediction.
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Table 3 Statistical properties of error of testing data samples. Minimum absolute error
Maximum absolute error
Mean
Standard deviation
0.0032
0.0784
0.0204
20.6431
Table 4 Statistical properties of training, validation, and testing samples. Partition
Source
Minimum
Maximum
Mean
Standard deviation
Training
Inflation pressure Velocity Vertical load Rolling resistance
100 0.7 82.10 −108.78
300 2.1 531.2 519.93
200.7 1.42 296.76 119.42
82.45 0.57 138.06 104.82
Validation
Inflation pressure Velocity Vertical load Rolling resistance
100 0.7 83.1 −78.4
300 2.1 532 506.66
201.01 1.42 295.54 121.24
82.13 0.58 138.80 107.75
Testing
Inflation pressure Velocity Vertical load Rolling resistance
100 0.7 81.9 −78.4
300 2.1 532.80 499.32
200.7 1.42 292.30 116.28
82.45 0.57 137.71 106.19
In order to develop the neural network representation, the method for training is to be decided. To evaluate the bestfitting representation, mean squared error (MSE) as index of network performance, was utilized. Five prominent training BP methods, Levenberg–Marquardt back-propagation as default algorithm in the software, Gradient descent back-propagation, BFGS quasi-Newton back-propagation, Resilient back-propagation, and Bayesian regulation back-propagation were used with the intention of achieving the lowest possible MSE. Training was conducted separately for each of the representations. Levenberg–Marquardt algorithm with Log-sigmoid transfer function provided the best results in training with the lowest MSE compared with the other methods being utilized in this study. The minimum MSE for different networks are presented in Table 3. It is seen minimum MSE is obtained for Levenberg–Marquardt BP algorithm with sigmoid transfer function for hidden layer. In Fig. 3, the MSE of training samples for different number of neurons in hidden layer with sigmoid transfer function and Levenberg–Marquardt BP algorithm is shown. As shown in Fig. 3a, MSE reduces considerably when N1 increases from 1 to 10 while it seems to be constant in the range of between 10 and 30. However more magnification of Fig. 3 between 10 and 30 numbers of neuron reveals that MSE decreases by increasing in number of neurons to be equal with 0.0256 which corresponds to the structure of 3-30-1 (Fig. 3b). Nevertheless, in order to have computationally efficient ANN and overcome overfitting of ANN, N1 equal to 10, which results in MSE of 0.0257, was selected as the optimal structure for the prediction. In Fig. 4, the MSE variations are shown for training and validation samples during number of epochs. In Table 4, statistical properties of MSE of testing set samples are presented. As seen in Table 4, the statistical properties of the training, testing, and validation sets are about the same under the
0.038
0.036
Mean Squared Error (MSE)
3. Results and discussion
a
0.034
0.032
0.03
0.028
0.026
0.024
0
5
10 15 20 25 Number of Neurons in the Hidden Layer (N1)
30
b 0.0257 0.0257
Mean Squared Error (MSE)
where Yi,a and Yi,p are ith output variables that obtained by experiment (actual) and neural network (predicted), respectively, and N is number of samples that used in each step. The index threshold of trained network was based on the accuracy of network based on test partition. Hence the closer value to zero was the criteria to decide which representation was better. The ANN is required to yield general solution than simply to learn the training data set.
0.0257
0.0257
0.0256
0.0256
0.0256 10
12
14 16 18 20 22 24 26 Number of Neurons in the Hidden Layer (N1)
28
30
Fig. 3. MSE of training and validation data for different number of epochs (a) between 0 and 30 and (b) between 10 and 30, respectively.
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18 16 14
MSE
12 10 8 6 4 2 0 0 10
1
2
10
10
3
10
Epoch
Fig. 4. Regression result of neural network training for MSE of all epochs (x-axis in log-scale).
effect of inflation pressure, velocity and vertical load. The range of input data for each of variables is shown for the partitions of training, test and validation, respectively. Also the minimum value and standard deviations for each of variables is inferable in Table 4. Representation accuracy of neural network for training is shown in Fig. 5 of R2 with 0.9322. As well, Representation accuracy of neural network test and validation are shown in Figs. 6 and 7 of R2 with 0.9064 and 0.9004, respectively. Coefficient of determination values for both network training and network test were obtained with acceptable accuracy. Other Transfer functions and BP training algorithms being utilized in ANN representations are presented in Table 5. The learning rate balances the level of descending the error after each epoch. The learning rate, LR, applies a larger or smaller portion of the respective adjustment to the old weight. If the factor is set to a large value, then the neural network may learn more quickly, however if there is a large changeability in the input
Fig. 5. Regression result of neural network training.
Fig. 6. Regression result of neural network test.
set then the network may not learn very well or at all. In real terms, setting the learning rate to a large value is inappropriate and counter-productive to learning. Usually, it is better to set the factor to a small value and edge it upward if the learning rate seems slow. Momentum operates as a low pass filter to settle sudden changes in the progress. Momentum basically allows a change to the weights to persist for a number of adjustment cycles. The magnitude of the persistence is controlled by the momentum factor. If the momentum factor is set to nonzero value, then increasingly greater persistence of previous adjustments is permitted in modifying the current adjustment. This can improve the learning rate in some situations, by helping to smooth out unusual conditions in the training set. The optimum values of learning rate and momentum of
Fig. 7. Regression result of neural network validation.
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Table 5 Transfer functions and BP training algorithms being utilized in ANN. Transfer function
Training algorithms
Topology
R2
MSE
Log-sigmoid transfer function Hyperbolic tangent sigmoid transfer function Hard-limit transfer function Normalized radial basis transfer function Triangular basis transfer function
lm (Levenberg–Marquardt backpropagation) gd (Gradient descent backpropagation) bfg (BFGS quasi-Newton backpropagation) rp (Resilient backpropagation) br (Bayesian regulation backpropagation)
3-10-1 3-14-1 3-17-1 3-16-1 3-17-1
0.9322 0.9237 0.8871 0.9037 0.8631
0.0257 0.3426 0.0898 0.3125 0.4916
Fig. 8. The effect of training rate and momentum values on learning ability of the ANN representation.
ANN used to predict the process was 0.3 and 0.6, respectively. Fig. 8 shows the effect of learning rate and momentum on the training MSE. The relation between each input variable and output parameter were separately extracted and plotted in Microsoft Office Excel 2007 in the condition of considering the other input variables to be constant. For example, in order to investigate the relation between velocity and rolling resistance (RR), two columns related to tire inflation pressure, and velocity were stabilized with the levels of 300 kPa and 1.4 m/s, respectively. The column related to velocity varied in the range of 0.7–2.1 m/s with scale of 0.05 m/s. After neural networks simulation, the outputs were returned to Microsoft Office Excel and were placed beside the column of velocity. Fig. 9 demonstrates the variation of rolling resistance with respect to velocity. Clearly, variation of rolling resistance in the range of tested velocities is negligible. It is perceived that the value of rolling resistance in the range of tested velocity in the soil bin is independent of velocity.
Fig. 9. Rolling resistance with respect to velocity.
Despite of reported results signifying increase of rolling resistance for speeds varying from 40 m/s to higher ones, rolling resistance has negligibly changed in this study when velocity increased from 0.7 to 2.1 m/s. In similar studies, Way and Kishimoto [6] reported an increasing linear relation between velocity and rolling resistance. This experiment was conducted for high velocities varying from 11 m/s and upper ones which are not frequently used as operational speeds of tractors in the farmlands. Unlikely, the results of this study is validated by the results reported by Zoz and Grisso [7] describing slight effect of velocity on rolling resistance in regular running velocities of tractors. The results reported by Coutermarsh [9] strengthens the results of present study while states in various inflation pressures, increase of velocity up to about 20 miles/h (8.9 m/s) does not seem to be effective although for higher speeds, rolling resistance commences to rise. Despite of reported results signifying increase of rolling resistance for speeds varying from 40 m/s to higher ones, rolling resistance has negligibly changed in this study when velocity varied from 0.7 to 2.1 m/s. Similar analysis comes factual when tire inflation pressure is considered as variable stabilizing the velocity and vertical load acting on wheel. The result of analysis is shown in Fig. 10 illustrating decrease of rolling resistance by increase of tire inflation pressure. Based on presented results, decrease of rolling resistance in higher inflation pressures is absolutely distinct while rapidly decreases in higher vertical loads. This phenomenon is possible to be interpreted regarding the important impact of tire deformation on rolling resistance since continuous tire deformation during rolling under high vertical loads require greater energy. Accordingly, increasing inflation pressure and decreasing tire deformation result in reduction of energy loss. A further input data to the network was vertical load as variable while the other input data were constant. Rolling resistance variation with respect to vertical load is demonstrated in Fig. 11 R2 value 0.9868 was obtained with high reliability as shown in Fig. 11.
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Fig. 12. Theoretical relation between vertical load and rolling resistance using Wismer and Luth suggested equation. Fig. 10. Rolling resistance with respect to tire inflation pressure.
It is noticeable that rolling resistance is approximately polynomial (with order of two) function of vertical load. Although the regression value in Fig. 11 suggests a linear relation between vertical load and rolling resistance but in contrast, it seems more reasonable to describe their relation as a quadratic equation while rolling resistance is function of vertical load. Of conventional predicting models, Wismer and Luth [18] equation can be exemplified based on wheel numerics as follows (Eq. (6)): R=
1.2 × W 2 + 0.04W CI · b · d
(6)
where W is vertical load in N, CI is cone index in kPa, b is width of tire in m, and d is wheel diameter in m. Fig. 12 demonstrates the relation between vertical load and rolling resistance using Eq. (4) where CI is 700 kPa, b is 0.2 m, and d is 0.7 m for the tested tire. Obviously, the results of current study expressing interrelation between vertical load and rolling resistance suggest an acceptable correlation. Reliability of this investigation is apparently validated by Eq. (6) and Fig. 12. The latest input variable to the network in order to investigate the impact of dynamic load on rolling resistance was a sinusoidal load with static load of 4 kN and dynamic load frequency of 1 Hz. This load with the equation of W(t) = 4000 + 500 sin ωt was created
Fig. 11. Rolling resistance with respect to vertical load.
as column of W(t) and was introduced to the network as variable (i.e. input data) while tire inflation pressure and vertical load were stable. The output data of trained neural network was obtained after plotting and conforming to sinusoidal equation of dynamic load as shown in Fig. 13. Accordingly, the fluctuations of both rolling resistance and dynamic load are in high concord while the variations of diagrams were acquired in sinusoidal form while RR was shifted to higher values to signify vertical load and RR relation. From the high harmony of these diagrams, it is inferred that dynamic load and rolling resistance have approximately linear relation. Application of ANN in the current study revealed that on the subject of conventional models, neither mathematical nor analytical models could express complex nonlinear relations between soil–tire parameters and in the cases being performed, the sophisticated models were incapable of being used extensively for all of soil–tire interaction conditions because of their restricted mathematical function shapes. Advantage of utilizing ANN in the present research was obtaining accurate simulation as well as precise estimation of wheel rolling resistance which is competent to be conducted for nonlinear relations existing in soil–tire interactions. The results generally confirm the reliability of the network in predicting the rolling resistance in a clay loam soil. However, more studies are required for other soils to make it a generalized ANN representation.
Fig. 13. Rolling resistance along with dynamic load.
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4. Conclusion
References
Single wheel-tester in a soil bin was utilized to investigate the influence of prominent parameters of velocity, inflation pressure, and vertical load on rolling resistance accurately. Experimentations were carried out at three levels of velocity (i.e. 0.7, 1.4, and 2.1 m/s), three levels of inflation pressure (i.e. 100, 200, and 300 kPa), five levels of vertical load (i.e. 1, 2, 3, 4, and 5 kN), and dynamic sinusoidal load with static load of 4 kN and dynamic load frequency of 1 Hz with the equation of W(t) = 4000 + 500 sin ωt. ANN representation was trained with BP feed-forward algorithm with trial and error method was developed, trained and tested for prediction of rolling resistance as affected by input variables. A 3-10-1 representation, consisted of three input data and one hidden layer with manifold nodes, represented relative error of predicted values with less than 10% which is in acceptable limit. ANN representation indicated following results:
[1] Wulfsohn, D., Tractive Characteristics of Radial Ply and Bias Ply Tires in a California Soil. M.S. Thesis, Dept. of Agr. Eng., University of California, Davis, 1987. [2] M.G. Bekkar, Off Road Locomotion. Research and Development in Terramechanics, The University of Michigan Press, Ann Arbor, Michigan, 1960. [3] J.Y. Wong, On the study of wheel–soil interaction, Journal of Terramechanics 21 (2) (1984) 117–131. [4] R.G. Pope, The effect of wheel speed on rolling resistance? Journal of Terramechanics 8 (1) (1971) 51–58. [5] A.K. Elwaleed, A. Yahya, M. Zohadie, D. Ahmad, A.F. Kheiralla, Effect of inflation pressure on motion resistance ratio of a high-lug agricultural tyre, Journal of Terramechanics 43 (2) (2006) 69–84. [6] T.R. Way, T. Kishimoto, Interface pressures of a tractor drive tyre on structured and loose soils? Biosystem Engineering 87 (3) (2004) 375–386. [7] F.M. Zoz, R.D. Grisso, Traction and Tractor Performance, ASAE Publication Number 913C0430, 2003. [8] M. McAllister, Reduction in the rolling resistance of tyres for trailed agricultural machinery, Journal of Agricultural Engineering Research 28 (2) (1983) 127–137. [9] B. Coutermarsh, Velocity effect of vehicle rolling resistance in sand, Journal of Terramechanics 44 (4) (2007) 275–291. [10] K. C¸arman, Prediction of soil compaction under pneumatic tires a using fuzzy logic approach, Journal of Terramechanics 45(4) (2008) 103–108. [11] G. Mittal, Zhang F S., Artificial neural network-based psychometric predictor, Biosystems Engineering 85 (3) (2003) 283–284. [12] Q. Zhang, S.X. Yang, G.S. Mittal, S. Yi, Prediction performance indices and optimal parameters of rough rice drying using neural networks, Biosystems Engineering 83 (3) (2002) 281–290. [13] S.S. Haykin, Neural Networks: A comprehensive Foundation, Prentice-Hall, Upper Saddle River, NJ, USA, 1999. [14] A.K. Roul, H. Raheman, M.S. Pansare, R. Machavaram, Predicting the draught requirement of tillage implements in sandy clay loam soil using an artificial neural network, Biosystems Engineering 104 (4) (2009) 476–485. [15] S. Jaiswal, E.R. Benson, J.C. Bernard, G.L. Van Wicklen, Neural network modelling and sensitivity analysis of a mechanical poultry catching system, Biosystems Engineering 92 (1) (2005) 59–68. [16] A. Mardani, K. Shahidi, A. Rahmani, B. Mashoofi, H. Karimmaslak, Studies on a long soil bin for soil–tool interaction, Cercet˘ari Agronomice în Moldova XLIII (2 142) (2010) 5–10. [17] Z.X. Zhang, R.L. Kushwaha, Application of neural networks to simulate soil tool interaction and soil behaviour, Canadian Agricultural Engineering 41 (2) (1999) 119–125. [18] R.D. Wismer, H.J. Luth, Off-road traction prediction for wheeled vehicles, Journal of Terramechanics 10 (2) (1973) 49–61.
1. A 3-10-1 ANN was effectively developed predicting the relation between rolling resistance as output data and each of predescribed input variables. 2. The rolling resistance has approximately constant relation with low velocities (0.7, 1.4, and 2.1 m/s) tested in this study which are in the range of practical speeds of tractors. 3. Increase of inflation pressure brings about reverse relation with rolling resistance particularly for higher values of vertical load. 4. Increases of vertical load results in increase of rolling resistance with polynomial order of two. 5. Dynamic load with sinusoidal function and rolling resistance have approximately linear relation indicating the increase of dynamic load induces increase or rolling resistance and reverse.