- Email: [email protected]
Application of artificial neural networks to skidder traction performance
Pergamon
Journal of Terramechanics, Vol. 32, No. 3, pp. 105-114, 1995 Elsevier Science Ltd Copyright ~ 1996 ISTVS Printed in Great Britain. All rights reserved 0022-4898/95 $9.50+0.00
0022--4898(95)00010-0
APPLICATION OF ARTIFICIAL SKIDDER TRACTION
NEURAL NETWORKS PERFORMANCE
TO
A. S. TOHMAZ* and A. E. HASSAN*
Summary--An artificial neural network simulating the tractive performance of a rubber-tired skidder operating on soft organic soil in the Coastal Plain region of North Carolina, U.S.A. was modeled for three tire sizes inflated at each of three inflation pressures (69, 103, and 172 kPa). The neural network (4-5-3-1) demonstrated good generalization of the pull-load relationship when presented with data not used in network training. The output of the network was in close agreement with the equations fitted using least squares methods for the actual pull-load data where the line pull increased linearly with the applied tree load.
INTRODUCTION Timber harvesting on wetlands in the South is normally conducted in the dry season. The unavailability of machines with appropriate traction devices hinders wood extraction of these wetlands during the wet season. Because of the extent of woodlands in the Coastal Plain region, maintaining a continuous flow of wood to the mills requires unlimited scheduling of mechanized logging operation on wetlands. Since the evolution of skidders in the 1960s, tire manufacturers have developed special logger tires to contend with the harsh environment experienced during wood extraction. A literature search indicated that most studies on tractive performance of vehicles have focused mainly on reporting experimental findings under certain conditions with specific parameters [1-4]. There was no attempt to model a more general system due to the various parameters affecting the results and to the non-linearity that exists in such a system. Under these conditions, a learning algorithm such as a neural network may succeed in simulating the behavior of such a system. Neural networks provide a way of using examples of a target function to determine the coefficients that make a certain mapping function capable of approximating the target function as closely as possible. The advantage of using neural networks over statistical methods lies in their ability to automate the process of model selection and in their ability to model non-linear mapping. Although the mapping function generated by the neural network is complex and training the network requires programming abilities, many software packages are available to simulate neural networks. Expert systems may also be used to model such complicated systems; however, they suffer from several drawbacks. Human experts may have difficulties in transferring their expertise into a set of rules and may also be unable to develop a complete set of rules. These difficulties have been described as the bottleneck in the development of *Departments of Forestry and Biological and Agricultural Engineering, North Carolina State University, Raleigh, NC 27695-8002, U.S.A. 105
106
A.S. Tohmazand A. E. Hassan
expert systems [5]. Also, for large scale systems, the development process and the management of the data base can be extremely difficult, prolong development time, and financially burden the project [6]. Finally, expert systems do not benefit from past experience during the operating stage, i.e. they are not self-tuning or adaptable and tend to be operationally slow due to their sequential nature. An artificial neural network consists of three categories of layers: namely input, hidden, and output layers. There are two types of learning modes: supervised and unsupervised learning. In the supervised learning, relationships between input and output are modeled by the network, while in the unsupervised learning, natural distribution of input data is learned by the network (e.g. clustering and self organizing maps). The three layers are linked through connections whose weights are modified during training to minimize the error between the network output and the actual output. The network operates in two modes: mapping mode, where information flows forward from inputs to outputs, and learning mode, where the flow of information alternates between forward and backward. The trained network can then make decisions, perform mapping association, or generalize within the realm of the input variables. Neural networks in the early 1980s were mostly dedicated to military applications for artificial intelligence. Commercial applications of neural networks have since followed and many more are in progress. A literature search in the field of agriculture indicated that the number of publications on neural networks and artificial intelligence is climbing. Brons et al. [7] combined neural network techniques with classical methods of image processing to determine a relationship between human judgments on the quality of pot plants and physical measurements. Yang [8] used a neural network with machine vision to classify apple surfaces with an average accuracy of 96.6%. Similar work was performed by Thai and Schewfett [9] to model color quality of tomatoes and peaches. Neural networks have also been used to detect fertility of eggs. Goodacre et al. [10] used neural networks with a pyrolysis mass spectrometer to assess the adulteration of virgin olive oils by other seed oils. Sato et al. [11] trained a neural network to differentiate between operator voice and tractor noise at 2500 rev/ rain engine speed. A literature search indicated traction prediction using neural networks was not available.
OBJECTIVES The main objective of this paper is to report the results of training a neural network using field data to predict the skidder pull-load relationship. These predictions would then be compared with the results of a regression-based model.
PREVIOUS STUDY AND MODEL DEVELOPMENT Description o f the 1984 traction study The study was conducted on lands owned by the Federal Paper Board Company in the 55,800 ha Green Swamp of Columbus and Brunswick Counties, North Carolina, U.S.A. This area is characterized by a high water table and poor water movement in the soil profile (Pocosin). Major roads with ditches on both sides in addition to secondary ditches, were constructed prior to harvesting to improve drainage and accessibility [4].
Application of artificial neural networks
107
The test vehicle, a John D e e r e 540 B skidder on loan from a local dealer, weighed 83.4, 93.19, and 96.79 kN when equipped with 23.1 x 26, 28.1 x 26, and 67 x 34 x 25 tires, with the engine rated at 67 k W at 2200 rev/min. The vehicle was tested with each tire size at one of three inflation pressures: 69, 103, and 172 kPa. The vehicle was tested with four loads comprised of tree lengths of limbed and topped loblolly pine trees ranging from 10 to 45 kN. Single-pass tests using a 30.5 m trail with 10 equally spaced stations were conducted to avoid changes in soil conditions due to machine traffic. The test vehicle was self-propelled, operating on its own power with its tire pressure set at one of the three set pressures. The test skidder operated in second gear with m a x i m u m engine governor setting at a ground speed of approximately 5 km/h. The skidding test was repeated with the skidder pulling each of the four loads. The sequence was repeated for the other two inflation pressures and then the entire sequence was repeated for each tire size. During each run, the line pull, line pull angle, wheel rotational speed, and time per station (manual and automatic), were recorded. In total there were nine combinations (three tire sizes and three pressures), and five loads (including zero pull) representing 45 test runs. Pull-load relation Very limited published data relating pull to tree load are available for skidders operating under wet conditions [4, 12]. The effect of tree load on the line pull for all tire pressures can be linearly represented by a straight line relationship. The equation of the fitted line using a least squares method based on all data for the line pull vs the load is: P = aiWL + bi where
(1)
ai, bi = constants slightly affected by the tire size i. P = m e a n line pull, kN, and Wc = load or log weight, kN.
The correlation coefficient (r) using linear regression for fitting all the data to equation (1) was 0.9998. Since r 2 = 0.9996, it can be estimated that approximately 99.96% of the variation in the values of the pull is accounted for by a linear relationship with the load. It is apparent from Table 1 that the tire size has an effect on the relationship between the line pull and pay load. The average slope of the line fit (a = 0,52) might be low in comparison with previously published data (0.61 and 0.62) [4, 13], because the John D e e r e 540 B was a grapple skidder and a pin replacing the grapple attachment simulated the arch of a cable skidder. Thus the height of the Table 1. Coefficients of the least squares fitted line for the actual and neural network pull-load data Tire size
Actual data
Network output
a~
b,
a,
b,
23.1 x 26 28.1 x 26 67 x 34 x 25
0.46 0.52 0.57
0.59 0.25 -0.05
0.46 0.48 0,49
1.77 t.76 0.89
Average all tires
0.52
0.26
0,48
1.45
108
A . S . Tohmaz and A. E. Hassan
simulated arch was very high in comparison with the ordinary cable skidders used in the previous studies.
Neural network dynamics The general term 'neural network' usually refers to a combined structure of layered artificial neurons. Each neuron has a set of input signals and one output. There are usually three types of layers: input, hidden, and output, and each layer consists of a number of neurons (the circles shown in Fig. 1). In general, the output of each neuron is adaptively weighted and disseminated to all neurons in the next layer. It is the adaptive nature of those weights that results in the learning nature of the neural network. The size of the input layer (number of neurons constituting the layer) is a function of the number of input variables and therefore is problem dependent, and the same is true for the size of the output layer. The main function of the hidden layer is to map the input to the output variables. This task is accomplished by determining the coefficients of the non-linearity governing such mapping, by varying the weights of the inter-neuron connections and by selecting an appropriate number of connections (i.e. number of nodes in the hidden layer) that would be capable of performing the mapping. A neural network with fewer hidden neurons may not be able to map the required input-output function, and too many neurons in the hidden layer may result in an over-generalization effect (i.e. the network basically memorizes the inputoutput function instead of deducing the input-output relationship). The search through the coefficient (parameter) space is governed by gradient descent and with the presence of enough degrees of freedom (number of nodes in the hidden layer) the search is more likely to yield the global minimum rather than a local minimum.
Neural Network Architecture John Deere Skidder
Line Pull Angle
~ Load
Pull
~Ire Size
Tire
Pressure
- -
I n p u t Layer
Hidden Layer 1
Hidden Layer 2
Output
Layer
Fig. 1. The neural network architecture for 4-5-3-1 showing the input and output parameters and two hidden layers for skidder tractive performance simulation.
Application of artificial neural networks
109
The output of each neuron is usually a non-linear function (sigmoid) of the total weighted sum of its inputs, presented by the following relationships [6]: N
Ok,i where
=
1
(1 + e (-ws~,'+b`,'))
; WSk,i = Z W(j,i)O(k-l,J) ,
j=l
(2)
Ok,i = Output of neuron i in layer (k), Ok-l,j = Output of neuron j in layer (k - 1), bk,i = A bias term associated with neuron i in layer (k), k= i= j = N = Wj,i =
Layer number, Node number in layer (k), Node number in layer (k - 1), Number of nodes in the previous layer (k - 1), Weight of the connection between node ] in previous layer (k - 1), and node i in the current layer (k), and WSk.i = Weighted sum of inputs for node i in layer (k). An output is generated by propagating the inputs from the input layer through the hidden layer(s) and to the output layer. The generated output is then compared with the actual output and an error signal is propagated backward to adjust the weights based on gradient descent (back propagation). The process in which the error signal is formed defines the type of learning. In batch learning, the error signal is accumulated for the entire set of training examples before weight adjustments take place. In incremental learning, the error signal is propagated back after presenting each example in the training set. Batch learning was chosen for this work because incremental learning suffers from loss of memory (forgetting what was learned) and from dependence on the order of examples in the training set.
Neural network simulation The objective of this study was to create a neural network model relating skidder operating parameters to vehicle pull capabilities under wet conditions. After training, the neural network model can generalize the skidder performance over the entire range of input variables. The neural network abilities to map non-linear relationships and to select the most appropriate model make it superior to statistical modeling. To test the potential use of the neural networks for traction prediction, the model was limited to the pull-load relationship with future applications to include traction ratio-slip relationships. Four input variables (namely tire size, tire inflation pressure, load weight, and line pull angle) and one output variable (tangential pull) were used. To train and simulate the neural network, a software package named NEURALNET, developed by the Electrical Engineering Department at North Carolina State University, was used. N E U R A L N E T ran on a DEC Station 5000 under a UNIX operating system and featured graphical user interfacing (GUI) to set the topology of the network. The user only needs to supply input nodes, output nodes, hidden layers, and nodes in each hidden layer. The number of epochs for training the network can be input through a slide-bar. N E U R A L N E T generates a file containing the weights of the network after training. A program (NN-OUT) was written to produce predicted neural network outputs based on the obtained weight file. This program helps in obtaining neural network outputs for seen and unseen data.
110
A . S . T o h m a z and A. E. Hassan
Neural network architecture and training The input layer of the model consisted of four nodes corresponding to the four input variables (tire size, inflation pressure, load, and line pull angle). The output layer consisted of one node, namely, the tangential component of the line pull. Using the 10-station data as replications for each tire size/inflation pressure combinations (nine possibilities) and the five loads, a total of 450 different training examples were generated. The data were normalized between zero and one prior to use with the model, using the following relationship: X normalized =
X original - X minimum X maximum - X minimum
(3)
Data de-normalization was achieved by multiplying the normalized output by (X maximum - X minimum) and adding X minimum. Several fully connected architectures were experimented with to select the final network configuration for this application. Networks with the following configurations were tested: 4-5-1, 4-3-l, 4-5-3-1, and 4-6-1. A 4-5-1 network refers to four input nodes, one hidden layer with five nodes, and one output node; while a 4-5-3-1 network refers to four input nodes, two hidden layers with five and three nodes, respectively, and one output node. The network with two hidden layers, 4-5-3-1 (Fig. 1) converged faster than the others since it could map more significant input patterns into related output. During the evaluation of the above four networks, the effect of learning rate was investigated using three values, namely 0.1, 0.3, and 0.5. The 4-5-3-1 network remained the fastest to converge for all learning rates and achieved the lowest sum of squares error of 0.3332 after 11,000 epochs. It was concluded that the learning rate had no influence on the superiority of the 4-5-3-1 network, and hence was selected for this study using a learning rate of 0.5. The starting weight values of the interconnections were randomly selected between _+0.5. Batch training, where the weights are adjusted after presenting all training examples, was used. The network converged after 11,000 epochs with a total sum of squares error of 0.3332. A plot of the neural network training behavior in terms of error against epochs, is shown in Fig. 2. NEURAL NETWORK PREDICTION
Pull-load output For each tire size at all inflation pressure combinations and a line pull angle of 50 °, the load was varied between zero and 44.59 kN. An additional inflation pressure of 138 kPa was used to test the generalization ability of the network model. This procedure is recommended to avoid over-fitting the data during training. The results of the neural network output for the 23.1 x 26 tire test at four inflation pressures are demonstrated in Fig. 3 which also depicts the actual data for the three original tire pressures. Similar graphs were also plotted for the other two tire sizes and demonstrated similar results. The network accurately predicted the pull-load relationship for all tested pressures and for additional pressures as well, and reduced the noise in the data especially at the high loads. The output of the neural network was fitted to a straight line equation using the least square method and compared with the line fitted in the original data (Table 1). The slopes of the two lines are almost the same, indicating that the network model
Application of artificial neural networks
I 11
2
0
I 2000
0
I
I
I
I
I
4000
6000
8000
10000
12000
Epoch Fig. 2. Neural network (4-5-3-1) training performance showing the total sum of the squares error at different stages of training (epochs).
25 T
PulIvs. Load
20 I
23.1X26 Tire
/ ~"
~,'~.-'l
10 -i-
I
.j,~///"
/
tt//
/
~
5 t
J~'~
0
Act.:103 kPaI
I-'- N.: 69kPa r'--'-Ni:~38kPa
lr~,~"
0
o
] * Act.: 69 kPa I 14- NN: 172 kPa I I-'- NN: 103 kPa I
I
I
I
10
20
30
I
40
50
Load [kNl Fig. 3. P u l l - l o a d relationships from actual data and neural network output for the 23.1 × 26 tires at the three inflation pressures tested and an additional hypothetical pressure, 138 kPa.
can be used to predict the pull needed for certain loads in conditions similar to this wetland. The output data for the tires at 138 kPa pressure fall in the range of data for tires at other pressures, indicating the suitability of the selected neural network to model the data. Techniques such as cross validation or stop training to estimate the true error rate and to improve the generalization of the neural network output, were not needed due to the sound behavior of the selected network when presented with the unseen data (138 kPa inflation pressure).
Pull-inflation pressure output To study the effect of tire inflation pressure on the skidder line pull, the tire pressure was varied from 69 kPa to 172 kPa while holding the load at 10.68 kN and
112
A . S . Tohmaz and A. E. Hassan
line pull angle of 50° for the three tire sizes (23.1 × 26, 28.1 x 26, 67 × 34 x 25) and an additional unseen tire size of 30.5 LX32 (Fig. 4). It should be noted that the variation in tire pressure has little effect on the pull. Again, the network ability to generalize on unseen data (30.5 LX 32 tire) was confirmed. Pull-tire size output A similar procedure to the pull-inflation pressure relationship above was generated by varying the tire size while holding the load and line pull angle constant for four tire inflation pressures (69, 103, 138, and 172 kPa). Figure 5 suggests that the pull was almost constant and was not affected by the tire size. Figures 4 and 5 confirmed that tire pressure and tire size (of seen and unseen data) have no effects on the line pull. On the other hand, Fig. 6 demonstrates the effect of load on the pull at a constant tire pressure (103 kPa) for four tire sizes. Figures 3 and 6 almost suggest a linear relationship between the line pull and the load for constant tire size and tire inflation pressure. CONCLUSIONS AND RECOMMENDATIONS (1) A 4-5-3-1 neural network simulated the pull-load relationship successfully and was appropriate for predicting results with conditions not used in network formulation (tire inflation pressure of 138 kPa and tire size of 30.5 LX 32). The network converged with a total sum of squares error of 0.332. (2) The network was capable of predicting vehicle performance when presented with unseen data (tire size and inflation pressure). (3) The line pull predicted by the network increased linearly with increases in load weights. Linear equations relating the model line pull to the loads for the three tire sizes tested were in close agreement with the experimental results.
Pull vs. Tire P r e s s u r e Load = 10.68 kN
Tire Size !-,-- :~3. i )<26 --,- 2 8 . 1 X 2 6 --*- 3 0 . 5 L X 3 2
i
--,- 67_X34X251 ~7 "5 a. m
65
I
I
I
I
I
85
105
125
145
165
Tire Pressure [kPe]
Fig. 4. Tire pressure-pull relationships for four tire sizes predicted by neural network for a load of 10.68 kN.
Application of artificial neural networks
113
15 Pull vs. Tire Size Load = 23.8 kN
14
13 a.
12
'-*'-138 kPa! 1 ---- 172_k=Pai
11 22
I
[
I
I
I
I
24
26
28
30
32
34
Tire Size Index (Width)
Fig. 5. Tire size-pull relationships predicted by neural network for a load of 23.8 kN and four tire inflation pressures. 25 Pull vs. Load Tire Prssure = 103 kPa
20
15 "5 a.
TireS ze f
10
-"~- 23.1X26
j
; ~ 6-/X34X2}:
,
]
I
I
I
I
I
I
t
5
10
15
20
25
30
35
40
q 45
Load [kNl
Fig. 6. Load-pull relationships predicted by neural network for four tire sizes at an inflation pressure of 103 kPa. (4) N o effects w e r e n o t i c e a b l e d u e to c h a n g e s in tire size o r tire i n f l a t i o n p r e s s u r e on t h e line pull, (5) F u t u r e studies s h o u l d e x p l o r e the use o f cross v a l i d a t i o n a n d / o r s t o p t r a i n i n g m e t h o d s for i m p r o v i n g t h e n e u r a l n e t w o r k g e n e r a l i z a t i o n o f field d a t a .
REFERENCES [1] T. P. McDonald, B. J. Stokes and J. Wilhoit, Field evaluation of skidder tire tractive performance. American Society of Agricultural Engineers Paper no. 92-7514, p. 12, American Society of Agricultural Engineers, St Joseph, MI (1992).
114
A . S . Tohmaz and A. E. Hassan
[2] C. R. Vechinski, R. L. Raper, C. E. Johnson and P. P. McDonald, Forestry tire tractive performance: new, worn with chains. American Society of Agricultural Engineers Paper no. 93-1519, p. 13~ American Society of Agricultural Engineers, St. Joseph, MI (1993). [3] J. L. Koger, C. Ashmore and B. J. Stokes, Ground skidding wetlands with dual-tires skidders: a South Carolina case study. American Society of Agricultural Engineers Paper no. 84-1618, p. 13, American Society of Agricultural Engineers, St. Joseph, MI (1984). [4] A. E. Hassan and D. L, Sirois, Traction and rolling resistance of a dual tired skidder on wetland. Transactions of the American Society of Agricultural Engineers" 28 (2), 1038-1042 (1985). [5] E. A. Feigenbaum and P. MacCordak, The fifth generation: artificial intelligence and Japan "s computer challenge to the world. Addison-Wesley, Reading, MA (1983). [6] L. R. Medsker, Hybird--neural network and expert systems. Springer-Verlag, New York, NY (1994). [7] A. Brons, G. Rabatel, F. Ros, F. Sevila and C. Touzet, Plant grading by vision using neural networks and statistics. Computers and Electronics in Agriculture 9 (1), 25-39 (1993). [8] Q. Yang, Classification of apple surface features using machine vision and neural networks. Computers and Electronics in Agriculture 9 (l), 1-12 (1993). [9] C. N. Thai and R. L. Shewfelt, Modeling sensory color quality of tomato and peach: neural networks and statistical regression. Transactions of the American Socie o, of Agricultural Engineers 3 (4), 950-955 (1991). [10] R. Goodacre, D. B. Kell and G. Bianchi, Rapid assessment of the adulteration of virgin olive oils by other seed oils using pyrolysis mass spectrometry and artificial neural networks. Journal of Science. Food and Agriculture 63 (3), 297-307 (1993). [11] K. Sato, M. Hoki and V. M. Salokhe, Voice recognition by neural network under tractor noise. Transactions of the American SocieO, of Agricultural Engineers 36 (4), 1223-1227 (1993). [12] D. L. Sirois and A. E. Hassan, Performance of skidder tires in swamps. American Society of Agricultural Engineers paper no. 85-1616, p. 18, American Society of Agricultural Engineers, St. Joseph, MI (1985). [13] A. E. Hassan, Trafficability study of a cable skidder. Transactions of the American Socie O' o] Agricultural Engineers 20 (1), 26-29 (1977).
Journal of Terramechanics, Vol. 32, No. 3, pp. 105-114, 1995 Elsevier Science Ltd Copyright ~ 1996 ISTVS Printed in Great Britain. All rights reserved 0022-4898/95 $9.50+0.00
0022--4898(95)00010-0
APPLICATION OF ARTIFICIAL SKIDDER TRACTION
NEURAL NETWORKS PERFORMANCE
TO
A. S. TOHMAZ* and A. E. HASSAN*
Summary--An artificial neural network simulating the tractive performance of a rubber-tired skidder operating on soft organic soil in the Coastal Plain region of North Carolina, U.S.A. was modeled for three tire sizes inflated at each of three inflation pressures (69, 103, and 172 kPa). The neural network (4-5-3-1) demonstrated good generalization of the pull-load relationship when presented with data not used in network training. The output of the network was in close agreement with the equations fitted using least squares methods for the actual pull-load data where the line pull increased linearly with the applied tree load.
INTRODUCTION Timber harvesting on wetlands in the South is normally conducted in the dry season. The unavailability of machines with appropriate traction devices hinders wood extraction of these wetlands during the wet season. Because of the extent of woodlands in the Coastal Plain region, maintaining a continuous flow of wood to the mills requires unlimited scheduling of mechanized logging operation on wetlands. Since the evolution of skidders in the 1960s, tire manufacturers have developed special logger tires to contend with the harsh environment experienced during wood extraction. A literature search indicated that most studies on tractive performance of vehicles have focused mainly on reporting experimental findings under certain conditions with specific parameters [1-4]. There was no attempt to model a more general system due to the various parameters affecting the results and to the non-linearity that exists in such a system. Under these conditions, a learning algorithm such as a neural network may succeed in simulating the behavior of such a system. Neural networks provide a way of using examples of a target function to determine the coefficients that make a certain mapping function capable of approximating the target function as closely as possible. The advantage of using neural networks over statistical methods lies in their ability to automate the process of model selection and in their ability to model non-linear mapping. Although the mapping function generated by the neural network is complex and training the network requires programming abilities, many software packages are available to simulate neural networks. Expert systems may also be used to model such complicated systems; however, they suffer from several drawbacks. Human experts may have difficulties in transferring their expertise into a set of rules and may also be unable to develop a complete set of rules. These difficulties have been described as the bottleneck in the development of *Departments of Forestry and Biological and Agricultural Engineering, North Carolina State University, Raleigh, NC 27695-8002, U.S.A. 105
106
A.S. Tohmazand A. E. Hassan
expert systems [5]. Also, for large scale systems, the development process and the management of the data base can be extremely difficult, prolong development time, and financially burden the project [6]. Finally, expert systems do not benefit from past experience during the operating stage, i.e. they are not self-tuning or adaptable and tend to be operationally slow due to their sequential nature. An artificial neural network consists of three categories of layers: namely input, hidden, and output layers. There are two types of learning modes: supervised and unsupervised learning. In the supervised learning, relationships between input and output are modeled by the network, while in the unsupervised learning, natural distribution of input data is learned by the network (e.g. clustering and self organizing maps). The three layers are linked through connections whose weights are modified during training to minimize the error between the network output and the actual output. The network operates in two modes: mapping mode, where information flows forward from inputs to outputs, and learning mode, where the flow of information alternates between forward and backward. The trained network can then make decisions, perform mapping association, or generalize within the realm of the input variables. Neural networks in the early 1980s were mostly dedicated to military applications for artificial intelligence. Commercial applications of neural networks have since followed and many more are in progress. A literature search in the field of agriculture indicated that the number of publications on neural networks and artificial intelligence is climbing. Brons et al. [7] combined neural network techniques with classical methods of image processing to determine a relationship between human judgments on the quality of pot plants and physical measurements. Yang [8] used a neural network with machine vision to classify apple surfaces with an average accuracy of 96.6%. Similar work was performed by Thai and Schewfett [9] to model color quality of tomatoes and peaches. Neural networks have also been used to detect fertility of eggs. Goodacre et al. [10] used neural networks with a pyrolysis mass spectrometer to assess the adulteration of virgin olive oils by other seed oils. Sato et al. [11] trained a neural network to differentiate between operator voice and tractor noise at 2500 rev/ rain engine speed. A literature search indicated traction prediction using neural networks was not available.
OBJECTIVES The main objective of this paper is to report the results of training a neural network using field data to predict the skidder pull-load relationship. These predictions would then be compared with the results of a regression-based model.
PREVIOUS STUDY AND MODEL DEVELOPMENT Description o f the 1984 traction study The study was conducted on lands owned by the Federal Paper Board Company in the 55,800 ha Green Swamp of Columbus and Brunswick Counties, North Carolina, U.S.A. This area is characterized by a high water table and poor water movement in the soil profile (Pocosin). Major roads with ditches on both sides in addition to secondary ditches, were constructed prior to harvesting to improve drainage and accessibility [4].
Application of artificial neural networks
107
The test vehicle, a John D e e r e 540 B skidder on loan from a local dealer, weighed 83.4, 93.19, and 96.79 kN when equipped with 23.1 x 26, 28.1 x 26, and 67 x 34 x 25 tires, with the engine rated at 67 k W at 2200 rev/min. The vehicle was tested with each tire size at one of three inflation pressures: 69, 103, and 172 kPa. The vehicle was tested with four loads comprised of tree lengths of limbed and topped loblolly pine trees ranging from 10 to 45 kN. Single-pass tests using a 30.5 m trail with 10 equally spaced stations were conducted to avoid changes in soil conditions due to machine traffic. The test vehicle was self-propelled, operating on its own power with its tire pressure set at one of the three set pressures. The test skidder operated in second gear with m a x i m u m engine governor setting at a ground speed of approximately 5 km/h. The skidding test was repeated with the skidder pulling each of the four loads. The sequence was repeated for the other two inflation pressures and then the entire sequence was repeated for each tire size. During each run, the line pull, line pull angle, wheel rotational speed, and time per station (manual and automatic), were recorded. In total there were nine combinations (three tire sizes and three pressures), and five loads (including zero pull) representing 45 test runs. Pull-load relation Very limited published data relating pull to tree load are available for skidders operating under wet conditions [4, 12]. The effect of tree load on the line pull for all tire pressures can be linearly represented by a straight line relationship. The equation of the fitted line using a least squares method based on all data for the line pull vs the load is: P = aiWL + bi where
(1)
ai, bi = constants slightly affected by the tire size i. P = m e a n line pull, kN, and Wc = load or log weight, kN.
The correlation coefficient (r) using linear regression for fitting all the data to equation (1) was 0.9998. Since r 2 = 0.9996, it can be estimated that approximately 99.96% of the variation in the values of the pull is accounted for by a linear relationship with the load. It is apparent from Table 1 that the tire size has an effect on the relationship between the line pull and pay load. The average slope of the line fit (a = 0,52) might be low in comparison with previously published data (0.61 and 0.62) [4, 13], because the John D e e r e 540 B was a grapple skidder and a pin replacing the grapple attachment simulated the arch of a cable skidder. Thus the height of the Table 1. Coefficients of the least squares fitted line for the actual and neural network pull-load data Tire size
Actual data
Network output
a~
b,
a,
b,
23.1 x 26 28.1 x 26 67 x 34 x 25
0.46 0.52 0.57
0.59 0.25 -0.05
0.46 0.48 0,49
1.77 t.76 0.89
Average all tires
0.52
0.26
0,48
1.45
108
A . S . Tohmaz and A. E. Hassan
simulated arch was very high in comparison with the ordinary cable skidders used in the previous studies.
Neural network dynamics The general term 'neural network' usually refers to a combined structure of layered artificial neurons. Each neuron has a set of input signals and one output. There are usually three types of layers: input, hidden, and output, and each layer consists of a number of neurons (the circles shown in Fig. 1). In general, the output of each neuron is adaptively weighted and disseminated to all neurons in the next layer. It is the adaptive nature of those weights that results in the learning nature of the neural network. The size of the input layer (number of neurons constituting the layer) is a function of the number of input variables and therefore is problem dependent, and the same is true for the size of the output layer. The main function of the hidden layer is to map the input to the output variables. This task is accomplished by determining the coefficients of the non-linearity governing such mapping, by varying the weights of the inter-neuron connections and by selecting an appropriate number of connections (i.e. number of nodes in the hidden layer) that would be capable of performing the mapping. A neural network with fewer hidden neurons may not be able to map the required input-output function, and too many neurons in the hidden layer may result in an over-generalization effect (i.e. the network basically memorizes the inputoutput function instead of deducing the input-output relationship). The search through the coefficient (parameter) space is governed by gradient descent and with the presence of enough degrees of freedom (number of nodes in the hidden layer) the search is more likely to yield the global minimum rather than a local minimum.
Neural Network Architecture John Deere Skidder
Line Pull Angle
~ Load
Pull
~Ire Size
Tire
Pressure
- -
I n p u t Layer
Hidden Layer 1
Hidden Layer 2
Output
Layer
Fig. 1. The neural network architecture for 4-5-3-1 showing the input and output parameters and two hidden layers for skidder tractive performance simulation.
Application of artificial neural networks
109
The output of each neuron is usually a non-linear function (sigmoid) of the total weighted sum of its inputs, presented by the following relationships [6]: N
Ok,i where
=
1
(1 + e (-ws~,'+b`,'))
; WSk,i = Z W(j,i)O(k-l,J) ,
j=l
(2)
Ok,i = Output of neuron i in layer (k), Ok-l,j = Output of neuron j in layer (k - 1), bk,i = A bias term associated with neuron i in layer (k), k= i= j = N = Wj,i =
Layer number, Node number in layer (k), Node number in layer (k - 1), Number of nodes in the previous layer (k - 1), Weight of the connection between node ] in previous layer (k - 1), and node i in the current layer (k), and WSk.i = Weighted sum of inputs for node i in layer (k). An output is generated by propagating the inputs from the input layer through the hidden layer(s) and to the output layer. The generated output is then compared with the actual output and an error signal is propagated backward to adjust the weights based on gradient descent (back propagation). The process in which the error signal is formed defines the type of learning. In batch learning, the error signal is accumulated for the entire set of training examples before weight adjustments take place. In incremental learning, the error signal is propagated back after presenting each example in the training set. Batch learning was chosen for this work because incremental learning suffers from loss of memory (forgetting what was learned) and from dependence on the order of examples in the training set.
Neural network simulation The objective of this study was to create a neural network model relating skidder operating parameters to vehicle pull capabilities under wet conditions. After training, the neural network model can generalize the skidder performance over the entire range of input variables. The neural network abilities to map non-linear relationships and to select the most appropriate model make it superior to statistical modeling. To test the potential use of the neural networks for traction prediction, the model was limited to the pull-load relationship with future applications to include traction ratio-slip relationships. Four input variables (namely tire size, tire inflation pressure, load weight, and line pull angle) and one output variable (tangential pull) were used. To train and simulate the neural network, a software package named NEURALNET, developed by the Electrical Engineering Department at North Carolina State University, was used. N E U R A L N E T ran on a DEC Station 5000 under a UNIX operating system and featured graphical user interfacing (GUI) to set the topology of the network. The user only needs to supply input nodes, output nodes, hidden layers, and nodes in each hidden layer. The number of epochs for training the network can be input through a slide-bar. N E U R A L N E T generates a file containing the weights of the network after training. A program (NN-OUT) was written to produce predicted neural network outputs based on the obtained weight file. This program helps in obtaining neural network outputs for seen and unseen data.
110
A . S . T o h m a z and A. E. Hassan
Neural network architecture and training The input layer of the model consisted of four nodes corresponding to the four input variables (tire size, inflation pressure, load, and line pull angle). The output layer consisted of one node, namely, the tangential component of the line pull. Using the 10-station data as replications for each tire size/inflation pressure combinations (nine possibilities) and the five loads, a total of 450 different training examples were generated. The data were normalized between zero and one prior to use with the model, using the following relationship: X normalized =
X original - X minimum X maximum - X minimum
(3)
Data de-normalization was achieved by multiplying the normalized output by (X maximum - X minimum) and adding X minimum. Several fully connected architectures were experimented with to select the final network configuration for this application. Networks with the following configurations were tested: 4-5-1, 4-3-l, 4-5-3-1, and 4-6-1. A 4-5-1 network refers to four input nodes, one hidden layer with five nodes, and one output node; while a 4-5-3-1 network refers to four input nodes, two hidden layers with five and three nodes, respectively, and one output node. The network with two hidden layers, 4-5-3-1 (Fig. 1) converged faster than the others since it could map more significant input patterns into related output. During the evaluation of the above four networks, the effect of learning rate was investigated using three values, namely 0.1, 0.3, and 0.5. The 4-5-3-1 network remained the fastest to converge for all learning rates and achieved the lowest sum of squares error of 0.3332 after 11,000 epochs. It was concluded that the learning rate had no influence on the superiority of the 4-5-3-1 network, and hence was selected for this study using a learning rate of 0.5. The starting weight values of the interconnections were randomly selected between _+0.5. Batch training, where the weights are adjusted after presenting all training examples, was used. The network converged after 11,000 epochs with a total sum of squares error of 0.3332. A plot of the neural network training behavior in terms of error against epochs, is shown in Fig. 2. NEURAL NETWORK PREDICTION
Pull-load output For each tire size at all inflation pressure combinations and a line pull angle of 50 °, the load was varied between zero and 44.59 kN. An additional inflation pressure of 138 kPa was used to test the generalization ability of the network model. This procedure is recommended to avoid over-fitting the data during training. The results of the neural network output for the 23.1 x 26 tire test at four inflation pressures are demonstrated in Fig. 3 which also depicts the actual data for the three original tire pressures. Similar graphs were also plotted for the other two tire sizes and demonstrated similar results. The network accurately predicted the pull-load relationship for all tested pressures and for additional pressures as well, and reduced the noise in the data especially at the high loads. The output of the neural network was fitted to a straight line equation using the least square method and compared with the line fitted in the original data (Table 1). The slopes of the two lines are almost the same, indicating that the network model
Application of artificial neural networks
I 11
2
0
I 2000
0
I
I
I
I
I
4000
6000
8000
10000
12000
Epoch Fig. 2. Neural network (4-5-3-1) training performance showing the total sum of the squares error at different stages of training (epochs).
25 T
PulIvs. Load
20 I
23.1X26 Tire
/ ~"
~,'~.-'l
10 -i-
I
.j,~///"
/
tt//
/
~
5 t
J~'~
0
Act.:103 kPaI
I-'- N.: 69kPa r'--'-Ni:~38kPa
lr~,~"
0
o
] * Act.: 69 kPa I 14- NN: 172 kPa I I-'- NN: 103 kPa I
I
I
I
10
20
30
I
40
50
Load [kNl Fig. 3. P u l l - l o a d relationships from actual data and neural network output for the 23.1 × 26 tires at the three inflation pressures tested and an additional hypothetical pressure, 138 kPa.
can be used to predict the pull needed for certain loads in conditions similar to this wetland. The output data for the tires at 138 kPa pressure fall in the range of data for tires at other pressures, indicating the suitability of the selected neural network to model the data. Techniques such as cross validation or stop training to estimate the true error rate and to improve the generalization of the neural network output, were not needed due to the sound behavior of the selected network when presented with the unseen data (138 kPa inflation pressure).
Pull-inflation pressure output To study the effect of tire inflation pressure on the skidder line pull, the tire pressure was varied from 69 kPa to 172 kPa while holding the load at 10.68 kN and
112
A . S . Tohmaz and A. E. Hassan
line pull angle of 50° for the three tire sizes (23.1 × 26, 28.1 x 26, 67 × 34 x 25) and an additional unseen tire size of 30.5 LX32 (Fig. 4). It should be noted that the variation in tire pressure has little effect on the pull. Again, the network ability to generalize on unseen data (30.5 LX 32 tire) was confirmed. Pull-tire size output A similar procedure to the pull-inflation pressure relationship above was generated by varying the tire size while holding the load and line pull angle constant for four tire inflation pressures (69, 103, 138, and 172 kPa). Figure 5 suggests that the pull was almost constant and was not affected by the tire size. Figures 4 and 5 confirmed that tire pressure and tire size (of seen and unseen data) have no effects on the line pull. On the other hand, Fig. 6 demonstrates the effect of load on the pull at a constant tire pressure (103 kPa) for four tire sizes. Figures 3 and 6 almost suggest a linear relationship between the line pull and the load for constant tire size and tire inflation pressure. CONCLUSIONS AND RECOMMENDATIONS (1) A 4-5-3-1 neural network simulated the pull-load relationship successfully and was appropriate for predicting results with conditions not used in network formulation (tire inflation pressure of 138 kPa and tire size of 30.5 LX 32). The network converged with a total sum of squares error of 0.332. (2) The network was capable of predicting vehicle performance when presented with unseen data (tire size and inflation pressure). (3) The line pull predicted by the network increased linearly with increases in load weights. Linear equations relating the model line pull to the loads for the three tire sizes tested were in close agreement with the experimental results.
Pull vs. Tire P r e s s u r e Load = 10.68 kN
Tire Size !-,-- :~3. i )<26 --,- 2 8 . 1 X 2 6 --*- 3 0 . 5 L X 3 2
i
--,- 67_X34X251 ~7 "5 a. m
65
I
I
I
I
I
85
105
125
145
165
Tire Pressure [kPe]
Fig. 4. Tire pressure-pull relationships for four tire sizes predicted by neural network for a load of 10.68 kN.
Application of artificial neural networks
113
15 Pull vs. Tire Size Load = 23.8 kN
14
13 a.
12
'-*'-138 kPa! 1 ---- 172_k=Pai
11 22
I
[
I
I
I
I
24
26
28
30
32
34
Tire Size Index (Width)
Fig. 5. Tire size-pull relationships predicted by neural network for a load of 23.8 kN and four tire inflation pressures. 25 Pull vs. Load Tire Prssure = 103 kPa
20
15 "5 a.
TireS ze f
10
-"~- 23.1X26
j
; ~ 6-/X34X2}:
,
]
I
I
I
I
I
I
t
5
10
15
20
25
30
35
40
q 45
Load [kNl
Fig. 6. Load-pull relationships predicted by neural network for four tire sizes at an inflation pressure of 103 kPa. (4) N o effects w e r e n o t i c e a b l e d u e to c h a n g e s in tire size o r tire i n f l a t i o n p r e s s u r e on t h e line pull, (5) F u t u r e studies s h o u l d e x p l o r e the use o f cross v a l i d a t i o n a n d / o r s t o p t r a i n i n g m e t h o d s for i m p r o v i n g t h e n e u r a l n e t w o r k g e n e r a l i z a t i o n o f field d a t a .
REFERENCES [1] T. P. McDonald, B. J. Stokes and J. Wilhoit, Field evaluation of skidder tire tractive performance. American Society of Agricultural Engineers Paper no. 92-7514, p. 12, American Society of Agricultural Engineers, St Joseph, MI (1992).
114
A . S . Tohmaz and A. E. Hassan
[2] C. R. Vechinski, R. L. Raper, C. E. Johnson and P. P. McDonald, Forestry tire tractive performance: new, worn with chains. American Society of Agricultural Engineers Paper no. 93-1519, p. 13~ American Society of Agricultural Engineers, St. Joseph, MI (1993). [3] J. L. Koger, C. Ashmore and B. J. Stokes, Ground skidding wetlands with dual-tires skidders: a South Carolina case study. American Society of Agricultural Engineers Paper no. 84-1618, p. 13, American Society of Agricultural Engineers, St. Joseph, MI (1984). [4] A. E. Hassan and D. L, Sirois, Traction and rolling resistance of a dual tired skidder on wetland. Transactions of the American Society of Agricultural Engineers" 28 (2), 1038-1042 (1985). [5] E. A. Feigenbaum and P. MacCordak, The fifth generation: artificial intelligence and Japan "s computer challenge to the world. Addison-Wesley, Reading, MA (1983). [6] L. R. Medsker, Hybird--neural network and expert systems. Springer-Verlag, New York, NY (1994). [7] A. Brons, G. Rabatel, F. Ros, F. Sevila and C. Touzet, Plant grading by vision using neural networks and statistics. Computers and Electronics in Agriculture 9 (1), 25-39 (1993). [8] Q. Yang, Classification of apple surface features using machine vision and neural networks. Computers and Electronics in Agriculture 9 (l), 1-12 (1993). [9] C. N. Thai and R. L. Shewfelt, Modeling sensory color quality of tomato and peach: neural networks and statistical regression. Transactions of the American Socie o, of Agricultural Engineers 3 (4), 950-955 (1991). [10] R. Goodacre, D. B. Kell and G. Bianchi, Rapid assessment of the adulteration of virgin olive oils by other seed oils using pyrolysis mass spectrometry and artificial neural networks. Journal of Science. Food and Agriculture 63 (3), 297-307 (1993). [11] K. Sato, M. Hoki and V. M. Salokhe, Voice recognition by neural network under tractor noise. Transactions of the American SocieO, of Agricultural Engineers 36 (4), 1223-1227 (1993). [12] D. L. Sirois and A. E. Hassan, Performance of skidder tires in swamps. American Society of Agricultural Engineers paper no. 85-1616, p. 18, American Society of Agricultural Engineers, St. Joseph, MI (1985). [13] A. E. Hassan, Trafficability study of a cable skidder. Transactions of the American Socie O' o] Agricultural Engineers 20 (1), 26-29 (1977).