SETTING UP A PROBABILISTIC NEURAL NETWORK FOR ...

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International Journal of Computational Intelligence and Applications Vol. 5, No. 4 (2005) 411–423 c Imperial College Press

SETTING UP A PROBABILISTIC NEURAL NETWORK FOR CLASSIFICATION OF HIGHWAY VEHICLES

MAJURA F. SELEKWA Department of Mechanical and Applied Mechanics North Dakota State University 205 Dolve Hall, Fargo, North Dakota, 58105, USA [email protected] VALERIAN KWIGIZILE Department of Civil and Environmental Engineering University of Nevada, Las Vegas, Nevada, USA [email protected] RENATUS N. MUSSA Department of Civil and Environmental Engineering Florida A&M University — Florida State University, Florida, USA [email protected] Received 16 November 2005 Revised 12 July 2005 Many neural network methods used for efficient classification of populations work only when the population is globally separable. In situ classification of highway vehicles is one of the problems with globally nonseparable populations. This paper presents a systematic procedure for setting up a probabilistic neural network that can classify the globally nonseparable population of highway vehicles. The method is based on a simple concept that any set of classifiable data can be broken down to subclasses of locally separable data. Hence, if these locally separable data can be identified, then the classification problem can be carried out in two hierarchical steps; step one classifies the data according to the local subclasses, and step two classifies the local subclasses into the global classes. The proposed approach was tested on the problem of classifying highway vehicles according to the US Federal Highway Administration standard, which is normally handled by decision tree methods that use vehicle axle information and a set of IF-THEN rules. By using a sample of 3326 vehicles, the proposed method showed improved classification results with an overall misclassification rate of only 2.9% compared to 9.7% of the decision tree methods. A similar setup can be used with different neural networks such as recurrent neural networks, but they were not tested in this study especially since the focus was for in situ applications where a high learning rate is desired. Keywords: Probabilistic neural network; vehicle classification.

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M. F. Selekwa, V. Kwigizile & R. N. Mussa

1. Introduction In the United States, federal, state and local agencies responsible for overseeing transportation facilities require vehicle classification data in the design, management, and maintenance of paved roads. The standards for collecting and analyzing vehicle classification data vary countrywide due to the fact that vehicle characteristics differ from one state to another, especially since truck type patterns are heavily affected by local economic activities. For example, multi-trailer trucks are common in most western states but make up a much smaller percentage of the trucking fleet in many eastern states.1 The Federal Highway Administration (FHWA), under a program called the Highway Performance Monitoring Systems, has set a standard for reporting highway vehicles classification data.1 This standard is known as “Scheme F” and was developed by the State of Maine.2 Scheme F classifies vehicles according to their body and axle configuration only. In brief, Scheme F classification is outlined as follows: (i) Class 1: Motorcycles (Optional ). All two- or three-wheeled motorized vehicles such as motorcycles, motor scooters, mopeds, motor-powered bicycles, and three-wheeled motorcycles, which have saddle type seats and are steered by handle bars rather than wheels. (ii) Class 2: Passenger Cars. All sedans, coupes, and station wagons manufactured primarily for the purpose of carrying passengers including those passenger cars pulling recreational or other light trailers. (iii) Class 3: Other Two-Axle, Four-Tire, Single Unit Vehicles. All twoaxle, four-tire, vehicles other than passenger cars, which include pickups, panels, vans, and other vehicles such as campers, motor homes, ambulances, hearses, carryalls, and minibuses. Other two-axle, four-tire single unit vehicles pulling recreational or other light trailers also are included in this classification. (iv) Class 4: Buses. All vehicles manufactured as traditional passenger-carrying buses (including school buses) with two axles and six tires or three or more axles. Modified buses should be considered to be trucks and be appropriately classified. (v) Class 5: Two-Axle, Six-Tire, Single Unit Trucks. All vehicles on a single frame including trucks, camping and recreational vehicles, motor homes, etc. that have two axles and dual rear wheels. (vi) Class 6: Three-axle Single Unit Trucks. All vehicles on a single frame including trucks, camping and recreational vehicles, motor homes, etc. that have three axles. (vii) Class 7: Four or More Axle Single Unit Trucks. All trucks on a single frame with four or more axles. (viii) Class 8: Four or Less Axle Single Trailer Trucks. All vehicles with four or less axles consisting of two units, one of which is a tractor or straight truck power unit.


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(ix) Class 9: Five-Axle Single Trailer Trucks. All five-axle vehicles consisting of two units, one of which is a tractor or straight truck power unit. (x) Class 10: Six or More Axle Single Trailer Trucks. All vehicles with six or more axles consisting of two units, one of which is a tractor or straight truck power unit. (xi) Class 11: Five or Less Axle Multi-Trailer Trucks. All vehicles with five or less axles consisting of three or more units, one of which is a tractor or straight truck power unit. (xii) Class 12: Six-Axle Multi-Trailer Trucks. All six-axle vehicles consisting of three or more units, one of which is a tractor or straight truck power unit. (xiii) Class 13: Seven or More Axle Multi-Trailer Trucks. All vehicles with seven or more axles consisting of three or more units, one of which is a tractor or straight truck power unit. In reporting information on trucks the following criteria are used: (a) Truck tractor units traveling without a trailer are considered single unit trucks. (b) Truck tractor units pulling other such units in a “saddle mount” configuration are considered as single unit trucks defined only by axles on the pulling unit. (c) Vehicles are defined by the number of axles in contact with the roadway; therefore, “floating” axles are counted only when in the down position. (d) The term “trailer” includes both semi- and full-trailers. In its basic form, this scheme provides information that cannot be quantified in a way suitable for computer application. To assign a vehicle to one of the 13 classes in Scheme F, normally a lookup table implemented through a decision tree is used. This decision tree is designed based on the number of axles and the inter-axle distances (axle spacings) of the vehicle. The Florida Department of Transportation (FDOT) has defined a set of common thresholds, shown in Table 1, that form a basis for the decision tree used in different vehicle classification equipment for the state of Florida. As seen in this table, classification conflicts can arise because of these thresholds; for example, some of the 4-axle vehicles in Class 5 can be classified as Class 8 and vice versa because of their overlapping axle distances. Automatic vehicle identification and classification is a well known problem that has been studied for over a decade.2,3 Applications of automated vehicle identification and classification systems range from simple traffic counts for traffic control in urban streets to detailed extraction of traffic parameters such as vehicle type, traffic lane change characteristics and traffic density, which are required for highway management and maintenance. Two distinct approaches have been proposed for the problem: vision based methods and sensor based methods. Generally, all vision based methods use a single or multiple cameras to capture video images of road traffic. The methods differ in the way the video data

40 44 60 50 70 54 80 84 90

28 34 38

24 30 4 9

1 2 3 10 20 3 7 11

Veh. Typ

1 2 3 4 5 2 3 4 5 6 8 2 3 5 7 8 8 3 5 9 9 11 10 12 10 13 13 13 15

Cls

2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 6 6 7 7 8 9

Num. Axls

2S23, 3S22, 3S13 3S23 PERMIT UNCLASSIFIED

Motorcycle Auto, Pickup Limo, Van, RV Bus 2D Auto +1 Axle Trlr Other +1 Axle Trlr Bus 2D +1 Axle Trlr 3 Axle 2S1, 21 Auto +2 Axle Trlr Other +2 Axle Trlr 2D +2 Axle Trlr 4 Axle 3S1, 31 2S2 Other +3 Axle Trlr 2D +3 Axle Trlr 3S2 32 2S12 3S3, 33 3S12

Description 0.1–6.0 6.01–10.0 10.01–13.30 23.01–40.00 13.31–23.0 6.01–10.0 10.01–13.30 23.01–40.0 13.31–23.0 6.01–23.0 6.01–23.0 6.01–10.0 10.01–13.30 13.31–23.0 6.01–23.0 6.01–23.0 6.01–23.0 10.01–13.30 13.31–23.0 6.01–26.0 6.01–26.0 6.01–26.0 6.01–26.0 6.01–26.0 6.01–16.7 1.0–45.0 1.0–45.0 1.0–45.0

Ax.1–2

6.0–25.0 6.0–25.0 0.1–6.0 6.0–25.0 0.1–5.99 11.0–40.0 6.0–25.0 6.0–25.0 6.0–25.0 0.1–6.0 0.1–6.0 11.0–40.0 6.0–25.0 6.0–25.0 0.1–6.0 0.1–6.0 11.0–26.0 0.1–6.0 0.1–6.0 0.1–6.0 1.0–45.0 1.0–45.0 1.0–45.0

Ax.2–3

0.1–6.0 0.1–6.0 0.1–6.0 0.1–13.0 6.01–44.0 0.1–10.99 0.1–6.0 0.1–6.0 6.01–46.0 6.01–23.0 6.1–20.0 0.1–46.0 11.01–26.0 13.3–40.0 1.0–45.0 1.0–45.0 1.0–45.0

Ax.3–4

0.1–6.0 0.1–6.0 0.1–10.99 11.0–27.0 11.01–26.0 0.1–11.0 6.01–24.0 0.1–13.3 1.0–45.0 1.0–45.0 1.0–45.0

Ax.4–5

0.1–11.0 11.01–26.0 0.1–13.3 1.0–45.0 1.0–45.0 1.0–45.0

Ax.5–6

Axle spacing [ft]

0.1–13.3 1.0–45.0 1.0–45.0 1.0–45.0

Ax.6–7

Axle spacing limits as defined by Florida DOT.

1.0–45.0 1.0–45.0

Ax.7–8

1.0–45.0

Ax.8–9 0.1+ 1.0+ 1.0+ 12.0+ 1.0+ 1.0+ 1.0+ 12.0+ 1.0+ 12.0+ 12.0+ 1.0+ 1.0+ 1.0+ 12.0+ 20.0+ 20.0+ 1.0+ 1.0+ 12.0+ 12.0+ 12.0+ 12.0+ 12.0+ 12.0+ 12.0+ 12.0+ 12.0+

Weight

10.0 22.0 26.0 45.0 40.0 32.0 60.0 52.0 60.0 40.0 75.0 45.0 60.0 60.0 45.0 75.0 75.0 60.0 60.0 80.0 80.0 85.0 85.0 110.0 85.0 110.0 120.0 120.0

Max Length

414

Table 1.

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is processed and used to classify vehicles. Among the popular processes employed include the image segmentation by background subtraction, various feature extraction techniques for capturing signature parameters of a vehicle, and the 2D or 3D modeling of a vehicle in conjunction with pattern matching.4 –7 The vehicle is classified to belong to a particular class based on the correspondence between the processed image data and a database of known vehicle images. While these methods are very effective under good visibility conditions, they naturally tend to be less effective under poor visibility conditions; hence, sensor based methods are still very popular on many highways. Sensor based methods classify vehicles based on sensor measurements of the vehicle axle lengths, number of axles and axle weights.8,9 There are several methods of processing the measured data depending on type sensors used to collect that data. Most of these methods are statistical in nature, focusing on the statistical parameters of the measured data, which are eventually used in a simple IF-THEN decision tree to classify the vehicle. Details on some of these methods can be found in the California PATH Technical Report No. UCB-ITSPRR-2002-4.10 This paper presents a different way of processing and using the measured data for the purpose of classifying vehicles in accordance to Scheme F. It views the vehicle classification problem as a pattern recognition problem, which can be handled in variety of ways,11,12 especially neural networks. However, choice of any particular pattern recognition technique for this problem has to be done carefully especially since the vehicle population is not globally separable. Some of the vehicle classes span over several axles, for example, Class 5 includes vehicles with two, three and four axles, which makes it difficult for common pattern classifiers to handle. The paper proposes using a Probabilistic Neural Network (PNN) for processing measured vehicle data on axle length, number of axles and axle weights; ultimately based on this data, the PNN classifies the vehicles according to Scheme F. Although other neural network architectures, such as recurrent neural networks, have been experimented with on different classification problems, the PNN was proposed because it is easy to train especially when the solution set is not large, and it does not overfit stochastic data as recurrent neural networks do.13 The ease of training is particularly important because the neural network is supposed to work online. The paper documents the development of a PNN, and gives the performance results that compare it with the current decision tree methods. The paper is organized as follows: Section 2 gives a brief review of the structure of a PNN; the actual set up of a PNN for vehicle classification is described in Sec. 3. Section 4 compares the performance of the proposed PNN and the current decision tree method employed by the FDOT and concluding remarks are given in Sec. 5. In all mathematical expressions, bold letters such as x represent vectors or matrices and lower case letters such as x represent scalars and elements of a vector. The symbol R is a field of real numbers and Rn is a field of n-tuple real vectors.


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2. Review of Probabilistic Neural Networks A probabilistic neural network14,15 is a pattern classification network based on the classical Bayes classifier, which is statistically an optimal classifier that seeks to minimize the risk of misclassifications. Details of this network can be found in many standard textbooks; however, a brief description of this network is given below. Any pattern classifier places each observed vector of data x in one of the predefined classes ci , i = 1, 2, . . . , m where m is the number of possible classes in which x can belong. The effectiveness of any classifier is limited by the number of data elements that vector x can have and the number of possible classes n. The classical Bayes pattern classifier implements the Bayes conditional probability rule that the probability P (ci |x) of x being in class ci is given by P (x|ci )P (ci ) , P (ci |x) = m j=1 P (x|cj )P (cj )

(1)

where P (x|ci ) is the conditioned probability density function of x given set ci , P (cj ) is the probability of drawing data from class cj . Vector x is said to belong to a particular class ci if P (ci |x) > P (cj |x), ∀j = 1, 2, . . . , m, j = i. This classifier assumes that the probability density function of the population from which the data was drawn is known a priori; this assumption is one of the major limitations of implementing Bayes classifier. The PNN simplifies the Bayes classification procedure by using a training set for which the desired statistical information for implementing Bayes classifier can be drawn. The desired probability density function of the class is approximated by using the Parzen windows approach.16 –19 In particular, the PNN approximates the probability that vector x ∈ RN belongs to a particular class ci as a sum of weighted Gaussian distributions centered at each training sample, i.e. nti (x − xij )T (x − xij ) 1 P (ci |x) = exp − , (2) N 2σ 2 (2π) 2 σ N nti j=1 where xij is the jth training vector for the patterns in class i, σ is known as a smoothing factor, N is the dimension of the input pattern, and nti is the number of training patterns in class i. For nonlinear decision boundaries, the smoothing factor σ needs to be as small as possible. The computational structure of the PNN is shown in Fig. 1. The network has an input layer, a pattern layer, a summation layer and an output layer. The input x to the network is a vector defined as x [x1 , x2 , x3 , . . . , xN ]T .

(3)

This input is fed into each of the patterns in the pattern layer. The summation layer computes the probability P (ci |x) of the given input x to be in each of the classes ci represented by the patterns in the pattern layer. The output layer picks the class for which highest probability was obtained in the summation layer. The input is then classified to belong to this class. The effectiveness of the network in


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INPUT VECTOR (x)

x

1

x

2

x

3

x

N

INPUT LAYER

Patterns for Class 1

Patterns for Class m

PATTERN LAYER

P(c 1|x)

P(c 2 |x)

P(cm|x) SUMMATION LAYER

OUTPUT LAYER

Output class for the given input vector Fig. 1.

A computational structure of the probabilistic neural network.

classifying input vectors depends highly on the value of the smoothing parameter σ and how the training patterns are chosen. 3. Setting Up a PNN for Vehicle Classification Setting up a PNN for this problem involves three tasks: determination of the dimension N of the input vector x ∈ RN , choice of the number j of training patterns for each class i and selection of the training patterns xij for all possible classes, and selection of the smoothing factor σ. This section describes how these tasks were accomplished. Since the number of axles for different vehicles is not constant, i.e. some vehicles have more axles than others, it was necessary to formulate an input vector that can fairly carry information that applies to all vehicles in the population. This was accomplished by assuming that all vehicles have 9 axles, which was observed to be the maximum number of axles for all vehicles recorded in different highways of Florida. Vehicles with less axles were assumed to have additional fictitious axles so that the total number is 9; axle spacings for these fictitious axles were fixed to be 0. Therefore the dimension of the input vector x was 8, i.e. x ∈ R8 . This dimension corresponds to the number of possible axle spacings for all vehicles including


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those with fictitious axles. An additional advantage of the PNN is that additional classification criteria can be added by just increasing the dimension of the input vector x. As will be shown later in this paper, this dimension was increased to 9 by including the vehicle weight as a classification criterion, and the PNN adopted it and worked quite easily. In order to set up training patterns for each class, field data collected from different sites along Florida’s highways were used. Highways in Florida, as in most states in the US, have sites with equipment for collecting vehicle axle data; these sites are spaced randomly throughout the stretch of the highway. Some of these sites are capable of recording the vehicle weight along with the axle data and vehicle length; they are known as Weigh-In-Motion (WIM) sites. Vehicle axle data along with video images were recorded at properly calibrated WIM sites. Each monitored vehicle was visually classified by using recorded video images, and its corresponding axle data was used as a training pattern for its class. Some types of vehicles have wider axle spacing than other types; therefore, classes corresponding to vehicles with wider axle spacings were represented by more training patterns than those with narrower axle spacing. Since some of the classes in Scheme F span over a different number of axles, which makes it difficult to automatically classify them into the same class, it was necessary to redesign the classes in a way that the PNN can easily handle. Classes that span over different number of axles were broken down to simple subclasses and redefined as shown in Table 2, which also shows the mean axle spacings and mean weights of vehicles in each subclass. These subclasses are globally separable, hence they can be handled by the PNN. A total of 28 subclasses were defined based on the 13 predefined standard classes, and the PNN patterns were drawn to reflect these subclasses. The classification problem was to place each observed vehicle into one of these 28 subclasses, for example, Subclasses 2a–2c, which all represent Class 2. To ensure classification accuracy, the mean values and standard deviations of the training patterns were carefully controlled. The training patterns for each class were chosen to have a sufficiently low standard deviation, and with a mean that was sufficiently far from those of the adjacent class in the Euclidean space. This type of control was in line with the decision to represent classes that involved wider axle spacings with more training patterns than those with narrow axle spacings. In total, there were 147 training patterns for the 28 classes, which is an average of 5 patterns for each subclass. The smoothing factor σ that determines the shape of the decision boundary was experimentally selected by trial and error guided by known standard deviations of data in each class. The shape of the decision boundary was assumed to depend on the standard deviation of the data being classified. In particular, since a small value of the standard deviation indicates that the data points are clustered at well defined points, then it is associated with a decision boundary that is almost linear, calling for a large value of σ. Similarly, a high value of the standard deviation, which indicates that the data points are widely scattered, calls for a nonlinear decision


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Table 2. Mean axle distances for the subclasses defined suitable for PNN implementation of Scheme F along with their mean weights. Mean Axle Spacing [ft] Cls.

Sbcls.

Ax.1–2

1 2

1 2a 2b 2c 3a 3b 3c 3d 4a 4b 5a 5b 5c 5d 6 7 8a 8b 8c 9a 9b 10a 10b 11 12 13a 13b 13c

2.95 8.50 9.35 9.4 12.0 11.69 11.75 11.60 24.77 25.40 18.61 13.80 13.88 13.53 18.77 12.44 13.67 17.14 15.94 15.63 16.17 17.83 16.31 14.13 16.26 16.02 17.15 16.30

3

4 5

6 7 8

9 10 11 12 13

Ax.2–3

Ax.3–4

Ax.4–5

14.87 18.7

2.56

16.59 19.47 22.33

2.53 2.63

2.70

2.78 2.80

2.77

Ax.5–6

Ax.6–7

Ax.7–8

Ax.8–9

Weight [Kips]

22.00

0.47 3.00 5.51 8.78 11.34 11.71 14.00 16.25 27.85 39.87 16.12 9.18 10.98 20.16 30.76 39.32 31.88 21.00 23.69 53.35 58.65 61.75 62.34 56.34 64.02 74.94 104.85 116.05

4.06 17.10 20.90 24.90 4.27 4.08 25.23 4.26 22.76 4.33 3.47 4.48 4.44 21.33 4.24 4.40 4.30 4.07

5.64 31.04 4.89 27.3 14.67 29.31 35.16 9.52 20.19 18.42 8.45 21.13

4.51 19.00 4.15 5.73 22.25 9.04 23.64 8.20 6.60

4.11 9.19

5.79

20.87 5.96 7.90 24.63

4.30 8.35 18.58

8.95 4.55

boundary with a very small value of σ. In general, σ is inversely proportional to the standard deviation of the data being classified; it was calculated as σ=

z , Σ

(4)

where z ∈ [1, 10] R is a number selected by the user, Σ is a Frobenius norm of a matrix Σ formed by concatenating the standard deviation vectors for each training set, i.e. Σ = trace(ΣΣT ). (5) This norm fairly represents the size of the standard deviation in the training patterns. Therefore, for any fixed z, the value of σ automatically became small when the training set had large variances, which called for nonlinear decision boundaries. In determining the value of z, an initial guess was made and the PNN was asked to classify a known set of test data. The performance of the PNN was monitored and


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the value of z was adjusted until the PNN showed error-free performance on that set of test data.

4. Performance and Discussion of the Results The developed PNN was tested by using vehicle data collected from several WIM sites along highways in the state of Florida. Video data were collected in the vicinity of the WIM sites and used to monitor the performance of the PNN. More than 3000 vehicles were used in the test, and the performance of the PNN was compared to the FDOT decision tree approach. All custom made vehicles that do not fall in any of the standard Classes 1 to 13 are classified as Class 15 by both the FDOT decision tree and the PNN; it is possible that the failure to classify a vehicle in its correct standard class may also result in the vehicle being misclassified as Class 15. Vehicles that were not correctly classified by each method were identified and recorded. Two PNN systems were tested; the first system used axle data only, and second system used both axle data and vehicle weight. The training patterns for the later system had a dimension of 9. Therefore, two sets of performance were recorded for the PNN. Table 3 shows a summary of the performance for the PNN compared to the FDOT approaches; the PNN performance is shown in two sets as stated above. For both of its data sets the PNN performs better, compared to the FDOT decision tree method. One of the limitations of the FDOT decision tree approaches is its failure to include vehicle weight in the classification process, perhaps since not many traffic monitoring sites are capable of capturing vehicle weights. Although it is true that vehicle weight is not a reliable criterion since it depends on the load carried by the vehicle, it had a significant effect in improving the performance of the PNN Table 3. A summary of the PNN classification performance compared to the FDOT decision tree approaches. FDOT Dec. Tree

PNN (Without Weight)

Misclassified

PNN (With Weight)

Misclassified

Misclassified

Vehicle Class

Total Observed

Total

Percentage (%)

Total

Percentage (%)

Total

Percentage (%)

1 2 3 4 5 6 7 8 9 10 11 12 13

20 669 603 57 329 112 19 214 1116 57 81 37 12

0 37 133 11 130 5 0 1 2 5 0 0 0

0.00 5.50 22.10 19.30 39.50 4.50 0.00 0.50 0.20 8.80 0.00 0.00 0.00

0 23 83 3 92 3 0 0 0 0 0 0 0

0.00 3.40 13.80 5.30 28.00 2.70 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0 11 41 0 46 0 0 0 0 0 0 0 0

0.00 1.60 6.80 0.00 14.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Total

3326

324

9.70

204

6.10

98

2.90


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in comparison to the FDOT decision tree. In general, the misclassification rate for the FDOT approaches was a 9.7% while it was 6.1% for the PNN without vehicle weight and 2.9% for the PNN that use vehicle weight also. The high misclassification rate by the FDOT decision tree can be attributed to its rigid structure; classes are separated by crisp boundaries, which require axle spacings to be confined in certain regions. It was observed that measured axial spacings for certain vehicles do not necessarily fall in the FDOT specified regions. This can be due to owner modifications in the vehicle structure, evolving vehicle designs of new vehicles with different dimensions, or the accuracy of data collection equipment. For instance, if the measured data for a 4-axle vehicle showed axle spacings between the first three axles to be within the FDOT table while the spacing between third and the fourth axles was out of this range even by a very small distance, then that vehicle will fail the FDOT classification test and be misclassified. However, the PNN can correctly classify it since the total probability, which is an amalgamation of all other decision factors, will still be high in the correct class. Field results showed that the classification error was higher for Class 5, Class 3, and Class 2 vehicles. It was observed that certain axle dimensions for some of Class 2 vehicles (sedans and passenger cars) tend to overlap with those in Class 3 vehicles (pickups, panels and vans). This overlap can sometimes make it difficult to distinguish between the two classes, which makes it harder for FDOT decision tree classification methods. There is also axle-dimensional overlap between certain vehicles in Class 4 (buses) and Class 5 (single unit trucks). However, by probabilistically combining the overlapping axle information with the non-overlapping axle information of the vehicle, the PNN was able to clearly distinguish the classes. It failed only in situations where the two or more classes scored near equal probability. It is possible that other methods also could solve this problem by treating it as a pattern recognition problem,20 especially if the data was to be processed and classified offline as in these results. However, this study focussed on developing classification algorithm that can be used online. The PNN was chosen for this problem because it is more flexible and can easily be trained in online problems.20 Further studies on this problem should be on comparing different classification algorithms using the same formulation as presented in this paper, i.e. by redefining the Scheme F classes into separable subclasses and then apply these classification algorithms. 5. Conclusions This paper presented a systematic procedure for designing probabilistic neural network for classification of highway vehicles according to FHWA Scheme F. The network accepts information about axle spacing and vehicle weight to determine the class into which the vehicle belongs. Field results showed that the proposed network outperforms the current FDOT decision tree methods; the difference in performance between the proposed PNN method and the FDOT decision tree becomes


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more conspicuous when the vehicle weight is used in the classification. The success of the network depends on both its design (i.e. selection of the smoothing factor (σ)) and selection of representative training patterns. The smoothing factor was selected as a function of the variances of the training patterns, and the pattern set for each class was chosen to have a sufficiently small variance and a mean that is sufficiently far from the mean of the pattern for the adjacent class. Due to the better performance showed by the PNN, it is hoped that after extensive field tests and validation, the FDOT may eventually consider adopting it as a classification tool to replace the existing classification methods in the State of Florida. Acknowledgment This research was financially supported by the Florida Department of Transportation through Grant Number BD-313. This support is highly acknowledged. References 1. FHWA, Traffic Monitoring Guide, Section 4: Vehicle Classification Monitoring. Office of Highway Policy Information (May 2001). 2. J. H. Wyman, G. A. Braley and R. I. Stephens, Field evaluation of FHWA vehicle classification categories, Maine Department of Transportation, Final Report for Contract DTFH-71-80-54-ME-03 for US Department of Transportation, FHWA, Office of Planning (January 1985). 3. P. Davies, Vehicle detection and classification, in Information Technology Applications in Transport, ser. Topics in Transportation, eds. M. Bell and P. Bonsall, Haarlem, the Netherlands, VNU Science Press (1986), pp. 11–40. 4. D. Beymer, P. McLauchlan, B. Coifman and J. Malik, A real time computer vision system for measuring traffic parameters, in Proc. IEEE Conf. Computer Vision and Pattern Recognition, Puerto Rico (1997), pp. 496–501. 5. M. J. J. Burden and M. G. H. Bell, Image classification using stereo vision, in Proc. 6th Int. Conf. Image Proc. Its Appl., Dublin, Ireland, 2 (1997), pp. 881–887. 6. G. D. Sullivan, K. D. Baker, A. D. Worrall, C. I. Attwood and P. M. Remagino, Model-based vehicle detection and classification using orthographic approximations, Image Vision Comput. 15 (1997) 649–654. 7. S. Gupte, O. Masoud, R. K. F. Martin and N. P. Papanikolopoulos, Detection and classification of vehicles, IEEE Trans. Intell. Trans. Syst. 3(1) (March 2002) 37–47. 8. T. Cherrett, H. Bell and M. McDonald, Traffic measurement parameters from single inductive loop detectors, Trans. Res. Rec. 1719 (2000) 112–120. 9. S. Cheung, S. Coleri, B. Dundar, S. Ganesh, C.-W. Tan and P. Varaiya, Traffic measurement and vehicle classification with a single magnetic sensor, in Compendium of Papers Presented at the TRB 84th Annual Meeting (January 2005). 10. C. Sun, An investigation in the use of inductive loop signatures for vehicle classification, California PATH, Research Report UCB-ITS-PRR-2002-4 (2000). 11. D. Michie, D. J. Spiegelhalter and C. C. Taylor, Machine Learning, Neural and Statistical Classification (Ellis Horwood, 1994), http://citeseer.ist.psu.edu/ michie94machine.html. 12. L. H. Tsoukalas and R. E. Uhrig, Fuzzy and Neural Approaches in Enegineering (John Willey, 1997).


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