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A wavelet-based freeway incident detection algorithm with adapting

threshold parameters

Young-Seon Jeong a, Manoel Castro-Neto b, Myong K. Jeong a,c,*, Lee D. Han d

a Department of Industrial and Systems Engineering, Rutgers University, Piscataway, NJ 08854, USAb Department of Transportation Engineering, Federal University of Ceara, Fortaleza, CE, 60455-760, Brazilc Department of Industrial and Systems Engineering, Korea Advanced Institute of Technology, Daejon 305-701, Koread Department of Civil and Environmental Engineering, University of Tennessee, Perkins Hall 223, Knoxville, TN 37996, USA

a r t i c l e i n f o

Article history:

Received 11 August 2008

Received in revised form 23 October 2009

Accepted 30 October 2009

Keywords:

Freeway operations

Incident detection algorithms

Multi-resolution analysis

WaveletsVarying threshold value

a b s t r a c t

This paper presents a wavelet-based novel freeway automated incident detection algo-

rithm with varying threshold parameters considering the level of traffic flow. In this

approach, new test statistics for incident detection are extracted from occupancy and

speed data using discrete wavelet transform, which decomposes traffic measurements into

different resolution-time components. Unlike conventional incident detection algorithms,

which apply fixed threshold values and often result in undesirably high false alarm rates,

our proposed algorithm varies its threshold values adaptively based on the level of traffic

volume. We have derived the mathematical relationship between the false alarm probabil-

ity and the threshold value of our proposed decision function. For a given target false alarm

rate, the threshold values can be changed adaptively depending on the traffic levels of nor-

mal traffic conditions. Also, we propose the new feature selection technique to measure the

quality of different features that may be used to discriminate between normal and incident

traffic conditions. Using both simulated data set and real-life incident data set, the perfor-

mance of our proposed algorithm was compared with existing popular approaches such as

California algorithm, Minnesota algorithm, conventional neural networks algorithm, and a

wavelet-based neural-net algorithm. Experimental results show that the proposed wave-

let-based algorithm consistently outperformed others with a higher detection rate, lower

false alarm rate, and shorter mean time to detection. It is conclusive that the proposed

algorithm is a superior alternative to existing algorithms.

2009 Elsevier Ltd. All rights reserved.

1. Introduction

The functionality of automatically detecting incidents on freeways is a primary objective of advanced traffic management

systems (ATMS), an integral component of the Nations Intelligent Transportation Systems (ITS). Because traffic incidents,

e.g. vehicular crashes, on freeways often result in serious injuries, if not fatalities, as well as extensive traffic congestion

and protracted delay, accurate and prompt incident detection is crucial to the timely response to such emergencies in order

to save lives, prevent secondary incidents, and restore normal operations in a timely fashion.

Since the1970s, a number of automated incident detection (AID) algorithms based on data from inductive loop detectors

have been developed. In the early years, California and Minnesotaalgorithms (Payne and Tignor, 1978; Stephanedes and Chas-

siakos, 1993) were regarded as themost notable andare still used for benchmarking newer algorithms. Othermodels based on

trafficflow theory (Kuhne, 1989), knowledge-based expert system (Hanand May, 1990), catastrophe theory (Persuad and Hall,

0968-090X/$ - see front matter 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.trc.2009.10.005

* Corresponding author. Tel.: +1 732 445 4858; fax: +1 732 445 5472.

E-mail address: [email protected] (M.K. Jeong).

Transportation Research Part C 19 (2011) 119

Contents lists available at ScienceDirect

Transportation Research Part C

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / tr c


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1989) and time-series techniques (Ahmed and Cook, 1982) were also proposed in the 1980s. Over the past decade, several ad-

vanced techniques for AID have been tested; these include artificial neural networks (Chen and Ritchie, 1995; Dia and Rose,

1997; Cheu et al., 2004; Abdulhai and Ritchie, 1999; Jin et al., 2002), partial least squares regression (Wang et al., 2008), fuzzy

logic (Lee et al., 1998; Hawas, 2007), Bayesian approaches (Thomas, 1998; Zhang and Taylor, 2006), and combinations (fusion)

of algorithms (Ishak and Al-Deek, 1998; Mak andFan, 2006a). However, somewhat disappointingly, as pointed out by Williams

andGuin(2007), thesenewer algorithms higher than desirablefalsealarmrate(FAR) and their need forcomplexand painstak-

ing calibrations, among other factors, have kept them from a wide deployment at ITS traffic management and control centers.In the early 2000s, wavelet theory was applied to traffic incident detection (Ghosh-Dastidar and Adeli, 2003; Teng and Qi,

2003) because of its superior ability of denoising and extracting new features through the transformation of raw traffic

measurements. Adeli and Samant (2000) and Ghosh-Dastidar and Adeli (2003) proposed the novel wavelet-based neural net-

works, which applied a wavelet transform for effective preprocessing of traffic measurements.

Teng and Qi (2003) utilized wavelet coefficients (finer and coarse level coefficients) directly in detecting changes in traffic

measurements. For the purpose of determining decision-making rules for incident detection, the finest level coefficients

were employed to detect significant and abrupt changes in traffic measurement while the coarser level coefficients were de-

vised to detect global incident trend, where the upstream traffic measurements of occupancy tend to increase as the down-

stream ones decrease in the wake of an incident. However, this algorithm fixes its threshold values for decision-making

regardless of traffic flow rate levels. By adaptively changing these thresholds depending on traffic, a more consistent algo-

rithm performance is produced.

The motivation of this paper is to propose a wavelet-based freeway incident detection algorithm that combines the multi-

resolution property of wavelet transform with varying threshold values. We also present a new feature selection techniqueto select the features that gives us good discrimination capability between normal and incident traffic conditions. In addi-

tion, the proposed algorithm adaptively changes its threshold values according to traffic flow rate. Even though the selection

Traffic pattern at 30-sec. interval:

Upstream and downstream

occupancy and speed information

Wavelet multi-resolution analysis:

Discrete wavelet transform

Selection of decision function:

Divergence technique

High DR and low FAR under

different level of traffic flow rate:

Varying threshold values

Incident alarm:

Satisfaction of two decision functions

Fig. 1. Flowchart of the proposed algorithm procedure for freeway incident detection.

2 Y.-S. Jeong et al. / Transportation Research Part C 19 (2011) 119


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of optimal threshold values for incident detection algorithms is an important issue for real-world implementation purposes,

there has been little systematic and methodological research in this area. From this perspective, it is advantageous to vary

the threshold values based on traffic flow rate. We also derive the mathematical relationship between the false alarm prob-

ability and the threshold value of our proposed decision function. As a result, our proposed algorithm, which does vary the

threshold values based on traffic condition, yields higher detection rate (DR), lower false alarm rate (FAR) and faster mean

time to detection (MTTD) than other algorithms. Fig. 1 illustrates the flowchart of the proposed algorithm for freeway inci-

dent detection. More details on performance comparisons are presented in Section 3.This paper is organized into six sections. A brief review of wavelet and multi-resolution wavelet techniques is given in

Section 2. The proposed methodology is presented in Section 3, which is followed by the comparison of the employed algo-

rithms in Section 4. In Section 5, case studies using real-world freeway data are presented. Finally, Section 6 concludes with a

brief summary as well as suggestions of future research directions.

2. Multi-resolution wavelet technique

2.1. Review of wavelet transform

Wavelet transform, which contains time-scale information, has been recognized as a powerful signal analysis tool ( Vida-

kovic, 1999; Jeong et al., 2006a). Wavelets are a family of functions derived from two basis functions,/(t) andw(t), known asthe father wavelet and the mother wavelet. If f(t) e L2(R), where L2(R) is the space of square integrable real functions de-

fined on the real line R, f(t) is described as the following:

ft X2L1k0

cL;k/L;kt XJjL

X2L1k0

dj;kwj;kt 1

where the CL,k and dj,k are the coefficients for the basis function /L,k(t) and wj,k(t), respectively.It is reasonable to assume that traffic measurements collected over time in normal operation, i.e. non-incident, conditions

can be expressed as:

yti fti eti; i 1;2; . . . ; n 2where f(ti) is a true traffic measurement and e(ti) are noises following independent and identically distributed (i.i.d.) normal

distribution N(0,r2). When a discrete wavelet transform (DWT) Wis used for a y, it is expressed by d =Wy, where d is thewavelet coefficients and W is the wavelet transform matrix.

The interpretation of relationship between time domain and wavelet domain is important for the detection of the change

point in the wavelet domain. Theorem 1 (Jeong et al., 2006b) below provides a clear understanding of the relationship be-

tween time domain and wavelet domain.

Theorem 1. When there is a mean change of traffic measurements such as flow, speed, or occupancy in qi units ofr for the timetis in the interval A = (ts, te) with t1 6 ts < ti < te 6 tn, i.e.,

Fnewti F0ti qir; ti 2 AF0ti; elsewhere

&3

wavelet coefficients have the following corresponding shift:

hi;new hi;0 dir; i 1;2; . . . ; n 4where h is a wavelet coefficient and di

Pj2Aqhhij and hijs are the elements of the DWT matrix W(see Jeong et al. (2006b) for the

proof of Theorem 1).

The importance of Theorem 1 is that it warrants that the locations of changes in the time domain can be detected by ana-

lyzing the wavelet domain.

2.2. Wavelet multi-resolution analysis on freeway incident detection

The general traffic phenomenon after the occurrence of an incident is the slowing down of vehicular speed and the in-

crease in highway occupancy upstream of the incident site. On the other hand, downstream speed will be comparatively fas-

ter and the occupancy lower. Recent incident detection studies (Adeli and Samant, 2000; Samant and Adeli, 2000; Teng and

Qi, 2003) found that wavelet can accurately identify a sharp change in traffic measurements that are obscured by noise. For

example, Adeli and Samant (2000) proposed a wavelet technique to filter out noises and utilized its multi-resolution prop-

erty for incident detection. They selected several wavelet coefficients in different resolution levels by using the filtering

method prior to entering the values into neural network models.

In this paper, the authors apply similar wavelet technique to take advantage of its multi-resolution property for the devel-opment of a new AID algorithm. Sixteen data points, including the upstream and downstream traffic occupancy and speed

information for 4 min, at 30 s time interval, are used to form the data vector:

Y.-S. Jeong et al. / Transportation Research Part C 19 (2011) 119 3


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OUDh i

16

fyout7;yout6; . . . ;yout ;yodt7;yodt6; . . . ;yodt g

SUDh i

16 fysut7;ysut6; . . . ;ysut ;ysdt7;ysdt6; . . . ;ysdt g

where yout ; yodt ; y

sut and y

sdt are upstream and downstream occupancy and speed data at time t. If two-level Haar wavelet

(Teng and Qi, 2003) is adopted, its DWT can be expressed as:

DTW OUDh i

co2;1; co

2;2; co

2;3; co

2;4;d

o2;1; d

o2;2;d

o2;3; d

o2;4;d

o1;1;d

o1;2;d

o1;3;d

o1;4;d

o1;5;d

o1;6;d

o1;7;d

o1;8

h i16

DTW SUDh i

cs2;1; cs

2;2; cs

2;3; cs

2;4;d

s2;1;d

s2;2;d

s2;3;d

s2;4;d

s1;1;d

s1;2;d

s1;3;d

s1;4;d

s1;5;d

s1;6;d

s1;7;d

s1;8

h i16

where cm,n and dm,n are the nth coarser and finer coefficients in scale m, respectively. The equations for these wavelet coef-

ficients are tabulated in Table 1.

Based on the 16 wavelet coefficients, we can develop a new AID algorithm. In Section 3, we will discuss how this new

wavelet-based AID algorithm is developed and evaluate the performance using simulated and real-world incident data.

3. Wavelet-based AID algorithm

This section proposes a new AID algorithm, which integrates wavelet multi-resolution analysis with varying threshold

values. The significant characteristics of the proposed approach will also be presented.

3.1. Extraction of test statistic for incident detection

Traffic measurements have a tendency to change after the occurrence of an incident. For example, occupancy increases

upstream and decreases downstream while the opposite happens to speed. These differences between up- and downstream

traffic measurements have been the basis of most freeway AID algorithms such as the California and the Minnesota ones. The

California algorithm only utilizes current time occupancy information, which may produce high FAR because of dynamic

traffic fluctuations. On the other hand, the Minnesota algorithm employs cumulative sum of differences between up and

downstream occupancies in order to alleviate the high FAR setback commonly yielded by the California algorithm.

In the previous section, 16 wavelet coefficients, which contain multi-resolution information, are presented. Finer coeffi-

cients present the difference between current and previous measurements, which is similar to the decision functions of Cal-

ifornia algorithm, while coarse coefficients illustrate the cumulative sum of traffic measurement for several time windows,which denotes the core component of the decision functions of Minnesota algorithm.

Based on Table 1, we can define the coarser coefficients as follows (in case of occupancy measurement):

Table 1

The equations of each wavelet coefficient.

Occupancy measurement Speed measurement

co2;1 yout7yout6yout5yout4ffiffi

4p cs2;1

ysut7ysut6ysut5ysut4ffiffi4

p

co2;2 you

t3yout2yout1yout ffiffi4

p cs2;2 ysu

t3ysut2ysut1ysut ffiffi4

p

co2;3

yodt

7

yod

t

6

yod

t

5

yod

t

4

ffiffi4p cs2;3

ysdt

7

ysd

t

6

ysd

t

5

ysd

t

4

ffiffi4pco

2;4 yodt3yodt2yodt1yodt ffiffi

4p cs

2;4 ysdt3ysdt2ysdt1ysdt ffiffi

4p

do2;1

yout7yout6yout5yout4ffiffi4

p ds2;1 ysut7ysut6ysut5ysut4ffiffi

4p

do2;2 you

t3yout2yout1yout ffiffi4

p ds2;2 ysu

t3ysut2ysut1ysut ffiffi4

p

do2;3

yodt7yodt6yodt5yodt4ffiffi

4p ds2;3

ysdt7ysdt6ysdt5ysdt4ffiffi

4p

do2;4 yod

t3yodt2yodt1yodt ffiffi4

p ds2;4 ysd

t3ysdt2ysdt1ysdt ffiffi4

p

do1;1

yout7yout6ffiffi

2p ds1;1

ysut7ysut6ffiffi

2p

do1;2 you

t5yout4ffiffi2

p ds1;2 ysu

t5ysut4ffiffi2

p

do1;3 you

t3yout2ffiffi2

p ds1;3 ysu

t3ysut2ffiffi2

p

do1;4 you

t1yout ffiffi2

p ds1;4 ysu

t1ysut ffiffi2

p

do1;5

yodt7yodt6ffiffi2p ds1;5

ysdt7ysdt6

ffiffi2p

do1;6

yodt5yodt4ffiffi

2p ds1;6

ysdt5ysdt4ffiffi

2p

do1;7 yod

t3yodt2ffiffi2

p ds1;7 ysd

t3ysdt2ffiffi2

p

do1;8 yod

t1yodt ffiffi2

p ds1;8 ysd

t1ysdt ffiffi2

p



6/20


co2;1

yout7 yout6

yout5 yout4 ffiffiffi4

p 1ffiffiffi4

pX4j1

yout4j1

co2;2

yout3 yout2

yout1 yout ffiffiffi4

p 1ffiffiffi4

pX3j0

youtj

co2;3 yod

t7 yod

t6 yodt5 yodt4 ffiffiffi4

p 1ffiffiffi

4p X4

j1yodt4j1

co2;4

yodt3 yodt2

yodt1 yodt ffiffiffi4

p 1ffiffiffi4

pX3j0

yodtj

Namely, co2;2 co2;4 1ffiffi4pP3

j0 youtj yodtj

n oand co2;1 co2;3 1ffiffi4p

P4j1 y

out4j1 yodt4j1

n o.

Therefore, we can obtain several test statistics that are similar to the decision functions of Minnesota algorithm in the

wavelet domain as follows:

For occupancy measurements,

WMocc1

co2;2

co2;4

maxfco2;1; co

2;3g

1

ffiffi4

pP3

i0 youti yodti

max 1ffiffi4p P4i1y

out

4

i

1;

1ffiffi4p P4i1yodt

4

i

1n o

5

WMocc2

co

2;2 co

2;4

co

2;1 co

2;3

maxfco

2;1; co

2;3g

1ffiffi4

pP3

i0 youti yodti

P4i1 yout4i1 yodt4i1 max 1ffiffi

4pP

4

i1yout4i1;

1ffiffi4

pP

4

i1yodt4i1

n o 6For speed measurements,

WMspe1

cs2;2

cs2;4

maxfcs2;1; cs

2;3g

1ffiffi4

pP

3

i0ysuti ysdtimax 1ffiffi

4pP4

i1ysut4i1;

1ffiffi4

pP4

i1ysdt4i1

n o 7

WMspe2

cs2;2

cs2;4

cs2;1

cs2;3

maxfcs

2;1; cs

2;3g

1ffiffi4

pP3

i0ysuti ysdti P4

i1ysut4i1 ysdt4i1

max 1

ffiffi4

p

P4

i1ysut4i1;

1

ffiffi4

p

P4

i1ysdt4i1

n o 8

It is worth noting that the relationship between Minnesota algorithm and wavelet-based test statistic can be extracted bycomparing Eqs. (5) and (6). The Minnesota algorithm (Stephanedes and Chassiakos, 1993) may be expressed as

M1 1

n

Pn1i0 y

outi

Pn1i0 y

odti

max 1

m

Pmi1y

outni1;

1

m

Pmi1y

odtni1

9

M2 1

n

Pn1i0 y

outi

Pn1i0 y

odti

1

m

Pmi1y

outni1

Pmi1y

odtni1

max 1

m

Pmi1y

outni1;

1

m

Pmi1y

odtni1

10When n is equivalent to m and both are 4, Eqs. (5) and (6) are the same as the Minnesota algorithm, representing

WMocc1 M1 and WMocc2 M2. Thus, the Minnesota algorithm is a special case of our proposed algorithm. By applying thewavelet multi-resolution analysis to traffic information, meaningful test statistic can be extracted for incident detection.

The next task is to select the best test statistic and develop a systematic method of varying threshold values depending on

the level of traffic volume.

3.2. Selection of best test statistic for incident detection

In the previous section, several test statistics (Eqs. (5)(8) and finer coefficients) were extracted for incident detection by

using wavelet multi-resolution analysis. Given these test statistics, the major task is to select the one that is most capable of

clearly discriminating between normal and incident-disturbed traffic conditions. Divergence, which can be used as a class

separability measure with respect to the adopted feature, is popular among other feature selection techniques (Guyon

and Elisseeff, 2003; Theodoridis and Koutroumbas, 2006). Assuming that the density functions of feature vector xi for inci-

dent data andxj for incident-free data are Gaussians N(li,Ri) and N(lj,Rj), respectively, we can compute the divergenceJij(x)

as:

Jij

x

1

2trace R1I Rj

R1j Ri

2In o

1

2

li

lj

T

R1i

R1j

li

lj

11

where li, Ri, lj andRj are means and covariances of xi and xj, and I is identity matrix.

For the one-dimensional case, Eq. (11) becomes:



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Jijx 1

2

r2jr2i

r2

i

r2j 2

! 1

2li lj2

1

r2i 1r2j

!12

where li, lj and r2i , r2

j are the means and variances of xi and xj, respectively.

In order to determine the best test statistic using divergence technique, seven simulation scenarios covering different lev-

els of traffic demand and incident severity conditions were implemented using VISSIM micro-simulation software (PTV Vi-

sion, 2007). The scenarios were divided according to traffic demand (low, medium, and high volume, labeled as LV, MV, andHV respectively) and incident severity (low, medium, and high blockage, labeled as LB, MB, and HB). The characteristics of

the simulation scenarios are summarized in Fig. 2. As shown in Fig. 2, the blockage level is determined by the number of

lanes blocked; that is, LB, MB, and HB relates to one, two, or three lanes blocked, respectively. The blockage was performed

by making vehicles stop for 10 min at traffic a signal located halfway between the detector stations, which were 0.5 miles

(800 m) apart from each other. The simulated roadway facility consisted of a four-lane freeway. The traffic-demand levels LV,

MV, and HV correspond to flow rates of 3000, 5000, and 7000 veh/h/4lanes. Fig. 3 shows a snapshot of a simulation-run un-

der scenario HVMB. Among the nine possible scenarios tabulated, two were excluded from the analysis: LVLB and HVHB.

The LVLB, or low-demand and low-blockage condition is excluded because it has minimum adverse effect on the traffic and

is very challenging to detect. On the other end of the spectrum, the HVHB, or high-demand and high-blockage condition is

also excluded because while it does have significant impact on traffic, it is very easy, if not trivial, to detect with a wide range

of methods.

(a) Diagram of simulation dataset

Simulationscenario

Traffic flow(vehicles/hour)

# of lanesblocked

(total lanes=4)

Number ofIncident runs

Incidentinterval

Incident -freeInterval

LV-MB 3000 2 30

LV-HB 3000 3 30

MV-LB 5000 1 30

MV-MB 5000 2 30

MV-HB 5000 3 30

HV-LB 7000 1 30

HV-MB 7000 2 30

20 ~ 30 min. 1 ~ 20 min.

(b) Detail condition of simulation

LV-HBLV-MBLV-LB

MV-HBMV-MBMV-LB

HV-HBHV-MBHV-LB

# of lanes blocked

Volumelevel

1 lane 2 lane 3 lane

Low

Medium

High

Fig. 2. Characteristics of simulation dataset.

Fig. 3. Simulated network: distance between stations is 800 m (0.5 mile). Incident is located halfway between the stations.



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Table 2 shows the several test statistics of occupancy and speed measurements that include the test statistics of California

and Minnesota algorithms. We chose occupancy and speed for the proposed algorithm because algorithms based on them

were found to be more efficient than those based only on one traffic parameter ( Mak and Fan, 2005). It has been reported

that speed and occupancy data tend to reflect incident-induced lane-blockage in a timelier manner than flow data (Mak and

Fan, 2005).

Based on the divergence results summarized in Table 3, Feature 1 yields the highest divergence values and, hence, is the

best test statistic for both occupancy and speed measurements (see Fig. 4). Feature 1 provides an indication of the trafficconditions in the freeway segment that lies between the two detectors because Feature 1 represents the cumulative spatial

difference between upstream and downstream traffic measurements (occupancy and speed). Therefore, higher Feature 1 can

be attributed to congestion created between the two detectors as a result of an incident or a bottleneck. Note that the effect

of incidents on traffic is more temporary and sharper frequency on traffic measurements than that of bottleneck. For the

cases of LVMB and MVLB, it is less clear which among the 16 is the best feature because they are not noticeably discrim-

inating between normal and incident-disturbed traffic cases. However, Feature 1 presents the best performance, in general,

among all candidate features.

Fig. 4 consists of a battery of histograms based on various scenarios for the comparison of the two best and the worst

occupancy-based features: Features 1, 2 and 6. Fig. 4 empirically shows that good features should have lower FAR under nor-

mal traffic conditions while larger DR under incident cases regardless of the level of traffic flow. The histograms on the left-side

relate to the incident-free condition whereas the ones on the right-side represent incident cases. When the observed test

Table 2

Several test statistics for incident detection.

Occupancy measurement Speed measurement

Feature 1 co2;2co

2;4

maxfco2;1

;co2;2g

Feature 1 cs2;2cs

2;4

maxfcs2;1

;cs2;2g

Feature 2 co2;2co2;4co2;1co2;3maxfco

2;1;co

2;2g

Feature 2 cs2;2cs2;4cs2;1cs2;3maxfcs

2;1;cs

2;2g

Feature 3 do2;1 Feature 3 ds2;1

Feature 4 do2;2

Feature 4 ds2;2

Feature 5 do2;3

Feature 5 ds2;3

Feature 6 do2;4

Feature 6 ds2;4

Feature 7 do1;1

Feature 7 ds1;1


Feature 9 d

o

1;3 Feature 9 d

s

1;3

Feature 10 do1;4

Feature 10 ds1;4





Table 3

Divergence of candidate features.

F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14

(a) Occupancy measurement

LVMB 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.3

LVHB 58.8 10.6 0.1 19.6 0.0 0.2 0.0 0.1 2.1 5.2 0.1 0.3 0.7 1.5

MVLB 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1

MVMB 134.4 24.3 5.5 19.2 0.1 0.3 0.2 1.5 3.5 5.5 0.2 0.3 0.5 0.7

MVHB 786.5 150.9 69.0 67.1 0.1 0.2 14.6 15.4 16.0 15.9 0.2 0.3 0.5 0.7

HVLB 36.2 6.3 1.8 3.2 0.1 0.2 0.3 0.6 0.9 1.2 0.1 0.2 0.5 0.5

HVMB 350.7 57.5 29.6 33.5 0.1 0.2 7.8 8.4 9.7 10.8 0.2 0.4 0.9 1.1

Average 195.3 35.7 15.1 20.4 0.1 0.2 3.3 3.7 4.6 5.5 0.1 0.2 0.5 0.7

(b) Speed measurement

LVMB 13.8 0.1 0.1 0.0 8.8 11.6 0.1 0.0 0.1 0.1 7.4 9.7 11.1 9.7

LVHB 436.1 57.2 4.6 12.5 6.7 7.2 0.6 1.3 2.2 2.1 6.4 7.7 8.4 6.6

MVLB 5.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

MVMB 1269.1 183.5 21.3 38.7 0.3 0.2 2.6 4.0 6.5 8.5 0.2 0.2 0.3 0.3

MVHB 6504.1 567.7 105.5 98.9 4.4 5.1 16.4 16.0 16.1 16.4 4.5 5.3 5.9 6.3

HVLB 735.5 119.7 22.7 35.2 0.0 0.1 4.4 7.1 9.4 11.8 0.0 0.0 0.0 0.1

HVMB 6191.3 544.1 115.6 118.4 0.1 0.2 31.8 34.2 36.5 38.1 0.1 0.1 0.1 0.1

Average 2165.0 210.3 38.5 43.4 2.9 3.5 8.0 8.9 10.1 11.0 2.7 3.3 3.7 3.3



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statistic value is greater than the threshold value (dotted vertical line), an incident alarm is sounded. The ideal feature/

threshold combination would place all incident-free observations to the left of the threshold line and all incident cases to

the right of it, thus yielding a 100% DR and 0% FAR. As shown in Fig. 4, when the threshold value is set to 0.2, Feature 1

(Fig. 4a) detects almost all incident cases while keeping its FAR low in comparison to those of Feature 2 (Fig. 4b). Therefore,

Feature 1 attains higher DR and low FAR compared to those of Feature 2. On the other hand, as suggested by the divergenceresults, Feature 6 (Fig. 4c) shows little discrimination between normal and incident cases. Results from speed measurements

present a similar phenomenon. In addition, depending on the level of traffic flow in normal traffic conditions, variance

Fig. 4. Histograms of Features 1, 2 and 6 using occupancy.



10/20


changes slightly even if the mean is almost zero for all cases. As such fixed, or pre-determined, threshold values tend to yield

higher FAR values. More details on varyingthreshold values are presented in Section 3.3.

Based on these results, Feature 1 will be used as the decision functions, for both occupancy and speed measurements, as

shown in Eqs. (5) and (7).

3.3. Varying threshold values

In Section 3.2, two test statistics based on divergence criterion were selected for incident detection. It has been observed

repeatedly that shortly after the occurrence of an incident, occupancy tends to increase upstream and decrease downstream

while the opposite happens to speed. Therefore, two decision functions for incident detection are proposed as the following:

WMocc1

1ffiffi

4pP3

i0youti yodtimax 1ffiffi

4pP4

i1yout4i1;

1ffiffi4

pP4

i1yodt4i1

n o > docc 13

WMspc1

1

ffiffi4

pP

3

i0ysuti ysdtimax 1ffiffi4p P4i1ysut4i1;

1ffiffi4p P4i1ysdt4i1n o< dspe 14

In other words, an incident alarm is sounded only when the conditions in both Eqs. (13) and (14) are met. The most impor-

tant issue is how to select optimal threshold values docc and dspe. Even though there was a research (ITS DECISIONS, 2001) to

try to find out an optimal threshold values, little published study has reported a theoretical approach to the optimal selection

of such parameters. In order to derive the mathematical relationship between the false alarm probability and the threshold

values of proposed decision functions, firstly, we can mathematically express false alarm rate as follows:

at PWMocc1 > docc;WMspe1 < dspejnormal traffic 15where WMocc1 and WM

spe1 are normal distributions Nl0;occ;r20;occ and Nl0;spe;r20;spe, respectively, and at is the target or desir-

able false alarm rate. Under incident-free traffic conditions, usually l0,occ = 0 and l0,spe = 0. Assuming that WMocc1 and WM

spe1

are independent, we obtain:

at P WMocc1 > doccjnormal traffic P WMspe1

< dspejnormal traffic 1 U docc l0;occ

r0;occ

U dspe l0;spe

r0;spe

16

Fig. 4 (continued)



11/20


where U denotes the cumulative distribution function of a standard normal distribution. By assuming that each term con-

tributes equally to at in Eq. (16), we can obtain the following approximated equations:ffiffiffiffiffiat

p % 1 U doccl0;occr0;occ

ffiffiffiffiffiat

p % U dspel0;sper0;spe 17

Because l0;occ 0 and l0;spe 0 under incident-free traffic conditions, the relationship between the false alarm probabilityand the threshold values can be found using the following equations:

docc U11 ffiffiffiffiatp r0;occdspe U1ffiffiffiffiatp r0;spe 18

Fig. 5. Block diagram of the proposed incident algorithm.



12/20


whereU1 represents the inverse of the cumulative distribution function of a standard normal distribution. As we can see inEq. (18), for a given target false alarm rate (at), the threshold values will be changed adaptively depending on the traffic lev-els of normal traffic, i.e., the standard deviations r0;occ;r0;spe ofWMocc1 and WMspe1 under normal traffic conditions.

With all the building blocks in place, Fig. 5 illustrates the core procedure of the proposed incident algorithm.

4. Case study with simulated data

To evaluate the proposed wavelet-based AID algorithm, its performance is compared with that of California, Minnesota,

and several neural network models. In this section, seven simulated incident scenarios, as presented previously in Section 3.1

and Fig. 2, are used for that purpose. Further comparisons using real-world incident cases are presented in Section 5.

To obtain the optimal values of the varying threshold parameters, which change with the level of traffic volume, both the

means and the variances of the test statistics WMocc1 and WMspe1 under normal traffic must be known beforehand. This is

accomplished by computing WMocc1 and WMspe1 for different levels of normal traffic conditions. Fig. 6 shows the box plots

of test statistics for different traffic levels from very light traffic, about 250 veh/h/lane, to the left, to near-capacity traffic,

over 2000 veh/h/lane to the right. It is interesting to note in Figs. 6 and 7, that whereas the means of test statistics are prac-

Fig. 7. Standard deviation of the test statistics versus traffic volume rate.

Fig. 6. Box plot of the test statistics versus traffic volume rate.



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tically zero across all traffic levels, their standard deviation decreases as the traffic volume increases. This is evidence that

any type of comparative AID algorithm that is based on threshold parameters such as WMocc1 and WMspe1 needs to vary the

parameters based on the traffic level in order to minimize false alarms and maximize detection rates.

Based on the experimental results, we can approximate the standard deviation curve over traffic flow rate with fourth-

degree polynomial functions as the following:

r0;occ

0:0001x4vol

0:0022x3vol

0:0195x2vol

0:0777xvol

0:1798

19

rspe 0:0018x

4

vol 0:0251x3vol 0:1282x2vol 0:2859xvol 0:245 for xvol 50:005 for xvol > 5

(20

where rocc and rspe are the estimated standard deviations ofWMocc1 and WM

spe1 in normal traffic, andxvol is the four-lane traf-

fic flow rate per hour divided by 1000. Fig. 8 shows the estimated curve of standard deviation over different traffic flow rates.

In Fig. 8, the small circle represents the actual standard deviation value at specific traffic volume rate. The estimated curve

can fit the standard deviation very well.

In order to evaluate the incident detection performance of the proposed algorithm, a total of 210 simulation runs or

cases, 30 for each of the 7 scenarios, were generated with different random-seeds. In each scenario, the runs were performed

using the multi-run feature of VISSIM, with the first run having random-seed equals to 1, and the last run having random-

seed equal to 30. The length period of each run was 60 min, with the incident (blockage) from starting at t= 20min and end-

ing at t= 30 min. The 30 cases of each scenario were then randomly divided into two groups 15 for training and the other

15 for testing purposes. As a result, a total of 105 (15 7) incident cases were available for training and the same amountwas available for testing. As for the incident-free cases, a run of 4 h was performed for each traffic demand level.

As commonly adopted in AID studies, the measures of effectiveness (MOE) used were the detection rate (DR), false alarm

rate (FAR), and mean time to detection (MTTD). DR is calculated as the ratio of the number of detected incidents to the total

number of incidents in the data set. FAR is defined as the ratio of the number of false alarms to the total number of appli-

cations of the algorithm, generally every 30 s, under incident-free conditions. MTTD is simply the average time from the

occurrence of an actual incident till the correct detection of the incident for all detected incidents. Obviously, it is desirable

for AID algorithms to yield high DR (near 100%), low FAR (near 0%), and short MTTD (as short as possible).

In an effort to evaluate the proposed wavelet-based AID algorithm, four algorithms were selected for comparison. These

include: California algorithm, Minnesota algorithm, wavelet-based radial basis function (WRBF) neural networks (Karim and

Adeli, 2002), wavelet-based multi-layer feed-forward neural networks (WMLF1 and WMLF2), and multi-layer feed-forward

neural networks (MLF1 and MLF2). California algorithm and Minnesota algorithm are well-established and widely-tested.

WMLF1, which relies on occupancy data alone, and WMLF2, which employees both occupancy and speed data, use wave-

let coefficients as neurons in the input layers of the neural network. This algorithm is based on the wavelet-filtering schemeproposed by Ghosh-Dastidar and Adeli (2003). The architecture of WMLF algorithms consists of 6 neurons in the input layer

for WMLF1 and 12 neurons for WMLF2, a single hidden layer with 10 neurons, and one output neuron. Tangent sigmoid

function and linear transfer function are used for activation function in the hidden and output layers. WRBF, which employs

occupancy, speed, and flow data, also use wavelet coefficients as neurons in the input layers of RBF neural network.

The architecture of MLF algorithms is identical to WMFL algorithms, except for the input neurons. MLF1 uses occupancy

data only as eight input neurons (upstream and downstream occupancy: (t 3), (t 2), (t 1) and (t)), while MLF2 com-bines both occupancy and speed data as 16 input neurons (upstream and downstream occupancy and speed: (t 3),(t 2), (t 1) and (t)). In other words, MLF employs raw traffic data as input neurons instead of wavelet coefficients.

Fig. 8. Estimated standard deviation curve.



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Table 4

Performance comparison (simulation dataset).

dCal1 dCal2 d

Cal3

California algorithm dMinn1 dMinn2

Minnesota algorithm

DR (%) FAR (%) MTTD (s) DR (%) FAR (%) MTTD (s)

(a) Training dataset

1 0.45 0.07 70 1 307 0.15 0.17 85 1 209

1 0.39 0.05 75 3 247 0.04 0.21 90 3 1911 0.35 0.05 81 5 228 0.09 0.01 98 5 121

1 0.31 0.09 88 7 216 0.08 0.01 100 7 114

aTh. WRBF Th. WMFL1 Th. WMFL2

DR (%) FAR (%) MTTD (s) DR (%) FAR (%) MTTD (s) DR (%) FAR (%) MTTD (s)

0.9 90 1 160 0.9 85 1 201 0.9 95 1 165

0.8 98 2 150 0.8 98 2 160 0.8 98 2 152

0.7 99 3 144 0.7 99 3 144 0.7 100 3 144

0.6 100 4 136 0.6 100 4 131 0.6 100 4 137

Th. MFL1 Th. MFL2 at Proposed algorithm


0.9 88 1 170 0.9 96 1 246 0.01 99 0.7 169

0.8 97 2 162 0.8 99 2 207 0.03 100 0.8 1600.7 99 3 148 0.5 100 4 191 0.05 100 0.8 156

0.6 100 4 147 0.4 100 6 175 0.07 100 0.8 147

Algorithm Threshold value DR (%) FAR (%) MTTD (s)

(b) Testing dataset

Proposed algorithm docc U11 ffiffiffiap t r0;occrspeU

1ffiffiffiffiat

p r0;spe99 1 150

California algorithm dCal1 1; dCal2 0:45; dCal3 0; 07 73 2 270Minnesota algorithm dMinn1 0:15; dMinn2 0:17 80 1 223WRBF Th. = 0.9 93 1 155

WMFL1 Th. = 0.9 92 1 161

WMFL2 Th. = 0.9 95 1 158

MFL1 Th. = 0.9 88 1 170

MFL2 Th. = 0.9 92 1 242a Th.: Threshold value.

Table 5

Detailed performance of the proposed algorithm.

at LV

docc dspe MB HB


0.01 U11 ffiffiffiap t r0;occ U1ffiffiffiffiat

p r0;spe 93 2 234 100 2 1640.03 100 2 246 100 2 164

0.05 100 2 234 100 2 154

0.07 100 2 220 100 2 154

at MV

docc dspe LB MB HB


0.01 U11 ffiffiffiap t r0;occ U1ffiffiffiffiat

p r0;spe 100 0 268 100 0 128 100 0 1080.03 100 0 236 100 0 128 100 1 108

0.05 100 1 226 100 0 128 100 1 108

0.07 100 1 190 100 0 120 100 1 108

at HV Average

docc dspe LB MB


0.01 U11 ffiffiffiap

t r0;occ U1

ffiffiffiffiat

p r0;spe 100 0 108 100 0 176 99 0.7 1690.03 100 0 158 100 0 84 100 0.8 1600.05 100 0 156 100 0 84 100 0.8 156

0.07 100 0 156 100 0 84 100 0.8 147



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Table 4 presents the results of performance comparison of different incident detection algorithms for training and testing

data sets. In Table 4, dCal1 , dCal2 , and d

Cal3 represent the threshold values in California algorithm and d

Minn1 ; d

Minn2 present the

threshold values in Minnesota algorithm. In addition, varying threshold values in the proposed algorithm were described

by docc and dspe. Table 4 shows the best performance each algorithm can achieve for a given level of FAR. For the purpose

of fair comparisons, we fixed the threshold values to those that yielded the best performance for the training dataset and

these threshold values were used to obtain the performance for testing data set. In Table 4, we emphasize the comparison

parts with bold fonts.In this experiment, threshold values were selected to achieve a FAR of 1% for training performance. As shown in Table 4b,

the proposed AID algorithm clearly outperformed others with a 99% DR, 1% FAR, and 150 s. MTTD for the testing data set.

Within the WMLF family, WRBF showed good performance compared to other neutral networks, especially faster MTTD than

other algorithms. In addition, WMLF2 yielded a higher DR than WMLF1, arguably because WMLF2 employed more traffic

information than WMLF1 did.

To further explore the effectiveness of the proposed algorithm, its performance under each simulated scenario is tabu-

lated in Table 5. It is evident, and not surprisingly, that higher traffic volume results in high DRs and low FARs irrespective

of the number of lanes blocked because any incident that occurs during high traffic volume causes obvious incident pattern

in the denoised traffic data. In this Table, we highlight the best average performance with 1% FAR.

Overall, the proposed wavelet-based AID algorithm consistently yielded the best DR, lowest FAR, and shortest MTTD. In

addition, of the four remaining algorithms, the WRBF algorithms yielded higher DR and fast MTTB than those from other

neutral network algorithms. This is indicative of the effectiveness of wavelet-based algorithms in filtering out traffic data

noises for incident detection purposes. At this point, the proposed algorithm seems very promising and is ready to be testedwith real-world incident cases.

5. Case study with real-world data: development of a new incident database

5.1. Real-world dataset description

One of the major challenges of AID research has been the scarcity of incident field data. Therefore, even some very recent

studies have been based solely on simulations (Crabtree and Stamatiadis, 2007; Cheu et al., 2002). The main reason for this is

the difficulty in obtaining accurate incident information that is precise and complete enough for AID research purposes; ba-

sic information such as incident start time and location are often not precisely, and occasionally erroneously, reported on

incident record systems such as those maintained by freeway patrols and incident management programs. The inaccuracy

and imprecision of such reports is often inherent to the data collection process; for instance, the recorded start time of an

incident usually comes from the perception of those involved in the incident, or merely from a rough estimate or guess fromthe officer filing the crash report. Even in the fortuitous case of someone actually observing a crash scene as it unfolded be-

fore him, the time he read from his watch and later reported very likely may not be in sync with the real-time traffic data

being collected at a traffic management center (TMC) elsewhere. This difference between the unsynchronized watch of a for-

tuitous witness and the computer clock at TMC, may it be a couple of minutes or even more, would embed an undesirable

time shift in the incident data.

This problem has kept researchers from computing, and, hence, optimizing the MTTD of their respective AID algorithms

correctly (Teng et al., 1999). Besides, it is known that a portion of incidents is never reported, according to Roess et al. (2004).

It is estimated that approximately only 50% of all traffic incidents are recorded on any type of incident log. This casts a sha-

dow on some so-called normal traffic data as they might not be really incident-free and are, therefore, unsuitable for algo-

rithm training purposes.

In light of these data quality challenges and the importance of evaluating and validating AID algorithms, some efforts

have been made towards the creation of incident data sets that are accurate enough for research purposes. These include

Browne et al. (2005), Mak and Fan (2006b), and Roy and Abdulhai (2003). For instance, a relatively well-known databasecontaining information of traffic and incident on a section of interstate I-880 was developed to investigate the effectiveness

of the Freeway Patrol Service (FPS) program in California (Petty et al., 1996; Skabardonis et al., 1997). A similar incident data

collection work was performed on freeway I-10 in Los Angeles area (Skabardonis et al., 1999). Since its creation, the I-880

incident database has been used in several studies including those of Jin et al. (2002), Yuan and Cheu (2003), and Srinivasan

et al. (2005).

As a part of the effort presented in this paper, we decided to create and use a new incident dataset, instead of using any

existing incident database, for two main reasons. First, the Freeway Performance Measurement System (PeMS) (http://

www.pems.eecs.berkeley.edu) has made their 30-s loop detector data available to the public. The richness of spatio

temporal traffic information provided by PeMS, along with the incident record of the California Highway Patrol, also

available though PeMS, has made it possible to construct a database that contains accurate incident information for the pur-

poses of this study. Second, the new incident dataset resultant from our research adds to the resource of the field of AID

study.

For this study, the northbound facility of Interstate 880, or I-880N, was selected as the test bed because this section offreeway was studied before and was deemed to have one of the highest crash frequencies in the San Francisco Bay Area, Cal-

ifornia (Skabardonis et al., 1997). In addition, as incident research on I-880 was developed in the 1990s, the creation of a new



16/20


dataset on the same interstate could foster comparative studies related to safety, e.g. incident frequency, by comparing

safety information from the database developed in the past and the one developed herein. For this research, 30-s and 5-

min lane-by-lane loop detector data were collected for all of the 79 vehicle detector stations (VDS) along I-880N from

Sep/01/2006 to Nov/15/2006.

The researchers studied the California Highway Patrol (CHP) incident log and scrutinized the corresponding PeMS traffic

data for the VDS pair just upstream and downstream of each incident site. The start time of an incident was defined to be one

interval before the traffic disturbance started, an approach similar to those implemented by Mak and Fan (2006a). This wasdone by a thorough visual inspection of the 30-s time series of flow and occupancy data for both up and downstream VDS

sites.

5.2. Evaluation results

A total of 40 real-world incident data sets were collected along I-880N for the training and testing of the AID algorithms.

In order to provide an idea of the severity of the collected incidents, Fig. 9 shows the histogram of the number o lanes

blocked according to the CHP reports. It is important to note that number of lanes blocked equal to zero means that the

0 1 2 3 40

2

4

6

8

10

12

14

Number of lanes blocked

Numberofincidents

Lane Blockage - CHP reports

Fig. 9. Histogram of reported number of lanes blocked by the incident. I-880 is for the most part a 4-lane freeway.

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

140

160

180

200

Incident #

Duration(minutes)

Incident Duration - CHP reports

Fig. 10. Reported duration of the incidents (min).



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Table 6

Training and testing performance of real-life dataset.

(a) Training dataset subset dCal1 dCal2 d

Cal3

California algorithm dMinn1 dMinn2

Minnesota algorithm*


1 1 0.83 0.05 50 0 166 0.33 0.85 77 0 98

1 0.65 0.05 87 1 130 0.38 0.59 90 1 92

1 0.59 0.05 93 2 120 0.25 0.49 97 2 882 1 0.61 0.31 63 0 153 0.22 0.82 73 0 95

1 0.43 0.21 90 1 123 0.22 0.57 90 1 93

1 0.43 0.15 97 2 120 0.22 0.34 97 2 90

3 1 0.83 0.05 53 0 113 0.33 0.85 67 0 86

1 0.63 0.17 87 1 125 0.31 0.56 87 1 92

1 0.55 0.15 93 2 119 0.41 0.40 97 2 94

4 1 0.83 0.05 60 0 188 0.33 0.85 73 0 102

1 0.69 0.21 83 1 154 0.22 0.56 90 1 102

1 0.59 0.11 93 2 119 0.22 0.41 97 2 95

Subset Th. MFL1 Th. MFL2


1 0.09 63 1 241 0.09 50 1 196

0.08 90 2 236 0.08 80 2 207

0.07 97 3 203 0.07 97 3 1962 0.09 57 1 213 0.09 73 1 268

0.08 93 2 208 0.08 93 2 240

0.07 97 3 181 0.07 97 3 174

3 0.09 57 1 254 0.09 70 1 224

0.08 67 2 204 0.08 83 2 212

0.07 93 3 184 0.07 93 3 194

4 0.09 87 1 236 0.09 73 1 268

0.08 93 2 210 0.08 90 2 222

0.07 97 3 182 0.07 93 3 156

Subset Th. WMFL1 Th. WMFL2


1 0.09 63 1 297 0.09 67 1 261

0.08 93 2 161 0.08 93 2 111

0.07 97 3 143 0.07 97 3 106

2 0.09 90 1 178 0.09 77 1 150

0.08 93 2 145 0.08 93 2 113

0.07 97 3 137 0.07 97 3 96

3 0.09 67 1 188 0.09 70 1 211

0.08 87 2 173 0.08 93 2 174

0.07 93 3 155 0.07 97 3 125

4 0.09 77 1 193 0.09 83 1 188

0.08 90 2 157 0.08 93 2 152

0.07 97 3 138 0.07 97 3 137

Subset Th. WRBF at docc dspe Proposed algorithm


1 0.09 70 1 137 0.01 U11 ffiffiffiap t r0;occ U

11 ffiffiffiap t r0;spe 97 1 73

0.08 93 2 98 0.03 97 2 66

2 0.09 87 1 91 0.01 97 0 880.08 93 2 87 0.03 100 1 80

3 0.09 70 1 110 0.01 93 1 77

0.08 93 2 107 0.03 97 2 65

4 0.09 87 1 109 0.01 97 1 88

0.08 93 2 98 0.03 97 2 76

(b) Testing dataset subset dCal1 dCal2 d

Cal3

California algorithm

DR (%) FAR (%) MTTD (s)

1 1 0.65 0.05 90 1 165

2 1 0.43 0.21 90 8 113

3 1 0.63 0.17 90 0 193

4 1 0.69 0.21 50 0 132

Average 80 2 150



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report only mentions that the vehicles involved were on the right shoulder or on the center divider. Therefore, the incident

might have blocked the traffic before the arrival of the CHP officers. Fig. 10 provides a plot of the reported duration of the

incidents. The missing points on that plot mean that no information regarding the incident duration was reported.

Because of the limited number of incident cases, a fourfold cross-validation (CV) procedure was implemented for the

comparison of testing performance of different algorithms. In other words, a total of 40 incident cases were divided into four

subsets where each subset consists of 10 incident cases. For each experiment, three of the subsets were used for training and

the remaining one was used for testing. All incident cases in the dataset were eventually used for both training and testing

purposes.

Table 6 tabulates the training and testing performance of five AID algorithms for average and for each fold of the fourfoldCV. For easy comparisons, we highlight the average performances of each algorithm with bold fonts. Once again, it is evident

that the proposed algorithm, showing high DR, low FAR, and fast MTTD, outperformed all the others. For instance, the pro-

Subset dMinn1 dMinn2

Minnesota algorithm


1 0.38 0.59 80 0 150

2 0.22 0.57 80 4 109

3 0.31 0.56 100 1 144

4 0.22 0.56 90 2 100Average 88 2 125

Subset Thresholds DR (%) FAR (%) MTTD (s)

MFL1

1 0.9 100 1 205

2 0.9 80 3 234

3 0.9 90 2 270

4 0.9 80 2 206

Average 88 2 228

MFL2

1 0.9 100 1 263

2 0.9 80 3 200

3 0.9 90 2 2254 0.9 70 2 173

Average 85 2 215

WMFL1

1 0.9 100 1 195

2 0.9 90 3 108

3 0.9 90 2 156

4 0.9 100 2 236

Average 95 2 173

WMFL2

1 0.9 90 1 243

2 0.9 90 2 172

3 0.9 100 2 210

4 0.9 90 2 128

Average 93 2 188

WRBF

1 0.9 100 2 162

2 0.9 90 2 72

3 0.9 90 1 123

4 0.9 100 2 81

Average 95 2 110

Subset docc dspe Proposed algorithm


1 U11 ffiffiffiap t r0;occ U11 ffiffiffiap t r0;spe 100 1 102

2 90 3 67

3 100 0 994 90 0 65

Average 95 1 83

Table 6 (continued)



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posed algorithm presents on an average 95% DR, 1% FAR, and 83 s. MTTD, which is the best performance among the five AID

algorithms. Particularly noteworthy is in the MTTD department where the proposed algorithm is the fastest to correctly de-

tect the incidents. Similar to the results when simulated incident scenarios were used, WREF algorithm yielded higher DR

and faster MTTD than other neural networks family. Also, WMFL algorithms showed good performance in comparison to

those of MFL algorithms.

Overall, the proposed algorithm yielded high DR, low FAR, and fast MTTD in comparison with other well established or

neural-net based algorithms for both simulated and real-world scenarios. It is clear that the proposed algorithm is a superioralternative for freeway incident detection applications.

6. Conclusions

This paper proposed a novel wavelet-based freeway automated incident detection algorithm, which utilizes both occu-

pancy and speed data. In addition, this research recognized the importance of developed varying threshold values as a func-

tion of traffic flow rate. The algorithm was implemented and tested with simulated and real-world incident data sets, which

were newly created via VISSIM simulation and data collection on I-880N.

Results of the comparative evaluation effort indicates that overall, wavelet-based algorithm with adaptive thresholding

parameters yielded better performance, in most of cases, with higher DR, lower FAR, and faster MTTD. Particularly, since the

threshold values can be adaptively changed depending on the traffic levels, the proposed algorithm could achieve high DR

while keeping its FAR low. As further study, we will integrate spatiotemporal data to further enhance the proposed algo-

rithm. Also, an extension of this research may employ varying weights for each observation of traffic data so that more recent

observations would feature more prominently in the incident detection algorithm.

Acknowledgment

This work was partially supported by the National Science Foundation (NSF) Grant Number CMMI-0644830 as well as by

the Federal Highway Administrations Dwight D. Eisenhower Graduate Transportation Fellowship.

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