Computer-Aided Civil and Infrastructure Engineering 28 (2013) 594–603

Freeway Travel Time Prediction UsingTakagi–Sugeno–Kang Fuzzy Neural Network

Yunlong Zhang* & Hancheng Ge

Zachry Department of Civil Engineering, Texas A&M University, TX, USA

Abstract: This article presents a Takagi–Sugeno–KangFuzzy Neural Network (TSKFNN) approach to predictfreeway corridor travel time with an online computing al-gorithm. TSKFNN, a combination of a Takagi–Sugeno–Kang (TSK) type fuzzy logic system and a neural net-work, produces strong prediction performance becauseof its high accuracy and quick convergence. Real worlddata collected from US-290 in Houston, Texas are usedto train and validate the network. The prediction perfor-mance of the TSKFNN is investigated with different com-binations of traffic count, occupancy, and speed as in-put options. The comparison between online TSKFNN,offline TSKFNN, the back propagation neural network(BPNN) and the time series model (ARIMA) is made toevaluate the performance of TSKFNN. The results showthat using count, speed, and occupancy together as in-put produces the best TSKFNN predictions. The onlineTSKFNN outperforms other commonly used models andis a promising tool for reliable travel time prediction ona freeway corridor.

1 INTRODUCTION

With an increasing need of accurate and reliable real-time traffic information for Intelligent TransportationSystems (ITS), travel time as an important traffic vari-able has become increasingly crucial to traffic anal-ysis and operations. For instance, as the input tothe Dynamic Route Guidance System (DRGS), traveltime information can be used to produce the shortestpath between an origin and a destination. Due to theheterogeneity of different circumstances and nonlin-ear interactions between drivers and traffic facilities,the prediction of traffic condition in the near futureis playing a more and more important role in manyITS applications such as Advanced Traveler Informa-

*To whom correspondence should be addressed. E-mail:yzhang@civil.tamu.edu.

tion Systems (ATIS), Advanced Traffic ManagementSystems (ATMS), and Emergency Management Sys-tems (EMS). As travel time is one of the most impor-tant measures of the traffic system and it is also criti-cal to system users, its prediction has both theoreticaland practical significance (Chen et al., 1999). In this arti-cle we present a freeway corridor travel time predictionmodel using Takagi–Sugeno–Kang Fuzzy Neural Net-work (TSKFNN) (Takagi and Sugeno, 1985) that notonly has the capabilities of neural networks but alsotakes into account the human-like thinking and reason-ing of fuzzy logic systems.

2 PREVIOUS STUDIES

There have been many methods used to predict traveltime. Earlier methods include time series models (Oda,1990; Al-Deek et al., 1998; Anderson, 1994), machinelearning methods (You and Kim, 2000), and regres-sion models (Zhang et al., 2003; Wu et al., 2004; Liet al., 2008). In recent years, the applications of artifi-cial intelligence, especially the techniques of neural net-works, have garnered much attention and have beenconsidered as effective tools for travel time predictions(Dharia and Adeli, 2003; Steven et al., 2002; Hoogen-doorn et al., 2005; Park and Rilett, 1998; Rilett and Park,1999; Park and Rilett, 1999; Van Lint, 2006; Krikke,2002; Chien et al., 2002).

A hybrid model combining the use of the empiricalmode decomposition (EMD) and a multilayer feed for-ward neural network with back propagation was devel-oped for travel time prediction (Hamad et al., 2009).The key part of EMD in this study is the Hilbert–Huang transform to address highly nonlinear and non-stationary speed series. The prediction performance ofthis proposed method was found to be superior to previ-ous forecasting techniques based on loop data from I-66in Virginia. A model (Yeon et al., 2008) was conducted

C© 2013 Computer-Aided Civil and Infrastructure Engineering.DOI: 10.1111/mice.12014

Freeway travel time prediction using TSKFNN 595

to predict travel time using Discrete Time MarkovChains (DTMC). The model demonstrated that pre-dicted travel time using DTMC does not differ fromthe measured travel time at the 99% confidence level.It was concluded that DTMC had a good ability topredict travel time in both uncongested and congestedconditions.

Even though most of the studies on travel time pre-diction were on freeway segments, travel time charac-teristics on signalized networks were studied based onloop and probe data (Bhaskar et al., 2011). Moreover,traffic performance including travel time was exploredby the fusion of different data sources (Heilmann et al.,2011). Neural network based models were often used intravel time predictions on signalized arterials (Liu et al.,2009; Singh and Abu-Lebdeh, 2007).

Generally neural networks have played an impor-tant role in the prediction of travel time due to theirstrong ability of nonlinear approximation. However,neural networks are difficult to design and implementbecause the opaqueness of the trained networks can-not be easily understood. Importantly, neural networksrequire a long training time and the values of param-eters such as initial weights and training rate can sig-nificantly affect the performance. Another drawback ofneural networks is that the local minima are very dif-ficult to be avoided because neural networks use thegradient descent method, a technique that is very sen-sitive to the initial weights to obtain optimized weights.Besides these, neural networks also have difficulties ap-proximating human reasoning capabilities to human-like thinking. A fuzzy system, which can model humanexpertise, is potentially an effective tool to predict thetravel time, as it has a systematic calculus to deal withsuch information linguistically. Because of this, fuzzyrepresentation and fuzzy systems are applied in manyrecent studies in civil engineering (Hsiao et al., 2012;Bianchini, 2012; Tagherouit et al., 2011). However, theinadaptability to deal with changing external environ-ment and the difficulty to model the complex system arethe main drawbacks of fuzzy system. Moreover, the de-sign of fuzzy rules and membership functions is mainlybased on the experts’ experience without numerical cri-teria. Therefore, there is a need to create a more effi-cient tool combining the capabilities of neural networksand fuzzy systems in many fields. In this case, the fuzzyneural network (FNN), which can automatically gen-erate a set of expert rules to model the problem andsubsequently use the rules independently, arouses re-searchers’ interest. The advantages of the FNN includeadaptability, parallelism, robustness, ruggedness, opti-mality, and the ability to solve system uncertainty withthe fuzzy set theory. The FNN is also adept at over-coming the local minima and fast converging (Jang andRoger, 1993).

FNN models have been applied to several areas oftransportation engineering in recent years. The appli-cation areas included incident detection (Samant andAdeli, 2001; Karim and Adeli, 2002), work zone ca-pacity estimation (Adeli and Jiang, 2003), and signalcontrol (Srinivasan et al., 2006). However, there havenot been many FNN applications in freeway travel timeprediction.

Prasad et al. (1999) studied travel time predictionwith the fuzzy logic and neural networks based on theloop detector data. They used fuzzy logic to convertdetector data to travel time and classified the detec-tor data. The neural network predicted the travel timebased on the clustering of the data. The fuzzy logic andneural network produced improved estimates of traveltime when compared with results from the linear regres-sion model. However, they did not use a true sense ofFNNs to predict travel time. It is considered to be a reg-ular neural network, and fuzzy logic is used to prepareinputs to the neural network.

In this study, TSKFNN was developed to predict thefreeway corridor travel time with an online computingalgorithm. TSKFNN simultaneously adjusts parametersof membership functions in the fuzzy logic part basedupon feedback from neural networks. In all, all param-eters of fuzzy logic and neural network will be updatedsimultaneously and interactively in the training process.The relationships between traffic variables and the pre-diction performance were investigated. Volume, speed,and occupancy were considered as input options andground-truth travel times were used in evaluation.

3 METHODOLOGY

3.1 TSKFNN model

TSKFNN embeds a TSK type fuzzy inference system ina general structure of a neural network using a neuralnetwork training method to find parameters of the fuzzyinference system. The TSKFNN is one of the most fre-quently used FNN schemes developed due to its pow-erful representation and prediction. Moreover, as theTSK model has an explicit analytical output, it is pos-sible to incorporate mathematical knowledge into thereal-time control and easily combine it with optimiza-tion and adaptive theories.

The general structure of TSKFNN is given inFigure 1 with multi-input and single output. TSKFNNconsists of two parts: one is antecedent network (AN)and the other is consequent network (CN). The func-tions of AN are to cluster the input space and to matchthe antecedent of fuzzy rules. Different kinds of specifictravel variable patterns are denoted by clusters. Thefunction of the CN is to generate the consequence offuzzy rules. The input of the model is the sampled traffic

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Fig. 1. The structure of fuzzy neural network.

variables data including volume, speed, and occupancyat time k–1, and the output of the model is the predictedtravel time of the same corridor at time k. The detailswith respect to the structure of Figure 1 are stated inthe following sections.

3.2 Antecedent network

AN, simulating the antecedent fuzzy rules, is the mainpart of a fuzzy system. The core of AN is a set ofIF- THEN rules with fuzzy implications, as well as themembership function, a generalization of the indica-tor function in classical sets. The membership func-tion μA(x) expresses the degree that x belongs to fuzzyset A. Therefore, the fuzzy set can be defined as A ={(x, μA(x))|x ∈ X} where X is a collection of objectives.The general rule of TSK fuzzy inference is as following:

Input: x = [x1, x2, . . . , xn]T where T is denoted as thetranspose of a matrix

(1)

Output: y (2)

Rule: if X1 is A1 AND X2 is A2 . . . AND Xn is An,

then y = p0 +n∑1

pi xi

(3)

A1, A2, . . . , and An denote the antecedent fuzzyrules expressed by natural language. y is the output ofthe system, expressed by a linear function. The numberof An is determined by the number of clusters in themembership function.

In this study a TSK type fuzzy system is embeddedinto the structure of a neural network, which consistsof four layers as shown in Figure 1. The first layer, theinput layer, is used to connect each component of theinput vectors for transmitting the input to the next layerdirectly, and the number of the node of the first layeris the same as the number of the input. In the secondlayer, each node represents a value of the linguistic vari-able, which is used to calculate the membership func-tion μ

ji (x) to which each component of the input vec-

tors belongs. After testing three types of membershipfunctions such as Triangular function, Gaussian func-tion, and Trapezoidal function, the following Gaussianfunction is adopted as the general membership func-tion in this article due to reported good performance(Kreinovich et al., 1992).

μji (x) = e

− (xi −cij)2

σ2ij (4)

where i = 1, 2, . . . , n, j = 1, 2, . . . , mi . n is the dimen-sion of the input. mi is the number of the clustering dataxi . The parameters of cij and σij denote the center andthe width of the membership function, respectively. Theinput can be directly transformed into linguistic infor-mation (fuzzification) by using the Equation (1). In thethird layer, each node represents a fuzzy rule to matchthe antecedent of fuzzy rules and calculate the member-ship grade of the rules α j .

α j = min{μ

i11 , μ

i22 , . . . , μin

n

}(5)

where i1 ∈ {1, 2, . . . , m1}, i2 ∈ {1, 2, . . . , m2}, . . . , in ∈{1, 2, . . . , mn}, j = 1, 2, . . . m, m = ∏n

i=1 mi . The num-ber of nodes in the third layer is the same as the num-ber of fuzzy rules. The fourth layer is for normalization,which has the same number of nodes as that of the thirdlayer.

α j = α jm∑

i=1

αi

(6)

It should be noticed that the initial weights of cij andσij were determined by Fuzzy Subtractive Clustering(FSC), which generates rules by enumerating all possi-ble combinations of membership functions of all inputs.FSC considers each data point as a potential cluster cen-ter and calculates the likelihood of being a cluster cen-ter based on the density of surrounding data points. Thedata point selected as a cluster center has the highest

Freeway travel time prediction using TSKFNN 597

density in a certain area. Meanwhile, data points aroundthis potential cluster center point are excluded as a po-tential center. For the data points {q1, q2, . . . , qn}, thedensity for each data point qi is defined as:

Di =n∑

j=1

e

(− qi −q2

j

(ra /2)2

)(7)

where ra is a positive constant which represents a neigh-borhood. It is obvious that the data point surroundedby more data points in the area of the radius ra wouldhave the higher density value Di . After calculating thedensity of each data point, the data point with the high-est density Dc1 is selected to be the first cluster centerdenoted by qc1. Then, the density DNew

i is recalculatedfor all other data points excluding qc1 according to therevised formula:

DNewi = Di − Dc1e

(− qi −q2

c1(rb/2)2

)(8)

Thus, the influence of the data points near the firstcluster center will be significantly reduced because thesepoints are excluded in the further calculation after thefirst cluster center is picked up. This process statedabove repeats until an adequate number of cluster cen-ters is generated. In this study, the input data of volume,speed, and occupancy are initially categorized by FSC.

When completing the subtractive clustering, each ofthe cluster centers and radii can generate initial mem-bership functions in the fuzzy inference system. The ini-tial weights of cij and σij were determined using the fol-lowing equations (Chiu 1994):

cij = xij (9)

σij = rij ∗ (qi j−max − qi j−min)√8

(10)

where xij is the center of the cluster j of the input qi ,rij is the radius for the cluster j of the input qi in thecalculation of subtractive clustering, qi j−max and qi j−min

are the maximum and minimum values in the cluster jof the input qi , respectively. However, a large numberof inputs would result in a huge number of IF-THENrules.

3.3 Consequent network

The CN is used to generate the consequence of fuzzyrules embedded in the structure of the neural network,which consists of three layers. The first layer is used totransmit the input vectors to the next layer. In the sec-ond layer, m nodes represent fuzzy rules and are used to

calculate the consequence of each fuzzy rule. The sub-net of CN for the cluster c is shown in Figure 1.

yc =∑i∈I

wci qi (k − 1) (11)

The third layer is used to calculate the output ofTSKFNN, the weighted sum of the consequence offuzzy rules. The predicted travel time at time intervalk is:

T (k) =∑c∈C

αc yc (12)

The weight is the output of AN stated previously,which is the normalized degree of membership.

3.4 Algorithm of learning process

The learning algorithm is developed and adjusted basedon the back-propagation algorithm of the BP neuralnetwork because TSKFNN is essentially a feed-forwardnetwork. Only the connection weight of CN wci , thecenter cij and the width σij of the membership functionneed to be adjusted. All parameters would be calibratedat the same time during the process of the optimization.The output of the network is

T (k) =∑c∈C

αc yc =∑c∈C

αc

∑i∈I

wci qi (k − 1) (13)

Minimizing the square of error represented by (11)determines all parameters.

E = 12

(Tk − T (k))2 (14)

where T (k) is the actual output and Tk is the observedvalue. The derivation of the square of error is given asfollowing:

∂ E

∂wci= ∂ E

∂T (k)∂T (k)

∂yc

∂yc

∂wci

= (T (k) − Tk) αcqi (k − 1)

(15)

Then, the updated parameter wci can be calculated by

wci (k + 1) = wci (k) − β∂ E

∂wci

= wci (k) + β (Tk − T (k)) αcqi (k − 1)(16)

where c is the number of cluster, i is the number of di-mension of the input, and β is the training rate. Aftercomputing the predicted corridor travel time T (k), theconnection weights of CN should be updated based onthe Equation (13) above.

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3.5 Online computing algorithm for travel timeprediction

Online adaptive freeway corridor travel time predictiondemands a faster convergent speed. The online com-puting process consists of four steps: data input, on-line training, input data updating, and corridor traveltime prediction. The first step inputs data in previousn intervals, including sampled traffic variables denotedby qi (t), t = k − n − 1, . . . , k − 2 and the corridor traveltimes denoted by Tt , t = k − n, . . . , k − 1. The secondstep trains the coefficients of TSKFNN including theconnection weights and parameters of the membershipfunction after inputting the data into the TSKFNN. Inthe third step, the data set is updated by collecting thenew traffic and travel time data at time k, and then shift-ing the input data by one interval. The traffic variablesand corridor travel time data are then passed back to thefirst step to update the coefficients of the system. The fi-nal step calculates the predicted value of corridor traveltime using the updated input data of the traffic vari-ables. This online computing process is shown in Figure2. Contrarily, without the iterative updating process, thetraining process is considered offline. In offline training,all training data items are used whereas online trainingonly uses the data from the most recent n intervals.

4 DATA DESCRIPTION

The actual data were collected on a freeway segmentlocated on US-290, in an urban area northwest of Hous-ton, Texas shown in Figure 3. This corridor is on oneof the busiest commuting routes that connect the down-town commercial districts and suburb an residential ar-eas. The study corridor, the section from node 31 tonode 32, is a 2.9-mile section. There are five Auto-mated Vehicle Identification (AVI) stations denoted as3997, 3890, 4026, 4010, and 4003 in this section. Speed,volume, and occupancy data were collected with mi-crowave detectors, and travel time data were from AVIstations, all obtained from the Houston TranStar trans-portation management center. TranStar operates 24/7and has been archiving AVI travel time and speed datasince October 1993. The data collected by recording ve-hicle toll tag IDs and the corresponding time stampswhen each time vehicles are passing the AVI stationsare used to determine the travel time for each vehicletraveling on AVI segment (32–31), as shown in Figure 3.

The data reduction and fusion is a necessary step inselecting a study period, aggregating data, filtering outfalse data entries, and interpolating missing data. Even-tually, data from three Fridays, February 1st, 8th, and29th in 2008, were reduced, and chosen as the base-

Fig. 2. The online computing process.

Fig. 3. The study corridor on US-290.

line data set to predict and validate TSKFNN. Fridayswere chosen because the travel time variations are typi-cally the largest, making it most difficult for prediction.The data of volume, speed, and occupancy were aggre-gated into 5-minute intervals. Within each 5 minutes,

Freeway travel time prediction using TSKFNN 599

the ground-truth travel time was determined by averag-ing all collected travel times for all vehicles passing theAVI stations between 31 and 32. The data on Febru-ary 1st and 8th were used to train TSKFNN, whereasthe data on February 29th were used to validate andtest TSKFNN. The ranges of all variables are from 49to 445 vehicles for 5-minute count, from 14 to 72 mphfor speed, from 0.5 to 22.7% for occupancy, and from133 to 839 seconds for travel time.

5 PERFORMANCE MEASURE

The root mean square error (RMSE) between the pre-dicted and observed values of the travel time is usedto assess the performance of the TSKFNN model. TheRMSE is calculated according to Equation (17):

RMSE =√√√√ 1

N

N∑k=1

(Tk − T (k))2 (17)

where N is the number of time intervals, Tk is the ob-served travel time for interval k, and T (k) is the pre-dicted travel time for interval k.

6 PRELIMINARY DATA ANALYSIS

The correlation analysis, as a preliminary analysis, wasused to identify the relationship among the collectedtraffic data, and examine the reliability of the data tosee whether the variables have expected relationships.In particular, the Pearson correlation shown in Equa-tion (18) was adopted to analyze the relationship be-tween traffic variables. The purpose of this analysis is tochoose proper traffic variables as the input of TSKFNN.

rxy =n

xi∑yi −

xi∑ yi∑√

nxi∑

2 −( xi∑ )

2

√√√√ny∑i2

−( yi∑)2

(18)

Here, rxy is the correlation coefficient, xi , yi are col-lected data points of two traffic variables, and n is thenumber of observations. The result of correlation anal-ysis is summarized in Table 1.

Based on Table 1, the correlation value between oc-cupancy and volume is 0.73, the value between oc-cupancy and speed is –0.95, and the value betweenspeed and volume is –0.54. Speed and occupancy hada higher correlation with travel time than volume, natu-rally speed and occupancy should be considered as theinput. Volume as a variable could be left out of the fur-

Table 1Correlation analysis between traffic variables

Volume Speed Occupancy Travel time

Volume 1 − 0.54 0.73 0.44Speed − 0.54 1 − 0.95 − 0.93Occupancy 0.73 − 0.95 1 0.91

Table 2RMSE (seconds) for training and testing TSKFNN with

different inputs

Input 1 Input 2 Input 3

Training 16.2 15.4 14.6Testing 32.4 28.4 25.1

ther analysis because of the low correlation with traveltime, however, because it is correlated with occupancy,it can still be considered as one input item for travel timeprediction.

7 RESULTS AND ANALYSIS

Three different input options (Input 1: Volume and Oc-cupancy, Input 2: Speed and Occupancy, and Input 3:Volume, Occupancy, and Speed) were used to evaluatethe performance of TSKFNN with the online comput-ing algorithm to predict corridor travel time. AVI traveltime data are used as ground truth for training andtesting.

It was found that the TSKFNN fit the training datavery well with a low RMSE as shown in Table 2, mean-ing that the TSKFNN can be developed to model thetraining data very well. Moreover, the training error de-creased very fast from the beginning of training thenstayed stable, indicating a very fast convergence with ashort training time. Input option 3 produced the low-est training RMSE when compared to the RMSEs ofthe other options, indicating that TSKFNN can per-form better in the training process with all three vari-ables as input items. After the TSKFNN was trained,the data set on February 29th was used for testing toevaluate TSKFNN’s ability to predict the corridor traveltime. The RMSE results for testing are also provided inTable 2. The overall RMSEs are lower than 33 seconds,indicating that the TSKFNN has a strong ability to ac-curately predict the tendency of the testing data.

The prediction results with testing data for all threeinput options are demonstrated in Figure 4. As statedpreviously, with the aggregation interval of 5 minutes,the whole day (1,440 minutes from 00:00 to 24:00)has 288 time intervals. Figure 4 shows that TSKFNN

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Fig. 4. Prediction results for different input options.

performed very well in prediction, as predictedvalues match well with the observed values for the threedifferent input options. Although the three plots do nothave significant differences, TSKFNN did not performvery well from time interval 170 to 180 and from 210 to220 for Input 1, and also performed poorly in Input 2from 180 to 210. On the contrary, the prediction withInput 3 has better performance than with the other twoinput options. This indicates that volume provided ex-tra useful information for better TSKFFN predictions,even though the correlation between volume and traveltime was not very high. This conclusion was supportedby results in both Table 2 and Figure 4.

We further extract and present the results by flowcondition in four categories: off-peak (Time 1 to 150 and251 to 288), congestion buildup (Time 150 to 200), re-covery (Time 201 to 220), and peak (Time 221 to 250).RMSEs for different corresponding periods are summa-rized in the following table. Considering the travel timesin non-off peak periods have much higher values (illus-trated in Figure 4), though elevated, these RMSE valuesare all satisfactory. In particular, with Input scenario 3,the RMSE for the peak is 40.1 seconds corresponding toan observed travel time of about 850 seconds.

Based on Tables 2 and 3, the overall RMSEs indicatethat the TSKFNN has a strong ability to accurately pre-dict the tendency of the testing data. The convergenceof the TSKFNN was also very fast. Moreover, it can befound that Input 3 has the lowest RMSE in each sce-

Table 3RMSE (seconds) of different periods for different input

patterns

Off-peak Buildup Peak Recovery

Input 1 14.31 45.89 70.87 44.46Input 2 15.74 58.38 52.36 36.55Input 3 13.82 39.17 40.13 35.06

nario, proving that TSKFNN can predict the most accu-rate results with this combination of input variables.

We also evaluated the performance of TSKFNN us-ing only the time series of travel time as input. Thetravel time T(k-2), T(k-1), and T(k) of the corridor wereused as input of the TSKFNN to predict the travel timeT(k+1). The data set was the same Friday baseline dataset. The data of February 1st and 8th were again usedfor training and the data of February 29th were usedfor testing. After training the whole network the train-ing RMSE was 15.3 seconds, which was low comparedto previous values in Table 2. Figure 5 also illustratedthat the performance of TSKFNN with the time seriesof travel time as the input seemed to look even betterthan some of the predictions in Figure 4. The RMSE of27.76 seconds is better than those from prediction withInput options 1 and 2, 28.4 and 32.4 seconds respec-tively, even though it is slightly worse than the RSMEof 25.1 seconds from Input 3. Overall, the TSKFNN

Freeway travel time prediction using TSKFNN 601

Fig. 5. Prediction results for inputs of past travel time.

prediction from the time series of past travel times canproduce good performance, however, the travel timehistory we have from the AVI data is not commonlyavailable while speed, volume, and occupancy data arecommonly available from loop detectors that are widelydeployed.

Model performance was also investigated on an ex-panded data set. This expanded data set was collectedon weekdays from February 1st to 22th, 2008. The week-days in the first two weeks are used for training, and theweekdays in the third week are employed for validat-ing the model. Count, speed, and occupancy are used asinputs, and the results are summarized below.

RMSEs from Monday to Friday are 27.5, 28.7, 38.8,33.5, and 24.1, respectively. The RMSE for Wednesdayprediction is somewhat higher than that for other days,but the travel times during the peak on that day werealso significantly larger. An investigation of a separateincident database revealed that there were several se-vere incidents during the peak period on that day. Over-all, the prediction performance was very similar to thatof the single-day prediction reported previously fromthe baseline data set. It should be noted the baselineFriday data set was selected also because it was affectedby incidents to a lesser degree.

8 COMPARISON EXPERIMENTS

The comparison of performance in corridor traveltime prediction was made among online TSKFNN, off-

line TSKFNN, the back propagation neural network(BPNN) and the time series model (ARIMA) using theFriday baseline data set. Rilett et al. (1999), Van Lintet al. (2005), and Guin (2006) indicated that Neural Net-work (NN) and ARIMA have good performance in theprediction of travel time, we wanted to compare the per-formance of the TSKFNN with the results from thesetwo commonly used approaches. Online TSKFNN andoffline TSKFNN were compared to illustrate the advan-tage of the online computing algorithm. Speed, volume,and occupancy are used as input to the TSKFNN.

The BPNN consisted of three layers with three in-put neurons and one output neuron. The sigmoid acti-vation function was used for each neuron and the backpropagation training procedure was adopted. The per-formance of BPNN in the prediction is significantly af-fected by the number of neurons in the hidden layer andthe training rate. To minimize the RMSE between thepredicted and observed results, 10 neurons in the hid-den layer and a training rate of 0.25 were found to pro-duce the best results by the BPNN. Auto Regressive In-tegrated Moving Average (ARIMA) model is generallyreferred to as ARIMA (p, d, q) where p, d and q arethe order of the autoregressive, integrated, and movingaverage parts of the model respectively. After the op-timization on parameters based on minimum resultingAIC value, ARIMA (3, 1, 5) was adopted to predict thecorridor travel time.

The numerical result on RMSEs in Figure 6 con-firmed that the two TSKFNN predictions have clearlyoutperformed BPNN and ARIMA (reduced RMSE

602 Zhang & Ge

Fig. 6. RMSEs of the comparison experiment.

by 30%). It is also obvious that online TSKFNN out-performed offline TSKFNN. The comparison stronglyindicated that the TSKFNN performed better than com-monly used BPNN and ARIMA and online comput-ing algorithm enhanced the prediction accuracy forTSKFNN.

9 CONCLUSIONS

Based on the theory of intelligent control system, aTSKFNN model was developed to predict the corridortravel time on a freeway with an online computing al-gorithm that enhances the predictive ability. With thestructure of multi-input and single output, the TSKFNNconsists of two parts: AN and CN. The functions ofAN are to cluster the input space and to match theantecedent of fuzzy rules. The function of CN is togenerate the consequence of fuzzy rules. Based on theresult of prediction based on the data collected fromUS-290 it was found that online TSKFNN can accu-rately predict future travel time in the corridor. More-over, it was demonstrated that the online TSKFNN per-formed better than a regular neural network (BPNN)and the ARIMA model in the prediction performanceas online TSKFNN is able to adaptively adjust its co-efficients with the recent training data prior to the pre-diction. TSKFNN with an online computing algorithmperformed best with volume, speed, and occupancy asthe input. This prediction performance is as good asthe TSKFNN prediction performance with past traveltime history as the input when the travel time history isavailable.

The performance of the online TSKFNN can be fur-ther improved by changing the function of membershipor by increasing the number of clusters used. Testingand validation of the online TSKFNN with other datasets should also be conducted in the future.

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