Abstract—Detection of alcohol-induced driving impairmentthrough vehicle-based sensor signals is of paramount importancefor road safety. To differentiate the driving conditions with andwithout alcohol-induced impairment, data were collected from 108drivers under both conditions in a high-fidelity driving simulator.With this data set, various quantitative measures of steering wheelmovement, including not only simple statistics such as the meanand the standard deviation but nonlinear dynamic invariant mea-sures such as sample entropy and Lyapunov exponent as well, arecompared in terms of their differentiating capabilities. Nonlinearinvariant measures are more robust and consistent than the simplemeasures in differentiating the impairment. Furthermore, peoplerespond to alcohol-induced impairment quite differently, and fora certain group of people, the alcohol-induced impairment canbe well detected using these nonlinear invariant measures. Manyinteresting insights into characterizing the effect of alcohol ondriving behavior are obtained in this paper. This paper lays afoundation for the future development of a real-time detectionmethod for alcohol-induced impairment.
A LCOHOL-induced impaired driving contributes to ap-proximately 31% of the traffic fatalities in the U.S. [1].
In recent years, about 1.5 million drivers have been arrestedfor driving under the influence of alcohol, which is more thanthe number of people arrested for other crimes such as theftor vandalism. In 2007, 22% of the 55 681 drivers involvedin fatal road accidents were found to have a blood alcoholconcentration (BAC) level of more than 0.08%, which is thelegal upper limit for BAC concentration. These statistics showthat, despite various educational and regulatory measures thatare adopted by local, state, and federal governments, alcohol-induced impaired driving crashes remain a major public healthand safety issue. Hence, alternative methods such as adoptingvehicle-based sensing technologies to detect impaired drivinghave recently attracted significant attention. A review that dis-cusses various driver condition monitoring techniques can befound in the work of Culp et al. [2]. The basic idea of driver
Manuscript received August 21, 2011; revised January 26, 2012; acceptedFebruary 6, 2012. Date of publication March 23, 2012; date of current versionAugust 28, 2012. This work was supported in part by the National ScienceFoundation under Grant CMMI-0545600 and Grant CMMI-0926084. TheAssociate Editor for this paper was Y. Liu.
The authors are with the Department of Industrial and Systems Engineering,University of Wisconsin–Madison, Madison, WI 53703 USA. The correspond-ing author for this paper is Shiyu Zhou.
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TITS.2012.2188891
condition monitoring is to first collect data through sensors thatare embedded in the vehicle, then use advanced data processingtechniques to identify characteristics of the data for differentlevels of driver impairment, and, finally, differentiate levels ofdriver impairment based on these characteristics. According tothe different types of sensor signals used, driver impairmentdetection and monitoring techniques can be classified into thefollowing three categories.
1) Signals that are directly from the driver, such as the eye-tracking measures, driver postural stability, and otherdriver physiological measures, e.g., electroencephalo-gram. Various researchers have used these signals tomonitor the driver condition and detect the driver cog-nitive distraction [3]–[6]. Advanced techniques such assupport vector machines, hidden Markov models, neuralnetworks, and fuzzy classifiers have been used to processthe driver signal for the real-time detection of impaireddriving. Because these signals are directly obtained fromdrivers, they contain rich information about the driver’sphysiological condition. However, the sensors that areused for collecting driver signals are highly sophisticatedand are not commonly found in the existing commercialvehicles.
2) Signals of vehicle motion such as the vehicle speed, lat-eral position, and time headway. Vehicle motion signalsare widely used in various collision avoidance systems[7], [8]. Recently, these signals have also been used indriver behavior modeling and monitoring. For example,Sekizawa et al. [9] have modeled human driving be-havior based on signals such as the distance betweencars on the road. Toledo et al. [10] performed a similaranalysis using signals that were related to lane changingand acceleration rate. Compared with the driver signals,the vehicle motion signals are relatively easy to collect.However, these signals include the influence of not onlythe driver condition but also the vehicle dynamics androad environment. Thus, it is quite challenging to developa generic driver condition monitoring scheme based onthese signals.
3) Signals from driver input such as the steering wheelactivity, gas/brake pedal, and other driving commandsignals. These driving signals are readily available inmodern vehicles, particularly vehicles that are equippedwith drive-by-wire systems. These signals are the directoutputs from the driver and are not contaminated by thevehicle dynamics and are thus better indicators of driverconditions compared with the vehicle motion signals.
1356 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 3, SEPTEMBER 2012
Indeed, these driving signals have been used as measuresof driver performance and impairment. In particular, theentropy of the steering wheel signals, called steering en-tropy, has been used as a measure of driver workload [11]and driver performance [12]. A concept of the spikinessindex, which is a heuristic measure of sharp changes inthe signal, is proposed by Desai et al. [14] to measure thedriver drowsiness using the driving signal.
Based on this brief review, we can see that most existingdriver condition monitoring techniques have focused on driverimpairments other than alcohol-induced impairment such asdrowsiness, fatigue, and distraction from nondriving tasks. Thiscase is particularly true for the monitoring techniques usingdriving signals. Rather limited work exists on the quantitativecharacterization of the driving signals (e.g., steering wheelangle signal) under alcohol-induced impairment. To fill thisresearch gap, we present a systematic study on the quantitativecharacterization of the steering wheel signal for the detectionof alcohol-induced driver impairment based on an empiricaldriving simulation data set, which is collected from the NationalAdvanced Driving Simulator (NADS), College of Engineering,University of Iowa, Iowa City, IA. The rationale of selectingthe steering wheel signal as the focus of this paper is due to itseasy access and its rich information content. The raw steeringwheel signal is in the form of a time series that was sampled ata regular time interval. Such a signal cannot usually be directlyused to differentiate whether the driver is impaired due to itshigh dimensionality and high level of noise content. Instead,quantitative characteristics (also called quantitative measures)that are computed from the raw signal need to be used tocondense the information content of the raw signal and identifydriver impairment. In this paper, we will answer the followingquestions: What quantitative measures of the steering wheelsignal can be used to differentiate drivers with and withoutalcohol-induced impairment, and how well can these measuresseparate impaired from unimpaired driving? We would like topoint out that, to detect the alcohol-induced impaired drivingbehavior based on driving signals, multiple processing stepsare needed. The first step is to find quantitative measures aseffective indicators for changes when the driving behavior isimpaired. In the second step, we need to study the robustnessof these quantitative measures to take into account differentdrivers and other environmental conditions. With these twosteps, in the third step, we can finally establish a detectionalgorithm using the identified quantitative measures as changeindicators. In this paper, we focused on only the first twosteps. Identifying the quantitative measures is necessary andvery useful for the future development of the final separationalgorithm.
To identify the good quantitative measures for driving be-havior differentiation, in this paper, we considered not onlythe ordinary statistics such as the mean and standard deviationof the steering wheel signal but various nonlinear dynamicinvariant measures as well. It has been verified in variousstudies that the underlying dynamics of the driver-vehicle sys-tem contains significant nonlinearity [9], [15]. The nonlineardynamic invariant measures such as the Lyapunov exponent,
correlation dimension, and sample entropy have widely beenused to characterize the time-series observations that werecollected from nonlinear dynamic systems [16]. In particular,these measures have been proven to be quite effective incharacterizing the human physiological signals [17]–[19]. Forexample, these invariant measures have been found to detectirregularities in the heart rhythm [20]. Thus, it is expected thatthese nonlinear dynamic invariant measures can describe thesignal characteristics that cannot be captured by the ordinarystatistics and can thus be a useful complement to those statisticsin differentiating driver conditions.
In this paper, various quantitative measures are computedfrom the steering wheel signal, collected from each driver witha BAC level of 0.0% and 0.1%, respectively. The BAC level0.0% indicates driving without alcohol-induced impairment,and the BAC level 0.1% indicates driving with alcohol-inducedimpairment. The value of 0.1% is selected, because in theU.S., the legal definition for driving under the influence is aBAC level of 0.08%, and the 0.10% BAC level is the high-est BAC that is practically and ethically possible to inducein a driving simulator study. Many epidemiological studieshave shown that a BAC level of 0.1% has serious safetyimplications [21].
We treat the data from the two different BAC levels as twodifferent clusters and use cluster separation indices, which areused in data mining to measure the “separation” among dataclusters [22] to evaluate how well the quantitative measures canseparate the normal driving condition and the alcohol-inducedimpairment. Intuitively, if, for a given quantitative measure, thedata clusters of the 0.0% and 0.1% BAC levels significantlydiffer, then we can claim that the given quantitative measure isgood. Furthermore, driving behavior is highly individualistic.Thus, certain quantitative measures might be better suited for acertain group of people. Following this intuition, we attemptedto cluster the drivers based on the separation indices withinsubgroups of people. We proposed a novel approach usingthe parallel genetic algorithm (PGA) to achieve this cluster-ing. Finally, the results are presented and analyzed to obtainsome interesting insights into the detection of alcohol-induceddriving impairment.
The remainder of this paper is organized as follows.Sections II and III describe the data collection method and thebasic data analysis procedure. In Section IV, we introduce thevarious quantitative measures and the various separation indicesused in the analysis. Section V describes the details of thePGA, which clusters drivers into subgroups according to theseparation of the two driving conditions. Section VI presentsthe results and the insights of the analysis. The conclusion anda discussion of future work are presented in Section VII.
II. DESCRIPTION OF THE DATA SET
The data set used for the analysis was collected from 108drivers who drove a 23-min route in a high-fidelity simulator,as shown in Fig. 1. All drivers held a valid U.S. driver’slicense, were more than 21 years old, and were moderate toheavy drinkers based on the Quality–Frequency–Variability andAlcohol Use Disorders Identification Test scales, but none was
DAS et al.: DIFFERENTIATING ALCOHOL-INDUCED DRIVING BEHAVIOR USING STEERING WHEEL SIGNALS 1357
Fig. 1. (Left) Driving simulator and (right) driving scene from inside the simulator. (Courtesy: NADS, University of Iowa.)
a problem drinker. Each participant made four visits. The firstvisit was for screening and included a practice drive in thesimulator. The practice drive involved a left-hand turn, drivingon two- and four-lane roads, and lasted approximately 10 min.The other three visits were separated by approximately oneweek. In two of these visits, the drivers were dosed withalcohol, and in the third visit, they were given a placebo sothat the drivers were not aware of when they had been dosedwith alcohol. The 108 drivers were equally distributed in agegroups 21–34, 38–51, and 55–68 years (equal number of maleand female drivers in each group).
The 23-min route included various driving scenarios (alsocalled driving events), which could broadly be classified asurban, rural, and freeway driving. The drives started with anurban segment that was composed of a two-lane roadwaythrough a city with posted speed limits of 25–45 mi/h withsignal-controlled and uncontrolled intersections. An interstatesegment that consisted of a four-lane divided expressway witha posted speed limit of 70 mi/h followed. The drivers, in aperiod in which they followed the vehicle ahead, encounteredinfrequent lane changes that associated with the need to passseveral slower moving trucks. The drives concluded with a ruralsegment that was composed of a two-lane undivided road withcurves. A portion of the rural segment was gravel. These threesegments mimicked a drive home from an urban bar to a ruralhome through an interstate.
Several precautions were taken to ensure a consistent BAClevel in the drivers in each experimental condition. All drivershave been screened when they arrived for the data collectionwith a breathalyzer. To ensure a rapid and consistent absorptionof alcohol, all participants were instructed not to eat 4 h preced-ing their visit. The Sahlgreska formula was used to calculatethe amount of alcohol that was given to each participant. Toachieve a 0.1% BAC level, the amount of alcohol consumedwas calculated to produce 0.115% BAC. The participants wereserved three equal-sized drinks to be consumed at 10-minintervals. Sixteen minutes after the third drink, the BAC levelwas measured at intervals of 2–3 min until the target BAClevel was reached. The participants began to drive after theBAC had peaked and had begun to decline, as measured bytwo declining measurements, which typically occurred 30 minafter their third drink. The participants drove for approximately23 min, and their BAC level was measured immediately after
they completed the drive. The drivers started the experimentafter the required BAC level was attained. The BAC leveldeclined through the test by an average of 0.01 BAC from thestart to the end of the drive.
Immediately following the drive, the drivers rated their alert-ness with the Stanford Sleepiness Scale, their BAC levels weremeasured, and then, they were assessed with the Standard FieldSobriety Test. Measurements of BAC were taken every 20 minafter exiting the simulator. The drivers were transported homeafter their BAC dropped below 0.03%. In the case of the 0.00%BAC condition, the participants were held for at least threemeasurements before being transported home. The participantswere not informed of their measured BACs until they completedthe third drive.
A comprehensive set of parameters, including the signalsfrom the driver (e.g., eye movement), vehicle motion signals(e.g., speed, lateral position), and driving signals (e.g., steer-ing wheel angle and gas/brake pedal), were collected fromthe simulator for each driver under different BAC levels. Asdiscussed in the Introduction, we will focus on the quantitativecharacterization of the steering wheel signal for two differentBAC levels, i.e., 0.0% and 0.1%. The graphs of a typicalsteering wheel signal for a driver while following traffic on aninterstate highway with 0.0% and 0.1% BAC levels are shownin Fig. 3(c) and (f), respectively.
III. DESCRIPTION OF THE DATA ANALYSIS PROCEDURE
The goal of this paper is to identify and evaluate quantitativemeasures of the steering wheel signal to differentiate the driverconditions with and without alcohol-induced impairment. Thisproblem can be described in mathematical terms as follows.
Let iθ1(t) and iθ2(t) denote the steering angle signal thatwas collected from the ith driver at time instant t for a certaindriving event with BAC levels of 0.0% and 0.10%, respectively.Fig. 3 illustrates a few such typical signals. Furthermore, denotefα as a function that computes a particular quantitative measurevalue for a given steering wheel signal. A typical example of fα
is the mean of the steering angle signal. As discussed in the In-troduction, the rationale of using the function fα is that the rawsteering signal is very high dimensional and is very difficult,if not impossible, to directly be used to differentiate drivingconditions. A quantitative measure or characteristic needs to
1358 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 3, SEPTEMBER 2012
Fig. 2. Separation in quantitative measures for different BAC levels.
be used instead to condense the information in the raw signal.Thus, without causing confusion, the function fα is also calleda quantitative measure or characteristic of the original signal.In this paper, various quantitative measures, including bothordinary statistics and nonlinear dynamics invariant measures,will be considered. These measures are briefly introduced inSection IV.
To compare the performance of different measures in dif-ferentiating driver conditions, a quantitative evaluation methodis needed. In this paper, we propose a performance evaluationmethod using the cluster separation indices as follows. Byusing fα, we compute the vectors A = A1, A2 . . . AN andB = B1, B2 . . . BN for all the drivers in the data set as
Ai = fα (iθ1(t))
Bi = fα (iθ2(t)) (1)
where N is the total number of drivers, and Ai and Bi are thequantitative measures of the ith driver for the 0.0% and 0.1%BAC levels, respectively. Clearly, these two vectors A and Brepresent two different clusters for the 0.0% and 0.1% BAClevels, respectively. Intuitively, a quantitative measure fα is agood measure of alcohol-induced impairment if A and B arewell separated. To illustrate this idea, assume that we obtainedthe values of A and B for three different quantitative measuresin Fig. 2. The two markers () and () represent the valuesof the quantitative measure for a driver from clusters A andB, respectively. Obviously, the separation between A and Bin Fig. 2(c) is better than in Fig. 2(a) or (b). In Fig. 2(a),the variances within clusters A and B are very large, and inFig. 2(b), the mean difference between A and B is very small.Building upon this idea, we propose to use cluster separationindices that have been used in statistical clustering to evaluateand compare various quantitative measures. Note that the datain Fig. 2 is for illustration only and is not from real experiments.In this paper, we adopted the following two typical clusterseparation indices: 1) the Fisher linear discriminant and 2) theGamma index. Section IV provides a brief introduction to thesetwo indices. Although only these two indices are presented in
this paper, we have tested many other indices, and they providevery similar results and insights.
The aforementioned procedure provides a quantitative wayof evaluating and comparing different measures. However, thedriving behavior generally differs across drivers. Thus, if weapply the aforementioned procedure to a large group of driverswith different backgrounds, then it is likely that no quantitativemeasures will separate the conditions of impairment equallywell for all drivers. Indeed, this is the case for our data set,as illustrated in Section VI. To deal with this situation and gainmore insights into the driving behavior under alcohol-inducedimpairment, we group the drivers according to the separationwithin groups. This way, we can identify which quantitativemeasures are suitable for which group of drivers and thus gaininsights into the corresponding driving behavior.
In particular, assume that N drivers will be clustered intoc groups. Let the vector G = G1, G2, . . . GN represent thisclustering, where Gi ∈ 1, 2, . . . c represents the cluster towhich the ith driver belongs. Let Aj = all Ai such that Gi =j and Bj = all Bi such that Gi = j, where i = 1, . . . , N ,j = 1, . . . , c, and Ai and Bi are defined in (1). Furthermore, letΩ(Aj ,Bj) represent the cluster separation index for Aj andBj . Clearly, a greater value of Ω(Aj ,Bj) indicates better sep-aration among Aj and Bj , and thus, the quantitative measureused is a better indicator of the impaired driver condition for thejth group of drivers. With this understanding, we can formulatean optimization problem for a given quantitative measure tofind the best clustering G such that the within-group separationΩ(Aj ,Bj) is maximized. In particular, we have
maxG
c∑j=1
njΩ(Aj ,Bj)/N (2)
where nj is the number of members in the jth cluster. Thisobjective function is essentially a weighted sum of the sepa-ration index for each group. Although easy to use, this objec-tive function sometimes leads to a singularity problem in theoptimization, particularly when the total number of drivers Nis relatively small. In such a situation, a very small number
DAS et al.: DIFFERENTIATING ALCOHOL-INDUCED DRIVING BEHAVIOR USING STEERING WHEEL SIGNALS 1359
of drivers with extremely high separation will be clusteredtogether into one group and the rest into others. Such aclustering result will not provide useful insights into the prob-lem and, thus, should be avoided. In this paper, we adjust the in-tuitive objective in (2) by introducing two thresholds λmax andλmin as
maxG
c∑j=1
nj min λmax,Ω(Ai,Bj)I (Ω(Aj ,Bj)>λmin) /N
(3)
where I(s) is an indicator function, which is equal to one whenthe statement s is true; otherwise, it is zero. The intuition behindthis objective function is that, when the separation index for agroup j is larger than a certain value (λmax), we claim thatthe separation is good enough, and thus, a bigger value ofΩ(Aj ,Bj) will not bring in more insights. Hence, to maintaingroups of a reasonable size, we ceil the value of Ω(Aj ,Bj)at λmax using the term minλmax,Ω(Aj ,Bj). Similarly,if the value of Ω(Aj ,Bj) is smaller than a certain value(λmin), then, essentially, we cannot differentiate the impaireddriving condition. Thus, we will simply neglect the value ofΩ(Aj ,Bj) by using the indicator function. By solving theoptimization problem in (3) for a given quantitative measure,we can classify the drivers in different groups and then identifyfor which group the given measure is the most sensitive andeffective.
In the previous paragraphs, we described the data analysisprocedure and the corresponding rationales. The procedure canbe summarized as in the following steps.Step 1. Compute various quantitative measures for all the
drivers under typical driving events and BAC levels of0.0% and 0.1%. The quantitative measures consideredin this paper are briefly introduced in Section IV-A.
Step 2. For each quantitative measure, compute the clusterseparation indices and compare. The two cluster sep-aration indices adopted are introduced in Section IV-B.
Step 3. For each quantitative measure, solve the optimizationproblem formulated in (3). In this paper, we propose touse the recently developed heuristic searching methodPGA to solve the optimization problem. The detaileddescription of this method is presented in Section V.
Step 4. Summarize the results obtained in steps 1–3 and ana-lyze the group composition that resulted in step 3 togain insights into the driving behavior with alcohol-induced impairment. These results and analyses arepresented in Section VI.
IV. QUANTITATIVE MEASURES AND CLUSTER
SEPARATION INDICES
A. Introduction to Various Quantitative Measures
Let X(t) be an observed signal from a generic system.In our problem, X(t) could be either iθ1(t) or iθ2(t). Weassume that X(t) is sampled at equal intervals of time τ , andthus, we have a time series of X(t) as x0, x1, . . . , xM−1,where xi = X(t0 + τ · i), t0 is the starting time instant, andM is the total number of data points. As discussed in the
previous section, the original time series is usually of veryhigh dimension and is very difficult to directly be used. Rather,we would like to use certain quantitative measures of theoriginal series to differentiate the driver conditions. Two naturalchoices of the quantitative measures are the sample mean andstandard deviation, which are given as X = (1/M)
∑M−1i=0 xi
and SX =√
(1/M)∑M−1
i=0 (xi − X)2, respectively. It is easyto understand that the standard deviation of the signal reflectsthe driving characteristics. However, it might appear that thesample mean may not depend on the driving characteristicsand, rather, only on the shape of the road. For example, for astraight freeway drive, the sample mean of the driving wheelsignal must be zero. However, a close look at the samplingscheme reveals that each xi is sampled at equal intervals oftime, and as a result, the sample mean may depend on multiplefactors such as the rate of change of steering wheel angle andthe vehicle speed. Thus, the sample mean may also reflect thedriving characteristics and is considered in our analysis. Thesample mean and standard deviation are two simple statistics,and they may not be able to extract sufficient information fromthe original signal. In this paper, we propose to also use variousnonlinear invariant measures as the quantitative measures.
There are quite a few invariant measures used in practice.To compute these measures, we first define a sample fromthe original series as zi = xi, xi+1, . . . , xi+(n−1) and i =0, . . . ,M − n. In the nonlinear dynamic analysis, the para-meters τ and n are often called the embedding lag and theembedding dimension, respectively. The embedded window zi
is the basis of calculation of most of the nonlinear invariantmeasures. Here, without getting into details of how we cancalculate the invariant measures, we discuss the basic idea ofthese measures. The formulas for calculating these measuresare shown in the Appendix for completeness. Details aboutthese measures can be found in [16]. The nonlinear invariantmeasures used here are listed as follows.
• Lyapunov exponent. The Lyapunov exponent measures theexponential divergence of nearby trajectories of orbits ofdynamic systems [24], [25]. This is a measure of how twopoints on a time series diverge along the length of theseries. In practice, the nonlinear prediction error is oftenused to estimate the Lyapunov exponent.
• Sample entropy. Sample entropy is a measure of the reg-ularity of a time series [19]. It belongs to a family ofstatistics called the approximate entropy [26].
• Correlation dimension and correlation entropy estimatedby the Gaussian kernel algorithm (GKA). Correlationdimension is the extension of the dimension of fractalobjects in nonlinear dynamic systems [27]. To deal withthe existence of noise in the data, an exponential kernelfunction is used to calculate the correlation integral [28].This algorithm is thus called the GKA.
Based on the aforementioned descriptions, we can see thatthese invariant measures tend to quantify the degree of nonlin-ear randomness of the signal. The more regular the signal is, thesmaller its invariant measures are. Therefore, these nonlinearinvariant measures indicate nonlinear dynamics in the signal, a
1360 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 3, SEPTEMBER 2012
property that is expected to be an important characteristic of thedriver–vehicle system.
B. Introduction to Cluster Separation Indices
As discussed in Section III, the performance of quantita-tive measures in identifying alcohol-induced impairment canbe evaluated by certain cluster separation indices. Here, weintroduce the following two typical cluster separation indices:1) the Fisher linear discriminant and 2) the Gamma index. Anexcellent review on various different cluster separation indicescan be found in [22]. In this paper, we have tested various otherindices as listed in [22], and the results are quite similar to thetwo indices, which are introduced as follows.
• Fisher linear discriminant. The Fisher linear discriminantis defined as follows:
J =(A − B)2
S2A + S2
B
(4)
where SA and SB are the standard deviation of the mem-bers in A and B, respectively. Intuitively, J will be largewhen the means of the two groups A and B are wellseparated, and their within-group variation is small. Thisindex is widely used in linear discriminant and clusteringanalysis [29]. An almost-perfect separation can be ob-served when J is larger than 4. Hence, in (3), we selectλmax as 4 and λmin as 0.1.
• Gamma index. The intuition behind the Gamma index isquite different from that for the Fisher linear discriminant.The Gamma index is based on the number of concordantpairs (S+) and the number of discordant pairs (S−) [22].The value of S+ is the number of occurrences that thedifference between the quantitative measures for a pairof drivers that belong to the same BAC group is lessthan the difference between the quantitative measures oftwo individuals that belong to two different BAC groups.Similarly, S− is the number of occurrences that the dif-ference between the quantitative measures for a pair ofdrivers that belong to the same BAC group is greaterthan the difference between the quantitative measures oftwo individuals that belong to two different BAC groups.Mathematically, we have
S+ =12
∑Bm∈B
∑Al∈A
12
∑Ai∈A
∑Aj∈A
i=j
I (|Ai−Aj |≤|Al−Bm|)
+12
∑Am∈A
∑Bl∈B
12
∑Bi∈B
∑Bj∈B
i=j
I (|Bi−Bj |≤|Bl−Am|)
(5)
S− =12
∑Bm∈B
∑Al∈A
12
∑Ai∈A
∑Aj∈A
i=j
I (|Ai−Aj |> |Al−Bm|)
+12
∑Am∈A
∑Bl∈B
12
∑Bi∈B
∑Bj∈B
i=j
I (|Bi−Bj |> |Bl−Am|)
(6)
where I(.) is the indicator function. Then, Gamma (Γ) isdefined as follows:
Γ =S+ − S−S+ + S−
. (7)
The Gamma value will be large if the number of concordantpairs is greater than the number of discordant pairs. Thus, ahigher Gamma value indicates better cluster separation. Themaximum value of Gamma is one. For the current problem in(3), we select λmax as 0.8 and λmin as 0.01.
Note that the goal of this paper is to investigate how well aquantitative measure can separate the known two classes (i.e.,the group with a BAC level of 0.0% and the group with a BAClevel of 0.1%) instead of developing a classification algorithmfor classifying the drivers. Thus, the indices used here providequantitative measures on the separation of two given clustersand fit the goal of this paper well.
V. OPTIMAL CLUSTERING OF THE DRIVERS
ACCORDING TO WITHIN GROUP SEPARATION
As mentioned in Section III, in the third step in this paper, weneed to optimally cluster drivers into different subgroups suchthat the adjusted separation index in (3) is maximized. This isa combinatorial optimization problem. The optimization algo-rithms could roughly be classified into nonheuristic methodssuch as the branch-and-bound method and heuristic methodssuch as the genetic algorithm (GA). To apply a nonheuristicoptimization algorithm to solve the problem, we need to havea clear understanding of how the cost function behaves in thesearch space. Unfortunately, the behavior of the cost functionin the current problem is very complex. On the other hand,there are many heuristic optimization methods such as the GA,simulated annealing, and tabu search. The basic ideas of theseheuristic methods are similar. Among these heuristic methods,the solution vector G of the problem can conveniently be rep-resented as a chromosome for the GA. Thus, we propose to usethe recently developed heuristic searching method PGA [31]to solve it. For completeness, we provide a brief introductionof the ordinary GA in Section V-A. A novel parallel evolutionmethod, which is unique to our current problem, is described indetail in Section V-B.
A. Introduction to the GA
The GA is a heuristic search algorithm that can convenientlybe applied to a variety of combinatorial optimization problems[30]. The algorithm can be summarized in the following foursteps.
Step 1—Encoding: In the GA, the first step is to encodea candidate solution as a chromosome. The vector G, as de-scribed in Section III, can naturally be treated as a chromosome.Let us assume that we have P such chromosomes and eachchromosome is denoted as Cp.
Step 2—Selection: After we have a population of chromo-somes, the next step is to select the best possible group of
DAS et al.: DIFFERENTIATING ALCOHOL-INDUCED DRIVING BEHAVIOR USING STEERING WHEEL SIGNALS 1361
chromosomes for the subsequent steps. For each chromosome,we calculate its fitness, which is the objective function in (3).The chromosomes for the next generation are selected in sucha way that the probability of selection of chromosome Cp isproportional to the value of the objective function. Thus, thebetter chromosomes (i.e., solutions) have a higher probabilityof being selected. Various selection methods are available inthe literature. In our current analysis, we use the roulette-wheelselection method [30].
Step 3—Crossover: Crossover involves the exchanging ofparts of a chromosome. First, a pair of chromosomes is picked,and then, a crossover point on the length of the chromosomeis chosen. Parts of the chromosomes are exchanged beyond thispoint to obtain a new pair of chromosomes. The crossover pointis randomly chosen, with each point on the chromosome havingthe probability pc to be chosen. This probability is called thecrossover probability.
Step 4—Mutation: Mutation involves altering any positionon the chromosome, i.e., we pick any point on the chromosomewith probability pm and change the group to which it is as-signed. The probability pm is called the mutation probability.After mutation, the fitness of the new population of chromo-somes is calculated, and steps 2–4 are repeated.
B. Parallel Evolution
The concept of parallel evolution was proposed in [31].It is theoretically shown that it is better to concurrently runseveral instances of GAs to optimize the objective functionrather than one GA run with a large number of iterations. Forthe variable selection problem in [31], Zhu et al. implementedvarious parallel runs of GA and then selected the final groupof variables by a majority voting among the results of theseparallel runs.
For the clustering problem formulated in Section III, wepropose a novel way of combining the results of the parallelruns to take the advantage of the parallel evolution. Assume thatthere are Q parallel GAs runs. Let the best solution from theqth run be represented as W q = 1Wq, 2Wq . . . NWq, whereeach element of W q indicates the cluster to which each ofthe N drivers have been assigned. Based on the Q number ofparallel run results, we can generate an N × N affinity matrixK, which is a measure of the closeness of two drivers in thefinal results of the parallel runs. Each element of K, kij iscalculated as follows:
kij =Q∑
q=1
I(iWq = jWq) (8)
where I is the indicator function. Clearly, if the value of kij islarge, then drivers i and j will often appear in the same groupin different parallel runs, and it is thus highly likely that theyshould be in the same group in the final combined result. Basedon this intuition, we can quantitatively utilize the informationin the affinity matrix by converting the affinity matrix into to adistance matrix, and then, based on the distance matrix, we can
cluster the drivers into different groups as the final combinedresults. In particular, the element of the distance matrix H ,which is denoted as hij , is given as follows:
hij =
1/kij ∀i = j0 ∀i = j.
(9)
Based on this distance matrix, we use the weightedpair–group average (WPGA) method for clustering [32] togroup the drivers into final groups. In WPGA, first, the closestpair of drivers is picked from the H matrix. They are puttogether in one cluster. The matrix H is again calculated,assuming that the pairs are in one cluster. This process isrepeated until we get the c groups.
The following definition is used to calculate the distancesbetween a cluster and an entity (individual driver in this case).
1) The distance between an entity and a cluster is definedas the average of distances between the entity and eachentity in the cluster.
2) The distance between two clusters is calculated as theaverage of distances between every pair of entities fromboth the clusters.
We applied the aforementioned PGA on our data set andfound that this algorithm is quite efficient and effective. Thedetailed results and more discussions on this algorithm can befound in the next section.
VI. RESULTS AND DISCUSSIONS
In this section, we show the analysis results and provide someinsights based on these results. Fig. 3 shows the raw steeringwheel angle signal in the time domain for three differentdriving scenarios. These three driving scenarios were part ofthe overall drive completed by each driver. Note that we haveperformed the analysis on many other driving scenarios andthe results are similar to the results from these three typicalscenarios.
In Fig. 3, we can see that the two raw steering wheelsignals from the same driver with different BAC levels forthe same driving scenarios are similar to each other. Visualinspection can also indicate that there are some fine differencesin these two signals. However, it is not easy to directly quantifythese differences using the time-domain signal. As aforemen-tioned, we applied various quantitative measures to the rawsignal.
The quantitative measures that were extracted from eachdriving scenario generate two groups of data: one for the 0.0%BAC level and the other for the 0.1% BAC level. The separationbetween these two groups is analyzed as follows. First, weconsider the separation of the quantitative measures extractedfrom all the drivers (108 in total). The results are presented inSection VI-A. Because the drivers are from a broad spectrumof backgrounds, the results of separation can provide insightsinto how well different quantitative measures can separate thenormal and alcohol-induced impaired drivers for the whole pop-ulation. Next, we divide the 108 drivers into multiple groups,and the separation within each subgroup is analyzed. The
1362 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 3, SEPTEMBER 2012
Fig. 3. Steering wheel angle in the time domain for a single driver for (a) and (d) urban drive, (b) and (e) urban curves, and (c) and (f) freeway driving for 0.0%and 0.1% BAC levels, respectively. The maps on top correspond to the three driving routes.
Fig. 4. Cluster separation for various quantitative measures, urban drive, urban curves, and following traffic on a freeway.
DAS et al.: DIFFERENTIATING ALCOHOL-INDUCED DRIVING BEHAVIOR USING STEERING WHEEL SIGNALS 1363
Fig. 5. Estimated probability density of three quantitative measures. (a) Correlation entropy. (b) Sample entropy. (c) Mean.
intuition is that there may not exist a very effective quantitativemeasure for detecting the alcohol-induced impairment for alldrivers. However, we may find quite-effective measures for asubgroup of drivers. Through this analysis, we can identifyand compare these subgroups for various quantitative measures.These results are presented in Section VI-B.
A. Separation of Quantitative Measures for theGeneral Population
In this analysis, for a given quantitative measure and a givendriving scenario, we apply the quantitative measure to the rawsteering wheel signal that was obtained from all the driversfor the two BAC levels. According to the BAC levels, weput the resulting quantitative measures into two groups andthen assessed the separation of these two groups using theFisher discriminant and the Gamma index. Fig. 4 summarizesthe final results for the six quantitative measures. The threesubfigures correspond to three different driving scenarios. Thelengths of the bars in Fig. 4 are proportional to the valuesof separation indices. Thus, a longer bar in Fig. 4 indicates abetter separation between the normal and the alcohol-inducedimpairment conditions.
Fig. 4 clearly shows that certain nonlinear invariant mea-sures provide much better separation between the normal andimpaired driving conditions than that provided by the simplestatistics such as the mean and the standard deviation. For ex-ample, the separation indices that were provided by the sampleentropy and GKA-based correlation entropy are much higherthan the separation indices provided by the mean and the stan-dard deviation. This result is further confirmed in Fig. 5, whichillustrates the estimated probability density function for thequantitative measures under both normal and impaired drivingconditions. In Fig. 5, the probability density is estimated byfitting a Gaussian kernel function over the quantitative measurevalue [33]. Fig. 5 clearly shows that the distributions of thesample entropy and the correlation entropy under different BAClevels are separated; however, the distributions of the meanunder these two conditions almost completely overlap. Thus,we can conclude that the nonlinear invariant measure is morerobust and consistent in detecting the alcohol-impaired drivingfor the generic population.
It is also interesting to note that not all the nonlinear invariantmeasures separate the drivers well. In particular, the Lyapunov
Fig. 6. Trajectories of the objective function in the PGA.
Fig. 7. Fisher discriminant value and the size of each group.
exponent performs similar to or worse than the simple statistics,and the correlation dimension performs well only under certaindriving scenarios. This case indicates that the signature ofalcohol-induced impairment depends on the driving context.Alcohol-impairment slows the driver response and diminishesdriver responsiveness to roadway demands; hence, fluctuationin the steering wheel angle can diminish. This is also observedin Fig. 3. Because entropy is a more direct measure of the
1364 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 3, SEPTEMBER 2012
TABLE IFISHER DISCRIMINANT VALUE OF VARIOUS GROUPS AND THE VALUE OF THE OBJECTIVE FUNCTION (3)
fluctuation or randomness in a signal, its performance is betterthan other nonlinear invariant measures. Based on the afore-mentioned results, we can also observe that, although certainnonlinear measures perform much better than the simple sta-tistics, the absolute values of the separation indices for thesemeasures are still not large enough to establish clear separation.Roughly speaking, if we have a value of 3 for the Fisher lineardiscriminant index, we can expect a 95% or better probabil-ity of correct differentiation for a well-designed classificationalgorithm. The values of 0.27–0.13 of the separation indicesare, in fact, not significant enough in practice. The overlap ofthe distributions in Fig. 5(a) and (b) also illustrates this point.In other words, if we use these nonlinear measures to detectthe alcohol-induced impairment for the general population, wewill have a quite-high error rate. Based on this observation, wepropose to cluster the driver population into smaller subgroupsand then apply these measures to these subgroups. The resultsare presented in the following section.
B. Separation of Quantitative Measures for Subgroups
As described in Section V, we cluster the driver populationinto subgroups by optimizing the objective function (3) usingthe PGA. The performance of the GA depends, to a largeextent, on the suitable choices of parameters. These parametersinfluence the convergence rate and the stability of the solution.In this paper, the parameters were picked through extensiveparameter tuning. In particular, the number of chromosomes ina generation was selected to be 30, because this value seemsto make a good tradeoff between the size of the populationand the computational load. The number of parallel runs wasfixed at 20, which is commonly used in the PGA. The crossoverprobability and the mutation probability were chosen throughextensive comparisons over a range of probability values, andit was found that a crossover probability value of 0.3 and amutation probability value of 0.02 were most suitable for thisproblem. Another critical parameter in the algorithm is thenumber of subgroups. In this paper, we decide to cluster thedrivers into three subgroups. It is expected that the separationwithin these three subgroups will be high, moderate, and low.Although more subgroups can be used, too many subgroupswill make the final results difficult to interpret and generalize.Thus, we believe that three groups balance the model flexibilityand ease of interpretation.
A typical run of the PGA is illustrated in Fig. 6. Eachline in Fig. 6 represents the value of the objective function[see (3)] for each run of the GA. Because we have 20 GAsrunning parallel, the figure has 20 lines. As shown, the objectivefunction converges to different values for different parallelruns. However, the combined results of all the parallel runs
Fig. 8. Probability density estimate of sample entropy values for (a) badseparation (group 1) and (b) good separation (group 3).
of GA are better than individual runs. Indeed, multiple runs ofthis algorithm have been conducted, and each time, we obtainvery similar results: The combined results are not only betterthan the individual results but are more stable as well. Thus,this algorithm and the proposed algorithm for combining theindividual results perform quite well for this problem.
Fig. 7 and Table I show the results of the PGA, includingthe Fisher discriminant value and the size of each group. Thethree bars represent the size of the three groups, and the Fisherdiscriminant value of each group is given in Table I. Thesteering wheel signal that was used here is collected duringurban drive. The results show some interesting characteristics.
1) As expected, the values of the separation index forthe three groups for each quantitative measure are low,medium, and high, respectively. In particular, the sepa-ration within group 3 is the highest, and the separationwithin group 1 is the lowest. Thus, roughly speaking,group 3 includes drivers who are sensitive to the alcohol-induced impairment, and the drivers in group 1 are notsensitive (at least in terms of the measures considered).Fig. 8 shows the probability distribution of sample en-tropy values for the drivers in groups 1 and 3 withBAC levels of 0.0% and 0.1%. Clearly, we can see thatthe separation within group 3 is much larger than ingroup 1.
2) The sizes of group 3 for different quantitative measuresare different. Note that the sizes of group 3 for nonlinearinvariant measures are larger than for the mean and thestandard deviation. In particular, the size of group 3for the correlation entropy is the largest, which meansthat the correlation entropy can identify alcohol-induced
DAS et al.: DIFFERENTIATING ALCOHOL-INDUCED DRIVING BEHAVIOR USING STEERING WHEEL SIGNALS 1365
Fig. 9. Probability density estimate of the mean steering wheel angle. (a) Group 2. (b) Group 3. (c) Groups 2 and 3.
impairment in more drivers than the other measures. Thisresult confirms that the nonlinear invariant measures canprovide consistent measures of the steering wheel signaland, thus, can separate a relatively large group of peoplewell.
3) The separation index and the size of group 2 for differentquantitative measures are intriguing. In general, the sep-aration and the size of group 2 for the nonlinear invariantmeasures are relatively small, which are particularly truefor the sample entropy and the correlation entropy. On theother hand, the size and the separation value of group 2for the mean and the standard deviation are reasonable.In other words, the drivers in group 2 are also sensitive tothe alcohol-induced impairment in terms of these simplestatistics but not to the more complex metrics. However,when we combine groups 2 and 3 to recompute theseparation index, we will get a very low value of theFisher discriminant (on the order of 0.02). Fig. 9 clearlyconfirms this observation. In Fig. 9, we have also shownthe probability density that was estimated from both BAClevel cases for groups 2, 3, and 2 and 3 combined. Theseplots are presented only for the mean, but the standarddeviation also exhibits similar properties. This phenom-enon indicates that the impact of the alcohol-inducedimpairment on the mean and standard deviation of thesteering wheel signal is not consistent. For some groupsof drivers, it causes the mean or standard deviation to behigher, but for other groups of drivers, it causes the meanor standard deviation to be lower. Within each group,we can differentiate the driver conditions well. However,combining the groups results in poor separation. Thisphenomenon again confirms that the nonlinear invariantmeasures are more consistent.
4) Aside from the size, the composition of each group fordifferent quantitative measures is quite different. Table IIshows the overlap of group members for various quantita-tive measures. The percentage similarity is the fraction of
TABLE IIPERCENTAGE SIMILARITY BETWEEN DIFFERENT MEASURES
individuals who are grouped into the same groups acrossvarious quantitative measures. In particular, the values inTable II are obtained as follows. Assume that we want tocompute the similarity between Measures 1 (e.g., mean)and 2 (e.g., entropy).a. For each group in Measure 1, find the group in Mea-
sure 2 with the highest number of common individualswith the given group in Measure 1.
b. Ensure that no group in Measure 2 is repeated in a).c. Add all the number of overlapping obtained for each
group of Measure 1 in a).d. Divide this number by the total number of drivers
to get the percentage similarity between Measures1 and 2.
In Table II, we can see that the trend is that the overlap amongthe simple statistics and among the nonlinear invariant mea-sures is high. However, the overlap across the simple statisticsand the nonlinear invariant measures is relatively low.
Because the group compositions are different, it is interestingto further analyze the overlaps of the groups across differentquantitative measures. Table III shows the number of individu-als across various groups for the mean, standard deviation, andcorrelation entropy. The values in the table are the numbersof drivers that are common in the crossed two groups. For
1366 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 3, SEPTEMBER 2012
TABLE IIINUMBER OF COMMON DRIVERS ACROSS GROUPS FOR THE CORRELATION ENTROPY AND MEAN
TABLE IVNONLINEAR DYNAMIC INVARIANT MEASURES
example, there are 18 common drivers in group 1 for the meanmeasure and for the correlation entropy measure. If groups 2and 3 are considered well separated for the mean and standarddeviation measures, whereas only group 3 is considered wellseparated for the correlation entropy measure, we can say thatwe can find drivers for whom the mean or the standard deviationcannot produce necessary separation, the correlation entropymight, and vice versa. For example, about 1/3 of drivers ingroup 3 for the correlation entropy fall in group 1 for the meanmeasure, which means that the mean measure cannot separatethem well. Thus, we can conclude that the nonlinear invariant
measures can capture the characteristics of the signal other thanthat captured by the simple statistics. This case also suggeststhat combining the simple statistics and the nonlinear invariantmeasures may separate the driving condition better than usingonly one type of measure.
VII. CONCLUSION
In this paper, we have introduced and compared variousquantitative measures of the steering wheel signal in termsof their ability to detect drivers with high alcohol levels.
DAS et al.: DIFFERENTIATING ALCOHOL-INDUCED DRIVING BEHAVIOR USING STEERING WHEEL SIGNALS 1367
A combinatorial optimization technique based on the PGAis introduced to cluster the drivers into subgroups, and thewithin-group separation capabilities of these quantitativemeasures are also analyzed and compared. Many interestinginsights are obtained in this analysis. For example, nonlinearinvariant measures such as the sample entropy and correlationentropy provide a more robust and consistent characterizationof the steering wheel signal than the simple statistics such asthe mean and the standard deviation. These nonlinear invariantmeasures usually capture different signal characteristics fromthat captured by the mean and the standard deviation, andthus, it is possible to combine different measures to improvethe differentiability. Furthermore, aside from characterizing thealcohol-induced impairment, these nonlinear measures may beuseful in evaluating the driver performance and impairmentinduced by other distractions to determine whether variousfactors distract a driver to a dangerous degree.
Detection of alcohol-induced driving impairment throughvehicle-based sensor signals is of paramount importance inpractice. The analysis that has been conducted in this paperprovides a good starting point for the development of a warningsystem for alcohol-induced impairment. However, there are stillmany open issues along this direction. First, in the currentanalysis, only the steering wheel signal is considered. Thegas/brake pedal signal is also an important driving signal andcould also provide very useful information in detecting alcohol-induced impairment. Second, the current analysis hinted thatcombining multiple quantitative measures may improve thecapability of differentiating driver conditions. Thus, efficientalgorithms are needed to find the best combination of quantita-tive measures. Third, it will be interesting to further investigatethe composition of clusters of drivers obtained in Section VI-Bbased on other driver characteristics such as drinking history.This will help determine for which type of drivers a givenquantitative measure is effective to be applied to the detection ofalcohol-induced impairment. Finally, we will need to develop aclassification algorithm to classify the driving conditions duringdriving using the effective quantitative measures developed. Wewill investigate these issues and report the results in the nearfuture.
APPENDIX
NONLINEAR DYNAMIC INVARIANT MEASURES
See Table IV.
ACKNOWLEDGMENT
The authors would like to thank the editor and the refereesfor their valuable comments and suggestions.
[2] J. Culp, M. El Guindy, and A. Haque, “Driver alertness monitoring tech-nique: A literature review,” Int. J. Heavy Veh. Transp. Syst., vol. 15,no. 2–4, pp. 255–271, 2008.
[3] Y. Liang, M. L. Reyes, and J. D. Lee, “Real-time detection of drivercognitive distraction using support vector machines,” IEEE Trans. Intell.Transp. Syst., vol. 8, no. 2, pp. 340–350, Jun. 2007.
[4] L. M. Bergasa, A. Sotelo, R. Barea, and M. E. Lopez, “Real-time systemsfor monitoring driver vigilance,” IEEE Trans. Intell. Transp. Syst., vol. 7,no. 1, pp. 63–77, Mar. 2006.
[5] P. Smith, M. Shah, and N. V. Lobo, “Determining driver visual attentionwith one camera,” IEEE Trans. Intell. Transp. Syst., vol. 4, no. 4, pp. 205–218, Dec. 2003.
[6] J. A. Healey and P. W. Picard, “Detecting stress during real-world drivingtasks using physiological sensors,” IEEE Trans. Intell. Transp. Syst.,vol. 6, no. 2, pp. 156–166, Jun. 2005.
[7] J. McCall and M. M. Trivedi, “Video-based lane estimation and trackingfor driver assistance: Survey, system and evaluation,” IEEE Trans. Intell.Transp. Syst., vol. 7, no. 1, pp. 20–37, Mar. 2006.
[8] J. McCall, D. Mipf, M. M. Trivedi, and B. Rao, “Lane change intent analy-sis using robust operators and sparse Bayesian learning,” IEEE Trans.Intell. Transp. Syst., vol. 8, no. 3, pp. 431–440, Sep. 2007.
[9] S. Sekizawa, S. Inagaki, T. Suzuki, S. Hayakawa, N. Tsuchida, T. Tsuda,and H. Fujinami, “Modeling and recognition of driving behavior based onstochastic switched ARX model,” IEEE Trans. Intell. Transp. Syst., vol. 8,no. 4, pp. 593–606, Dec. 2007.
[10] T. Toledo, H. N. Koutsopoulos, and M. Ben-Akiva, “Integrated drivingbehavior modeling,” Transp. Res. C, vol. 15, no. 2, pp. 96–112,Apr. 2007.
[11] O. Nakayama, T. Futami, T. Nakamura, and E. R. Boer, “Develop-ment of a steering entropy method for evaluating driver workload,”presented at the Int. Congr. Expo., Detroit, MI, Mar. 1–4, 1999,SAE Paper 1999-01-0892.
[12] E. R. Boer, “Behavioral entropy as a measure of driving performance,” inProc. Driving Assessment, Aspen, CO, 2001, pp. 225–229.
[13] E. R. Boer, M. E. Rakauslas, N. J. Ward, and M. A. Goodrich, “Steeringentropy revisited,” in Proc. 3rd Int. Driving Symp. Human Factors DriverAssess., Training Veh. Des., Iowa City, IA, 2001, pp. 25–32.
[14] A. V. Desai and M. A. Haque, “Vigilance monitoring of operator safety:A simulation study on highway driving,” J. Safety Res., vol. 37, no. 2,pp. 139–147, 2006.
[15] J. Fukuda, E. Akustu, and K. Aoki, “Estimation of driver’s drowsinesslevel using interval of steering adjustment for lane keeping,” JSAE Rev.,vol. 16, no. 2, pp. 197–199, Apr. 1995.
[16] M. Small, “Applied nonlinear time series analysis: Applications inphysics, physiology and finance,” in Nonlinear Science Series A. Sin-gapore: World Scientific, 2005.
[17] D. T. Kaplan and R. J. Cohen, “Searching for chaos in fibrillation,” Ann.New York Acad. Sci., vol. 591, pp. 367–374, Jun. 1990.
[18] M. Akay, Nonlinear Biomedical Signal Processing. Piscataway, NJ:IEEE Press, 2001.
[19] J. S. Richman and J. R. Moorman, “Physiological time-series analy-sis using approximate entropy and sample entropy,” Amer. J. Phys-iol. Heart Circulatory Physiol., vol. 278, no. 6, pp. H2039–H2049,Jun. 2000.
[20] U. R. Acharaya, K. P. Josheph, N. Kannathal, C. M. Lim, and J. S. Suri,“Heart rate variability: A review,” Med. Bioeng. Comput., vol. 44, no. 12,pp. 1031–1051, Dec. 2006.
[21] P. L. Zador, S. A. Krawchu, and R. B. Voas, “Alcohol-related relativerisk of driver fatalities and driver involvement in fatal crashes in relationto driver age and gender: An update using 1996 data,” J. Stud. Alcohol,vol. 61, no. 3, pp. 387–395, May 2000.
[22] L. Vendramin, R. J. G. B. Campello, and E. R. Hruschka, “Relativeclustering validity criteria: A comparative overview,” Stat. Anal. DataMining, vol. 3, no. 4, pp. 209–235, Aug. 2010.
[23] F. Takens, “Detecting strange attractors in turbulence,” in Proc.Dyn. Syst. Turbulence, Warwick, vol. 898, Lecture Notes Math., 1981,pp. 366–381.
[24] J. P. Gollub, E. J. Romer, and J. E. Socolar, “Trajectory divergence forcoupled relaxation oscillators: Measurements and models,” J. Stat. Phys.,vol. 23, no. 3, pp. 321–333, Sep. 1980.
[25] A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “DeterminingLyapunov exponents from a time series,” Phys. D, vol. 16, no. 3, pp. 285–317, Jul. 1985.
[26] S. M. Pincus, “Approximate entropy (ApEn) as a complexity measure,”Chaos, vol. 5, no. 1, pp. 110–117, Mar. 1995.
[27] P. Grassberger and I. Procaccia, “Measurement of strangeness of strangeattractors,” Phys. D, vol. 9, no. 1/2, pp. 189–208, Oct. 1983.
[28] C. Dicks, “Estimating invariants of noisy attractors,” Phys. Rev. E, vol. 53,no. 5, pp. R4263–R4266, May 1996.
[29] R. O. Duda, P. E. Hart, and D. G. Strok, Pattern Classification. NewYork: Wiley, 2001.
[30] D. E. Goldberg, Genetic Algorithms in Search, Optimization and MachineLearning. Boston, MA: Addison-Wesley, 1989.
1368 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 3, SEPTEMBER 2012
[31] M. Zhu and H. A. Chipman, “Darwinian evolution in parallel universes: Aparallel genetic algorithm for variable selection,” Technometrics, vol. 48,no. 4, pp. 491–502, Nov. 2006.
[32] V. P. Lessig, “Comparing cluster analyses with Cophentic correlation,”J. Market. Res., vol. 9, no. 1, pp. 82–84, Feb. 1972.
[33] E. Parzen, “On estimation of probability density function and mode,” Ann.Math. Stat., vol. 33, no. 3, pp. 1065–1076, Sep. 1962.
Devashish Das received the B.Tech (Hons.) degreein manufacturing science and engineering from theIndian Institute of Technology, Kharagpur, India,in 2010. He is currently working toward the Ph.D.degree in industrial engineering with the Departmentof Industrial and Systems Engineering, University ofWisconsin, Madison.
Shiyu Zhou received the B.S. and M.S. degrees inmechanical engineering from the University of Sci-ence and Technology of China, Hefei, China, in 1993and 1996, respectively, and the M.S. degree in indus-trial engineering and the Ph.D. degree in mechanicalengineering from the University of Michigan, AnnArbor, in 2000.
He is currently a Professor with the Departmentof Industrial and Systems Engineering, Universityof Wisconsin, Madison. His research interests in-clude in-process quality and productivity improve-
ment methodologies by integrating statistics, system and control theory, andengineering knowledge. His research is sponsored by the National ScienceFoundation, the Department of Energy, the Department of Commerce, andindustry.
Dr. Zhou is a member of the Institute of Industrial Engineers (IIE), theInstitute for Operations Research and the Management Sciences, the AmericanSociety of Mechanical Engineers, and the Society of Manufacturing Engineers.He received a Faculty Early Career Development Award from the NationalScience Foundation and the Best Application Paper Award from the IIETransactions.
John D. Lee received the B.A. degree in psychol-ogy and the B.S. degree in mechanical engineeringfrom Lehigh University, Bethelem, PA, in 1987 and1988, respectively, and the M.S. degree in industrialengineering and the Ph.D. degree in mechanical en-gineering from the University of Illinois at Urbana-Champaign in 1986 and 1992, respectively.
He is currently a Professor with the Departmentof Industrial and Systems Engineering, Universityof Wisconsin, Madison. His research enhances thesafety and acceptance of complex human-machine
systems by considering how technology mediates attention. His research in-terests include technology-mediated attention, trust in technology, supervisorycontrol, and collision warning systems and driver distraction.
