Localizing Changes in Driver Behavior via Frequency-pattern-analysis

M. Schneider, M. Sieber and B. F

arber

Human Factors Institute (IfA), Universit

at der Bundeswehr M

unchen, Werner-Heisenberg-Weg 39, Neubiberg, Germany

Keywords:

Data Analysis, Driver Behavior, Driver Assistance Systems, T-Test, Fourier-Series.

Abstract:

Explorative analysis of driver behavior, a key variable in the context of automotive research and development,

can be tedious. The authors present a quick and easy method to identify changes in recorded driver behavior

data. The method consists of a data processing algorithm that uses Fourier-series and statistical t-tests to

identify points in time where changes in the frequency of the recorded signal occur. An exemplary use-

case for the method is presented for driver steering torque data obtained in an experiment with an automatic

obstacle-avoidance maneuver. The results allow for the assumption that changes in frequency of driver steering

torque may mark meaningful, implicit changes in driver behavior even when driver behavior does not explicitly

change, thereby making obvious the potential of the proposed analysis method.

1 MOTIVATION

Driver behavior is a key variable in the context of au-

tomotive research and development. For the evalua-

tion of a driver assistance system, for example, driv-

ing experiments are conducted to observe the human-

machine-interaction. Manual processing of the at-

tained data is tedious but often the only option where

the analysis is of an explorative nature and points of

interest within the analyzed data are yet unknown.

For this reason the authors of this paper devised a

method to automatically identify changes in subjects’

driving behavior without the need to manually sight

individual data.

2 ALGORITHM

The proposed method utilizes a combination of

Fourier-series, see e.g. (Goebbels and Ritter, 2011),

and t-tests, see e.g. (Bortz, 1977). Based on the

assumption that changes in recorded driver behav-

ior (e.g. driver steering wheel torque) manifest in a

change of the frequency pattern of the recorded sig-

nal, the method poses a viable tool for the explorative

analysis of driver behavior.

2.1 Theoretical Approach

In order to be able to detect points of interest within

recorded data, where the recorded signal changes sig-

niﬁcantly, the processing algorithm must employ sta-

tistical tests comparing the data preceding the point of

interest to the data following it.

To do so, at least one of the data’s characteristics

must be chosen for comparison. The authors chose

the frequency of the recorded signal. Fourier-ﬁtting

the data and comparing frequencies allows for com-

parison of trends and tendencies rather than merely

absolute values, and can therefore potentially prove

more revealing. Other methods of ﬁtting the recorded

signal (linear, polynominal, Gaussian and spline ﬁt-

ting) and comparing the resulting characteristic pa-

rameters have been considered but not been found to

yield better results.

The authors employed Fourier ﬁtting of the fourth

order based on the equation (Mathworks, 2015)

g(x) = a

∑

i=4

i=1

· cos(i · x · f ) + b

· sin(i · x · f )

Comparing the entire range of parameters of the

Fourier series (a

to a

, b

to b

and f ) in order

to identify points of interest using multivariate anal-

ysis of variance has not proven more advantageous

than comparing only the frequencies f , which in turn

requires less computational power and is therefore

preferable.

In a ﬁrst approach, the authors chose a repeated

measures t-test for the purpose of testing for signiﬁ-

cance. The repeated measures or paired t-test calcu-

lates the probability of yielding a difference between

paired samples of at least the observed mean differ-

ence, given its distribution (estimated by the observed

standard deviation of the differences) and sample size.

Schneider M., Sieber M. and Färber B..

Localizing Changes in Driver Behavior via Frequency-pattern-analysis.

DOI: 10.5220/0005486800330038

In Proceedings of the 1st International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS-2015), pages 33-38

ISBN: 978-989-758-109-0

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Speciﬁed widths around data point.

The test is based on the assumption that the dif-

ferences are normally distributed, a requirement that

may not necessarily be met. It should be noted, how-

ever, that the t-test has proven very robust even when

this requirement is violated. Moreover, replacing the

suggested t-test with any other signiﬁcance test (e.g.

non-parametric tests) within the method will work

equally well.

2.2 Requirements

For optimal results and fast processing, the data

should comply with the following criteria:

• Data of all test subjects should be synchronized

to a well-deﬁned point in time (e.g. the onset of

a driver assistance function’s intervention). Well-

parallelized data leads to higher accuracy of the

results.

• Data should be recorded in high frequency. A

higher number of measurements per time unit fa-

cilitates convergence of the analysis.

Beyond these requirements, a time window within

the recorded data must be selected as subject of the

analysis.

2.3 Processing the Data

In order to detect a change in driver behavior, the fre-

quency patterns of the recorded signal preceding ev-

ery measurement point within the examined time win-

dow are compared to those following the measure-

ment point.

To do so, an algorithm ﬁrst isolates data in a spec-

iﬁed width around one point in time (Figure 1) from

each test subject’s data set (Figure 2) and then per-

forms a Fourier-ﬁtting of the isolated data left (Figure

3), as well as of the data right (Figure 4) of this point.

In a second step, the attained Fourier-frequencies

for the local data preceding and following this point in

Figure 2: Current point of analysis in synchronized data.

Figure 3: Fourier-ﬁtting (solid line) of the data points (dots)

left of an exemplary point of analysis.

Figure 4: Fourier-ﬁtting (solid line) of the data points (dots)

right of an exemplary point of analysis.

time (Table 1) are compared to each other for all test

subjects using a within-subjects t-test. The p-value

and effect size resulting from the comparison at this

data point are saved and plotted.

A variation of the widths of the seperated time

windows entails the option of weighting an effect in

the analysis depending on its time scale. Effects with

long-term inﬂuence are detected more easily and re-

aliably when utilizing larger widths, while smaller

area-widths facilitate the detection of short term ef-

fects. Utilizing an entire spectrum of widths for the

VEHITS2015-InternationalConferenceonVehicleTechnologyandIntelligentTransportSystems

Table 1: Calculated frequencies for t-test.

sub ject f

le ft

right

1 f

2 f

3 f

... ... ...

n f

analysis enables a broader examination of both long

and short term effects.

The two steps of Fourier-ﬁtting and statistical test-

ing are repeated progressively for each data point

within the examined time frame. In the end, the

procedure returns the p-values plotted over time, en-

abling the data analyst to quickly assess brief periods

of interest where p-values are low and driver behavior

has apparently changed.

The entire procedure is pictured in Figure 5.

Figure 5: Structogram of the algorithm.

2.4 Analysis and Results

Experimental use of this method has shown that a plot

of the averaged p-values for all area-widths over time

is a valuable way to visually process the results of

such an analysis. Local or global minima in this curve

mark points of interest in the analyzed data, that in-

vite further investigation into the cause of change in

driver behavior at these points. The resulting knowl-

edge can then be used to retrospectively analyze the

data of each test subject at the identiﬁed points of in-

terest.

3 PRACTICAL USE IN DRIVER

BEHAVIOR ANALYSIS

3.1 Background

Driver steering torque data obtained in a driving ex-

periment with an automatic obstacle-avoidance ma-

neuver will serve as an exemplary use-case for the

proposed analysis method.

In the experiment 60 test subjects drove an instru-

mented car with electrical power steering. During the

experiment, a driver assistant system applied torque to

the steering wheel to steer left in order to avoid collid-

ing with an obstacle on the road ahead. The assistance

system would subsequently apply torque to the steer-

ing wheel to steer right in order to restore the car’s

original heading. Each test subject experienced the

automatic steering intervention under two conditions:

the legitimate condition where the steering interven-

tion was triggered in reaction to a suddenly appear-

ing obstacle, and the illegitimate condition where the

steering intervention was triggered on an empty road,

simulating a faulty activation (Figure 6).

It was expected a priori that driver steering torque

would initially be opposed to the torque applied by

the assistance system due to the inertia of the driver’s

hands as well as that of the steering wheel itself, and

possibly due to drivers’ ﬁrst reaction of unreﬂect-

edly holding the steering wheel in position as they

would in reaction to other steering perturbances such

as wind gusts or potholes. It was further expected

that, shortly thereafter, drivers would uphold their re-

sistance against the torque applied by the assistance

system in the illegitimate condition in order to over-

ride the unjustiﬁed steering intervention, while resis-

tance would decline or disappear entirely in the legit-

imate condition, as drivers give in to or even support

the efforts of the assistance system.

While the expectations for the illegitimate condi-

tion were met, the resulting data showed that the over-

whelming majority of test subjects did not lessen their

resistance against the torque applied by the assistance

system during the steering left phase of the maneuver

even in the legitimate condition. This may be a result

of the assistant system’s target trajectory aiming for a

transverse offset of unnecessary extent, attempting to

take the car much further to the left than drivers felt

the need for.

3.2 Research Question

Despite the initial, supposedly unreﬂected, reaction

and the later, supposedly reﬂected, reaction of the

drivers to the automatic steering intervention having

LocalizingChangesinDriverBehaviorviaFrequency-pattern-analysis

Figure 6: Qualitative mean steering torque in the legitimate (solid line) and illegitimate (dashed line) conditions.

been the same, i.e. trying to hold the steering wheel in

place, in both conditions, the authors intended to in-

vestigate whether it was possible to identify the point

in time where the supposedly unreﬂected initial reac-

tion ends. The underlying hypothesis hereby having

been that the later, supposedly reﬂected, reaction of

the drivers may be of a different quality regarding the

frequency pattern of the driver steering torque.

4 RESULTS AND FURTHER USE

4.1 Results

The test subjects’ data were synchronized to the on-

set of the automatic steering intervention (deﬁned as

time=0s) and processed using the proposed method as

described in (2.2). Using an alpha-level of 5%, the re-

sulting p-value plot for the legitimate condition (Fig-

ure 7) yields points of interest at the onset of the auto-

matic steering event (A), as well as at approximately

120ms (B), 360ms (C), 1130ms (D), and 1840ms (E)

thereafter. The resulting p-value plot for the illegit-

imate condition (Figure 8) yields the same points of

interest with the exception of (E).

The changes in driver steering torque frequency

discovered in the legitimate condition at (A), (D) and

(E) are trivial. They mark the onset of the automatic

steering intervention, the change of direction of the

steering torque applied by the assistance system in or-

der to restore the car’s original heading, and the end

of the automatic steering event respectively. The sig-

niﬁcant changes in steering torque applied by the as-

sistance system via electrical power steering at these

points consequentially manifest in the observed driver

steering torque.

In the illegitimate condition, drivers almost en-

tirely compensated for the applied steering torque, so

that steering right in order to restore the car’s original

heading was unnecessary. In this condition, (D) there-

fore does not mark a change in direction of the steer-

ing torque applied by the assistance system, but in-

stead the end of the automatic steering event, thereby

replacing the effect observed at (E) in the legitimate

condition.

The change in driver steering torque discovered

in both conditions at (B) can also be dismissed as a

system-induced effect, as it coincides with a prepro-

grammed readjustment of the steering torque applied

by the assistance system performed at a ﬁxed time of

0.1s after the onset of the automatic steering interven-

VEHITS2015-InternationalConferenceonVehicleTechnologyandIntelligentTransportSystems

Figure 7: Mean steering torque (dashed line) and frequency-pattern analysis results (solid line) in the legitimate condition.

tion, where the previously applied torque was eval-

uated in regard to the fraction of the target steering

angle it had been able to attain, and was subsequently

adjusted.

The change in driver steering torque at (C), how-

ever, does not coincide with an obvious change in the

steering torque applied by the assistance system. The

signiﬁcant change of driver steering torque frequency

at this point is therefore a possible candidate for the

point in time where the initially unreﬂected reaction

of the drivers becomes a reﬂected one.

4.2 Discussion

The presented method has reliably identiﬁed various

points in time throughout the automatic steering inter-

vention, where driver behavior changed signiﬁcantly.

It has succeeded in pointing out all of the explicit

changes in driver steering torque induced by changes

in the steering torque applied by the assistance sys-

tem, as well as in identifying a change in driver steer-

ing torque frequency that is not accompanied by a

signiﬁcant change in the magnitude driver steering

torque itself.

The change in driver steering torque frequency

identiﬁed in this experiment’s data at approximately

360ms after the onset of an automatic steering in-

tervention does not coincide directly with system-

induced changes in steering torque and can therefore

not be dismissed as a mere artefact. It is considered

by the authors as an indication of a possible change in

driver behavior from an initially unreﬂected to a re-

ﬂected action, though no explicit change in driver re-

action is observed in regard to working with or against

the steering intervention.

Reviewing literature on drivers’ reaction times to

road stimuli (Triggs and Harris, 1982), 360ms appears

a short time span for a driver’s reaction to take place.

Considering, however, that drivers only had to per-

ceive the situation and decide how to react while the

physical reaction itself, i.e. holding the steering wheel

in place, was already being acted out, the time span

appears reasonable. Other researchers reported recog-

nition reaction times to be of this size, e.g. (Laming,

1968). Neuroimaging methods during an experiment,

where test subjects were instructed to decide whether

a presented number was greater or smaller than ﬁve -

a simple decision task perhaps comparable to decid-

ing whether to steer more intensely or not - found that

the motor regions of the cortex were activated to carry

out the test subject’s decision approximately 330ms

after the onset of the stimulus, a time span that is well

LocalizingChangesinDriverBehaviorviaFrequency-pattern-analysis

Figure 8: Mean steering torque (dashed line) and frequency-pattern analysis results (solid line) in the illegitimate condition.

compatible with the time span observed in the data

reported here.

In a driving experiment very similar to the one re-

ported in this paper but using a target trajectory with

far less transverse offset for the automatic steering in-

tervention, a recline in driver steering torque opposing

the torque applied by the steering automaton was ob-

served at approximately 500ms after the onset of the

steering intervention, giving further support to the hy-

pothesis that the drivers’ decision on how to react in

this scenario is being made approximately at 360ms

after onset of the steering intervention, since 140ms

appear to be a reasonable time span for the physical

part of the reaction to be carried out, see e.g. (Houli-

han et al., 1994).

Though not yet throughly researched, the method

proposed in this paper provides a quick and conve-

nient way to perform an explorative analysis of driver

behavior. Beyond that, it also provides some evidence

that implicit changes in driver behavior may reﬂect

in changes of the frequency pattern of driver steer-

ing torque, which the proposed method is also able

to detect. The subject should be systematically re-

searched to collect further evidence for or against this

hypothesis. If the hypothesis proves correct, the anal-

ysis method proposed by the authors for driver be-

havior data should prove an even more useful tool

to quickly identify changes in driver behavior, even

those of implicit nature where the driver reaction does

not explicitly change, potentially granting unprece-

dented insight to experimentally observed driver be-

havior.

REFERENCES

Bortz, J. (1977). Lehrbuch der Statistik fuer Sozialwis-

senschaftler. Springer-Verlag, Berlin Heidelberg, 1st

edition.

Goebbels, S. and Ritter, S. (2011). Mathematik verstehen

und anwenden - von den Grundlagen bis zu Fourier-

Reihen und Laplace-Transformation. Springer Spek-

trum, Heidelberg, 1st edition.

Houlihan, M., Campbell, K., and Stelmack, R. M. (1994).

Reaction time and movement time as measures of

stimulus evaluation and response processes. Intelli-

gence, 18:289–307.

Laming, D. R. J. (1968). Information theory of choice-

reaction times. Academic Press, London.

Mathworks (2015). Fourier Series. The MathWorks, Inc.,

http://de.mathworks.com/help/curveﬁt/fourier.html.

Triggs, T. J. and Harris, W. G. (1982). Reaction time of

drivers to road stimuli. Human Factors Report, HFR-

12:14f.

VEHITS2015-InternationalConferenceonVehicleTechnologyandIntelligentTransportSystems