ENRI Int. Workshop on ATM/CNS. Tokyo, Japan. (EIWAC 2010)[EN-­111]	
  	
  Development	
  of	
  “cereameter”	
  (EIWAC	  2010)	
  +

K. Shiomi

AST Department
Electronic Navigation Research Institute (ENRI)
Tokyo, Japan
shiomi@enri.go.jp
Abstract: The “cereameter” is a result where the seed found by chance bore fruit as a longtime study result. In 1998, theauthor and Mr. Shozo Hirose discovered that the time averaged values of the first Lyapunov exponent calculated fromhuman voice changes according to the speaker’s psychosomatic condition. The degree of fluctuation of the spoken humanvoice changes according to the speaker's level of cerebral activity—it decreases when the speaker is fatigued withexhaustion. This discovery enables us to enter a new paradigm of human performance management. Using a new chaotic
spoken voice analysis method, it will be possible to measure the so-called “human cerebral resource condition” and “humancerebral activity level” under normal working conditions. The cereameter is am implementation of this voice signal
processing technology. The newest and smallest cereameter has an ability to diagnose the human subjects’ exhaustion fromhis or her utterance of five seconds in real time.
Keywords:

human voice, cerebral activity, fatigue management, chaos theory
1. INTRODUCTION
If the cereameter is able to measure actual human cerebral
resource condition and its activity level, it would give a
top stream preventive safety device for any industrial
fields.

The “cereameter” is a Cerebral Resource and Activity
Measurement Equipment developed at ENRI by the author
and collaborative companies.
We believe that the
cereameter is able to measure human cerebral conditions
by analyzing his or her uttered voice. It is named“CENTE” and provided as equipment for researchconcerning to human factor and human performance by
one of collaborative companies. Fig. 1 shows the newest
and smallest cereameter stand-alone system consists of amain body of CENTE and a microphone. The main bodyconsists of a small computer as a signal processor, anaudio input and output device, and a LCD with touch input
device.

Figure 1

2. BACKGROUND
In 1994, ENRI developed and built a total computer
graphics virtual reality simulation facility for airports andairspace Air Traffic Control (ATC) simulation in real time.
Fig. 2 and Fig. 3 show the inside and outside views of the
facility.

Figure 2

Newest and Smallest “cereameter” Named “CENTE”

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Inside of Virtual Reality Simulation Facility

K. Shiomi

In 1994, the author developed ATC workstation as a userinterface system for an ATC controller to access Aircraft
Flight Data Management System, and to communicate
with pilots of aircrafts via digital data link.
Fig. 5 is a prototyped ATC workstation for an airport ATC
controller. The infrared remote control device at the ATCworkstation could put out the ATC instructions.

Figure 3

In 1994, while we were developing the virtual reality
simulation facility, a serious aircraft accident was
happened. On April 26th, China Airlines Flight 140 was
crashed at “Komaki” Nagoya International Airport.
“Human Factor” and “Human Error” as terms attracted
attention as a cause o the accident, and the system designof Airbus A300-600 was improved after this accident.

Outside View of Virtual Reality Simulation Facility

The virtual reality simulation facility that has a projection
screen whose diameter of 15m, and height of 6m, was thelargest in the world in 1994.

After this accident the author was requested from theinvestigation committee to make an animation movie forreproducing the behavior of the crashed aircraft. And theauthor was also requested to develop software to improvearticulation of the recorded pilot’s voice in the cockpit
voice recorder.

Fig. 4 shows one scene of air traffic control simulation of“Haneda” Tokyo International Airport. In this picture, one
aircraft had just taken-off and vertical take-off and landing
aircraft V-22 “Osprey” was flying.

In 1994, the author started to develop software todiscriminate human voice from mechanical noises in order
to extract pilots’ voices from recordings those wereretrieved from an aircraft cockpit voice recorder. In 1998,
by chance, after about five years from the starting ofdevelopment, the author and Mr. Shozo Hirose a
researcher worked at OGIS-R.I. discovered that the time
averaged values of the first Lyapunov exponent calculated
from human voice changes according to the speaker’s
psychosomatic condition.

Figure 4

One Scene of Airport Traffic Control Simulation

Figure 6

Figure 5Long Reading Aloud Experiment Demonstration

Fig. 6 and Fig. 7 are pictures captured from BBC WorldNews broadcasted in 2000. We had demonstrated a longtime reading aloud experiment as shown in Fig. 6. Fig. 7
shows the “Look and Feel” of the graphical user interfaceof the first prototyped voice analysis system.

The Airport ATC Workstation

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ENRI Int. Workshop on ATM/CNS. Tokyo, Japan. (EIWAC 2010)
When a strange attractor is reconstructed from a longsingle vowel sound, it can be analyzed approximately bymethods proposed in current chaos theory. These showthat the fractal dimension of the human voice is four or
higher, and that the first Lyapunov exponent is positive. A
reconstructed strange attractor can be thought of as avisualization of a time series signal, and the author
believes that the first Lyapunov exponent indicate thedegree of fluctuation of a time series.

Figure 7

Fig. 10 and Fig. 11 show the change in fluctuations in a
vocalized the “oh” sound extracted from a railway driver’s
verbal call-out “Heisoku Shinkoh!” (“Proceed into thenext block”). The strange attractor on Fig. 10 was
generated from a voice recording taken some tens ofminutes after the start of a driving exercise in a railroad
simulator, and that on Fig. 11 was generated from a voicerecording taken after about five hours of simulated driving.
Five hours of simulated railroad driving causes fatigue,
and the author hypothesized that the degree of fluctuationsin the spoken voice decreased as the speaker tired.

Look & Feel of a Voice Analysis System

3. CHAOTIC VOICE ANALYSIS
3.1 Strange Attractor
It can be shown that the human voice has chaotic
characteristics by reconstructing its strange attractor inphase space according to Takens’ embedding theorem asshown in Fig. 8 and Fig. 9.[1,2,3]

Figure 10

Figure 8

Strange Attractor of voiced “o” sound:the speaker is not fatigued.

“o” Sound Wave Form

Figure 11 Strange Attractor of voiced “o” sound:the speaker is sleepy with exhaustion.

Figure 9

3.2 Variations of Lyapunov Exponent
In the earliest experiment conducted at OGIS-R.I. by Mr.
Hirose in September 1998, a recorded voice signal was
divided into one-second long processing units, and the first“o” Sound Strange Attractor

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K. Shiomi
Lyapunov exponent was calculated for each processing
unit. Fig. 12 and Fig. 13 show changes of the timeaveraged value of the first Lyapunov exponent with anaveraging window size of five minutes. [4,5]In the early 2000s, the author believed simply that the
time-averaged first Lyapunov exponent calculated fromthe spoken voice might be useful as an index formeasuring human tiredness level, since its value appears toincrease when a speaker’s workload level is comparatively
high.

In the case shown in Fig. 12, a male test subject began
reading a story after lunch in the afternoon, and felt tired
and stopped reading after about 50 minutes. Fig. 12 showsthat the 5-minute average of the first Lyapunov exponent
increased by about 120%, and reached this level about 20
minutes before the test subject noticed his tiredness
himself. Fig. 12 shows the typical variations of timeaveraged first Lyapunov exponent observed from longreading aloud voice signal.

4. HUMAN STRESS & CEREBRAL EXPONENTIn 2000, we stepped into the next phase of research anddevelopment of chaotic voice analysis.

In the case shown in Fig. 13, a female test subject read a
newspaper in the morning immediately after arriving at her
office. The time averaged first Lyapunov exponent
maintained a comparatively high level while she read thepolitics and economics pages, but decreased by about 70%
when she moved to the sports pages.

4.1 Human Stress and Variations of Lyapunov Exp.
Fig. 14 and Fig. 15 show the environment for recording ofreading voice.

From these results, we hypothesized that a high value ofthe first Lyapunov exponent might correspond to highmental workload, since politics and economics pages
contain many difficult concepts described with complex
Chinese characters. But now in 2010, the author thinks
simply that the test subject did not be interested in sports.

Figure 12

Variations of Time-Averaged First Lyapunov Exponent of
Voice Signal (Reading a Novel)

Figure 13

Variations of Time-Averaged First Lyapunov Exponent of
Voice Signal (Reading a Newspaper)

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Figure 14

Equipments for Reading Experiments

Figure 15

Environments of Reading Experiments

ENRI Int. Workshop on ATM/CNS. Tokyo, Japan. (EIWAC 2010)
As shown in Fig. 14, this environments for experimentconsisted of a display to present texts for reading, andmany audio equipments, such as a high-performancecondenser-microphone, a microphone amplifier, an audio
signal delay and effects processor, a digital audio taperecorder and so on. And as shown in Fig. 15, the test
subject wore a headset laud speakers, and his reading
voice could be able to give him as feedback.

To evaluate the fluctuation level of general speech from its
chaotic characteristics, it is necessary to define a newindex or exponent that could be said to be the first timelocal Lyapunov exponent. [8]In 2002, the author succeeded in defining such indices oftime-local chaotic characteristics, which are termed the“Cerebral Exponent micro (CEm)” and the “Cerebral
Exponent Macro (CEM).” Since it is hypothesized that the
CEM values indicate human cerebral activity, the author
created an algorithm named SiCECA (Shiomi’s Cerebral
Exponent Calculation Algorithm) to calculate the CEM
rapidly.

Fig. 16 shows the first expected result obtained in theexperimental environment mentioned above. The fiveminutes time-averaged values of the first Lyapunov
exponent were increased from about 500 to about 540 after
starting of voice feedback. It can be thought that theincrease of the values means that voice feedback gave
mental stress to the test subject, and then the cerebral
activity level of the test subject was changed to higher.

CEm/M can be calculated from time series even if it is not
sampled from voice signal. But in this paper, all CEm/M
values are calculated from human voice signal.
4.3 Simplest Experiment and Results
4.3.1 Method
A subject reads aloud from one reading card under two
conditions. The reading card is an excerpt from an old
Japanese tale that can be read in about ten or less seconds.
The subject first reads the card normally. The subject thenreads the same card again but with his/her fingers in
his/her ears to induce mental stress. Each reading voice
was recorded using a microphone and a PCM recorder atsampling frequency of 48.0 kHz with 16 bits/sample.

Figure 16

A total of 41 subjects participated in the experiment: 36
males and five females.

Variations of Time-Averaged First Lyapunov Exponent of
Reading Voice under Mental Stressed Condition

4.3.2 Results
Fig. 18 shows CEM values that calculated from the utteredvoice recordings of the card readings. For each subject,
the CEM values are plotted as a point on a graph with thenormal Reading-CEM value along the abscissa, and themental stress CEM value along the ordinate. For instance,
the point labeled subject-A in Fig. 18 shows the case of anormal Reading-CEM value of about 460, and a stressed
Reading-CEM value of about 580.

4.2 Cerebral Exponent micro / Macro
Through the experiments mentioned above, the author
understood that the first Lyapunov exponent is not
sufficient as a measure of the degree of fluctuation in theuttered voice. To calculate the first Lyapunov exponent,
the system that generates the time series signal must be
sufficiently stable, but since general speech contains many
phonemes per second, it is not possible to calculate thefirst Lyapunov exponent directly from a complex generalspeech signal containing two or more vowels.
There are five vowel sounds in Japanese, ”a”, “i”, “u”, “e”
and “o”, and each has its own unique shaped strange
attractor. When a Japanese railroad conductor announces“Tsugi wa Koenji! (The next stop is Koenji),” the shape ofthe strange attractor changes as shown in Fig. 17.

Figure 17

Figure 18

Strange Attractors Re-Constructed from Japanese Five
Vowels “a”, ”i”, ”u”, ”e” and “o.”199

A Distribution of CEM Values

K. Shiomi
Points along the diagonal line (x=y) have no difference
between the CEM values in each experimental condition(normal / stressed), while points above the line have higher
CEM values in the stressed condition than in the normal
condition. It is considered that subjects become more
conscious of the sound of their voice when closing theirears, and the stress this causes increases the CEM value.
As Fig. 18 shows, the majority of points do indeed lie
above the x=y line. For other points, it may be the casethe some subjects were initially stressed for some reason
causing their normal Reading-CEM values to becomparatively high, resulting in a smaller differences
between their “normal” and “stressed” reading states.
Also, the average female CEM values appears to besmaller those of males.
The author believes that this experiment has confirmedthat the quantitative evaluation of human cerebral activity
had become possible by processing uttered voice signals
by the SiCECA algorithm.
5. ANOTHER FOUNDAMENTAL EXPERIMENT
We thought that it was necessary to investigate thecharacteristics of CEm/M.

Figure 19

Timetable of Mental Arithmetic Calculation Experiment5.1.2 Arithmetic Exercise as Mental Workload
Mental workload was provided by simple mentalarithmetic calculations: two one- or two-digit numbers
were presented aurally, and the subjects were required toanswer the sum of the numbers by voice within fiveseconds, or before the presentation of the next pair of
numbers as shown in Fig. 20. Each single exercise
required the subject to perform 60 calculations in 10
minutes.

5.1 Mental Workload and CEM
5.1.1 Timetable and Subjects
In 2005, another fundamental experiment was carried out
to investigate the relationship between mental workload
and the CEM value. The experiment consisted of a numberof short mental arithmetic exercises each of which could
be carried out in about 20 minutes, as shown in Fig. 19.
A subject’s arousal level can be estimated from the change
of Critical Flicker Frequency (CFF) values and subjective
Visual-Analog-Scale of Sleepiness-Level (VAS-SL)
scores.
In mental arithmetic exercises, mental workload level canbe estimated from the number of wrong answers (NWA),
the subjective Visual-Analog-Scale of Fatigue-Level(VAS-FL) score, and cardiac pulse rate (Heart Rate: HR).
HR also indicates the difficulty of exercise. These were
measured in the experiment and compared with CEM
values derived from voice recordings.

Figure 20

Six adult males participated in the experiment. Their ages
were ranged from 25 to 50 years (mean: 36.4, standard
deviation: 9.7). Each subject performed three exercises
under the conditions of light, medium and heavy workload,with one exercise per condition.

Number Presentation Patterns of Arithmetic Exercise

The exercise workload level was varied between light,
medium and heavy by adjusting the difficulty of thecalculations. In the light workload case, two single-digit
numbers A and B were presented, and subjects wererequired to speak their sum C (= A+B). In the medium andheavy workload cases, two two-digit numbers were
presented as four single-digits A, B, C and D, and subjects
were required to speak E (= {10A+B} + {10C+D}) as

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ENRI Int. Workshop on ATM/CNS. Tokyo, Japan. (EIWAC 2010)
shown in Fig. 20. In the medium workload case, 80% of
the calculations had the condition that (A+C < 10) and(B+D < 10). In the heavy workload case, 50% of
calculations had the condition that (A+C > 10) and (B+D >10), 45% of calculations had the condition that (A+C > 10)or (B+D > 10), and only 5% of calculations had thecondition that (A+C < 10) and (B + D < 10).

2.
3.
4.

5.1.3 Measurement Methods and Results
Before and after each mental arithmetic calculation
exercise, a subject’s CFF values were measured, and heread aloud from a text to obtain a “Reading-CEM” value.

5.
6.

The subject also made “check mark” indications to record
his subjective sleepiness level on a VAS-SL scale, and his
subjective fatigue level was on a VAS-FL scale as shownin Fig. 21 according to how sleepy and tired he felt.
During each exercise, the NWA was counted, and HR was
measured, and the subject’s verbal responses wererecorded to determine “Callout-CEM” values.

Figure 21
Table 15.1.4 Characteristics of CEM
The CEM value calculated from verbal responses duringmental arithmetic exercises appears to correlate with thedifficulty of the exercise as well as with traditional
measurement methods and indices of human arousal level.
As the result, it is suggested that it may be possible tomeasure human arousal level by calculating the CEM
value. Our experiment also shows that the Reading-CEM
calculated from utterances recorded during reading out
loud from a presented text, differ from Callout-CEM
calculated from utterances without any text. The author
believes that this discrepancy may arise due to the fact thatthe reading aloud voice for Reading-CEM is voice output
from the subject’s main task, but the call-out voice for
Callout-CEM is one from a subtask.

Visual-Analog-Scales and “Check Marks”

Averaged values and standard deviations of indices measured
during the experiments.

Fig. 22 shows the relationship between the Callout-CEM
value and workload level of exercise (Relationship-A), andthe relationship between HR and workload level(Relationship-B). The trend shown in Relationship-A isdifferent from that of the Relationship-B, and then the
Callout-CEM seems to show the state of the function of
the neo cortex while the HR shows the state of thefunction of the autonomic nervous system.

The Student’s t test was used for comparison between the Light and Med.
groups, the Med. and Heavy groups, and the Light and Heavy groups.
A probability value p < 0.01 was considered statistically significant.
Table 2to the increase of workload.
The averages of HR during answering eachcalculation increase according to the increase ofworkload.
The averages of Callout-CEM increase according to
the increase of workload.
The values of CFF and Reading-CEM decrease
according to the increase of workload.
The change of the VAS-FL value before exercise andthe value after exercise increases according to theincrease of its workload.
VAS-SL for light workload exercises was positive(i.e. indicating drowsiness), but for medium andheavy-workload levels all subjects reported little
drowsiness.

Averaged values and standard deviations of indices measured
before and after the experiment.

The Students’ t test was used for comparison between the groups.
A probability value p < 0.05 was not considered statistically significant.
Figure 22 Relationship between Callout-CEM Value And Workload
Level (Blue), and between Heart Rate and Workload Level (Red)

Table 1 and 2 show the results of experiment. These leadto the followings findings.
1.

The proportion of wrong answer increases according

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K. Shiomi
6. FATIGUE MEASUREMENT EXPERIMENT

Fig. 24 shows the timetable of the experiment. Eachsubject spent three days to be familiar with the driving
simulator. Then the last two days were for fatigue
measurement test. Subjects were requested to carry out
about 12-minutes train driving exercises over and over in
two days. At first, subjects performed a set of train
driving exercises during the morning, followed by fourhours of physical exercise in the afternoon to induce
fatigue and sleepiness, then subjects were requested toperform eleven hours of driving exercises from about 6
p.m. in the evening to about 5 a.m. of the next morningwith two breaks during the period, sleep from 6 a.m. tonoon, and then performed a final train driving session.
The physical exercise consisted of walking up and down
stairs shouldering a weight of more than 20 kg. To obtainspoken voice signals for assessing fatigue level, between
train driving exercises, subjects were requested to readthree cards containing excerpts from Japanese folk tales.
Each card could be read in about ten seconds. In addition
to the card reading, while exercise subjects were requested
to speak some predetermined short call-out periodically inthe simulator cab. The Voice recording was by a headset
microphone and a PCM sound recorder at sampling
frequency of 48.0 kHz with 24 bits/sample. The CFF
values were also measured at the same time for reference.

We thought that it was necessary to find an appropriate
combination of SiCECA processing parameters that gave
the greatest cross-correlation coefficient between thepattern of changes of Reading-CEM values and that of
CFF values.
6.1 An Experiment Using A Railroad Simulator[10]6.1.1 Experimental Environments, Test Subjects and Etc.
A fatigue measurement experiment was carried out using arailroad-driving simulator as shown in Fig.23 at Railroad
Technical Research Institute (Tokyo, Japan) from 1 Aug.
to 29 Sep. 2005. Eleven male university students andpostgraduates participated in the experiment. As results,
effective data were obtained from ten of the subjects.

6.1.2 Typical Result of ExperimentFig. 25 shows results of typical subjects.

Figure 23

In the case of Fig. 25, card Reading-CEM and CFF show
similar trends, and the cross-correlation coefficient
between the pattern of changes of Reading-CEM and CFF
is more than 0.6 under the data size of 49. On the other
hand, Callout-CEM increases with the passage of time. It
can be thought that the subject was relaxed and could

Railroad-Driving Simulator

Figure 24

Timetable of Experiment202

ENRI Int. Workshop on ATM/CNS. Tokyo, Japan. (EIWAC 2010)

Figure 25

Typical Experimental Result Obtained from Test Subject 3

easily handle the task at the start of the continuous work
period, and it might be not difficult for him to perform thetask correctly, but eventually he was getting harder tomaintain performance.

Subjects slept in the observation room a night before thetest day, and the test started from the next morning. The
test consisted of driving around the oval course for 10
times, starting at the front of the observation room,
returning to the front of the observation room. When thesubject returned back to the observation room, then subject
took 10 minutes break for rest. This scenario of the test
was repeated 5 times before noon without breakfast andtook a lunch, then repeated 5 times in the afternoon. A
longer break was given after the 8th test.

6.2 An Experiment Using An Actual Vehicle
6.2.1 Experimental Environments, Test Subjects and Etc.
In 2006 and 2007, for assessment of the degree of fatigue
from human voice while driving in real world, an
experiment was conducted using an actual vehicle.

Subjects were forced to keep driving speed at 40km/h.
This was because we intended to induce dozing off ofdrivers by such a slow speed. Reading cards were
performed at the front of observation room and voice
during driving was recorded by having drivers speak"Passing checkpoint X. Speed okay," when passing eachcheckpoint of 1, 2, 3 and 4 on the course.

A compact truck was used as the vehicle for the test andprofessional truck drivers participated as test subjects. Fig.
26 shows the pictures of the cockpit of the test vehicle andthe test course whose configuration is as shown in Fig. 27
in Tomakomai, Hokkaido.

6.2.2 Typical Result of Experiment
As an example, Fig. 28 plots, for a driver, average valuesof Callout-CEM values for 10 minutes in red dots. A
strong and distinguishing trend of decreasing of CEM wasobserved especially in tests after lunch. It can be said thatthe subject had performed driving task with strong senseof sleepiness.

Figure 26

Pictures of Experiment

Figure 28

Typical Experimental Result

If we had a “Fatigue and Drowsiness Predictor (FDP)” andset the alarm level to 500 CEM, the FDP had made alert
Figure 27

Configuration of The Test Course203

K. Shiomi
sound around 1:30pm to warn of dozing off of driver fromhis voice.

[4] Shiomi and Hirose, “Trial for detecting sleepiness andfatigue of a speaker from his/her voice.” Proc. of 37th
Airplane Symposium, Japan, 1999.
[5] Shiomi and Hirose, “Fatigue and Drowsiness

7. CURRENT STATUS & FUTURE PLAN

Predictor for Pilots and Air Traffic Controllers,” Proc.
of 45th Annual ATCA Conference, Oct. 2000.

It is possible to quantify fluctuation level of human voice.
As the result of experiments, it was observed fluctuationlevel of human voice changed according to speaker’s
psychosomatic condition. Fluctuation levels of the test
subjects were decreased after a long time driving exercise
in the railroad simulator and the actual vehicles.

[6] Aihara, “Guide of chaotic theory”, Teaching materialof University of the Air, 2001.
[7] Takaoka, Shiomi and et al., “On the possibility ofdiagnosing the psychosomatic state of a speaker from
his/her spoken voice,” General Health Check, Vol.29,
No.3, 2002.

In June 2008, the US National Transportation Safety
Board issued Safety Recommendations A-08-44 and -45(NTSB 2008) in which it recommended that the US
Federal Aviation Administration develop and introduce
fatigue management systems based on empirical andscientific evidence. [11] In 2010, ENRI started research toevaluate workload of air traffic controllers according to therequest from Japanese Civil Aviation Bureau. ENRI is
now preparing the equipment for recording and analyzing
ATC controllers’ voices.

[8] Shiomi, “Chaotic Voice Analysis and Model of

Cerebral Dynamics,” Journal of Japan Society ofKansei Engineering, Vol.4, No.1, pp.3-12, 2004.
[9] Shiomi, “Voice Processing Technique for Human

Cerebral Activity Measurement,” Proc. of IEEE-SMC
2008, P0660, Singapore.
[10] Shiomi, Sato and et.al., “Experimental Results of

Measuring Human Fatigue by Utilizing Uttered Voice
Processing,” Proc. of IEEE-SMC 2008, P557,
Singapore.

8. ACKNOWLEDGMENTS[11] NTSB 2008. Safety Recommendation A-08-44 and045.
Mr. Kiyoshi Sato, a former senior researcher at theRailroad Technical Research Institute in Japan, conducted
the fatigue measurement experiment mentioned in section
5 and 6.

[12] Shiomi, “Chaotic Voice Analysis Method for Human

The system of uttered voice chaotic analysis used in theexperiments described in this paper has been granted thefollowing patents in the U.S.A.: US 6,876,964 (Oct. 19,
2005), US 7,321,842 (Jan. 22, 2008), US 7,363,226 (Apr.
22, 2008) and so on.

Human Arousal Level Evaluation,” Proc. of ESREL2010, Rohdos.

Performance Monitoring,” Proc. of ESREL-2009,
Prague.
[13] Shiomi and Sato, “Chaotic Voice Analysis Method for

10. COPYRIGHTThe authors confirm that they, and/or their company or
institution, hold copyright of all original material includedin their paper. They also confirm they have obtained
permission, from the copyright holder of any third party
material included in their paper, to publish it as part oftheir paper. The authors grant full permission for the
publication and distribution of their paper as part of the
EIWAC2010 proceedings or as individual off-prints fromthe proceedings.

9. REFERENCES[1] Takens, “Determining strange attractors inturbulence,” Lecture Note in Mathematics, vol. 898,
pp.366–381, 1981
[2] Sano and Sawada, “Measurement of the Lyapunov

Spectrum from a Chaotic Series,” Physical Review
Letters, Vol.55, No.10, pp.1082-1085, 1985.
[3] Ikeguchi and Aihara, “Lyapunov Spectral Analysis on

Random Data,” International Journal of Bifurcation
and Chaos, Vol.7, No.6, 1267-1282, 1997.

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