A HIGHER-ORDER STATISTICS-BASED VIRTUAL INSTRUMENT

FOR TERMITE ACTIVITY TARGETING

Juan Jos´e Gonz´alez de la Rosa, Jos´e Melgar Camarero, Stephane Bouaud, J. G. Ramiro

Univ. C´adiz, Electronics Area, Research Group PAI-TIC-168, EPSA, Av. Ram´on Puyol S/N, E-11202-Algeciras-C´adiz, Spain

Antonio Moreno Mu˜noz

Univ. C´ordoba. Electronics Area. Research Group PAI-TIC-168

Campus Rabanales, A. Einstein C-2, E-14071, C´ordoba, Spain

Keywords: Acoustic Emission, Discrete Wavelet Transform, Higher-Order Statistics, Insect detection, Spectral kurtosis,

Transient detection.

Abstract: In this paper we present the operation results of a portable computer-based measurement equipment conceived

to perform non-destructive testing of suspicious termite infestations. Its signal processing module is based

in the spectral kurtosis (SK), with the de-noising complement of the discrete wavelet transform (DWT). The

SK pattern allows the targeting of alarms and activity signals. The DWT complements the SK, by keeping

the successive approximations of the termite emissions, supposed more non-gaussian (less noisy) and with

less entropy than the detail approximations. For a given mother wavelet, the maximum acceptable level, in

the wavelet decomposition tree, which preserves the insects’ emissions features, depends on the comparative

evolution of the approximations details’ entropies, and the value of the global spectral kurtosis associated to

the approximation of the separated signals. The paper explains the detection criterion by showing different

types of real-life recordings (alarms, activity, and background).

1 INTRODUCTION

Biological transients gather all the natural complex-

ity of their associated sources, and the media through

which they propagate. As a consequence, ﬁnding the

most adequate method to get a complete characteriza-

tion of the emission, implies the selection of the ap-

propriate model, which better explains the processes

of generation, propagation and capture of the emitted

signals. This description matches the issue of mea-

surement termite activity.

This paper deals with the performance of a ﬁnal-

version equipment (computer-basedsignal processing

unit), whose previous prototype’s performance, based

in the time-frequency domain analysis of the kurto-

sis, was described in (De la Rosa and Mu˜noz, 2008,

). In this ﬁnal version, the measurement method is

mainly based in the interpretation of the spectral kur-

tosis graph, along with the wavelet analysis, which is

thought as an aid. At the same time, we use a simple

data acquisition unit, the sound card (maximum speed

at 44,100 Hz), which simpliﬁes the hardware unit and

the criterion of detection.

The instruments for plague detection are thought

with the objective of decreasing subjectiveness of the

ﬁeld operator. On-site monitoring implies reproduc-

ing the natural phenomenon of insect emissions with

high accuracy. As a consequence it is imperative the

use of a deep storage device, and high sensitive probes

with selective frequency characteristics. These fea-

tures make the price paid very high, and still do not

guarantee the success of the detection. Besides, the

expert’s subjectiveness plays a crucial role, because

only trained ﬁeld operators can separate the signals of

interest from the non-usable background.

Regarding the procedures, the methods in which

the instruments are based are very much dependent on

the detection of excess of power in the signals; these

are the so-called second-order methods. For example,

the RMS calculation can only characterize the inten-

sity (amplitude level of the signal), and does not pro-

vide information regarding the envelope of the signal

nor the time ﬂuctuations of the amplitude. Another

handicap of the second-order principle, e.g. the clas-

sical power spectrum, attends to the preservation of

the energy during data processing. Consequently, the

eradication of additive noise lies in ﬁlter design and

sub-band decomposition, like wavelets and wavelet

155

José González de la Rosa J., Melgar Camarero J., Bouaud S., G. Ramiro J. and Moreno Muñoz A. (2008).

A HIGHER-ORDER STATISTICS-BASED VIRTUAL INSTRUMENT FOR TERMITE ACTIVITY TARGETING.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - SPSMC, pages 155-162

DOI: 10.5220/0001493701550162

 SciTePress

packets.

As an alternative to improve noise rejection and

complete characterization of the signals, in the past

ten years, a myriad of higher-order methods are being

applied in different ﬁelds of Science and Technology,

in scenarios which involve signal separation and char-

acterization of non-Gaussian signals. Concretely, the

area of diagnostics-monitoring of rotating machines

is also under our interest due to the similarities of the

signals to be monitored with the transients from ter-

mites. Many time-series of faulty rotating machines

consist of more-or-less repetitive short transients of

random amplitudes and random occurrences of the

impulses.

This paper describes a method based in the spec-

tral kurtosis (related to the fourth-order cumulant at

zero lags) to detect infestations of subterranean ter-

mites in a real-life scenario (southern Spain). Wavelet

decomposition is used as an extra tool to aid detection

from the preservation of the approximation of the sig-

nal, which is thought to be more Gaussian than the

details.

The interpretation of the results is focussed on the

classical peakedness of the statistical probability dis-

tribution associated to each frequency component of

the signal, to get a measure of the distance from the

Gaussian distribution. The spectral kurtosis serves as

a twofold tool. First, it enhances non-Gaussian sig-

nals over the background. Secondly, it offers a more

complete characterization of the transients emitted by

the insects, providing the user with the probability as-

sociated to each frequency component.

The paper is structured as follows: in Section 2 a

review on termite detection and relevant HOS expe-

riences sets the foundations. In Section 3 we make a

brief report on the deﬁnition of kurtosis; we use an

unbiased estimator of the spectral kurtosis, success-

fully used in (De la Rosa and Mu˜noz, 2008, ), using

a higher measurement bandwidth. Results are pre-

sented in Section 5. Finally, conclusions are drawn

in Section 6.

2 TERMITE DETECTION AND

HIGHER-ORDER STATISTICS

2.1 Subterranean Termites:

Fundamentals

Termites have become a threat in all the modern coun-

tries, mainly due to the advent of central heating in the

buildings. Cause more damage to homes in U.S.A.

than storms and ﬁre combined, on the average, there

could be as many as 15 to 20 subterranean termite

colonies per hectare, which means that for example

a typical U.S.A. home may easily have three to four

colonies situated under or around it. Colonies can

contain up to 1,000,000 members (De la Rosa and

Mu˜noz, 2008, ).

Termite detection has been gaining importance

within the research community in the last two

decades, mainly due to the urgent necessity of avoid-

ing the use of harming termiticides, and to the joint

use of new emerging techniques of detection and hor-

monal treatments (IGR

products), with the aim of

performing an early treatment of the infestation. A

localized partial infestation can be exterminated af-

ter two or three generations of the colony’s members

with the aid of these hormones, which stop chitin syn-

thesis. A chitin synthesis inhibitor kills termites by

inhibiting formation of a new exoskeleton when they

shed their existing exoskeleton. As a direct conse-

quence, the weakened unprotected workers stop feed-

ing the queen termite of the colony, which dies of star-

vation, ﬁnishing the reproduction process, and conse-

quently cutting any possible replacement of the mem-

bers of the colony with a new generation. In this paper

the specie reticulitermes lucifugus is under study.

2.2 Subterranean Termites: Detection

Project towards HOS

The primary method of termite detection consists of

looking for evidence of activity. But only about 25

percent of the building structure is accessible, and the

conclusions depend very much on the level of exper-

tise and the criteria of the inspector (De la Rosa and

Mu˜noz, 2008, ),(Robbins et al., 1991). As a conse-

quence, new techniques have been developed to re-

move subjectiveness and gain accessibility.

User-friendly equipment is being currently used in

targeting subterranean insect infestations by means of

temporal analysis of the vibratory data sequences

An acoustic-emission (AE) sensor or an accelerome-

ter is ﬁxed to the suspicious structure. This class of in-

struments is based on the calculation of the root mean

square (RMS) value of the vibratory waveform. The

RMS value comprises information of the AE raw sig-

nal power during each time-interval of measurement

(averaging time). This measurement strategy conveys

a loss of potentially valuable information both in the

time and in the frequency domain (De la Rosa and

Mu˜noz, 2008, ).

Inhibitor Growth Regulators

The system AED2000 (Acoustic Emission Consulting)

has proven to be an advance in the detection of several insect

species.

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156

On the other hand, the use of the RMS value

can be justiﬁed both by the difﬁculty of working

with raw AE signals in the high-frequency range, and

the scarce information about sources and propagation

properties of the AE waves through the substratum.

Noisy media and anisotropy makes even harder the

implementation of new methods of calculation and

measurement procedures. A more sophisticated fam-

ily of instruments makes use of spectral analysis and

digital ﬁltering to detect and characterize vibratory

signals (Mankin and Fisher, 2002).

Other complementary second-order tools, like

wavelets and wavelet packets (time-dependent tech-

nique) concentrate on transients and non-stationary

movements, making possible the detection of singu-

larities and sharp transitions, by means of sub-band

decomposition. The method has been proved under

controlled laboratory conditions, up to a SNR=-30 dB

(De la Rosa et al., 2006, ).

Higher-order statistics, are being widely used in

several ﬁelds. The following are relevant due to the

similarities of the problems they study. The spectral

kurtosis has been successfully described and applied

to the vibratory surveillance and diagnostics of rotat-

ing machines (Antoni, 2006a),(Antoni, 2006b), show-

ing an inedit set of results that include kurtogram-

based calculations of optimal band-pass ﬁlters and

their performance in detecting two types of machin-

ery faults (ball faults and outer race fault in rolling

elements bearings); the kurtosis of the ﬁltered signals

is enhanced, which improves the detection of the fault

type under study.

In the ﬁeld of insect detection, the work presented

in (De la Rosa and Mu˜noz, 2008, ) set the founda-

tions of the present paper. The combined used of the

spectral kurtosis and the time-domain sliding kurtosis

showed marked features associated to termite emis-

sions. In the frequency domain (sample frequency

64,000 Hz) three frequency zones were identiﬁed in

the spectral kurtosis graph as evidence of infestation;

two in the audio band (which will be also checked in

the present paper) and one in the near ultrasound (≈

22 kHz). In the present paper the sample frequency

was ﬁxed to 44,100 Hz and the sound card was di-

rectly driven by MATLAB, which presents the results

in an user-oriented interface, which is forwarded in

Fig. 1. In the measurement situation shown in Fig.

1, the time-raw data contains alarms an activity sig-

nals from termites. This is a clear example of positive

detection.

The developed virtual instrument also calculates

and presents the spectrum (up-right graph) and the

raw data (bottom-left). The ﬁeld operator adds there-

fore visual information to the classical audio-based

Figure 1: The graphical user interface which presents the

results to the ﬁeld operator. The spectral kurtosis is in the

bottom-right corner.

criterion, which was by the way very subjective and

very expertise-depend.

Other relevant achievements related to HOS are

the following. Cumulants have been modeled in order

to characterize the ultrasound waves in materials (Mi-

ralles et al., 2004). Bi-cepstrum, have been success-

fully used in blind identiﬁcation of acoustic emissions

(Iturrospe et al., 2005). Bi-spectrum has been applied

to enhance reﬂections in ring-type samples of steel

pipes, in a non-destructive testing frame (De la Rosa

et al., 2007b, ).

In the ﬁeld of termite detection, a cumulant-based

independent component analysis algorithm has

proven to separate termites’ alarm signals from

synthetics noise backgrounds (De la Rosa et al., 2005,

) in a blind source separation scenario. The informa-

tion contained in the diagonal of the bi-spectrum data

structure has proven to enhance the frequency pattern

of the termites’ emissions (De la Rosa et al., 2007a,

). The conclusions of these works were funded in

the advantages of cumulants; in particular, in the

capability of enhancing the SNR of a signal buried

in noise processes, whose probability dnsity function

is symmetrically distributed. The computational

cost (memory consuming) could be pointed as the

main drawback of the technique. Calculation of

the cumulants’ is made for all the combinations of

time lags, giving rise to complex multidimensional

data structures. The exam of this data sets leads to

the selection of a privileged direction, whose which

data are analyzed. In this paper, time-lags are set

to zero in order to reduce the cost of computation.

Statistically speaking, zero time lags lead to kurtosis,

in a fourth-order cumulant.

A HIGHER-ORDER STATISTICS-BASED VIRTUAL INSTRUMENT FOR TERMITE ACTIVITY TARGETING

157

3 KURTOSIS AND SPECTRAL

KURTOSIS

3.1 Kurtosis, 4th-order Cumulants and

its Interpretation

Kurtosis is a measure of the ”peakedness” of the prob-

ability distribution of a real-valued random variable.

Higher kurtosis means more of the variance is due to

infrequent extreme deviations, as opposed to frequent

modestly-sized deviations. This fact is by the way

used in this paper to detect termite emissions in an ur-

ban background. Kurtosis is more commonly deﬁned

as the fourth central cumulant divided by the square

of the variance of the probability distribution, which

is the so-called excess kurtosis:

− 3, (1)

where µ

= κ

+ 3κ

is the 4th-order central mo-

ment; and κ

is the 4th-order central cumulant, i.d.

the ideal value of Cum

4,x

(0, 0, 0). This deﬁnition of

the 4th-order cumulant for zero time-lags comes from

a combinational relationship among the cumulants of

stochastic signals and their moments, and is given by

the Leonov-Shiryaevformula. A complete description

for these statistics are found for example in (Nikias

and Mendel, 1993; Mendel, 1991; Chonavel, 2003).

The ”minus 3” at the end of this formula is a cor-

rection to make the kurtosis of the normal distribution

equal to zero. Excess kurtosis can range from -2 to

+∞.

The sample kurtosis is calculated over a sample-

− 3 =

i=1

− ¯x)

i=1

− ¯x)

− 3,

(2)

where m

is the fourth sample moment about the

mean, m

is the second sample moment about the

mean (that is, the sample variance), and ¯x is the sam-

ple mean. The sample kurtosis deﬁned in Eq. (2)

is a biased estimator of the population kurtosis, if we

consider a sub-set of samples from the population (the

observed data).

3.2 Spectral Kurtosis Estimation and

Interpretation

Ideally, the spectral kurtosis is a representation of the

kurtosis of each frequencycomponent of a process (or

data from a measurement instrument x

). For esti-

mation issues we will consider M realizations of the

process; each realization containing N points; i.d. we

consider M measurement sweeps, each sweep with N

points. The time spacing between points is the sam-

pling period, T

, of the data acquisition unit.

A biased estimator for the spectral kurtosis for a

number M of N-point realizations at the frequency

index m, is given by:

N,M

2,X

(m) =

M − 1







(M + 1 )

i=1

(m)|



i=1

(m)|



− 2







(3)

This estimator is the one we have implemented in

the program code in order to perform the data com-

putation and it was also used successfully in (Vrabie

et al., 2003; De la Rosa and Mu˜noz, 2008, ).

Regarding the experimental signals, we expect to

detect positivepeaks in the kurtosis’s spectrum, which

may be associated to termite emissions, character-

ized by random-amplitude impulse-like events. This

non-Gaussian behavior should be enhanced over the

symmetrically distributed electronic noise, introduced

in the measurement system. Speech is perhaps also

reﬂected in the spectral kurtosis but not in the fre-

quencies were termite emissions manifest. Besides,

we assume, as a starting point, that non-Gaussian

behavior of termite emissions is more acute than in

speech. As a consequence, these emissions would be

clearly outlined in the kurtosis spectrum. As a ﬁnal

remark, we expect that constant amplitude interfer-

ences are clearly differentiate due to their negative

peaks in the spectral kurtosis. To show the ideal per-

formance of the estimator, which has been described

in these lines, and also described in (De la Rosa and

Mu˜noz, 2008, ), we show an example based in syn-

thetics. A mix of six different signals have been

designed. Each mixture is the sum of a constant-

amplitude sine of 2 kHz, a constant-amplitude sine

at 9 kHz, a Gaussian-distributed-amplitude sine al

5 kHz, a Gaussian-distributed-amplitude sine at 18

kHz, a Gaussian white noise, and a colored Gaussian

noise between 12 and 13 kHz. Each mixture (realiza-

tion or sample register) contains 1324 points.

Negative kurtosis is expected for constant-

amplitude processes, positive kurtosis should be as-

sociated to random-amplitudes and zero kurtosis will

characterize both Gaussian-noise processes.

A simulation has been made in order to show the

inﬂuence of the number of sample registers (M) in

the averaged results for the SK graph. Fig. 2 shows

a good performance because enough registers have

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158

been averaged (M=500). For M ¡ 100, roughly, per-

formance degenerates.

0 5 10 15 20

−60

−50

−40

−30

−20

−10

Frequency, kHz

Normalised amplitude, dB

Averaged−normalised power spectrum

2 kHz

fixed ampl.

9 kHz

fixed ampl.

5 kHz

random ampl.

18 kHz

random ampl.

Colored

Gaussian

noise:

12−13 kHz

0 5 10 15 20

−0.5

0.5

Frequency, kHz

Kurtosis value

Averaged spectral kurtosis

2 kHz, kurtosis≈−1 9 kHz, kurtosis≈−1

5 kHz, kurtosis>0 18 kHz

kurtosis>0

Colored

Gaussian

noise: 12−13 kHz

kurtosis≈0

Figure 2: Performance over a set of synthetics, for M=500

realizations.

Once we have expose the main criterion used by

the instrument, we make a brief recall of wavelets

transforms, which are used as a complement in the

following way. First of all, they manage to extract

the impulses buried in noise and other parasitic sig-

nals. Secondly, the successive approximations of the

signals, in the wavelet decomposition tree are sup-

posed to gather all the non-Gaussian features or com-

ponents, while the details are mainly composed by

random signals, with a high entropy. So, the global

SK (averaged SK, over all the frequency components)

will be higher as the decomposition level increases.

4 THE WAVELET TRANSFORM

DECOMPOSITION:

FUNDAMENTALS AND

DECISION CRITERIA

A mother wavelet is a function ψ with ﬁnite energy

and zero average:

+∞

−∞

ψ(t)dt = 0, (4)

This function is normalized

, kψk = 1, and is cen-

tered in the neighborhood of t=0.

ψ(t) can be expanded with a scale parameter a,

and translated by b, resulting the daughter functions

f ∈ L

(ℜ), the space of the ﬁnite energy functions,

verifying

+∞

−∞

|f(t)|

dt < +∞.

kfk =



+∞

−∞

|f(t)|



1/2

= 1.

or wavelet atoms, which remain normalized:

a,b

(t) =

√



t − b



; (5)

The CWT can be considered as a correlation between

the signal under study s(t) and the wavelets (daugh-

ters). For a real signal s(t), the deﬁnition of CWT

is:

CW T s(a, b) =

√

+∞

−∞

s(t)ψ

∗



t − b



dt; (6)

where ψ

∗

(t) is the complex conjugate of the mother

wavelet ψ(t), s(t) is the signal under study, and a

and b are the scale and the position respectively (a ∈

ℜ

− 0, b ∈ ℜ). The scale parameter is proportional

to the reciprocal of the frequency. Eq. (6) establishes

that each coefﬁcient provide numerical information

about the similarity between the signal under study

and the time-shifted frequency-scaled wavelet daugh-

ter.

The Discrete Time Wavelet Transform (DTWT)

is introduced in order to to reduce the computational

cost of calculating all these coefﬁcients. Only a sub-

set of scale and time shifts are chosen in the DTWT.

A tree-structure arrangement of ﬁlters allows the sub-

band decomposition of the signal. The original signal

passes through two complementary ﬁlters (quadra-

ture mirror ﬁlters), and two signals are obtained as

a result of a down-sampling process, corresponding

to the approximation and detail coefﬁcients.

The lengths of the detail and approximation coef-

ﬁcient vectors are slightly more than half the length of

the original signal, s(t). This is the result of the dig-

ital ﬁltering process (convolution) (Angrisani et al.,

1999). The approximations are the high-scale, low-

frequency components of the signal. The details are

the low-scale, high-frequency components.

Daubechies 5 has been selected as most similar

wavelet mother, because of the highest coefﬁcients in

the decomposition tree. Given the wavelet mother, to

show the process of selecting the maximum decom-

position level in the wavelet tree, we have adopted

a criterion based on the calculation of Shannon’s en-

tropy (information entropy), which is a measure of the

uncertainty associated with a random variable X; this

entropy denoted by H(X), and deﬁned by:

H(X) := −

i=1

p(x

) log

p(x

), (7)

where X is an N-outcome measurement process

, i = 1, ··· , N }, and p(x

) is the probability den-

sity function of the outcome x

We show this strategy via the following example,

based on real-life data, presented in Fig. 6 and in Fig.

A HIGHER-ORDER STATISTICS-BASED VIRTUAL INSTRUMENT FOR TERMITE ACTIVITY TARGETING

159

1 2 3 4 5

Entropy evolution (Shannon)

Wavelet decomposition level

Entropy

Details

Approximations

Global difference: eA

−(eA

i+1

+eD

i+1

)

Successive approximations differences eA

−eA

i+1

Figure 3: Evolution of the entropy.

7, in the results section. The entropy of the approxi-

mations and the details are compared for each level of

comparison and shown in Fig. 3.

By looking at the graph of Fig. 3, at level 4, the

entropy of the approximations is less than the entropy

of the details. So level 4 is in a sense, a point of inver-

sion. No improvement is obtained for level 5, where

the entropies are very similar.

We can also see that the global difference of en-

tropies increases towards zero, at level 5, as a com-

plementary indication that further decomposition will

not suppose progress in de-noising.

5 EXPERIMENTS AND RESULTS

5.1 The Instrument and the

Measurement Procedure

A piezoelectric probe-sensor (model SP-1L from

Acoustic Emission Consulting) is used in the ﬁnal ver-

sion of the instrument, and was described in detail in

(De la Rosa and Mu˜noz, 2008, ). The sensor is con-

nected to the sound card of a lap-top computer and the

acquisition is driven by MATLAB, via the Graphical

User Interface (GUI).

The user interface was presented in Fig. 1. The

operator can select the acquisition time and the sam-

ple frequency (maximum 44,100 Hz if the sound card

is driven). In the bottom-right corner of Fig. 1, the

spectral kurtosis graph is presented. The user can also

examine the raw data and the spectrum. Automati-

cally, the instrument save the acquired data (labeling

the ﬁle with the date). Additionally, the operator can

recall the stored ﬁles.

The transducer SP-1L was used to record the data

registers in the ﬁeld experience, and the ICP unit

(Integrated Circuit Piezoelectric; ICP interface) was

connected to the sound card of a lap-top computer,

conﬁguring an autonomous measurement unit. The

sampling frequency was F

=44,100 Hz for all the

registers analyzed in this paper, both in the sliding-

cumulant results as in the spectral kurtosis subsection.

The recording stage took place in a garden with ev-

idence of infestation and the bare waveguide of the

sensor was introduced in the lawn, over the suspicious

zone. Termite sounds from feeding are like sharp pops

and crackles in the audio output.

The key of the spectral kurtosis detection strategy

used in this work lies in the potential enhancement

of the non-Gaussian behavior of the emissions. If

this happens, i.e. if an increase of the non-Gaussian

activity (increase in the kurtosis, peakedness of the

probability distribution) is observed-measured in the

spectral kurtosis graph, there may be infestation in the

surrounding subterranean perimeter, where the trans-

ducer is attached.

Termite emissions are non-stationary, so the in-

strument treats data by ensemble averaging of the

sample registers, following the indications in (Ben-

dat and Piersol, 2000) (pp. 463-465). Each spec-

trum and spectral kurtosis graph presented in this

section is the result of averaging the spectra of the

sample registers, or realizations. As a ﬁnal remark,

acquired data is normalized according to the norm:

ksk =



i=1



1/2

5.2 Operating Cases

In this subsection we present the possible situations

associated to the measurement cases. We present the

signals out of the instrument display in order to be

analyzed more precisely. A data acquisition time of

5 seconds and a sample frequency of 44,100 Hz have

been selected. So every time the user performs an ac-

quisition (pressing the button ”Go”) 220,500 points

are stored. The software-engine is adjusted to cal-

culate the averaged spectral kurtosis (SK) over a set

of 220 realizations, each of them containing 1,000

points.

Two couples of data registers have been selected

as signiﬁcant examples, corresponding to typical

measurements situations. For a given couple, ﬁrst we

present the results without applying wavelets. Then

we explain the information wavelets add.

Fig. 4 presents a clear detection case, character-

ized by termite activity signals without alarms. Two

peaks are clearly enhanced in the SK graph (near 5

kHz, and near 15 kHz).

The de-noised data in the time main are shown

in the upper grpah of Fig. 5. Applying the spec-

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160

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−0.02

−0.01

0.01

0.02

Time, s

0 0.5 1 1.5 2

x 10

−60

−50

−40

−30

Frequency, Hz

Amplitude, dB

0 0.5 1 1.5 2

x 10

Frequency, Hz

Kurtosis value

Figure 4: A clear measurement of activity detection.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−0.01

0.01

Time, s

0 0.5 1 1.5 2

x 10

−100

−80

−60

−40

Frequency, Hz

Amplitude, dB

0 0.5 1 1.5 2

x 10

100

150

Frequency, Hz

Kurtosis value

Figure 5: De-noising results for data in Fig. 4. A general

enhancement of the spectral kurtosis occurs.

tral kurtosis to the de-noised version it is seen that

all the frequency components are enhanced, specially

those ones in the detection band. This fact conﬁrms

the presence of insects, and it is of special value in

doubtful situations, when they are really needed.

In Fig. 6 a doubtful measurement case is pre-

sented. Activity evidence is outlined only near 5 kHz.

Once, the wavelets have been applied (shown in Fig.

7), the enhancement near 5 kHz and 15 kHz conﬁrm

the detection.

Hereinafter, we present the conclusions.

6 CONCLUSIONS AND

ACCOMPLISHMENTS

Assuming the starting hypothesis that the insect emis-

sions may have a more peaked probability distribution

than any other simultaneous source of emission in the

measurement perimeter, we have design a termite de-

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−0.02

−0.01

0.01

0.02

Time, s

0 0.5 1 1.5 2

x 10

−50

−40

−30

Frequency, Hz

Amplitude, dB

0 0.5 1 1.5 2

x 10

Frequency, Hz

Kurtosis value

Figure 6: A doubtful measurement situation.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−0.01

0.01

Time, s

0 0.5 1 1.5 2

x 10

−120

−100

−80

−60

−40

Frequency, Hz

Amplitude, dB

0 0.5 1 1.5 2

x 10

100

150

Frequency, Hz

Kurtosis value

Figure 7: De-noising results of data in Fig. 6.

tection strategy and a virtual instrument based in the

calculation of the 4th-order cumulants for zero time

lags, which are indicativeof the signals’ kurtosis. The

instrument is actually in use by an Spanish company.

An estimator of the spectral kurtosis has been used

to perform a selective analysis of the peakedness of

the signal. It has been shown that new frequency

components gain in relevance in the spectral kurtosis

graphs.

The main goal of this signal-processing method

is to reduce subjectiveness due to visual or listening

inspection of the registers. This means that in a noisy

environment, it may be possible to ignore termite

feeding activity even with an ad hoc sensor because,

despite the fact that the sensor is capable of register

these low-level emissions, the human ear can easily

ignore them (De la Rosa and Mu˜noz, 2008, ).

A HIGHER-ORDER STATISTICS-BASED VIRTUAL INSTRUMENT FOR TERMITE ACTIVITY TARGETING

161

ACKNOWLEDGEMENTS

The authors would like to thank the Spanish Min-

istry of Science and Education for funding the project

DPI2003-00878, where the different noise processes

have been modeled and contrasted; and also for sup-

porting the PETRI project PTR95-0824-OP dealing

with plague detection using higher-order statistics.

Our unforgettable thanks to the trust we have from

the Andalusian Government for funding the excel-

lency project PAI2005-TIC00155,where higher-order

statistics are modeled and applied to plague detection

and power quality analysis.

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