計測自動制御学会産業論文集
Vol.8, No.15, 117/124（2009）

Nondestructive Inspection of the Diameter of Reinforcing Bars inConcrete Using an Electromagnetic Wave (Radar)
Halima Begum∗ , Masayuki Okamoto∗ and Shogo Tanaka∗
For the measurement of the diameter of a deformed bar in concrete, an electromagnetic wave (EMW) radar isused which scans along the bar. In our previous method, the radar was run while keeping it in contact with theconcrete surface, because this is the usual procedure of scanning with a radar. This resulted in a larger angle ofincidence of the EMW to the bar, which consequently elevated the frequency of receiving reflections both fromthe rib and the base of the bar simultaneously. Therefore, the frequency of erroneous measurement of the propagation time of the EMW to the point on the bar just below the radar and back became large. This consequently
aﬀected the success in the measurement of the diameter greatly. Therefore, the present paper proposes a new
method. The new method introduces a better scanning procedure, which involves the lift-oﬀ of the radar during
the scanning. Experiments show the comparison of the successful measurements with and without the lift-oﬀ of
the radar and verify the eﬀectiveness of the method.
Key Words: non-destructive inspection, diameter, reinforcing bar, electromagnetic wave (radar), lift oﬀ,
Kalman filter, maximum likelihood method.

1.

rib’s pitch by the method, the bar was scanned along its

Introduction

length with a radar. During the scanning, the radar was incontact with the concrete surface, because this manner ofReinforcing bars are used in concrete structures to endure any tensile force . Specially, deformed bars are usedscanning is usually practiced. From the received signal atfor their better adherence to the concrete. A deformed bar

each scanning point, the information on the propagation

has some protruding parts from its base, known as thetime of the EMW to the bar and back was measured byribs, which are responsible for the bonding strength witha pattern matching procedure described in the previous

the concrete. The spacing between the ribs, i.e. the rib’s

method 2) . But in our previous method, the EMW trans-

pitch, is related to the diameter of the deformed bar 2) .

mitted into the concrete had a large angle of incidence

1)

The selection of the deformed reinforcing bars of ade-to the bar. So the frequency of simultaneously obtaining

quate diameter must of course be made to avoid a riskreflections both from the rib and the base became higher.

of collapse of concrete structures.

But, sometimes to

Therefore, the measurement of the propagation time ofminimize the cost of construction, bars of smaller diam-

the EMW reflected from the point on the bar just below

eters than the recommended ones are used. To checkthe scanning point was diﬃcult.

whether the guidelines about the diameter of the bar are

That’s why we propose here to lift the radar oﬀ thefollowed properly, inspection is generally conducted. But,

concrete surface during the scanning of the bar. By in-

the inspection is done after the construction, regrettably.

creasing the lift-oﬀ we can expect to obtain a smaller angle

That’s why we have a great demand for a reliable methodof incidence of the EMW to the bar. That is, we can ex-

to measure the diameter of the bar nondestructively.

pect to realize an almost vertical propagation path of the

The authors previously proposed a method for the non-

EMW inside the concrete. This will consequently enable

destructive inspection of the diameter of the bar using an

us to obtain a much more accurate propagation time ofelectromagnetic wave (EMW) radar . The method fo-

the reflected EMW from the point (on the bar) just below

cused on the rib’s pitch measurement and then indirectly

the scanning point.

2)

measured the diameter from the relationship between theThen, by applying our previous signal processing

rib’s pitch and the diameter of the bar. To measure themethod 2) (i.e., the method using a Kalman filter andmaximum likelihood) to the propagation time variation∗

Graduate School of Science and Engineering,
Yamaguchi University.
2-16-1, Tokiwadai, Ube, 755-8611, Japan(Received December 26, 2008)

along the length of the bar, we can achieve a much moreaccurate measurement of the rib’s pitch, i.e., that of thediameter of the bar. Experiments will show the reliability

117and eﬀectiveness of our new method.

2.

components. Also, φi denotes the phase angle.
Now, by defining the state vector x(l) as x(l)=(z0 , z1 , ż1 ,Overview of the previous method

z2 , ż2 , · · · , zn , żn )T , variation of the propagation time is

In our previous method 2) a radar scanned the bar alongmodeled as an output of a dynamic system 2) 5) . The es-

its length while being in contact with the concrete surface.

timation of x(l) is performed using a Kalman filter for

At each scanning point, the received signal r(t) is mod-diﬀerent assigned values of L.
The optimal value of L (i.e. L∗ ) is obtained by maxi-

eled as the linear combination of the surface wave (themizing the likelihood function

reflected wave from the surface) and the reflected EMWfrom the bar as below

2) 3) 4)r̃(t) = p1 rs (t − T1 ) + p2 ro (t − T2 )K³´
Yp yk /L, Y k−1

(1)

(5)

k=1

¢
¡
with respect to L. In Eq.(5), p yk /L, Y k−1 is a con-

where rs (t) and ro (t) are respectively the fundamental

ditional probability density function for yk for a given

surface wave and the fundamental reflected EMW signal

observation sequence Y k−1 = {y1 , y2 , · · · , yk } and the as-from the bar. Here, T1 and T2 are the propagation times

signed parameter L. Once the rib’s pitch is solved, theof the surface wave and the EMW reflected from the bar

diameter of the deformed bar can easily be obtained fromrespectively. Again p1 and p2 denote the linear combi-

the standard table relating the rib’s pitch and the diam-nation coeﬃcients of the surface wave and the reflectedeter of the bar.

EMW. rs (t) and ro (t) are known a priori from experiments. The unknown parameters in the modeled received

3.

Proposed scanning proceduresignal are p1 , p2 , T1 and T2 .
To obtain the propagation times of the EMWs, pattern

During the scanning with the radar along the bar, thematching 2) 3) 4) is performed between the actual and theradar transmits an EMW signal at each scanning point.

modeled received signal. The values of p1 and p2 being

Due to the diﬀerence in permittivity between the air andobtained analytically for any T1 and T2 (see appendix), T1

the concrete, a part of the EMW reflects from the con-and T2 are the only parameters to be solved numerically.

crete surface 6) . The other part of the EMW transmits

The evaluation function θ for the pattern matching is

into the concrete and reflects from the bar to go back to
the receiver.

expressed as−1

θ = cosµ(r(t), r̃(t))kr(t)k kr̃(t)k¶

In the previous method, the radar scanned the bar while
being in contact with the concrete surface, i.e. the scan-(2)

ning was performed with no lift-oﬀ. In the situation thewhere, (· , ·) and k·k represent the inner product and the

propagation path of the EMW from the radar to the bar

norm in Hilbert space respectively. From the values ofand vice versa are far from that under the Snell’s law.

T1∗ and T2∗ for which θ is minimized, we can obtain theThis is because the wave length of the EMW is much

optimal propagation time (i.e., T2∗ ) of the EMW reflectedlarger than the gap between the radar base and the con-from the bar just below the scanning point 2) .

crete surface. Note that both the transmitter and theNow, the propagation time variation of the EMW re-receiver are attached on the base of the radar. At thatflected from the bar along the length of the bar is periodic

case the emitted EMW is expected to fall on the con-in nature 2) and thus is modeled as a linear combination

crete surface almost vertically (see Fig.1(a)). Therefore,of several sinusoidal functions with an additional bias .

the angle of incidence θ1 of the EMW becomes large as

That is,shown in Fig.1(a). As a result, frequency of simultaneousy(l) = z0 +nXzi (l)(3)

reception of the reflected waves both from the rib and thei=1base, instead of obtaining reflection from only the point

where l represents the scanning distance and z0 is the bias

on the bar just below the scanning point, is high andandthus it becomes diﬃcult to obtain the propagation timezi (l) = ai sin(ωi l + φi )(4)of the EMW reflected from the bar just below the scan-with ωi = (2π/L)i. Here, L corresponds to the rib to ribning point. This is caused from the non-sharpness of the

distance i.e. the rib’s pitch, while i = 1 corresponds to thedirectivity characteristics of the radar.

fundamental frequency component of the sinusoidal wave

To avoid this, we propose here to lift-oﬀ the radar dur-and i = 2, 3 . . . n correspond to the harmonic frequency

ing the scan. With the increase of the lift-oﬀ the propa-

118

gation path is expected to tend to follow the Snell’s law.
As a result, the angle of incidence θ2 becomes smaller
as in Fig.1(b). Such smaller incidence and reflection angles mean an almost vertical propagation of the EMW
to and from the bar inside the concrete. This minimizes
the frequency of simultaneous reception of any unwanted
reflected waves. So, at that case we can expect to get a received signal as composed of the reflected waves from thesurface and the bar just below the scanning point only.
And by such a scanning, we get much more informative
propagation time variation which enables us to guess theaccurate shape of the bar, i.e., the shape of periodical
change of the base and the rib.

Fig. 2: Test specimen

signal at 5mm pitch.
The reinforced concrete specimen we used has D19 typebars placed at 60mm depth from the concrete surface asshown in Fig.2. According to JIS standards 2) , the diameter of this type of deformed bar is 19.1mm, while therib’s pitch can take a value between 11.1mm and 13.4mm.
However, the average rib’s pitch of the bar in the test specimen is 12.08mm with a standard deviation of 0.4mm.
Experiments were conducted in two steps. The first experiment is to observe the eﬀect of the lift-oﬀ of the radaron the propagation path of the EMW from the radar tothe bar and vice versa. The second experiment is to verify the eﬀectiveness of the new approach in measuring thediameter non-destructively.
4. 1

The eﬀect of the lift-oﬀ on the propagation
path of the EMW signal from the radar to

Fig. 1: Eﬀect of the lift-oﬀ on the incidence angle of the electromagnetic wave

the bar and vice versa
The radar is first placed over the concrete surface justover a reinforcing bar with the radar axis perpendicular4.

to the bar. This is to identify the propagation path of theExperimental results

radar when it has no lift-oﬀ. By the way, strictly speak-

The EMW radar used in the experiment was manufactured by Japan Radio Co.

Ltd.

ing, the substantial air gap between the radar base (orThe radar (bow-the surface of the transmitter and the receiver) and thetie type) has separate transmitter and receiver antennae

concrete surface for the formal 0mm lift-oﬀ is 4mm.

on the base of the radar with the center to center dis-

Next, a thin strip of aluminium having a dimension oftance of 69mm between them. The specifications of the

200mm×3mm is placed on the concrete surface under-

radar are: central frequency 800 MHz and sampling pe-neath the radar at a distance x from the radar center (seeriod ∆T = 0.04 ns. The radar sends and receives EMW

Fig.3(a)). Here, x is taken positive for the positions to119

Fig. 6: Eﬀective value of the diﬀerence signal versus the position of the aluminium strip for the case of lift-oﬀ 0mm

Now, keeping the aluminium strip at the same distancex from the center of the radar, we obtain a received signalby the radar for the case of no bar in the concrete (seeFig.3(b)). For this set up, the received signal contains
only reflected EMWs from the concrete surface and thealuminium strip. For reference, Fig.4 shows the two received signals in the presence and absence of the bar whenx = −20mm.

Fig. 3: Experimental set up for identifying the propagation
path of the EMW to the bar and back to the radar

Now the diﬀerence between the two received signals

shown in Fig.5 is the reflected wave signal from the bar
only for the aluminium strip at x = −20mm. The eﬀec-

tive value of the diﬀerence signal represents the strengthof the reflected wave from the bar. For diﬀerent positionsof the strip, the eﬀective values of the diﬀerence signals
are calculated and plotted in Fig.6. Here, Pt and Pr
represent the positions of the strip at which the eﬀective
values of the diﬀerence signals are minimum.
By placing the strip at Pt , we block the EMW fromthe radar to the concrete. Similarly, by placing the strip
Fig. 4: Received signals in the presence and absence of the bar
with the position of the aluminium strip at x = −20mm

at Pr , we prevent the reflected EMW from the bar fromgoing back to the receiver. In both cases the radar does
hardly receive reflected EMWs from the bar.
The distance d between the positions Pt and Pr for theformal 0mm lift-oﬀ is found to be 65mm which is very
close to the specified value 69mm of the distance between
the transmitter and receiver of the radar.
Now, by changing the formal lift-oﬀ of the radar fromzero to 10 and 20mm respectively, the change in d is calculated. Table 1 lists the distance d between Pt and Pr
obtained for each of the lift-oﬀs . From the table we cansee that as the lift-oﬀ increases, the value of d decreases.

Fig. 5: Diﬀerence signal of the two received signals in Fig.4

Fig.7 shows the propagation paths from the radar tothe bar and back for the two cases of the formal lift-oﬀs
the right side of the radar center and negative for the po-

0mm and 20mm using the values of their corresponding

sitions to the left side. For this experimental set up, thed in Table 1. We can see that the angle of incidence andradar receives three reflected EMWs from the concretereflection on the bar for the case of formal lift-oﬀ 20mm

surface, the aluminium strip and the bar.

is much smaller than that for the formal lift-oﬀ 0mm. For

120

Table 1: Distance between the two minima of the eﬀective valueof the diﬀerence signal

formal lift-oﬀ substantial lift(mm)0oﬀ (mm)4

10
20

the 20mm formal lift-oﬀ, the angle of incidence to thebar obtained from the experiment is 11.2 deg, which isvery close to the angle of incidence 13.23 deg calculated

distance d (mm)according to the Snell’s law. So, we can say that with65

the increase of the lift-oﬀ the propagation path tends to14

50

follow the Snell’s law and almost vertical incidence and2420reflection of the EMW to and from the bar is realized.
In Fig.8 we compare the eﬀective values of the reflectedwave from the bar for the formal lift-oﬀs 0mm and 20mm.
We observe that the eﬀective values of the diﬀerence signals for the lift-oﬀ 20mm are by far smaller than those obtained for the lift-oﬀ 0mm. So, we can say that, althoughwith the increase of the lift-oﬀ almost vertical incidence
and reflection to and from the bar is realized, the strengthof the reflected wave from the bar decreases. Thus, we canconclude that further increase of the lift-oﬀ to obtain vertical incidence and reflection of the EMW to and fromthe bar may not yield any fruitful result, because at thatcase the EMW emitted from the radar merely injects into
the concrete and consequently the reflected EMW fromthe bar is hardly received by the radar. Therefore, we
consider the formal lift-oﬀ 20mm may be the limit. The
conclusion is proved later in the next section.
4. 2

Measurement of the diameter of the bar

To obtain the propagation time variation of the EMWs
reflected from the bar, the radar is run along the lengthof the bar, while being lifted oﬀ the concrete surface. We
scanned the bar with the formal lift-oﬀ set as 0, 5, 10, 15,
20 and 25mm respectively and for each of the cases the
propagation time variation is obtained 2) . Fig.9 shows
the variation in the propagation time along the length of
the bar while the formal lift oﬀ is 20mm.
We can see a low frequency bias in the variation. This

Fig. 7: Comparison of the propagation paths of the EMWs
from the radar to the bar for the formal lift-oﬀs 0mm and20mm

might have resulted from the fact that the scanning lineof the radar is not exactly parallel to the bar. To obtain the relative variation of the propagation time, weremove the low frequency component from the variation.

Fig. 8: Comparison of the eﬀective values of the diﬀerence signals for the formal lift oﬀs 0mm and 20mm
Fig. 9: Propagation time variation for the radar formally lifted
20mm oﬀ the concrete surface

121For this purpose, we used a 7-point moving average filter.

variation along the length of the bar increases.

Since the allowable ranges of ribs’ pitches of all the bars

However, we can see that with the increase of the lift-oﬀ

must lie within the passband of the filter, so considering

the strength of EMW injection into the concrete as well as

the frequency characteristics of the filter, a 7 or a higherthat of the EMW signal reflected from the bar decreases,

point moving average filter is desirable. But the number

making it diﬃcult to obtain an adequate information onof data points in the filtered output reduces with the use

the propagation time of the EMW. As a result, successof higher point moving average filter. That’s why we con-in the measurement of the diameter starts decreasing be-

sider to use the 7-point moving average filter here. Fig.10

yond the formal lift-oﬀ 20mm.

shows the relative variation in the propagation time after

For the case of successful trials of each of the lift-oﬀs, weremoving the low frequency component, which is treatedalso calculated the normalized diﬀerences between the two

as a new observation sequence in applying our previous

largest extrema in likelihood functions (for mode number

signal processing method 2) .

3) in percentage as Q = |ξ1 − ξ2 | / |ξ1 | × 100%, whereξ1 , ξ2 are respectively the likelihood values of the 1st andFor each lift-oﬀ, we scan with the radar for 15 times andthe 2nd maxima and | . | represents the absolute value.

obtained the corresponding new observation sequences.

Table 2 lists the minimum, the mean and the standard

We then analyze the observation sequences with our previous method 2) i.e. the method using Kalman filter anddeviation of the normalized diﬀerences obtained from the

maximum likelihood method.

successful trials for each of the lift-oﬀs. We observe that

The success rate in measuring the diameter of the bar

with the increase of the lift-oﬀ, both the minimum as

for the diﬀerent lift-oﬀs is listed in Table 2. From thewell as the mean of the normalized diﬀerence between thetable we can see that with the increase of the formal lift-

two extrema increases (up to the formal lift-oﬀ 20mm).

oﬀ up to 20mm the success rate increases monotonically.

This means that the maximum of the likelihood func-

The reason is that with the increase of the lift-oﬀ the fre-tion becomes easily distinguishable. The fact enable us

quency of simultaneous reception of the reflected waves

to achieve a reliable measurement in the diameter.

from the base and the rib of a bar decreases and thus theWe also observe that the standard deviation of the nor-frequency of obtaining the informative propagation time

malized diﬀerences for the 20mm formal lift-oﬀ is large
compared to those of other lift-oﬀs. Such a result was
obtained due to the fact that for some of the trials withthe 20mm lift-oﬀ, the diﬀerences between the two extrema
were found comparatively large, although the details areomitted here.
For reference, Fig.11 shows the observation sequencefor 0mm formal lift-oﬀ selected from one of the successful
trials, while Fig.12 shows another example of observation sequence for 20mm formal lift-oﬀ. After analyzing

Fig. 10: Observation sequence after removing the low frequency
component from the propagation time variation in Fig.9

both of them by our signal processing method, we get thelikelihood functions as shown in Fig.13 and Fig.14. Although the maximum of the likelihood function lies within

Table 2: Measurement results for diﬀerent lift-oﬀs of the radarformal lift- trials sucoﬀ (mm)ceeded (%)

the allowable range of rib’s pitch in the trial with thenormalized diﬀerence between
the two largest extrema in
likelihood, Q (%)
mean
minimum

std

0

80

0.26

4.72

6.79

5

80

0.73

5.98

5.21

10

93

1.03

6.04

3.8

15

100

1.4

6.99

3.83

20

100

2.4

12.14

10.13

25

87

1.4

7.4

5.5

Fig. 11: Observation sequence for a successful trial for the formal lift-oﬀ 0mm

std: standard deviation122

the length of the bar, the success rate in the right identification of the rib’s pitch (and consequently the diameter ofthe bar) was found to increase significantly. The proposed
method was found to be much more reliable in measuring
the diameter of the bar compared to our previous one.
References
1) A.M. Neville, “Properties of Concrete,” Prentice Hall,(1995)
2) H. Begum, M. Okamoto and S. Tanaka “Measurementof the Diameter of Deformed Reinforcing Bar in Reinforced Concrete Structure Using an Electromagnetic Wave
Radar,” Proc. of the 39th ISCIE International Symposiumon Stochastic Systems Theory and Its Applications, 26/31(2007)
3) S. Tanaka and M. Yamada, “Non-Destructive Inspection of Concrete using an Electromagnetic Wave (Radar)
Based on a Signal Propagation Model,” Transaction of
SICE, 39, 5, 432/440 (2003)
4) S. Tanaka, “An Accurate and Real Time Non-Destructive
Inspection method of Tunnel Using an Electromagnetic
Wave Radar,” (in Japanese) Journal of SICE, 44, 3,
173/179 (2005)5) S. Tanaka, “Measurement Systems Engineering,” Asakura
Pub. Co., (1994)
6) K. Hongo, “Fundamentals of Electromagnetic Wave Engineering,” Jikkyo Pub. Co., (1985)

Fig. 12: Observation sequence for the formal lift-oﬀ 20mm

Fig. 13: Likelihood function for the formal lift-oﬀ 0mm

Appendix A.
The error function e(t) between the actual received signal r(t) and the modeled received signal r̃(t) is written
asFig. 14: Likelihood function for the formal lift-oﬀ 20mme(t) =r(t) − r̃(t)=r(t) − p1 rs (t − T1 ) − p2 ro (t − T2 )formal lift-oﬀ 0mm, the normalized diﬀerence between
the two largest extrema is only 1.07%. However, for the(A. 1)For any given values of T1 and T2 , the optimal values of

20mm formal lift-oﬀ, the normalized diﬀerence is as large

p1 and p2 are obtained by minimizing the square of the er-

as 17.02%. Therefore, the maximum of the likelihood

ror function (e2 (t)) with respect to p1 and p2 respectively.

function is more reliable to be accurately picked up as we

The square of error function can be written in vector form

increase the lift-oﬀ.

as5.

ConclusioneT e =(r − p1 rs − p2 ro )T (r − p1 rs − p2 ro )=rT r − 2p1 rs T r − 2p2 ro T r + p1 2 rs T rs

For the nondestructive inspection of the diameter of thedeformed reinforcing bars in concrete, an EMW radar was2

T(A. 2)T+ p2 ro ro + 2p1 p2 ro rs

proposed to use for scanning the bar while being lifted oﬀ
Where, e, r, rs and ro are the vectors corresponding to

the concrete surface. The experiments showed that with
the increase of the lift-oﬀ a smaller angle of incidence ofthe functions e(t), r(t), rs (t) and ro (t), respectively. Now

the EMW to the bar could be achieved, which in turn en-

diﬀerentiating Eq.(A.2) with respect to p1 and p2 respec-

sured the obtaining of a much more accurate propagation

tively and equating them to zero, we gettime of the EMW from the point (on the bar) just below
the scanning point.

p1 (rs T rs ) + p2 (ro T rs ) = rs T r

By applying our previous signal processing method,

p1 (ro T rs ) + p2 (ro T ro ) = ro T rwhich applied a Kalman filter and maximum likelihood toFinally, we get p∗1 and p∗2 asa dynamic model of the propagation time variation along

123(A. 3)

"

p∗1
p∗2

#

=

"

rs T rs

ro T rs

ro T rs

ro T ro#−1 "rs T rro T r

#(A. 4)

Halima BEGUM (Student Member)
She received her BSc. in Electrical and Electronic Engineering from Bangladesh University of Engineering & Technology, Bangladesh
in 2002 and received M.Engg. in Electricaland Electronic Engineering in 2007 from Yamaguchi University, Japan, and is currently
enrolled in the doctorate course at the same
University. Her current research interests include non-destructive inspection using electromagnetic wave radar, advanced signal processing and system modeling.

Masayuki OKAMOTO
He received the B.S. and the M.S. degrees
both in electronic engineering from Yamaguchi
University in 1994 and 1996 respectively. He
then received Ph.D. degree in system engineering from the same University in 1999. Since
1999, he has been a Research Associate ofElectrical & Electronic Engineering, Facultyof Engineering, Yamaguchi University. His
current research interests lie in the intelligent
sensing and the anomaly diagnosis. He received the Research and Technology Promotion Award from the Instrument Departmentof SICE (2002).

Shogo TANAKA (Member)He received the B.S. degree in electronic engineering from Kyushu University in 1971, andthe M.S. and Ph.D. degrees both in electricalengineering from the University in 1973 and1979, respectively. From 1976 to 1979, he waswith the Department of Electrical Engineering of the University as a Research Associate,and from 1979 to 1990, an Associate Professor of Electronic Engineering, Faculty of Engineering, Yamaguchi University. Since 1991, hehas been a Professor of Electrical & Electronic
Engineering of the University. His current research interests lie in the intelligent sensing andthe anomaly diagnosis. He is a member of theSociety of Instrument and Control Engineers(SICE), the Institute of Electrical Engineers ofJapan and the Institute of Systems, Control
and Information Engineers. He received the
Chugoku Cultural Award (2003), the Awardof the Japanese Ministry of Education and Science (2004) and SICE Awards (2005 and 2006).
He is a fellow of SICE.

124