PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Defect detection using the identification of resonance frequency byspatial spectral entropy for noncontact acoustic inspection method
Kazuko SUGIMOTO1; Tsuneyoshi SUGIMOTO2; Noriyuki UTAGAWA3; Chitose KURODA4
1,2

Toin University of Yokohama, Japan
3,4

SatoKogyo Co., Ltd., Japan

ABSTRACTIn a noncontact non-destructive manner, our noncontact acoustic inspection method can detect and visualizedinternal defects (crack peeling, cavity, etc.) in shallow layer of concrete from a long distance. The
measurement surface was acoustically excited by airborne sound waves, and a two-dimensional vibration
velocity distribution is measured by a highly sensitive scanning laser Doppler vibrometer (SLDV). When
there is an internal defect, a flexural resonance occurs in a defective part, and vibration energy difference
from a healthy part can be detected and imaged as vibrational energy ratio. If the resonance frequency rangeof an internal defects is known, a clear acoustic image can be generated by narrowing the analysis frequency
range rather than using over the entire measurement frequency range. The resonance frequency in ameasurement plane can be detected by ‘spatial spectral entropy (SSE)’ we proposed. In addition, in order toperform sound waves excitation, resonance may occur in a laser head of highly sensitive laser Doppler
vibrometer due to the influence of reverberation from the surroundings. This resonance frequency can also
be detected. It is necessary to perform acoustic imaging except for the resonance frequencies of the laser
head.
Keywords: Noncontact acoustic inspection, NDT, Spatial spectral entropy, Laser Doppler vibrometer, LRAD

1. INTRODUCTION
In a closed space such as a large underground cavity, when detecting internal defects of concreteby noncontact acoustic inspection method, it is necessary to increase the sound pressure as the distanceincreases. Then, it is known that the reverberation from the surroundings cause resonance on the laser
head of a high sensitivity scanning laser Doppler vibrometer (SLDV). In a closed space, resonancepeaks of a laser head tend to be larger than that in a released space, and the frequency band ofresonance also tends to widen. Because they adversely affect acoustic image visualized by vibrationalenergy, defect image is need to be calculated excluding the resonance frequency. The resonancefrequency of internal defects of concrete is estimated to some extent from experience, and thefrequency band of the transmitted sound waves is determined. But the real resonance frequency is notknown in advance. For the measurement results, some resonance peaks can be seen by visual checking
the vibration velocity spectrum at each measurement point one by one. However, there is no
information on the frequency where the resonance frequency of the internal defect is found. And when
the difference between the resonance peak and the noise floor is small, it is difficult to identify theresonance peak. It is also necessary to distinguish between the resonance peak of the internal defectand that of the laser head. By the SSE analysis using spatial spectral entropy we proposed, all theresonance frequency in the measurement plane can be detected and displayed in a Figure. Not only
the resonance frequency of internal defects, but also that of the laser head of SLDV can be detected
and identified.

1

kazukosu@toin.ac.jp
tsugimot@toin.ac.jp
3utagawa@satokogyo.co.jp
4kuroda@satokogyo.co.jp
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2. EXPERIMENTAL METHOD
2.1 Experimental setup
Figure 1 shows the experimental setup. In order to detect Internal defects, such as a crack or apeeling, in shallow layer of concrete in noncontact non-destructive manner, strong plane waves were
irradiated from a long-range acoustic device (LRAD; LRAD corp., LRAD-300X) installed at a
distance of about 5 m from the measurement plane, and the concrete measurement surface was
acoustically excited. A scanning laser Doppler vibrometer (SLDV; Polytec, RSV-500Xtra scanningvibrometer) was installed at a distance of 5-7 m from the measurement surface, and the twodimensional vibration velocity distribution on the measurement plane was measured.

Figure 1 – Experimental setup
2.2 Signal processing
Using the difference in arrival time of the sounds and the light, the signal processing of 'TimeFrequency gate' was performed to reduce the noise caused by such as the direct waves from a soundsource to a laser head and the reflected waves from the concrete measurement surface or thereverberation from the surroundings. As a transmission waveform, tone burst wave was used. It hassounding time and not sounding time. Sound changes in frequency step by step.

3. PRINCIPLE
3.1 Defect detection algorithm
When drawing a scatter diagram such as Figure 2 using two acoustical feature quantities(vibrational energy ratio and spectral entropy), measurement points in a healthy part of concrete showtendency to gather in an area where vibrational energy is low and spectral entropy is high. And themeasurement points of defective part exist in the area with high vibrational energy and low spectral
entropy. This defect detection algorithm was described in the reference (2).

Figure 2 – Scatter diagram of vibrational energy ratio and spectral entropy
3.1.1 Vibrational energy ratio

The vibrational energy ratio is represented by the following equation (1) in the reference (1),

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௙మ

ሾܸ‫ܴܧ‬ሿௗ஻ ൌ ͳͲ ଵ଴

‫׬‬௙ ൫ܲܵ‫ܦ‬ௗ௘௙௘௖௧ ൯݂݀భ௙మ‫׬‬௙ ൫ܲܵ‫ܦ‬௛௘௔௟௧௛௬ ൯݂݀భ

(1)where f 1 and f2 are, respectively, the lower and upper limits of the analysis frequency within thefrequency range of the transmitted airborne sound waves and PSD is the power spectral density. The
ratio of vibrational energy of defective part to vibrational energy of a healthy part of con crete is
calculated in the measurement frequency range.
3.1.2 Spectral entropy
The spectral entropy (SE) is represented as H by the following equation (2),
ܵ௙
ܲ௙ ൌ

‫ ܪ‬ൌ െ ෍ ܲ௙ ݈‫݃݋‬ଶ ܲ௙
σ௙ ܵ௙

(2)

௙

where S f is the power spectrum of the vibration velocity at a measured point. The spectral entropy
expresses the white characteristic of the signal. The spectrum of the signal is regarded as a probability
distribution and the information entropy is calculated.
3.1.3 Statistical evaluation of a healthy part of concrete
Each distribution of acoustic feature quantity (vibrational energy ratio and spectral entropy) in ahealthy part of concrete tends to show a normal distribution as stated in the reference (3).
3.2 Spatial Spectral Entropy (SSE)
The spectral entropy (SE) is a feature quantity that expresses the whiteness of a signal, assuming
the signal spectrum as a probability distribution and calculating information entropy. SE has a highvalue in a signal having a uniform spectrum such as a white noise, and a low value in a signal in which
the spectrum like a voice signal is not uniform.

Figure 3 – Illustration of ‘Spatial Spectral Entropy (SSE)’
As shown in Figure 3, consider the frequency axis of vibration velocity spectrum perpendicular to
the measurement plane. Several examples of vibration velocity spectrum at a measured point are
displayed from each measured point in the direction perpendicular to the measuremen t surface. We
propose a method of simultaneously detecting not only the resonance frequency of internal defects
but also the resonance frequency of a laser head of SLDV by calculating the ‫ܪ‬ௌௌா ሺ݂ሻ on a planarmeasurement plane. The SE expanded to such a planar measurement plane is referred to as ‘Spatial
Spectral Entropy (SSE)’ and is defined by the following equation (3) in the reference (4).
௠௡‫ܪ‬ௌௌா ሺ݂ሻ ൌ െ ෍ ෍ ܲ௜ǡ௝ ሺ݂ሻ ݈‫݃݋‬ଶ ܲ௜ǡ௝ ሺ݂ሻ(3)

௜ୀଵ ௝ୀଵ

ܲ௜ǡ௝ ሺ݂ሻ ൌܵ௜ǡ௝ ሺ݂ሻ௡σ௠σ௜ୀଵ ௝ୀଵ ܵ௜ǡ௝ ሺ݂ሻ

Where ‫ܪ‬ௌௌா ሺ݂ሻ is spectral entropy (a function of frequency f ) extended to real space. For example,

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when considering a two-dimensional measurement plane, the grating measured point ‫ݎ‬ሺ‫ݔ‬ǡ ‫ݕ‬ሻ isexpressed as an array ‫ݎ‬௜ǡ௝ ሺ݅ ൌ ͳǡ ݉Ǣ ݆ ൌ ͳǡ ݊ሻ. ܵ௜ǡ௝ ሺ݂ሻ is the spatial frequency component f [Hz] of thepower spectrum obtained by performing discrete Fourier transform on the signal measured at themeasurement point ‫ݎ‬௜ǡ௝ . ܲ௜ǡ௝ ሺ݂ሻ is the probability that the spatial frequency component f [Hz] of thepower spectrum at the measurement point ‫ݎ‬௜ǡ௝ exists within the measured plane. Therefore,‫ܪ‬ௌௌா ሺ݂ሻ
indicates the information entropy calculated for the frequency component f of vibration velocity
spectrum at all measured points.

4. EXPERIMENTAL RESULTS
4.1 Specimen with circular peeling defects
Internal defects of concrete include a different shape of defect such as a crack, a peeling, or acavity. We investigated peeling defects that were more difficult to detect than the same size of cavity
defect. Figure 4 shows the shape, size, and burial depth of peeling defects.

Figure 4 – Position and size of a circular peeling defect embedded in concrete
4.2

Analysis results of spatial spectral entropy and acoustic visualization of defects

4.2.1 Circular peeling defect (diameter = 200 mm, burial depth = 40mm)
Figure 5 shows the result of SSE analysis from the vibration velocity data obtained by noncontact
acoustic inspection method for a circular peeling defect (diameter 200 mm, burial depth 40 mm).

(a)Figure 5 – Analysis result by spatial spectral entropy (SSE)(b)

Figure 6 – Acoustic visualization of circular peeling defect (Φ200, 40) by vibrational energy ratio
Frequency band for imaging (a) 2000-6000Hz, (b) 4400-4600Hz
A resonance peak is observed around the frequency 4500 Hz in the figure. The black dotted line in the8151

figure is the median of SSE value, 5.72, in the measurement frequency range (2000 -6000 Hz).
Figure 6 is an acoustic image of a circular peeling defect. The frequency range for imaging of (a)was 2000-6000 Hz, and that of (b) was 4400-4600 Hz. Based on the SSE result, vibrational energy
ratio was calculated in a narrower frequency range and (b) was visualized. The white dotted circle in
Figure 6 shows the size and approximate position of the defect. The area of a peeling defect is morefaithfully reproduced in (b) than in (a). Max color scale in (b) is 21 dB, which is larger than 8.2 dB in(a). The difference of vibrational energy ratio between the defective part and the healthy part ofconcrete looks larger in (b) than in (a). Therefore, defect image of (b) looks more clearly than that of(a).
4.2.2 Circular peeling defect (diameter = 200 mm, burial depth = 60mm)
Figure 7 shows the result of SSE analysis from the vibration velocity data obtained by noncontact
acoustic inspection for a circular peeling defect (diameter 200 mm, burial depth 60 mm). A resonancepeak is observed in the frequency range 4000-4500 Hz in red frame of the figure. The black dottedline in the figure is the median of SSE value, 5.65, calculated in the measurement frequency range(2000-6000 Hz).

Figure 7 – Analysis result by spatial spectral entropy (SSE)
Figure 8 is an acoustic image of a circular peeling defect. The frequency range for imaging of (a)was 2000-6000 Hz, and that of (b) was 4000-4500 Hz. Based on the SSE result, vibrational energy
ratio was calculated in a narrower frequency range and (b) was visualized. The dotted circle in Figure
8 shows the size and approximate position of the defect. The area of a peeling defect is more faithfully
reproduced in (b) than in (a). Color scale in (b) is 17 dB, which is larger than 8 dB in (a). The differenceof vibrational energy ratio between the defective part and the healthy part looks larger in (b) than in(a). Therefore, defect image of (b) looks more clearly than that of (a).
(a)

(b)

Figure 8 – Acoustic visualization of circular peeling defect (Φ200, 60) by vibrational energy ratio
Frequency band for imaging (a) 2000-6000Hz, (b) 4000-4500Hz
4.2.3 Circular peeling defect (diameter = 300 mm, burial depth = 40 mm)
Figure 9 shows the result of SSE analysis from the vibration velocity data obtained by noncontact
acoustic inspection method for a circular peeling defect (diameter 300 mm, burial depth 40 mm). A
resonance peak is observed in the frequency range 1800-2400 Hz in red frame of the figure. The black
dotted line in the figure is the median of SSE value, 5.64, calculated in the measurement frequency
range (2000-6000 Hz).

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Figure 9 – Analysis result by spatial spectral entropy (SSE)
Figure 10 is acoustic images of a circular peeling defect. (a) was visualized in the measurement
frequency range of 2000-6000 Hz. Based on the SSE result, it can be seen that the resonance frequency
range started from the frequency 1800Hz lower than the measurement frequency 2000Hz. Moreover,vibrational energy ratio was calculated in a narrower frequency range and the acoustic images of thedefect were visualized. Therefore, in (b) the frequency range for imaging was 1800 -2250 Hz, and in(c) the frequency range was 1800-2400 Hz. The upper right part of the peeling defect in (a) is missing,but in (b) and (c), the missing part looks to be compensated by setting the start frequency to 1800 Hz.
Although (b) looks the same as (c), max color scales were 26 dB in (b), 23 dB in (c), which werelarger than 11 dB in (a). The difference of vibrational energy ratio between the defective part and thehealthy part of concrete looks largest in (b) compared the others. Therefore, a clearer image is obtainedin (b). The dotted circle in Figure 10 shows the size and approximate position of the defect. The areaof a peeling defect is more faithfully reproduced in (b), (c) than in (a).
(a)

(b)

(c)

Figure 10 – Acoustic visualization of circular peeling defect (Φ300, 40) by vibrational energy ratio
Frequency band for imaging (a) 2000-6000Hz, (b) 1800-2250Hz, (c) 1800-2400Hz
4.2.4 Circular peeling defect (diameter = 300 mm, burial depth = 60 mm)
Figure 11 shows the result of SSE analysis from the vibration velocity data obtained by noncontact
acoustic inspection method for a circular peeling defect (diameter 300 mm, burial depth 60 mm). A
resonance peak is observed in the frequency range 2550-2850 Hz in red frame of the figure. The black
dotted line in the figure is the median of SSE value, 5.71, calculated in the measurement frequency
range (1000-4800 Hz).

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(a)

(c)

Figure 11 – Analysis result by spatial spectral entropy (SSE)
(b)

(d)

Figure 12 – Acoustic visualization of circular peeling defect (Φ300, 60) by vibrational energy ratio
Frequency band for imaging (a)1000-4800Hz, (b)2550-2850Hz, (c)2850-3000Hz, (d)2550-3000Hz
4.3 Summary and discussion
From the above, the relationship between resonance frequency of circular peeling defect and thediameter or buried depth of the defect is, in the condition of this experiment, as shown in Table 1 .
Table 1 Relationship between resonance frequency range of circular peelings and diameter or buried depthA circular peeling defect was considered to have a certain range of resonance frequency, not asingle resonance frequency. That frequency range was thought to be broader than that of a circular
cavity defect. In Table 1, the local minimum of SSE is shown as a representative value. The range ofresonance frequency is indicated by the lower limit value and the upper limit value.
The above results are summarized as shown in Figure 13. From this figure, in case of a circular peelingdefect with a diameter of 300 mm, as the burial depth increases from 40 to 100 mm, the resonancefrequency increases in proportion. That is, as the depth of a circular peeling defect is deeper, the8154

resonance frequency becomes higher, however in the range of conditions such as these diameter anddepth. In addition, the resonance frequency is higher at a circular peeling defect with a diameter of
200 mm than that of 300 mm. That is, the smaller the cross-sectional area of the peeling defect, thehigher the resonance frequency. The dotted line in the figure is a result of linear least squares fitting.

Figure 13 – Relation between resonance frequency of circular peeling defect and diameter or burial depth
In our noncontact acoustic inspection method, flexural resonance is assumed as a vibration stateof cavity or peeling defect. As the theoretical formula of flexural resonance of a solid circular plate(clamped all around or simply supported all around), the natural frequency is known as
݂௠௡ ൌ

‫݄ܧ‬ଶ
ͳ ߣ௠௡
ඨ
ʹߨ ܽଶ ͳʹሺͳ െ ߥ ଶ ሻߩ

(4)

where f mn: natural frequency [Hz], E: Young’s modulus [Pa], a: radius of disk [m], ρ: mass per unit
volume [kg/m 3 ], h: plate thickness [m], ν: Poisson’s ratio, m: number of nodal circles, n: number of
nodal diameters.
In a peeling defect in the shallow layer of concrete, although there exists no void around peeling,
since it is applied to the theoretical formula of flexural resonance of a flat disk under this experimental
condition, it can be seen that flexural vibration actually occurs. If the concrete measurement surface
can be acoustically excited enough, the phenomenon of flexural resonance may be able to be caught.

5. CONCLUSIONSIn noncontact acoustic inspection method, using remotely measured vibration velocity data, spatial
spectral entropy (SSE) analysis can detect the resonance frequencies and those frequency range in themeasurement plane. By identify the resonance frequency and narrowing the frequency range for
imaging, acoustic image of a circular peeling defect in shallow layer of concrete was visualized clearly.  

ACKNOWLEDGEMENTS
This work was supported by JSPS KAKENHI Grant Numbers 17K06542.

REFERENCES
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3. Sugimoto K, Sugimoto T, Utagawa N, Kuroda C, and Kawakami A. Detection of internal defects ofconcrete structures based on statistical evaluation of healthy part of concrete by the noncontact acoustic
inspection method. Jpn. J. Appl. Phys. 2018, 57, 07LC13.
4. Sugimoto K, Sugimoto T, Utagawa N, Kuroda C. Detection of resonance frequency of both the internal
defects of concrete and the laser head of a laser Doppler vibrometer by spatial spectral entropy fornoncontact acoustic inspection. to be published in Jpn. J. Appl. Phys. 2019; 58.

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