― 1 ―Research Reports of the National Instituteof Industrial Safety, NIIS-RR-2002（2003）
UDC 620.179.16:620.192:621.785

Time-Frequency Analysis of Ultrasonic Echoes and its Application to
Nondestructive Evaluation of Thermal Damage of Steelby

Shiwei MA*, Tetsuya SASAKI**, Etsuji YOSHIHISA** and Takashi HONDA**

Abstract: Recent trend to extend the original design life of pressure vessels and piping may increase
the possibility of failure accident of these components caused by material degradation due to creep
or creep-fatigue. Since sudden rupture of these components usually results in a serious industrial
accident, such material damages must be detected using nondestructive evaluation technique toensure the safety of workers at the industrial sites. Although there are a lot of different methods
in nondestructive evaluation technique, ultrasonic pulse-echo technique is supposed to be one of thebest methods to detect creep or creep-fatigue damage. In this method, reflected ultrasonic echoes
by material internal defects and specimen interface often exhibit critical time and frequency
information. However, it is difficult to determine creep or fatigue-creep damage using conventionalsignal processing technique. To conquer such a difficulty, the time-frequency analysis method isapplied in this study. Because the time-frequency analysis method can provide an effective tool torepresent a signal in a two-dimensional time and frequency plane, it is possible to obtain frequency
dependent ultrasonic characteristics related to certain material properties in a time-frequency planerather than only in a time domain or frequency, and these characteristics can be applied to identify
internal defects or to assess creep damage of crucial structure material.
In this study, ultrasonic tests with high frequency contact transducers were carried out using
thermally degraded steel in order to confirm the effectiveness of the time-frequency analysis method.
Measured echo signals were analyzed by the Morlet function based wavelet transform, one of themethods for the time-frequency analysis. It is shown that with the increase of thermal degradation,
both the ultrasonic attenuation and its change with frequency gradually increased within a significant
frequency band but ultrasonic velocity was relatively unchanged. The effectiveness of the wavelet
analysis to ultrasonic signals for the quantitative evaluation of material thermal damage is clarified.
Keywords; Nondestructive evaluation, Ultrasonic echo, Time-frequency analysis, Wavelet transform,
Ultrasonic attenuation, Ultrasonic velocity, Thermal damage, Heat treatment, Grain size

1. Introduction
In industrial application, a large number of components in vital areas of infrastructure and largescale plants, such as a power plant, tubing
pipelines, etc., are manufactured from various kindsof steel. These structural steels subjected to****

STA Fellow
Mechanical and System Safety Research Groupenvironments of high temperature and highpressure suffered from thermal degradation
including creep or creep-fatigue damage during
their service lives. It is strongly desired to detectand evaluate such a material phenomenon and adamage state with ultrasonic nondestructive test
1）,2）
. However, the signal obtained in an
technique― 2 ―

産業安全研究所研究報告

NIIS-RR-2002（2003）

actual ultrasonic measuring system is generally nonstationary and difficult to be analyzed due tofrequency dependent scattering, attenuation anddispersion. Since the joint time-frequency analysis
of a signal can provide its detailed time information

Distribution（WVD）, Short Time Fourier Transform（STFT）and Continuous Wavelet Transform（CWT）
are three elementary methods.
For a given signal （t）
f, its WVD is defined as
the Fourier transform of its bilinear product at

at a concerned frequency and a detailed frequency
distribution at any time indices, it should be aneach time, that is:appropriate tool for ultrasonic signal processing. A
lot of results about the application of timefrequency analysis to ultrasonic non-destructive
tests have been reported in recent years

3）,4）. Thesestudies indicated that it was possible to obtainfrequency dependent ultrasonic characteris-tics ina time-frequency plane rather than only in a time
domain or in a frequency domain, and these characteristics could be applied to identify internal
defects or to assess creep damage of crucial struc-∫−jtw
WVD（t,w）f＝ f（* t−0.5t）f（t＋0.5t）
e dt

（1）

where t is time, w is angular velocity, t is timelag, and * represents complex conjugate.
The STFT of a signal （t）
f
is defined as:∫

STFT（t,w）f＝ f（t）w （* t−t）e−jtwdt（2）

where w is a selected window function used forobserving the signal’s local spectrum by translating

measurement system we developed. This paper notit along time.
The CWT of a signal （f t）is defined as its
convolution with a serial of scaled and translated
wavelet base function y（t）
, that is:
1 •t−t
CWT（t,s）
f
＝√
f y*
dt
（3）
s −• （t）￣
sonly describes this system and discusses theperformances of some typical time-frequency
methods used to analyze the obtained ultrasonicechoes but also introduces the conducted ultrasonic
testing on thermally degraded Cr-Mo steel speci-

where scale s>0. The key of wavelet analyses is
to choose a suitable wavelet function for actual
applications. A commonly used wavelet function isMorlet wavelet, consisting of a plane wave
modulated by a Gaussian function:

ture material.
In this study, ultrasonic nondestructive evaluation
for material damage was carried out using amens with a high frequency contact transducer. We
also present the obtained results and discussions
concerning the effect of growth in specimen’sinternal grain size due to thermal degradation on
certain frequency dependent ultrasonic behaviors
by using wavelet transform.

2. Basis of Time-Frequency Analysis
The time-frequency analysis aims to deal withsignal possessing of non-stationary properties（∫y（t）＝p−0.25ejw te−0.5t
0

2

（

（4）

where w 0 is non-dimensional frequency, here taken
to be 6 to satisfy the admissibility condition6）.
The time-frequency methods mentioned above
can be easily implemented by fast algorithm, taking
advantage of fast Fourier transform. This makes it
possible to use them in various actual applicationsof signal processing.

encountered in practice. It represents a signal in

2.2 Performance Comparison

a time-frequency plane with a two-dimensional
time-frequency distribution function in order toobtain the signal’s time-varying spectra.

As is shown in Fig. 1 , it is usually known that an

2.1 Basic Methods

and is very similar to a Gaussian pulse in nature.

A lot of time-frequency representation methods
have been developed and improved5）. Although the
behavior of these methods is quite different andeach has peculiar properties, Wigner-Ville

ultrasonic echo is a broadband pulse modulated
near the center frequency of the transducer used,
Fig. 2 plots the contours of WVD, STFT and CWTfor the actually obtained echoes given in Fig. 1 .
It gives an intuitive performance comparison ofthese methods used for analyzing ultrasonic echoes.
Theoretically, a high time resolution and a highTime-Frequency Analysis of Ultrasonic Echoes and its Application to Nondestructive Evaluation of Thermal Damage of Steel

Fig. 1

Waveform of two tested ultrasonic echoes andtheir amplitude spectrum.

frequency resolution can be achieved by WVD.
However, in the case of multi-component signals,

Fig. 2― 3 ―Time-frequency distribution of two tested
echoes:（a） WVD;（b） CWT based onMorlet wavelet;（c） STFT with 31-Hamming
window;（d） STFT with 9-Hamming window.

it can also introduce unwanted cross-term interference due to the bilinear product in the definitionof WVD.
The STFT is free of cross-term interference, but
its behavior greatly depends on the window

The developed ultrasonic measurement system inthis study is shown in Photo 1 . A pulsar/receiver,function used. Although most of the commonlyused window functions can be applied to it, it isdifficult to make a tradeoff between time resolution
and frequency resolution by STFT due to thelength-fixed window.

Imaging Supersonic Lab. Inc., BLP-12R, which iscapable of high frequency application up to
150MHz, was employed to generate, receive andpre-amplify ultrasonic pulses and echoes. Througha NBC connector, the received waves were acquired

The scale-varying structure of CWT makes it
possible to have finer frequency resolution for low

with a digital oscilloscope LeCroy 9354C whose
maximum sampling rate is 2GHz in a single channel
or 500MHz in quad channels. Thus, the system iscapable of accurate measurement for time of flight（TOF） with resolution up to 0.5ns. Each of thescope’s channels has an 8-bit A/D converter tofrequency components than high frequency
components, and a finer time resolution for highfrequency contents than low frequency contents.
This is quite useful for most of the actual

3. Ultrasonic Measurement System Developed

applications.
From theory and performance comparison, it isclear that the wavelet transform based on Morlet
function is suitable for analyzing ultrasonic echoes
since it can achieve excellent time and frequency

digitize the acquired analog signal. The digital
oscilloscope was connected to a personal computerconcentration and can track the frequency trend
at local time better than other methods. The

A single transducer was used to conduct
ultrasonic measurement in this system. It received

presented results in the following parts of thispaper are based on this kind of wavelet transform.

all of the echoes reflected from the surface andthe bottom of the tested specimen. The systemwith GPIB bus to make it easier to store andanalytically process ultrasonic wave data by acomputer.

can operate with a wide range of transducers with

産業安全研究所研究報告― 4 ―NIIS-RR-2002（2003）

Table 1

Photo 1

Photograph of the system developed toundertake ultrasonic measurement.

Photo 2

An example of the time-frequency analysis
window.

different types of acoustic couple.
System software was developed using Microsoft
Visual C++ and MathCAD. It is able to control theoscilloscope’s activity, transmit and store a large
amount of data, and perform time-frequency
transform including WVD, STFT, CWT, spectrum
analysis, graph displaying and zooming, parametermeasurement, etc. Photo 2 gives an example of thetime-frequency analysis window.

Heat treat condition and grain size of 21/4Cr-1Mo specimens.

Photo 3Grain structures of specimens.

different types of heat treatment followed by aircooling. As shown in Table 1 , the grain size,
measured according to JIS G0551, increased with
the increase of heated temperature and holding

4.1 Specimen and Transducer

time. Photo 3 gives grain structures of specimens.
Each specimen was machined to a plate of theunified dimensions, 80mm long, 12mm wide and
6mm thick, which has smooth and parallel faces toensure precise measurement.

Tested specimens for present work were made of
2-1/4Cr-1Mo steel, mainly used for power boiler
heating tubes and high pressure piping. To simulate
thermal degradation, they were processed by four

For a given specimen, statistical results presented
were based on multiple tests at different locations
on its surface. Furthermore, one hundred results
were averaged at each location so as to reduce
random noise.

4. Ultrasonic Testing for Thermally Degraded
SteelTime-Frequency Analysis of Ultrasonic Echoes and its Application to Nondestructive Evaluation of Thermal Damage of Steel

Fig. 3― 5 ―Method of measurement.

Ultrasonic tests were conducted using a commercial longitudinal wave high frequency contact
transducer, PANAMETRICS V214-BC whose nominal
frequency is 50MHz, element size is 6.34mm anddelay is 2.5μs. See Fig. 3 , the method of measurement, in which the surface echo（ S）appeared
immediately behind the delay line echo of atransducer. The first bottom echo is B1 and thesecond one is B2.

Fig. 4Ultrasonic echoes measured from tested CrMo steel specimens.

4.2 Obtained Waveforms and Their CWT
Fig. 4 gives the signal waveforms obtained fromfour specimens.

limited, it is important to determine a significant
frequency band in advance, so as to obtain

The CWT based on the Morlet function wasapplied to analyze these received signals. The CWTof above waves is plotted in Fig. 5 . The differences
between echoes are clearly depicted in the timefrequency plane. Thus, it is possible to calculate

meaningful results. Below this band, accurate timeof the echo was obscured due to wavelet transform.
Above this band, the transducer was unable toeffectively
receivethosehighfrequency
components from the reflected wave.

frequency
dependent
ultrasonicparameters
according to the value and location of the peakaround each echo.

5.1 Group velocity

5. Results and Discussions

Velocity is one of the basic ultrasonic properties.
Its change is related to the alteration of elastic

Generally, ultrasonic measurement involves compar-

modulus and the density of a material as the sounding the time of flight and the change of amplitude
between a surface echo and a bottom echo.
However, in the situation of contact measurement,
it was difficult to distinguish surface echo from thedelay line echo of a transducer. Therefore, thewave travels through it.
The group velocity means the velocity at eachfrequency. In a time-frequency plane, it wascalculated as the time of flight between the local
peak around B1 and that of around B2 at eachdifference between the first bottom echo B1 andfrequency, divided by transmitted distance（twice

the second one B2 was usually compared since
they are directly related to time of sound flightthe specimen thickness）.
Fig. 6 gives the results of group velocity

and loss of sound energy.
Because an ultrasonic echo is generally band-

obtained. Fig. 7 shows the change of velocity withthe grain size, in which error bars show the range

産業安全研究所研究報告― 6 ―Fig. 5NIIS-RR-2002（2003）

CWT of echoes measured from tested Cr-Mo steel specimens.

of change at different frequencies within asignificant frequency band of 10MHz~50MHz. It wasobserved from these results that the relatively low
levels of change in ultrasonic velocity appear tobe due to small differences in the phase present

the increase of thermal degradation within asignificant frequency band of 10MHz to 50MHz.
Fig. 9 gives the dependence of the attenuation on
grain size, in which error bars indicate the rangeof the attenuation’s change with frequency withinratherany

this frequency band. It was found that the grain

thermalsize greatly affected the ultrasonic attenuation andthe change of attenuation in terms of frequency.

than

the

directconsequenceincreasing in grain size caused
degradation in Cr-Mo steel.

byof

5.2 Attenuation coefficient6. Conclusions
This study concerned the application of time-

Attenuation is principally caused by the heatcondition and scattering as the sound wave travels
through material.
The attenuation coefficient at each frequency
obtained in a time-frequency plane was the ratio

frequency analyses in the field of ultrasonicnondestructive material evaluation. It is concluded
that the wavelet transform provides an effective
tool to obtain frequency dependent ultrasoniccharacteristics, such as group velocity andof the local maximum value near B1 to that of B2

attenuation coefficient related to certain material

at that frequency, divided by the transmitted
distance.

properties. Present results indicated that, with theincrease of thermal degradation of Cr-Mo steel,From the results shown in Fig. 8 , it was observedthat ultrasonic attenuation gradually increased withboth the attenuation and its change with frequency
gradually increased within a significant frequency

Time-Frequency Analysis of Ultrasonic Echoes and its Application to Nondestructive Evaluation of Thermal Damage of Steel

Fig. 6

Fig. 7

Group velocity vs. frequency

Relationship of group velocity and grain size.

Fig. 8Fig. 9― 7 ―Attenuation coefficient vs. frequency.

Relationship of attenuation coefficient and grain
size.

band although velocity was observed relatively
unchanged. These results obtained in a time-3）H.Inoue, K.Kishimoto, T.Nakanishi, et al.,Determination of Ultrasonic Velocity andfrequency plane are certainly useful for quantitativeevaluation of material damage.

Attenuation by Wavelet Analysis of Echo
Waveform, Nondestructive Inspection, Vol.43,
No.3,（1997）, pp.206-213.（In Japanese）
4）Y.Fukuda and H.Kitagawa, Ultrasonic Inspection
by Means of Time-Frequency Analysis of Bottom
Echo, Trans. Jpn. Soc. Mech. Eng., Vol.64,

Acknowledgement
This research was supported by the STA fellowship
program.
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No.618, C,（1998）, pp.558-564.（In Japanese）
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