Journal of Nondestructive Evaluation, VoL 13, No. 3, 1994
An Adaptive Time Domain Deconvolution Technique to Characterize Planar Flaws in Highly Attenuative Composites H. A. H u a n g , ~ C. E. Bakis, 1 H. T. H a h n , 2 and A. P. Diwanji 3
Received September 27, 1993; revised June 3, 1994
To identify planar heterogeneities or flaws inside a structure using ultrasonic tests, it is necessary to characterize reflections originating from the boundaries of the heterogeneities. However, for composite materials with high, frequency-dependent wave attenuation, it is often not possible to clearly identify the reflections with either A-scan signals or conventional deconvolution techniques due to the combined effect of signal distortion and overlap. To enable deconvolution of a distorted propagating wave, a new time domain deconvolution technique which includes the frequencydependent acoustic properties of the host material has been developed. This approach is shown to be superior to conventional time domain deconvolution with L1 norm minimization in resolving flaw reflections in highly attenuative glass fiber reinforced polyurethane composites.
KEY WORDS: Deconvolution; flaw characterization; signal processing; waveform prediction; nondestructive evaluation; polyurethane; composite materials.
with L1 norm (least absolute value) minimization has given superior temporal solution.O~ The resolution enhancement is accomplished by deconvolving the received signal and the source signal to isolate acoustic impedance discontinuities in the material. However, the techniques developed to date assume an approximately time invariant source signal so that they are only applicable to material systems with frequency independent acoustic properties. For the NDE of highly attenuative composite laminates, these techniques may not provide any benefit and could potentially produce erroneous results. The objective of the present investigation is to develop an improved time domain deconvolution technique for the ultrasonic inspection of composite materials with high attenuation. The approach taken was to modify a conventional time domain deconvolution technique (3) by incorporating into the source signal matrix a prediction of distortion of the propagating wave. The waveform prediction is processed in the frequency domain using the experimentally determined attenuation coefficient and phase velocity. The waveform of the re-
1. I N T R O D U C T I O N Thick composites, toughened epoxy composites, and elastomer matrix composites are under consideration for many applications because of the increasing demands of heavy loading and impact resistance. Although these composites offer many advantageous mechanical properties, it is generally difficult to pass high frequency, broad bandwidth ultrasonic energy through them for the purpose of nondestructive evaluation (NDE). Wave attenuation in these composites is not only high, but also frequency dependent. Consequently, the waveforms of the received flaw signals are overlapped and distorted. Many deconvolution methods have been developed with an aim of temporal resolution enhancement for flaw detection. Among them, the time domain deconvolution ~Department of Engineering Science and Mechanics, Composites Manufacturing Technology Center, The Pennsylvania State University, University Park, Pennsylvania 16802. 2 Department of Mechanical, Aerospace, and Nuclear Engineering, University of California, Los Angeles, California 90024. 3 Chemical Products Division, Lord Corporation, Erie, Pennsylvania 16514.
101 0195-9298/94/0900-0101507.00/0 6) 1994.PlenumPublishingCorporation
102
Hua~g, BaNs, Hahn, and DiwaN~ 0.6 0.4
-8 o.2
0.0 -0.1 -0,2
-= e~ o.o <
-0.2
-0.4 0
2
1 2 Time (p-s)
(a)
3 Time (p-s) (b)
4
6 Time (p-s) (d)
7
0.08 o.1
0.04
~. o.o
0.00
2
< -0.1
-0.04 3
4
5
5
Time (p.s) (e) 0.12
0.08
.-=
0.04
=_ <
0.00 -0.04 -0.08 3
4
5
6
7
Time (p-s) (e) Fig. 1. Predicted back-surface reflections for a glass/PPDI polyurethane composite with thicknesses of (a) 0.3, (b) 1.8, (c) 3.6, and (a) 5 ram; (e) measured back-surface reflection from a 5-ram-thick specimen (2.25 MHz, 50.8 focal length transducer).
flection at any depth inside the material which forms the source signal matrix is obtained from the predicted FFT spectra. With the improved technique, planar flaws can be more accurately identified according to type and location.
x1(i) x2(1) x1(2)
~yl ~ 1~
x3(1) &(2) = e
9
X3(2 ) o
xk(1) 9 xk(2)
~2
n3 I ~
~
xlim)
(2)
~ " x2(m) , x3(m )
o
2. L1 T I M E D O M A I N D E C O N V O L U T I O N
Y, A pulse-echo signal is composed of reflections from acoustic impedance discontinuities along the path of wave propagation. In time domain deconvolution, the received signal y(t) is modeled as a convolution of material response h(t) and a source signal x(t), and an additive noise term n(t) (5-8) as follows:
y(O=x(O * h(t) + n(t)
l-h3
(1)
where * denotes convolution. The discretized counterpart of the signal y(t) can be represented explicitly in the matrix form
&(m)
The ith (i = 1, 2, 3 o o o m) column of the source signal matrix X represents the expected reflection at the ith time interval. The non-zero constants of each column are shifted one step down as the wave propagates an additional time interval corresponding to one sampling period in the digital data acquisition process, tf the propagating wave does not distort with time, all the possible reflections at any depth inside the material would be identical, i.e., all the no_~i-zero trains in each o f the columns would be identicaU 5-7) Whereas if the propagating
Planar Flaws in Attenuative Composites
103
Table I. Specifications of the Glass/Polyurethane Specimens m
Specimen thickness (mm)
Flaw material
Flaw dimension (ram)
Flaw impedance (10 6 kg/m2s)
Flaw wave velocity (m/sec)
Plies of glass preform
Steel
5.04
50 • 50 • 1.5
45
5660
16 (5)a
Aluminum Polypropylene
5.28 4.77
50 X 50 X 1.27 50 X 50 • 0.5
17 1.85
No flaw
4.64
--
6320 1950 15606
16(4) ~ 16 (2)~ 16 (0)~
2.3# 6
" Number in parentheses is the number of plies cut out to accommodate flaw material. J' Properties of glass/polyurethane composite.
oO eo 9
Oe ~ oo 0 O|
ooO o ~ 1 4 9 O 9174
O 9oe
e
OooOO <
The experimentally determined attenuation coefficient and phase velocity in the frequency domain are used to predict the waveforms of expected reflections. With the FFT amplitude spectrum of the front surface reflection, Pj~ of the specimen as a reference, the amplitude spectrum of the waveform from any depth inside the specimen, Po, with a unit reflection coefficient is determined by the expressionO~:
e 9~
Pe = PI 9 exp (-2c~d) 9 % - T 2
9176
(3)
0| t
1
I
I
2
3
4
,
Frequency (MHz) Fig. 2, Attenuation coefficient of the glass/polyurethane composite.
g
where a is attenuation coefficient for a planar wave, d is the depth inside the specimen, % is the loss due to non-planar effects such as beam divergence and beam shift caused by refraction and reflection at the interfaces, and T 2 is the echo transmittance which is the product of the forward and backward transmission coefficients. In Eq. (3), the terms % and T are assumed to be frequencyindependent. The frequency-dependent phase angle of the expected reflection, ~d, is given by: 2rod @d = % - -
c~
>
I
1
2
i
I
i
3
I
4
Frequency (MHz) Fig. 3. Phase velocity of the glass/polyurethane composite.
waveform distorts with propagation depth, the non-zero trains in the source signal matrix would represent a series of waveforms with changing amplitude and shape. Certain columns in the matrix, such as reflections at the front and back surfaces of the specimen, may be measured experimentally. The remaining columns, representing reflections that could occur between the front and back surfaces, must be predicted by a method such as that outlined in this paper. The predictions will be verified by experimental measurements of reflections from planar defects imbedded in the composite laminate.
(4)
where ~I is the phase angle of the reference, o~ is the angular frequency, and cp is the frequency-dependent phase velocity. Using the predicted amplitude (Pa) and phase (qbd) spectra in the frequency domain according to Eqs. (3) and (4), the time-domain reflection from depth d inside the specimen is obtained via the inverse FFT process. This discretized waveform corresponds to a certain column of the source signal matrix. X. Other columns in the source signal matrix consist of a series of reflections from increasing depths where the spacing was calculated according to wave speed and the sampling period in the digital data acquisiton process. Equations (3) and (4) are used to predict both the amplitude decrease and waveform distortion of a propagating wave in a highly attenuative composite materials. Predicted back-surface reflections from glass fiber reinforced PPD! (paraphenylene diisocyanate) polyure-
Huang, BaNs, Hahn, and Diwanji
104
1-:t
~, 0 . 5 0 <
,~ 6 8 1"0 1'2 14
0
Time (~s)
-0.5 .1 84
0
4
(a)
1
6
8
Time (gs) (b)
10
12
14
1,2..
0.8,
,-, 0.5
0.4.
0 ~'~ -0.4. < -0.8
< -0.5 ~1
-1.2. -
--'---"r'-
o
2
4
6
8
Time (~s)
10 12 14
0
2
4
6 8 10 12 14 Time (gs)
(d)
(e)
Fig. 4. Pulse-echo signals at 2.25 MHz (a) composite with a stainless steel insert, (b) composite with an aluminum insert (c), composite with a polypropylene insert, (d) unreinforced PMMA (polymethylmethacrylate).
thane composites with thicknesses of 0.3, 1.8, 3.6, and 5 mm and a measured back-surface reflection from a 5ram-thick specimen are shown in Fig. 1, where the arrival time is indicative of the overall wave propagation distance. The predictions were made assuming an incident signal produced by a 2.25 MHz, 25.4-mm diameter, 50.8-mm focal length transducer. The attenuation coefficient, phase velocity, echo transmittance were as measured, and the average beam pattern shift loss due to reflection and refraction at the water-composite interfaces' was calculated to be 0.36 dB/mm. Using the received signal and predicted source signal matrix, the material response matrix, h, is extracted with a one-at-a-time algorithm by minimizing the L1 norm of the noise matrix, n . (6'8)
II n II = ~ l Y, - X (i) ha I i=|
(5)
During each of the iterations, only one additional spike is extracted. The iterations continue until either a maximum number of non-zero spikes is reached, the L1
norm no longer decreases, or the L1 norm becomes sufficiently small. This procedure yields a spike train, h, whose convolution with the source signal, X, closely approximates the received signal, y.
3. P R O C E D U R E F O R DATA G E N E R A T I O N AND ANALYSIS S-glass/polyurethane specimens with planar foreign material inserts were fabricated to simulate potential flaws in composites (Table I). The matrix system was Airthane PET-75A 4 CHDI (cyclohexane diisocyanate) polyurethane intermediate cured with diamine-based curative Ethacure 3005. The dry fiber preform was unidirectional S-glass mat (275 g / m 2) CUt tO dimensions of 100 mm by 100 mm and stacked in a [0/90]~ sequence. Square holes were cut out of severa! plies in order to 4 Tradename, Air Products and Chemicals Inc.. Allentown, Pennsylvania. 5 Trademark. Ethyl Co~oration. Baton Rouge, .~uis~ana.
Planar Flaws in A t t e n u a t i v e Composites
1.0
105
lution process removes the effects of the test system, transducers, and water-specimen interfaces from the overall attenuation. Here a theoretical value of echo transmittance was used(9):
Time Interval 1 TI=27.7 ns
o.o <
4ZwZ~ (zw + zc) 2
Tz = -1.0
1
2
3
4
5
6
7
Time ( ~t s) Fig. 5, The spike train of (1/1/-1/-1) used to generate synthetic signals.
accommodate the thickness of the square inserts. Each dry glass fiber mat was hand brushed with a mixture of polyurethane prepolymer and curative, and placed in a mold. Specimens were then bagged, subjected to a vacuum for 12 minutes, and cured with a hot press at 100 psi and 212~ for 3 hours. The cured specimens were taken out of the mold and post-cured in an oven at 212~ for 24 hours. To measure the acoustic properties of the glass/polyurethane composite, an experiment was conducted in a water tank on a specimen without any flaw inserts. A Panametrics model 5055UA pulser/receiver was used to generate the electric pulses and to amplify the received signals. A Data Precision model Data-6000 wave analyzer was used to digitize and record signals with a sampling period of 27.7 ns (36 MHz sampling frequency). To obtain a broad bandwidth for the Fast Fourier Transform (FFT) analysis, a pair of 5 MHz, 12.7-mm-diameter, unfocused broad bandwidth transducers were used in these tests. While maintaining a fixed distance between the transducers, transmitted signals were recorded with and without a specimen between the transducers. In all instances, the ultrasonic wave traveled through the thickness of the specimen (perpendicular to the plane of the flaw insert). The time domain signals were transformed to Fourier spectra using the FFT technique. Around each center frequency (point of maximum amplitude), a frequency range was chosen to ensure an FFT amplitude greater than 5% of the maximum value. The wave attenuation spectrum was calculated with the amplitude spectra as follows:
1 PwT2 (x = - 20 log - -
d
Pc
(6)
where Pc and Pw are the amplitude spectra of the signals measured with and without a specimen. This deconvo-
(7)
where Z is acoustic impedance and subscripts w and c denote water and composite, respectively. The resulting frequency-dependent attenuation coefficient for the glass/polyurethane composite is shown in Fig. 2. The phase spectra were used to calculate the phase velocity, Cp, as follows(l~
cp-
1
1 ~w-~c
Cw
o)d
(8)
where +c and +~ are the phase spectra of the signal measured with and without a specimen and Cw is the wave velocity in water, 1483 m/sec. (9) The phase velocity of glass/polyurethane, as shown in Fig. 3, was approximately 1560 m/sec over the entire useful range of frequency. Since little dispersion was observed in the frequency range being used, it was assumed that the phase velocity and group velocity were the same so that the term "wave velocity" represents both in the following discussion. Pulse-echo mode experiments were conducted on the specimens with intentional flaws. A 2.25 MHz focused transducer was used as an optional compromise between temporal resolution and signal-to-noise ratio. The received signals, together with a reference signal measured with an unreinforced, unflawed PMMA (polymethylmethacrylate) sheet are shown in Fig. 4. All the flaws could be detected from the signals; however, details of the reflections from the flaw-composite interfaces used to identify the flaws were overlapped and unresolvable. Compared with the signal from the PMMA specimen, the received glass/polyurethane signals also contained strong structural noise. Clear front surface reflections from the composites, as shown in Figs. 4a-c were not available for use as reference signals due to the strong material inhomogeneity at or near the surfaces. Therefore, the reflection from the front surface of the PMMA specimen, as shown in Fig. 4d, was used as the reference. This substitute reference is referred to as the system response even though it may be slightly different from the front surface reflection of the composite. As a result, the deconvolved surface reflection from the composite may contain a
106
Huang, Bakis, Hahn, and Diwanji
>~, 0.4f ~ A
12[
TI=2
o.o lIVW
rI=2 l
,
0.6
- -,,..--
0.0 -0.6
-o.81. ', F.s . . . . . . . . . .
-1.2 0 1 2 3 4 5 6 7
0 1 2 3 4 5 6 7 >~ 0.4t
,~
1.2
TI=4
,
TI=4
0.6 0.0
0.0
~ -0.4~
~
Flaw
< -o.8 r, ', FS . 0
.
.
.
FS
-0.6 .
.
.
.
.
-1.2
.
1 2 3 4 5 6
1 2 3 4 5 6 7
9
TI=.8
TI=8
0.6 ~'~ 0.4 0.0 I
0.0
.,.., e.x.
-0.4
-0.8
-0.6 -1.2
. . . . . .
0
2
3
4
5
6
01
7
2 3 4 5 6 7
1.2 >_. 0.4 0.0
0.0
e~
E -0.4
-0.6
<
-0.8 1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
Time (Its) Time (~,s) Fig. 6. Typical synthetic 2.25 MHz signals (left) and the deconvolved spike train of (1/1/,1/-1) (right). Time intervals for the spike pair in die center, TI, are 2, 4, 8, and 12 sampling periods (one period = 27.7 ns). FS, BS denote reflections from the front and back surfaces of the specimen, respectively.
group of spikes instead of a single spike. In these cases, the major spike would be the reflection at the interface and the minor spikes would represent the near-surface inhomogeneity of the composite. The capability of the previously-described deconvolution algorithm to resolve overlapped signals was evaluated by applying it to synthetic signals generated by convolving the source signal matrix with closelyspaced material response spikes. A train of four non-zero spikes arranged in (1/1/-1/-1) fashion, as shown in Fig. 5, was used to simulate the front and back surfaces of the specimen and an embedded flaw with acoustic impedance greater than that of the surrounding material. The spike pair in the middle with opposite sign, representing the front and back surface reflections from the flaw, were separated by gradually increased time intervals between 1 and 20 (27.7 ns for each interval) such
that the actual signals reflected by the ~wo interfaces of the flaw would overlap by varying amounts, as shown in the left column of Fig. 6. Ideally, the original spikes used to generate the synthetic signals (Fig. 5) should be recovered through the deconvolution process: however, the numerical computation process usually limits the capability to recover very close reflections. Comparing the deconvolved spikes with the synthetic signals, the deconvolution definitely enhanced the temporal resolution of flaw interfaces, as shown in the right column of Fig. 6. Signals generated with a higher frequency, broader bandwidth transducer should have better resolvability of close spikes in the deconvolution process3s~ For reflections separated by less than half a period of the transducer's resonance frequency (for example, eight sampling periods for a 2~ MHz signal), the closely spaced spikes were not fully recovered~ Sig-
Planar Flaws in Attenuative Composites
4 I =
li0
107
Ri, = --T2wcRIc
4.19
2
J I[ , -1.01
11 -2
"
0
2
"
4
6 8 Time (gs)
i0
12
14
(a)
"~
3
~
2
.~
o -2
.
'
where T 2weis the echo transmittance of water-composite interfaces, RI~ is the reflection coefficient of the first flaw-composite interface, and Rwc is the reflection coefficient of water-composite interfaces. If attenuation within the flaw is low in comparison with reflection losses at the flaw-composite interfaces, the theoretical reflection for the second faw-composite interface, Ri2, of a flaw is given by: R,2 = - R , .
0
2
4
6 8 Time (g s)
10
12
14
d=
15t ! 1.0
1
0.22
0.5
-~ -0.5
Y~
-1
I I
-0.55 0
2'
4
-o.88
t
6 S 10 f2 14 Time(~s) (c) Fig. 7. The material response extracted with the new time domain deconvolution method applied to glass/polyurethanecomposites: (a) stainless steel flaw, (b) aluminum flaw, and (c) polypropyleneflaw.
hal overlaps as close as two sampling periods were detectable although the proper amplitudes were not accurately recovered.
4. RESULTS AND DISCUSSION The deconvolved material response from signals acquired with a pulse-echo inspection of glass/polyurethane specimens containing intentional stainless steel, aluminum, and polypropylene flaws are shown in Fig. 7. The spikes of the material response were normalized by the front surface reflection such that the relative reflectivity at the various interfaces could be compared. Relative reflectivities at the major points of interest are also marked in each case. The theoretical relative reflectivity of the first flaw-composite interface, Ril, is given by:
G2
(10)
where T~c is the echo transmittance of flaw-composite interfaces. The flaw thickness is calculated from the wave velocity in the flaw and the time-of-flight between the two interface reflections by:
(b)
"~"
(9)
Rwc
At'c 2
(11)
where d is thickness, At is time-of-flight (minimum detectable At is the 27.7 ns sampling period of the data acquisition equipment) and c is wave velocity in the flaw. The extracted reflectivity and thickness of the flaws along with the theoretical values are given in Table II, where theoretical values were calculated based on the acoustic impedances of 1.485 and 2.3 (106 kg/m2s) for water and glass/polyurethane, respectively. The extracted relative reflectivities for the first flaw-composite interfaces are very close to their respective theoretical values. Reflection at the second flaw-composite interface is clearly detected although the correct relative reflectivity is not accurately recovered. The extracted flaw thicknesses are very close to the respective actual values, especially considering that the resolution of digitization of 27.7 ns corresponds to 0.078, 0.088, and 0.026 mm propagation distances in steel, aluminum, and polypropylene, respectively. A few observations can be made from the results in Fig. 7. First, the flaw and composite must be in intimate contact and free from discontinuities since the reflectivities from the front interfaces closely matched the theoretical values, m ) The flaw material could be identified by the acoustic impedance which was calculated from the relative reflectivity of the flaw-composite interface. Second, the structural noise from the inhomogeneity of the composite was high enough to affect signals with low amplitude such as the reflections from the second flaw--composite interface. In such cases, the reflection was still detectable although the exact reflectivity was not accurately recovered. Locations of the de-
Huang, BaMs, Hahn, and Diwanji
108
Table II. Extracted Reflectivity and Thickness of the Flaws with Time Domain Deconvolution
Reflectivity (lst interface)
Reflectivity (2nd interface)
Thickness (tara)
Flaw material
Theoretical
Extracted
Theoretical
Extracted
Exact
Extracted
Steel Aluminum Polypropylene
4.07 3,44 -0,50
4.19 3.73 -0.55
-.75 - 1.44 0.49
-1.28 -0,74 0.22
1.58 1.27 0.50
1.64 1.31 0.46
2 ~" 1.5 r-
,,~ 0.5
~
o
~ -0.5 -1
0
2
4
6 8 Time (1~s)
10
12
14
(a)
5. SUMMARY
1.5 1.0
1.11
I ]
0.5
0 .-g '~ -0.5 -1
spikes are necessary to represent a single reflection, resuiting poor temporal resolution. Additionally, the value of the extracted reflectivity at the flaw-composite interface is attenuated such that one cannot accurately determine the acoustic impedance of the flaw based on the deconvolved data. Furthermore, because improper waveforms are used in the processing, significant errors such as the spike of -0.47 amplitude shown in Fig. 8b may be produced.
-0.53 2
-0.47 4
6 8 Time (l~s)
10
12
14
(b) Fig. 8. The material response extracted with the conventional L1 time domain deconvolution method applied to glass/epoxy composites: (a) stainless steel flaw, (b) aluminum flaw.
convolved spikes the extracted spike indicates the relative acoustic impedance of the flaw; a negative value for the front interface means the acoustic impedance of the flaw is lower than that of the glass/polyurethane. To demonstrate the improved resolving capability of the new time domain deconvolution model developed in this investigation, the same ultrasonic signals from specimens with stainless steel and aluminum flaws were also processed with the conventional time domain deconvolution method33-7) The deconvolved material responses are shown in Fig. 8 (compare with Figs. 7a and b). Because the frequency-dependent wave attenuation is not included in the conventional method, the system response used to construct the source signal matrix does not match the actual reflections. Consequently, several
To improve the temporal resolution of pulse-echo signals in ultrasonic flaw inspection, a new time domain deconvolution technique with L1 norm (least absolute value) minimization was developed. The deconvolufion technique incorporates adaptive waveform prediction, which enables the prediction of wave distortion in highly attenuative composite media. For the intentional plana r flaws studied, the first interface reflections were accu~ rately located and fully recovered, and the second interface reflections were accurately located. These improvements enhance the capability to identify the type and thickness of the flaws in media with high acoustic atten-: uation, such as elastomeric composites. The conventional time domain deconvolution technique was also applied to the same signals for comparison, it was dem~ onstrated that because of the use of an improper ex. pected source signal, the conventional deconvolufion method cannot improve the temporal resolution of flaws and even may produce erroneous results for the material system studied.
ACKNOWLEDGMENTS The present paper is based on the work funded by Lord Corporation and the Ben Franklin Program through contract 91C.1170R-3. The authors wish to thank Dr. Gerald M. Estes of Lord Corp, and Mr. J: E. Werner and Ms. B. L. Baughman of Ben Franklin Technology
Planar Flaws in Attenuative Composites C e n t e r for t h e i r s u p p o r t o f this w o r k . A l s o s u p p o r t b y the C o m p o s i t e s M a n u f a c t u r i n g T e c h n o l o g y C e n t e r at P e n n State U n i v e r s i t y is greatly a p p r e c i a t e d .
REFERENCES
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