The Application of a Time-domain Deconvolution Technique for Identification of Experimental Acoustic-emission Signals S i g n a t u r e a n a l y s i s of p u l s e e x c i t a t i o n s b y r e c o n s t r u c t i o n of t h e p u l s e ( s ) p r i o r to p a s s i n g t h r o u g h t h e m e a s u r e m e n t s y s t e m - - s y s t e m s m o d e l i n g , t e c h n i q u e analytical evaluation, and experimental application and results

by J.R. Houghton, M.A. Townsend and P.F. Packman

ABSTRACT--A method is presented for the signature analysis of pulses by reconstructing in the time domain the shape of the pulse prior to its passing through the measurement system. This deconvolution technique is first evaluated using an idealized system and analytical pulse models and is shown to provide improved results. An experimental situation is then treated; system-component models are developed for the digitizer, tape recorder, filter, transducer and mechanical structure. To accommodate both calibration results and manufacturer's data, and to provide stable mathematical models entails considerable effort: some 30 parameters must be identified to model this system--which is stiii a substantial approximation--albeit of very high order. Experimental pulses generated by a ball drop, spark discharge and a tearing crack are then deconvoluted 'back through' the system as modeled, using this technique. These results are compared and indicate (a) that consistent shapes may be expected from a given type of source and (b) that some sources can be identified with greater clarity using the deconvolution approach.

Introduction Acoustic-emission measurement is a relatively new tool in the field of nondestructive testing. A major interest of acoustic-emission research is to detect and characterize those emissions which indicate the presence of a growing crack in a structure; this task is usually further complicated by the presence of many acoustic-emission generators which are not crack-growth related (noise). To date, three

J.R. Houghton is Associate Professor, Mechanical Engineering Department, Tennessee Technical University, Cookeville, TN 38501. M.A. Townsend is Professor, Mechanical Engineering and Materials Science Department, Vanderbilt University, Nashville, TN 37235~ P.F. Packman was Professor, Mechanical Engineering and Materials Science Department, Vanderbilt University; is now Projessor and Chairman, Department o f Mechanical Engineering, Southern Methodist University, Dallas, TX 75275. Paper was presented, in part, at 1976 SESA Spring Meeting held in Silver Spring, M D on May 9-14.

approaches have had considerable application to this problem : (1) Pulse counting. All pulses whose amplitude is greater than a preselected baseline signal level are presumed to be crack-related emanations. These are counted as a function of time or some loading variable. Both the total count and the counts per unit time have been used to correlate acoustic emissions with plastic deformations, crack growth, etc. ~ (2) Fourier frequency spectra of acoustic emissions. Frequency spectra are examined to detect differences in signatures between one type of acoustic-emission source and another. 2 This approach has been handicapped because the acoustic-emission transducers may resonate at one or more natural frequencies when excited by a pulse. (3) Rise-time analysis of the leading edge of a pulse. In. this approach, the initial portion of the signal trace from the transducer is examined. The time to rise from a preselected level to a maximum height is measured and related to the severity of the energy released by the source? In this paper, a fourth approach, d e c o n v o l u t i o n , is presented in the context of an experimental setup. Pulseshape deconvolution is an analytical-computational method in which the dynamical influence of the measurement system components is assessed, modeled and then 'removed' from the recorded data (output) so that the actual input may be studied. Basic theory may be found elsewhere, e.g. Ref. 4, and some aspects of system design for deconvolution are in Ref. 5. The deconvolution approach shares some features with Fourier-transferfunction technique.' In this paper, the implications of modeling of a r e a l system and deconvoluting experimental pulses are addressed after a brief introduction to the general techniques. 9 First, numerical solutions for analytical pulses (approximations to acoustic emissions) are obtained for a simplified system (model); in addition to providing a basis for presenting the technique, these indicate that the deconvoluted (time-domain) output signal is a much improved representation of the original pulse vis-a-vis other

Experimental Mechanics 9 233

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characterizations. Second, an actual experimental setup is then modeled, and the deconvolution technique is implemented to 'counteract' the dynamical influences of the transmitting medium in the presence of this real system composed of the transducer, filters, amplifier and tape recorder. Results for several experimental pulses are presented.

The essential features of an acoustic-emission measuring system are shown schematically in Fig. 1. In this section, the transducer is represented by a single-degree-of-freedom oscillator and the filters are single-pole designs. Neglecting the digital-data-recording equipment, the differential equation which describes the system shown in Fig. 1 is as follows : ( D 2 + 2 ~ . D + oJ~)(D + o~h~)(D +

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The numerical solutions of differential .eqs (1) and (2) are obtained using a modified Runge-Kutta integration method. To provide some motivation and background for what follows, in the early stages of our investigations into acoustic emissions, we were interested in designing a measuring system that would have the best match of the frequency spectra Y~ and }'4, to extend previous investigations. Among other things, s it was eventually shown that the two curves Will never be a good match as 10ng as there is a high-pass filter in the system. High-pass filters

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operator damping ratio oJ, = x/K/J~, transducer natural frequency (27rf,) oJhp = corner frequency of high-pass filter (21rf,p) o~,. = corner frequency of low-pass filter (2~rf,~) K~, = calibration constant of transducer It is assumed that the transducer is designed to respond to an input force (acceleration) at the base, hence the input is denoted Z, merely for clarity. Deconvolution is defined as solving for Zs which is to be a faithful representation of the input trace ZI in the time domain, given the actual output signal Z. and the system differential-equation model. Deconvolution of the system described by the eq (1) is as follows : = d/dt = C/2

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are used because most of the early work in acoustic. emission measurements showed that to obtain meaningful pulse measurements from a system under stress, lowfrequency machinery noises must be filtered out. This provided some motivation for considering alternate approaches, one being the present deconvolution approach. To initiate the studies, three different geometric shapes (square., triangle and [l-cosine]) were selected for the input ZI. These pulse shapes are passed through eq (1) to get an output signal Z4. Then Z4 is deconvoluted via eq (2) to find how close the approximation of the input s h a p e Zs would be to the original input ~1. The com-

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For comparison, the Fourier-spectra computations are also indicated in Fig. 1. Figures 2 and 3 show the relationships between input and output signals in time and frequency domains and the deconvoluted output for selected cases. The time axes are nondimensionalized by multiplying the time units by the dominant natural frequency of the transducer. Figure 2 shows results for a long rectangular-pulse input (duration of 8 times the transducer natural frequency) impressed upon representative system parameters. Transducer characteristics are those of a commercially available acoustic-emission transducer for pulse-counting applications.? These typically have low damping ratios (e.g., .01) which results in the distinctive ringing of the transducer which appears in the output signal Z4 and its Fourier spectrum Y4. The deconvoluted output Z~ does not have exactly the same shape as the input pulse, but the shape

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t For example, Dunegan/Endevco acoustic-emission transducer model no. D9202, commonly used f o r pulse counting. In general, pulse-counting transducers are the most highly developed devices.

Experimental Mechanics 9 235

between shapes. An exhaustive study of such numerical experiments suggests some comments that can be made about the acoustic-emission methods listed in the Introduction (which tend to be corroborated by the experimental results presented later in the paper) : (1) Pulse-counting instrumentation would have counted 15 or more pulses in this example depending on the trigger signal level setting. There are only four pulses present. (2) Fourier spectrum analysis would indicate the highest energy content at the transducer natural frequency. The triangular and square signals could not be identified from the Fourier spectrum. (3) Rise-time analysis would show the largest rise time for the shortest pulse and the value will be near the quarter period of the transducer natural period for all pulses. Critical to this technique is the development of suitable dynamical models of the system components. These are developed in the next sections and then implemented with

of Zs is a good approximation of Z1. The error between the two plots is on the order of 3 percent. In Fig. 2(b), the Fourier spectra of ,~, and Z4 ( Y , and Y4, respectively) indicate the types of errors one can expect when analyzing a pulse after it has been modified by the measuring system. The first point of interest is that the highest energy content of Y, is at the transducer natural frequency. The second point is that the Fourier signature of this pulse loses a significant part of the signature for frequencies below the high-pass-filter cutoff frequency fhp. However, the Fourier signatures for all of the geometric pulses tested have their energy concentrations highest at the low frequencies, tapering off as the frequency increases. In these studies, the long rectangular pulse (Fig. 2) represents one of the more difficult cases (see Ref. 5). To further demonstrate .the potential of pulse-shape deconvolution, sequences of analytical pulses were generated and analyzed as above. A typical result is shown in Fig. 3, for which similar observations as above can be made; Fig. 3 clearly shows the ability to differentiate

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The digital event recorder (Bruel and Kjaer Model 7502), by the very nature of its operation, caused a cluster of high-frequency additions in the data in the region of the effective digitization frequency (3.2 MHz) and at half the digitization frequency. (The signals were recorded at 60 in./s, played back at 1 7/8 in./s and digitized at 100 KHz.) This recorder also showed a frequency component at one-fifth the digitization frequency. The two highest frequency contributions did not interfere with the calculated result after incorporating a low-pass filter into the program, but the 640 KHz component did affect the results. [See Fig. 5(b).]

Deconvolution of experimental data requires an acceptable mathematical model for each of the components in the measurement system. When commercial equipment i s available, a frequency-response curve is frequently provided or a specification is given for the bandwidth of the instrument. This information and experimental frequency-response curves can be used to create component models of arbitrary complexity. An information flow diagram and components are shown in Fig. 4 for experimental implementation of the system of Fig. 1. This setup was employed to record the acoustic emissions from a spark discharge, a dropped steel ball and a tearing crack. The deconvolution models of a few of the components using the manufacturer's curves and the experimental data tended to generate excessive high-frequency noise or were susceptible to d-c drift. In order to reduce these effects, suitable poles and zeros were placed outside of the frequency range of interest in acoustic-emission studies in the mathematical models to eliminate any infinite gains at extreme frequencies. The model equations which were developed for each of the components are described in the following paragraphs. The respective diagrams in Fig. 5 show the resulting transfer function.

Tape Recorder An Ampex Corporation type PR 2200 configuration for direct recording was used to record the experimental pulse traces at a speed of 60 in./s. The steady-state frequency response of the tape recorder was measured experimentally and the results are shown in Fig. 7. The current mathematical model used to deconvolute the effects of the recorder on the data is rather complex in order to fit the experimental plot. In the transfer function of the tape-recorder model and the corresponding response plot [in Fig. 5(c)] poles and zeros have been added to reduce very high gains at the extreme frequencies.

Amplifier and Filter

Lowpass Filter The low-pass filter is not inherently a component of the system, but is found to be desirable to attenuate the spurious high-frequency noise from the digitizer and the tape recorder. The roll-off frequency for this filter was 400 KHz, about twice the high frequency cut-off of the tape recorder. This frequency was selected by experimenting with the deconvolution procedure. Higher values of rolloff frequency admit extraneous signals that could mask over the significant pulse information. [See Fig. 5(a).]

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Fig. 6--Compact tensile-test specimen

The short compact single-edged fracture specimen is shown in Fig. 6, with loading as indicated. The specimen is fatigue precracked to 25 mm from the load line, ' A ' denoting the acoustic-emission source zone. The model developed for the aluminum-plate compact tensile specimen is an approximation arrived at by the following empirical approach :

Experimental Mechanics 9

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Experimental Results The modeling portion of this investigation involved the determination of more than thirty variables. The methods for establishing the model coefficients are in a continuous state of improvement. Thus, the solutions tend to be a little 'better' with each new model innovation. At this point, several experimental tests have been conducted to evaluate the deconvolution models of actual acoustic emissions. Acoustic emissions were induced in the compact tensile specimen with the fatigue crack as shown in Fig. 6 in three ways : (1) Electric-spark discharge. This is a fairly standard calibration device which provides a simple, short pulsewidth acoustic pressure wave by a spark discharging a capacitor across an air gap. Details of the electrodes are shown in Fig. 7. 3500 V are unloaded by a 0.025-#F capacitor across the 0.5-mm gap, 1.5 mm above the plate region A. The electrodes are tungsten. The spark is insulated from the test specimens. (2) Steel ball dropping. A 1.01-g bail (bearing) is dropped 10 mm onto region A of Fig. 6 .

238 9 June 1978

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(l) All of the test traces recorded on the compact tensile specimen with the Dunegan/Endevco transducer were deconvoluted to the base of the pickup. (2) The frequency spectrum of each deconvolution trace was computed. (3) Dominant frequencies were identified which appeared in most of the frequency spectra. These were assumed t o be common resonant frequencies excited by different experiments and, thus, inherent frequencies in the plate. (4) Another deconvolution step was performed with a model using the frequencies selected. When the frequency spectrum of this deconvolution trace approached the pattern of the frequency-spectrum signatures shown in Fig. 2 (}'1) for analytical pulses, it was considered to be an acceptable model for the test specimen. This rationale is based on the fact that the transducers are very lightly damped and show virtually identical frequency spectra for almost any pulse shape. Accordingly, having verified all other components of the system using analytical pulses such as in Fig. 2, the remaining component which must resonate suitably is the specimen. This ad-hoc 'correlation' was employed to identify the parameters and degree of an assumed model form. This model is probably not sufficiently developed to give the true deconvolution of the wave shape at the initiation site, but it does serve as an approximation. The model transfer function and the frequency plot for an approximation of the specimen are shown in Fig. 5(f),

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(3) Crack growing. The specimen was pulled apart in an Instron screw-driven tensile-testing machine. The deformation rate was .013 mm/min. Because the spark discharge is a fairly standard calibration device, it is presented to show the repeatability of acoustic emissions from the same source. Samples of three acousticemission measurements (Z4) and the respective deconvoluted signals (Z6) from this source are shown in Fig. 8. (Recall Z6 differs from the previously-used Zs by inclusion of the test specimen.) The shapes of the original pulses are similar and the deconvolution results are approximately the same. Comparable repeatability is obtained with the ball drop and crack growth. (Obviously, each crack-growth experiment involves a different specimen and some differences, accordingly.) Therefore, ability to discriminate between sources is now investigated. In Fig. 9, the 'as-recorded' data and deconvoluted signatures are shown in juxtaposition for the three sources. From the deconvoluted signatures Z6, a ball dropping can be clearly distinguished from a crack growing or a spark discharge; the distinctions are less clear in the as-recorded data (Z,): Closer comparison of the spark and crackgrowth deconvolution signatures suggests slight differences between these also. These are seen in respective frequency spectra in Fig, 10. In general, however, from Figs. 9 and 10 it appears that the growing crack has a signature similar to the electric-spark discharge. This may be due to some analogism of these events in that stored energy is released in a short time interval. Future refinements should indicate how closely these two events resemble one another. From the foregoing, the as-recorded data are less sensitive to source differences than the deconvolution signatures. These differences would also be seen in comparisons of 'as-recorded' pulse counting techniques with the deconvolution signatures.

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In examining the deconvoluted data of Figs. 8 and 9 one may detect a slight negative ramp over this time span. It turns out that this is an artifact of the deconvolution due to an inadequacy of the model at low frequencies (below the range of interest in acoustic emissions)--i.e., a failure to filter out certain low frequencies. Presumably, the low-frequency cutoff could be modified to eliminate this--probably in the specimen model, which continues to be a source of model improvement. What is at present significant is the repeatability (reliability) of the deconvolution procedure for a given source and the ability to discriminate between different sources.

Summary Deconvolution shows promise as a signature-analysis method for the examination of individual acoustic-emission pulses. To test this new technique, an idealized measurement system model was used and analytical pulses were introduced as input signal shapes. The output signals were then sent through the inverse of the system model and this deconvoluted result was compared with the input signal. These results were compared with pulse counting and frequency-analysis techniques now used in the analysis of acoustic-emission signals; the deconvolution method was demonstrated to be a significant improvement. To apply this technique to an actual experimental situation, an acoustic-emission measuring system was then modeled component-by-component in terms of the manufacturers' cover and observed results. This is an essential link in the deconvolution technique. In the present study, more than 30 parameters had to be determined.

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After confirming that this technique would yield reliable and repeatable data for a given situation, a 'discrimination of acoustic-emission sources' experiment showed that 'asrecorded' data is not as sensitive to source differences as the deconvolution signatures. It also appeared that crack growth and the spark discharge had some similarities in their signatures, the dropped ball being markedly different. However, well-defined input pulses must be developed and used in a number of circumstances before stronger assertions can be made about the deconvolution method of analysis (and, perhaps, any such method). This is now under way. Acknowledgment Financial support for this research was provided by the National Aeronautics and Space Administration, Measuring Sensors Branch, Marshall Space Flight Center, under Grant Number NSG 8012.

References 1. Liptai, R.G., Harris, D.O. and Tatro, C.A., Acoustic Emission, A S T M Special Tech. Pub., ASTM, Philadelphia, STP 505 (1972). 2. Beattie, A.G., "'An Analysis o f the Frequency and Energy Characteristics o f Acoustic-emission Signals from Tensile and Structural Tests, ""presented at SESA Spring Meeting, Chicago (1975). 3. Shinners, S.M., Modern Control System Theory and Applications, Addison-Wesley, Reading, M A (1972). 4. Gabel, R.A. and Roberts, R.A., Signals and Linear Systems, John Wiley & Sons, New York (1973). 5. Houghton, J.R., Townsend, M.A. and Packman, P.F., "'Optimal Design and Evaluation Criteria f o r Acoustic Emission Pulse Signature Analysis, "" J. Acous. Soc., 61 (3), 859-871 (Mar. 1977). 6. Favour, J.D., "'Transient Data Distortion Compensation, '" Shock & Vibration Bull., (35) Part 4, 231-238 (Feb. 1966).

Experimental Mechanics 9 239