1. INTRODUCTION

Digital Signal Processing (DSP) concepts [1, 2] were introduced many years ago and later emerged as the primary means of detecting, conditioning and automatically classifying a variety of signal types. DSP techniques have been proven successful in radar, aeronautics, communications, acoustics, seismology, speech/image restoration and recognition, energy generation/distribution systems, and financial prediction. DSP hardware realization capacities have increased geometrically (according to Moore's Law), decreasing computation time and instrument dimensions to the point where hardware implementation of certain algorithmic approaches requiring a given degree of storage and processing throughput would have been unthinkable only a year ago.

Unfortunately Ultrasonic Nondestructive Evaluation (UNDE) and UNDE Instrumentation Development have not exploited the advantages offered by DSP implementations as much as one would expect. This is in spite of the fact that compared to analog signal processing systems, digital systems have the following advantages:

1. Greater Signal Transmission Fidelity
2. Large Non-volatile Storage capabilities
3. Processing/calculation/classification capabilities, and
4. More sophisticated filtering and signal analysis methods

The paper opens with a review of several key DSP fundamentals that impact UNDE. Next, signal filtering techniques, such as correlation and FIR filters, will be described and demonstrated on steel plates, even though these techniques are equally applicable to many other test scenarios (e.g. air-coupled inspection of cement, pultrusion, and wood testing). The paper closes with a discussion applying DSP to acousto-ultrasonic (AU) NDE (also known as resonant testing), which is suited to high volume, rapid throughput component test scenarios needed to minimize scrap in manufacturing, as well as certain in-service test scenarios.

2. DIGITAL SIGNALS AND SYSTEMS

2.1 General Architechture And Methods
A DSP-based UNDE system will have many components shared by its analog counterpart, as shown in Figure 1. It will have an ultrasonic pulser, a receiver and several piezo-electric transducers (PZTs) situated near or coupled to the part or material under test. Because a DSP-based system is under some kind of CPU control, it inherently has the ability to automate several test functions, in addition to its DSP capabilities that would include filtering, signal conditioning, and signal classification.

Fig 1: DSP-Based UNDE System

An optional addition to the DSP UNDE system could be a switch matrix/multiplex unit, enabling multi-channel acquisitions (e.g. pulse-echo, through-transmission, etc.). If however, multi-channel acquisitions need to be performed simultaneously, than individual pulser/receiver channels need to be used. Whether single or multi-channel, the continuously varying received analog output, x(t), is sampled to create a discrete digital sequence, x[n], that is sent to the digital signal processor for manipulation.

Commercially available (e.g. Texas Instruments, Analog Devices, etc.) DSP-specific chips used for these various signal conditioning and classification functions are either fixed or floating-point processor. Typically, fixed-point processors have greater processing speeds but require careful scaling to avoid round-off errors due to numerical over/underflow. Recently, general-purpose chip manufacturers have started to add DSP capabilities to their floating-point processors (e.g. Motorola's G4 PowerPC Altivec vector capabilities) to put DSP within easier reach of the overall programming community. However, because we are dealing with discrete time samples, care must still be taken when converting from the analog, x(t), to the digital, x[n], domain.

2.2 Digitizing the Time Axis
A continuous time analog signal x_a(t) has to be converted into a sequence of discrete time signals, represented by a sequence of numbers x, denoted x[n], with n being the n^th number in the sequence. Such a sequence is the result of periodic sampling of the continuous time analog signal x_a(t),

x[n] = x_a(nT) T is the sampling period, and 1/T the sampling rate or sampling frequency. For ultrasonic applications this is typically in the MHz range. The sampling frequency, W_S = (1/T), has to be greater than the bandwidth W_N of the signal being sampled. More precisely, according to the Nyquist Sampling Theorem, for a correct representation of a digitized signal, the sampling frequency W_S has to be at least twice as high as the bandwidth W_N:

W_S = 2p/T > W_N

Under-sampling, or sampling at rates less than the Nyquist requirement will cause "aliasing", which results in "shadow frequency images" of the original signal.

2.3 Digitizing Signal Amplitude
The A/D converter in Figure 1 performs the initial amplitude discretization for the input analog ultrasonic signal prior to further conversion needed during processing by either a fixed or floating-point signal processor. This conversion process quantizes the signal amplitudes into a sequence of finite-precision samples. The precision or quantization error is determined by the number of amplitude quantization levels. This quantization error can be represented as an additional noise signal component, as illustrated below in Figure 2.

Fig 2: Ultrasonic Transducer impulse response used to illustrate the effects of Analog-to-Digital Conversion Quantization Error

Part (a) of Figure 1 is the infinite precision plot of an ultrasonic transducer's impulse response. A 3-bit A/D converter (b=3) will have 2^b or only 8 levels of amplitude granularity resulting in the digital representation illustrated in part (b), with its associated quantization error in (c). Parts (d) and (e) illustrate the case for 8 bit quantization-note the decrease in quantization error from 0.2 to < 5.0x10^-3 for the 8-bit case. The effect of quantization error on the signal retrieval capabilities of a DSP-based UNDE instrument can best be understood in terms of loss in the system's dynamic range, approximated by 6b, in dB. Stated differently, the dynamic range of the 3-bit system is approximately 18 dB, while that of the 8-bit is 48dB. That means that if the signal of interest is below that value it can never be retrieved simply because it was never sampled properly in the first place. The dynamic range of the DSP-based UNDE instrument must always have enough room to allow accurate digitization of both the signal and the competing noise. For this reason, certain special ultrasonic applications may require 12-bit granularity; however, 8 bits is typically adequate for most situations.

2.4 Linear and Nonlinear Systems
All ultrasonic NDE systems discussed in this paper belong to the so-called Linear Time Invariant (LTI) class of systems [1,2]. LTI systems are completely described by their impulse response, meaning that the system's output for any input signal can be predicted, if its response to an input impulse is known. This implies that the response of the material is always linear to the ultrasonic stress wave that is used to interrogate it. Under certain circumstances, flawed material (e.g. fractures and disbonds) will deviate from the linear stress-strain relation implied by Hook's law-therefore, DSP-based UNDE systems of the future can modify their algorithms to differentiate the nonlinear properties related to these flaws from the surrounding returns that are linear. One such interesting effort is described in [3].

3. TIME AND FREQUENCY

The Fourier Transform is one of the most powerful tools for signal analysis and processing. It was developed by Jean Baptiste Joseph Fourier two centuries ago. Any signal (periodic and aperiodic) can be approximated by superimposing sinusoidal functions sin(wt) and cos (wt) of different frequencies w. The higher the number of sinusoidal functions used, the more accurate the approximation. Figure 3 shows an example of synthesizing a square wave with 1, 2, and 6 functions.

Fig 3: Synthesizing a square wave with (a) one, (b) two, and (c) six sinusoidal functions.

Fig 4: Fourier Transform of signal of figure 3 (c)

If signals can be synthesized from sinusoidal functions, the process can also be inverted. A mathematical algorithm called the Fourier Transform performs this. The result performed on the signal of Figure 3 (c), is shown in Figure 4, with the abscissa representing the discrete frequencies. The ordinate shows the amplitude of these frequencies.

Both Figure 4 and Figure 3 (c) represent the same signal. Figure 3 represents the signal in the time domain, whereas Figure 4 represents the signal in the frequency domain. The conversion process from the frequency to the time domain is called Inverse Fourier Transform.

Many signal processing and analysis procedures use frequency domain signal representation. Fourier analysis is of particular importance in acousto-ultrasonics, where material features are analyzed using the entire ultrasonic signal duration. It can be a complementary tool to conventional ultrasonic testing, where it is common to use only amplitude measurements at one particular instance.

4. DIGITAL FILTERS

Digital filters can be designed for precise purposes and are not restricted by the availability and characteristics of hardware components. Two classes of such filters, Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filters, is possible-the latter being selected most often for ultrasonic testing. Linear phase FIR filters have the advantage of filtering specific frequencies without disturbing their phase relation, and allowing a precise reconstruction of the signal in the time domain.

Averaging the ultrasonic signal is a common method of enhancing the signal-to-noise (S/N) ratio. This method slows down data acquisition, because the pulse repetition rate of ultrasonic instruments is orders of magnitudes slower than the processing time needed to perform averaging. In addition, the efficiency of averaging is limited and the method can be insufficient, as demonstrated in the following example. Figure 5 illustrates the pulse-echo signal from a 4 MHz transducer applied to a 200-mm thick steel plate. All spikes represent noise. No characteristic signal can be distinguished. The results of averaging are shown in Fig.6.

Fig 5: Unfiltered, unprocessed pulse-echo signal from 200 mm thick steel plate. Baseline is in mm.

Fig 6: Averaged signals from set-up of fig.5. Upper trace: 4x average, Lower trace: 64x average

Averaging in Fig. 6 resulted in a lowering of the amplitude from 100% to 60 and 30 %. The 1.5-mm flat bottom hole present in the specimen does not show up as a signal. The power of a correlation FIR filter for 4 MHz is demonstrated on the same set-up as used for Figure 5. The results are shown in figure 7 (a) and (b). Additional signal averaging was used. Note the clear reflection from the flat bottom hole at 120 mm depth and the backwall echo at 200 mm. Averaging did not lower the amplitudes from these signals, but it did reduce the noise between them.

Fig 7: FIR filter 4 MHz on 200 mm steel plate with 1.5 mm flat bottom hole. (a) with additional averaging of 4x, (b) with averaging of 64x.

The superiority of the FIR filter over averaging is further demonstrated on a larger scale of 1 m, using the same specimen as in Figure 5. Fig. 8(a) is unprocessed.

Fig 8 (a): unprocessed signal from steel

Fig 8 (b): averaged signal 64x.

Fig 8 (c): Signal obtained with FIR 4 MHz .

The result of averaging is shown in Fig. 8 (b). The multiple backwall echoes from the 200 mm steel plate are discernible, but with a low dynamic range. Fig. 8 (c), obtained with the FIR filter, shows these echoes with a good, large dynamic range. This demonstrates the possibility of detecting flaws in steel of at least 1m thickness using the FIR filter.

Last, it should be noted that the roughness or granularity evident in Figures 5 through 8 is due to round off granularity from actual screen captures from the DIO-562 flaw detector instrument. It is not due to internal quantization, since this instrument initially digitizes signals with 8 bits.

5. ACOUSTO-ULTRASONICS

Acousto-Ultrasonics (AU) [4] is a nondestructive method of evaluating a manufactured component or material region, which may be part of a larger structure, by analyzing the received simulated stress waves to detect and map variations of mechanical material properties. The simulated stress waves are generated by placing two contact transducers typically on the same side of the specimen, separated by some prescribed distance. The transmitting piezoelectric transducer issues a highly damped broad band impulse, which is scattered in all directions propagating through the medium, and the collective wave components are received by one or more remotely located transducers, as illustrated in Figure 1. The receiving probes are typically not in a line-of-sight position, and therefore, they collect a continuum of reflections and scattered wave modes. In essence, they collect the "impulse response" of the material segment or part being characterized. Thus, the term "Acousto-Ultrasonics" denotes a combination of acoustic emission monitoring and ultrasonic characterization.

AU has the advantage of being able to rapidly assess the collective effects of many sub-critical flaws and material anomalies, and therefore, AU waveform attributes or features may be related to structural in-service performance, or part reliability. As an example, one of the authors designed a system [5] for use by a manufacturer that was originally using a CATscan for inspecting composite billets that were to undergo a further, expensive machining process. Several years and 500,000 parts later, the AU system has since replaced the CATscan for various reasons. First, inspection throughput was reduced from 17 minutes to 50 seconds (it should be noted that according to Moore's Law, inspection throughput for this system built today would be around 10 seconds-the time needed for signal acquisition). Second, the AU system classified flaws into several categories that were endemic to that manufacturing process. Lastly, the total hardware cost needed to realize the AU system 7 years ago, cost less than 10% of the CATscan (~$500,000 or < $50,000). It would cost less today.

Fig 9: AU Spectrograms for Riveted Plates

There are a host of applications where the AU NDE configuration is applicable-many of which are listed in [4]. A recent application of AU was detecting micro-corrosion between riveted plates [6]. This was directed towards the aging aircraft problem. Figure 9 illustrates two joint-time-frequency spectrograms where it is quite evident that even in its very early stages, micro-corrosion tends to damp the lower frequency response in the time domain, while attenuating the higher frequency components that would normally occur with uncorroded plates.

6. SUMMARY

Whether the application is a general purpose NDE situation, as depicted in Figures 5 through 8, or a very product-specific test scenario, as illustrated above in Figure 9, none of these would have been possible without the use of highly sophisticated DSP algorithms. DSP is the enabling technology furthering NDE science in the new millennium.

7. REFERENCES

1. A.V. Oppenheim and R.W. Schafer: Discrete Time Signal Processing. Prentice Hall, New Jersey, 1989. ISBN 0-13-216292-X.
2. A.V. Oppenheim and S. Willsky: Signals and Systems.Prentice Hall, New Jersey, 1983. ISBN 0-13-809731-3.
3. A.M. Sutin and D. M. Donskoy: "Nonlinear Vibro-Acoustic Nondestructive Testing Technique," Nondestructive Characterization of Materials VIII, Robert E. Green, Jr., ed., Plenum Press, 1998
4. A. Vary, The Acousto-Ultrasonic Approach, in Acousto-Ultrasonics, Theory and Applications, J. C. Duke, Jr., ed., Plenum Press, 1988.
5. T. J., Gill, Jr., Bartos, A. L., "An Acousto-Ultrasonic Platform for the Quality Assessment of Thick Radial Ply Composite Structures," Nondestructive Characterization of Materials VI, R. E. Green, Jr., et al., eds., Plenum Press, 1994.
6. K. Shiloh, A. Bartos, A. Frain, and E. Lindgren "Detecting Corrosion between Riveted Aluminum Plates using Acousto-Ultrasonics and Dynamic Impact Testing," SPIE Proceedings of the 5^th Annual International Symposium on Nondestructive Evaluation and Health Monitoring of Aging Infrastructure (March, 2000)