A strategy is presented here to develop guided wave inspection systems using short-range ultrasonic guided waves. A hybrid analytical finite element method (FEM) is presented. The importance of dispersion curve computation, wave structure analysis in the test part, actuator design, the establishment of appropriate boundary conditions from the actuator design to be used in any FEM computations leading to key experiments, and aspects of system design are discussed. Several interesting problems reported by the author in previous publications are used here to stress the importance of mode and frequency choice when solving guided wave problems.

## Introduction

Computation plays a critical role in the development of any ultrasonic guided wave inspection system. Beyond hardware and software development, modeling analysis is essential for evaluating various designs and ultimately relates to making a good choice from hundreds of test points available on the dispersion curves. The process is illustrated in Fig. 1. Highlights of seven sample problems reported in previous works of the author are discussed that considers aspects of the hybrid analytical finite element modeling (FEM) approach for ultrasonic guided wave system design.

First, phase and group velocity dispersion curves must be calculated for a particular waveguide structure being considered. Wave structure computation is also critical. The early part of the process is the analytical portion of the hybrid analytical FEM approach for solving guided wave problems and leads to a mode and frequency choice based on experience, further modeling of wave interactions with certain defects in specific structures, or an intuitive selection and evaluation. Basic principles of guided wave phase, group, and attenuation dispersion curves along with wave structure details can be found in Rose [1].

The actuator design could be, for example, a normal or angle beam device, or a comb-type array utilizing a piezoelectric, electromagnetic acoustic, magnetostrictive, laser, or controlled mechanical impact device. Closeness to other mode points in an attempt at mode isolation, or phase velocity spectrum source influence, and a center frequency and frequency spectrum must be considered. See Figs. 2 and 3, which depict phase velocity dispersion curves with conceptual phase and frequency spectra for a simple plate-like structure, illustrating the difficulty of the generation of a single mode in a structure. Quite often, guided wave signals appear noisy, but the information is not noise, it is coherent wave propagation from different modes. Nevertheless, proper transducer design can narrow the phase velocity and frequency spectra and also reduce side lobes in the spectra if they are present. In order to select a specific point in the phase velocity dispersion curve space, a frequency is selected to cross the activation line for the particular actuator design, but note that, because of the excitation zones, other modes can propagate. Additional reading material on specific mode and frequency selection tips can be found in Philtron and Rose [2].

The most important issues are mode and frequency choice and sensitivity to the particular inspection situation. The actuator design, often derived from the wave structure information, can then be tested with suitable FEM models and computation. Success here could lead to key experiments, or failure could prompt additional wave structure analysis and new actuator designs in a feedback process to optimize a design. If key experiments are successful, the process leads to a system design. If experiments are unsatisfactory, additional feedback is required as shown in Fig. 1 in an attempt to get to a final system design.

As a result of the significance of mode and frequency choice for solving new critical guided wave problems, a few sample problems are discussed in this paper. Additional examples can be found in Rose, Appendix D [1]:

1. (1)

a surface-breaking defect;

2. (2)

transverse crack detection in a rail head;

3. (3)

a weak interface in a bonded repair patch;

4. (4)

5. (5)

aircraft problems of lap splice, tear strap, and skin-to-core delamination;

6. (6)

coating delamination in pipe; and

7. (7)

corrosion under pipe support and elbow inspection.

The solutions presented are not necessarily unique. Multiple solutions are possible because of the many mode and frequency choices available. Optimization is generally not possible because of the required numerical solutions as opposed to analytical solutions. Even the choice of sensitivity variable in the wave structure could be different, including, for example, in-plane or out-of-plane displacement at a particular region, a stress variable, an energy variable, a wave velocity parameter, or energy absorption.

These discussions are presented to enhance creativity and logic for finding solutions to inspection problems that might benefit from a guided wave approach, especially for short-range guided wave propagation.

## A Surface-Breaking Defect

Let us start by considering a fairly simple problem of finding and sizing a surface-breaking crack. Early work on mode and frequency selection based on certain features and wave structures was reported by Ditri et al. [3]. At any frequency, a finite but possibly large number of Lamb wave modes could propagate in a layer. Each mode, when excited, will produce a different deformation field inside the layer; that is, the particle displacements and velocities as well as the stress and strain fields will all vary with depth inside the layer in a different manner for each mode. In fact, even the same mode at a different frequency (times thickness) will cause different field distributions. Ditri et al. [3] investigated in early work the possibility of using, as a selection criteria, a mode's energy distribution across the thickness of the layer. This is only one of many criteria that may be tested, but it was chosen because it had a somewhat appealing intuitive basis behind it.

Studies of energy distribution across the layer can be utilized, therefore, for mode and frequency selection to carry out crack detection and depth studies. To find a small surface-breaking crack, sufficient energy must be at the surface of the plate. Also, to find an almost-through crack approaching 100% in depth, the wave structure must have sufficient energy on the opposite side of the plate. This is the starting point. Find the proper mode and frequency via an appropriate wave structure. The solution here is straight forward. If further detail is needed on this problem, see Refs. [1,3].

## Transverse Crack Detection in the Head of a Rail

The goal of this study was to develop a guided wave method that could detect transverse cracks in the head of a rail, even with random shelling on the head of the rail, typical spalling that occurs in a Hertzian contact stress loading situation. Ordinary bulk wave measurements used today in a wheel probe are often not effective for detecting such transverse cracking. Following the strategy in Fig. 4, the first step was to obtain dispersion curves in a rail. Hayashi et al. [4] accomplished this task with the SAFE technique, but found so many close-by dispersion curves that it proved difficult to analyze. Subsequently, Lee et al. [5] tackled the problem by examining wave structures at various regions of the dispersion curve (see Figs. 46).

In Fig. 4, the areas of concern are listed as 30–1, 30–2, 30–3, 30–4, and so on, as noted in the figure. The wave structures at specific points in the dispersion curve space were examined to find special points that would have maximum energy, for example, on the surface, in the head, in the web, or in the base of a rail. It was found that at position 30–1, as the lower-order mode moves to higher frequencies, this lower-order mode energy will propagate in the head only, especially from 30 to 200 kHz. This would work well for finding shelling or transverse cracks in the head of a rail. We could call this lower-order mode a pseudo-Rayleigh surface wave mode.

It was shown that the impingement onto the surface of a rail head could be induced through an angle beam or comb-type piezoelectric or electromagnetic acoustic transducer (EMAT) sensor probe on the head surface with the wave structure result as illustrated in Fig. 5. Time-delays are incorporated in the FEM model to illustrate the approach times of the waves at the interface between the angle beam probe and the rail head itself. Computations have been carried out to show that this model can be used to simulate ultrasonic wave transmission from the angle beam piezoelectric probe or EMAT into a rail structure. A sample wave structure along the pseudo-Rayleigh surface wave mode (30–1, 60–1, to 200–1) is illustrated in Fig. 5. For further details, see Refs. [1,5]. Other points on the dispersion curves shown in Fig. 4 have energy wave structures covering overall head, web, and base.

Finite element modeling can be used in any of these problems to illustrate either resulting wave propagation in the structure, or response from a modeled defect in pulse-echo and through-transmission. A sample computation for a rail head is illustrated in Fig. 6. Commercial software can be used to prepare animation of a guided wave traveling in a structure (see Ref. [1], Chap. 8). After selecting a specific point on a phase velocity dispersion curve with appropriate desired wave structure, the FEM computation can take place in a variety of different fashions to test the choice. For example, using angle beam excitation on the rail head with an actuator of specific dimensions and selected frequency, an animation can be produced. Three positions in time are shown to illustrate a wave traveling in the head only or into the head, web, and base as the wave travels along the rail. Comb excitation on the railhead can also be considered as in the case of an EMAT, for example, to get the same result. From a modeling viewpoint, it would also be possible to load the end of a rail with the wave structure selected as a boundary condition.

## Repair Patch Bonded to an Aluminum Layer

Adhesive bonding inspection problems have been addressed for years. Cohesive situations have adequate solutions via ultrasonic “C” scan testing or vibration mode bond testers. Adhesive or interface situations, including the elusive “kissing bond” issue, are more complex. Experience has shown that getting shear waves into the interface, or possible in-plane displacement waves onto the interface, can often solve the problem.

Puthillath and Rose [6] studied the problem of the ultrasonic guided wave inspection of a titanium repair patch bonded to an aluminum aircraft skin. They reported the phase velocity dispersion curves for a titanium—epoxy—aluminum test specimen. Repairs are made by grinding out defects, filling with epoxy, and bonding a titanium plate over the area. The problem is complex because each repair is slightly different, so a knowledge base had to be established to successfully solve this problem. Superimposed onto the dispersion curves in Fig. 7 is the in-plane interfacial displacement at the Al-epoxy interface. There are test regions with strong in-plane displacement. The regions at 2.5 MHz and high phase velocity were selected for the test system because of mode separation and reasonable source influence profile for a comb-type EMAT sensor. See Fig. 8 for a source influence result. The system was designed, and excellent test results were obtained. Tests were conducted in a through-transmission test mode with sensors just a few inches apart. Comb element spacing was equivalent to the wavelength described by the activation line slope on the phase velocity dispersion curve from the origin to the point in question at 2.5 MHz with a phase velocity of 15 km/s, for an EMAT coil spacing of 7.2 mm. See Fig. 9 for a photograph of the dual-element EMAT probe. See Ref. [6] for more detail.

A major concern in many inspection problems is an inability to inspect structures covered with water splashes or perhaps even structures that are completely submerged. Energy absorption and imaging artifacts can occur as the guided wave ultrasound can leak into the water.

Presented in Ref. [1] on guided waves in plates was a section on finding dominant in-plane displacement at the surface of a plate so that energy leakage into water would not occur because of shear loading of the fluid (see Pilarski et al. [7]). It was found that total in-plane displacement on the surface of a plate was possible wherever the dilatational velocity value along the phase velocity ordinate intersected the symmetric modes in the plate at the symmetric modes S1, S2, S3, and so forth. Hence, the frequency and phase velocity were known and actuators, either angle beam or comb type, could be designed to generate this mode. A sample tomographic image of a small corrosion defect on a dry plate shows successful imaging with two different modes in Fig. 10. Aspects of the guided wave tomographic image reconstruction process are presented in Refs. [1,8]. On the other hand, an incorrect image appears in Fig. 11 for the A1 mode. A water drop appears as a defect because the out-of-plane component leaks into the water drop. An excellent image, however, when using the proper mode is illustrated in Fig. 11(b). Only the corrosion defect is seen. The water drop is not seen.

Note that successful imaging could also come about by using a lower-frequency S0 mode, which also has dominant in-plane displacement on the plate surface. A shear horizontal guided wave would also produce excellent results.

## Aircraft, Lap Splice, Tear Strap, and Skin-to-Core Delamination Inspection Potential

A few interesting ideas on mode and frequency selection for inspection problems associated with aircraft components are discussed here. Let us consider three sample problems:

• (a)

lap splice joints,

• (b)

tear straps, and

• (c)

honeycomb structure.

• (a)

Lap splice joints: See Fig. 12 for a lap splice joint inspection concept. The overall idea is illustrated in Fig. 12(a). The logic is quite simple. The amount of energy traveling from transmitter to receiver provides an indication of the quality of the lap splice joint. Because the system is being used in a through-transmission mode, the rivets' influence is minimal. Though simple, one must select an appropriate mode and frequency that allows sufficient energy to leak into the lower skin structure. An incorrect mode and frequency choice can lead to a false alarm as little or no energy would reach the receiver. Examine mode structures to solve this problem (see Rose and Soley [9] for more detail).

• (b)

Tear straps: The idea here is similar to that presented for lap splice inspection to allow sufficient energy to leak into the tear strap from the fuselage, but this time, a pulse-echo mode is recommended, whereby energy from the end of the tear strap is reflected and leaks back into the fuselage to the receiver (see Fig. 13). The transmitter can search for tear straps without having precise location information.

• (c)

Honeycomb: The inspection process here is illustrated in Fig. 14. Guided wave energy travels from the transmitter to the receiver over some fixed distance. Energy leakage into honeycomb reduces the amount of energy that gets to the receiver. As a consequence, the signal is strong for complete delamination. Again, though a simple concept, a suitable mode and frequency must be selected to allow leakage into the honeycomb to occur. Mode and frequency selections could come from the phase velocity dispersion curve associated with a plate model, a layer on a half-space model, or a clever theoretically driven experiment examining aspects of mode and frequency tuning to obtain the best possible result for a particular honeycomb structural configuration.

## Coating Delamination in Pipe

This problem is addressed from a circumferential guided wave point of view. See Chap. 11 on circumferential guided waves for additional information in Ref. [1] for more detail. A schematic to the debond problem and feature solutions is shown in Figs. 1518. The approach is to use EMAT sensors to send circumferential guided waves around the circumference of the pipe from the inside surface (see Fig. 19). Special modes and frequencies that are sensitive to the presence of coatings are used to determine coating integrity.

Three features were considered, the first being a wave velocity around the circumference of the pipe. It turns out that with coating bonded correctly, the group wave velocity is reduced compared to the value for an uncoated pipe. Hence, this change in time of flight (TOF) provides an indication of debond extent. Consequently, why not find the mode and frequency that give the greatest difference in TOF between these two extreme situations? This would make it easier to estimate debonding length around the circumference. Sample results of TOF are illustrated in Fig. 15. Note that TOF decreases as debond length increases. Beyond this primary feature of time of flight, two additional features worked well. One feature was signal attenuation, which obviously is impacted as more energy is absorbed by the coating. Another feature was a lost high-frequency component percentage. Higher frequencies are more readily absorbed by the coating material, and of course are not absorbed in the coating disbond situation. Note that redundancy in solving any problem is always good. The use of multiple features improves reliability and overall probability of detection.

## Corrosion Detection Under Pipe Supports and Elbow Inspection

A short-range guided wave inspection system for pipe is discussed here. But before introducing details, let us consider a brief explanation of the long-range guided wave inspection of pipe. Long range ultrasonic guided wave inspection for pipelines was introduced in the 1990s and is quite popular today. Several versions are available consisting of piezoelectric and magnetostrictive loading systems. Real-time guided wave focusing was introduced by Rose et al. [10]. The concept is further reviewed by Mu and Rose [11]. Most common is the use of the lowest-order torsional guided wave modes in the pipe because of shear stress in the wave structure across the pipe wall that makes inspection of a fluid-filled pipe possible. The torsional mode most often also has less mode conversion when defects are encountered compared to using longitudinal waves, therefore simplifying the signal analysis process. Piezoelectric transducers, when used, are pressed against the outside pipe wall without couplant because of the lower frequencies used, on up to 80 kHz. Theoretical details can be found in Ref. [1].

Elements of Fig. 1 were explored in the development of a handheld portable guided wave inspection device for a variety of different applications, two sample problems of which will be discussed here. Consideration of wave structure was of significant concern pointing to the use of a torsional nonaxisymmetric wave mode possible by partial loading on the circumference of a pipe. Since short range was considered, the torsional flexural mode was close to a shear horizontal test mode, again for the lowest-order shear mode. See Ref. [1] for details on aspects of a shear horizontal guided wave.

Feasibility studies were conducted on a variety of different defect situations in pipe where an easy short-range guided wave solution was desired. A magnetostrictive solution was adopted. See details in Ali et al. [12]. Of many benefits of the magnetostrictive probe was one of easily generating the shear horizontal guided wave test mode. Also, coupling efficiency and signal stability were excellent compared to piezoelectric shear probe coupling as a scan was taking place.

As a consequence, a short-range portable handheld ultrasonic guided wave magnetostrictive probe was designed and fabricated. A photograph of the probe is shown in Fig. 20. Magnetic wheels allow the probe to circle the pipe with an encoder to record position as data is collected. One probe can cover pipes from 4 in diameter on up. Note the FeCo strip that is mounted on the pipe such that the coil in the probe is designed to generate shear horizontal waves in the pipe. The horizontal shear wave propagation vector is shown in Fig. 21 along with shear horizontal shear wave particle velocity vector being in the same direction as the scan direction.

The MRUT probe can be used to detect corrosion under a pipe support that is a common problem today. Sample results are shown in Fig. 22. Note the correlation of the pulse-echo image with the elliptical section shown in the pipe after examining the physical damage upon removal of the pipe from the support. The MRUT probe can also be used to detect defects in an elbow as shown in a sample result in Fig. 23. Many other inspection problems can be tackled with this probe. It can even be used with two probes across a region of interest in through-transmission mode.

## A Note on System Design

Implementation aspects of the final system design can often become software intensive. How do we objectively take the signal features and scans that we see by eye, that are obtained by theory and experiment, into an appropriate decision algorithm in our final test system? The entire field of data acquisition, signal processing, and pattern recognition are required at this point. See Duda et al. [13] for some tips for implementation, especially when a multifeature solution is considered, but be careful here. Utilization of probabilistic or statistically based features of a waveform or image can be misleading. Results can be obtained that will not hold up over time. Physically based features are crucial for success. Physically based features come from the physics and mechanics of wave propagation that lead to specific changes in a waveform or image. The solution must make sense. Physically based features could be for example, arrival times, pulse duration or rise time in time domain, or energy absorption characteristics in frequency domain, such as high-frequency content over a low frequency content, peak frequency, etc. The key to success is the establishment of an appropriate physically based feature vector. The use of probability density functions for different features for different characteristics, say, defect versus no defect, can be used to find the best features. The smaller the number of features, the better. Training and test data are required in the development of any decision algorithm. See Duda et al. [13] for pattern recognition details. Neural nets are efficient but must have as input key physically based features in order to be successful. Be careful here also, as many investigators believe that neural nets can provide magical solutions. Obviously, many other challenges as final products move to a commercialization phase can be encountered for all aspects of instrumentation, sensors, and software concerns.

## Conclusion

The system design philosophy outlined in Fig. 1 has been applied to a number of short range guided wave inspection problems. Among several design considerations, wave structure understanding and selection is essential and has been demonstrated time and time again to be one of the major keys to success. Portions of the overall hybrid analytical FEM approach philosophy in Fig. 1 have been discussed in this paper and applied to several sample problems.

For the surface-breaking crack and transverse crack detection in the head of a rail, it is easy to see that wave structure across the plate thickness or rail requires sufficient energy in the wave structure to be close to the upper surface of the plate or rail head.

In the repair patch problem, it was desired to achieve a strong in-plane displacement component in the wave structure at the bondline interface regions. For water-loaded structures, a strong in-plane displacement component in the wave structure was also required on the surfaces for the plate for the ultrasonic guided wave to not be affected by water loading that leads to a false alarm indication.

In the case of the aircraft lap splice joint, tear strap, and skin-to-core honeycomb delamination, wave structure was again critical, where guided wave modes and frequency had to be found to create sufficient energy at the interface to leak into the lap splice joint, tear straps, or honeycomb structure.

In the case of coating delamination in a pipe, the circumferential group velocity in a bare pipe was generally larger than that in a coated pipe regardless of the mode used, but for certain modes the difference was small. Hence, a search for a mode that produced the greatest difference in group velocity took place that would have the greatest sensitivity to delaminated areas which were the bare pipe regions of the pipe.

For the corrosion detection under a pipe support or elbow inspection, a shear horizontal type wave was desired to simplify the inspection. So wave structure was again critical in calling for a constant shear horizontal stress across the thickness of the structure.

Finally, a warning on pattern recognition is presented, aspects of which for implementation purposes will become a part of many guided wave inspection systems. Physically based guided wave features must be utilized.

## Acknowledgment

Thanks are given to my graduate students over the years at Penn State University and also to employees of FBS, Inc., DBA Guidedwave for work from fundamental wave mechanics to commercialization efforts of the guided wave technology.

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