A Guided Wave Transducer with Sprayed Magnetostrictive Powder Coating for Monitoring of Aluminum Conductor Steel-Reinforced Cables

Aluminum conductor steel-reinforced (ACSR) cables are typically used in overhead transmission lines, requiring stringent non-destructive testing owing to the severe conditions they face. Ultrasonic guided wave inspection provides promising online monitoring of the wire breakage of cables with the advantages of high sensitivity, long-range inspection, and full cross-sectional coverage. It is a very popular method to generate and receive guided waves using magnetostrictive and piezoelectric transducers. However, uniformly coupling the acoustic energy excited by transducers into multi-wire structures is always a challenge in the field application of guided waves. Long-term field application of piezoelectric transducers is limited due to the small coupling surface area, localized excitation, and couplant required. Conventional magnetostrictive transducers for steel strand inspection are based on the magnetostrictive effect of the material itself. Two factors affect the transducing performance of the transducers on ACSR cables. On one hand, there is a non-magnetostrictive effect in aluminum wires. On the other hand, the magnetostriction of the innermost steel wires is too weak to generate guided waves. The bias magnetic field is attenuated by the outer layers of aluminum wires. In this paper, an alternative sprayed magnetostrictive powder coating (SMPC) transducer was developed for guided wave generation and detection in ACSR cables. The Fe83Ga17 alloy powder with large magnetostriction was sprayed uniformly on the surfaces of certain sections of the outermost aluminum wires where the transducer would be installed. Experimental investigations were carried out to generate and receive the most commonly used L(0,1) guided waves for wire breakage detection at frequencies of 50 and 100 kHz. The results demonstrate that the discernable reflected waves of the cable end and an artificial defect of three-wire breakage (5.5% reduction in the cable’s cross-sectional area) were received by the transducer with SMPC, which was impossible for the transducer without SMPC. This method makes long-term and online monitoring of ACSR cables feasible due to the high coupling efficiency and good structural surface adaptability.


Introduction
Multi-wire cables are widely used in a number of engineering applications to meet various demands, such as load carrying in elevators, lifting machinery, and cable-stayed and suspension generation relies on the contact between adjacent wires to transfer waves into inner layers from the outermost layer, where the transducers are installed [34]. The coupling efficiency of the piezoelectric transducers is mainly affected by the stability of the contact surfaces between the transducer and the wire bundle of the ACSR cable. Therefore, the field application of piezoelectric transducers in long-term SHM is limited by the possibility of slippage and abscission under wind loads. Although the piezoelectric polyvinylidene fluoride (PVDF) transducer [35] is flexible, the low energy-conversion efficiency limits the application in ACSR cable.
In addition to the above mentioned two types of transducers, electromagnetic acoustic transducer (EMAT) [36,37] and laser-based ultrasonic transducer [38,39] are also commonly used to excite and receive ultrasonic wave in industrial applications. The major advantage of EMAT is that they are non-contacting, coupling-free, and efficient to generate horizontal shear (SH)-guided wave [40], which is particularly important when testing high temperature structures [41]. However, EMAT gives relatively low transmitted ultrasonic energy, with low signal-to-noise ratio, and the induced energy is critically dependent on the transducer proximity to the test object. Well established applications of laser ultrasonic system are composite inspections for the aerospace industry and online high temperature pipe thickness measurements for the metallurgical industry [42]. However, the complexity and high cost of laser ultrasonic equipment has limited its application in ACSR cable online monitoring.
Due to the small saturation magnetostriction coefficient of the wires in cable, the application of long-distance structural monitoring using guided waves is limited. In recent years, researchers developed cobalt ferrite composites [43] with certain advantages, such as: large saturation magnetostrictive coefficient, high sensitivity, and high electrical resistivity. Plasma spraying has been used in making ferrite coatings and has been shown to be useful for magnetoresistance sensors [44]. Cold spraying has been used in making magnetostrictive commercially pure nickel cold spray patch sensor [45,46] for long-term crack monitoring of plates.
For a better performance of UGW inspection techniques on ACSR cables in engineering applications, an alternative sprayed magnetostrictive powder coating (SMPC) transducer is developed for guided wave generation and detection. The Fe 83 Ga 17 alloy powder with large magnetostriction was sprayed uniformly on the surface of a section of cable where the transducer would be installed on site. Experimental investigations were carried out to generate and receive the fundamental longitudinal L(0,1) guided wave. The results demonstrate that the transducer with SMPC enhanced the amplitudes of the guided wave signals compared with the conventional transducer. The discernable reflected waves of the ACSR cable ends and the defects of three-wire breakage were received by the transducer with SMPC, which was impossible for the transducer without SMPC. This method makes long-term and online monitoring of ACSR cable feasible due to the high coupling efficiency and good structural surface adaptability.

Aluminum Conductor Steel-Reinforced (ACSR) Cable Information
ACSR cables are widely used in power transmission line cables. They are composed of a number of twisted steel and aluminum wires. The diameter and number of individual aluminum and steel wires vary according to the model of the cable. The specimen tested in this experiment was a 1.6 meter-long LGJ-400/35 ACSR cable (Tianhong Electric Power Fitting Co., Ltd., Zhejiang, China). The cable is composed of 7 steel wires for load carrying and 48 aluminum wires for electric conduction, which are distributed as 5 layers: 1-6-10-16-22, from internal to external. The wire bundle is arranged into a helical shape with each layer twisted in the opposite direction. The diameters of the individual steel and aluminum wires are 2.5 mm and 3.2 mm, respectively. The overall diameter of the entire cable is 26.6 mm. The cross-section of the cable is shown in Figure 1.

Dispersion Curves of Guided Waves
UGWs travel with different velocities depending on the frequency of the wave. Group velocity dispersion curves are needed to determine the wave propagation speed for each mode. With this information, it is possible to convert the time-of-flight (ToF) into the distance traveled by wave packets in a structure. There are several techniques for calculating the dispersion curves of guided waves, such as the analytical method based on Pochhammer-Chree equations [47] and the semi-analytical finite element (SAFE) method [48]. The SAFE method is more attractive for analyzing a structure with an arbitrary geometry of the cross-section. The dispersion curves of multi-wire strands were obtained by Treyssède et al. They found that the group velocity curves of the fundamental order modes, such as L(0,1), T(0,1), and F(1,1), of the multi-wire helical structures with small helix lay angles (less than 15°) at low frequencies are very similar to the straight and helical wires [49][50][51]. The cable tested in this study is consistent with this situation.
The case of a single straight wire can be considered to be the same as a simple rod, whose dispersion properties can be analytically obtained using Pochhammer-Chree equations. The phase velocity and group velocity are derived from the (ω, k) solutions of the transcendental characteristic equation for longitudinal waves given by: with, where a, ω, k are the rod radius, angular frequency, and wave number, respectively; VL and VS are the longitudinal and transverse velocities, respectively; and J0 and J1 are Bessel functions of order 0 and 1, respectively. The phase and group velocity expressions are, respectively: The group velocity dispersion curves of individual steel wire with a diameter of 2.5 mm and aluminum wire with a diameter of 3.2 mm were acquired using a software package named PCDISP written in the Matlab (MathWorks Inc., Natick, NA, USA) environment, as shown in Figure 2. PCDISP is described in more detail in [52,53]. The material and geometric properties used in the dispersion models of PCDISP are summarized in Table 1.

Material
Diameter Density Young Modulus Poisson Ratio

Dispersion Curves of Guided Waves
UGWs travel with different velocities depending on the frequency of the wave. Group velocity dispersion curves are needed to determine the wave propagation speed for each mode. With this information, it is possible to convert the time-of-flight (ToF) into the distance traveled by wave packets in a structure. There are several techniques for calculating the dispersion curves of guided waves, such as the analytical method based on Pochhammer-Chree equations [47] and the semi-analytical finite element (SAFE) method [48]. The SAFE method is more attractive for analyzing a structure with an arbitrary geometry of the cross-section. The dispersion curves of multi-wire strands were obtained by Treyssède et al. They found that the group velocity curves of the fundamental order modes, such as L(0,1), T(0,1), and F(1,1), of the multi-wire helical structures with small helix lay angles (less than 15 • ) at low frequencies are very similar to the straight and helical wires [49][50][51]. The cable tested in this study is consistent with this situation.
The case of a single straight wire can be considered to be the same as a simple rod, whose dispersion properties can be analytically obtained using Pochhammer-Chree equations. The phase velocity and group velocity are derived from the (ω, k) solutions of the transcendental characteristic equation for longitudinal waves given by: where a, ω, k are the rod radius, angular frequency, and wave number, respectively; V L and V S are the longitudinal and transverse velocities, respectively; and J 0 and J 1 are Bessel functions of order 0 and 1, respectively. The phase and group velocity expressions are, respectively: The group velocity dispersion curves of individual steel wire with a diameter of 2.5 mm and aluminum wire with a diameter of 3.2 mm were acquired using a software package named PCDISP written in the Matlab (MathWorks Inc., Natick, NA, USA) environment, as shown in Figure 2. PCDISP is described in more detail in [52,53]. The material and geometric properties used in the dispersion models of PCDISP are summarized in Table 1.  Guided wave modes in a cylindrical waveguide are composed of longitudinal waves L(m,n), torsional waves T(m,n), and flexural waves F(m,n), where m∈{0, 1, 2, …} denotes the circumferential order and n∈{1, 2, 3, …} stands for the nth root of the characteristic equation [54]. Longitudinal wave mode has displacement in the radial and z-axial directions. Torsional wave mode has displacement in the circumferential direction. Flexural wave mode has displacement in all three directions [16]. All of the curves are dispersive in nature, although certain parts of the curves are flatter and less dispersive than the others, particularly in the low-frequency range for the low-order fundamental L(0,1) mode, which is the preferred mode for experiments and engineering applications. Another advantage of the longitudinal mode is the convenience of excitation and low-propagation attenuation. The group velocities of L(0,1) mode at frequencies of 50 kHz and 100 kHz are almost identical ( = 5065 m/s) with less dispersion.

Magnetostrictive Powder Spraying System
The feedstock of the coating was Fe83Ga17 gas-atomized powders with particle diameters between 30 and 50 µm, which were characterized by almost perfect spherical particles, as shown by the scanning electron microscope (SEM) photograph in Figure 3a. The coatings were sprayed by high-pressure, high-velocity oxygen fuel-spraying equipment (SX-JP8000, Siemens Co. Ltd., Munich, Germany). The torch was provided by a Praxair-TAFA 5220 (Praxair S.T. Technology, Inc., CT, Danbury, USA) with kerosene and oxygen as fuel gases, as shown in Figure 3c. Prior to spraying, the cable surface was cleaned using acetone solution and preheated to 100-200 °C, and then sandblasted  Guided wave modes in a cylindrical waveguide are composed of longitudinal waves L(m,n), torsional waves T(m,n), and flexural waves F(m,n), where m ∈ {0, 1, 2, . . . } denotes the circumferential order and n ∈ {1, 2, 3, . . . } stands for the nth root of the characteristic equation [54]. Longitudinal wave mode has displacement in the radial and z-axial directions. Torsional wave mode has displacement in the circumferential direction. Flexural wave mode has displacement in all three directions [16]. All of the curves are dispersive in nature, although certain parts of the curves are flatter and less dispersive than the others, particularly in the low-frequency range for the low-order fundamental L(0,1) mode, which is the preferred mode for experiments and engineering applications. Another advantage of the longitudinal mode is the convenience of excitation and low-propagation attenuation. The group velocities of L(0,1) mode at frequencies of 50 kHz and 100 kHz are almost identical (v g = 5065 m/s) with less dispersion.

Magnetostrictive Powder Spraying System
The feedstock of the coating was Fe 83 Ga 17 gas-atomized powders with particle diameters between 30 and 50 µm, which were characterized by almost perfect spherical particles, as shown by the scanning electron microscope (SEM) photograph in Figure 3a. The coatings were sprayed by high-pressure, high-velocity oxygen fuel-spraying equipment (SX-JP8000, Siemens Co., Ltd., Munich, Germany). The torch was provided by a Praxair-TAFA 5220 (Praxair S.T. Technology, Inc., CT, Danbury, USA) with kerosene and oxygen as fuel gases, as shown in Figure 3c. Prior to spraying, the cable surface was cleaned using acetone solution and preheated to 100-200 • C, and then sandblasted with corundum powder. The cable was placed in a stainless steel cylindrical holder, and the axis of the torch was orthogonal to that of the holder with a rotating speed of 30 rpm. The spray distance was kept at 300 mm. with corundum powder. The cable was placed in a stainless steel cylindrical holder, and the axis of the torch was orthogonal to that of the holder with a rotating speed of 30 rpm. The spray distance was kept at 300 mm. The coatings were uniformly deposited to a thickness of t = 350 µm on the outermost aluminum wire surfaces of the cable, as shown in Figure 3b. In order to compare the magnetostrictive energy conversion performance of the SMPC, only one cable end was sprayed, as shown in Figure 3d. The length of the SMPC (L = 60 mm) was slightly wider than the width of the UGW transducer coil used in the follow-up experiments. To facilitate transducer installation, the distance from the center of the spray area to the wire end was P = 100 mm.
In order to evaluate the magnetostriction of the SMPC, the same sprayed system and parameters were employed to spray a coating on an aluminum plate with a thickness of t = 350 µm. A resistance strain gauge positioned along the coating plane with a gauge area of 2.8 × 2.0 mm 2 (base area of 6.4 × 3.5 mm 2 ) was used to measure the magnetostriction. The magnetostriction of the as-deposited coating reached 30 ppm under a maximum external magnetic field of 1500 Oe at room temperature, as shown in Figure 4. The coatings were uniformly deposited to a thickness of t = 350 µm on the outermost aluminum wire surfaces of the cable, as shown in Figure 3b. In order to compare the magnetostrictive energy conversion performance of the SMPC, only one cable end was sprayed, as shown in Figure 3d. The length of the SMPC (L = 60 mm) was slightly wider than the width of the UGW transducer coil used in the follow-up experiments. To facilitate transducer installation, the distance from the center of the spray area to the wire end was P = 100 mm.
In order to evaluate the magnetostriction of the SMPC, the same sprayed system and parameters were employed to spray a coating on an aluminum plate with a thickness of t = 350 µm. A resistance strain gauge positioned along the coating plane with a gauge area of 2.8 × 2.0 mm 2 (base area of 6.4 × 3.5 mm 2 ) was used to measure the magnetostriction. The magnetostriction of the as-deposited coating reached 30 ppm under a maximum external magnetic field of 1500 Oe at room temperature, as shown in Figure 4.

Working Mechanism
In a non-ferromagnetic conductive material subject to a static bias magnetic field, an applied dynamic magnetic field induces the Lorentz force [55] within it, thereby generating mechanical guided waves. In the case of a ferromagnetic material, an applied magnetic field induces magnetostriction [56] as well as the Lorentz force.
When an ACSR cable without SMPC was subjected to a dynamic magnetic field (provided by an alternating current coil) superimposed on a static magnetic field (provided by a permanent bias magnet), the Lorentz force was generated in the outermost aluminum wires due to the eddy current effect. Longitudinal guided waves were excited by the Lorentz force in the direction along the radius of the cable. Axial strain was also produced in the innermost steel wires of the ACSR cable due to the magnetostrictive effect, but this became too weak to generate longitudinal guided waves. Bias magnetic field was attenuated by the three layers of aluminum wire, as shown in Figure 5.

Working Mechanism
In a non-ferromagnetic conductive material subject to a static bias magnetic field, an applied dynamic magnetic field induces the Lorentz force [55] within it, thereby generating mechanical guided waves. In the case of a ferromagnetic material, an applied magnetic field induces magnetostriction [56] as well as the Lorentz force.
When an ACSR cable without SMPC was subjected to a dynamic magnetic field (provided by an alternating current coil) superimposed on a static magnetic field (provided by a permanent bias magnet), the Lorentz force was generated in the outermost aluminum wires due to the eddy current effect. Longitudinal guided waves were excited by the Lorentz force in the direction along the radius of the cable. Axial strain was also produced in the innermost steel wires of the ACSR cable due to the magnetostrictive effect, but this became too weak to generate longitudinal guided waves. Bias magnetic field was attenuated by the three layers of aluminum wire, as shown in Figure 5.

Working Mechanism
In a non-ferromagnetic conductive material subject to a static bias magnetic field, an applied dynamic magnetic field induces the Lorentz force [55] within it, thereby generating mechanical guided waves. In the case of a ferromagnetic material, an applied magnetic field induces magnetostriction [56] as well as the Lorentz force.
When an ACSR cable without SMPC was subjected to a dynamic magnetic field (provided by an alternating current coil) superimposed on a static magnetic field (provided by a permanent bias magnet), the Lorentz force was generated in the outermost aluminum wires due to the eddy current effect. Longitudinal guided waves were excited by the Lorentz force in the direction along the radius of the cable. Axial strain was also produced in the innermost steel wires of the ACSR cable due to the magnetostrictive effect, but this became too weak to generate longitudinal guided waves. Bias magnetic field was attenuated by the three layers of aluminum wire, as shown in Figure 5. As for an ACSR cable sprayed with magnetostrictive powder coating, guided waves were generated on account of the superposition of Lorentz force and magnetostrictive force, but magnetostriction was the dominant mechanism of transduction due to the greater resistivity and smaller eddy current effect of the powder coating. The direction of the Lorentz force was along the radius of the cable and the direction of the magnetostrictive force was along the axial of the cable, which happened to be consistent with the displacement distribution of the longitudinal mode guided wave, as shown in Figure 5c. This caused mechanical strain in the wires of the cable through the eddy effect and the magnetostrictive effect, known as the Joule effect. Conversely, for detection, the inverse magnetostrictive effect, known as the Villari effect, enabled guided waves to be detected through modifications in the magnetic induction.

Experimental Setup
In order to investigate the performance of the Fe 83 Ga 17 coating transducer used in NDT and online SHM on the ACSR cable, magnetostrictive longitudinal mode guided wave generation and detection experiments were conducted to obtain the reflected wave signals of the cable ends and artificial wire breakage defect.
The pulse-echo guided wave inspection configuration [57,58] was employed, as shown in Figure 6. Guided waves were generated in the experiments through a dynamic magnetic field (provided by a specially designed coil module) superimposed on a static magnetic field (provided by a permanent bias magnet). For versatility and ease of installation, the coil module consisted of a 50.8 mm wide 40-pin encircling ribbon cable and an adapter. The role of the adapter was to switch certain turns of the coil to be turned on to conveniently adjust the width of the wave source corresponding to the excitation frequency. The width of the conducting portion of the coil W en was equal to one-quarter wavelength λ of the guided wave at center excitation frequency, given by: where v g and f are group velocity and center excitation frequency, respectively. As for an ACSR cable sprayed with magnetostrictive powder coating, guided waves were generated on account of the superposition of Lorentz force and magnetostrictive force, but magnetostriction was the dominant mechanism of transduction due to the greater resistivity and smaller eddy current effect of the powder coating. The direction of the Lorentz force was along the radius of the cable and the direction of the magnetostrictive force was along the axial of the cable, which happened to be consistent with the displacement distribution of the longitudinal mode guided wave, as shown in Figure 5c. This caused mechanical strain in the wires of the cable through the eddy effect and the magnetostrictive effect, known as the Joule effect. Conversely, for detection, the inverse magnetostrictive effect, known as the Villari effect, enabled guided waves to be detected through modifications in the magnetic induction.

Experimental Setup
In order to investigate the performance of the Fe83Ga17 coating transducer used in NDT and online SHM on the ACSR cable, magnetostrictive longitudinal mode guided wave generation and detection experiments were conducted to obtain the reflected wave signals of the cable ends and artificial wire breakage defect.
The pulse-echo guided wave inspection configuration [57,58] was employed, as shown in Figure 6. Guided waves were generated in the experiments through a dynamic magnetic field (provided by a specially designed coil module) superimposed on a static magnetic field (provided by a permanent bias magnet). For versatility and ease of installation, the coil module consisted of a 50.8 mm wide 40-pin encircling ribbon cable and an adapter. The role of the adapter was to switch certain turns of the coil to be turned on to conveniently adjust the width of the wave source corresponding to the excitation frequency. The width of the conducting portion of the coil Wen was equal to one-quarter wavelength λ of the guided wave at center excitation frequency, given by: where vg and f are group velocity and center excitation frequency, respectively. The role of the bias magnet is to provide a static magnetic field that is consistent with the direction of the dynamic magnetic field and overcome the frequency-doubling effect of the ferromagnetic materials [32]. These two parallel magnetic fields will cause the wires in the cable to alternately expand and contract based on the magnetostrictive effect, thereby generating longitudinal guided waves. For bias magnet configuration, the components include two Ne-Fe-B N50 permanent magnets 30 × 40 × 30 mm 3 in size and a yoke iron 30 × 120 × 25 mm 3 in size. The role of the bias magnet is to provide a static magnetic field that is consistent with the direction of the dynamic magnetic field and overcome the frequency-doubling effect of the ferromagnetic materials [32]. These two parallel magnetic fields will cause the wires in the cable to alternately expand and contract based on the magnetostrictive effect, thereby generating longitudinal guided waves. For bias magnet configuration, the components include two Ne-Fe-B N50 permanent magnets 30 × 40 × 30 mm 3 in size and a yoke iron 30 × 120 × 25 mm 3 in size.
The coil and the bias magnet were made up of the UGW transducer, which served as the transmitter and receiver simultaneously. These were used to generate and receive the L(0,1) guided waves at the center frequencies of 50 kHz and 100 kHz. For excitation, the coil was driven by a PC-controlled power amplifier (RAM-5000, Ritec Inc., Warwick, RI, USA) with a Hann-windowed 5-cycle sinusoidal tone burst, as shown in Figure 7. Meanwhile, the detected voltage signal in the coil was bandpass filtered and amplified by about 45 dB. The installation of the transducer with a distance of L T = 0.1 m close to one of the cable ends (with and without the SMPC) was carried out on the ACSR cable. The coil and the bias magnet were made up of the UGW transducer, which served as the transmitter and receiver simultaneously. These were used to generate and receive the L(0,1) guided waves at the center frequencies of 50 kHz and 100 kHz. For excitation, the coil was driven by a PC-controlled power amplifier (RAM-5000, Ritec Inc., Warwick, RI, USA) with a Hann-windowed 5-cycle sinusoidal tone burst, as shown in Figure 7. Meanwhile, the detected voltage signal in the coil was bandpass filtered and amplified by about 45 dB. The installation of the transducer with a distance of LT = 0.1 m close to one of the cable ends (with and without the SMPC) was carried out on the ACSR cable.

ACSR Cable End Detection
Two sets of experiments were conducted on the 1.6 m long ACSR cable described in Section 2.1. The UGW transducers (with and without the SMPC) were placed respectively close to the two ends of the cable with a distance of LT = 0.1 m. The distance from the transducer to the far end was LEND = 1.5 m. The propagation paths of guided waves associated with the configuration of transducers are shown in Figure 8. The figure shows all the propagation paths of the guided waves excited by the transducer with SMPC. They are similar to the transducer without SMPC, since the distances of the two transducers between the installation locations and cable ends were the same.

ACSR Cable End Detection
Two sets of experiments were conducted on the 1.6 m long ACSR cable described in Section 2.1. The UGW transducers (with and without the SMPC) were placed respectively close to the two ends of the cable with a distance of L T = 0.1 m. The distance from the transducer to the far end was L END = 1.5 m. The propagation paths of guided waves associated with the configuration of transducers are shown in Figure 8 The plots in Figure 9 show the time domain waveforms received by the transducers installed near two ends with center excitation frequencies of 50 kHz and 100 kHz. Signals of the end-reflected waves were not received by the transducer installed on the cable end without SMPC. This is because of the nonmagnetostriction of the aluminum wires and the inability of the magnetic field distribution of the bias magnet to reach into the steel wires located in the inner layers of the cable due to the liftoff distance. This also demonstrates that the guided wave excited by the eddy current effect was so weak that no guided wave could be generated in the cable. Conversely, the discernable reflected waves of the cable ends were received by the transducer installed on the cable end with SMPC.
(a) (b) Figure 9. Signals obtained at transducer installed on ACSR cable with frequency of (a) 50 kHz and (b) 100 kHz.
The first portion of received signals consist of the initial electromagnetic pulse and superposition of the near-end reflection wave. The other four wave packets correspond to the multiple-end reflected waves with various acoustic travel paths, as summarized in Figure 8. The temporal resolution of guided wave detection increases as the excitation frequency increases, since The plots in Figure 9 show the time domain waveforms received by the transducers installed near two ends with center excitation frequencies of 50 kHz and 100 kHz. Signals of the end-reflected waves were not received by the transducer installed on the cable end without SMPC. This is because of the nonmagnetostriction of the aluminum wires and the inability of the magnetic field distribution of the bias magnet to reach into the steel wires located in the inner layers of the cable due to the liftoff distance. This also demonstrates that the guided wave excited by the eddy current effect was so weak that no guided wave could be generated in the cable. Conversely, the discernable reflected waves of the cable ends were received by the transducer installed on the cable end with SMPC. The plots in Figure 9 show the time domain waveforms received by the transducers installed near two ends with center excitation frequencies of 50 kHz and 100 kHz. Signals of the end-reflected waves were not received by the transducer installed on the cable end without SMPC. This is because of the nonmagnetostriction of the aluminum wires and the inability of the magnetic field distribution of the bias magnet to reach into the steel wires located in the inner layers of the cable due to the liftoff distance. This also demonstrates that the guided wave excited by the eddy current effect was so weak that no guided wave could be generated in the cable. Conversely, the discernable reflected waves of the cable ends were received by the transducer installed on the cable end with SMPC.
(a) (b) Figure 9. Signals obtained at transducer installed on ACSR cable with frequency of (a) 50 kHz and (b) 100 kHz.
The first portion of received signals consist of the initial electromagnetic pulse and superposition of the near-end reflection wave. The other four wave packets correspond to the multiple-end reflected waves with various acoustic travel paths, as summarized in Figure 8. The temporal resolution of guided wave detection increases as the excitation frequency increases, since The first portion of received signals consist of the initial electromagnetic pulse and superposition of the near-end reflection wave. The other four wave packets correspond to the multiple-end reflected waves with various acoustic travel paths, as summarized in Figure 8. The temporal resolution of guided wave detection increases as the excitation frequency increases, since the higher the frequency, the shorter the wavelength. All four wave packets can be clearly distinguished in the signals (transducer with SMPC at 100 kHz excitation frequency) in Figure 9b corresponding to the propagation paths of the guided waves. However, in Figure 9a, the first and second wave packets are difficult to distinguish, as are the third and fourth wave packets.
The amplitudes of the wave packets decrease with an increased wave travel distance. This is attributed to the acoustic energy attenuation caused by multiple total reflections of cable ends. The estimated end-reflected wave packet travel distances and amplitudes for a transducer with frequencies of 50 kHz and 100 kHz are summarized in Table 2. It is worth pointing out that the signal-to-noise ratio of the cable end-reflected wave after repeatedly passing through another end was reduced, caused by the contact and friction stresses between the adjacent wires in the cable. Time of flight (ToF) represents the time history of the guided wave from excitation to reception as indicated by the abscissa of wave signals. The wave packet travel distances were calculated by Equation (2): where d is the estimated distance, t(f ) is the ToF of each wave packet at the frequency f, and v g ( f ) is the group velocity of L(0,1) mode at f = 50 kHz or 100 kHz. None identifiable end-reflected wave packet was received by the transducer without SMPC, so the amplitudes are denoted by N/A (not available) in Table 2. The estimated distances of the wave packets were very close to the exact distances, with less than 5% error, which demonstrates the accuracy of the theoretical dispersion curves. The estimated acoustic distance of the cable end-reflected wave was slightly bigger than the exact distance due to the helical arrangement of the aluminum wires in the cable.

ACSR Cable Defect Detection
The UGW-based method is able to detect and monitor defects because reflections of waves occur when they encounter structural discontinuities. In multi-wire structures, structural discontinuities lead to changes in cross-sectional area (CSA), such as wire breakage.
In order to investigate the applicability of the UGW transducer with SMPC to detect defects in the ACSR cable, artificial defects were made on the cable used in the previous experiments. The experiments of defects detection were carried out in two stages, as shown in Figure 10. Each stage of broken wires is summarized as: Stage 0: Same as the case in Section 5.1. (No defect) Stage I: Stage 0 and Defect-1. Defect-1 was a saw cut of three wires (5.5% reduction in CSA), which was machined into the cable at a distance of L D1 = 1.0 m from the transducer.
Stage II: Stage I and Defect-2. Defect-2 was a saw cut of the same three wires as Defect-1, which was machined into the cable at a distance of L D2 = 0.7 m from the transducer. The time domain signals received at the transducer with a center excitation frequency of 100 kHz is shown along with the Hilbert envelope in Figure 11. Three wave packets represent the reflected waves of two saw cut defects and cable end in sequence. At stage Ⅰ, the reflected wave of Defect-1 was received. As the defect was introduced, the peak amplitude of the cable end wave packet decreased correspondingly, compared with that with no defect at stage 0. At stage Ⅱ, after wave passes through Defect-2, the wave energy in these three wires was approximately equal to zero because total reflection occurs at saw cut. Therefore, only the reflected wave packet of Defect-2 was received in the signals. The peak amplitude of the cable end reflected wave packet was almost equal to that of Stage Ⅰ, because the number of broken wires was same for two defects. The results are summarized in Table 3, which shows the practicability of defect detection and localization of the transducer with SMPC.

Initial pulse
Cable end
The time domain signals received at the transducer with a center excitation frequency of 100 kHz is shown along with the Hilbert envelope in Figure 11. Three wave packets represent the reflected waves of two saw cut defects and cable end in sequence. At stage I, the reflected wave of Defect-1 was received. As the defect was introduced, the peak amplitude of the cable end wave packet decreased correspondingly, compared with that with no defect at stage 0. At stage II, after wave passes through Defect-2, the wave energy in these three wires was approximately equal to zero because total reflection occurs at saw cut. Therefore, only the reflected wave packet of Defect-2 was received in the signals. The peak amplitude of the cable end reflected wave packet was almost equal to that of Stage I, because the number of broken wires was same for two defects. The results are summarized in Table 3, which shows the practicability of defect detection and localization of the transducer with SMPC. The time domain signals received at the transducer with a center excitation frequency of 100 kHz is shown along with the Hilbert envelope in Figure 11. Three wave packets represent the reflected waves of two saw cut defects and cable end in sequence. At stage Ⅰ, the reflected wave of Defect-1 was received. As the defect was introduced, the peak amplitude of the cable end wave packet decreased correspondingly, compared with that with no defect at stage 0. At stage Ⅱ, after wave passes through Defect-2, the wave energy in these three wires was approximately equal to zero because total reflection occurs at saw cut. Therefore, only the reflected wave packet of Defect-2 was received in the signals. The peak amplitude of the cable end reflected wave packet was almost equal to that of Stage Ⅰ, because the number of broken wires was same for two defects. The results are summarized in Table 3, which shows the practicability of defect detection and localization of the transducer with SMPC.

Conclusion
In this study, an alternative sprayed magnetostrictive powder-coated UGW transducer was developed for the inspection and online monitoring of overhead transmission line cables. The Fe 83 G 17 magnetostrictive powder with particle diameters ranging from 30 to 50 µm was uniformly sprayed onto the surface of an ACSR cable with a thickness of 350 µm. A magnetostrictive longitudinal guided wave transducer was installed at the corresponding position of the spraying area of the cable. It could increase the detection range of UGW and amplitudes of the wave signals. The discernable reflected waves of the cable end and defect of a three-wire breakage were received by the transducer with SMPC, which was impossible for the transducer without SMPC. This makes long-term and online monitoring of the ACSR cables feasible due to the high coupling efficiency and good structural surface adaptability. Combining the SMPC and wire surfaces on a molecular level ensures stable coupling and energy conversion, which is the basic requirement of a UGW transducer applied in the NDT and SHM. SMPC transducers can also be used for SHM of other irregular structures with large curvature in which it is difficult to excite guided waves using conventional transducers, such as steel wire ropes, rails, heat exchange tubes, and so on.
During the thermal spraying process, high temperature may affect the mechanical properties of the aluminum wires of the ACSR cable. More work is needed to investigate the effects and other spraying parameters and methods, such as cold spraying.