Damage detection and localization based on different types of actuators using the electromechanical impedance method in 3D-printed material

Electromechanical impedance (EMI) measurement, using piezoelectric transducers (PZTs) in the high-frequency range is a potential method for assessing the health of lightweight structures. The major objective of this work is to comprehend how different actuators react to damage in additively manufactured (AM) polymer structures. A novel frequency-range selection technique was suggested based on the maxima of the standard deviation of the impedance frequency spectra gathered for the referential and damage cases. A 3D-printed acrylonitrile butadiene styrene (ABS) plate was used for the investigation, where two PZT and one macro fiber composite (MFC) actuator were glued to the surface. Small magnets were used to simulate damage and were positioned at increasing distances from each transducer as EMI measurements were made using the MFC and 1 PZT. This served both in studying the transducers’ sensitivity to damage and selecting the proper frequency range for damage detection utilizing the standard-deviation approach. The EMI-acquired data from the MFC actuator displays damage-sensitive peaks in a low-frequency band (0–58 kHz ), while the PZT shows a good sensitivity in a higher frequency range (94–304 kHz ). In order to evaluate the PZT and MFC actuators’ sensitivity to damage in the 3D-printed ABS plate, impact damage is also generated in the plate’s center. The impedance-based damage indices obtained from different types of PZTs (2 PZTs and 1 MFC) were projected to the same base level and then fused—for the first time—for impact-damage localization and further added magnetic mass damage localization. The obtained damage index values of impedance are encouraging for the evaluation of AM polymer structures with a 4.48 mm positional error from a real location by fusing data in the different frequency ranges for PZTs and MFC. The damage localization error increases significantly to the new location beyond the damage sensitivity range of the PZT2 and MFC for the added magnetic mass on the 3D printed structure.


Introduction
The Electromechanical impedance (EMI) approach is one of the potential non-destructive evaluation (NDE) techniques for identifying structural anomalies because of its capacity to conduct inspections in a variety of environments.EMI uses a high-frequency range to analyze the local structural reaction and detect damage in a variety of materials, including composite polymer constructions, by comparing the spectra of undamaged and damaged structures.Piezoelectric transducers (PZTs) and macro fiber composites (MFC) are used in current EMI-based NDE techniques because they are inexpensive and lightweight [1,2].PZT generates electric charges when subjected to mechanical stress and deforms when subjected to the electric field while MFC actuators consist of piezoelectric ceramic fibers embedded in a polymer matrix which provides deformation when subjected to an electric field [3,4].The electrical impedance, 'Z (ω)' is the ratio of the applied voltage 'V (ω)' to the flowing current 'I (ω)' in circuit [4][5][6]: ( Electrical impedance correlated with the structure's mechanical impedance, and the presence of damage affects impedance responses in EMI-based tests in the structures, according to the literature [7,8].The effective frequency is often higher than 10 kHz in comparison to the conventional vibration-based structural health monitoring (SHM) techniques [9].At such high frequencies, the wavelength is small enough to make the EMI method sensitive to even the smallest variations in structural physical features.On the other hand, the localized detection makes the EMI less reliant on the boundary conditions of the structure to be investigated.In order for damage detection and classification, several frequency ranges with 20-30 peaks are often used since a larger mode density indicates a more dynamic interaction between actuators and host structures [10].The performance of the EMI technique is significantly influenced by the choice of an appropriate effective frequency spectrum to detect inchoate structural damage.Trial and error can be used to determine the damage detection in the EMI method's robust frequency range.The experimental data cannot theoretically infer the actuators' effective frequency range [11].Baptista and Vieira Filho et al used the high-mode density frequency spectrum when using the EMI approach for damage sensitivity study [12].In [13], Yang et al have created a sub-frequency-interval-based damage detection method using the root mean square deviation (RMSD) index by sliding the intervals along the broad frequency spectrum to consider the PZT resonance's impact on the selection of the effective frequency range.Generally, the EMI approach employs damage-identification calculations based on the correlation coefficient, RMSD [14][15][16].Typically, these measurements based on damage indices contrast the healthy and damaged spectrums.Recently, Soman et al utilized an inverse model updating in damage localization, but the frequency range selection for the damage metric calculation used a trial and error-based approach [17].According to [15], choosing the effective frequency and damage index (DI) with care is essential for successful damage detection.Zuo et al propose a damage feature approach for pipeline crack detection that uses data from several sensors.Pipeline crack severity and location are investigated using RMSD measurements [18].The EMI measurements of the various frequency bands were employed in a chessboard distance metric to determine the degree of damage under various temperature conditions [19].Further, Du et al converted the EMI signal into an image based on the Hank matrix to monitor the bolt loosening in the temperature-varying environment [20].The study in [21] presents an analysis that contrasts structural mechanical impedance and electromechanical admittance.To investigate the damage by demonstrating the variation in the structural qualities, present a united mechanical impedance (UMI) that integrates the mechanical impedance of the structure with PZT sensors.To detect corrosion damage in steel beams, the theoretically derived UMI from EMI has been implemented into practice.Singh et al established a robust damage detection approach based on improved data fusion employing the conductance and resistance variables.Both aluminum and composite data are investigated utilizing variable multiplication as well as an integrated principal component analysis model [22,23].However, applying these metric-based approaches to identify damage location and severity is never easy.Scheyer and Anton recently used embedded sensors to track the health of 3D polylactic acid (PLA) additively manufactured (AM) structures using an EMI-based RMSD DI.Fused deposition modeling (FDM) was used to print the specimen and drill holes and simulated damage was used to track health performance [24].The use of AM has advanced quickly from making simple prototypes to producing lightweight, complicated geometries for a variety of industries, including the aerospace, oil & gas, and automotive sectors.A few examples include Bluetooth sensor devices, which are frequently 3D-printed on substrates made of acrylonitrile butadiene styrene (ABS), one of the recyclable thermoplastics with insulating qualities.Jain et al discussed the primary recycled ABS substrate's rheological (melt flow), mechanical (tensile), morphological (surface hardness, roughness (Ra), porosity, etc), 3D printability, and radio frequency properties [25].Lazarus et al demonstrate glass fiber reinforced ABS, which possesses outstanding mechanical qualities and is created for 3D printing gears using FDM, a low-cost, effective manufacturing technique [26].
Bodaghi et al manufactured 3D circuit boards and electronic packaging involves a hybrid technique that starts with 3D printing on the highly conductive thermoplastic filament and ends with electroplating on the copper surface [27].Further industrialization has been hampered by the lack of suitable NDE procedures to validate the high-quality end products of AM [28,29].3D printed structures are monolithic, and parts are not equally strong in all directions when designing and printing load-bearing parts.AM structures have therefore required appropriate monitoring to guarantee their safe use.An in-situ guided-wave experiment was carried out by Kizer and Kube [30] utilizing a 3D-printed ultrasonic wedge that was intended to produce S0-guided waves for the detection of delamination during printing.The infill density of ABS has been identified by Jin et al [31] using non-destructive ultrasound imaging.Different infill densities in 3D printed items were identified using effective density photographs and validated using computed values.In order to track the beginnings of fatigue-damage buildup in an AM aluminum plate, Vien et al [32] explored the second-harmonic production in Lamb waves; with an increase in the number of fatigue cycles, the nonlinear parameters showed a monotonic increase.Sturm et al also looked into the layer-to-layer sensitivity of a controlled sample produced by material jetting.The printing process was monitored by the authors by creating flawed components and comparing them to flawless control sample signatures [33].By comparing the baseline measurements of the defectfree parts, Albakri et al used the EMI approach to evaluate dimensional errors, positional errors, and internal porosity flaws.For the nylon and jetting VeroWhite Plus parts, the authors showed that the technique is adequate for detecting mass change of layers with a minimum change of 1% of mass and feature displacement with a minimum of 1 mm [34].Further, Three different varieties of reversible thermoresponsive composite (TRC), namely vertical, horizontal, and diagonal, were manufactured and compared based on the printing angle condition by Shin and So using the FDM method of 3D printing of PLA.Compared to vertical-type TRCs, the horizontal-type TRCs showed a wider range of average actuation performance [35].The author continues on to construct simple 3D printing of an electrical switch utilizing a soft thermal actuator as well as the creation of transient analysis to determine the location of soft actuators at a given moment [36].Unfortunately, there is a dearth of literature on the subject of EMI-based SHM in 3D-printed structures.
This paper focuses on EMI-based health monitoring of a 3D-printed ABS plate with a horizontal layout, employing two different types of actuators: PZTs and MFC transducers.First, the frequency domain EMI signatures of PZT and MFC sensors are investigated using simulated mass damage scenarios for the ABS plate.A new methodology based on data variability is developed for determining damage-sensitive frequency ranges.The technique is based on the standard deviation of all acquired data for various damage placement scenarios using single maxima.The paper robustly investigated damage sensitivity using three damage indices.Further, using the damage-sensitive frequency ranges, a methodology was proposed to fuse the EMI data from different actuators to achieve damage location imaging for real impact and artificial damage.The method investigated the distribution of actuators for optimal SHM of AM under the sensitivity range and beyond the sensitivity range of actuators for the added mass-based simulated damage.

EMI experimental setup
The EMI experiments are performed on an AM plate manufactured from ABS using the FDM technique of size 200 mm × 200 mm × 3 mm.Two surface-bonded SONOX P502 PZTs of 0.5 mm thick and 5 mm radius were glued to its surface.A MFC transducer (Smart Material M-2814-P1) was also positioned so that its sensitivity in printed ABS could be compared with a typical PZT.The ABS plate was damaged on its surface resulting from a 30 J energy collision with a steel projectile bullet.Using a dial gauge micrometer, the deepest point of the created indentation was measured to be 1.03 mm, and the planar dimension of the dent is roughly 15 mm major axis and 10 mm minor axis.Each frequency domain healthy and damage state measurement is an average of 50 measurements.In the EMI experiment of the ABS plate, a range of frequency spectrum of 1-500 kHz @100 Hz step is considered.The sample experimental setup is shown in figure 1 and more details can be cited from the [37].

Methodology
This section includes a sensitivity study of PZT and MFC actuators to detect and localize the presence of real impact damage and simulated damage in the AM structure.PZT sensitivity utilizes the piezoelectric effect, while an MFC patch even possesses greater actuation forces than a PZT patch due to the d 33 effect dominating the actuation mode in MFC.A theoretical standard deviation-based frequency range selection is explained in assessing the health of the structure.Further, for the data fusion-based damage imaging-based impact localization using various actuators for the assessment of AM samples, a projected DI at the same reference level is explained since the DI is calculated for the different types of actuators in different frequency ranges.

Study of frequency range selection.
The efficacy of the EMI approach is determined by the effective frequency spectra selection for damage sensitivity, which is typically difficult to estimate for the early structural response.The damage sensitivity of the MFC and PZT2 transducer actuators was tested in the same frequency range as the magnet-simulated damage, which was 1-500 kHz.Due to the piezoelectric effect, alteration in a structure's mechanical impedance brought on by damage (impact or magnet-simulated damage) indicates a corresponding change in the electrical impedance of the MFC, PZT1, and PZT2 bonded to the AM structure.Consequently, it is possible to detect structural defects by the variation in the electrical impedance at an identified sensitive frequency range  by applying appropriate damage metric indices.Table 1 shows the distances between the centers of the simulated damage and the PZT2 and MFC actuators.For the sensitivity research, the simulated damage locations were chosen to be at 30 mm steps by moving two strong magnets on opposite sides of the plate along the vertical line.The diameter and thickness of the magnet that simulates damage are 10 mm and 2 mm, respectively.In order to identify the damage-sensitive frequency range, the entire frequency range data of the healthy and 5 damage cases (D1, D2, D3, D4, and D5) is processed together by analyzing its variability using standard deviation.In the experiment, for each PZT and MFC, 12 measurements (6 measurements at a time × 2 repetitions) are acquired.The standard deviation spectrum of the data set is calculated after rescaling the measurements which are used only for the selection of effective frequency range in the various types of actuators.The rescaling methodology was adopted using |Z| of healthy and damaged state data and grouped in one matrix τ , as expressed in equation ( 2) where |Z| is the modulus of impedance sampled over N frequency values; the indices H correspond to the healthy plate status and D1, D2, …, D5 correspond to damage status; the indices 1, 2, 3, …, N correspond to the frequency-sampled data points of |Z|.τ was rescaled corresponding to each frequency value by dividing each column with respect to the maximum value within the column and expressed by equation ( 3) and shown in figures 2 and 3 where, i is the index corresponding to the frequency-sampled data points, where i ∈ [1, 2, 3, . . ., N].
Further, the study is focused on frequency band selection using maxima of impedance standard deviation in standard deviation vs. frequency plot.The method simultaneously uses the healthy and damaged scenario data while studying the standard deviation based |Z|.Two different types of actuators, PZT and MFC are used for the damage localization.They have different selected frequency bands.To the best of the author's knowledge, this is the first time such an approach issued for damage localization.The determination of the sensitive frequency range is done as follows: 1. Determine the maximum standard deviation (M) 2. Calculate 'm' = 25% of M. The change in the standard deviation value of the spectrum due to the introduction of the noise or temperature variation is considered below 25%. 3. Find 3 consecutive peaks that drop by at least 'm' on the left side of M. The frequency of the first of these peaks is denoted f 1 4. Find 3 consecutive peaks that drop by at least 'm' on the right side of M. The frequency of the first of these peaks is denoted f 2  Based on the above study, the MFC's active damagedetecting frequency zone (0-58 kHz) is in the lower frequencies, whereas the PZT's frequency region (94−304 kHz) is in the higher frequencies.The MFC is in lower frequencies, and PZTs in higher frequencies are related to their resonance frequency ranges [22].This method is different from Shishir and Malinowski's [38] based standard deviation approach which uses multiple common local maxima of the standard deviation plot of the G and R and is divided in the subfrequency band for the PZT-based transducer only and does not use the rescaled data of healthy and damage state together.Further, the method utilized C-index to cover the differences in the area of the curve in healthy and damaged conditions in different frequency sub-bands and was not used for the damage localization.

Damage sensitivity study.
Further, the damage sensitivity was studied in the frequency interval f 1 -f 2 based on |Z|.Three DIs, namely RMSD, RMSD based on normalized cumulative electrical power (RMSDNCP), and DV based on distance between the healthy and damage curve are computed to show the robustness of the damage sensitivity method for the 3D printed structure.Firstly, the EMI |Z| raw measurements were normalized with respect to their maximum values in the f 1 -f 2 interval, as expressed by equation ( 4)  The RMSD, a prominent DI, was used to investigate the spectrum changes of the different actuators after damage, as expressed in equation ( 5) [1] where n is the number of frequency samples from f 1 to f 2 ; H and D are, respectively, the healthy and damaged measurements of |Z| normalized .
The Frechet distance metric was chosen for the current investigation due to its dependability and superior performance.Although [39] contains information on the metric's development and comparative analysis, it is included for inclusiveness.The normalized cumulative electrical power (NCP) is calculated using equation ( 6) from an impedance signature vs. frequency plot where, f min ⩽ f ⩽ f max , f min, and f max correspond to the maximum and minimum of |Z| data in the frequency band chosen (f 1 ⩽ f min , f max ⩽ f 2 ).The Frechet distance provides the shortest distance between the two non-uniform curves.To eliminate scaling effects, the amplitudes of the two signals are normalized to lie within [0, 1].To represent the data points on the normalized curves, a collection of 2D points obtained by equation ( 7) can be employed [40]  The shortest Euclidean distance given by equation ( 8) between a certain coordinate on curve q i and all coordinates on curve q j given by equation ( 8) is used to calculate the distance between the curves for a given point 'f' The distance between the two curves is integrated to calculate the DV DI, as shown in equation ( 9) [39,40] As explained in the above equations, the three types of DI were studied to check the robustness in the frequency range from f 1 = 0 kHz to f 2 = 58 kHz, and from 94 kHz to 304 kHz of MFC and PZT toward damage sensitivity.Figures 6(a)-(c) based bar plot results analysis show that the impedance magnitude based DI (RMSD, RMSDNCP, and DV) considerably decreases with the increase in mass-to-actuators distance and that, in all the situations investigated for the PZT2.RMSD, RMSDNCP, and DV-based DI also decrease with the increase in mass-to-actuators distance for the MFC as shown in figures 7(a)-(c).
Another alternative for the sensitivity testing for the PZT2 is to use the entire frequency range of 1-500 kHz.However, as can be seen from figure 8, the DI (RMSD, RMSDNCP, and DV) do not demonstrate a growing or decreasing pattern as the mass moves away from the PZT2 actuator as shown in figures 8(a)-(c).

Impact damage detection
As shown in figure 1, the damage evaluation was carried out for the impact damage (D) at a middle point on the line joining the MFC and PZT2.The distances between the three actuators and the impact damage D are displayed in table 2. The absolute impedance rescaled spectra of the PZTs and MFC are obtained from experiments for a frequency range of 1-500 kHz shown in figure 9.The data from the MFC actuator displays damagesensitive peaks in a low-frequency band (0-58 kHz), while the PZT shows a good sensitivity in a higher frequency range (94−304 kHz) and justifies the study in this frequency range.The damage detection and localization hereafter are realized using the |Z| spectrums within the tested frequency range of PZT2 and MFC.Figures 10 and 11     with respect to a healthy state and can be calculated from figures 10 and 11.In recent research, damage study based on damage image algorithm is gaining importance.There are just a few EMI-based SHM approaches documented in the literature, and there is a significant opportunity to create new SHM tactics for damage localization in composite and polymer materials employing various actuator types.The problem with this approach is the calibration of MFC and PZT sensors in the different frequency ranges.The sensors' damage indices are compared on the same reference to determine which type of sensor is most susceptible to impact damage.The effectiveness of determining the sensitivity radius depends on the accurate determination of rescaling the impact damage DI.The DIs are projected based on the same reference of the healthy state of both actuators.Let us suppose the DIs for the healthy and damaged state of MFC are DVH m , DVD m and for PZT are DVH p , DVD p respectively.The multiplication factor to project the DI of the MFC and PZT is k.Then, the projected DI for the MFC are k, DVDm  DVHm × k, and for PZT are DVHp DVHm × k, DVDp DVHm × k for healthy and damaged state respectively.After projecting the DIs using the same reference as the healthy state value, it is discovered that PZT2's RMSD value is slightly greater than that of the MFC actuator while PZT2 displays a lower DI for the RMSDNCP and DV damage metric as shown in figures 12(a)-(c) respectively.

Damage localization.
Zhu et al's damage mapping method was used to illustrate the suitability of the suggested methodology [41].This method is based on a modified probability-weighted algorithm that changes linearly with the actuator's location's distance from the potential damage site.A known impact damage case calibration was used to calculate a radius of maximum sensitivity.The radius was considered to be constant for all actuators, regardless of where they were located, and ranged from 10 mm to 500 mm based on a 5 mm step.An optimal radius (r) can be determined using damage location accuracy as given in [41,42].
Figure 13 illustrates the use of, r = 216 mm of the sensitivity radius based on the projected DV damage metric measure to assess the effectiveness of various actuators.The proposed approach for localization is examined for the three actuators using k = 1.Using the probability-weighted approach, figure 14 displays the damage localization maps for the impact damage situations.The precision of location was found to be 4.48 mm which is less than to 5 mm step of the sensitivity    Figure 15 illustrates the use of the projected DV metric to assess the added magnetic mass at another location different from the center.The proposed SHM approach's potential for localization is examined for each of the three actuators using the r = 216 mm.The probability-weighted based approach displays the damage localization maps for the added magnetic damage simulation in figure 16.The damage localization outcomes for new locations beyond the damage sensitivity range of the PZT2 were demonstrated using the Euclidian distance and showed a large error for the added magnetic mass simulated as the mass moved away from the sensitivity range of PZT2.The precision of location is found to be 24.48 mm.That is more than a 5 mm step of the radius.Hence, two actuators with damage between them are accurately identifying the damage.The damage accuracy further decreased when the mass moved beyond the sensitivity range of PZT1 and MFC actuators as shown in figure 17.The precision of location is found to be 75.5 mm.This should stress that for both actuators the damage should be at a distance falling within the sensors' sensitivity ranges calculated based on the mass movement.Further, the placements of the actuators for the optimal SHM of the AM structures should encircle the damage point.

Conclusions
A SHM approach for impact-damage detection and localization is proposed based on the measured damage sensitivity of PZT and MFC actuators in an AM plate.The different types of actuator utilize similar working methods but different damage sensitivity ranges within AM material.The two actuator type's damage sensitivity is first examined for the selection of an appropriate frequency range in relation to the distance between the actuator and the simulated damage.Furthermore, damage imaging-based impact localization employing various actuators for the AM samples is carried out, and the research can be summarized in the following points.
• A 3D-printed ABS plate with two different damage kinds (artificial/simulated and real impact damage) was the subject of the study.• A theoretical standard deviation-based frequency range selection f 1 -f 2 is used in assessing the damage sensitivity of the structure.The effectiveness of the suggested SHM approach was also proved for mass-based simulated damage in the selected frequency range.• Additionally, utilizing various damage indices DI (RMSD, RMSDNCP, DV), the actuators' robust performance during the impact-damage event was compared.The outcomes show the potential of the EMI method in damage localization in AM polymer.• For, data-fusion-based damage location imaging, a projected DI with respect to the same reference health state is used to implement impact damage imaging and added magnetic mass damage localization using both types of actuators.The impact damage localization of two PZT actuators and one MFC actuator was then compared with true impact near the middle of the plate and found the positional error of 4.48 mm.However, The positional error for damage localization is increased to 75.5 mm for the damage located out of the actuator sensitivity range.• The actuators with impact damage between them accurately identified the damage within their sensitivity ranges.Further, the maximum number of actuators positioned within the sensitivity range, and the distribution of the actuators should encircle the damage point for the optimal SHM of AM structures.
This study is anticipated to contribute to the creation of a robust EMI-based method for damage detection and localization using different types of actuators in AM structures.Future research would focus on developing a reliable multiple damage localization approach in AM under noisy and changeable ambient conditions.

Figure 1 .
Figure 1.(a) Experimental setup for EMI measurements (b) the 3D printed ABS plate with impact damage (D).

Table 1 .
The distances between the centers of magnet-simulated damage and the outer edges of the MFC and PZT2 actuators.

Figure 2 .
Figure 2. |Z| rescaled plot for the PZT2 with simulated mass damage scenario.

Figure 4 .
Figure 4.The standard deviation (σ) plots using rescaled impedance amplitude for PZT2 in the frequency domain.
present a comparison of the utilized DI indices of PZT2 and the MFC, respectively.The DIs of both actuators show a large deviation between the healthy and impact-damage cases.RMSD, RMSDNCP, and DV-based DI of the PZT2 are shown in figures 10(a)-(c), and of the MFC shown in figures 11(a)-(c) for the healthy and impact damage case.The scale of healthy and damaged DI (RMSD, RMSDNCP, and DV) are on different scales e.g.DV DI of PZT1, PZT2, and MFC is 14.34, 31.89, and 37.2 times

Figure 7 .
Figure 7.The MFC actuator's comparative (a) RMSD, (b) RMSDNCP, and (c) DV damage index for various mass locations in the 3D-printed ABS plate.

Figure 8 .
Figure 8.The comparison of the (a) RMSD, (b) RMSDNCP, and (c) DV DIs of the PZT2 actuator for various simulated damage locations.

Table 2 .Figure 9 .
Figure 9. Experimental plot of the impact damage using impedance data on the surface of a 3D-printed ABS plate.

Figure 12 .
Figure 12.Projected DI (RMSD, RMSDNCP, and DV) on the same reference of the healthy state of actuators for the impact damage.

Figure 13 .
Figure13.DV-metric-based damage-sensitivity radius study using all the actuators for the impact damage.

Figure 14 .
Figure 14.Damage-localization imaging for impact damage located within the actuators' sensitivity range.

Figure 15 .
Figure 15.Projected DV damage index of actuators for the added mass-based simulated damage.

Figure 16 .
Figure 16.Damage-localization imaging for simulated damage at the top left corner of the plate.

Figure 17 .
Figure 17.Damage-localization imaging for simulated damage at the bottom right corner of the plate.