Wireless power transfer-based eddy current non-destructive testing using a flexible printed coil array

Eddy current testing (ECT) has been employed as a traditional non-destructive testing and evaluation (NDT&E) tool for many years. It has developed from single frequency to multiple frequencies, and eventually to pulsed and swept-frequency excitation. Recent progression of wireless power transfer (WPT) and flexible printed devices open opportunities to address challenges of defect detection and reconstruction under complex geometric situations. In this paper, a transmitter–receiver (Tx–Rx) flexible printed coil (FPC) array that uses the WPT approach featuring dual resonance responses for the first time has been proposed. The dual resonance responses can provide multiple parameters of samples, such as defect characteristics, lift-offs and material properties, while the flexible coil array allows area mapping of complex structures. To validate the proposed approach, experimental investigations of a single excitation coil with multiple receiving coils using the WPT principle were conducted on a curved pipe surface with a natural dent defect. The FPC array has one single excitation coil and 16 receiving (Rx) coils, which are used to measure the dent by using 21 C-scan points on the dedicated dent sample. The experimental data were then used for training and evaluation of dual resonance responses in terms of multiple feature extraction, selection and fusion for quantitative NDE. Four features, which include resonant magnitudes and principal components of the two resonant areas, were investigated for mapping and reconstructing the defective dent through correlation analysis for feature selection and feature fusion by deep learning. It shows that deep learning-based multiple feature fusion has outstanding performance for 3D defect reconstruction of WPT-based FPC-ECT. This article is part of the theme issue ‘Advanced electromagnetic non-destructive evaluation and smart monitoring’.

Eddy current testing (ECT) has been employed as a traditional non-destructive testing and evaluation (NDT&E) tool for many years. It has developed from single frequency to multiple frequencies, and eventually to pulsed and swept-frequency excitation. Recent progression of wireless power transfer (WPT) and flexible printed devices open opportunities to address challenges of defect detection and reconstruction under complex geometric situations. In this paper, a transmitter-receiver (Tx-Rx) flexible printed coil (FPC) array that uses the WPT approach featuring dual resonance responses for the first time has been proposed. The dual resonance responses can provide multiple parameters of samples, such as defect characteristics, lift-offs and material properties, while the flexible coil array allows area mapping of complex structures. To validate the proposed approach, experimental investigations of a single excitation coil with multiple receiving coils using the WPT principle were conducted on a curved pipe surface with a natural dent defect. The FPC array has one single excitation coil and 16 receiving (Rx) 2020 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/ by/4.0/, which permits unrestricted use, provided the original author and source are credited.

Introduction
The eddy current testing (ECT) has been developed for various non-destructive testing and evaluation (NDT&E) applications, such as defect detection, thickness, coating and conductivity measurements for material identification; heat damage detection; case depth determination and heat treatment monitoring. In its development, the ECT has metamorphosed through different stages, namely single-frequency [1], multiple-frequency [2], swept-frequency ECT [3,4] and pulsed or transient ECT [1,5]. In terms of the probe design, recently the ECT has adopted the use of flexible arrays [6][7][8].
A single-frequency ECT [1] uses a single-frequency excitation which inherently limits its sensitivity due to the skin depth effect for surface or subsurface defect detection. To increase its penetration depth, it requires reducing its excitation frequency at the expense of coil sensitivity [5]. The multiple-frequency ECT [2] has been developed with simultaneous or sequential excitations for detecting defects at different depths and resolving the acquired signals that are affected by many variables, such as conductivity, permeability, geometry and probe's liftoff. The simultaneous excitation method results in a shorter testing time with less power consumption in each frequency component compared with the sequential excitation, which requires each system excitation to reach a steady-state before the next excitation. The sweptfrequency approach [4] overcomes the multiple excitation problems with high precision and broad bandwidth potential for inspection of complicated areas by using a fixed probe. It has been applied for crack quantification [3], detection of thickness, measurement of permeability, and conductivity of materials coating [4,9,10] and object detection in more complex geometric areas [11]. However, the longer frequency sweep duration leads to lengthy inspection time scanning for defect positioning [12,13]. The pulsed ECT [5] has the potential for a shorter testing time with information of different depths due to its wide frequency bandwidth. It surpasses singleand multiple-frequency testing techniques due to its transient system response that potentially contains this wide spectrum of frequencies. It also contains, through the features, information on defect size, location and depth in the transient signal. However, it has lift-off variation including geometry and coupling between transmitter and receiver (Tx and Rx) coils, which carries no sample information. Moreover, lift-off effect by different normalization techniques has not effectively dealt with surface defects as effectively as with the subsurface, as the former presents similar signals to lift-offs [14].
The ECT works through a transmit-receive system by detecting induced eddy currentgenerated magnetic field from the material under inspection. The transmitter is usually made up of an induction coil, whereas the receiver could be using some magnetic field sensor. Traditional Tx-Rx coils have a high response and sensitivity to alternating flux linkage [15]. However, they are more sizeable than the defect and physically inflexible, which makes them possess lower spatial resolution and being prone to lift-off variations. Therefore, the quantification of natural defects in a metallic structure, especially with complex geometry like the curved surface in the pipeline, remains a challenging task.

2.
Principles of the transmitter-receiver wireless power transfer system for the eddy current testing A Tx-Rx WPT system comprises of an excitation circuit, two coils as a receiver (Rx) and a transmitter (Tx), and a load. The resonance property is achieved by series and/or parallel connection of multiple reactive elements like inductors and capacitors. The Rx and Tx can be configured as series-series (SS), parallel-parallel (PP) or a combination of series and parallel each with a compensating capacitor for efficient energy transfer [28,29]. As discussed in [28][29][30], different topologies have different impedance matching and quality factor equations that can lead to different measurement performance of WPT-based ECT systems. The PP resonant circuit was shown to have a higher sensitivity to metallic objects and a lower sensitivity to noise compared with the SS-resonant circuit due to its larger input impedance [31]. Therefore, the PP topology is selected for this study. Figure 1 shows the equivalent circuit diagram of the PP, Tx-Rx, WPT system including a metallic sample and an excitation voltage source V that is used in this paper. I 1 , I 2 and I S are the excitation currents through Tx's, Rx's induced current due to field linkage and sample's induced eddy current, respectively. Similarly, R 1 , R 2 and R S are the resistances of the Tx coil, Rx coil and the metallic sample, respectively. L 1 , L 2 and L S are the Tx, Rx and sample self-inductance, respectively. C 1 and C 2 are the compensated capacitors for Tx and Rx, respectively. The circuit in figure 1 can be evaluated using Kirchoff's laws to find the current flows through each element and voltage drop around each loop.
Kirchhoff's voltage law (KVL) states that the algebraic sum of all voltages around any closed loop in a circuit is zero. Applying KVL to the circuit shown in figure 1, the three loops in the circuit including Tx's excitation current, Rx's induced current and the sample's induced eddy current are represented by equation (2.1), where M 12 , M 1S and M 2S are the mutual inductances for Tx-Rx, Tx sample and Rx sample, respectively; each depends on their appropriate coupling coefficients and inductances. ⎛ where the transmitter, receiver and sample units' equivalent impedances, Z 1, Z 2 and Z s , respectively, are given as: From the last, the sample's loop KVL expression in equation (2.1), the expression for current, I s , is derived and given by (2.2). The derived value of I s in (2.2) is substituted into Tx and Rx loop KVL in equation (2.1) to generate an equation model for Tx and Rx circuits in figure 1, which includes the effect of sample parameters. The circuits of Tx and Rx units are analytically described by the derived expression given by (2.3) and (2.5). The models given by (2.3) and (2.5) for Tx and Rx ports, respectively, described their self-and transfer impedances. The self-impedance of each port includes the effect of the nearby metallic sample as seen in figure 1:  Figure 1. Equivalent circuit of Tx-Rx and metallic sample. (Online version in colour.) 3) The first part of V 1 expression given by (2.3) is the voltage drop due to the new self-input impedance, Z 1_new , of the Tx unit, while the second part is due to the reflected transfer impedance contributed by the Rx unit in the presence of the metallic sample. The affected parameter of Z 1_new is the actual Tx probe impedance, R 1 + jωL 1 , which is in parallel with the compensating capacitor, C 1 .
On rearranging Z Tx_new and collecting the like terms, we have the new probe's impedance given by the following equation: Similarly, by substituting the expression of I s (equation (2.2)) in the Rx loop KVL equation (2.1), we have (2.5) The first part of (2.5) is the reflected voltage drop from the Tx unit due to the transfer impedance, while the second term is the self-induced voltage across the Rx unit. By taking the second term, the new Rx self-impedance which includes the effect of the metallic sample, we finally derived the new resistance and inductance of the Rx coil as given by the following equation: (2.6) Equation (2.1) is used for determining the inductance and resistance in each of the resonant circuits as a function of the sample's and coil's parameters. The dominant coil's parameters are the self-inductance and -resistance which vary according to the sample conductivity, permeability and geometric nature due to eddy current interruption. The sample behaves as an inductor through which the eddy current circulates. The magnetic field generated by the induced eddy current in the sample affects the primary field linking Rx and, in turn, the equivalent parameters of Tx and Rx coils. The variations of effective resistance and inductance of the Tx and Rx royalsocietypublishing.org/journal/rsta Phil. Trans. R. Soc. A 378: coils as a result of the induced eddy current's influence on the Tx-Rx coupling depend on the excitation frequency, mutual coupling between the coil and the sample, and sample parameters. The relationship is derived from (2.1) and given in equations (2.7) and (2.8), which is similar to the model used for metallic object detection based on the WPT system [31][32][33]. The presence of the metal sample near the Tx or Rx increases losses due to the reduction in the magnetic field passing through the coil section as a result of the eddy current's effect in the sample. It then reduces Tx and Rx inductances as seen in (2.7), and hence, the resonance frequency point increases. Similarly, it increases the equivalent self-inductor resistance, which affects the voltage and current responses at the resonance point. However, at the point of defect, the voltage and current change slightly due to the variation in sample parameters as a result of the high influence of eddy current density around the defect area. and where i = 1 for Tx and 2 for Rx.
The new inductance and resistance values of Tx and Rx change the resonance point and the voltages across Rx and Tx. The change of input and output voltages at the resonance point contains the information about the sample's electrical conductivity, magnetic permeability and the defect parameters. The performance of a Tx-Rx WPT system is measured by its forward voltage gain, which is described by a transmission coefficient of the scattering parameters, S 21 , as defined by equation (2.9) [34][35][36]. It can be seen that the response depends on the sample's permeability, conductivity, geometry, the defect parameters and the operating frequency.
The Tx-Rx voltage ratio in equation (2.9) is derived by evaluating KVL on Tx and Rx circuits in figure 1 in the absence of a metallic sample. The derived voltage ratio of Rx output voltage across R L and input voltage, V, as a function of frequency is given in equation (2.13). To derive the S 21 response for the Tx-Rx WPT circuit in figure 1, the two-loop equations are generated from the Tx and Rx sides of the WPT circuit and Rx output voltage across the R L resistor given by equations (2.10)-(2.12), respectively. V(ω) = (Z 1 )I 1 − jωM 12 I 2 , (2.10) 0 = −jωM 12 I 1 + (Z 2 )I 2 . (2.11) By substituting the expression of I 2 in equations (2.10) and (2.12), we have On substituting Z 1 and Z 2 , in the expression of V(ω) and V RL (ω), their ratio is given by the following equation:  where V RL (ω) is the voltage across the Rx load (R L ) as a function of the frequency, which depends on the eddy current's influence from the sample and the Rx's induced voltages. The mutual coupling between Tx and Rx, M 12 , is mathematically defined by an expression K 21 √ L 1 L 2 ; also, r s and R L are the impedances of port 1 and port 2 of the vector network analyser (VNA) and their values are equal in our case. Therefore, the absolute values of the transmission coefficient, S 21 , over a certain range of frequencies can be plotted to give the frequency response behaviour of the Tx-Rx WPT system as seen in figure 2a for the model in the following equation: (2.14) Similarly, the resonance frequency for the Tx and Rx circuits in figure 1 considered being equal for achieving a maximum power transfer efficiency and for the dual peak of S 21 response to be symmetric about a resonance point, f 0 . It is theoretically obtained from the circuit in figure 1 by setting the imaginary part of the equivalent admittance of each Tx and Rx network to zero as a condition for a resonance point. The derived resonant frequencies are given by the following equations for Tx (f 0Tx ) and Rx (f 0Rx ), respectively.
However, according to the circuit theories, analysis and experimental study, the Tx-Rx WPT response given by equation (2.14) has two split resonance frequencies in an over-coupled operation region [34,37]. The over-coupled region occurred at the higher mutual coupling between Tx and Rx coils, which depends on the distance between the two coils and their parameters. The interaction of the Tx-Rx coils with the sample affects the mutual coupling between Tx and Rx, proportional to the sample parameters. Equations (2.9) and (2.14) describe the response of the Tx-Rx probe system for the circuit given in figure 1. The coupling factor linearly depends on the Tx-Rx mutual inductance which depends on the sample influences as determined by equation (2.7    by equation (2.14). Figure 2a shows S parameter of the reflected and transmitted signal values (S 21 ) for different coupling coefficients (K 21 ) of Tx-Rx as an indication of the response to the mutual coupling between the Tx-Rx and the sample. The two peak points of the response, S 21 , increases due to an increase of the mutual coupling between Tx-Rx coils. As discussed in [29], different topologies of magnetically coupled resonant Tx-Rx systems can be designed and developed through the selection of Tx-Rx capacitors C 1 and C 2 . This extracts more power from the transmitter in the form of eddy current losses which has a significant impact on the system's parameters, especially for low-power applications [31,38]. For our FPC coil array, the Tx and each Rx mutual coupling results from the interaction with the metallic sample and defect. Figure 2b shows  The values in table 1 show the PP topology's parameters and their operating frequency range and quality factors for the study. Different resonance networks or components will be optimized in terms of feature selection and fusion to achieve optimal sensitivities and functionality of WPTbased ECT in future work.
In our proposed work, the mutual couplings of the FPC array are assumed to remain the same for bending it to sample surface geometry because Tx and Rx array are integrated on the same substrate. Therefore, the Tx and Rx array's mutual couplings are only affected by the influence of the metallic sample within their coverage area. Now, this paper will demonstrate the advantages of the WPT-based ECT systems using the FPC array, which include area mapping and scanning on a curved sample and multiple feature extraction, selection and fusion for defect characterization. The design, development and experimental implementations of the proposed system are described in §3.

Experimental studies
The system includes the probe, sample measuring instrument, data mining, feature imaging and defect characterization. The details of the sample used for the investigation are described in table 1. The probe is an FPC array fabricated on polyimide film with a thinner trace thickness and line spacing, which are advantageous for spatial resolution and sensitivity enhancement. The FPC array is made up of four layers with Tx covering the top and bottom layers, while 64 equally spaced similar Rx coils are distributed in the two middle layers. The coils, Tx and Rx arrays, composed of two parts each from different layers, are connected in series through vias [7]. The structure maximizes the mutual inductance between the Tx and Rx coil array, which then improves the Rx response and increases the signal-to-noise ratio. Figure 3 shows the Tx-Rx coil array used in this work, showing an excitation Tx coil surrounding a uniformly spaced and multiple detection Rx coil array. The Rx coils have identical inductance values which are 1.9 µH, while the Tx has an inductance of 1.26 µH, which were measured using HAMEG ® programmable LCR bridge HM8118 operating at 200 kHz. The Tx coil allows a considerable magnetic field to be evenly distributed across the Rx array. When the Tx coil is excited, it generates a spatially periodic magnetic field that induces a voltage in each Rx and eddy currents in the sample surface. According to the current continuity theorem, whenever there is a defect on the surface, the original flow path of the eddy current changes and flows around the edge of the defect. Hence, the generated eddy current field affects the primary field linking Rx, which manifests on the Rx's induced voltage carrying information on the sample and the defect. A flexible sensor made of an array of receivers was used because of its advantages for area mapping at higher spatial resolution and flexibility to different geometric shapes [7]. First, 16 channels were used for dent-area inspection using a VNA to capture an 'M' shape response of Tx-Rx. The Tx and Rx channels were configured as parallel resonance network topology by connecting a capacitor in parallel as seen in figure 1. The values of L 1 , L 2 , R 1 and R 2 of the FPC array were inherent, while C 1 and C 2 were determined based on the resonance frequency, specific coil inductance and quality factors. The high resonance frequency is used for Rx channels for the inspection of surface dent defects. The parameters and values of the FPC array and their compensating capacitors are presented in table 1. The swept-frequency range is 300 KHz-19 MHz for the WPT ECT system. The optimal selection of the parameters of WPT topology and optimal operational frequency-dual resonance frequency will be discussed in our next paper.
The system diagram is presented in figure 4. The system includes WPT-based ECT instrumentation using the VNA and FPC array, signal collection, multiple feature extraction, selection and fusion for quantitative non-destructive evaluation (NDE). The experimental setup and the FPC coil array over the pipeline sample with natural dent defects are illustrated in figure 5, which is discussed in the next two paragraphs. The multiple feature extraction, feature selection and feature fusion are investigated in §4 with comparisons. Figure 4 area is illustrated in figure 5a as an experimental set-up in the photo. Figure 5 shows the experimental set-up using the FPC array over a cast-iron pipeline (cut) sample with a natural   dent from the industry. The Tx and each Rx coils were configured and connected to a VNA (VNA-E5071B) with Tx to port 1 and Rx to port 2. The Rx channels were connected sequentially, one at a time, because of the VNA connection constraint. The E5071B (300 kHz to 8.5 GHz) model has only two test ports. The VNA operates on a sweep signal, measures the transmission coefficients, S 21 , and displays the results on the screen. The Tx and Rx signals from the VNA ports are internally converted into an intermediate frequency signal by a mixer, then into a digital signal by an inbuilt analogue-to-digital converter (ADC) and finally sent to the processor. One ADC is available for each port signal, and the conversions take place simultaneously. Each of the inbuilt ADCs has a 16bit resolution and a sampling rate of 570 k samples per second. Then, a microprocessor analyses the digital data and displays the results on the screen at a sweep speed of 9.6 µs/point. Finally, the computer unit is where the signal processing, features selection, extraction and processing for the defect evaluation take place. The data measured by the VNA system, S 21 , have 1601 swept-frequency points among 300 kHz-19 MHz for every channel at a measurement point on the sample as illustrated in figure 5, the experimental set-up. For each measurement position of each C-scan, each of the 16 Rx channels covered 0.8 mm Y-spatial position and 2 mm X-spatial position with lift-off for the Z-spatial position. For our measurement of the dented area, the probe C-scan measurement was conducted by moving the sample axially at an equal interval of 2 mm for 40 mm distance for the defect to cross the probe. The first C-scan measurement point of 16 Rx channels, as presented in figure 2b, shows that the multiple responses with 'M' shape have multiple variables and features including lift-off for mapping to parameters. As illustrated in figure 2b, the 'M' shape response or double resonances have information related to the Tx-Rx probe-samples system relationship (lift-off and geometry), defect geometry and material inhomogeneity due to a wide range of frequencies. To investigate the capability of the proposed system for surface dent mapping and reconstruction, multiple features including resonant magnitudes and PCA were extracted on the dual resonance response and demonstrated in §4.

Multiple feature extraction, selection and fusion
The data for feature extraction, selection and fusion for mapping defect parameters are obtained and investigated using the proposed system response as shown in figure 2b and the dedicated cut pipeline sample with a natural dent. The dedicated dent sample is measured using a stylus profilometer. The depths of the dent are used for the comparison of multiple features in §4a, feature analysis and feature selection using cross-correlation analysis between the actual depths and extracted features in §4b, evaluation and comparison of feature fusion using deep learning and correlation method in §4c. Also §4c gives comparison of the highly correlated single feature from correlation analysis and the fused feature from the deep learning approach for best mapping to the actual depth of the dented area.   The four features profile can be visualized and compared with the dent profile measured by a stylus profilometer in figure 6. The 3D plots in figure 6 use measurement positions of array spaces and C-scan as an Rx channel and the sample position in line with the x-and y-axis of the measured dent profile. Figure 6a illustrates the dent depth profile against the curvature surface; figure 6b illustrates the M 1 feature of the peak values of Tx resonance (first resonance); figure 6c shows the M 2 feature of the peak values of Rx resonance (second resonance); figure 6d shows P 11 PCA feature of Tx resonance principal component (first); figure 6e illustrates P 21 PCA feature of Rx (second) resonance. The M 1 is negatively correlated to the actual depth of the dented area as it shows decreasing behaviour towards the dented area points. The M 2 feature is positively correlated to the depth of the dented area as detected by Rx coils. As different features have different characteristics with the depth, a different feature extraction has a different reflection of defect characters. None of the extracted features reflect the defect contour with a good correlation. A comparison of different feature correction with defect depths for feature analysis, feature selection and feature fusion using correlation and deep learning methods for defect mapping are investigated in the next section.

(b) Feature analysis and selection for defect depth
The extracted multiple features have different characters of the defect depths as illustrated in figure 6. The relevant features for defect depth information need to be selected and fused for 3D defect mapping and reconstruction. The correlation method is used for multiple feature analysis and selection. The correlation coefficients for a set of features at every measurement point give a measure of its relevancy to the actual depth parameter. The cross-correlation between actual depths of the dented area along with the Rx array (x-axis) and the extracted features at every measurement point (y-axis) was evaluated. The set of correlation coefficients between each array of the extracted feature and the depths of the dented area for each measurement point were obtained. Figure 7 shows the extracted features' correlation, each with its dedicated depth at each measurement point. A feature coefficient of ±1 indicates a perfect degree of correlation with the defect parameter. The positive correlation by M 2 and PC 21 and negative one by M 1 features were due to the behaviour of the WPT system's dual response towards the two peak resonance values and overall response shape as shown in figure 2b. The first resonance peak M 1 decreases, while the second peak M 2 increases as the distance to the dent decrease, which are caused by decreasing  mutual coupling between Tx-Rx coils. PC 11 has the lowest correlation, whereas the second magnitude M 2 has the highest correlation coefficient with the defect depth due to the Rx response with the sample and defect. It can be applied for a single feature application. It is understandable, one single Tx excitation and multiple Rx illustrate location information during NDT&E without scanning. For using multiple features, correlation-based and deep learning-based feature fusions are applied and compared in this study.

(c) Feature fusion for defect depth and 3D mapping
In this section, two feature fusion approaches including deep learning-based fusion and canonical correlation analysis (CCA)-based fusion are used to strengthen the WPT-based ECT's capability for mapping the defect area. The quantitative analyses of different feature extractions and fusion strategies are conducted in terms of R 2 value and mean square error (MSE) values between defect parameters and features. The value of R 2 is a statistical measure of data fit that indicates the proportion of the variation of dependent variables described by the independent variables in a regression model, whereas the MSE represents how close a regression line is to a set of points.
To implement the deep learning-based feature fusion for the four extracted features for defect 3D mapping, this work applied the two-layer feed-forward deep learning network to build the learning model between features and defect depths. The first 50% of the features and actual depths data served as training, and the rest of 50% is used for validation using the trained neural network model. Four features each with the same dimension F 16×21 were reshaped to 1D signal F 1×336 . Thus, the whole feature set is F 4×336 and serves as an input for the network. The target to train the model is real defect depth parameters with the same dimension of 1 × 336. The model used a Levenberg-Marquardt technique for optimizing the network structure at different iterations. The MSE of the training set is lower than 0.001 and that of testing and validation set is lower than 0.01, which indicates that the model can well describe the relationship between four features and the defect depths. After validation of the deep learning model, the whole four feature sets including M 1 , M 2 , PC 11 and PC 21 are fused by the model, mapping the 3D profile of the defect shown in figure 8b.
To validate the deep learning techniques' capability for feature fusion, the feature fusion was also achieved using the CCA [40][41][42][43]. The CCA combines multiple datasets into a common representation across subjects for denoising and dimensionality reduction. The CCA forms a linear combination from both datasets for maximizing an individual variable's weight and   effectiveness of the parameter set as a whole. In this work, the CCA-weighted factors were calculated between defect depths and individual feature sets. Then, each feature set is multiplied by the weighted factors and summed together to obtain the CCA fusion feature. It is observed that the true defect profile as shown in figure 7a has a good agreement with fused features in figures 8b and 8c. There are only minor differences seen in non-defect areas. To quantitatively evaluate the fused features' capability for mapping the defect areas, the R 2 value, which is the square of the correlation between the defect parameters and the fused features, and the MSE are used for different feature sets. It is shown that in table 2 and figure 8, the fused features by the deep learning network have the highest R 2 value and the lowest MSE value, proving it is the best feature for mapping the defect using the WPT-based ECT system. The CCA fusion feature shows reasonable R 2 and MSE values. Thus, it is well understood that fusion features including deep learning and CCA can merge the behaviour of sub-features and show their capability for defect mapping and reconstruction. Besides the fused features, M 2 (second resonant magnitude) also has an R 2 value of 0.9104 and an MSE value of 0.0016, indicating the frequency band 14.5-16.0 MHz of the system is sensitive to surface dent. PC 11 and PC 21 , from the two resonances, can also illustrate that Rx resonance has better depth responses than Tx resonance as resonance peak values. The fusion of multiple features with different weightings by using deep learning and correlation methods has better performance of depth estimation than a single feature in terms of R 2 and MSE values. The deep learning method for the multiple feature fusion has the best performance of depth prediction.

Conclusion and future work
In this paper, WPT and flexible coil array were integrated for the ECT of a pipeline sample with a dented area due to metal loss and corrosion. The dual resonance response S 21 of the integrated system was investigated for multiple feature extraction, selection, fusion and mapping for a 3D defect reconstruction and characterization. The experimental system of WPT-based eddy current NDT using the FPC array has demonstrated its feasibility for NDT&E of curved surface. The multiple responses with double resonances can provide multiple features for depth characterization. The extracted feature correlation analysis shows that the feature of the second resonance peak values has the highest correlation with the depth profile of the dented area for having the highest R 2 value and the lowest MSE value. It can be explained that the FPC array has one excitation coil (Tx) and multiple received coils (Rxs), and the second resonances from Rxs have better local information. This demonstrates the capability of the Rx resonance unit on responding to eddy current losses in the sample and defect compared with the Tx resonance point. Also, the deep learning has shown to surpass the canonical correlation analysis in the feature fusion for the 3D reconstruction of the dent, as the former has the highest R 2 value and the lowest MSE value.
Based on the proposed multiple feature extraction and fusion for defect mapping, further optimization of comparison of topologies of the WPT-based ECT system including a selection of WPT topologies, coils and capacitance parameters, their equivalent quality factors [29,30] and their performance for sensitivity and functionality of quantitative NDE needs to be further investigated. The results are only given to the depths of surface dent-area characterization of complex metallic structures inspection. The future work can extend the proposed work of WPTbased ECT systems and multiple feature extraction, selection and fusion for different types of defects and their parametric estimation like rolling contact fatigue, stress corrosion crack and other hidden defects [44,45]. Also, the proposed system will be miniaturized using WPT IC chips for operating at optimal frequency ranges. It can be implemented as a portable system or a permanently installed sensor system for in situ structural health monitoring.
Data accessibility. This article has no additional data. Authors' contributions. L.U.D. implemented the study and undertook the experimental study and validation; G.Y.T. proposed the work and supervision; Q.Y. joined the study including algorithms and signal processing and data validation. A.S. joined work on paper development and discussion.