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Defect Characterization With Eddy Current Testing Using Nonlinear-Regression Feature Extraction and Artificial Neural Networks Luis S. Rosado, Fernando M. Janeiro, Member, IEEE, Pedro M. Ramos, Member, IEEE, and Moisés Piedade
Abstract—The estimation of the parameters of defects from eddy current nondestructive testing data is an important tool to evaluate the structural integrity of critical metallic parts. In recent years, several works have reported the use of artificial neural networks (ANNs) to deal with the complex relation between the testing data and the defect properties. To extract relevant features used by the ANN, principal component analysis, wavelet decomposition, and the discrete Fourier transform have been proposed. In this paper, a method to estimate dimensional parameters from eddy current testing data is reported. Feature extraction is based on the modeling of the testing data by a template of additive Gaussian functions and nonlinear regressions to estimate their parameters. An ANN was trained using features extracted from a synthetic data set obtained with finite-element modeling of the eddy current probe. The proposed method was applied to both simulated and measured data, providing good estimates. Index Terms—Artificial neural networks (ANNs), defect parameter estimation, eddy current testing (ECT), feature extraction, nonlinear regression.
I. I NTRODUCTION
N
ONDESTRUCTIVE testing (NDT) represents the group of techniques used to evaluate and characterize materials without changing their original properties. It has been widely applied in medical procedures [1], food processing [2], and industrial applications [3] that require high levels of reliability and high material/equipment costs. Moreover, the use of these techniques on quality control has dramatically increased, and today, it is seen as a cost-saving tool for many manufacturing companies. There are several NDT techniques based on
Manuscript received June 22, 2012; revised October 24, 2012; accepted October 25, 2012. Date of publication January 28, 2013; date of current version April 3, 2013. This work was supported by the Fundação para a Ciência e Tecnologia through the Ph.D. Program under Reference SFRH/BD/65860/ 2009. The Associate Editor coordinating the review process for this paper was Dr. Zheng Liu. L. S. Rosado is with the Instituto de Telecomunicações, Instituto de Engenharia de Sistemas e Computadores-Investigação e Desenvolvimento, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001 Lisboa, Portugal (e-mail:
[email protected]). F. M. Janeiro is with the Instituto de Telecomunicações, Universidade de Évora, 7000-671 Évora, Portugal (e-mail:
[email protected]). P. M. Ramos is with the Instituto de Telecomunicações, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001 Lisboa, Portugal (e-mail:
[email protected]). M. Piedade is with the Instituto de Engenharia de Sistemas e ComputadoresInvestigação e Desenvolvimento, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001 Lisboa, Portugal (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2012.2236729
different physical principles of operation, such as ultrasonic, eddy current, X-ray, magnetic particles, and dye penetrant. The choice of the correct technique should take into account safety, economical, practical, and efficiency issues. The application of NDT techniques to metallic parts is a common practice in the aerospace [4], railway [5], automotive [6], power generation [7] and petrochemical industries [8], [9]. It has been used to test riveted or welded metallic joints that can compromise the mechanical integrity of critical parts. Because of their high sensitivity and portable instrumentation, ultrasonic and eddy current techniques are the most commonly used on such applications when the part is already deployed and there must be an assessment of its correct ability to perform as expected and designed. Eddy current testing (ECT) is based on the magnetic induction and sensing of electrical currents on the superficial layers of metallic parts. In its simplest form, the technique relies on positioning a coil, the so-called probe, over the metallic part while measuring the coil/probe impedance. The current flowing on the coil produces a magnetic field that also induces electrical currents on the metallic part. These currents, in turn, when subject to modifications resulting from a defect or other sources, will change the original magnetic field and consequently alter the coil impedance. In addition to the detection of possible defects, the measured impedance profiles can also be used to estimate some of the defect properties. However, the relation between the defects and the generated impedance profiles is, in most cases, very complex. To estimate the defect depth based on ECT data, the discrete wavelet transform allied with an artificial neural network (ANN) was used in [10]. The main difficulty was separating the defect contribution from the part itself, which can have already some characteristics that change the eddy currents (e.g., in [11], this is caused by rivets). After decomposing the input signal into the wavelet coefficients, they are compared with a set of reference coefficients from a nondefective situation. A feature based on the energy of the difference between the two sets of coefficients was proposed. This feature is the input of the ANN which was previously trained. Although the proposed method appears to give reasonable results without excessive complexity, it requires a nondefective part to be used as reference, which may not be available in every application. In [12], the use of ANNs to reconstruct the defect profile from ECT data was studied. A dynamic ANN (with a moving input window) was proposed to model the ECT probe. Later, the application of the method on multifrequency ECT data was reported in [13]. In
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[14], an implementation of ANNs for multifrequency ECT on conducting layers and ferrous tubes was presented. Defects can be modeled by nonconductive notches in the metallic part. This may be a good approximation when the defect width is considerable, but in some applications, it may be extremely reduced. On those situations, the defect may include some contact spots with different conductivities from the metallic part. This behavior was modeled by representing the defect with a mesh of variable conductivity cells in [15]. The authors proposed an ANN trained to recover the defect profiles from the ECT data. Later, the same authors introduced a parameter intended as a figure of merit to the defect profile estimates [16]. In [17], the method reported in [15] was compared with the inversion of the probe electromagnetic model to estimate the defect. The results from the electromagnetic approach have shown to be slightly better than the use of the neural network. Nevertheless, the electromagnetic approach has shown significant drawbacks by requiring the design of a complex model and huge computational resources for its inversion. Another interesting approach on the inversion of ECT data has used a sequential Monte Carlo method [18]. A particle filter was used to recursively compute the state which was chosen to represent the defect depth. A Markov state transition model was selected to match the defect propagation behavior and the dependence on its neighborhood. The adopted observation model was based on a polynomial function whose coefficients were obtained with a synthetic data set of defects and responses. In [19], parameters of approximation functions on both time and frequency domains were used to extract relevant features. The approximation functions used were selected in agreement with the observed data. An ANN was used to estimate the defect profile. The main advantage of these approximation functions is that, when well selected, they can extremely reduce the number of relevant features and, consequently, the computational complexity of the estimation or classification procedure. However, this approach requires nonlinear-regression algorithms to approximate the data introducing a significant complexity. The study of a neural network classifier using features extracted with several methods was reported in [20]. The discrete wavelet transform, Fourier descriptors, principal component analysis, and block mean values to extract features from ECT data were considered. The classification results between the different procedures were similar, but the conclusion was that the principal component analysis allows the use of a smaller number of features as input of the ANN. In [21], the performance comparison between two machine learning systems, namely, ANN and support vector machine, for a probe with two drive and pickup coils coaxially wired onto a thin ferromagnetic sheet of annealed metallic glass [22] was reported. In this paper, which is an extended version of the paper presented in [23], the estimation of defect properties from testing data performed using a custom eddy current probe is reported. The proposed method is based on ANN estimation and feature extraction using a model function to approximate the testing data. The selected model function is composed by a set of additive Gaussians whose parameters are estimated using a nonlinear regression. The ANN was trained using a large simulated data set and applied to both simulated and measured data.
Fig. 1.
Layout of the driver trace, sensing coils, and defect.
Fig. 2. Simulation results for a sweep with a defect with 0.5-mm depth and 1-mm width. Real and imaginary parts of the output induced voltage as a function of the relative probe position before rotation.
II. M EASUREMENT S ETUP In this work, the differential planar probe proposed in [24] and represented in Fig. 1 was used to measure defects. In this probe, the excitation and sensing circuits are separated: The excitation current flows in one linear excitation strip, and two pickup coils that share a common terminal are placed symmetrically around the excitation strip, thus forming a differential magnetic field sensor. This operation method enables very confined eddy currents due to the thin current excitation strip and high-sensitivity measurements due to the differential sensitive coils. Immunity to liftoff [25] is not an issue with this probe as long as the sensor is parallel to the material under test. The probe has a driver trace (the current excitation strip located between the two sensitive coils) with 1-mm width and 10-mm length, while each of the sensitive coils has 12 turns with 100-μm width spaced by 100-μm gaps. The size of the sensor affects the spatial resolution with which measurements can be made since the sensor output is affected by the region covered by the sensitive coils and the confinement of the eddy currents. Testing is done by measuring the output voltage phasor (using the input current as reference) while positioning the probe above the metallic part. More details on the probe operation principle can be found in [26]. The excitation current can be changed up to 1-A amplitude and up to 1-MHz frequency using a dedicated measurement system. Details regarding the
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Fig. 3. Simulation results for a sweep with a defect with 0.5-mm depth and 1-mm width. (a) Real and imaginary parts of the output induced voltage and corresponding phase offset. (b) Real and imaginary parts of the output induced voltage after applying the phase offset.
complete electronic measurement setup that excites the driver trace, measures the sensitive coil outputs, and preprocesses the signals are described in [24] and [27]. The excitation current was set at 1-A amplitude and 1-MHz frequency. The maximum achievable frequency (with this current electronic measurement setup) was selected since the probe sensitivity increases with the increase in the operating frequency. This selection allowed the improved measurement and preprocessing of the probe signals which otherwise may become noisy. Fig. 2 shows the simulated probe response with the real and imaginary components as a function of the relative probe position where x = 0 corresponds to the defect position. As shown in the figure, the response components resemble the addition of Gaussian functions with different locations, amplitudes, and widths. The feature extraction will be done by fitting one of the response components with a template composed by the sum of Gaussian functions. To avoid processing both response components (real and imaginary components) in the feature extraction, a phase offset was added in order to maximize the imaginary component. Fig. 3(a) shows the response representation of Fig. 2 in the complex plane and the applied phase offset. To compute the phase offset value, a line segment was fitted to the real–imaginary pairs using a least mean squares approach. The slope of this line segment was used to compute the phase offset to include in all the real–imaginary pairs of this response. Fig. 3(b) shows the real and imaginary components of Fig. 3(a) after applying the described operation. For each of the responses, the imaginary component is adjusted accordingly and used as the input of the feature extraction stage. The phase offset obtained with this method does not include significant information on the defect properties since it remains constant with the defect modification [26], and therefore, it is not used in the feature extraction. III. F EATURE E XTRACTION The decomposition of signals by means of a combination of nonlinear functions is commonly used to extract relevant features needed by estimation or classification procedures. The use of such approach greatly reduces the dimensionality of the data set and, consequently, the complexity of the following pro-
cedure. One way to solve the nonlinear regression is by using the Gauss–Newton or the Levenberg–Marquardt algorithms. Both methods allow computing the least squares solution on the regression of nonlinear functions. The Levenberg–Marquardt algorithm is based on the Gauss–Newton algorithm with some improvements introduced by Levenberg [28] and Marquardt [29]. It is typically used to perform nonlinear regressions where the Gauss–Newton algorithm may fail to converge. The extraction of the relevant features was done by approximating the output voltage response rotated imaginary component by the sum of two Gaussian paired odd functions described by 2 (x−μn −x0 )2 (x+μn −x0 )2 − − 2 2 wn wn an e −e (1) f (x) = n=1
where μn is the relative center, an is the amplitude, and wn is the width of each Gaussian pair. x0 is the center of the defect which must be included because, in measurements, the actual defect location is unknown and it is directly estimated by the feature extraction. Considering a set of N input data pairs describing the relative probe position (xi ) with (i = 1, . . . , N ) and the rotated imaginary part of the sensor output voltage (ui ), the regression is done by minimizing the cost function S(β) =
N
[ui − f (xi , β)]2
(2)
i=1
where β = [a1 w1 μ1 a2 w2 μ2 x0 ]T is the vector containing all the regression parameters. To solve this minimization problem, the Levenberg–Marquardt algorithm was used to estimate the parameters of the Gaussian pairs in each response. The algorithm is based on the iterative update of the estimated solution by approximating the function by the linearization f (xi , β + δ) = f (xi , β) + Ji δ
(3)
where Ji is the function gradient vector with respect to β. Using (3) in (2), the cost function becomes S(β + δ) =
N i=1
[ui − f (xi , β) − Ji δ]2
(4)
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Fig. 4. Simulation results of the output induced voltage as a function of the relative probe position for defects with 0.5-mm depth and (a) 1- and (b) 0.2-mm widths. The red squares represent the simulated points, the dashed blue lines represent the two Gaussian pairs, and the thick blue line is the final fitting result (the sum of the two Gaussian pairs).
which may be expressed in vector notation as S(β + δ) = u − f (x, β) − Jδ2
(5)
where J is the Jacobian matrix with elements given by Ji,j =
∂f (xi , β) . ∂βj
(6)
Setting the derivative of (5), with respect to δ, to zero, the increment may be found solving the linear equation system (J T J)δ = J T [u − f (x, β)] .
(7)
The main steps in the Gauss–Newton algorithm consist in updating the parameter vector β with the solution of the linear equation system (7) with respect to δ. As matrix J T J may be badly conditioned, the algorithm may fail to converge. Levenberg and Marquardt proposed a way to mitigate this illconditioned problem through the introduction of an additional term, replacing the linear equation system by T J J + λdiag(J T J) δ = J T [u − f (x, β)] (8) where λ is the so-called Levenberg–Marquardt parameter. When this nonnegative parameter takes a small value, the algorithm has a behavior close to the Gauss–Newton algorithm. However, if the parameter has a higher value, the step will take approximately the direction of the gradient. Usually, λ is updated along the algorithm execution using heuristic-based rules as the one proposed by Marquardt, which is controlled by the cost function evolution. In this case, for each iteration, the updated cost function is computed using the last λ value and an updated version λ/v, where v is a constant greater than one. If the updated λ/v value leads to greater cost function reduction than λ, it is selected as the new value for λ. If none of these two values reduces the cost function, λ is increased until the cost function value decreases. In the implemented algorithm, the initial values of the Gaussian pairs’ widths and centers were selected according to the typical values in the √ range of defects considered (the center Gaussians have w2 = 0.5 √ mm and μ2 = 0.3 mm, and the outer Gaussians have w1 = 7 mm and μ2 = 2 mm). The initial amplitudes (an ) are the amplitudes of the measured
values at the corresponding mean value positions, and the initial value of x0 is derived from the minimum spatial location of the cumulative measured response. In Fig. 4, the results obtained with the nonlinear regression for the situation in Fig. 3(b) are shown along with the results from another situation with reduced width. The two Gaussian pairs are shown together with the result from the complete fitting. It can be seen that, in both cases, the fit is quite good and that the use of the two Gaussian pairs is adequate to this problem. Notice that the two vertical scales are considerably different and that the amplitude for the largest defect width is much higher. As mentioned previously, the symmetry around x = 0 cannot be used because one does not have prior information on where the defect is, and therefore, x = 0 is an arbitrary reference value (e.g., the defect position is known in the simulations but cannot be a priori known in the measurements). Therefore, the value of x0 is also estimated in the feature extraction step. For the results in Fig. 4, the regression parameters provided a fitting whose mean square errors (MSEs) were 1.78 × 10−9 V2 [Fig. 4(a)] and 4.52 × 10−10 V2 [Fig. 4(b)], respectively. For all the responses, the fitting has demonstrated to be consistently good with a maximum MSE of 6.77 × 10−9 V2 . In Table I, the parameters of the Gaussians for the two situations depicted in Fig. 4 are presented. From these results, it can be seen how the different defects change the parameters of the Gaussian pairs. The final step in the feature extraction is to order the results of the Gaussian pairs so that the ANN will find the input parameters in a consistent form (otherwise, it would be impossible to obtain good results with the ANN since multiple combinations would be expected to estimate the same target parameters). The first step in the ordering process is to ensure that an > 0. If an < 0, then an becomes −an , and μn is transformed into −μn . This step is used because switching the signs of both an and μn corresponds to the same solution. Afterward, the two Gaussian pairs are ordered by their position. IV. ANN S ANNs were originally developed as an attempt to give computers artificial intelligence. Their structure tries to emulate
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TABLE I PARAMETERS OF THE G AUSSIANS O BTAINED FOR T WO D EFECTS W ITH 0.5-mm D EPTH
Fig. 5. ANN with an eight-neuron intermediate layer. The input layer has six inputs corresponding to the six parameters of the two independent Gaussians. The output layer estimates the depth and width of the defect. The defect position is directly estimated by the Gaussian parameter extraction.
the way brains compute information, which occurs through the interaction between their neurons. In nature, a neuron has a single output that gets activated depending on its thousands of inputs. A network of neurons has the ability to learn from previous experiences and is fault tolerant since the failure of some neurons is overcome by the interconnection between other neurons. ANNs are scaled down versions of biological neural networks as the number of neurons, inputs, and interconnections is much smaller. However, they behave in a similar way to a biological brain. ANNs have been used in pattern recognition, sequence recognition, data mining, and decision making and can be used to model the complex relationship between inputs and outputs of a system. Their use in the instrumentation and measurement field has seen a significant increase, as shown in [30] and [31]. Its basic building block is the neuron. Neurons are grouped in layers, including an input layer and an output layer. The neurons in the different layers are interconnected, and there is a weight associated with each interconnection. Each neuron has multiple inputs but only one output which is the result of an activation function [32]. In this implementation, an option was made to have only an intermediate layer together with an input and an output layer. The input layer receives the six parameters associated with the two independent Gaussian pairs that resulted from the nonlinear regression described in the last section. Normalization of the input parameters is used to improve the learning speed of the network. The output layer has two outputs which correspond to the depth and width of the defect. The intermediate layer was chosen to have eight neurons, which is a compromise
Fig. 6. Training performance evaluation.
between an overly simple network that may not have the capacity to model the input/output relationship and a more complex network that may lead to undesired overfitting. The activation function of the intermediate layer is the typically used sigmoid function, also known as logistic function. For the output layer, the linear activation function is used. A graphical representation of the neural network is presented in Fig. 5. The defect position x0 is estimated by the Gaussian feature extraction and is available at the output, although it does not play a part in the neural network, as can be seen in Fig. 5. The training of the network consists in finding the appropriate weights of the neuron’s interconnections. This is accomplished by training the network with a data set and comparing the network results with the known defect’s width and depth. The error is then used to update the network weights through a Levenberg–Marquardt back-propagation training algorithm. With the updated weights, a new iteration (also known as epoch) starts, and the training data are once again fed into the network. The training can be performed online, where the weights are updated each time an element of the training set is propagated through the network, or in batch mode, where the weights are only updated after the propagation of the various elements of the training set [32]. To obtain the training set, simulations were performed using a CST EM Studio finite-element model. For each different profile defect, the probe was moved with a step of 0.1 mm relative to the defect location. Overall, the relative location was analyzed between −7 and +7 mm, where the defect was set at x = 0 mm. The defect depths ranged from 0.25 up to 2.5 mm, and the widths ranged from 0.1 up to 1 mm. The simulations provided testing data of 100 different defects covering the
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Fig. 7. Histogram of the depth and width errors.
whole parameter range under study. The different cases are split into train, validation, and test sets according to the percentages: 70%, 15%, and 15% respectively. The training set is used to train the network using batch training. The validation set is used to check if overfitting is occurring (i.e., when the performance on the validation set is much poorer than on the training set). It is also used to stop the training process, which occurs when the performance on the validation set decreases over a fixed number of epochs, which, in this case, is set to six. The test data is used for independent testing of the network performance. Fig. 6 presents the performance of the network training process along the epochs. The performance is measured with the MSE of the output parameters relative to the target values for the three data sets. Training stopped at epoch 35 after six epochs without improvements in the validation set. Thus, the best validation result occurred at epoch 29, and it can be seen that the test set performance also stopped improving at this epoch. The network weights used for the trained network are those that occurred at epoch 29. Since the ANN has two outputs, the MSE (as presented in Fig. 6, which corresponds to the MSE between the targets and the actual ANN outputs) is weighted taking into account the average target values (depth and width) of the testing set. This ensures that uneven target values do not overly influence the ANN training by having a higher weight on the optimization cost function (the MSE). The error distributions of the estimated depth and width are shown in Fig. 7. Errors are distributed around zero with a high number of occurrences close to zero. The depth error histogram shows that all the depth errors are below 0.15 mm. Relative to the width error histogram, it can be seen that all errors are below 0.05 mm. These values are a major improvement of the results presented in [23] with a generalized Gaussian template.
V. M EASUREMENT R ESULTS For the measurement results, a set of three defects was made using electrical discharged machining. The defects have depths of 0.5, 1.0, and 1.5 mm with a maximum error of 0.05 mm. The width of the defects is 0.35 mm with a maximum error of 0.05 mm.
Fig. 8. Measurement results of the output induced voltage as a function of the relative probe position for a defect with 0.5-mm depth and 0.35-mm width. The red squares represent the measured points, the dashed blue lines represent the two Gaussian pairs, and the thick blue line is the final fitting result.
Fig. 9. Measurement results of the output induced voltage as a function of the relative probe position for a defect with 1.5-mm depth and 0.35-mm width. The red squares represent the measured points, the dashed blue lines represent the two Gaussian pairs, and the thick blue line is the final fitting result.
In Fig. 8, measurement results are presented for the defect with 0.5-mm depth. The measurement spatial resolution is around 26 μm, which means that the measurement profile is
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Fig. 10. Estimated depth and width profiles for the measured ramp defect.
better defined than the simulation profile. For this case, the estimated depth is 0.474 mm while the estimated width is 0.338 mm. The results presented in Fig. 9 correspond to the defect with 1.5-mm depth. For this case, the estimated depth is 1.402 mm while the estimated width is 0.358 mm. The increase in depth first causes a significant overall increase in the amplitude of the measured response. Second, the outer Gaussians are higher than the inner Gaussians, and both are basically in the same location. From these results, it is possible to see that the outer Gaussians are caused by the influence of the defect on the field detected by the nearest sensitive coil while the innermost Gaussians are directly caused by the influence of the defect on the field generated by the excitation strip. Therefore, to improve defect detection resolution, the excitation strip should be as thin as possible, and the area underneath the sensitive coils should be also as small as possible. For the 1-mm-depth defect, the estimated depth is 0.988 mm while the estimated width is 0.345 mm. To test the proposed method in a wider set of measurements, a defect with a ramp profile was measured. The defect width is 0.5 mm (maximum error of 0.05 mm), and the ramp profile has a 10% slope that extends up to y = 40 mm on the material surface (maximum error of 0.05 mm). The probe was positioned with the driver trace parallel to the defect extension, and multiple measurements were performed while moving the probe across the defect. Using each of the measurements performed, the defect depth and width were estimated using the described method. The estimated depth profile and the width along the defect are shown in Fig. 10(a) and (b), respectively. Measurements start at y = 2.5 mm to ensure that a good part of the probe (which has a y length of 10 mm) is above the ramp. The defect depth shows good agreement with the estimated depths between 0.5 and 3 mm. For the depths outside this range, the estimated depth error will increase. This behavior was already expected since the training set includes responses with depths ranging from 0.25 to 2.5 mm and the performance of ANNs outside the training range is usually poor. In the width parameter, almost all the estimates are around 500 μm except in the defect beginning where the estimates are worst.
Note that this whole measurement situation is different from the situation for which the system was trained. For each measurement position, the depth of the defect below the probe is not constant. Nevertheless, the overall system measurements are quite good. VI. C ONCLUSION In this paper, the use of nonlinear regressions and ANNs to estimate parameters of defects tested using an eddy current probe has been reported. A nonlinear regression was used in the feature extraction stage to extract parameters of a template with additive Gaussian functions. An implementation of the Levenberg–Marquardt algorithm was used to find the best set of parameters in the least squared error sense. Special attention was given to the initial parameter estimates, so good convergence was achieved. After the regression-based feature extraction, a total of six parameters define the Gaussians which are ordered so that they can be applied to the ANN. This ordering step was necessary as the regression output parameters are not necessarily coherent since the template Gaussians may change their locations. The regression parameters were ordered by making the Gaussian central position always increasing. Estimates were achieved using an ANN trained to estimate the width and depth of the defects. The selected ANN architecture has six neurons in the input layer and eight neurons in the intermediate layer. The two output neurons generate estimates for the defect width and depths. The ANN was trained using simulated data obtained using a finite-element model of the probe, and cross-validation partition was used to avoid overfitting. The trained ANN was applied to the overall synthetic data set, showing quite good results. In this case, the relative errors on the depth and width estimates were always below 0.15 and 0.05 mm, respectively. For the measured notch defects with constant depth, the method provided estimates with errors (when compared with the nominal values) better than 0.1 mm for the depth and 0.015 mm for the width. It should be noted that the measurement final uncertainty may be much higher specifically due to the uncertainty in the nominal values of the defect width and depth. For the ramp defect, and in the situations
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where the defect has dimensions outside the training set range or in its limits, the relative estimate errors were significantly higher. Although the ANNs have good generalization ability inside the range used in the train, the same is not true when inputs fall outside this range. Future work will focus on the evaluation of a different ANN architecture and activation functions to improve the estimates outside the training set range. Other developments will target the method adaptation to real defects on welded joints. R EFERENCES [1] E. Krestel, Imaging systems for medical diagnosis: Fundamentals and technical solutions—X-ray diagnostics- computed tomography—Nuclear medical diagnostics—Magnetic resonance imaging—Ultrasound technology. Berlin, Germany: Siemens Aktiengesellschaft, 2005. [2] S. Mukhopadhyay and C. Gooneratne, “A novel planar-type biosensor for noninvasive meat inspection,” IEEE Sensors J., vol. 7, no. 9, pp. 1340– 1346, Sep. 2007. [3] L. Cartz, Nondestructive testing: Radiography, Ultrasonics, Liquid Penetrant, Magnetic Particle, Eddy Current. Novelty, OH: ASM International, 1995. [4] Z. Liu, D. Forsyth, A. Marincak, and P. Vesley, “Automated rivet detection in the EOL image for aircraft lap joints inspection,” NDT E Int., vol. 39, no. 6, pp. 441–448, Sep. 2006. [5] R. Pohl, A. Erhard, H. Montag, H. Thomas, and H. Wüstenberg, “NDT techniques for railroad wheel and gauge corner inspection,” NDT E Int., vol. 37, no. 2, pp. 89–94, Mar. 2004. [6] J. Allin, P. Cawley, and M. Lowe, “Adhesive disbond detection of automotive components using first mode ultrasonic resonance,” NDT E Int., vol. 36, no. 7, pp. 503–514, Oct. 2003. [7] G. Sposito, C. Ward, P. Cawley, P. Nagy, and C. Scruby, “A review of non-destructive techniques for the detection of creep damage in power plant steels,” NDT E Int., vol. 43, no. 7, pp. 555–567, Oct. 2010. [8] N. Gloria, M. Areiza, I. Miranda, and J. Rebello, “Development of a magnetic sensor for detection and sizing of internal pipeline corrosion defects,” NDT E Int., vol. 42, no. 8, pp. 669–677, Dec. 2009. [9] D. Vasic, V. Bilas, and D. Ambrus, “Pulsed eddy-current nondestructive testing of ferromagnetic tubes,” IEEE Trans. Instrum. Meas., vol. 53, no. 4, pp. 1289–1294, Aug. 2004. [10] M. Bodruzzaman and S. Zein-Sabatto, “Estimation of micro-crack lengths using eddy current C-scan images and neural-wavelet transform,” in Proc. IEEE Southeastcon, Apr. 2008, pp. 551–556. [11] Y. Le Diraison, P.-Y. Joubert, and D. Placko, “Characterization of subsurface defects in aeronautical riveted lap-joints using multi-frequency eddy current imaging,” NDT E Int., vol. 42, no. 2, pp. 133–140, Mar. 2009. [12] R. Sikora, M. Komorowski, and T. Chady, “A neural network model of eddy current probe,” in Proc. Electromagn. Nondestruct. Eval., 1997, pp. 231–237. [13] T. Chady, M. Enokizono, R. Sikora, T. Todaka, and Y. Tsuchida, “Natural crack recognition using inverse neural model and multi-frequency eddy current method,” IEEE Trans. Magn., vol. 37, no. 4, pp. 2797–2799, Jul. 2001. [14] M. Wrzuszczak and J. Wrzuszczak, “Eddy current flaw detection with neural network applications,” Measurement, vol. 38, no. 2, pp. 132–136, Sep. 2005. [15] N. Yusa, Z. Chen, and K. Miya, “Quantitative profile evaluation of natural crack in a steam generator tube from eddy current signals,” Int. J. Appl. Electromagn. Mech., vol. 12, no. 3/4, pp. 139–150, 2000. [16] N. Yusa, W. Cheng, Z. Chen, and K. Miya, “Generalized neural network approach to eddy current inversion for real cracks,” NDT E Int., vol. 35, no. 8, pp. 609–614, Dec. 2002. [17] N. Yusa, W. Cheng, T. Uchimoto, and K. Miya, “Profile reconstruction of simulated natural cracks from eddy current signals,” NDT E Int., vol. 35, no. 1, pp. 9–18, Jan. 2002. [18] T. Khan and P. Ramuhalli, “A recursive Bayesian estimation method for solving electromagnetic nondestructive evaluation inverse problems,” IEEE Trans. Magn., vol. 44, no. 7, pp. 1845–1855, Jul. 2008. [19] T. Chady and P. Lopato, “Flaws identification using an approximation function and artificial neural networks,” in Proc. 12th IEEE Biennial Conf. Electromagn. Field Comput., 2006, p. 311.
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Luis S. Rosado received the M.Sc. degree in electronics engineering from the Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa, Portugal, in 2009, where he is currently working toward the Ph.D. degree. His doctoral studies are focused on the development and application of eddy current probes and digital signal processing algorithms for nondestructive testing.
Fernando M. Janeiro (M’04), for photograph and biography, see this issue, p. 1381.
Pedro M. Ramos (M’02), for photograph and biography, see this issue, p. 1381.
Moisés Piedade received the Ph.D. degree in electrical and computer engineering from the Instituto Superior Técnico, Universidade Técnica de Lisboa (UTL), Lisboa, Portugal, in 1983. He is currently a Professor with the Department of Electrical and Computer Engineering, UTL, where his research is done in the Signal Processing Systems (SIPS) Research Group, Instituto de Engenharia de Sistemas e Computadores-Investigação e Desenvolvimento. His research interests include electronic systems, signal-acquisition and processing systems, and circuits and systems for biomedical applications.
