An SVM approach with alternating current potential drop technique to classify pits and cracks on the bottom of a metal plate An SVM approach with alternating current potential drop technique to classi[.]
An SVM approach with alternating current potential drop technique to classify pits and cracks on the bottom of a metal plate Yuting Li, Fangji Gan, Zhengjun Wan, and Junbi Liao Citation: AIP Advances 6, 095202 (2016); doi: 10.1063/1.4962550 View online: http://dx.doi.org/10.1063/1.4962550 View Table of Contents: http://aip.scitation.org/toc/adv/6/9 Published by the American Institute of Physics Articles you may be interested in Micro-effects of surface polishing treatment on microscopic field enhancement and long vacuum gap breakdown AIP Advances 6, 095103095103 (2016); 10.1063/1.4962549 AIP ADVANCES 6, 095202 (2016) An SVM approach with alternating current potential drop technique to classify pits and cracks on the bottom of a metal plate Yuting Li, Fangji Gan,a Zhengjun Wan, and Junbi Liao College of Manufacturing Science and Engineering, Sichuan University, Chengdu, 610065, P R China (Received 15 July 2016; accepted 30 August 2016; published online September 2016) The alternating current potential drop (ACPD) is a nondestructive technique that is widely used to detect and size defects in conductive material This paper describes a combined ACPD and support vector machine (SVM) approach to accurately recognize typical defects on the bottom surface of a metal plate, i.e., pits and cracks We first conducted a simulation study, and then, based on ACPD, measured five voltage ratios between the test region and reference region The analysis of finite simulation data enables the binary classification of two kinds of defects To obtain an accurate separating hyperplane, key parameters of the SVM classifier were optimized using a genetic algorithm with training data from the simulations Based on the optimized SVM classifier, reliable estimates of the defects in a metal plate were then obtained The recognition results of the simulation dataset shows that the trained and optimized SVM model has a high classification accuracy, and the metal plate experiment also indicates that the model has good precision in actual defect classification C 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4962550] I INTRODUCTION It is well known that metal structures suffer from defects during their service period These defects are caused by factors such as corrosion, stress, and air entrainment Defect classification is a general issue that focuses on the location and type of the defect.1–3 This paper mainly discusses the classification of different defects in the bottom surface of metal plate In most cases, two common types of defect, pits and cracks, correspond to a loss of efficacy in the metal structure.4 Furthermore, there are different methods of evaluating the dimensions of pits and cracks and analyzing the resulting risks Therefore, the classification of pits and cracks is a necessary part of risk analysis to avoid huge losses of lifespan and property The alternating current potential drop (ACPD)5 technique is a well-established and reliable nondestructive testing method that has been widely and successfully used to measure defects in conductive material over many years ACPD offers good resolution, interference rejection, and accuracy with low excitation currents.6 Typical applications include the measurement of surface crack depth in metal plates and cylinders, subsurface crack and pit depth in thick and thin metal plates, and conductive material properties such as conductivity and permeability ACPD is often used to measure surface cracks in welded parts of metallic structures.7,8 In 2005, Saguy and Rittel proposed the ACPD model to bridge the thin and thick skin solutions of surface crack depth,9 and studied how to determine the size of bottom cracks based on ACPD In 2011, Bowler used ACPD to measure metallic material properties in different frequency ranges.10 Recently, the multi-frequency alternating current potential drop technique which is an extension of ACPD has been used to test a Corresponding author E-mail: gfj0318@foxmail.com 2158-3226/2016/6(9)/095202/10 6, 095202-1 © Author(s) 2016 095202-2 Li et al AIP Advances 6, 095202 (2016) bottom cracks in metal plates.11 ACPD has been applied to test defects in both top and bottom surfaces Support vector machine (SVM),12 originated by Vladimir Vapnik in 1970, is a kind of machine learning algorithm based on structural risk minimization (SRM) Various improvements have been done by previous researchers And these previous studies make SVMs have advantages in both linear and nonlinear classification, such as high generalization ability, global convergence, and insensitivity to the dimensions and size of the training set SVMs are mostly used for classification and regression problems using well-trained datasets They have been effectively used for classification applications such as metal plate thickness assessments,13 image-based cable defect classification,14 ultrasonic-based pipeline defect predictions,15 and fingerprint classification.16 This paper introduces a novel approach that can accurately recognize crack and pit defects using ACPD and an SVM The proposed approach is described in detail in the following sections, along with the establishment of the classifier and experimental verification Experimental results show that the proposed SVM classifier achieves promising classification accuracy II CLASSIFICATION PRINCIPLES A ACPD principles ACPD is based on the skin effect phenomenon.17 When an AC current flows through a metal conductor at some frequency f , the current is constrained to a skin whose thickness δ is: δ= π µ r µ0σ f (1) where µ0 = 4π × 10−7H/m is the magnetic permeability of a vacuum, µr is the relative magnetic permeability, and σ is the electrical conductivity With a high-frequency current, the limited current distribution can be exploited to detect and measure the size of surface defects However, the ACPD technique is not applicable to the detection of bottom surface defects with high-frequency currents.18 Therefore, a low frequency is used in our study As the current is distributed over the entire conductor in low-frequency conditions, bottom defects can be detected Fig depicts an AC flowing in and out of the upper surface of a metal plate, with the current distributed across the entire plate at Hz The potential drop over the defect is measured by a pair of probes with a fixed gap ∆ between its electrodes V1 and V2 are measured across the pit and crack flanks, VR is a reference voltage measured far from the defects, and d is the depth of the bottom defect The voltage ratios V1/VR and V2/VR can be used to detect bottom pits and cracks by theoretical approximation or by means of a calibration procedure When a current flows through the defect, the current density in the upper surface changes measurably The current density also varies significantly according to whether the defect is a crack or a pit Moreover, the current density changes differ in the current flowing direction and the vertical direction The vertical density increases near the defect outline, whereas there is a slight density FIG Schematic description of ACPD 095202-3 Li et al AIP Advances 6, 095202 (2016) FIG Schematic description of probe array decrease in the other direction.19 As the current density changes are indicated by voltage changes, it is feasible to measure four auxiliary voltages20 V1−4, as shown in Fig In the proposed approach, a variable dragi is defined as the eigenvalues of a defect These values are calculated as: dragi = Vi /VR − (i = 1, 2, 3, 4) V/VR − (2) where Vi are the voltages measured in the vicinity of the measuring region, V is the main voltage, and VR is the reference voltage Therefore, four eigenvalues compose the eigenvector < drag1, drag2, drag3, drag4 >, and this vector can be used for classification by an SVM classifier To find an applicable SVM classification model, many kinds of defects were simulated in COMSOL and their corresponding eigenvectors were obtained The training and testing data are introduced in Section III B SVM principles SVMs form a hyperplane that separates two classes with a maximum distance, as shown in Fig H2 is the classification line, and H1, H3 are parallel to H2 and pass through points of the same distance from H2 These points are called support vectors (SVs) In most cases, data cannot be separated linearly, so a nonlinear transformation is applied The hyperplanes of an SVM are represented by Eqs (3)–(5), where w is normal to H2 and b is the bias The training vectors are linearly separated by H2, which is the optimal hyperplane represented by Eq (4) As the training vectors belong to different classes, indicated by +1 and −1, H1 and H3 are the support hyperplanes represented by Eqs (3) and (5) H1 : w · x − b = +1, class + H2 : w · x − b = H3 : w · x − b = −1, class − FIG Classification of two classes within a dataset (3) (4) (5) 095202-4 Li et al AIP Advances 6, 095202 (2016) The values of w and b are altered to give the maximal margin, or distance, between the parallel hyperplanes that separate different classes Thus, the maximal margin can be obtained to solve Eq (6) with the inequity constraint of Eq (7), which is derived from Eqs (3) and (5) Note that the factor of 1/2 is only used for mathematical convenience, allowing the problem to be changed into a quadratic programming (QP) problem without changing the solution ∥w∥ w,b s.t yi ((w · xi ) + b) ≥ 1,i = 1, 2· · ·, l (6) (7) In many cases, different classes are inseparable using a linear hyperplane Therefore, a positive slack variable ξ i can be introduced into Eq (7) to give: s.t yi ((w · xi ) + b) ≥ − ξ i ,i = 1, 2· · ·, l (8) If an error appears, the corresponding ξ i exceeds unity, and the upper bound of the classification errors is |Σξ i | To find a logical way of assigning an extra cost for these errors, the objective function of Eq (8) is minimized, i.e., l { w, b,ξ 2 w +C ξi } i (9) where C is a tuning variable that allows users to control the trade-off of either maximizing the margin or classifying the training set without errors By minimizing Eq (9) and using Eq (8), a generalized optimal separating hyperplane is obtained This becomes a QP problem that can be solved using a Lagrange multiplier vector Therefore, the solution of QP problem involves finding the Lagrange vector α that minimizes the objective function: l min{ α l l yi y j α i α j (x Ti x j ) − αj} i=1 j=1 j=1 (10) The SVM algorithm can be generalized to nonlinear classification by mapping the input data into a high-dimensional feature space using a mapping function ϕ: R n → R m with m ≥ n This transformation leads to a nonlinear decision boundary in the input space By introducing the kernel function in Eq (11), the costly calculation of scalar products in the high-dimensional space can be avoided K(x i , x j ) = (ϕ(x i ) · ϕ(x j )), x ∈ R n (11) Therefore, the nonlinear separating hyperplane depends on Eq (12), which is derived from Eqs (10) and (11), and the hyperplane is also subject to the constraint of Eq (13) l min{ α s.t l l yi y j α i α j K(x i , x j ) − αj} i=1 j=1 j=1 l yi α i = 0, ≤ α i ≤ C (12) (13) i=1 The final decision function used to classify new data is given in Eq (14) If f (x) is positive, the new data point x belongs to class +1, and if f (x) is negative, x belongs to class −1 l f (x) = sgn( α i yi K(x, x i ) + b) (14) i=1 The summation in Eq (14) is only implemented over SVs, because only the SVs have nonzero Lagrange multiplier vectors This simplifies the SVM computations, and means that the computations in the feature space are less complex than in the input space Thus, it is beneficial to select an appropriate kernel for a particular classification model 095202-5 Li et al AIP Advances 6, 095202 (2016) FIG Parameter optimization using a GA C Optimization of SVM parameters The kernel function not only maps the input data into a high-dimensional feature space, but also transfers the nonlinear problem to a linear one Furthermore, it removes the need for costly scalar product computations Therefore, an appropriate kernel function is the key to the SVM model In this study, the commonly used radial basis function (RBF) in Eq (15) was selected as the kernel function The RBF kernel possesses excellent learning and generalization abilities 2 K(x i , x j ) = exp(−γ x i − x j ), γ > (15) We can see that Eqs (12), (13), and (15) require two parameter values, C and γ If these are incorrectly specified, large errors can occur Therefore, an optimal process based on a genetic algorithm (GA) is used to identify the best parameter values This optimization uses the accuracy of the training dataset as the fitness function, and applies K-fold cross-validation21 to analyze the variable generalization ability of each generation The program flow of the GA used in the proposed method is shown in Fig 4; the actual GA was executed in Matlab2010 III EXPERIMENTAL VERIFICATION The COMSOL finite element simulation software (COMSOL Inc., Stockholm, Sweden) was used to obtain training and test data for the classification SVM Furthermore, several pits and cracks were machined for an experiment This section presents details of the classifier performance and experimental verification A Classification model training and testing A metal plate model with different defects was simulated in a quasi-direct current condition in which the AC frequency should be low Therefore, an excitation current of Hz was chosen Fig shows the simulation plate and its properties are listed in Table I Ω is the solution domain, S1 and S2 are the current excited boundaries, and S3 represents all boundaries except S1 and S2 095202-6 Li et al AIP Advances 6, 095202 (2016) FIG COMSOL simulation model TABLE I Current amplitude, properties, and model dimensions I/A àr /MS /mm L ì W ì T/mm3 110 5.5 20 500 × 200 × 10 FIG Schematic description of variables TABLE II Sweep of pit parameters variable P x /mm P y /mm Φ/mm d/mm sum Training set Test set -8∼4∼8 -9∼4∼7 -9∼2∼9 -8∼2∼10 5∼5∼20 4∼5∼14 1∼2∼9 1.5∼2∼9.5 1000 750 ∆ is the distance between the two electrodes All voltages were measured on the top surface As there are many factors that influence the classification result and defects like pits and cracks have randomness in the location and shapes, it is assumed that the shape of pit is cylinder and the shape of crack is narrow cuboid And the locations concentrate on the places which are not close to sample boundaries we selected seven parameters as variables, four belonging to the pits (diameter Φ, depth d, position Px and Py ; see Fig 6(a)) and three belonging to the cracks (length L, depth d, and position Px ; see Fig 6(b)) The center of the measuring region was defined as the coordinate origin To obtain sufficient training data and defect features, each variable was assigned a sweep interval The variables of all pits and cracks are shown in Tables II and III Each table cell gives the range and interval of a particular variable For instance, the Px values in the training set are −8 mm, −4 mm, mm, mm, and mm with a 4-mm interval In the table, we can see that the simulation provided 2100 training data (1000 pits and 1100 cracks) and 1470 test data (750 pits and 095202-7 Li et al AIP Advances 6, 095202 (2016) TABLE III Sweep of crack parameters variable Training set Test set P x /mm L/mm d/mm sum -10∼ ∼10 -9∼2∼9 20∼20∼200 50∼20∼190 0.5∼1∼9.5 1∼1∼9 1100 720 FIG Fitness curve of GA TABLE IV Classification result Actual class Predicted class pit crack pit crack 733 17 720 720 cracks) As COMSOL only supplies voltages, all of the simulated results were processed using Eq (2) In the training and test phases, Matlab2010 was used to build a classification model Moreover, the LIBSVM toolbox (http://www.csie.ntu.edu.tw/∼cjlin/libsvm) was also used Fig shows the GA fitness curve for a maximum generation number of 50 and population size of 20 As illustrated in Fig 7, the optimal fitness is stable, though the average fitness fluctuates Because the fitness is defined as the classification accuracy of the training set, the maximum fitness is 100% The optimal fitness of 99.9% represents good accuracy The GA optimization and SVM training processes yielded the optimal parameter values (C = 76.7674, γ = 32.7347) and the SVM classifier Substituting the test set into the SVM classifier produced a classification accuracy of 98.84% (1453/1470) The specific results are given in Table IV It can be seen that all 17 misclassified defects are pits, and so the model built by the SVM is liable to give bigger errors in the classification of pits than of cracks B Metal plate experiment To verify the accuracy of the proposed method, experiments were conducted using an SR850 digital lock-in amplifier (Stanford Research System, CA, USA), a power amplifier, a homemade spring probe array, and a personal computer (see Fig 8) The SR850 has a voltage measurement 095202-8 Li et al AIP Advances 6, 095202 (2016) FIG Experimental setup accuracy of nV, and was used to supply the source signal for the power amplifier The power amplifier provided a maximum sinusoidal current of A and an excitation frequency range of 0.5 Hz–10 kHz All probes in the spring probe array shown in Fig were distributed as the electrodes shown in Fig 2, and each pair of probes was separated by a distance of 20 mm The spring probes were numbered from P11 to P32 A personal computer was used to record and analyze the data Before taking any measurements, two AISI 1045 carbon steel plates were selected as test specimens The relative permeability and conductivity of these specimens were µr = 110 and σ = 5.6 MSm−1, respectively Plate measured 1000 × 150 × 10 mm3 and plate measured 500 × 200 × 10 mm3 As shown in Fig 10, three pits were made in plate by a drilling machine Three cracks were machined in plate using a wire-cut electric discharge machine (WEDM) with a maximum processing width of less than 0.5 mm To ensure a fairly even current flow, the current-injected electrodes were welded symmetrically along the lengthwise direction, and were placed sufficiently far from the measurement areas The power amplifier provided a sinusoidal current with a frequency of Hz and amplitude of A First, the spring probe array was placed on the top surface of the machined defect to measure five voltages (V and V1-4) between probes (P11, P12), (P21, P22), (P22, P23), (P23, P24), and (P31, P32) Second, the spring probe array was moved to the top surface of the reference area to measure one reference voltage VR between probes (P22, P23) Third, the relative position between the probe array and one particular defect was changed, meaning that the defect position (Px , Py ) relative to the measuring region changed Therefore, by moving the probe array, we obtained many different measurements for each machined defect The experimental parameters are shown in Table V There were 36 cases to be measured and classified After the voltage measurements, six voltages for each defect were obtained and transformed according to Eq (2) Thus, a 36 × eigenvector matrix was built Substituting the matrix into the classifier established by the SVM, we acquired the results given in Table VI As all 36 defects were FIG Schematic of spring probe array 095202-9 Li et al AIP Advances 6, 095202 (2016) FIG 10 (a) pits on plate 1; (b) cracks on plate TABLE V Pit and crack parameters used in the experiments (unit: mm) pit Py = −5 or or +5 crack Px Φ d Px L d -5 +5 -5 +5 -5 +5 13.1 13.1 13.1 15.0 15.0 15.0 22.0 22.0 22.0 0.89 0.89 0.89 2.92 2.92 2.92 0.36 0.36 0.36 -5 +5 -5 +5 -5 +5 200 200 200 200 200 200 200 200 200 2 4 6 TABLE VI Classification result of experiment Actual class Predicted class pit crack pit crack 27 0 classified accurately, the classification accuracy is 100% (36/36) From the experimental results, it is clear that the proposed method can accurately recognize pit and crack defects The experiment described here was limited by the constant crack length The cracks had to be machined through the entire width of plate by WEDM Therefore, if the model requires more thorough verification, a better machining method should be selected IV CONCLUSION In summary, we used COMSOL to compute theoretical formulae and analyzed the different shapes in the current distribution along the top surface of a metal plate A novel method was 095202-10 Li et al AIP Advances 6, 095202 (2016) proposed to classify pits and cracks The simulation testing and experimental results have shown that: (i) Five voltages (V and V1-4) can express the current distribution on the top surface of the plate and can be used by the SVM to classify defects (ii) SVMs are a useful method for building a classifier using an RBF kernel and GA optimization Moreover, the classifier constructed for our experiments exhibited good accuracy in both simulation testing and experimental verification In proposed approach, the main factor that influences the sensitiveness is the voltage measurement accuracy, because the accurate measurement of voltage change can recognize very small defects Therefore, the method sensitiveness can be obtained experimentally by using this method to classify smaller and shallower defects than that computed in Tables II and III Considering the randomness of defects, there are some limitations to this study that require further research For instance, the length of the cracks did not change throughout the experiment, because of the WEDM machining limitation Furthermore, there may be more kinds and shapes of defects appearing in practice, such as multi-type defects, multi-shape defects and defects close to plate boundaries Consequently, how to classify multi-shape and multi-type defects is in our future work as well Another issue is why the proposed classifier was more liable to misclassify pits than cracks in the simulation test Moreover, the crack width, which may influence the results, was neglected in this study Thus, certain improvements can be made in future studies ACKNOWLEDGEMENT This work was supported by the National Natural Science Foundation of China (Grant Nos 61271329 and 51105260) G Y Tian and A Sophian, Ndt & E International 38(1), 77 (2005) T Chen, G Y Tian, A Sophian, and P W Que, Ndt & E International 41(6), 467 (2008) X Qiu, P Zhang, J Wei, X Cui, C Wei, and L Liu, Sensor Actuat A Phys 203, 272 (2013) R M Pidaparti, B S Aghazadeh, A Whitfield, A S Rao, and G P Mercier, Corrosi Sci 52(11), 3661 (2010) N Merah, J Qual Technol 9(2), 160 (2003) M K Raja, S Mahadevan, B P C Rao, S P Behera, T Jayakumar, and Baldev Raj, Meas Sci Technol 21(10), 105702 (2010) W D Dover and C C Monahan, Fatigue Fract Eng M 17(12), 1485 (1994) I.S Hwang, Meas Sci Technol 3(1), 62 (1992) H Saguy and D Rittel, Applied Physics Letters 87(8), 084103 (2005) 10 N Bowler, Meas Sci 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pits and cracks on the bottom of a metal plate Yuting Li, Fangji Gan ,a Zhengjun Wan,... measured on the top surface As there are many factors that influence the classification result and defects like pits and cracks have randomness in the location and shapes, it is assumed that the. .. vector machine (SVM) approach to accurately recognize typical defects on the bottom surface of a metal plate, i.e., pits and cracks We first conducted a simulation study, and then, based on ACPD,