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 classify pits and cracks on the bottom of a metal plate An SVM approach with alternating current potential drop technique to classi[.]

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

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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,aZhengjun 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 7 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 3This 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.4Furthermore, there are different methods of evaluating the dimensions of pits and cracks and analyzing the result-ing 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.7,8In 2005, Saguy and Rittel proposed the ACPD model to bridge the thin and thick skin solutions of surface crack depth,9and 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.10Recently, 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.

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 ma-chine 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 classi-fication 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,14ultrasonic-based pipeline defect predictions,15and 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.17When an AC current flows through a metal conductor at some frequency f , the current is constrained to a skin whose thickness δ is:

δ =  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.18Therefore, 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.1depicts an AC flowing in and out of the upper surface of a metal plate, with the current distributed across the entire plate at 1 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/VRand V2/VRcan 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 1 Schematic description of ACPD.

095202-3 Li et al. AIP Advances 6, 095202 (2016)

FIG 2 Schematic description of probe array.

decrease in the other direction.19As the current density changes are indicated by voltage changes, it

is feasible to measure four auxiliary voltages20V1−4, as shown in Fig.2 In the proposed approach, a variable dragiis defined as the eigenvalues of a defect These values are calculated as:

dragi=Vi/VR− 1

where Vi are the voltages measured in the vicinity of the measuring region, V is the main voltage, and VRis 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 SectionIII

B SVM principles

SVMs form a hyperplane that separates two classes with a maximum distance, as shown in Fig.3 H2 is the classification line, and H1, H3are parallel to H2and 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

bis 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,

H1and H3are the support hyperplanes represented by Eqs (3) and (5)

FIG 3 Classification of two classes within a dataset.

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

min

w,b

1

s.t yi((w · xi) + b) ≥ 1,i = 1, 2· · ·, l (7)

In many cases, different classes are inseparable using a linear hyperplane Therefore, a positive slack variable ξican be introduced into Eq (7) to give:

s.t yi((w · xi) + b) ≥ 1 − ξi,i = 1,2· · ·,l (8)

If an error appears, the corresponding ξiexceeds unity, and the upper bound of the classifica-tion errors is|Σξi| To find a logical way of assigning an extra cost for these errors, the objective function of Eq (8) is minimized, i.e.,

min

w,b,ξ{12w2

+ C

l



i

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:

min

α {1 2

l



i =1

l



j =1

yiyjαiαj(xT

ixj) −

l



j =1

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: Rn→ Rm 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(xi, xj) = (ϕ(xi) · ϕ(xj)), x ∈ Rn (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)

min

α {1 2

l



i =1

l



j =1

yiyjαiαjK(xi, xj) −

l



j =1

s.t

l



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

f(x) = sgn(

l



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 computa-tions 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 4 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

K(xi, xj) = exp(−γ xi− xj

2

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-validation21to 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 1 Hz was chosen Fig.5shows the simulation plate and its properties are listed in TableI Ω is the solution domain,

S and S are the current excited boundaries, and S represents all boundaries except S and S

FIG 5 COMSOL simulation model.

TABLE I Current amplitude, properties, and model dimensions.

FIG 6 Schematic description of variables.

TABLE II Sweep of pit parameters.

∆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 in-terval The variables of all pits and cracks are shown in Tables IIand 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, 0 mm, 4 mm, and 8 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.

FIG 7 Fitness curve of GA.

TABLE IV Classification result.

Actual class

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.7 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 classi-fier produced a classification accuracy of 98.84% (1453/1470) The specific results are given in TableIV 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

FIG 8 Experimental setup.

accuracy of 2 nV, and was used to supply the source signal for the power amplifier The power amplifier provided a maximum sinusoidal current of 5 A and an excitation frequency range of 0.5 Hz–10 kHz All probes in the spring probe array shown in Fig.9were distributed as the elec-trodes shown in Fig.2, and each pair of probes was separated by a distance of 20 mm The spring probes were numbered from P11to 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 1 measured 1000 × 150 × 10 mm3 and plate 2 measured 500

× 200 × 10 mm3 As shown in Fig 10, three pits were made in plate 1 by a drilling machine Three cracks were machined in plate 2 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 1 Hz and amplitude of

2 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 VRbetween 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 TableV 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 × 4 eigenvector matrix was built Substituting the matrix into the classifier established by the SVM, we acquired the results given in TableVI As all 36 defects were

FIG 9 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 2.

TABLE V Pit and crack parameters used in the experiments (unit: mm).

pit

TABLE VI Classification result of experiment.

Actual class

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 2 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