# Strip Steel Surface Defects Recognition Based on SOCP Optimized Multiple Kernel RVM

Authors: Hou Jingzhong; Xia Kewen; Yang Fan; Zu Baokai
Journal: Mathematical Problems in Engineering
 (2018)

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## Abstract

Strip steel surface defect recognition is a pattern recognition problem with wide applications. Previous works on strip surface defect recognition mainly focus on feature selection and dimension reduction. There are also approaches on real-time systems that mainly exploit the autocorrection within some given picture. However, the instances cannot be used in practical applications because of a bad recognition rate and low efficiency. In this paper, we study the intelligent algorithm of strip steel surface defect recognition, where the goal is to improve the accuracy and save running time. This problem is very important in various applications, especially the process testing of steel manufacturing. We propose an approach called the second-order cone programming (SOCP) optimized multiple kernel relevance vector machine (MKRVM), which can recognize strip surface defects much better than other methods. The method includes the model parameter estimation, training, and optimization of the model based on SOCP and the classification test. We compare our approach with existing methods on strip surface defect recognition. The results demonstrate that our proposed approach can improve the recognition accuracy and reduce the time costs of the strip surface defect.


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## Body

## 1. Introduction

There are different types of defects in strip steel production due to various causes. These defects affect the appearances of the products and cause concentrated stress and weak spots. Moreover, these defects will decrease the product’s properties in varying degrees, such as corrosion resistance and wear resistance [1]. Therefore, it is very important for enterprises to strengthen the inspection and control of strip surface defects and improve the strip surface quality [2]. If we want to improve the strip surface quality, detection and classification problems must be solved for the strip surface quality. These years, there are many study methods on strip surface defect recognition, including the exhaustive method and branch and bound method. For example, there are also the support vector machine (SVM) method, the principal component analysis method, the neural networks method, the magnetic flux leakage detection method, the infrared detection method, and the eddy current testing method. However, some of these methods may damage the topological structures of the data and some may get local optimal solutions. The Particle Swarm Optimization algorithm is an efficient optimization method, but its complex genetic operations make it difficult to meet the expected recognition speed and accuracy. These algorithms cannot take into account defects recognition.Therefore, further study is necessary to improve the accuracy of strip surface defect recognition. Compared with the SVM, the RVM compensates for the disadvantages of the SVM [3] that include the lack of sparsity, the lack of probabilistic factors, the limitation by Mercer, and more. To improve the universal applicability of the RVM algorithm, multiple kernel learning (MKL) has been applied instead of one specific kernel function. However, the training time of the multiple kernel RVM (MKRVM) is long because of the inverse matrix problem in the algorithm. If the training sample and iteration numbers are increased, the training process becomes very slow.Second-order cone programming (SOCP) [4, 5] is a convex optimization in which a linear function is minimized. Linear programs and convex quadratic programs can all be formulated as SOCP optimizations. Therefore, a SOCP optimized MKRVM algorithm is proposed, which optimizes the MKRVM parameters using the SOCP model. Through the optimized SOCP, the classification accuracy and time costs of the MKRVM algorithm can be largely improved. First, typical strip defect images are collected for model training and building the data set. Second, the simplified information and the key indicators that reflect the defects are obtained after strip defect images are addressed. This process can reduce the learning time of the MKRVM. Third, the model of the MKRVM based SOCP is trained, which is used to recognize the defect images data set. To improve the recognition accuracy, the design and construction of the multikernel RVM classifier are completed, and multikernel learning is transformed into the SOCP problem. Finally, the proposed SOCP-MKRVM [6] model is used for classification and identification. The effectiveness of the proposed method is verified.


## 2. Principle of Identification Method

### 2.1. Traditional RVM Method

Assuming that the training set is{xi,yi}i=1,2,…,m, the target value yn and the input value xn are independently distributed samples. The output of the RVM [7, 8] can be expressed as(1)yj=∑i=1mwiKXj,Xi+w0+εj.Here,K(,) is the kernel function. The Gauss kernel function is used as the kernel function in this paper:(2)Kx1,x2=exp⁡-x1-x222σ12.w is the weight vector of the model. εn is the additional noise that satisfies the Gaussian distribution:(3)εn~N0,σ2.Deriving from formula (1) and formula (3), we get(4)py∣w,σ2=NΦw,σ2.In the formula,Φ is a designed m×(m+1) order matrix consisting of kernel functions such that Φ=ϕx1,ϕx2,…,ϕxmT and ϕ(xi)=1,kxi,x1,kxi,x2,…,kxi,xm. The ARD Gaussian prior probability distribution of the defined weights is (5)pw∣α=∏i=0mNwi∣0,αi-1.Here,α is the m+1 dimension vector composed of super parameters that control the distribution of w, A=diag⁡α0,α1,…,αm.According to Bayesian theory, the posterior probability distribution ofw can be decomposed as(6)pw∣y,α,σ2=Nu,Σ,where (7)py∣α,σ2=∫py∣w,σ2pw∣αdw.(8)Σ=σ-2ΦTΦ+A-1(9)u=σ-2ΣΦTyu and Σ are the mean vector and covariance matrix of w. It can be seen from formula (9) that the parameter σ2 and the super parameter α need to be estimated. The posterior probability distribution of the parameter σ2 and the super parameter α is obtained according to the Bayesian theory as follows:(10)pα,σ2∣y=py∣α,σ2pα,σ2py.The estimation of the parameterσ2 and the super parameter α is the calculation of the maximum value of the posterior probability distribution. It can be seen from (10) that the value of the posterior probability distribution of the two parameters is mainly determined by the likelihood function py∣α,σ2:(11)py∣α,σ2=N0,C.Here,C=σ2I+ΦA-1ΦT.The maximum likelihood estimation method is used to calculate the maximum value of (11). The parameter σ2 and the super parameter α are obtained as(12)αinew=1-αiΣiiui2σ2new=y-Φu2m-∑i=0m1-αiΣii.In the iterative operation, much of the super parameterαi tends to infinity. w obtained from formula (9) corresponds to the trend of zero. Therefore, you can make a small number of sample points work to achieve the RVM’s sparse effect [9], and these sample points are of relevance to the vector machine.


### 2.2. Multiple Kernel Learning (MKL) Algorithms

To improve the universal applicability of the RVM algorithm, MKL has been applied instead of one specific kernel function:(13)Kμxi,xj=fμKmxi,xjm=1M∣μ,where Kμ is the multikernel function. The multiple kernel Kμ can be obtained by function fμ:RD→RP and by combining M different Km. μ is the proportion parameter of the kernel.The kernel weights are regarded as a regularization itemrμ, which is taken as 1/2μ-1/MTμ-1/M. Thus, the objective function and gradient function can transform into(14)Jμ=12∑i=1n∑j=1nyiyjαiαjKμxi,xj-∑i=1nαi-rμ,∂Jμ∂μm=12∑i=1n∑j=1nyiyjαiαj∂Kμxi,xj∂μm-∂rμ∂μm∀m.The kernel combined function is(15)Kμxi,xj=∏m=1Mexp⁡-μmxim-xjm2=exp⁡∑m=1M-μmxim-xjm2.


### 2.3. Second-Order Cone Programming (SOCP)

The above classification algorithm is based on the edge likelihood estimation method. However, this algorithm has an extensive matrix inversion process, and thus the training time is longer. To solve this problem, the MKRVM method based on the SOCP algorithm is proposed in this paper.The standard form of the second-order cone programming is(16)min⁡∑i=1nciTxi:∑i=1nAixi=b,xi∈Ki,i=1,…,n.Here,xi∈Ki,i=1,…,n, is the variable. b∈Rm and Ai∈Rm×k, ci∈Rki,i=1,…,n, is the known quantity. Ki,i=1,…,n, is the second-order cone of dimension ki. Thus(17)Ki≔xi=xi0,xi1∈R×Rki-1:xi0-xi1≥0.In this,· is the Euclidean norm of the vectors. It is easy to know that Ki is self-dual and (18)Ki0≔xi=xi0,xi1∈R×Rki-1:xi0-xi1>0.For the MKRVM, the focus of its operations is the iterative computation ofαi. The purpose of the SOCP is to change the original solution and efficiently solve this parameter. The Gauss kernel function is a typical local kernel, and the polynomial kernel function is a typical global kernel. The combination of the two kernel functions can have the advantages of both local and global kernels. Let xi and yi be the sample points in the data space. The combination kernel function is(19)K=μ1G1xi,yj+μ2G2xi,yj+μ3Pxi,yj.Here,(20)G1xi,yj=-xi-yj2θ12;G2xi,yj=-xi-yj2θ22;Pxi,yj=xiyjθ32+12.θ 1, θ2, and θ3 are the kernel parameters obtained by nuclear correction. μ1, μ2, and μ3 are the undetermined combination coefficients.In the multikernel functions, the kernel correction value of the kernel functionK is (21)Aβ=AS,Kβ,yyT=∑kβkyTKky∑k1βkβlKk,KlFmin which S is the sample data.Then, the process of obtaining the best correction value of the kernel function is transformed into the following planning problem:(22)maxβ:Aβsubject  to:1≥βi≥0∑j=1Mβi=1.After calculatingβi of each kernel function, the validity of the kernel parameter is judged according to the value of βi. If βi approaches 0, it means that the corresponding kernel parameter of βi is not suitable for use on this data set. If the value of βi is close to 1, then the corresponding kernel parameter of βi is valid.


### 2.4. MKRVM Method Based on SOCP Algorithm

SOCP is used to optimize the MKRVM [10, 11], and μ1, μ2, and μ3 are the kernel work parameters that need to be optimized. The previous part of (21) is the reciprocal of a Euclidean paradigm, and the latter exponential function is a convex function. In this case, the optimization problem can be solved by being transformed into a standard SOCP problem [12]. In the SOCP form, the parameters are solved efficiently through the MKRVM training and the optimization process by using the SeDuMi and Yamlip toolboxes.The SOCP-MKRVM algorithm, which mainly uses the MKRVM, calculatesαi by using the method of base vector filling, which efficiently calculates the multikernel parameters. The main algorithmic steps of the SOCP-MKRVM are as follows.Step 1.
Load the training samples and initialize the parameters of the MKRVM.Step 2.
Construct a multikernel function as (19).Step 3.
Use formula (22) for the nuclear correction and solve the nuclear parameters.Step 4.
Put the unknown kernel working parameters into the SOCP and calculate it.Step 5.
Get the optimal values of the kernel function parameters and put them into the MKRVM model for classification.


### 2.5. Classic Example Simulation

In the MKRVM classification verification, Pipley’s synthetic (a commonly used data set for classification) is used for the test. The data set is a two-dimensional classification sample set with 250 training samples and 1000 test samples. There is much Gaussian mixed noise in Pipley’s synthetic data set. We use the edge likelihood estimation iteration and the SOCP optimization to classify the data by computer simulation, and the results are shown in Figures1 and 2. The effect of the two methods is shown in Table 1.Table 1
Comparison of the two methods.
Algorithm Test error (%) Number of iterations Computation time (s) Number of RVM RVM 8.6 446 2.7520 4 SOCP-MKRVM 8.1 255 0.5620 4Figure 1
Pipley classification results of the RVM.Figure 2
Pipley classification results of the SOCP-MKRVM.As seen from Table1, under the training and testing of the same data set, the number of RMV is reduced, the model is sparser and the running time is shortened after the SOCP optimizes the MKRVM. In addition, in the classification test of the Pipley data set, the test error in the optimized program is smaller, which indicates that the classification accuracy is improved.


## 2.1. Traditional RVM Method

Assuming that the training set is{xi,yi}i=1,2,…,m, the target value yn and the input value xn are independently distributed samples. The output of the RVM [7, 8] can be expressed as(1)yj=∑i=1mwiKXj,Xi+w0+εj.Here,K(,) is the kernel function. The Gauss kernel function is used as the kernel function in this paper:(2)Kx1,x2=exp⁡-x1-x222σ12.w is the weight vector of the model. εn is the additional noise that satisfies the Gaussian distribution:(3)εn~N0,σ2.Deriving from formula (1) and formula (3), we get(4)py∣w,σ2=NΦw,σ2.In the formula,Φ is a designed m×(m+1) order matrix consisting of kernel functions such that Φ=ϕx1,ϕx2,…,ϕxmT and ϕ(xi)=1,kxi,x1,kxi,x2,…,kxi,xm. The ARD Gaussian prior probability distribution of the defined weights is (5)pw∣α=∏i=0mNwi∣0,αi-1.Here,α is the m+1 dimension vector composed of super parameters that control the distribution of w, A=diag⁡α0,α1,…,αm.According to Bayesian theory, the posterior probability distribution ofw can be decomposed as(6)pw∣y,α,σ2=Nu,Σ,where (7)py∣α,σ2=∫py∣w,σ2pw∣αdw.(8)Σ=σ-2ΦTΦ+A-1(9)u=σ-2ΣΦTyu and Σ are the mean vector and covariance matrix of w. It can be seen from formula (9) that the parameter σ2 and the super parameter α need to be estimated. The posterior probability distribution of the parameter σ2 and the super parameter α is obtained according to the Bayesian theory as follows:(10)pα,σ2∣y=py∣α,σ2pα,σ2py.The estimation of the parameterσ2 and the super parameter α is the calculation of the maximum value of the posterior probability distribution. It can be seen from (10) that the value of the posterior probability distribution of the two parameters is mainly determined by the likelihood function py∣α,σ2:(11)py∣α,σ2=N0,C.Here,C=σ2I+ΦA-1ΦT.The maximum likelihood estimation method is used to calculate the maximum value of (11). The parameter σ2 and the super parameter α are obtained as(12)αinew=1-αiΣiiui2σ2new=y-Φu2m-∑i=0m1-αiΣii.In the iterative operation, much of the super parameterαi tends to infinity. w obtained from formula (9) corresponds to the trend of zero. Therefore, you can make a small number of sample points work to achieve the RVM’s sparse effect [9], and these sample points are of relevance to the vector machine.


## 2.2. Multiple Kernel Learning (MKL) Algorithms

To improve the universal applicability of the RVM algorithm, MKL has been applied instead of one specific kernel function:(13)Kμxi,xj=fμKmxi,xjm=1M∣μ,where Kμ is the multikernel function. The multiple kernel Kμ can be obtained by function fμ:RD→RP and by combining M different Km. μ is the proportion parameter of the kernel.The kernel weights are regarded as a regularization itemrμ, which is taken as 1/2μ-1/MTμ-1/M. Thus, the objective function and gradient function can transform into(14)Jμ=12∑i=1n∑j=1nyiyjαiαjKμxi,xj-∑i=1nαi-rμ,∂Jμ∂μm=12∑i=1n∑j=1nyiyjαiαj∂Kμxi,xj∂μm-∂rμ∂μm∀m.The kernel combined function is(15)Kμxi,xj=∏m=1Mexp⁡-μmxim-xjm2=exp⁡∑m=1M-μmxim-xjm2.


## 2.3. Second-Order Cone Programming (SOCP)

The above classification algorithm is based on the edge likelihood estimation method. However, this algorithm has an extensive matrix inversion process, and thus the training time is longer. To solve this problem, the MKRVM method based on the SOCP algorithm is proposed in this paper.The standard form of the second-order cone programming is(16)min⁡∑i=1nciTxi:∑i=1nAixi=b,xi∈Ki,i=1,…,n.Here,xi∈Ki,i=1,…,n, is the variable. b∈Rm and Ai∈Rm×k, ci∈Rki,i=1,…,n, is the known quantity. Ki,i=1,…,n, is the second-order cone of dimension ki. Thus(17)Ki≔xi=xi0,xi1∈R×Rki-1:xi0-xi1≥0.In this,· is the Euclidean norm of the vectors. It is easy to know that Ki is self-dual and (18)Ki0≔xi=xi0,xi1∈R×Rki-1:xi0-xi1>0.For the MKRVM, the focus of its operations is the iterative computation ofαi. The purpose of the SOCP is to change the original solution and efficiently solve this parameter. The Gauss kernel function is a typical local kernel, and the polynomial kernel function is a typical global kernel. The combination of the two kernel functions can have the advantages of both local and global kernels. Let xi and yi be the sample points in the data space. The combination kernel function is(19)K=μ1G1xi,yj+μ2G2xi,yj+μ3Pxi,yj.Here,(20)G1xi,yj=-xi-yj2θ12;G2xi,yj=-xi-yj2θ22;Pxi,yj=xiyjθ32+12.θ 1, θ2, and θ3 are the kernel parameters obtained by nuclear correction. μ1, μ2, and μ3 are the undetermined combination coefficients.In the multikernel functions, the kernel correction value of the kernel functionK is (21)Aβ=AS,Kβ,yyT=∑kβkyTKky∑k1βkβlKk,KlFmin which S is the sample data.Then, the process of obtaining the best correction value of the kernel function is transformed into the following planning problem:(22)maxβ:Aβsubject  to:1≥βi≥0∑j=1Mβi=1.After calculatingβi of each kernel function, the validity of the kernel parameter is judged according to the value of βi. If βi approaches 0, it means that the corresponding kernel parameter of βi is not suitable for use on this data set. If the value of βi is close to 1, then the corresponding kernel parameter of βi is valid.


## 2.4. MKRVM Method Based on SOCP Algorithm

SOCP is used to optimize the MKRVM [10, 11], and μ1, μ2, and μ3 are the kernel work parameters that need to be optimized. The previous part of (21) is the reciprocal of a Euclidean paradigm, and the latter exponential function is a convex function. In this case, the optimization problem can be solved by being transformed into a standard SOCP problem [12]. In the SOCP form, the parameters are solved efficiently through the MKRVM training and the optimization process by using the SeDuMi and Yamlip toolboxes.The SOCP-MKRVM algorithm, which mainly uses the MKRVM, calculatesαi by using the method of base vector filling, which efficiently calculates the multikernel parameters. The main algorithmic steps of the SOCP-MKRVM are as follows.Step 1.
Load the training samples and initialize the parameters of the MKRVM.Step 2.
Construct a multikernel function as (19).Step 3.
Use formula (22) for the nuclear correction and solve the nuclear parameters.Step 4.
Put the unknown kernel working parameters into the SOCP and calculate it.Step 5.
Get the optimal values of the kernel function parameters and put them into the MKRVM model for classification.


## 2.5. Classic Example Simulation

In the MKRVM classification verification, Pipley’s synthetic (a commonly used data set for classification) is used for the test. The data set is a two-dimensional classification sample set with 250 training samples and 1000 test samples. There is much Gaussian mixed noise in Pipley’s synthetic data set. We use the edge likelihood estimation iteration and the SOCP optimization to classify the data by computer simulation, and the results are shown in Figures1 and 2. The effect of the two methods is shown in Table 1.Table 1
Comparison of the two methods.
Algorithm Test error (%) Number of iterations Computation time (s) Number of RVM RVM 8.6 446 2.7520 4 SOCP-MKRVM 8.1 255 0.5620 4Figure 1
Pipley classification results of the RVM.Figure 2
Pipley classification results of the SOCP-MKRVM.As seen from Table1, under the training and testing of the same data set, the number of RMV is reduced, the model is sparser and the running time is shortened after the SOCP optimizes the MKRVM. In addition, in the classification test of the Pipley data set, the test error in the optimized program is smaller, which indicates that the classification accuracy is improved.


## 3. Experiment Simulation and Result Analysis

### 3.1. Identification System Design

The whole detection algorithm is divided into the offline processing part and the online detection and recognition part. The offline processing part includes training sample set selection, image defect pretreatment, SOCP-MKRVM model training, and the preservation of the trained SOCP-MKRVM model for online defect recognition. The online detection and recognition part is divided into real-time processing section and on-time processing section. For the real-time processing part, first we obtain a binary image by preprocessing the image. Then, label the binary image by judging whether the binary image has a defect. If a defect appears in the image, we locate the defective region and save the single defect area as a bitmap. After that, the defect bitmaps are put into on-time processing section for processing. If there is no defect in the image, process the next image frame. The algorithm of this section is simple, but it requires processing every frame of an image, which increases the amount of data to be processed. The on-time processing section extracts the features of a single defective image region obtained from the real-time processing section. Then, load the selected features into the SOCP-MKRVM model for classification and recognition. Simultaneously, load the defect location information and the category information into the database in real time. The algorithm is complex, but the amount of data processing is small after the real-time processing section screens it. Thus, the two sections’ times could be linked. Finally, fast and accurate defect detection is realized.The algorithm training process flow chart and the strip defect recognition process flow chart are shown in Figures3 and 4.Figure 3
SOCP-MKRVM model training flow chart.Figure 4
Flow chart of strip defectdetection.


### 3.2. Application Environment and Sample Selection

The experimental environment is as follows. The PC hardware consisted of an Intel Core i5 760 2.8 GHz CPU with 2 GB of RAM. The software platform was comprised of the Windows 7 Operating system and MATLAB 7.0 simulation software.In the strip production process, the continuous casting billet, rolling equipment, processing technology, and more result in different kinds of surface defects. These defects include abrasions, scar, scratches, bonding, roller marks, needle, holes, epidermal stratification, pitting, welds, inclusions, cracks, frown lines, scales, stains, burrs, bubbles, and more. The SOCP optimized MKRVM technology can be used to model and identify the strip surface defects and then correspondingly analyze the cause of the defects. Finally, the solution to eliminate the defects is proposed. In this experiment, the strip defect images are required from a steel factory. We choose the most common 8 kinds of defects as the research objects: scratches, abrasions, scars, roller marks, holes, edge cracks, and surface upwarping and pitting, as shown in Figures5(a)–5(h), respectively.Figure 5
Strip steel defect images.
(a)
Scratches (b)
Abrasions (c)
Scars (d)
Roller marks (e)
Holes (f)
Edge cracks (g)
Surface upwarping (h)
Pitting


### 3.3. Feature Parameter Extraction

The data set formed from parts of the required images is used in image preprocessing. In the recognition model training, three types of features are used, which include grayscale (mean value, mean square error, peak signal-to-noise ratio (PSNR), and the gray histogram), morphology (area, perimeter, and center of gravity), and texture (rectangular degree, roundness, and edge defects). The trained model is applied in the real-time recognition of defect images. Extract the feature information parameters, which are shown in Table2. The gray histogram extracted from the defect images are shown in Figures 6(a)–6(h) and the edge information of the defect images is shown in Figures 7(a)–7(h).Table 2
Table of defect feature parameters.
Perimeter Centroid Rectangularity Roundness Defect area Average value Mean square error PSNR Scratches 6752511.4677 95 63 2.2573 e - 005 1.3081 23547 202.1134 17.3348 40.2710 Abrasions 8059327.7211 124 91.5 5.1263 e - 005 1.2885 21564.5 126.7753 12.5693 40.0457 Scar 6336816.5311 129 88.5 7.0503 e - 005 1.3047 5309.375 99.2674 25.6033 40.1967 Roller marks 4230693.2402 81.5 63.5 4.167 e - 005 1.2719 20172.75 146.5667 10.0764 40.2564 Holes 5535146.4921 82.5 81.5 2.2391 e - 005 1.2545 22112.75 147.6829 26.3304 40.1245 Edge crack 4684413.5541 76.5 93.5 3.1132 e - 005 1.2679 6652.125 117.1682 19.1387 40.1197 Surface upwarping 9993410.5839 143.5 109.5 4.9846 e - 005 1.3733 20552.625 113.3258 29.1838 40.0771 Pitting 7861938.1007 106 83.5 1.5379 e - 005 1.2752 34749.125 159.3857 13.4814 40.0777Figure 6
Gray histogram of defect images.
(a)
Scratches (b)
Abrasions (c)
Scars (d)
Roller marks (e)
Holes (f)
Edge cracks (g)
Surface upwarping (h)
PittingFigure 7
Edge information of the defect images.
(a)
Edge of scratches (b)
Edge of abrasions (c)
Edge of scars (d)
Edge of roller marks (e)
Edge of holes (f)
Edge of edge cracks (g)
Edge of surface upwarping (h)
Edge of pittingDue to the use of the second-order cone programming method to optimize the parameters of the relevant vector machine, the time consumption of the SOCP-MKRVM algorithm in this paper is longer than the traditional RVM algorithm. However, the sample training modeling process is an offline process, and the real-time defect detection classification has no effect.According to the above method, we extract the features of multiple images to establish the defect data set and then extract more factual information to build a high-dimensional matrix. We capture numerous images to establish the database and constitute a matrix with 10-dimensional features as the training set, as shown in Table3.Table 3
A matrix with 10-dimensional features.
Perimeter Centroid Rectangularity Roundness Defect area Average value Mean square error PSNR Histogram Edge x i 1 x i 2 x i 3 x i 4 x i 5 x i 6 x i 7 x i 8 x i 9 x i 10


### 3.4. Results and Analysis

We simulate 8 respective types of common defects using the SOCP-MKRVM algorithm. There are 100 defect images for each defect. The testing samples and the defect recognition results are shown in Table4. After that we simulate the 8 types of common defects with the traditional RVM algorithm and the traditional SVM algorithm; the results are shown in Table 4.Table 4
Defect recognition performance comparison of SOCP-MKRVM, RVM and SVM.
Defect type Scratches Abrasions Scar Roller marks Holes Edge crack Surfaceupwarping Pitting Testing sample number 100 100 100 100 100 100 100 100 Error number (SOCP-MKRVM) 0 0 1 2 0 0 1 2 Recognition accuracy (SOCP-MKRVM) 100% 100% 99% 98% 100% 100% 99% 97% Time consuming (ms) (SOCP-MKRVM) 6.42 6.27 7.87 7.87 5.87 6.02 7.37 7.28 Error number (RVM) 1 0 4 5 0 0 3 2 Recognition accuracy (RVM) 99% 100% 96% 95% 100% 100% 97% 96% Time consuming (ms) (RVM) 6.81 6.34 7.89 7.88 6.03 6.95 7.89 7.31 Error number (SVM) 4 1 6 5 0 1 5 7 Recognition accuracy (SVM) 96% 99% 94% 95% 100% 99% 95% 93% Time consuming (ms) (SVM) 6.95 7.34 8.29 9.18 6.73 8.05 8.32 8.16As shown in Table4, the classification recognition accuracy of the SOCP-MKRVM algorithm is very high, and some of the defects have a 100% classification accuracy, such as scratches, abrasions, holes, and edge cracks. Only pitting has a slightly lower accuracy (97%). Overall, the average recognition accuracy for the 8 types of defects is up to 99%, which is very ideal.The overall recognition accuracy of the traditional RVM algorithm and the traditional SVM algorithm is lower than that of the SOCP-MKRVM algorithm. Some types of defects also have very high recognition accuracy of RVM; however, three types (scars, roller marks, and surface upwarping) have relatively low recognition accuracy. The overall recognition accuracy of the traditional SVM algorithm is clearly lower than that of the SOCP-MKRVM algorithm. The average time consumption of the three algorithms is very short and is in milliseconds. For most of the overall detection results, the average time consumption of the SOCP-MKRVM algorithm is shorter than that of the two other algorithms. It is obvious that the SOCP-MKRVM algorithm is superior and more suitable than the traditional RVM algorithm and the traditional SVM algorithm in strip surface defect detection.


## 3.1. Identification System Design

The whole detection algorithm is divided into the offline processing part and the online detection and recognition part. The offline processing part includes training sample set selection, image defect pretreatment, SOCP-MKRVM model training, and the preservation of the trained SOCP-MKRVM model for online defect recognition. The online detection and recognition part is divided into real-time processing section and on-time processing section. For the real-time processing part, first we obtain a binary image by preprocessing the image. Then, label the binary image by judging whether the binary image has a defect. If a defect appears in the image, we locate the defective region and save the single defect area as a bitmap. After that, the defect bitmaps are put into on-time processing section for processing. If there is no defect in the image, process the next image frame. The algorithm of this section is simple, but it requires processing every frame of an image, which increases the amount of data to be processed. The on-time processing section extracts the features of a single defective image region obtained from the real-time processing section. Then, load the selected features into the SOCP-MKRVM model for classification and recognition. Simultaneously, load the defect location information and the category information into the database in real time. The algorithm is complex, but the amount of data processing is small after the real-time processing section screens it. Thus, the two sections’ times could be linked. Finally, fast and accurate defect detection is realized.The algorithm training process flow chart and the strip defect recognition process flow chart are shown in Figures3 and 4.Figure 3
SOCP-MKRVM model training flow chart.Figure 4
Flow chart of strip defectdetection.


## 3.2. Application Environment and Sample Selection

The experimental environment is as follows. The PC hardware consisted of an Intel Core i5 760 2.8 GHz CPU with 2 GB of RAM. The software platform was comprised of the Windows 7 Operating system and MATLAB 7.0 simulation software.In the strip production process, the continuous casting billet, rolling equipment, processing technology, and more result in different kinds of surface defects. These defects include abrasions, scar, scratches, bonding, roller marks, needle, holes, epidermal stratification, pitting, welds, inclusions, cracks, frown lines, scales, stains, burrs, bubbles, and more. The SOCP optimized MKRVM technology can be used to model and identify the strip surface defects and then correspondingly analyze the cause of the defects. Finally, the solution to eliminate the defects is proposed. In this experiment, the strip defect images are required from a steel factory. We choose the most common 8 kinds of defects as the research objects: scratches, abrasions, scars, roller marks, holes, edge cracks, and surface upwarping and pitting, as shown in Figures5(a)–5(h), respectively.Figure 5
Strip steel defect images.
(a)
Scratches (b)
Abrasions (c)
Scars (d)
Roller marks (e)
Holes (f)
Edge cracks (g)
Surface upwarping (h)
Pitting


## 3.3. Feature Parameter Extraction

The data set formed from parts of the required images is used in image preprocessing. In the recognition model training, three types of features are used, which include grayscale (mean value, mean square error, peak signal-to-noise ratio (PSNR), and the gray histogram), morphology (area, perimeter, and center of gravity), and texture (rectangular degree, roundness, and edge defects). The trained model is applied in the real-time recognition of defect images. Extract the feature information parameters, which are shown in Table2. The gray histogram extracted from the defect images are shown in Figures 6(a)–6(h) and the edge information of the defect images is shown in Figures 7(a)–7(h).Table 2
Table of defect feature parameters.
Perimeter Centroid Rectangularity Roundness Defect area Average value Mean square error PSNR Scratches 6752511.4677 95 63 2.2573 e - 005 1.3081 23547 202.1134 17.3348 40.2710 Abrasions 8059327.7211 124 91.5 5.1263 e - 005 1.2885 21564.5 126.7753 12.5693 40.0457 Scar 6336816.5311 129 88.5 7.0503 e - 005 1.3047 5309.375 99.2674 25.6033 40.1967 Roller marks 4230693.2402 81.5 63.5 4.167 e - 005 1.2719 20172.75 146.5667 10.0764 40.2564 Holes 5535146.4921 82.5 81.5 2.2391 e - 005 1.2545 22112.75 147.6829 26.3304 40.1245 Edge crack 4684413.5541 76.5 93.5 3.1132 e - 005 1.2679 6652.125 117.1682 19.1387 40.1197 Surface upwarping 9993410.5839 143.5 109.5 4.9846 e - 005 1.3733 20552.625 113.3258 29.1838 40.0771 Pitting 7861938.1007 106 83.5 1.5379 e - 005 1.2752 34749.125 159.3857 13.4814 40.0777Figure 6
Gray histogram of defect images.
(a)
Scratches (b)
Abrasions (c)
Scars (d)
Roller marks (e)
Holes (f)
Edge cracks (g)
Surface upwarping (h)
PittingFigure 7
Edge information of the defect images.
(a)
Edge of scratches (b)
Edge of abrasions (c)
Edge of scars (d)
Edge of roller marks (e)
Edge of holes (f)
Edge of edge cracks (g)
Edge of surface upwarping (h)
Edge of pittingDue to the use of the second-order cone programming method to optimize the parameters of the relevant vector machine, the time consumption of the SOCP-MKRVM algorithm in this paper is longer than the traditional RVM algorithm. However, the sample training modeling process is an offline process, and the real-time defect detection classification has no effect.According to the above method, we extract the features of multiple images to establish the defect data set and then extract more factual information to build a high-dimensional matrix. We capture numerous images to establish the database and constitute a matrix with 10-dimensional features as the training set, as shown in Table3.Table 3
A matrix with 10-dimensional features.
Perimeter Centroid Rectangularity Roundness Defect area Average value Mean square error PSNR Histogram Edge x i 1 x i 2 x i 3 x i 4 x i 5 x i 6 x i 7 x i 8 x i 9 x i 10


## 3.4. Results and Analysis

We simulate 8 respective types of common defects using the SOCP-MKRVM algorithm. There are 100 defect images for each defect. The testing samples and the defect recognition results are shown in Table4. After that we simulate the 8 types of common defects with the traditional RVM algorithm and the traditional SVM algorithm; the results are shown in Table 4.Table 4
Defect recognition performance comparison of SOCP-MKRVM, RVM and SVM.
Defect type Scratches Abrasions Scar Roller marks Holes Edge crack Surfaceupwarping Pitting Testing sample number 100 100 100 100 100 100 100 100 Error number (SOCP-MKRVM) 0 0 1 2 0 0 1 2 Recognition accuracy (SOCP-MKRVM) 100% 100% 99% 98% 100% 100% 99% 97% Time consuming (ms) (SOCP-MKRVM) 6.42 6.27 7.87 7.87 5.87 6.02 7.37 7.28 Error number (RVM) 1 0 4 5 0 0 3 2 Recognition accuracy (RVM) 99% 100% 96% 95% 100% 100% 97% 96% Time consuming (ms) (RVM) 6.81 6.34 7.89 7.88 6.03 6.95 7.89 7.31 Error number (SVM) 4 1 6 5 0 1 5 7 Recognition accuracy (SVM) 96% 99% 94% 95% 100% 99% 95% 93% Time consuming (ms) (SVM) 6.95 7.34 8.29 9.18 6.73 8.05 8.32 8.16As shown in Table4, the classification recognition accuracy of the SOCP-MKRVM algorithm is very high, and some of the defects have a 100% classification accuracy, such as scratches, abrasions, holes, and edge cracks. Only pitting has a slightly lower accuracy (97%). Overall, the average recognition accuracy for the 8 types of defects is up to 99%, which is very ideal.The overall recognition accuracy of the traditional RVM algorithm and the traditional SVM algorithm is lower than that of the SOCP-MKRVM algorithm. Some types of defects also have very high recognition accuracy of RVM; however, three types (scars, roller marks, and surface upwarping) have relatively low recognition accuracy. The overall recognition accuracy of the traditional SVM algorithm is clearly lower than that of the SOCP-MKRVM algorithm. The average time consumption of the three algorithms is very short and is in milliseconds. For most of the overall detection results, the average time consumption of the SOCP-MKRVM algorithm is shorter than that of the two other algorithms. It is obvious that the SOCP-MKRVM algorithm is superior and more suitable than the traditional RVM algorithm and the traditional SVM algorithm in strip surface defect detection.


## 4. Conclusion

In this paper, we propose strip steel surface defect detection based on the SOCP optimized multiple kernel RVM. For the SOCP-MKRVM, the second-order cone programming method is used to optimize the relevance vector machine kernel function, which can make a more optimal selection for the kernel function and improve the classification accuracy and generalization ability. The SOCP-MKRVM algorithm has the advantages of high calculation accuracy and operation speed that effectively improves the working efficiency, reduces the intensity of workers, and has a very wide range of uses. The simulation experimental results show that the SOCP-MKRVM has significant advantages in accuracy and operation speed compared to the traditional RVM algorithm and the traditional SVM algorithm.



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*Source: 9298017-2018-03-29.xml*