CN103268491A - Weld defect ultrasound phased array sector scanned image feature extraction method - Google Patents

Abstract

The invention provides a weld defect ultrasound phased array sector scanned image feature extraction method and belongs to the technical field of weld defect research. The weld defect ultrasound phased array sector scanned image feature extraction method solves the problems that when weld defects are classified and identified, defect ultrasound phased array sector scanned images are directly utilized to conduct defect identification, image data are large in dimensionality, a disaggregated model is complex, and learning time is long. The weld defect ultrasound phased array sector scanned image feature extraction method mainly includes the steps of setting up a defect image data array by using the weld defect ultrasound phased array sector scanned images, calculating a covariance array of the defect image data array, solving a feature value and a feature vector of the covariance array, determining the number of main components of each defect image, and setting up a weld defect feature expression function. The weld defect ultrasound phased array sector scanned image feature extraction method keeps a large amount of information of the defect images, represents the type of defects, ensures a correct identification rate of the disaggregated model, reduces dimensionality of defect image data, and greatly improves the learning speed of the disaggregated model.

Description

A kind of weld defects ultrasonic phase array sector display image characteristic extracting method

Technical field

The present invention relates to a kind of weld defects ultrasonic phase array sector display image characteristic extracting method, belong to the weld defects studying technological domain.

Background technology

Before the Intelligent Recognition of research weld defects, at first to carry out the feature extraction of defective ultrasonic phase array sector display image (hereinafter to be referred as defect image).Feature extraction is one of committed step of classification of defects identification, and its principle is to select most representative feature, will reduce the dimension of defect image data simultaneously.Because the diversity of defective form in the weld seam, feature complexity such as the shape of defective size and texture make that the difficulty of feature extraction is bigger in the sector display image.If do not carry out feature extraction, directly adopt the sector display image, for defect recognition, the dimension of defect image data is excessive, can cause the classification function complexity, and operand is big, and learning time is long, therefore is necessary defect image is carried out feature extraction.

Every width of cloth weld defects image contains 161 bundle ultrasound wave a-signals, and every bundle ultrasound wave a-signal contains 1520 point data, comprises echo amplitude and defective three-dimensional coordinate information in every point data again, calculates as can be known, and the data volume of weld defects image can reach 1,000,000 orders of magnitude.Carry out feature extraction in the face of like this big data volume and how to accomplish farthest to keep the defect image most information of determining, extract the feature relevant with the defective classification, reduce simultaneously the dimension of defect image data as best one can, reducing the study and work amount of follow-up support vector machine disaggregated model, is the technical matters that the utmost point need solve.

Summary of the invention

The present invention directly adopts defective ultrasonic phase array sector display image to identify in order to solve in the existing weld defects Study on Classification and Recognition technology, cause the dimension of data excessive, the disaggregated model complexity, the technical matters that learning time is long provides a kind of weld defects ultrasonic phase array sector display image characteristic extracting method.

The inventive method specifically describes as follows based on the basic thought of principal component analysis (PCA):

Defective is being carried out in the research of Classification and Identification, in order to reflect the feature of defective more comprehensively, exactly, often will consider in the defect image and the related a plurality of data of its classification.So just produced following problem: consider data as much as possible for fear of omitting the information relevant with the defective classification on the one hand, and increased the complicacy of Classification and Identification on the other hand along with increasing of data.Based on the problems referred to above, the present invention wishes that the dimension of the data that relate to is less in defect recognition research, and the quantity of information relevant with the defective classification that obtains is more.Principal component analysis (PCA) is studied a kind of multivariate statistical method of how explaining the most information of raw data by a few linear combination of raw data just.By the research to raw data correlation matrix or covariance matrix inner structure relation, utilize the linear combination of raw data to form several overall targets (major component), under the prerequisite that keeps the main information of raw data, play the effect of simplification problem, make the easier principal contradiction of catching when the research challenge.Therefore the invention provides a kind of feature extracting method of the weld defects ultrasonic phase array sector display image based on principal component analysis (PCA), covariance by research defective ultrasonic phase array sector display image data matrix, utilize the linear combination of defect image data, try to achieve the feature relevant with defect type, set up defect characteristic and express function, carry out the Classification and Identification of defective.

In general, utilize following fundamental relation arranged between major component that principal component analysis (PCA) obtains and the original variable:

(1) each major component all is the linear combination of each original variable;

(2) number of major component is much smaller than the number of original variable;

(3) major component has kept the most information of original variable;

(4) uncorrelated mutually between each major component.

By principal component analysis (PCA), can between things, find out some principal ingredients the complicated relation, thereby can effectively utilize a large amount of statisticss to carry out quantitative test.

If the research to a certain things relates to p variable, use X respectively ₁, X ₂..., X _pExpression, the p dimension random vector of this p variable formation is X=(X ₁, X ₂..., X _pIts mean vector of) ', is μ=E (X), and covariance matrix is ∑=D (X).In order to replace original variable with less New Set, New Set should keep the information of original variable as much as possible, and uncorrelated to each other, constructs X for this reason ₁, X ₂..., X _pLinear combination:

$\left\{\begin{array}{c}{F}_1=a_1^{\&prime;}X=a_{11}{X}_1+a_{12}{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HDA00003276676800011.png"\; state="\{\{state\}\}">X</figure-callout>}}_2+\&CenterDot;\&CenterDot;\&CenterDot;+a_{1p}{\mathrm{<figure-callout\; id="2"\; label="X\; p\; F"\; filenames="HDA00003276676800011.png"\; state="\{\{state\}\}">X</figure-callout>}}_p& \\ F_{}{}_2=a_2^{\&prime;}X=a_{21}{X}_1+a_{22}{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HDA00003276676800011.png"\; state="\{\{state\}\}">X</figure-callout>}}_2+\&CenterDot;\&CenterDot;\&CenterDot;a_{2p}{X}_p\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\\ F_p=a_p^{\&prime;}X=a_{p1}{X}_1+a_{p2}{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HDA00003276676800011.png"\; state="\{\{state\}\}">X</figure-callout>}}_2+\&CenterDot;\&CenterDot;\&CenterDot;a_{\mathrm{pp}}{X}_p\end{array}\right.---(1-1)$

A wherein _j=(a _1j, a _2j..., a _Pj) ' (j=1,2 ..., p).Yi Zhi:

VarF _i＝a′ _i∑a _i (1-2)

If use F ₁Replace original variable X ₁, X ₂..., X _p, this just requires F ₁The information that should reflect p original index to greatest extent.Because more big this index susceptibility that just illustrates of index variance is more good, the information that comprises is more many, therefore uses F ₁Variance VarF ₁Express its quantity of information.By formula (1-2) as can be known, to any given constant c, have:

Var(ca′ _iX)＝ca′ _i∑a _ic＝c ²a′ _i∑a _i (1-3)

If to a _iDo not add restriction, can make VarF _iIncrease arbitrarily, it is nonsensical that problem will become.Therefore linear transformation is constrained under the following principle:

(1) a ' _ia _i=1, namely $a_{i1}^2+a_{i2}^2+\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="a\; ip"\; filenames="HDA00003276676800011.png"\; state="\{\{state\}\}">a</figure-callout>}}_{\mathrm{ip}}^{}=1,(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,p);$

(2) F _iWith F _jUncorrelated (i ≠ j; I, j=1,2 ..., p);

(3) F ₁Be X ₁, X ₂..., X _pAll satisfy variance the maximum in the linear combination of principle (1); F ₂Be and F ₁Incoherent X ₁, X ₂..., X _pAll linear combinations in variance the maximum; , F _pBe and F ₁, F ₂..., F _P-1Incoherent X all ₁, X ₂..., X _pVariance the maximum in all linear combinations.

Generalized variable F based on above three principles decision ₁, F ₂..., F _pBe called original variable first, second ..., a p major component.Wherein, the proportion that accounts in population variance of each generalized variable successively decreases successively.

The geometric meaning of principal component analysis (PCA) for convenience, is only discussed the geometric meaning of major component as shown in Figure 1 in two-dimensional space, the gained conclusion can expand to the situation of multidimensional.Be provided with N sample, each sample has two observational variable x ₁, x ₂, by variable x ₁, x ₂In the determined two dimensional surface, N situation such as the ellipticity that sample scatters.No matter this N sample point is along x as seen from the figure ₁Direction of principal axis or x ₂Direction of principal axis all has bigger discreteness, and its discrete degree can be used observational variable x respectively ₁Variance and x ₂Variance represent quantitatively.Obviously, if only consider x ₁And x ₂In any one, the information that is included in so in the raw data will have bigger loss.

If with x ₁Axle and x ₂The first translation of axle by counterclockwise rotating the θ angle, obtains new coordinate axis F simultaneously ₁And F ₂The purpose of translation, rotational transform is in order to make N sample spot at F ₁Dispersion degree maximum on the axle, i.e. F ₁The variance maximum.Variable F ₁Most information of raw data have been represented, even do not consider variable F ₂Also can't harm overall situation.After translation, rotation, the most information of raw data focuses on F ₁On the axle, the information that comprises in the data has been played inspissation.The process of principal component analysis (PCA) is exactly the process of coordinate system translation and rotation, each major component expression formula is exactly the transformational relation of new coordinate system and former coordinate system, the purpose of principal component analysis (PCA) is found out transition matrix exactly, and carries out the effect of principal component analysis (PCA) and geometric meaning is also just very clear.

By matrix algebra as can be known, random vector X=(X ₁, X ₂..., X _p) ' the covariance matrix ∑ be the nonnegative definite battle array, its eigenvalue is non-negative, thereby can be designated as λ ₁〉=λ ₂〉=... 〉=λ _p〉=0, α ₁, α ₂..., α _pBe the standard orthogonal characteristic vector of each eigenwert correspondence, X so ₁, X ₂..., X _pThe j major component can be expressed as:

F _j＝α′ _jX＝α _j1X ₁+α _j2X ₂+…+α _1pX _p (1-4)

Its variance is:

VarF _j＝α′ _j∑α _j＝λ _j (1-5)

So, ask X ₁, X ₂..., X _pThe major component problem just be summed up as the eigenwert of asking its covariance matrix ∑ and the problem of proper vector.

One of purpose of carrying out principal component analysis (PCA) is to reduce the number of variable, thus generally can not get p major component, but get m＜p major component, this needs following definition with regard to relating to the problem of choosing of m for this reason, claims

${\mathrm{\&lambda;}}_m/\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j---(1-6)$

Be m major component F _mVariance contribution ratio, variance contribution ratio has reflected that major component distinguishes the ability of original variable, variance contribution ratio is more big, the major component comprehensive X that expression generates ₁, X ₂..., X _pThe ability of information is more strong, also namely explains stochastic variable X by major component ₁, X ₂..., X _pThe ability of difference more strong, claim

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i/\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j---(1-7)$

Be major component F ₁, F ₂..., F _mThe accumulation contribution rate.Usually get m and make the accumulation contribution rate reach more than 85%, like this, can make loss of information not many, reach the purpose that reduces variable, simplifies problem again.

The present invention solves the problems of the technologies described above the concrete technical scheme of taking to be:

The method of weld defects sector display image characteristics extraction is as follows:

Step 1, get n width of cloth defect image, every width of cloth defect image contains the p data, p=k * l * t wherein, k is ultrasound wave a-signal number in every width of cloth defect image, the data of l for containing in each ultrasound wave a-signal, t is echo amplitude and the defective three-dimensional coordinate information that comprises in the data, obtains n * p data so altogether, and X is as follows for the defect image data matrix:

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{1p}\\ x_{21}& x_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{2p}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ x_{n1}& x_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00003276676800011.png"\; state="\{\{state\}\}">n</figure-callout>}2}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{\mathrm{np}}\end{array}\right]---(1-8)$

The covariance matrix ∑ of step 2, calculating defect image data matrix X:

∑＝(σ _ij) _p×p (1-9)

σ wherein _Ij=Cov (X _i, X _j) (i, j=1,2 ..., p), Cov (X _i, X _j) be to ask X _iAnd X _jCovariance.

Step 3, ask the eigen vector of covariance matrix ∑.

Tried to achieve p eigenvalue of ∑ by formula (1-10) _i(i=1,2 ..., p), be arranged as λ by descending order ₁〉=λ ₂〉=λ _pCalculate λ according to formula (1-11) _iCorresponding standard orthogonal characteristic vector α _i(i=1,2 ..., p).

|λE-∑|＝0 (1-10)

(λE-∑)α＝0 (1-11)

Step 4, determine defect image major component number m (m＜p), the m deterministic process is:

Utilize formula (1-6) to try to achieve the variance contribution ratio of m defect image major component, utilize formula (1-7) to try to achieve preceding m defect image major component accumulation contribution rate.

${\mathrm{\&lambda;}}_m/\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j---(1-6)$

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i/\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j---(1-7)$

Current m defect image major component accumulation contribution rate satisfies the condition more than or equal to 85%:

Can determine the value of m.

Step 5, after obtaining defect image major component number m, make up weld defects feature representation function:

F _i＝α _i1X ₁+α _i2X ₂+…+α _ipX _p i＝1，2，…，m (1-12)

F wherein ₁Be called feature 1, F ₂Be called feature 2, by that analogy, F _mBe called feature m.

The invention has the beneficial effects as follows: the invention provides a kind of weld defects ultrasonic phase array sector display image characteristic extracting method based on principal component analysis (PCA), covariance matrix by research defect image data matrix, from the mutual incoherent major component of defect image extracting data, set up defect characteristic and express function, carry out the Classification and Identification of defective, this method had both kept the defect image most information of determining, characterized the type of defective, guaranteed the correct recognition rata of disaggregated model, reduced the dimension of defect image data again, greatly improved the pace of learning of disaggregated model, directly adopt defective ultrasonic phase array sector display image to carry out defect recognition when having solved the weld defects Classification and Identification, the view data dimension is big, disaggregated model complexity, the difficult problem that learning time is long.

Description of drawings

Fig. 1 is the geometric meaning synoptic diagram of the principal component analysis (PCA) of the inventive method employing, and Fig. 2 is that the sector display of welded specimen ultrasonic phase array detects synoptic diagram, and Fig. 3 is a width of cloth weld defects ultrasonic phase array sector display image.

Embodiment

Embodiment one: with reference to figure 2, welded specimen is carried out the ultrasonic phase array sector display detect, the initial angle that sector display detects is 30 °, and termination point is 70 °, and scanning step is 0.25 °.

With reference to figure 3, the detailed process of the described a kind of weld defects ultrasonic phase array sector display image characteristic extracting method of present embodiment is:

Step 1, get n width of cloth defect image, every width of cloth defect image contains the p data, p=k * l * t wherein, k is ultrasound wave a-signal number in every width of cloth defect image, the data of l for containing in each ultrasound wave a-signal, t is echo amplitude and the defective three-dimensional coordinate information that comprises in the data, obtains n * p data so altogether, and X is as follows for the defect image data matrix:

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{1p}\\ x_{21}& x_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{2p}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ x_{n1}& {\mathrm{<figure-callout\; id="2"\; label="x\; n"\; filenames="HDA00003276676800011.png"\; state="\{\{state\}\}">x</figure-callout>}}_n& \&CenterDot;\&CenterDot;\&CenterDot;& x_{\mathrm{np}}\end{array}\right]---(1-8)$

The covariance matrix ∑ of step 2, calculating defect image data matrix X:

∑＝(σ _ij) _p×p (1-9)

σ wherein _Ij=Cov (X _i, X _j) (i, j=1,2 ..., p), Cov (X _i, X _j) be to ask X _iAnd X _jCovariance.

Step 3, ask the eigen vector of covariance matrix ∑.

Tried to achieve p eigenvalue of ∑ by formula (1-10) _i(i=1,2 ..., p), be arranged as λ by descending order ₁〉=λ ₂〉=λ _pCalculate λ according to formula (1-11) _iCorresponding standard orthogonal characteristic vector α _i(i=1,2 ..., p).

|λE-∑|＝0 (1-10)

(λE-∑)α＝0 (1-11)

Step 4, determine defect image major component number m (m＜p), the m deterministic process is:

Utilize formula (1-6) to try to achieve the variance contribution ratio of m defect image major component, utilize formula (1-7) to try to achieve preceding m defect image major component accumulation contribution rate.

${\mathrm{\&lambda;}}_m/\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j---(1-6)$

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i/\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j---(1-7)$

Current m defect image major component accumulation contribution rate satisfies the condition more than or equal to 85%:

Can determine the value of m.

Step 5, after obtaining defect image major component number m, make up weld defects feature representation function:

F _i＝α _i1X ₁+α _i2X ₂+…+α _ipX _p i＝1，2，…，m (1-12)

F wherein ₁Be called feature 1, F ₂Be called feature 2, by that analogy, F _mBe called feature m.

Embodiment: the characteristic extraction procedure of weld defects sector display image is as follows:

Respectively choose 200 width of cloth respectively in the ultrasonic phase array sector display image of pore, crackle, incomplete fusion and incomplete penetration defect, four kinds of defectives are totally 800 width of cloth images.Every width of cloth defect image contains 161 bundle ultrasound wave a-signals, every bundle ultrasound wave a-signal contains 1520 point data, comprise flaw echo amplitude and three-dimensional coordinate totally 4 information in every point data again, the data volume that comprises in every like this width of cloth defect image is that 978880,800 width of cloth defect image data matrix X are as follows:

The covariance matrix ∑ of the defect image data matrix that calculates is:

Obtain the eigenvalue of covariance matrix ∑ again, and by descending being arranged as:

λ＝[31.1，4.5，…，0.00001]

The standard orthogonal characteristic vector of the λ correspondence that calculates is:

α ₁＝[-0.0252，-0.0357，-0.0352，…，-0.0311]′

α ₂＝[-0.0418，-0.0112，0.0043，…，0.0007]′

…

α ₉₇₈₈₈₀＝[-0.0373，-0.0445，-0.0438，…，-0.0034]′

According to formula (1-6) and (1-7) calculate the defect image major component variance contribution ratio and the accumulation contribution rate, as the table 1-1 shown in.As can be seen from the table, the variance contribution ratio of major component 1 is 57.9%, and major component 2 is followed successively by 8.3%, 5.4%, 4.9%, 4.4%, 3.4% and 2.9% to the variance contribution ratio of major component 7, and the accumulation variance contribution ratio of the first seven major component is 87.3%.According to major component number selection principle, select the first seven major component, set up defect characteristic and express function, carry out follow-up Study on Classification and Recognition.

The variance contribution ratio of table 1-1 major component and accumulation contribution rate

Major component	Variance contribution ratio, %	The accumulation contribution rate, %
			F 1	57.9	57.9
F 2	8.3	66.2
			F 3	5.4	71.5
F 4	4.9	76.5
			F 5	4.4	80.9
F 6	3.4	84.4
			F 7	2.9	87.3
…	…	…

The expression function of seven defect characteristics is:

F ₁＝-0.0252X ₁-0.0357X ₂-0.0352X ₃+…-0.0311X ₉₇₈₈₈₀

F ₂＝-0.0418X ₁-0.0112X ₂+0.0043X ₃+…+0.0007X ₉₇₈₈₈₀

F ₃＝-0.0199X ₁-0.0149X ₂-0.0019X ₃+…-0.0263X ₉₇₈₈₈₀

F ₄＝0.0233X ₁+0.0596X ₂+0.0279X ₃+…+0.0068X ₉₇₈₈₈₀

F ₅＝-0.0091X ₁+0.0050X ₂-0.0550X ₃+…-0.0027X ₉₇₈₈₈₀

F ₆＝-0.0048X ₁-0.0393X ₂-0.0469X ₃+…-0.0057X ₉₇₈₈₈₀

F ₇＝-0.0063X ₁-0.0017X ₂-0.0186X ₃+…-0.0053X ₉₇₈₈₈₀

X wherein _j=(x _1j, x _2j..., x _800j) ', j=1,2 ..., 978880.

From weld defects ultrasonic phase array sector display image, seven features have been extracted, whether both kept the defect image most information of determining, characterized the type of defective, guaranteed the correct recognition rata of disaggregated model, reduced the dimension of defect image data again, improved the pace of learning of disaggregated model, this from the defect classification model correct recognition rata and learning time two angles illustrate the validity of feature extracting method, the results are shown in Table 1-2.Provide the employing feature extracting method in the table and directly adopted weld defects ultrasonic phase array sector display image to carry out classification of defects identification, the correct recognition rata of model and learning time.Compare from the correct recognition rata angle of defective, the correct recognition rata of defective does not reduce behind the employing feature extracting method; Compare from the learning time angle of model, the model learning time shortens greatly behind the employing feature extracting method.As seen, weld defects ultrasonic phase array sector display image extraction method provided by the invention, this method had both kept the defect image most information of determining, characterized the type of defective, guaranteed the correct recognition rata of disaggregated model, reduce the dimension of defect image data again, greatly improved the pace of learning of disaggregated model.

Table 1-2 feature extraction performance evaluation

Method	Correct recognition rata, %	Learning time, s
			Feature extracting method	91.5	9
Ultrasonic phase array sector display image	89.5	40071

Claims (1)

1. weld defects ultrasonic phase array sector display image characteristic extracting method, it is characterized in that: the detailed process of described method is:

Step 1, get n width of cloth defect image, every width of cloth defect image contains the p data, p=k * l * t wherein, k is ultrasound wave a-signal number in every width of cloth defect image, the data of l for containing in each ultrasound wave a-signal, t is echo amplitude and the defective three-dimensional coordinate information that comprises in the data, obtains n * p data so altogether, and X is as follows for the defect image data matrix:

$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{1p}\\ x_{21}& x_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{2p}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ x_{n1}& x_{n2}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{\mathrm{np}}\end{array}\right]---(1-8)$

The covariance matrix ∑ of step 2, calculating defect image data matrix X:

∑=(σ _Ij) _{P * p}(1-9) σ wherein _Ij=Cov (X _i, X _j) (i, j=1,2 ..., p), Cov (X _i, X _j) be to ask X _iAnd X _jCovariance;

Step 3, ask the eigen vector of covariance matrix ∑;

Tried to achieve p eigenvalue of ∑ by formula (1-10) _i(i=, 2 ..., p), be arranged as λ by descending order ₁〉=λ ₂〉=λ _pCalculate λ according to formula (1-11) _iCorresponding standard orthogonal characteristic vector α _i(i=1,2 ..., p):

|λE-∑|＝0 (1-10)

(λE-∑)α＝0 (1-11)

Step 4, determine defect image major component number m (m＜p), the m deterministic process is:

Utilize formula (1-6) to try to achieve the variance contribution ratio of m defect image major component, utilize formula (1-7) to try to achieve preceding m defect image major component accumulation contribution rate:

${\mathrm{\&lambda;}}_m/\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j---(1-6)$

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i/\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_j---(1-7)$

Current m defect image major component accumulation contribution rate satisfies the condition more than or equal to 85%:

Can determine the value of m;

Step 5, after obtaining defect image major component number m, make up weld defects feature representation function:

F _i＝α _i1X ₁+α _i2X ₂+…+α _ipX _p i＝1，2，…，m (1-12)

F wherein ₁Be called feature 1, F ₂Be called feature 2, by that analogy, F _mBe called feature m.

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