CN113192114A - Blade multi-field point cloud registration method based on overlapping features and local distance constraint - Google Patents

Abstract

The invention discloses a blade multi-field point cloud registration method based on overlapping features and local distance constraint, which comprises the following steps of 100: acquiring multi-view field point cloud data of the blade, solving an overlapping area of the point cloud data between two adjacent view fields, and constructing data sets X and Y; step 200: establishing an overlap feature constraint matrix F_MN(ii) a Step 300: establishing a local distance constraint matrix D_MN(ii) a Step 400: matrix-based Hadamard product, constraining matrix F by overlapping features_MNAnd a local distance constraint matrix D_MNConstructing a membership probability matrix P between data set X and data set Y_MN，P_MN=F_MN

D_MN，

Is the Hadamard product; step 500: and calculating a rotation matrix and a translation matrix between the data sets X and Y based on an EM algorithm, and splicing a complete blade section profile through the calculated rotation matrix and translation matrix. The invention provides a blade multi-field-of-view point cloud data registration method independent of the motion precision of a detection system, and aims to improve the blade detection precision and reliability.

Description

Blade multi-field point cloud registration method based on overlapping features and local distance constraint

Technical Field

The invention belongs to the field of blade detection, and particularly relates to a blade multi-field point cloud registration method based on overlapping features and local distance constraint.

Background

The blade is used as a core component of an aeroengine, and the profile precision of the blade directly influences the energy conversion efficiency and the working reliability of the whole machine. Therefore, accurate blade profile inspection has long been a key step in the blade manufacturing process. In recent years, the blade detection method based on optical measurement has attracted much attention due to the characteristics of good efficiency, flexibility and the like.

At present, the registration accuracy of multi-field point clouds mainly depends on the geometric accuracy and the operational reliability of an established detection system. Chinese invention patent No. 202011134900.7 discloses a method for calibrating a rotation center based on the characteristics of a local leading edge curve of a blade, which can effectively complete the registration of multi-field point cloud data by directly utilizing the motion parameters of a detection platform, but the registration result is easily influenced by multiple factors such as the geometric accuracy and the motion reliability of a detection system, and after all, the motion parameters of the detection platform have certain mechanical errors, so that the final blade detection reliability is poor; from fig. 1a and b, two adjacent joint results are obtained from the result of registering the multi-field point cloud data by using the method, and it can be seen that the overlapping areas between the adjacent fields are not completely matched, and the density is not uniform (point cloud data in the dotted line in fig. 1 a).

Disclosure of Invention

The invention aims to provide a blade multi-field point cloud registration method based on overlapping features and local distance constraints, which is used for realizing blade multi-field point cloud data registration without depending on the motion precision of a detection platform so as to achieve the purpose of improving the blade detection precision and reliability.

In order to achieve the purpose, the invention adopts the following technical scheme:

a blade multi-field point cloud registration method based on overlapping features and local distance constraints comprises the following steps:

step 100: acquiring point cloud data of multiple fields of view of the blade, solving an overlapping area of the point cloud data between two adjacent fields of view, and constructing a data set X = (X) of the overlapping area₁,…,x_m,…,x_M) And Y = (Y)₁,…,y_n,…y_N）；

Step 200: establishing an overlap feature constraint matrix F_MN；

First, with point X in data set X_mDrawing J sampling circles as the center of the circle, and centering on a point x_mThe radius of the jth sampling circle of (a) is as in formula i,

（Ⅰ）

in formula I, r_mjIs the radius of the jth sampling circle, r_mJRadius of the maximum sampling circle, r_m1Is the radius of the minimum sampling circle, J is the number of sampling circles, Ln (J) is a logarithmic function of a variable J, and Ln (J) is a logarithmic function value of a fixed value J;

then, construct point x_mCovariance matrix C of_mAs shown in the formula II,

（Ⅱ）

in formula II, C_mIs a point x_mOf (2) covariance matrix, Sp_jA sampling point corresponding to the jth sampling circle;

secondly, solving a covariance matrix C_mλ 1 and λ 2, and λ 1 ≧ λ 2, point x_mLocal characteristic factor fx of_m= λ 1/λ 2; sequentially calculating local characteristic factors of M points in the data set XAnd the local characteristic factor dataset of dataset X is F_X=（fx₁,…,fx_m,…,fx_M) (ii) a And calculating a local feature factor data set F of the data set Y_Y=（fy₁,…,fy_n,…,fy_N）；

Finally, an overlap feature constraint matrix F between the data sets X and Y is constructed_MNOverlap feature constraint matrix F_MNThe element in the m-th row and the n-th column is f_mn=∣fx_m-fy_n∣，f_mnFor a point X in the data set X_mWith point Y in data set Y_nLocal feature similarity, and sequentially calculating an overlapped feature constraint matrix F_MN；

Step 300: establishing a local distance constraint matrix D_MN；

First, let a distance matrix d between data set X and data set Y_MNDistance matrix d_MNM-th row and n-th column element d_mnIs a point x_mAnd point y_nThe euler distance therebetween;

then, a distance matrix d is searched_MNMinimum value in each line, and constitutes a minimal value data set Dis = (Dis) of distances₁,…,dis_m,…,dis_M) Calculating the average value Dd of the minimum value data set Dis;

finally, the distance matrix d_MNSetting the value of the middle distance larger than the constraint radius Crm as 0, setting the value of the middle distance smaller than or equal to the constraint radius Crm as 1, and establishing a local distance constraint matrix D_MN(ii) a Wherein the constraint radius Crm = γ R × Dd, γ R is an amplification factor, and Dd is an average value of the minimum data set Dis;

step 400: constraining the feature bundle matrix F by overlapping based on the Hadamard product between the matrices_MNAnd a local distance constraint matrix D_MNConstructing a membership probability matrix P between data set X and data set Y_MNI.e. P_MN=F_MN

D_MN，

Is the product of Hadamard, P_MNThe m-th row and the n-th column of the element are p_mn=f_mn×d_mn，f_mnAnd d_mnAre respectively F_MNAnd D_MNRow m and column n elements in (1); updating the membership probability matrix P_MNThe method comprises the following steps:

first, a membership probability matrix P_MNAll non-0 elements in (a) are included under the framework of a gaussian function, as shown in equation iii,

（Ⅲ）

in formula III, p_mnIs a member probability matrix P_MNM-th row and n-th column element, delta_F ²Is a member probability matrix P_MNThe variance of the non-0 term in the middle,

d =2 is the dimension of the point set to be registered, and W is the member probability matrix P_MNThe number of non-0 elements;

then to the member probability matrix P_MNAll the elements in the solution are normalized; let the current membership probability matrix P_MNThe sum of the m-th row elements is S_mThen member probability matrix P_MNAny element in the m-th row is updated to p_mn=p_mn/S_mAnd sequentially updating the member probability matrix P_MNAll of the elements in (A);

step 500: and calculating a rotation matrix and a translation matrix between the data sets X and Y based on an EM algorithm, and splicing the section profile of the blade through the calculated rotation matrix and translation matrix.

Further, the solving of the overlapping area of the point cloud data between two adjacent fields of view and the construction of the data set of the overlapping area in step 100 are as follows:

step 101: setting two adjacent point cloud data sets as V₁And V₂By a point cloud data set V₁End point V of_1HFor reference points, points V are calculated separately_1HAnd pointCloud data set V₂The distance between all the points is solved, and the point corresponding to the minimum distance value is solved as V_2pPoint cloud data set V₂The overlap region data set Y is the point cloud data set V₂End point V of_2PAnd V_2pAll points in between;

step 102: in the same way, with a point cloud data set V₂End point V of_2PFor reference points, points V are calculated separately_2PWith the point cloud data set V₁The distance between all the points is solved, and the point corresponding to the minimum distance value is solved as V_1hPoint cloud data set V₁The overlap region data set X is the point cloud data set V₁End point V of_1HAnd V_1hAll points in between.

Further, the calculation of the rotation matrix and the translation matrix between the data sets X and Y based on the EM algorithm in step 500 is performed according to the following steps:

step 501: initializing parameters, setting a rotation matrix as

And translation matrix

Iteration threshold xi and noise ratio alpha;

step 502: calculating a membership probability matrix P_MNThe sum of all elements in the composition is S_PAnd respectively calculating the weight centers mu of the data set X and the data set Y_XAnd mu_YThen according to the weight center mu_XAnd mu_YCalculating central vectors of a data set X and a data set Y;

step 503: calculating a covariance matrix Cov between the data set X and the data set Y according to the central vector, then performing singular value decomposition on the covariance matrix Cov, and updating a rotation matrix and a translation matrix according to a singular value decomposition result;

step 504: calculating a convergence coefficient d tau according to the updated rotation matrix and translation matrix, comparing the convergence coefficient d tau with an iteration threshold xi, repeating the steps 501 to 503 to iterate when d tau is larger than or equal to xi, stopping iterating until d tau is smaller than xi, and outputting an optimal rotation matrix and translation matrix between the data sets X and Y.

Compared with the prior art, the invention has the following beneficial effects:

(1) the registration algorithm specially aiming at multi-field-of-view point cloud data in the blade detection process is provided, the problems that the density of the measured data is non-uniform and the characteristics in an overlapping area are not prominent in the conventional algorithm are solved, and particularly, the algorithm shows good adaptability and robustness aiming at a measured object with complex geometric characteristics, such as a blade;

(2) a new characteristic constraint mechanism is provided, the non-uniformity problem among data points is solved by adopting a uniform sampling mode, and the problem that the characteristics in an overlapping area are not outstanding is solved by utilizing a self-adaptive sampling radius; meanwhile, a constraint mechanism based on local distance is also provided, so that the calculation complexity of the algorithm is effectively reduced, the overall calculation efficiency and accuracy are increased, and the problems of mis-registration and the like are avoided;

(3) based on the proposed multi-field-of-view point cloud registration algorithm, a high-precision and high-efficiency blade detection method is further provided, and the method effectively improves the detection precision and the universality on the premise of not improving the equipment cost of a detection system, and has a good application prospect.

Drawings

Fig. 1 is a registration result of an overlapping area between adjacent fields of view using motion parameters of an inspection platform, where a is a registration result of density unevenness of the overlapping area between two fields of view, and b is a registration result of registration inconsistency of the overlapping area between two fields of view.

FIG. 2 is a schematic diagram of the present invention for solving overlapping region data sets.

FIG. 3 shows a point x according to the present invention_mDrawing a schematic diagram of J sampling circles as the center of the circle.

FIG. 4 is a schematic diagram of the relationship of the sampling radius function of the sampling circle drawn by the present invention.

FIG. 5 shows point x of the present invention_mAs a local spatial schematic of a reference point.

Fig. 6 shows the registration result of the overlapped region between adjacent fields of view by using the method of the present invention, wherein a is the registration result of fig. 1a by using the method of the present invention, and b is the registration result of fig. 1b by using the method of the present invention.

Detailed Description

The blade multi-field-of-view point cloud registration method based on the overlapping features and the local distance constraint provided by the embodiment comprises the following steps:

step 100: the method includes the steps of obtaining a point cloud data set of a blade with multiple view fields, in the embodiment, adopting a four-axis measuring device and a line laser sensor to collect the point cloud data set of the blade, obtaining the point cloud data set of the blade with the multiple view fields by rotating or translating the four-axis measuring device, and obtaining the point cloud data set of the blade by adopting the four-axis measuring device and the line laser sensor, which belong to common technical means in the field, so that the embodiment is not repeated.

Extracting the data sets of the overlapping areas of the point cloud data sets of two adjacent field-of-view blades according to the extraction principle shown in FIG. 2, and specifically implementing the following steps:

step 101: setting point cloud data set of two view field blades as V₁And V₂By a point cloud data set V₁End point V of_1HFor reference points, points V are calculated separately_1HWith the point cloud data set V₂The distance between all the points is solved, and the point corresponding to the minimum distance value is solved as V_2pPoint cloud data set V₂The overlap region data set Y is the point cloud data set V₂End point V of_2PAnd V_2pAll points in between;

step 102: in the same way, with a point cloud data set V₂End point V of_2PFor reference points, points V are calculated separately_2PWith the point cloud data set V₁The distance between all the points is solved, and the point corresponding to the minimum distance value is solved as V_1hPoint cloud data set V₁The overlap region data set X is the point cloud data set V₁End point V of_1HAnd V_1hAll points in between. Data sets X and Y of the overlap region within the dashed box in fig. 2, data set X and data set Y are renumbered and sorted for ease of subsequent understanding and writing, with the renumbered sorted post data set X = (X) being₁,…,x_m,…,x_M) And data setY=（y₁,…,y_n,…y_N）。

Step 200: establishing an overlap feature constraint matrix F_MNThe data of the overlapping region are overlapping features, and the overlapping feature constraint mechanism is to disclose the potential matching probability between two data sets from the feature similarity, x_mConstructing a point x for a reference point_mLocal characteristic factor fx of_mAnd further establishing an overlapping feature constraint matrix F_MNThe establishment process is as follows:

step 201: at point X in data set X_mDrawing J sampling circles for the circle center, as shown in FIG. 3, in order to overcome the non-prominent feature of the overlap feature, more sampling circles far away from x_mTo enhance the local characteristic factor fx_mSensitivity to local features makes it easier to distinguish the best match from data set X and data set Y, and therefore, for point X_mThe radius of the jth sampling circle of (a) is as follows:

（Ⅰ）

in formula I, r_mjIs the radius of the jth sampling circle, r_mJRadius of the maximum sampling circle, r_m1Is the radius of the minimum sampling circle, J is the number of sampling circles, Ln (J) is a logarithmic function of a variable J, and Ln (J) is a logarithmic function value of a fixed value J; the sampling radius of the sampling circle is shown in fig. 4;

step 202: as shown in FIG. 3, let the sampling point corresponding to the jth sampling radius be Sp_jPoint x_mAll sampling point sets SP of^m=（Sp₁,…,Sp_j,…,Sp_J) Constructed with a point x_mCovariance matrix C of_mAs shown in the formula II,

（Ⅱ）

in formula II, C_mIs a point x_mOf (2) covariance matrix, Sp_jIs a sampling point corresponding to the jth sampling circle, J is a point x_mThe number of all sampling points is the number of sampling circles;

step 203: solving out covariance matrix C_mλ 1 and λ 2, and λ 1 ≧ λ 2, point x_mLocal characteristic factor fx of_m=λ1/λ2；

Step 204: calculating the local characteristic factors of M points in the data set X in sequence according to the steps 201 to 203, wherein the data set of the local characteristic factors of the data set X is F_X=（fx₁,…,fx_m,…,fx_M) (ii) a And calculating a local feature factor data set F of the data set Y_Y=（fy₁,…,fy_n,…,fy_N）；

Step 205: constructing an overlap feature constraint matrix F between datasets X and Y_MNOverlap feature constraint matrix F_MNThe element in the m-th row and the n-th column is f_mn=∣fx_m-fy_n∣，f_mnFor a point X in the data set X_mWith point Y in data set Y_nLocal feature similarity, and sequentially calculating an overlapped feature constraint matrix F_MN。

Step 300: establishing a local distance constraint matrix D_MNAs shown in FIG. 5, at point x_mAs a reference point, and in x_mAs a circle center and the radius of which is specified to be Cr_mIs a point x_mBy controlling the radius Cr_mCan flexibly specify the point x_mLocal space, local distance constraint matrix D_MNThe establishment process is as follows:

step 301: let the distance matrix d between dataset X and dataset Y_MNDistance matrix d_MNM-th row and n-th column element d_mnIs a point x_mAnd point y_nThe euler distance therebetween;

step 302: searching for a distance matrix d_MNMinimum value in each row of, e.g., dis as shown in FIG. 4_m，dis_mIs a point x_mAnd point y_nMinimum value between, and constitutes a minimal value data set Dis = (Dis) of distance₁,…,dis_m,…,dis_M) Calculating the average value Dd of the minimum value data set Dis,

（Ⅳ）

in the formula IV, Dd is an average value of the minimum value data set Dis, and M is the minimum value number in the minimum value data set Dis;

step 303: will distance matrix d_MNMiddle greater than restraint radius Cr_mIs set to 0 and is less than or equal to the constraint radius Cr_mIs set to 1, a local distance constraint matrix D is established_MN(ii) a Wherein the radius of constraint Cr_m= γ R × Dd, γ R is an amplification factor, the amplification factor value in this embodiment is 10, Dd is an average value of the minimum value data set Dis, and the local distance constraint matrix D_MNM-th row and n-th column element D_mnComprises the following steps:

（Ⅴ）

in formula V, D_mnConstraining the matrix D for local distances_MNThe element of the m-th row and the n-th column; d_mnIs a distance matrix d_MNElement of m-th row and n-th column, Cr_mIs a constraint radius; completing the distance matrix d according to a formula_MNThe judgment of all elements can solve the local distance constraint matrix D_MN。

Step 400: constraining the feature bundle matrix F by overlapping based on the Hadamard product between the matrices_MNAnd a local distance constraint matrix D_MNConstructing a membership probability matrix P between data set X and data set Y_MNI.e. P_MN=F_MN

D_MN，

Is the product of Hadamard, P_MNThe m-th row and the n-th column of the element are p_mn=f_mn×d_mn，f_mnAnd d_mnAre respectively F_MNAnd D_MNRow m and column n elements in (1); updating the membership probability matrix P_MNThe updating steps are as follows:

step 401: the member probability matrix P_MNAll non-0 elements in (a) are included under the framework of a gaussian function, as shown in equation iii,

（Ⅲ）

in formula III, p_mnIs a member probability matrix P_MNM-th row and n-th column element, delta_F ²Is a member probability matrix P_MNThe variance of the non-0 term in the middle,

d =2 is the dimension of the point set to be registered, and W is the member probability matrix P_MNThe number of non-0 elements;

step 402: for member probability matrix P_MNAll the elements in the solution are normalized; let the current membership probability matrix P_MNThe sum of the m-th row elements is S_mMember probability matrix P_MNAny element in the m-th row is updated to p_mn=p_mn/S_mAnd sequentially updating the member probability matrix P_MN。

Membership probability matrix P_MNRespectively calculating a density function between each point in the data set (X) and all points in the data set (Y) to be registered by taking one data set (X) as a Gaussian kernel, and constructing a fully-connected Gaussian kernel function between all points in the two data sets; a maximum likelihood function is further constructed. In this embodiment, the data set X is used as the Gaussian kernel, and all rotation and translation are applied to the data set Y, so that the point X_mDensity function P (x)_m) Comprises the following steps:

（Ⅵ）

in formula VI, P (x)_m) Is a point x_mA is the noise ratio, and M is in the data set XTotal number of data of p_mnIs a member probability matrix P_MNThe element of the m-th row and the n-th column;

for conditional probability, σ is variance, D =2 is dataset dimension, x_mFor the mth data in data set X, dR_XYTo rotate the matrix, y_nFor the nth data in data set Y, dT_XYFor the translation matrix, the maximum likelihood function is further constructed as:

（Ⅶ）

in formula VII, P (X) is an exponent of the logarithmic function Ln, P (X) is a density function of the data set X, P (y)_n) Is a member probability p_mn，P（x_m∣y_n) Is a conditional probability.

Step 500: computing a rotation matrix dR between data sets X and Y based on an EM algorithm_XYAnd a translation matrix dT_XYAnd splicing the section profile characteristics of the blade through the calculated rotation matrix and translation matrix.

Computing a rotation matrix dR between data sets X and Y based on an EM algorithm_XYAnd a translation matrix dT_XYThe method comprises the following specific steps:

step 501: initialization of parameters, initializing a rotation matrix

Translation matrix

Iteration threshold ξ =10^-5The noise ratio alpha =0.01, and the noise ratio is related to the parameters of the line laser sensor;

step 502: the membership probability matrix P calculated according to the steps 100 to 400_MNUpdating a density function and a maximum likelihood function; calculating a membership probability matrix P_MNSum of all elements in S_PAnd respectively calculating the weight centers of the data set X and Y

And

，

is a member probability matrix P_MNThe column vector of all the middle elements is 1, and then the center mu is determined according to the weight_XAnd mu_YCalculating the central vectors of the data set X and the data set Y

And

，

is a member probability matrix P_MNRow vectors with all the middle elements being 1;

step 503: a covariance matrix Cov between the data set X and the data set Y is calculated from the central vector,

then, singular value decomposition is carried out on the covariance matrix Cov, and the decomposition result is set as

U and V are matrixes decomposed by singular values;

step 504: setting matrix

Wherein det (UV)^T) As matrices U and V^TThe product between corresponds to the value of the determinant, the rotation matrix between the data sets X and Y is dR_XY=UηV^TThe translation matrix is dT_XY=μ_X-dR_XYμ_Y(ii) a Updating the rotation matrix to dR^t _XY=dR^t-1 _XYdR_XYWherein dR^t-1 _XYFor the rotation matrix obtained from the previous iteration, dR if the current iteration is the first iteration^t-1 _XYFor initialising the rotation matrix dR⁰ _XYUpdate the translation matrix dT similarly^t _XYCalculating Y according to the updated rotation matrix and translation matrix^new=dR^t _XYX+dT^t _XY；

Step 505: calculating convergence coefficient as d τ = | dT^t _XY-dT^t-1 _XYII, wherein dT^t-1 _XYThe translation matrix calculated for the previous iteration, if the first iteration, then dT^t-1 _XYIt is to initialize the translation matrix dT⁰ _XY. If the convergence coefficient is larger than the iteration coefficient, namely d tau is larger than or equal to xi, repeating the steps 501 to 504 to iterate until d tau is smaller than xi, and stopping the iteration.

Optimal rotation matrix dR updated based on multiple iterations_XYAnd Y^newSeparately calculate Y at this time^newAnd the center of gravity of the data set Y, and solving a translation vector between the two centers of gravity to obtain a final translation matrix dT between X and Y_XYAnd finally completing the registration between X and Y. The currently calculated dR_XYAnd dT_XYThe original data V1 and V2 are fed back to update the detection data V2^newComprises the following steps: v2^new=dR_XYV1+dT_XY。

Sequentially extracting the point cloud data sets of the overlapping areas between the adjacent view fields until the original point cloud data sets of all the view fields are updated, namely completing the multi-view-field data registration and accurate reconstruction of the blade profile, as shown in fig. 6, wherein a is a result of the registration of fig. 1a by adopting the method of the embodiment, b is a result of the registration of fig. 1b by adopting the method of the embodiment, and the result of the point cloud data registration of the adjacent view fields is obviously prior to the result of the motion accuracy registration by using the motion platform; and carrying out deviation analysis on the obtained blade profile and the CAD model of the blade, and finally finishing the precision detection and evaluation of the blade.

The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any modification and replacement based on the technical solution and inventive concept provided by the present invention should be covered within the scope of the present invention.

Claims (3)

1. A blade multi-field point cloud registration method based on overlapping features and local distance constraints is characterized by comprising the following steps:

step 100: acquiring point cloud data of multiple fields of view of the blade, solving an overlapping area of the point cloud data between two adjacent fields of view, and constructing a data set X = (X) of the overlapping area₁,…,x_m,…,x_M) And Y = (Y)₁,…,y_n,…y_N）；

Step 200: establishing an overlap feature constraint matrix F_MN；

First, with point X in data set X_mDrawing J sampling circles as the center of the circle, and centering on a point x_mThe radius of the jth sampling circle of (a) is as in formula i,

（Ⅰ）

in formula I, r_mjIs the radius of the jth sampling circle, r_mJRadius of the maximum sampling circle, r_m1Is the radius of the minimum sampling circle, J is the number of sampling circles, Ln (J) is a logarithmic function of a variable J, and Ln (J) is a logarithmic function value of a fixed value J;

then, construct point x_mCovariance matrix C of_mAs shown in the formula II,

（Ⅱ）

in formula II, C_mIs a point x_mOf (2) covariance matrix, Sp_jA sampling point corresponding to the jth sampling circle;

secondly, solving a covariance matrix C_mλ 1 and λ 2, and λ 1 ≧ λ 2, point x_mLocal characteristic factor fx of_m= λ 1/λ 2; sequentially calculating local characteristic factors of M points in the data set X, wherein the data set of the local characteristic factors of the data set X is F_X=（fx₁,…,fx_m,…,fx_M) (ii) a And calculating a local feature factor data set F of the data set Y_Y=（fy₁,…,fy_n,…,fy_N）；

Finally, an overlap feature constraint matrix F between the data sets X and Y is constructed_MNOverlap feature constraint matrix F_MNThe element in the m-th row and the n-th column is f_mn=∣fx_m-fy_n∣，f_mnFor a point X in the data set X_mWith point Y in data set Y_nLocal feature similarity, and sequentially calculating an overlapped feature constraint matrix F_MN；

Step 300: establishing a local distance constraint matrix D_MN；

First, let a distance matrix d between data set X and data set Y_MNDistance matrix d_MNM-th row and n-th column element d_mnIs a point x_mAnd point y_nThe euler distance therebetween;

then, a distance matrix d is searched_MNMinimum value in each line, and constitutes a minimal value data set Dis = (Dis) of distances₁,…,dis_m,…,dis_M) Calculating the average value Dd of the minimum value data set Dis;

finally, the distance matrix d_MNSetting the value of the middle distance larger than the constraint radius Crm as 0, setting the value of the middle distance smaller than or equal to the constraint radius Crm as 1, and establishing a local distance constraint matrix D_MN(ii) a Wherein the constraint radius Crm = γ R × Dd, γ R is an amplification factor, and Dd is an average value of the minimum data set Dis;

step 400: constraining the feature bundle matrix F by overlapping based on the Hadamard product between the matrices_MNAnd a local distance constraint matrix D_MNConstructing a membership probability matrix P between data set X and data set Y_MNI.e. P_MN=F_MN

D_MN，

Is the product of Hadamard, P_MNThe m-th row and the n-th column of the element are p_mn=f_mn×d_mn，f_mnAnd d_mnAre respectively F_MNAnd D_MNRow m and column n elements in (1); updating the membership probability matrix P_MNThe method comprises the following steps:

first, a membership probability matrix P_MNAll non-0 elements in (a) are included under the framework of a gaussian function, as shown in equation iii,

（Ⅲ）

in formula III, p_mnIs a member probability matrix P_MNM-th row and n-th column element, delta_F ²Is a member probability matrix P_MNThe variance of the non-0 term in the middle,

d =2 is the dimension of the point set to be registered, and W is the member probability matrix P_MNThe number of non-0 elements;

then to the member probability matrix P_MNAll the elements in the solution are normalized; let the current membership probability matrix P_MNThe sum of the m-th row elements is S_mThen member probability matrix P_MNAny element in the m-th row is updated to p_mn=p_mn/S_mAnd sequentially updating the member probability matrix P_MNAll of the elements in (A);

step 500: and calculating a rotation matrix and a translation matrix between the data sets X and Y based on an EM algorithm, and splicing the section profile of the blade through the calculated rotation matrix and translation matrix.

2. The blade multi-field point cloud registration method based on the overlapped features and the local distance constraint according to claim 1, wherein: in step 100, solving an overlapping area of point cloud data between two adjacent fields of view and constructing a data set of the overlapping area comprises the following steps:

step 101: setting two adjacent point cloud data sets as V₁And V₂By a point cloud data set V₁End point V of_1HFor reference points, points V are calculated separately_1HWith the point cloud data set V₂The distance between all the points is solved, and the point corresponding to the minimum distance value is solved as V_2pPoint cloud data set V₂The overlap region data set Y is the point cloud data set V₂End point V of_2PAnd V_2pAll points in between;

step 102: in the same way, with a point cloud data set V₂End point V of_2PFor reference points, points V are calculated separately_2PWith the point cloud data set V₁The distance between all the points is solved, and the point corresponding to the minimum distance value is solved as V_1hPoint cloud data set V₁The overlap region data set X is the point cloud data set V₁End point V of_1HAnd V_1hAll points in between.

3. The blade multi-field point cloud registration method based on the overlapped features and the local distance constraint according to claim 1, wherein: in step 500, the rotation matrix and the translation matrix between the data sets X and Y are calculated based on the EM algorithm according to the following steps:

step 501: initializing parameters, setting a rotation matrix as

And translation matrix

Iteration threshold xi and noise ratio alpha;

step 502: calculating a membership probability matrix P_MNThe sum of all elements in the composition is S_PAnd respectively calculating the weight centers mu of the data set X and the data set Y_XAnd mu_YThen according to the weight center mu_XAnd mu_YCalculate the center of data set X and data set YVector quantity;

step 503: calculating a covariance matrix Cov between the data set X and the data set Y according to the central vector, then performing singular value decomposition on the covariance matrix Cov, and updating a rotation matrix and a translation matrix according to a singular value decomposition result;

step 504: calculating a convergence coefficient d tau according to the updated rotation matrix and translation matrix, comparing the convergence coefficient d tau with an iteration threshold xi, repeating the steps 501 to 503 to iterate when d tau is larger than or equal to xi, stopping iterating until d tau is smaller than xi, and outputting an optimal rotation matrix and translation matrix between the data sets X and Y.

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