CN110245395B

CN110245395B - Method, system and medium for monitoring cylindrical shape error with spatial correlation

Info

Publication number: CN110245395B
Application number: CN201910457490.0A
Authority: CN
Inventors: 杜世昌; 赵晨; 邓亚飞; 李贵龙
Original assignee: Shanghai Jiaotong University
Current assignee: Shanghai Jiaotong University
Priority date: 2019-05-29
Filing date: 2019-05-29
Publication date: 2021-02-12
Anticipated expiration: 2039-05-29
Also published as: CN110245395A

Abstract

The invention provides a method, a system and a medium for monitoring cylindrical shape errors with spatial correlation, wherein the method comprises the following steps: surface measurement: measuring the surface of the cylinder to obtain three-dimensional coordinate data of a measuring point; and (3) data processing: obtaining an error value of the measuring point according to the obtained three-dimensional coordinate data of the measuring point; and a spatial correlation judgment step: and judging whether the error value of the measuring point has spatial correlation or not according to the obtained error value of the measuring point, and obtaining a spatial correlation judgment result. The monitoring of the geometric error of the cylinder with the spatial correlation provided by the invention can reflect the form of the processing error more accurately, remove the influence of the spatial correlation on the measurement result and effectively improve the identification rate of unqualified products. The defects that the traditional cylinder quality monitoring cannot reflect the geometric shape of the cylinder and the spatial correlation caused by a large number of measuring points are overcome.

Description

Method, system and medium for monitoring cylindrical shape error with spatial correlation

Technical Field

The invention relates to the technical field of quality monitoring of cylindrical parts, in particular to a method, a system and a medium for monitoring cylindrical shape errors with spatial correlation.

Background

Form and position errors are important control objects of mechanical parts in modern manufacturing, and directly influence the quality of products. The shape error of the cylinder is an important index of the high-precision rotating part. The improvement of the manufacturing accuracy puts higher demands on the accurate measurement of the error of the cylindrical shape. The traditional accuracy index of the error of the cylindrical shape is cylindricity, and the measuring method comprises a two-point method, a three-coordinate measuring method, a measuring method of connecting a data acquisition instrument with a dial indicator and the like. The methods consider the actual cylindrical surface to determine the minimum containing area (the two coaxial cylindrical surfaces with the minimum radius difference contain all the actual cylindrical surface elements) as the evaluation index of the cylindricity. Cylindricity, however, provides only an overall range of errors in the shape of a cylinder and does not describe its geometric information. The geometric error of the cylinder can be analyzed to describe the shape of the cylinder more truly and thoroughly, and the detection precision is improved.

Three-coordinate measurement methods can measure the coordinates of a large number of points on the surface of a part, providing a large amount of data for analysis of the shape of a cylinder. However, under such large-scale, high-dimensional and complex data collection, strong spatial correlation exists between data, and the data cannot be directly used. Modeling analysis is carried out on the data with the characteristics, so that the detection precision of the cylindrical shape can be improved, and guidance is provided for the improvement of the part machining process.

In the prior art, the invention patent with the patent number of CN201310227766.9 entitled "method for evaluating error of cylindricity of part based on minimum region" provides a method for evaluating error of cylindricity of part based on minimum region, and provides a method for judging error containing region, which can accurately calculate error of cylindricity meeting minimum region. However, the method does not consider the geometric shape information of the cylinder, and the geometric shape of the cylinder cannot be obtained, so that whether the cylindrical part is qualified or not is difficult to accurately identify.

Zhang in the article "Unified functional systematic approach for precision cylindrical components" ("International Journal of Production Research" in 2005, Vol.43, No. 1, p.25-43) proposes Fourier-Legendre model to represent the geometry of the cylinder, which can accurately represent the periodic fluctuation of the geometry of the cylinder and reveal the detailed information of the cylinder. However, this method cannot evaluate the processing quality because of spatial correlation between the measurement points.

Disclosure of Invention

In view of the defects in the prior art, the present invention provides a method, a system and a medium for monitoring a cylindrical shape error with spatial correlation.

The invention provides a method for monitoring a cylindrical shape error with spatial correlation, which comprises the following steps:

surface measurement: measuring the surface of the cylinder to obtain three-dimensional coordinate data of a measuring point;

and (3) data processing: obtaining an error value of the measuring point according to the obtained three-dimensional coordinate data of the measuring point;

and a spatial correlation judgment step: judging whether the error value of the measuring point has spatial correlation or not according to the obtained error value of the measuring point, and obtaining a spatial correlation judgment result;

establishing an error model: establishing a cylindrical shape error model according to the obtained space correlation judgment result;

a system error term determining step: dividing the error value of the measuring point into a systematic error term and a random error term according to the obtained error value of the measuring point, decomposing the error value and determining the systematic error term;

model parameter estimation: performing parameter estimation on the cylindrical shape error model according to the obtained system error term to obtain a parameter estimation value;

a process monitoring step: and acquiring a monitoring process control chart according to the acquired parameter estimation value, and monitoring the cylindrical profile.

Preferably, the data processing step:

converting the coordinates of the measuring points under the three-dimensional rectangular coordinate system into coordinates of a polar coordinate system, fitting the circle center and the radius of the cylinder by using a least square method, and subtracting the standard radius of the cylinder from the radius value of the polar coordinate of the measuring points to obtain the error value of the measuring points, wherein the calculation formula is as follows:

y＝r(z,θ)-R

wherein the content of the first and second substances,

y represents an error value of the measurement point;

r (z, theta) represents the value of the radius of the polar coordinate of the measuring point at the height of z and the angle of theta;

r, z and theta are respectively the radius, height and angle values of a measuring point under a polar coordinate system;

and R is the standard radius of an ideal cylinder.

Preferably, the spatial correlation determination step:

and (3) carrying out spatial autocorrelation analysis on the error values of the measuring points, and judging whether the test statistic is significant: if the test statistic is significant, the error values have spatial correlation, and a spatial correlation judgment result is output; if the test statistic is not significant, no spatial correlation exists between the error values, and a spatial correlation judgment result is output.

Preferably, the error model establishing step:

according to the obtained space correlation judgment result, if the space correlation does not exist, a least square regression model is established to be used as a cylindrical shape error model; if the spatial correlation exists, establishing a spatial autocorrelation model as a cylindrical shape error model;

the least squares regression model refers to a model that does not include an error term representing spatial correlation, and the expression is as follows:

y＝Xβ+ε

wherein the content of the first and second substances,

y represents an error value of the measurement point;

ε represents a random error term;

x β represents a systematic error term;

in the spatial autocorrelation model, the error value of a measuring point consists of three parts, namely an adjacent point error term, a system error term and a random error term, and the expression is as follows:

wherein the content of the first and second substances,

y represents an error value of the measurement point;

p represents the overall order of the spatial weight matrix;

s denotes the order of the spatial weight matrix, s ═ 1,2,3, …, p;

ε represents a random error term;

rho represents an unknown lag coefficient and is used for measuring the strength of spatial correlation between error values, and the stronger the rho is close to 0, the weaker the correlation is, and the stronger the rho is;

W^(s)representing an s-order spatial weight matrix, i.e. the weights of a certain point and a distance s from itIs 1, the rest is 0;

representing the spatial adjacency condition of the tth measuring point and the qth measuring point, if | t-q | ≦ s

If t-q->s, then

t represents the tth measurement point;

q represents the qth measurement point;

n represents a total of N measurement points;

x β represents a systematic error term;

ε represents a random error term, obeying a normal distribution of ε -N (0, σ)²) And σ represents a standard deviation.

Preferably, the systematic error term determining step:

dividing the error value of the measuring point into a systematic error term and a random error term according to the obtained error value of the measuring point and the periodicity of the systematic error term, performing Fourier decomposition on the error value, separating the systematic error term and the random error term, and determining the systematic error term, wherein the calculation formula is as follows:

wherein the content of the first and second substances,

x beta represents a system error term, namely the product of an X matrix and a beta matrix, namely the matrix multiplication of a Fourier-Legendre polynomial matrix and a coefficient;

x represents a matrix of all Fourier-Legendre polynomials contained in the error term, i.e. [ P ]_j(z)cos(iθ)P_j(z)sin(iθ)]；

Beta represents the coefficient matrix of the systematic error term, i.e. [ A ]_ijB_ij]′；

m represents the order of the fourier polynomial of the cylindrical axial variation;

n represents the order of the Legendre polynomial of the cylindrical radial variation;

P_j(z) denotes a legendre polynomial of degree j at the axial coordinate z;

A_ijrepresenting polynomial coefficients;

B_ijrepresenting polynomial coefficients;

j is the order of the legendre polynomial, j is 0,1,2, …, n;

i is the order of the fourier polynomial, i is 0,1,2, …, m;

t represents the number of axial measurement points;

u represents the number of radial measurement points;

k represents the axial kth measurement point;

l denotes the radial ith measurement point;

r_klrepresenting the measurement value of the axial k-th and radial l-th sampling points;

P_j(z_l) Representing an axial description function Legendre polynomial;

z_laxial coordinates representing the ith sample point;

Δ θ represents the radial sampling interval;

the expression of the legendre polynomial is as follows:

P₀(z)＝1

P₁(z)＝z

…

the differential form is:

wherein the content of the first and second substances,

d represents a differential sign;

z represents the axial coordinate of the sampling point;

j represents the order of the legendre polynomial.

Preferably, the model parameter estimation step:

and performing parameter estimation on the cylindrical shape error model according to the obtained system error term:

when parameter estimation is carried out, firstly, assuming that spatial correlation can be represented by a first-order spatial weight matrix, namely s is 1, the spatial correlation can be brought into a spatial autocorrelation model for parameter estimation, whether the residual error items still have spatial correlation is checked, if the spatial correlation still exists, a second-order spatial weight matrix is added, namely s is 2, and the process is repeated until the checking result shows that the spatial correlation does not exist in the residual error items;

the likelihood function is maximized by a nonlinear optimization method, and the obtained parameter estimation value is expressed as follows:

c＝[ρ₁…ρ_sA₁…A_ijB₁…B_ij]

wherein the content of the first and second substances,

c represents a parameter estimation value matrix;

[. cndot. ] represents a matrix symbol;

ρ_srepresenting s-term lag coefficients, i.e. an s-order spatial weight matrix W^(s)The corresponding coefficients;

A_ijexpressing the coefficients of an i-th order Fourier j-th order Legendre polynomial;

B_ijexpressing the coefficients of an i-th order Fourier j-th order Legendre polynomial;

the likelihood function expression is:

wherein the content of the first and second substances,

L(y|ρ,β,σ²) Representing a likelihood function;

sigma represents the standard deviation epsilon-N (0, sigma) of the random error term epsilon²)；

N represents the number of measurement points;

I_Nan identity matrix representing order N;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

tab-in A_ijAnd B_ijTo the likelihood function L (y | ρ, β, σ)²) In the method, a rho value at the maximum value of the likelihood function is obtained by a nonlinear optimization method.

Preferably, the process monitoring step:

designing a multivariate T of the monitoring parameters according to the obtained parameter estimation value c²Control chart and unitary control chart for monitoring residuals, using a multivariate T²Control chart pair T²Monitoring is carried out, T²The statistic calculation formula is as follows:

T²＝(c-μ)^T∑^-1(c-μ)

wherein the content of the first and second substances,

T²representing control chart statistics;

μ represents the mean value of c;

superscript T represents matrix transposition;

Σ represents the covariance matrix of c;

∑^-1represents the inverse of the covariance matrix of c;

the upper control line UCL1 is:

wherein the content of the first and second substances,

UCL1 denotes T²The upper control line of (1);

expressing chi-square distribution with quantile alpha and degree of freedom c;

α' represents a false positive rate;

α represents a first class error probability;

and monitoring the estimated variance of the residual estimated value by using a unitary control chart, and calculating the residual estimated value by using the following calculation formula:

e＝(I-ρW)y-Xβ

e represents a residual estimate;

i represents an identity matrix;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

y represents an actual measurement value;

x represents a systematic error term;

β represents a coefficient of a systematic error term;

and calculating the estimation variance of the residual estimation value according to the following calculation formula:

σ²representing the estimated variance of the residual estimate;

e' represents an inverse matrix of the residual estimate;

n represents the number of measuring points;

estimated variance σ for residual estimates²Monitoring is carried out, and the upper control line and the lower control line are as follows:

UCL2 denotes σ²The upper control line of (1);

LCL stands for σ²A lower control line of (a);

χ²representing a chi-square distribution;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

using multivariate T based on the obtained UCL1, UCL2, LCL²Control chart pair T²Values are monitored, residual variance σ is monitored using a univariate control chart²The value of (c) is monitored.

According to the invention, the monitoring system of the cylindrical shape error with the spatial correlation comprises:

a surface measurement module: measuring the surface of the cylinder to obtain three-dimensional coordinate data of a measuring point;

a data processing module: obtaining an error value of the measuring point according to the obtained three-dimensional coordinate data of the measuring point;

a spatial correlation determination module: judging whether the error value of the measuring point has spatial correlation or not according to the obtained error value of the measuring point, and obtaining a spatial correlation judgment result;

an error model establishing module: establishing a cylindrical shape error model according to the obtained space correlation judgment result;

a systematic error term determination module: dividing the error value of the measuring point into a systematic error term and a random error term according to the obtained error value of the measuring point, decomposing the error value and determining the systematic error term;

a model parameter estimation module: performing parameter estimation on the cylindrical shape error model according to the obtained system error term to obtain a parameter estimation value;

a process monitoring module: and acquiring a monitoring process control chart according to the acquired parameter estimation value, and monitoring the cylindrical profile.

Preferably, the data processing module:

y＝r(z,θ)-R

wherein the content of the first and second substances,

y represents an error value of the measurement point;

r is the standard radius of an ideal cylinder;

the spatial correlation determination module:

and (3) carrying out spatial autocorrelation analysis on the error values of the measuring points, and judging whether the test statistic is significant: if the test statistic is significant, the error values have spatial correlation, and a spatial correlation judgment result is output; if the test statistic is not significant, no spatial correlation exists between the error values, and a spatial correlation judgment result is output;

the error model establishing module:

y＝Xβ+ε

wherein the content of the first and second substances,

y represents an error value of the measurement point;

ε represents a random error term;

x β represents a systematic error term;

wherein the content of the first and second substances,

y represents an error value of the measurement point;

p represents the overall order of the spatial weight matrix;

s denotes the order of the spatial weight matrix, s ═ 1,2,3, …, p;

ε represents a random error term;

W^(s)representing an s-order spatial weight matrix, namely the weight of a certain point and a point which is separated by s is 1, and the rest is 0;

denotes the t thThe adjacent space between the measurement point and the qth measurement point is less than or equal to s

If t-q->s, then

t represents the tth measurement point;

q represents the qth measurement point;

n represents a total of N measurement points;

x β represents a systematic error term;

ε represents a random error term, obeying a normal distribution of ε -N (0, σ)²) And σ represents the standard deviation;

the systematic error term determination module:

wherein the content of the first and second substances,

P_j(z) denotes a legendre polynomial of degree j at the axial coordinate z;

A_ijrepresenting polynomial coefficients;

B_ijrepresenting polynomial coefficients;

j is the order of the legendre polynomial, j is 0,1,2, …, n;

i is the order of the fourier polynomial, i is 0,1,2, …, m;

t represents the number of axial measurement points;

u represents the number of radial measurement points;

k represents the axial kth measurement point;

l denotes the radial ith measurement point;

P_j(z_l) Representing an axial description function Legendre polynomial;

z_laxial coordinates representing the ith sample point;

Δ θ represents the radial sampling interval;

the expression of the legendre polynomial is as follows:

P₀(z)＝1

P₁(z)＝z

…

the differential form is:

wherein the content of the first and second substances,

d represents a differential sign;

z represents the axial coordinate of the sampling point;

j represents the order of the legendre polynomial;

the model parameter estimation module:

c＝[ρ₁…ρ_sA₁…A_ijB₁…B_ij]

wherein the content of the first and second substances,

c represents a parameter estimation value matrix;

[. cndot. ] represents a matrix symbol;

the likelihood function expression is:

wherein the content of the first and second substances,

L(y|ρ,β,σ²) Representing a likelihood function;

N represents the number of measurement points;

I_Nan identity matrix representing order N;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

tab-in A_ijAnd B_ijTo the likelihood function L (y | ρ, β, σ)²) In the method, a rho value of the maximum value of the likelihood function is obtained by a nonlinear optimization method;

the process monitoring step:

T²＝(c-μ)^T∑^-1(c-μ)

wherein the content of the first and second substances,

T²representing control chart statistics;

μ represents the mean value of c;

superscript T represents matrix transposition;

Σ represents the covariance matrix of c;

∑^-1represents the inverse of the covariance matrix of c;

the upper control line UCL1 is:

wherein the content of the first and second substances,

UCL1 denotes T²The upper control line of (1);

expressing chi-square distribution with quantile alpha and degree of freedom c;

α' represents a false positive rate;

α represents a first class error probability;

e＝(I-ρW)y-Xβ

e represents a residual estimate;

i represents an identity matrix;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

y represents an actual measurement value;

x represents a systematic error term;

β represents a coefficient of a systematic error term;

σ²representing the estimated variance of the residual estimate;

e' represents an inverse matrix of the residual estimate;

n represents the number of measuring points;

UCL2 denotes σ²The upper control line of (1);

LCL stands for σ²A lower control line of (a);

χ²representing a chi-square distribution;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

According to the present invention, there is provided a computer-readable storage medium storing a computer program, which when executed by a processor implements the steps of the method for monitoring a cylindrical shape error with spatial correlation according to any one of the above.

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

1. the invention analyzes the outline shape of the cylinder, can describe the shape of the cylinder more truly and thoroughly, and improve the detection precision;

2. the invention considers the spatial correlation among large-scale measuring points and weakens the influence of the spatial correlation on the accuracy of the measured data;

3. the invention combines a plurality of control charts to monitor the cylinder quality, can comprehensively reflect the state of the production process and take corrective measures in time.

4. The monitoring of the geometric error of the cylinder with the spatial correlation provided by the invention can reflect the form of the processing error more accurately, remove the influence of the spatial correlation on the measurement result, effectively improve the recognition rate of unqualified products, and improve the defects that the traditional cylinder quality monitoring can not reflect the geometric shape of the cylinder and the spatial correlation caused by a large number of measurement points.

Drawings

Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:

FIG. 1 is a schematic flow chart of a method for monitoring a cylindrical shape error with spatial correlation according to the present invention;

FIG. 2 is a schematic diagram of measuring point selection according to the present invention;

FIG. 3 is a schematic diagram of the error in the shape of a cylindrical bore of an engine block according to specification requirements measured according to a three-coordinate measurement technique provided by the present invention;

FIG. 4 is a schematic illustration of an engine block cylindrical bore shape error that is off specification as measured according to a three coordinate measurement technique as provided by the present invention;

FIG. 5 is a schematic diagram illustrating the process control for detecting a cylindrical hole of an engine cylinder according to specification requirements provided by the present invention;

FIG. 6 is a schematic diagram of the process control for detecting a cylinder bore of an engine block that does not meet the specification requirements provided by the present invention.

Detailed Description

The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.

Specifically, the data processing step:

y＝r(z,θ)-R

wherein the content of the first and second substances,

y represents an error value of the measurement point;

and R is the standard radius of an ideal cylinder.

Specifically, the spatial correlation determination step:

Specifically, the error model establishing step:

y＝Xβ+ε

wherein the content of the first and second substances,

y represents an error value of the measurement point;

ε represents a random error term;

x β represents a systematic error term;

wherein the content of the first and second substances,

y represents an error value of the measurement point;

p represents the overall order of the spatial weight matrix;

s denotes the order of the spatial weight matrix, s ═ 1,2,3, …, p;

ε represents a random error term;

If t-q->s, then

t represents the tth measurement point;

q represents the qth measurement point;

n represents a total of N measurement points;

x β represents a systematic error term;

Specifically, the system error term determining step:

wherein the content of the first and second substances,

P_j(z) denotes a legendre polynomial of degree j at the axial coordinate z;

A_ijrepresenting polynomial coefficients;

B_ijrepresenting polynomial coefficients;

j is the order of the legendre polynomial, j is 0,1,2, …, n;

i is the order of the fourier polynomial, i is 0,1,2, …, m;

t represents the number of axial measurement points;

u represents the number of radial measurement points;

k represents the axial kth measurement point;

l denotes the radial ith measurement point;

P_j(z_l) Representing an axial description function Legendre polynomial;

z_laxial coordinates representing the ith sample point;

Δ θ represents the radial sampling interval;

the expression of the legendre polynomial is as follows:

P₀(z)＝1

P₁(z)＝z

…

the differential form is:

wherein the content of the first and second substances,

d represents a differential sign;

z represents the axial coordinate of the sampling point;

j represents the order of the legendre polynomial.

Specifically, the model parameter estimation step:

c＝[ρ₁…ρ_sA₁…A_ijB₁…B_ij]

wherein the content of the first and second substances,

c represents a parameter estimation value matrix;

[. cndot. ] represents a matrix symbol;

the likelihood function expression is:

wherein the content of the first and second substances,

L(y|ρ,β,σ²) Representing a likelihood function;

N represents the number of measurement points;

I_Nan identity matrix representing order N;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix; further, W represents a spatial weight matrix of a certain order, and the calculation is started from the spatial weight matrix of the first order, that is, W is W⁽¹⁾Checking whether the residual error item still has spatial correlation, if the residual error item still has spatial correlation, adding a second-order spatial weight matrix, namely W ═ W⁽²⁾This process is repeated until the test results show that there is no spatial correlation in the remaining error terms.

Tab-in A_ijAnd B_ijTo the likelihood function L (y | ρ, β, σ)²) In the method, a rho value at the maximum value of the likelihood function is obtained by a nonlinear optimization method. Further, ρ_sIs an s-order spatial weight matrix W^(s)Corresponding coefficients, ρ being the coefficients corresponding to a spatial weight matrix of a certain order, i.e. calculated from the first order spatial weight matrix W⁽¹⁾Initially, the corresponding ρ is calculated₁If there is still a null, checking whether the residual error term still has spatial correlationThe inter-correlation is added to a second-order spatial weight matrix, i.e., W ═ W⁽²⁾Calculating corresponding rho₂Until the test results show that there is no spatial correlation in the remaining error terms.

Further, the likelihood function is

The likelihood function of (2).

Specifically, the process monitoring step:

T²＝(c-μ)^T∑^-1(c-μ)

wherein the content of the first and second substances,

T²representing control chart statistics;

μ represents the mean value of c;

superscript T represents matrix transposition;

Σ represents the covariance matrix of c;

∑^-1represents the inverse of the covariance matrix of c;

the upper control line UCL1 is:

wherein the content of the first and second substances,

UCL1 denotes T²The upper control line of (1);

expressing chi-square distribution with quantile alpha and degree of freedom c;

α' represents a false positive rate;

α represents a first class error probability;

e＝(I-ρW)y-Xβ

e represents a residual estimate;

i represents an identity matrix;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

y represents an actual measurement value;

x represents a systematic error term;

β represents a coefficient of a systematic error term;

σ²representing the estimated variance of the residual estimate;

e' represents an inverse matrix of the residual estimate;

n represents the number of measuring points;

UCL2 denotes σ²The upper control line of (1);

LCL stands for σ²A lower control line of (a);

χ²representing a chi-square distribution;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

Specifically, the data processing module:

y＝r(z,θ)-R

wherein the content of the first and second substances,

y represents an error value of the measurement point;

r is the standard radius of an ideal cylinder;

the spatial correlation determination module:

the error model establishing module:

y＝Xβ+ε

wherein the content of the first and second substances,

y represents an error value of the measurement point;

ε represents a random error term;

x β represents a systematic error term;

wherein the content of the first and second substances,

y represents an error value of the measurement point;

p represents the overall order of the spatial weight matrix;

s denotes the order of the spatial weight matrix, s ═ 1,2,3, …, p;

ε represents a random error term;

If t-q->s, then

t represents the tth measurement point;

q represents the qth measurement point;

n represents a total of N measurement points;

x β represents a systematic error term;

epsilon represents random error term, clothesFrom normal distribution epsilon to N (0, sigma)²) And σ represents the standard deviation;

the systematic error term determination module:

wherein the content of the first and second substances,

P_j(z) denotes a legendre polynomial of degree j at the axial coordinate z;

A_ijrepresenting polynomial coefficients;

B_ijrepresenting polynomial coefficients;

j is the order of the legendre polynomial, j is 0,1,2, …, n;

i is the order of the fourier polynomial, i is 0,1,2, …, m;

t represents the number of axial measurement points;

u represents the number of radial measurement points;

k represents the axial kth measurement point;

l denotes the radial ith measurement point;

P_j(z_l) Representing an axial description function Legendre polynomial;

z_laxial coordinates representing the ith sample point;

Δ θ represents the radial sampling interval;

the expression of the legendre polynomial is as follows:

P₀(z)＝1

P₁(z)＝z

…

the differential form is:

wherein the content of the first and second substances,

d represents a differential sign;

z represents the axial coordinate of the sampling point;

j represents the order of the legendre polynomial;

the model parameter estimation module:

c＝[ρ₁…ρ_sA₁…A_ijB₁…B_ij]

wherein the content of the first and second substances,

c represents a parameter estimation value matrix;

[. cndot. ] represents a matrix symbol;

the likelihood function expression is:

wherein the content of the first and second substances,

L(y|ρ,β,σ²) Representing a likelihood function;

N represents the number of measurement points;

I_Nan identity matrix representing order N;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

the process monitoring step:

T²＝(c-μ)^T∑^-1(c-μ)

wherein the content of the first and second substances,

T²representing control chart statistics;

μ represents the mean value of c;

superscript T represents matrix transposition;

Σ represents the covariance matrix of c;

∑^-1represents the inverse of the covariance matrix of c;

the upper control line UCL1 is:

wherein the content of the first and second substances,

UCL1 denotes T²The upper control line of (1);

expressing chi-square distribution with quantile alpha and degree of freedom c;

α' represents a false positive rate;

α represents a first class error probability;

e＝(I-ρW)y-Xβ

e represents a residual estimate;

i represents an identity matrix;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

y represents an actual measurement value;

x represents a systematic error term;

β represents a coefficient of a systematic error term;

σ²representing the estimated variance of the residual estimate;

e' represents an inverse matrix of the residual estimate;

n represents the number of measuring points;

UCL2 denotes σ²The upper control line of (1);

LCL stands for σ²A lower control line of (a);

χ²representing a chi-square distribution;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

The present invention will be described more specifically below with reference to preferred examples.

Preferred example 1:

referring to fig. 1, a method for monitoring a cylindrical error with spatial correlation includes the following steps:

step 1: and measuring the surface of the cylinder to obtain three-dimensional coordinate data of each measuring point. Measuring the surface of the cylinder at equal intervals to obtain three-dimensional coordinate data (x, y, z) of each measuring point;

step 2: and processing the data, specifically, converting the coordinates of the measuring points in the three-dimensional rectangular coordinate system into the coordinates of a polar coordinate system. And fitting the center and the radius of the cylinder by using a least square method, and subtracting the standard radius of the cylinder from the radius value of the polar coordinate of the measuring point to obtain the error between a real value and an ideal value. The error value of the measurement point is expressed as:

y＝r(z,θ)-R (1)

wherein the content of the first and second substances,

y represents an error value of the measurement point;

r, z and theta are respectively the radius, height and angle values of the measuring point under the polar coordinate system,

and R is the standard radius of an ideal cylinder.

And step 3: whether the error values have spatial correlation is determined. Specifically, a spatial correlation test is carried out on the error values, and if the test statistic is not significant, no spatial correlation exists among the error values; if the test statistic is significant, then there is spatial correlation between the error values.

And 4, step 4: and establishing a cylindrical shape error model. According to the judgment result of the step 3, if no spatial correlation exists, a least square regression model is established; and if the spatial correlation exists, establishing a spatial autocorrelation model.

In the spatial autocorrelation model, the error value of a measurement point consists of three parts, namely an adjacent point error term, a system error term and a random error term, and the expression is shown as the formula (2):

wherein the content of the first and second substances,

y represents an error value of the measurement point;

p represents the total order of the spatial weight matrix

s denotes the order of the spatial weight matrix, s 1 … p

ε represents a random error term;

and rho is an unknown lag coefficient and is used for measuring the strength of the spatial correlation between error values. The closer ρ is to 0, the weaker the correlation and vice versa.

Is an s-order spatial weight matrix, i.e. the weight of a certain point and the distance s from the point is 1, and the rest is 0. X beta is a system error term, the calculation mode is shown in step 5, epsilon is a random error term, and the obedience of epsilon-N (0, sigma)²)。

W^(s)Representing an s-th order spatial weight matrix

If t-q->s, then

t denotes the tth measurement point

q denotes the qth measurement point

N denotes a total of N measurement points

And 5: and determining a systematic error term, dividing an error value of a measuring point into the systematic error term and a random error term, and performing Fourier decomposition on the error value, wherein the systematic error term has periodicity and can determine an error source, and the random error term is a noise term. A system error term model is established using fourier-legendre equations.

The formula expression is as follows:

wherein the content of the first and second substances,

x beta represents a systematic error term, i.e. a matrix multiplication of a Fourier-Legendre polynomial with coefficients

X represents a matrix composed of all Fourier-Legendre polynomials contained in the error term, namely [ P ] in formula (3)_j(z)cos(iθ)P_j(z)sin(iθ)]

Beta represents the coefficient matrix of the systematic error term, i.e. [ A ] in equation (3)_ijB_ij]′

m represents the order of the Fourier polynomial of the axial variation of the cylinder

n represents the order of the Legendre polynomial of the radial variation of the cylinder

P_j(z) denotes a legendre polynomial of degree j at the axial coordinate z (which is meant to include the meaning of the parameters in the formula)

A_ijSystem of expression polynomialsNumber of

B_ijRepresenting polynomial coefficients

j is the order of the legendre polynomial (j is 0 … n) and i is the order of the fourier polynomial (i is 0 … m).

A_ijAnd B_ijFor polynomial coefficients, the calculation formula is as follows:

wherein the content of the first and second substances,

t represents the number of axial measurement points

u denotes the number of radial measurement points

k denotes the k-th axial measurement point

l denotes the radial ith measurement point

r_klRepresenting measured values of sampled points

P_j(z_l) Representing an axial description function Legendre polynomial; z is a radical of_lAxial coordinate representing the l-th sampling point

Delta theta denotes the radial sampling interval

The expression of the legendre polynomial is as follows:

the differential form is:

wherein z represents the axial coordinate of the sampling point, j is the order of the Legendre polynomial

Step 6: and (4) estimating model parameters, namely performing parameter estimation on the model according to the determined system error term.

In the parameter estimation, it is first assumed that the spatial correlation can be represented by a first-order spatial weight matrix, i.e., s is 1, and then the first-order spatial weight matrix is substituted into a spatial autocorrelation model to perform parameter estimation. And checking whether the residual error terms still have spatial correlation, and adding a second-order spatial weight matrix if the spatial correlation still exists, namely s is 2. This process is repeated until the test results show that there is no spatial correlation in the remaining error terms.

c＝[ρ₁…ρ_sA₁…A_ijB₁…B_ij] (8)

wherein the content of the first and second substances,

c represents a parameter estimation value matrix

[. The ] representation matrix symbol

ρ_sRepresenting the hysteresis coefficient of the s term

A_ijRepresenting coefficients of an i-th order Fourier j-th order Legendre polynomial

B_ijRepresenting coefficients of an i-th order Fourier j-th order Legendre polynomial

And 7: making a control chart of the monitoring process, and combining the multiple T in the control chart²The monitoring method of the control chart and the residual variance control chart monitors the cylindrical contour.

In this step, a multivariate T of monitoring parameters needs to be designed²Control charts and a single control chart for monitoring residuals. Assuming that the false positive rate is α', the first type of error probability is

Using T²Control charts monitor their parameters, T²The statistics are calculated as follows:

T²＝(c-μ)^T∑^-1(c-μ) (9)

wherein the content of the first and second substances,

T²representing control chart statistics

c represents the parameter estimation value obtained in step 6

μ represents the mean value of c

Superscript T denotes matrix transpose

Covariance matrix of Σ representation c

∑^-1Inverse of covariance matrix representing c

The upper control line UCL is:

wherein the content of the first and second substances,

expressing a chi-square distribution with a quantile of alpha and a degree of freedom of c

The residual control map is calculated as follows:

the residual estimate value is expressed as:

e＝(I-ρW)y-Xβ (11)

e denotes residual estimate

I denotes an identity matrix

ρ represents a hysteresis coefficient

W represents a spatial weight matrix

y denotes the actual measured value

X represents a systematic error term

Beta represents coefficient of system error term

The estimation variance of the residual estimation value is as follows:

σ²representing residual estimate variance

e' denotes the inverse matrix of the residual estimate

N represents the number of measurement points

For residual variance sigma²Monitoring is carried out, and the upper control line and the lower control line are as follows:

σ²representing residual estimate variance

χ²Indicating chi-square distribution

N-1 represents a quantile of

Chi-square distribution with degree of freedom of N-1

LCL denotes lower control line

n-1 represents a quantile of

Chi-square distribution with degree of freedom of N-1

And after the control line determined by the qualified product in the stage I is obtained, the production process can be monitored.

Preferred example 2:

specifically, the following description will further describe a specific implementation of the present invention by taking a cylinder block of a certain type of in-line four-cylinder engine produced by a certain automobile engine plant as an example, with reference to the accompanying drawings.

In this embodiment, the implementation process is described by taking the cylindrical profile monitoring as an example.

As shown in fig. 1, a method for monitoring a cylindrical profile with spatial correlation includes the following steps:

step 1: as shown in fig. 2, three-coordinate data of each measurement point is obtained by sampling the inner wall of the engine cylinder bore at equal intervals using a three-coordinate measuring machine, 10 layers for each cylinder bore, and 98 points for each layer.

Step 2: the data is processed. And converting the coordinates of the measuring points in the three-dimensional rectangular coordinate system into the coordinates of a polar coordinate system. And fitting the center and the radius of the cylinder by using a least square method, and subtracting the standard radius of the cylinder from the polar coordinate value of the measuring point to obtain the error between a real value and an ideal value. As shown in fig. 3 and 4.

And step 3: and (5) carrying out spatial correlation test. Carrying out space correlation test on the error values, and if the error values have no space correlation, modeling by using a least square regression model; if there is a spatial correlation, a spatial lag model is used for modeling. The Moire test was performed on the measurement points obtained in this example, and the results showed that the test statistics were significant, i.e., there was a spatial correlation between the error values.

And 4, step 4: and establishing a cylindrical shape error model. According to the judgment result of the step 3, spatial correlation exists between the error values. And (3) establishing a spatial autocorrelation model for the error value according to the expression (2).

And 5: and determining a system error term, dividing the error value into the system error term and a random error term, and establishing a system error term model by using a Fourier-Legendre equation.

Performing Fourier decomposition on the error value, and determining a system error term Fourier-Legendre equation as follows:

Xβ＝β₁P₀(z)+β₂P₁(z)cos(2θ)+β₃P₁(z)sin(2θ) (15)

step 6: and (4) estimating model parameters, namely performing parameter estimation on the model according to the determined system error term. By establishing a maximum likelihood model, a non-linear optimization method is adopted to enable the likelihood function to obtain a maximum value, and a parameter estimation value of the cylindrical space autocorrelation model is obtained.

And 7: making a control chart of the monitoring process, and combining the multivariate T²The control map and the residual variance control map monitor the cylindrical contour. The control chart of the control line phase I, which is obtained by calculating the control line according to the 24 cylinders meeting the quality requirement, is shown in FIG. 5. And monitoring the quality characteristic of the cylindrical profile according to the stage I control line, and if the control line is exceeded, indicating that the production process is possibly out of control and needing to carry out additional detection on an out-of-control point. FIG. 6 shows a pair of failThe inspection chart of the product, the reject detection rate of the method in this example is 83.3%.

Preferred example 3:

a method for monitoring cylindrical shape errors with spatial correlation, comprising the steps of:

step 1: measuring the surface of the cylinder to obtain three-dimensional coordinate data of each measuring point;

step 2: and processing the data, specifically, converting the coordinates of the measuring points in the three-dimensional rectangular coordinate system into the coordinates of a polar coordinate system. And fitting the center and the radius of the cylinder by using a least square method, and subtracting the standard radius of the cylinder from the radius value of the polar coordinate of the measuring point to obtain the error between a real value and an ideal value.

And 5: a systematic error term is determined. During the machining of rotating parts, harmonic errors typically occur, which can be expressed as a periodic function. The systematic error term has periodicity, the error source can be determined, and the random error term is a noise term. And performing Fourier decomposition on the error value, separating a system error term and a random error term, and determining a system error term model.

Step 6: and estimating model parameters. A parameter estimation is performed on the model based on the selected model and the determined systematic error term.

And 7: making a control chart of the monitoring process, and combining the multivariate T²The control map and the residual variance control map monitor the cylindrical contour.

A three coordinate measuring machine is used to sample the surface of the cylinder in step 1.

The sampling is carried out on the surface of the cylinder at equal intervals, the interval between the transverse direction and the longitudinal direction is 0.15mm at the minimum, and the measurement precision is 2-3 mu m.

In step 3, a Moire test is adopted to carry out a spatial correlation test, and if the test statistic is significant, the spatial correlation between the measurement points is shown.

In step 5, a Fourier-Legendre equation is adopted to establish a system error term model.

The model parameters are solved using maximum likelihood estimation in step 6.

Those skilled in the art will appreciate that, in addition to implementing the systems, apparatus, and various modules thereof provided by the present invention in purely computer readable program code, the same procedures can be implemented entirely by logically programming method steps such that the systems, apparatus, and various modules thereof are provided in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.

The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims

1. A method for monitoring cylindrical shape errors with spatial correlation, comprising:

a process monitoring step: acquiring a monitoring process control chart according to the acquired parameter estimation value, and monitoring the cylindrical profile;

the data processing step comprises:

y＝r(z，θ)-R

wherein the content of the first and second substances,

y represents an error value of the measurement point;

r is the standard radius of an ideal cylinder;

the spatial correlation judging step:

the error model establishing step:

y＝Xβ+ε

wherein the content of the first and second substances,

y represents an error value of the measurement point;

ε represents a random error term;

x β represents a systematic error term;

wherein the content of the first and second substances,

y represents an error value of the measurement point;

p represents the overall order of the spatial weight matrix;

s denotes the order of the spatial weight matrix, s ═ 1,2,3, …, p;

ε represents a random error term;

If t-q > s, then

t represents the tth measurement point;

q represents the qth measurement point;

n represents a total of N measurement points;

x β represents a systematic error term;

the system error term determining step:

wherein the content of the first and second substances,

P_j(z) denotes a legendre polynomial of degree j at the axial coordinate z;

A_ijrepresenting polynomial coefficients;

B_ijrepresenting polynomial coefficients;

j is the order of the legendre polynomial, j is 0,1,2, …, n;

i is the order of the fourier polynomial, i is 0,1,2, …, m;

t represents the number of axial measurement points;

u represents the number of radial measurement points;

k represents the axial kth measurement point;

l denotes the radial ith measurement point;

P_j(z_l) Representing an axial description function Legendre polynomial;

z_laxial coordinates representing the ith sample point;

Δ θ represents the radial sampling interval;

the expression of the legendre polynomial is as follows:

P₀(z)＝1

P₁(z)＝z

…

the differential form is:

wherein the content of the first and second substances,

d represents a differential sign;

z represents the axial coordinate of the sampling point;

j represents the order of the legendre polynomial;

the model parameter estimation step:

c＝[ρ₁…ρ_sA₁…A_ijB₁…B_ij]

wherein the content of the first and second substances,

c represents a parameter estimation value matrix;

[. cndot. ] represents a matrix symbol;

A_ijrepresenting coefficients of an i-th order Fourier j-th order Legendre polynomial；

the likelihood function expression is:

wherein the content of the first and second substances,

L(y|ρ，β，σ²) Representing a likelihood function;

N represents the number of measurement points;

I_Nan identity matrix representing order N;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

the process monitoring step:

T²＝(c-μ)^T∑^-1(c-μ)

wherein the content of the first and second substances,

T²representing control chart statistics;

μ represents the mean value of c;

superscript T represents matrix transposition;

Σ represents the covariance matrix of c;

∑^-1represents the inverse of the covariance matrix of c;

the upper control line UCL1 is:

wherein the content of the first and second substances,

UCL1 denotes T²The upper control line of (1);

expressing chi-square distribution with quantile alpha and degree of freedom c;

α' represents a false positive rate;

α represents a first class error probability;

e＝(I-ρW)y-Xβ

e represents a residual estimate;

i represents an identity matrix;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

y represents an actual measurement value;

x represents a systematic error term;

β represents a coefficient of a systematic error term;

σ²representing the estimated variance of the residual estimate;

e' represents an inverse matrix of the residual estimate;

n represents the number of measuring points;

UCL2 denotes σ²The upper control line of (1);

LCL stands for σ²A lower control line of (a);

χ²representing a chi-square distribution;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

2. A system for monitoring cylindrical form errors with spatial correlation, comprising:

a process monitoring module: acquiring a monitoring process control chart according to the acquired parameter estimation value, and monitoring the cylindrical profile;

the data processing module:

y＝r(z，θ)-R

wherein the content of the first and second substances,

y represents an error value of the measurement point;

r is the standard radius of an ideal cylinder;

the spatial correlation determination module:

the error model establishing module:

y＝Xβ+ε

wherein the content of the first and second substances,

y represents an error value of the measurement point;

ε represents a random error term;

x β represents a systematic error term;

wherein the content of the first and second substances,

y represents an error value of the measurement point;

p represents the overall order of the spatial weight matrix;

s denotes the order of the spatial weight matrix, s ═ 1,2,3, …, p;

ε represents a random error term;

If t-q > s, then

t represents the tth measurement point;

q represents the qth measurement point;

n represents a total of N measurement points;

x β represents a systematic error term;

the systematic error term determination module:

wherein the content of the first and second substances,

P_j(z) denotes a legendre polynomial of degree j at the axial coordinate z;

A_ijrepresenting polynomial coefficients;

B_ijrepresenting polynomial coefficients;

j is the order of the legendre polynomial, j is 0,1,2, …, n;

i is the order of the fourier polynomial, i is 0,1,2, …, m;

t represents the number of axial measurement points;

u represents the number of radial measurement points;

k represents the axial kth measurement point;

l denotes the radial ith measurement point;

P_j(z_l) Representing an axial description function Legendre polynomial;

z_laxial coordinates representing the ith sample point;

Δ θ represents the radial sampling interval;

the expression of the legendre polynomial is as follows:

P₀(z)＝1

P₁(z)＝z

…

the differential form is:

wherein the content of the first and second substances,

d represents a differential sign;

z represents the axial coordinate of the sampling point;

j represents the order of the legendre polynomial;

the model parameter estimation module:

c＝[ρ₁…ρ_sA₁…A_ijB₁…B_ij]

wherein the content of the first and second substances,

c represents a parameter estimation value matrix;

[. cndot. ] represents a matrix symbol;

the likelihood function expression is:

wherein the content of the first and second substances,

L(y|ρ，β，σ²) Representing a likelihood function;

N represents the number of measurement points;

I_Nan identity matrix representing order N;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

the process monitoring module:

T²＝(c-μ)^T∑^-1(c-μ)

wherein the content of the first and second substances,

T²representing control chart statistics;

μ represents the mean value of c;

superscript T represents matrix transposition;

Σ represents the covariance matrix of c;

∑^-1represents the inverse of the covariance matrix of c;

the upper control line UCL1 is:

wherein the content of the first and second substances,

UCL1 denotes T²The upper control line of (1);

expressing chi-square distribution with quantile alpha and degree of freedom c;

α' represents a false positive rate;

α represents a first class error probability;

e＝(I-ρW)y-Xβ

e represents a residual estimate;

i represents an identity matrix;

ρ represents a hysteresis coefficient;

w represents a spatial weight matrix;

y represents an actual measurement value;

x represents a systematic error term;

β represents a coefficient of a systematic error term;

σ²representing the estimated variance of the residual estimate;

e' represents an inverse matrix of the residual estimate;

n represents the number of measuring points;

UCL2 denotes σ²The upper control line of (1);

LCL stands for σ²A lower control line of (a);

χ²representing a chi-square distribution;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

n-1 represents a quantile of

Chi-square distribution with the degree of freedom of N-1;

3. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method for monitoring cylindrical shape errors with spatial correlation of claim 1.