CN109029328A - A kind of steady spline filtering method of surface profile based on M estimation - Google Patents
A kind of steady spline filtering method of surface profile based on M estimation Download PDFInfo
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- CN109029328A CN109029328A CN201810640971.0A CN201810640971A CN109029328A CN 109029328 A CN109029328 A CN 109029328A CN 201810640971 A CN201810640971 A CN 201810640971A CN 109029328 A CN109029328 A CN 109029328A
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- spline
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
Abstract
The steady spline filtering method of surface profile based on M estimation belongs to precision instrument and field of measuring technique；This method obtains the spline filtering model of open contours and closed outline by introducing spline theory；By introducing M estimation theory, the steady spline filtering model for open contours and closed outline is obtained；Determine robust iterative weight function used in the above-mentioned open loop gaussian filtering model for open contours；Spline filtering is carried out to surface profile measurement data, the iterative initial value of M estimation is determined using spline filtering model；The steady spline filtering of surface profile data is carried out with iteration weighted least-squares method and steady spline filtering model；The steady spline filtering method of surface profile based on M estimation of the invention, can eliminate boundary effect, and improve the robustness of filter.
Description
Technical field
The invention belongs to precision instrument and field of measuring technique, in particular to a kind of surface profile based on M estimation is steady
Spline filtering method.
Background technique
Surface measurement techniques, surface evaluation theory and method have become an important technology point in field of precision measurement
Branch, circularity and cylindricity are to evaluate the important indicator of rotary part performance, and filtering technique is the important ring in roundness measurement
Section, different filtering methods can have a huge impact the result of roundness evaluation, therefore filtering accuracy directly affects surface wheel
Wide evaluation quality and result.
2013, the old boundary effect filtered after superfine people to Gaussian linear profile was handled, and expanded method using profile
Profile information is supplemented, it is simple and effective, but all profiles can not be adapted to, in practical application, due to filtering
Complexity and rapidity select corresponding profile extended method for different profile inclination conditions, operate very many and diverse.
(processing method [J] Zhongyuan Technical Faculty of Gaussian linear profile filtering boundary effect in Chen Jichao, Zhang Linna new generation of GPS
Report .2013,24 (3): 18-21)
2015, D.Janecki was the computational efficiency for improving two-dimensional silhouette filtering, and proposition is carried out using B-spline function
Filtering, the algorithm introduce B-spline function theory, do not consider the bending energy for minimizing filter profile in Filter Principle function,
But the appropriate smoothness of filter profile, B-spline function are realized by the suitable distance between the node of selection B-spline function
Node-to-node distance be equal to filter expectation dead length half, so if having selected sufficiently high batten letter
Number, then can obtain arbitrarily large slope characteristic in the transition zone.(J.Dariusz,C.Leszek,
Z.Jarosaw.Separation of Non-periodic and Periodic 2D Profile Features Using
B-spline Functions[J].Metrology&Measurement Systems.2015,22(2):289-302)
2015, Zhang H et al. was directed to the approximation problem of gaussian filtering characteristic, proposed based on a kind of improvement variation side
The high-order spline filter of method, higher derivative item is added in the structural parameters determined by broad sense Taylor series, to realize
The convergence of Gaussian filter function.(H.Zhang, Y.Yuan, J.Hua, Y.Cheng.High-order spline filter:
Design and application to surface metrology[J].Precision Engineering.2015,40:
74-80)
2017, M.Rathod proposed a kind of generalized splines nonlinear adaptable filter, and the filter is using adaptive
It answers spline function as basic function, suitable parameter is generated to update the control point in spline function by input signal, according to
The update rule derived carries out the update at control point, and carries out Mean sware analysis, finally output signal combines available filter
The result of wave.This filter is able to solve several benchmark problems in Dynamic System Identification, and in single-input single-output and
Enhance modeling accuracy in the identification of multiple-input and multiple-output dynamical system.(M.Rathod,V.Patel,
N.V.George.Generalized Spline Nonlinear Adaptive Filters[J].Expert Systems
with Applications.2017,83:122-130.)
" the gaussian filtering side for the surface finish measurement with surface deep valley signal patent CN201610907699.9
Method ", it is theoretical by introducing regression theory and robust iterative, it obtains the open loop gaussian filtering model for open contours and determines steady
Surface finish measurement data with surface deep valley signal are carried out gaussian filtering by strong estimation weight function.
Patent CN201610199443.7 " a kind of adaptive Gaussian mixture model method " proposes a kind of detection in noise spot
In the process, filter window adaptive change, filter window dynamic self-adapting is adjustable, and home window to maximized window is with step-length for 2
Amplified step by step, until being had reached the maximum in window there are extreme point or filter window.
Comprehensive analysis common problem of the existing technology is can not to solve contour filter simultaneously for non-close profile
The processing problem of existing edge effect and abnormal signal.
Summary of the invention
The purpose of the present invention is to the above-mentioned problems of the prior art, propose a kind of surface wheel based on M estimation
Wide steady spline filtering method, redesigns spline filter by M estimation, robust iterative weight function is constructed, to reach
There is the requirement of robustness to the edge effect eliminated in the filtering of non-close circle contour and to exceptional value.
Above-mentioned purpose is realized by the following technical solution:
A kind of steady spline filtering method of surface profile based on M estimation, this method is using spline filtering result as iteration
Initial value redesigns spline filter by M estimation, selects suitable residual error statistic, construct the weight function of robust iterative,
And data filtering processing is carried out by steady spline filtering equation:
1) batten energy minimal condition is introduced, spline filtering model is obtained:
It is replaced by difference and the Spline Model is solved, obtain spline filtering equation:
[I+α4Q] s=z
In formula, I is unit matrix, α=1/ (2sin π Δ x/ λc), λcIt is off frequency, Q is coefficient matrix, and S is after filtering
Data, Z be original contour data；
2) M estimation theory is introduced, steady spline filtering model is obtained:
It is replaced by difference and to the steady spline filtering model solution, obtains steady spline filtering equation:
[δ(m-1)+α4Q]s(m)=δ(m-1)z
In formula, δ is weight function matrix, and Q is coefficient matrix, and S is filtered data, and Z is original contour data, α=1/
(2sinπΔx/λc), λcIt is off frequency；
3) spline filtering is carried out to surface profile measurement data, determines M using the spline filtering model obtained in step 1)
The iterative initial value of estimation；
4) it is filtered using the steady spline filtering model in iteration weighted least-squares method and step 2), is estimated using M
Tukey weight function in meter determines weight function δ:
In formula, viFor the difference of i-th filter result and (i-1)-th filter result, c=4.4478 | median (v) |, this
In median expression take intermediate value；
5) judge whether to meet following stopping criterion for iteration:
Wherein ε is iteration precision, vi+1For the residual error of i+1 time filter result and i-th filter result, ciFor i-th filter
Wave result；If being unsatisfactory for stopping criterion for iteration, return step 4) continue steady spline filtering；If meeting iteration ends item
Part then stops iterating to calculate, and obtains steady spline filtering result.
Spline filtering equation and steady spline filtering equation in the step 1) and step 2), coefficient matrix Q's
Value are as follows:
For closed outline:
For non-close profile:
The invention has the characteristics that and the utility model has the advantages that
1, traditional filtering method can be overcome special due to the inherence of convolution algorithm completely using spline filtering method in the present invention
Property, the data in surface profile two sections of cutoff wavelengths of head and the tail cannot be used to carry out the evaluation of surface characteristics, existing edge effect
Problem.
2, robust filtering model is used in the present invention, and there is the surface signal of convex peak and deep valley feature for measurement surface,
The abnormal datas such as Ru Keng, paddy, indentation have good Robustness least squares.This method introduces robust statistics theory, has robust filtering
Characteristic solves traditional filtering method because robustness is poor, causes extracted surface middle line to deviate real surface, generates big filter
Wave distortion, and then the problem of influence evaluating precision.
3, weight function is estimated as robust iterative weight function using the Tukey in M estimation in the present invention, Tukey estimation belongs to
In the truncation M estimation and image smoothing that have superseded point at both ends, thus very to the data that middle section is normal distribution
Effectively, especially suitable for the filtering of surface profile data.
The present invention is especially suitable for field of precision measurement, especially can solve profile side in non-close circle contour Measurement and evaluation
Edge effect is eliminated and takes into account problem to the robustness filtering of abnormal data.
Detailed description of the invention
Fig. 1 is the surface profile steady spline filtering method flow diagram of the invention based on M estimation；
Fig. 2 is straight line degree measurement original contour data and the comparison diagram using this method filtered data；
Fig. 3 is roundness measurement original contour data and the comparison diagram using this method filtered data.
Specific embodiment
It elaborates with reference to the accompanying drawing to the embodiment of the present invention.
Specific embodiment 1: as shown in Figure 1, a kind of steady spline filtering method of surface profile based on M estimation, the party
Method redesigns spline filter by M estimation, selects suitable residual error using spline filtering result as the initial value of iteration
Statistic constructs the weight function of robust iterative, and is filtered by steady spline filtering equation, specific implementation method are as follows:
Step 1: batten energy minimal condition is introduced, spline filtering model is obtained:
It is replaced by difference and the Spline Model is solved, obtain spline filtering equation:
[I+α4Q] s=z
In formula, I is unit matrix, λcIt is off frequency and is taken as 0.08mm, α=1/ (2sin π Δ x/ λc), S is filtered
Data, Z are initial data profile as shown in Fig. 2, Q is coefficient matrix:
Step 2: M estimation theory is introduced, steady spline filtering model is obtained:
It is replaced by difference and to the steady spline filtering model solution, obtains steady spline filtering equation:
[δ(m-1)+α4Q]s(m)=δ(m-1)z
In formula, δ is weight function matrix, and Q is coefficient matrix, and S is the m times filtered data, after Z is the m-1 times filtering
Data, λcIt is off frequency and is taken as 0.08mm, α=1/ (2sin π Δ x/ λc)。
Step 3: spline filtering is carried out to surface profile measurement data, the iteration of M estimation is determined using spline filtering model
Initial value.
Step 4: residual error v is calculatedi, then estimate to determine weight function δ by M, using iteration weighted least-squares method and steadily and surely
Spline filtering model carries out steady spline filtering, and δ is Tukey weight function here:
In formula, viFor the residual error of i-th, according to iso standard, c generally takes 4.4478MAD (median absolute
Deviation), MAD=| median (v) | (median expression takes intermediate value).
Step 5: taking iteration precision ε=0.001, and altogether through 9 iteration, iteration result meets stopping criterion for iteration, stops changing
In generation, calculates, and the filter result for obtaining steady spline filtering is as shown in Figure 2.
Specific embodiment 2: the steady spline filtering side of surface profile based on M estimation as described in embodiment one
The step of method uses, introduces abnormal signal, initial data profile is as shown in figure 3, with cutoff frequency N in roundness measurement datac
Initial data is filtered based on the M estimation steady spline filtering method of surface profile in=50upr, iteration precision ε=0.001
Wave, total the number of iterations are 14 times, and the filter result for obtaining steady spline filtering is as shown in Figure 3.
Claims (2)
1. a kind of steady spline filtering method of surface profile based on M estimation, this method is using spline filtering result as the first of iteration
Value redesigns spline filter by M estimation, selects suitable residual error statistic, construct the weight function of robust iterative, and
Data filtering processing is carried out by steady spline filtering equation, it is characterised in that:
1) batten energy minimal condition is introduced, spline filtering model is obtained:
It is replaced by difference and the Spline Model is solved, obtain spline filtering equation:
[I+α4Q] s=z
In formula, I is unit matrix, α=1/ (2sin π Δ x/ λc), λcIt is off frequency, Q is coefficient matrix, and S is filtered number
According to Z is original contour data；
2) M estimation theory is introduced, steady spline filtering model is obtained:
It is replaced by difference and to the steady spline filtering model solution, obtains steady spline filtering equation:
[δ(m-1)+α4Q]s(m)=δ(m-1)z
In formula, δ is weight function matrix, and Q is coefficient matrix, and S is filtered data, and Z is original contour data, α=1/ (2sin
πΔx/λc), λcIt is off frequency；
3) spline filtering is carried out to surface profile measurement data, determines that M estimates using the spline filtering model obtained in step 1)
Iterative initial value；
4) it is filtered using the steady spline filtering model in iteration weighted least-squares method and step 2), is estimated using M
Tukey weight function determine weight function δ:
In formula, viFor the difference of i-th filter result and (i-1)-th filter result, c=4.4478 | median (v) |, here
Median expression takes intermediate value；
5) judge whether to meet following stopping criterion for iteration:
Wherein ε is iteration precision, vi+1For the residual error of i+1 time filter result and i-th filter result, ciIt filters and ties for i-th
Fruit；If being unsatisfactory for stopping criterion for iteration, return step 4) continue steady spline filtering；If meeting stopping criterion for iteration,
Then stop iterating to calculate, obtains steady spline filtering result.
2. a kind of steady spline filtering method of surface profile based on M estimation according to claim 1, it is characterised in that:
Spline filtering equation and steady spline filtering equation in the step 1) and step 2), the value of coefficient matrix Q are as follows:
For closed outline:
For non-close profile:
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109802655A (en) * | 2019-02-25 | 2019-05-24 | 哈尔滨工业大学 | Isotropism two dimension high-order spline filtering method for surface metrology |
| CN110363743A (en) * | 2019-06-10 | 2019-10-22 | 长安大学 | Surface texture separation method based on asphalt concrete pavement laser three-D data |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1645360A (en) * | 2004-01-19 | 2005-07-27 | 株式会社三丰 | Signal noise filtering method, program, device and recording medium |
| JP2007253226A (en) * | 2006-03-25 | 2007-10-04 | Dainippon Printing Co Ltd | Method for correcting precision of surface plate face in pressing machine and cubic correction sheet |
| CN101793522A (en) * | 2010-03-31 | 2010-08-04 | 上海交通大学 | Steady filtering method based on robust estimation |
| CN105115573A (en) * | 2015-07-18 | 2015-12-02 | 厦门理工学院 | Correction method and device for flood flow forecasting |
-
2018
- 2018-06-21 CN CN201810640971.0A patent/CN109029328A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1645360A (en) * | 2004-01-19 | 2005-07-27 | 株式会社三丰 | Signal noise filtering method, program, device and recording medium |
| JP2007253226A (en) * | 2006-03-25 | 2007-10-04 | Dainippon Printing Co Ltd | Method for correcting precision of surface plate face in pressing machine and cubic correction sheet |
| CN101793522A (en) * | 2010-03-31 | 2010-08-04 | 上海交通大学 | Steady filtering method based on robust estimation |
| CN105115573A (en) * | 2015-07-18 | 2015-12-02 | 厦门理工学院 | Correction method and device for flood flow forecasting |
Non-Patent Citations (1)
| Title |
|---|
| 占伟伟: "形状误差精密测量中滤波和评价方法的研究", 《中国优秀硕士学位论文全文数据库工程科技I辑》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109802655A (en) * | 2019-02-25 | 2019-05-24 | 哈尔滨工业大学 | Isotropism two dimension high-order spline filtering method for surface metrology |
| CN110363743A (en) * | 2019-06-10 | 2019-10-22 | 长安大学 | Surface texture separation method based on asphalt concrete pavement laser three-D data |
| CN110363743B (en) * | 2019-06-10 | 2021-08-10 | 长安大学 | Surface texture separation method based on laser three-dimensional data of asphalt concrete pavement |
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Application publication date: 20181218 |