CN106152964B - A kind of measuring method of plane planted agent's variability field based on speed linearity fitting - Google Patents
A kind of measuring method of plane planted agent's variability field based on speed linearity fitting Download PDFInfo
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- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract
The present invention proposes a kind of measuring method for the plane planted agent's variability field being fitted based on speed linearity, belong to object deformation rate field field of measuring technique, the present invention acquires multiple images during testee stand under load, obtain each measuring point coordinate of image intermediate cam shape block of pixels, the velocity field of measuring point is obtained according to the interval time of image, according to the coordinate and speed of each measuring point in each triangular pixel block, obtain the fitting data point of each triangular pixel block, and then obtain the coefficient of the fit Plane of each triangular pixel block, the deformation rate field in testee plane is finally obtained according to the relationship of the coefficient of acquisition and speed partial derivative；The present invention is based on the thoughts of data fitting, better than existing correlation technique, its process is simple, step is convenient and should be readily appreciated that, the coefficient of only demand solution fit Plane equation can obtain result, the present invention considers the information of measuring point inside discrete pixels block, the accuracy rate and confidence level for improving final result increase the flexibility of measuring point selection.
Description
Technical field
The invention belongs to object deformation rate field field of measuring technique, and in particular to a kind of plane based on speed linearity fitting
The measuring method of planted agent's variability field.
Background technology
Deformation of body measurement is the important content of Experimental Mechanics；Compared with other measurement methods, measuring method due to
It has many advantages, such as the non-contact, whole audience, high spatial resolution and high measurement accuracy, plays in Experimental Mechanics irreplaceable
Key player；In practical applications, deformation of body measurement is usually referred to the measurement deformed in object plane；
Digital Image Correlation Method is a kind of important method in measuring method, is the object to being acquired before and after deformation
The two images (speckle field) on surface carry out relevant treatment, to realize that deformation of body measures；It is flat that this method can not only carry out object
In-plane deformation measures, and can also carry out surface deformation measurement；
Test specimen or structure are under loaded condition, and after certain phase, the distribution of strain rate is simultaneously uneven；In strain rate
Upper zone, strain increase very fast, the region region that often the following crackle occurs；By detecting strain rate upper zone
Time space distribution can know the specific location in future subversion region in advance, this for material or structure failure mechanism analysis and
Disaster prevention research is of great advantage；
Using Digital Image Correlation Method, deformation measurement method includes mainly in object plane：
1) it is based on the Digital Image Correlation Method of newton-La Feixun (N-R) method, while obtaining the position in object plane
It moves and strains, but the error of strain calculation result is larger；
2) Digital Image Correlation Method based on centered Finite Difference Methods is answered by carrying out centered difference to displacement field
Variable field, but the noise for including in displacement field can be such that the confidence level of strain calculation result reduces；
3) Digital Image Correlation Method based on finite element smoothing method carries out displacement field using finite element method smooth
Obtain strain field, but mathematical form and programming execute all more complex, are unfavorable for promotion and application.
Invention content
In view of the deficiencies of the prior art, the present invention proposes a kind of light for the plane planted agent's variability field being fitted based on speed linearity
Measurement method is learned, accuracy rate, confidence level and calculating speed purpose are improved to reach.
A kind of measuring method of plane planted agent's variability field based on speed linearity fitting, includes the following steps：
Step 1, multiple images using the capture apparatus acquisition a certain plane of testee during stand under load；
Step 2 selectes the shooting time for measuring image, and determining every measurement image in multiple images of acquisition, into
And obtain the interval time of the measurement image at two adjacent moment；
Step 3 measures first image place plane as the faces xoy, establishes three-dimensional cartesian coordinate system oxyz, and by first
The testee region measured in image is discretized into non-overlapping and gapless triangular pixel block；
Step 4, the coordinate for obtaining three vertex of triangular pixel block are arranged in each vertex position of triangular pixel block
1 measuring point, and the non-vertex position of each triangular pixel block arranges that N number of measuring point, N are more than or equal to 0 in the faces xoy, obtaining should
Coordinate of the measuring point in x-axis and y-axis；
Step 5, using Digital Image Correlation Method, obtain the displacement of measuring point of testee during stand under load in plane
, according to the interval time of the measurement image at two adjacent moment, obtain the velocity field of the measuring point in plane；
Step 6, according to x coordinate, y-coordinate and the speed of each measuring point in each triangular pixel block, obtain three-dimensional right angle
Two groups of fitting data points of each triangular pixel block in coordinate system；
Step 7, Select Error type obtain each triangle according to every group of fitting data point of each triangular pixel block
The coefficient of the fit Plane of shape block of pixels；
Step 8, the relationship according to the coefficient and speed partial derivative of acquisition, obtain the strain rate of each triangular pixel block,
Obtain the deformation rate field in testee plane.
X coordinate, y-coordinate and the speed of each measuring point in each triangular pixel block of basis described in step 6 obtain three-dimensional
Two groups of fitting data points of each triangular pixel block in rectangular coordinate system；Specifically include following steps：
In step 6.1, each triangular pixel block on the faces xoy, using the x coordinate of each measuring point as fitting data point
X coordinate, using the y-coordinate of each measuring point as the y-coordinate of fitting data point, by the speed of each measuring point x-axis direction point
The z coordinate as fitting data point is measured, first group that each triangular pixel block is constructed in three-dimensional cartesian coordinate system oxyz is quasi-
Close data point；
In step 6.2, each triangular pixel block on the faces xoy, using the x coordinate of each measuring point as fitting data point
X coordinate, using the y-coordinate of each measuring point as the y-coordinate of fitting data point, point by the speed of each measuring point in y-axis direction
The z coordinate as fitting data point is measured, second group that each triangular pixel block is constructed in three-dimensional cartesian coordinate system oxyz is quasi-
Close data point.
Select Error type described in step 7 obtains each according to every group of fitting data point of each triangular pixel block
The coefficient of the fit Plane of triangular pixel block；
Plane is as follows：
Wherein,Each of indicate in first fit Plane of each triangular pixel block point the directions z coordinate,
Point each of is indicated in second fit Plane of each triangular pixel block in the coordinate in the directions z, x indicates the seat in the directions x
Mark, y indicate the coordinate in the directions y, A1、B1And C1Indicate the coefficient of first fit Plane of each triangular pixel block, A2、B2
And C2Indicate the coefficient of second fit Plane of each triangular pixel block.
The relationship of the coefficient and speed partial derivative of acquisition described in step 8, it is specific as follows：
Wherein,Each of indicate in first fit Plane of each triangular pixel block point the directions z coordinate,Table
Each of showing in second fit Plane of each triangular pixel block point in the coordinate in the directions z, x indicates the coordinate in the directions x,
Y indicates the coordinate in the directions y, A1And B1Indicate the coefficient of first fit Plane of each triangular pixel block, A2And B2It indicates
The coefficient of second fit Plane of each triangular pixel block；
The strain rate of each triangular pixel block, formula are as follows：
Wherein,Indicate the strain rate tensor of each triangular pixel block；I denotation coordination axis i are x-axis or y-axis；J is indicated
Reference axis j is x-axis or y-axis.
Advantage of the present invention：
The present invention proposes a kind of measuring method for the plane planted agent's variability field being fitted based on speed linearity, is based on data
The thought of fitting, be better than the existing Digital Image Correlation Method based on centered Finite Difference Methods, process is simple, step is convenient and
It can be readily appreciated that the coefficient of only demand solution fit Plane equation can obtain as a result, improving measuring speed and programming convenience；This
Invention considers the information of measuring point inside discrete pixels block, improves the accuracy rate and confidence level of final result, and increase survey
The flexibility of point selection；The present invention has wide practical use in solid Experimental Mechanics field.
Description of the drawings
Fig. 1 is the measuring method flow chart of the deformation rate field in the object plane of an embodiment of the present invention；
Fig. 2 be an embodiment of the present invention selected Failure under Uniaxial Compression in surface of test piece measurement image schematic diagram,
Wherein, figure (a) is first measurement image, and figure (b) is second measurement image, and figure (c) is that third measures image；
Fig. 3 is the triangle after the first testee region discretization measured in image of an embodiment of the present invention
Shape block of pixels distribution map；
Fig. 4 is that each measuring point of an embodiment of the present invention measures the position view on image at first；
Fig. 5 is that the speed and coordinate by measuring point of an embodiment of the present invention obtain the several of triangular pixel block fit Plane
What schematic diagram；
Fig. 6 is the strain rate by second to third image obtained using the method for the present invention of an embodiment of the present invention
Field blank map, wherein figure (a) is the line strain rate field blank map in the directions x, and figure (b) is the line strain rate field blank map in the directions y,
It is inplane shear deformation rate field blank map to scheme (c)；
Fig. 7 is the strain by second to third image obtained using the Digital Image Correlation Method based on N-R methods
Rate field blank map, wherein figure (a) is the line strain rate field blank map in the directions x, and figure (b) is that the line strain rate field in the directions y is filled
Figure, figure (c) are inplane shear deformation rate field blank map；
Fig. 8 is to open image by second to third using what the Digital Image Correlation Method based on centered Finite Difference Methods obtained
Deformation rate field blank map, wherein figure (a) is the line strain rate field blank map in the directions x, and figure (b) is that the line strain rate field in the directions y is filled out
Figure is filled, figure (c) is inplane shear deformation rate field blank map；
In figure, 1 is triangular pixel block, and 2 be the vertex of triangular pixel block, and 3 be measuring point, and 4 be triangular pixel block, 5
It is fitting data point for measuring point, 6,7 be triangular pixel block, and 8 be fit Plane；A is the first vertex of triangular pixel block, b
For the second vertex of triangular pixel block, c is the third vertex of triangular pixel block.
Specific implementation mode
An embodiment of the present invention is described further below in conjunction with the accompanying drawings.
A kind of measuring method of plane planted agent's variability field based on speed linearity fitting, method flow diagram such as Fig. 1 institutes
Show, includes the following steps：
Step 1, multiple images using the capture apparatus acquisition a certain plane of testee during stand under load；
In the embodiment of the present invention, testee is cuboid test specimen, is highly 90mm, test specimen is placed in by width 50mm
On platform, coating manufacturing artificial speckle is used on a surface of test specimen, carries out Bit andits control load in upper surface, acquisition should
The speckle pattern on surface；
Step 2 selectes the shooting time for measuring image, and determining every measurement image in multiple images of acquisition, into
And obtain the interval time of the measurement image at two adjacent moment；
In the embodiment of the present invention, 3 measurement images, selected measurement image such as Fig. 2 are selected in multiple images of acquisition
Shown in middle figure (a) to figure (c), the shooting time of every measurement image is obtained, and then obtains first and measures image and second survey
The shooting interval time of spirogram picture is 198s, and acquisition second measures image and the shooting interval time of third measurement image is
2s；
Step 3 measures first image place plane as the faces xoy, establishes three-dimensional cartesian coordinate system oxyz, and by first
The testee region measured in image is discretized into non-overlapping and gapless triangular pixel block；
In the embodiment of the present invention, (in figure, 1 indicates triangular pixel block, and 2 indicate the top of triangular pixel block as shown in Figure 3
Point, a indicate that the first vertex of triangular pixel block, b indicate that the second vertex of triangular pixel block, c indicate triangular pixel block
Third vertex), by first measure image in testee region be discretized into 5762 it is compact arranged, non-overlapping
And gapless triangular pixel block；
Step 4, the coordinate for obtaining three vertex of triangular pixel block are arranged in each vertex position of triangular pixel block
1 measuring point, and the non-vertex position of each triangular pixel block arranges that N number of measuring point, N are more than or equal to 0 in the faces xoy, obtaining should
Coordinate of the measuring point in x-axis and y-axis；
It is as shown in Figure 4 (3 indicate measuring point in figure, and 4 indicate triangular pixel block), every in the faces xoy in the embodiment of the present invention
The non-vertex position of a triangular pixel block arranges 1 measuring point；
Step 5, using Digital Image Correlation Method, obtain the displacement of measuring point of testee during stand under load in plane
, according to the interval time of the measurement image at two adjacent moment, obtain the velocity field of the measuring point in plane；
It is specific as follows：
Step 5.1 measures at first position on image according to each measuring point, is obtained using Digital Image Correlation Method every
A measuring point measures the position on image in second and third；
Step 5.2 measures at first position on image according to each measuring point and each measuring point measures image at second
On position, obtain each measuring point and measure displacement on image at second, each measuring point is obtained in third using same procedure
Open the displacement measured on image；
Step 5.3 obtains second displacement difference for measuring image and each measuring point on third image, and according to second
It opens and measures the shooting interval time that image measures image with third, obtain the speed of each measuring point, i.e. survey in acquisition plane
The velocity field of point；
Step 6, according to x coordinate, y-coordinate and the speed of each measuring point in each triangular pixel block, obtain three-dimensional right angle
Two groups of fitting data points of each triangular pixel block in coordinate system；
In the embodiment of the present invention, as schemed in Fig. 5 shown in (a), 5 indicate measuring point in figure, and 6 indicate fitting data point, and 7 indicate three
Angular block of pixels obtains two groups of fitting data points of each triangular pixel block in three-dimensional cartesian coordinate system, specifically includes following
Step：
In step 6.1, each triangular pixel block on the faces xoy, using the x coordinate of each measuring point as fitting data point
X coordinate, using the y-coordinate of each measuring point as the y-coordinate of fitting data point, by the speed of each measuring point x-axis direction point
The z coordinate as fitting data point is measured, first group that each triangular pixel block is constructed in three-dimensional cartesian coordinate system oxyz is quasi-
Close data point；
In step 6.2, each triangular pixel block on the faces xoy, using the x coordinate of each measuring point as fitting data point
X coordinate, using the y-coordinate of each measuring point as the y-coordinate of fitting data point, point by the speed of each measuring point in y-axis direction
The z coordinate as fitting data point is measured, second group that each triangular pixel block is constructed in three-dimensional cartesian coordinate system oxyz is quasi-
Close data point；
Step 7, Select Error type obtain each triangle according to every group of fitting data point of each triangular pixel block
The coefficient of the fit Plane of shape block of pixels；The error type includes worst error, mean error and root-mean-square error etc., is belonged to
Common knowledge in this field can voluntarily be selected according to actual demand；
Step 7.1, two fit Plane equations for determining each triangular pixel block；
In the embodiment of the present invention, scheme shown in (b) in the plane such as Fig. 5 that fit, wherein 8 indicate fit Plane；
Plane equation is as follows：
Wherein,Each of indicate in first fit Plane of each triangular pixel block point the directions z coordinate,Table
Each of showing in second fit Plane of each triangular pixel block point in the coordinate in the directions z, x indicates the coordinate in the directions x,
Y indicates the coordinate in the directions y, A1、B1And C1Indicate the coefficient of first fit Plane of each triangular pixel block, A2、B2With
C2Indicate the coefficient of second fit Plane of each triangular pixel block；
Step 7.2, selection root-mean-square error obtain each according to two groups of fitting data points of each triangular pixel block
The root-mean-square error of two fit Planes of triangular pixel block, the minimum fitting data point of root-mean-square error are flat to fitting
The quadratic sum of the vertical range (i.e. fitting data point is at a distance from the direction to fit Plane parallel with z-axis) in face, formula are as follows：
Wherein, E1Indicate the root-mean-square error of first fit Plane of each triangular pixel block；E2Indicate each triangle
The root-mean-square error of second fit Plane of shape block of pixels；xkIndicate the fitting data point of each triangular pixel block in the side x
To coordinate；ykIndicate coordinate of the fitting data point in the directions y of each triangular pixel block；Indicate each triangular pixel
Coordinate of the first group of fitting data point of block in the directions z；Indicate second group of fitting data point of each triangular pixel block in z
The coordinate in direction；K indicates that k-th of fitting data point in every group of fitting data point, value range are [1,2,3,4]；
Step 7.3, by ensureing that root-mean-square error is minimum, obtain two groups of least square fittings of each triangular pixel block
The normal equation of plane, specially：
The guarantee root-mean-square error is minimum to make partial derivativeWithWithIt is zero,
Formula is as follows：
Step 7.4, solution formula (5) and formula (6) obtain the coefficient A of least square fitting plane1、B1、C1、A2、B2With
C2；
Step 8, the relationship according to the coefficient and speed partial derivative of acquisition, obtain the strain rate of each triangular pixel block,
Obtain the deformation rate field in testee plane；Specifically include following steps：
The equation of two least square fitting planes in formula (1) is sought local derviation by step 8.1 respectively, obtains minimum two
Multiply the relationship of the coefficient and speed partial derivative of fit Plane；
Formula is as follows：
Wherein,Each of indicate in first fit Plane of each triangular pixel block point the directions z coordinate,Table
Each of showing in second fit Plane of each triangular pixel block point in the coordinate in the directions z, x indicates the coordinate in the directions x,
Y indicates the coordinate in the directions y, A1And B1Indicate the coefficient of first fit Plane of each triangular pixel block, A2And B2It indicates
The coefficient of second fit Plane of each triangular pixel block；
Step 8.2 obtains speed partial derivative and strain rate using geometric equationBetween relationship；
Formula is as follows：
Wherein,Indicate the strain rate tensor of each triangular pixel block；Indicate the velocity component in the directions i；XjIt indicates
Coordinate in the directions j；Indicate the velocity component in the directions j；XiIndicate the coordinate in the directions i；I denotation coordination axis i, be x-axis or
Y-axis；J denotation coordination axis j are x-axis or y-axis；
Strain rate formula (7) is converted to the common type in engineering by step 8.3；
Specially：
The strain rate of each triangular pixel blockIt is a tensor, for two-dimensional problems,It is expressed as：
Wherein, XxIndicate the coordinate in the directions x, as x；XyIndicate the coordinate in the directions y, as y；
It enablesThenIt can be expressed as：
Wherein,Indicate the line strain rate in the directions x；Indicate inplane shear strain rate；Indicate the line strain in the directions y
Rate；
Step 8.4 merges formula (2) and formula (7), obtains the strain rate of each triangular pixel block, that is, obtains
The deformation rate field in testee plane is obtained, formula is as follows：
In the embodiment of the present invention, Fig. 6 is the deformation rate field by second to third image obtained using the method for the present invention
Blank map (including figure (a), figure (b) and figure (c))；In order to be compared, Fig. 7 gives using the digitized map based on N-R methods
The deformation rate field blank map (including figure (a), figure (b) and figure (c)) by second to third image obtained as correlation technique；Figure
8 give the strain rate by second to third image obtained using the Digital Image Correlation Method based on centered Finite Difference Methods
Field blank map (including figure (a), figure (b) and figure (c))；By Fig. 6~Fig. 8 it can be found that various deformation rate fields are in uneven distribution,
EspeciallyWithIt is observed that some are in band-like strain rate Spring layer or low value area, the strain variations of these positions compared with
Soon, it is the region of the following macroscopic cracking generation；
In the embodiment of the present invention, using based on centered Finite Difference Methods Digital Image Correlation Method and the method for the present invention obtain
's WithMeasurement range have certain difference, better than utilize the Digital Image Correlation Method based on N-R methods to obtain
Measurement result；Specifically, obtained using the Digital Image Correlation Method based on centered Finite Difference MethodsMeasurement range be
(- 7~19) × 10-3s-1,Measurement range be (- 16~6) × 10-3s-1,Measurement range be (- 17~8) × 10-3s-1, and the method for the present invention is used to obtainMeasurement range be (- 15~33) × 10-3s-1,Measurement range be (- 21~
9)×10-3s-1,Measurement range be (- 29~17) × 10-3s-1；In contrast, the measurement obtained using the method for the present invention
Range is more than the measurement range obtained using the Digital Image Correlation Method based on centered Finite Difference Methods, this makes main strain rate
Spring layer more highlights, meanwhile, the narrower width of Spring layer, it means that the method for the present invention can portray deformation rate field more
It is careful；From the measurement result obtained using the method for the present invention, it is observed that being more in clearly band-like strain rate high level
Area and low value area, and the measurement result for utilizing the Digital Image Correlation Method based on centered Finite Difference Methods to obtain is more fuzzy, answers
Variability Spring layer seems more mottled；In conclusion being better than other two methods using the measurement result that the method for the present invention obtains.
Claims (4)
1. a kind of measuring method of plane planted agent's variability field based on speed linearity fitting, which is characterized in that including following
Step：
Step 1, multiple images using the capture apparatus acquisition a certain plane of testee during stand under load；
Step 2 is selected the shooting time for measuring image, and determining every measurement image in multiple images of acquisition, and then is obtained
Obtain the interval time of the measurement image at two adjacent moment；
Step 3 measures first image place plane as the faces xoy, establishes three-dimensional cartesian coordinate system oxyz, and first is measured
Testee region in image is discretized into non-overlapping and gapless triangular pixel block；
Step 4, the coordinate for obtaining three vertex of triangular pixel block arrange 1 in each vertex position of triangular pixel block
Measuring point, and the non-vertex position of each triangular pixel block arranges that N number of measuring point, N are more than or equal to 0, obtain N number of survey in the faces xoy
Coordinate of the point in x-axis and y-axis；
Step 5, using Digital Image Correlation Method, obtain the displacement field of measuring point of testee during stand under load in plane,
According to the interval time of the measurement image at two adjacent moment, the velocity field of the measuring point in plane is obtained；
Step 6, according to x coordinate, y-coordinate and the speed of each measuring point in each triangular pixel block, obtain three-dimensional rectangular coordinate
Two groups of fitting data points of each triangular pixel block in system；
Step 7, Select Error type obtain each triangle image according to every group of fitting data point of each triangular pixel block
The coefficient of the fit Plane of plain block；
Step 8, the relationship according to the coefficient and speed partial derivative of acquisition, obtain the strain rate of each triangular pixel block, that is, obtain
Obtain the deformation rate field in testee plane.
2. the measuring method of plane planted agent's variability field according to claim 1 based on speed linearity fitting, step 6
X coordinate, y-coordinate and the speed of each measuring point in each triangular pixel block of the basis obtain in three-dimensional cartesian coordinate system
Two groups of fitting data points of each triangular pixel block；Specifically include following steps：
In step 6.1, each triangular pixel block on the faces xoy, using the x coordinate of each measuring point as the x of fitting data point
Coordinate, using the y-coordinate of each measuring point as the y-coordinate of fitting data point, the component by the speed of each measuring point in x-axis direction is made
For the z coordinate of fitting data point, first group of fitting number of each triangular pixel block is constructed in three-dimensional cartesian coordinate system oxyz
Strong point；
In step 6.2, each triangular pixel block on the faces xoy, using the x coordinate of each measuring point as the x of fitting data point
Coordinate, using the y-coordinate of each measuring point as the y-coordinate of fitting data point, the component by the speed of each measuring point in y-axis direction is made
For the z coordinate of fitting data point, second group of fitting number of each triangular pixel block is constructed in three-dimensional cartesian coordinate system oxyz
Strong point.
3. the measuring method of plane planted agent's variability field according to claim 1 based on speed linearity fitting, special
Sign is that the Select Error type described in step 7 obtains each according to every group of fitting data point of each triangular pixel block
The coefficient of the fit Plane of triangular pixel block；
Plane is as follows：
Wherein,Each of indicate in first fit Plane of each triangular pixel block point the directions z coordinate,Indicate every
Point is in the coordinate in the directions z each of in second fit Plane of a triangular pixel block, and x expressions are in the coordinate in the directions x, y tables
Show the coordinate in the directions y, A1、B1And C1Indicate the coefficient of first fit Plane of each triangular pixel block, A2、B2And C2Table
Show the coefficient of second fit Plane of each triangular pixel block.
4. the measuring method of plane planted agent's variability field according to claim 1 based on speed linearity fitting, special
Sign is that the relationship of the coefficient and speed partial derivative of the acquisition described in step 8 is specific as follows：
Wherein,Each of indicate in first fit Plane of each triangular pixel block point the directions z coordinate,Indicate every
Point is in the coordinate in the directions z each of in second fit Plane of a triangular pixel block, and x expressions are in the coordinate in the directions x, y tables
Show the coordinate in the directions y, A1And B1Indicate the coefficient of first fit Plane of each triangular pixel block, A2And B2Indicate every
The coefficient of second fit Plane of a triangular pixel block；
The strain rate of each triangular pixel block, formula are as follows：
Wherein,Indicate the strain rate tensor of each triangular pixel block；I denotation coordination axis i are x-axis or y-axis；J denotation coordinations
Axis j is x-axis or y-axis.
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