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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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 the technical field of measurement of strain rate fields of objects, and particularly relates to an optical measurement method of an in-plane strain rate field based on velocity linear fitting.
Background
The object deformation measurement is the important content of experimental mechanics; compared with other measuring methods, the optical measuring method plays an irreplaceable important role in experimental mechanics due to the advantages of non-contact, full field, high spatial resolution, high measuring precision and the like; in practical applications, the object deformation measurement often refers to the measurement of deformation in the plane of the object;
the digital image correlation method is an important method in the optical measurement method, and is used for performing correlation processing on two images (speckle fields) of the surface of an object, which are acquired before and after deformation, so as to realize object deformation measurement; the method can measure the deformation of the object in the plane and can also measure the out-of-plane deformation;
under the loaded condition, the distribution of the strain rate of the test piece or the structure is not uniform after a certain period; in the region of higher strain rate, where the strain increases more rapidly, this region tends to be the region where future cracks occur; by detecting the space-time distribution rule of the region with higher strain rate, the specific position of a future damage region can be known in advance, which is very beneficial to the analysis of material or structure damage mechanism and the research of disaster prevention;
the method for measuring the deformation in the object plane mainly comprises the following steps of:
1) based on a digital image correlation method of a Newton-Raphson (N-R) method, displacement and strain in an object plane are obtained simultaneously, but the error of a strain calculation result is large;
2) according to the digital image correlation method based on the central difference method, a strain field is obtained by carrying out central difference on a displacement field, but the reliability of a strain calculation result is reduced due to noise contained in the displacement field;
3) the digital image correlation method based on the finite element smoothing method utilizes the finite element method to smooth the displacement field to obtain the strain field, but the mathematical form and the programming execution are complex, and the method is not beneficial to popularization and application.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an optical measurement method of an in-plane strain rate field based on velocity linear fitting, so as to achieve the purposes of improving the accuracy, the reliability and the calculation speed.
An optical measurement method of an in-plane strain rate field based on velocity linear fitting comprises the following steps:
step 1, adopting shooting equipment to collect a plurality of images of a certain plane of a measured object in a loading process;
step 2, selecting a measurement image from the collected multiple images, determining the shooting time of each measurement image, and further obtaining the interval time of the measurement images at two adjacent times;
step 3, taking the plane of the first measurement image as an xoy plane, establishing a three-dimensional rectangular coordinate system oxyz, and discretizing the area of the measured object in the first measurement image into a non-overlapping and gapless triangular pixel block;
step 4, obtaining coordinates of three vertexes of the triangular pixel block, arranging 1 measuring point at each vertex position of the triangular pixel block, arranging N measuring points at non-vertex positions of each triangular pixel block in the xoy plane, wherein N is more than or equal to 0, and obtaining the coordinates of the measuring points on the x axis and the y axis;
step 5, obtaining a displacement field of a measuring point in a plane of a measured object in a loading process by adopting a digital image correlation method, and obtaining a velocity field of the measuring point in the plane according to the interval time of the measured images at two adjacent moments;
step 6, obtaining two groups of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system according to the x coordinate, the y coordinate and the speed of each measuring point in each triangular pixel block;
step 7, selecting error types, and obtaining the coefficient of the fitting plane of each triangular pixel block according to each group of fitting data points of each triangular pixel block;
and 8, obtaining the strain rate of each triangular pixel block according to the relation between the obtained coefficient and the velocity partial derivative, namely obtaining a strain rate field in the plane of the measured object.
6, obtaining two groups of fitting data points of each triangular pixel block in the three-dimensional rectangular coordinate system according to the x coordinate, the y coordinate and the speed of each measuring point in each triangular pixel block; the method specifically comprises the following steps:
step 6.1, in each triangular pixel block on the xoy surface, taking the x coordinate of each measuring point as the x coordinate of a fitting data point, taking the y coordinate of each measuring point as the y coordinate of the fitting data point, taking the component of the speed of each measuring point in the x-axis direction as the z coordinate of the fitting data point, and constructing a first group of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system oxyz;
and 6.2, in each triangular pixel block on the xoy surface, taking the x coordinate of each measuring point as the x coordinate of a fitting data point, taking the y coordinate of each measuring point as the y coordinate of the fitting data point, taking the component of the speed of each measuring point in the y-axis direction as the z coordinate of the fitting data point, and constructing a second group of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system oxyz.
Selecting the error type in the step 7, and obtaining the coefficient of the fitting plane of each triangular pixel block according to each group of fitting data points of each triangular pixel block;
the planes are as follows:
wherein,the coordinates of each point on the first fitting plane of each triangular pixel block in the z-direction are represented,representing the coordinates of each point on the second fitting plane of each triangular pixel block in the z-direction, x representing the coordinates in the x-direction, y representing the coordinates in the y-direction, A1、B1And C1Coefficient representing the first plane of fit of each triangular pixel block, A2、B2And C2The coefficients representing the second plane of fit for each triangular pixel block.
The relationship between the obtained coefficient and the speed partial derivative in step 8 is as follows:
wherein,the coordinates of each point on the first fitting plane of each triangular pixel block in the z-direction are represented,representing the coordinates of each point on the second fitting plane of each triangular pixel block in the z-direction, x representing the coordinates in the x-direction, y representing the coordinates in the y-direction, A1And B1Coefficient representing the first plane of fit of each triangular pixel block, A2And B2Coefficients representing the second fitted plane for each triangular pixel block;
the strain rate of each triangular pixel block is as follows:
wherein,a strain rate tensor representing each triangular pixel block; i represents a coordinate axis i which is an x axis or a y axis; j represents a coordinate axis j, either x-axis or y-axis.
The invention has the advantages that:
the optical measurement method of the in-plane strain rate field based on the velocity linear fitting is superior to the existing digital image correlation method based on the central difference method based on the idea of data fitting, the process is simple, the steps are convenient and fast to understand, the result can be obtained only by solving the coefficient of the fitting plane equation, and the measurement speed and the programming convenience are improved; the invention considers the information of the measuring points in the discrete pixel block, improves the accuracy and the reliability of the final result, and increases the flexibility of measuring point selection; the invention has wide application prospect in the field of solid experimental mechanics.
Drawings
FIG. 1 is a flow chart of a method for optical measurement of a strain rate field in a plane of an object according to one embodiment of the present invention;
FIG. 2 is a schematic view of a measurement image of a surface of a test piece during a selected uniaxial compression process according to one embodiment of the present invention, wherein (a) is a first measurement image, (b) is a second measurement image, and (c) is a third measurement image;
FIG. 3 is a discretized triangular pixel block distribution diagram of the region of the measured object in the first measurement image according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of the position of each station on the first measurement image according to one embodiment of the present invention;
FIG. 5 is a geometric schematic diagram of a triangle pixel block fitting plane obtained from the velocity and coordinates of the measured points according to an embodiment of the present invention;
FIG. 6 is a strain rate field fill map of second through third images obtained by the method of the present invention, wherein (a) is a linear strain rate field fill map in the x-direction, (b) is a linear strain rate field fill map in the y-direction, and (c) is an in-plane shear strain rate field fill map, according to an embodiment of the present invention;
fig. 7 is a strain rate field fill map obtained from the second to third images by the digital image correlation method based on the N-R method, in which (a) is a linear strain rate field fill map in the x-direction, (b) is a linear strain rate field fill map in the y-direction, and (c) is an in-plane shear strain rate field fill map;
fig. 8 is a strain rate field filling diagram obtained from the second to third images by using a digital image correlation method based on a center difference method, wherein (a) is a linear strain rate field filling diagram in the x direction, (b) is a linear strain rate field filling diagram in the y direction, and (c) is an in-plane shear strain rate field filling diagram;
in the figure, 1 is a triangular pixel block, 2 is a vertex of the triangular pixel block, 3 is a measuring point, 4 is the triangular pixel block, 5 is the measuring point, 6 is a fitting data point, 7 is the triangular pixel block, and 8 is a fitting plane; a is a first vertex of the triangular pixel block, b is a second vertex of the triangular pixel block, and c is a third vertex of the triangular pixel block.
Detailed Description
An embodiment of the present invention will be further described with reference to the accompanying drawings.
An optical measurement method of in-plane strain rate field based on velocity linear fitting, the flow chart of the method is shown in figure 1, and the method comprises the following steps:
step 1, adopting shooting equipment to collect a plurality of images of a certain plane of a measured object in a loading process;
in the embodiment of the invention, a measured object is a cuboid test piece with the height of 90mm and the width of 50mm, the test piece is placed on a platform, artificial speckles are made on one surface of the test piece by adopting paint, displacement control loading is carried out on the upper end surface, and a speckle pattern of the surface is collected;
step 2, selecting a measurement image from the collected multiple images, determining the shooting time of each measurement image, and further obtaining the interval time of the measurement images at two adjacent times;
in the embodiment of the invention, 3 measurement images are selected from a plurality of acquired images, the selected measurement images are shown in (a) to (c) in fig. 2, the shooting time of each measurement image is obtained, the shooting interval time between the first measurement image and the second measurement image is further 198s, and the shooting interval time between the second measurement image and the third measurement image is 2 s;
step 3, taking the plane of the first measurement image as an xoy plane, establishing a three-dimensional rectangular coordinate system oxyz, and discretizing the area of the measured object in the first measurement image into a non-overlapping and gapless triangular pixel block;
in the embodiment of the invention, as shown in fig. 3 (in the figure, 1 represents a triangular pixel block, 2 represents a vertex of the triangular pixel block, a represents a first vertex of the triangular pixel block, b represents a second vertex of the triangular pixel block, and c represents a third vertex of the triangular pixel block), a region where a measured object in a first measured image is located is discretized into 5762 triangular pixel blocks which are arranged closely, have no overlap and have no gap;
step 4, obtaining coordinates of three vertexes of the triangular pixel block, arranging 1 measuring point at each vertex position of the triangular pixel block, arranging N measuring points at non-vertex positions of each triangular pixel block in the xoy plane, wherein N is more than or equal to 0, and obtaining the coordinates of the measuring points on the x axis and the y axis;
in the embodiment of the present invention, as shown in fig. 4 (in the figure, 3 represents a measuring point, and 4 represents a triangular pixel block), 1 measuring point is arranged at a non-vertex position of each triangular pixel block in the xoy plane;
step 5, obtaining a displacement field of a measuring point in a plane of a measured object in a loading process by adopting a digital image correlation method, and obtaining a velocity field of the measuring point in the plane according to the interval time of the measured images at two adjacent moments;
the method comprises the following specific steps:
step 5.1, obtaining the position of each measuring point on the second measuring image and the third measuring image by adopting a digital image correlation method according to the position of each measuring point on the first measuring image;
step 5.2, obtaining the displacement of each measuring point on the second measuring image according to the position of each measuring point on the first measuring image and the position of each measuring point on the second measuring image, and obtaining the displacement of each measuring point on the third measuring image by adopting the same method;
step 5.3, obtaining the displacement difference of each measuring point on the second measuring image and the third measuring image, and obtaining the speed of each measuring point according to the shooting interval time of the second measuring image and the third measuring image, namely obtaining the speed field of the measuring point in the plane;
step 6, obtaining two groups of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system according to the x coordinate, the y coordinate and the speed of each measuring point in each triangular pixel block;
in the embodiment of the present invention, as shown in fig. 5 (a), in the diagram, 5 denotes a measuring point, 6 denotes a fitting data point, and 7 denotes a triangular pixel block, and two groups of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system are obtained, which specifically includes the following steps:
step 6.1, in each triangular pixel block on the xoy surface, taking the x coordinate of each measuring point as the x coordinate of a fitting data point, taking the y coordinate of each measuring point as the y coordinate of the fitting data point, taking the component of the speed of each measuring point in the x-axis direction as the z coordinate of the fitting data point, and constructing a first group of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system oxyz;
step 6.2, in each triangular pixel block on the xoy surface, taking the x coordinate of each measuring point as the x coordinate of a fitting data point, taking the y coordinate of each measuring point as the y coordinate of the fitting data point, taking the component of the speed of each measuring point in the y-axis direction as the z coordinate of the fitting data point, and constructing a second group of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system oxyz;
step 7, selecting error types, and obtaining the coefficient of the fitting plane of each triangular pixel block according to each group of fitting data points of each triangular pixel block; the error types comprise maximum error, average error, root mean square error and the like, belong to common knowledge in the field, and can be selected according to actual requirements;
step 7.1, determining two fitting plane equations of each triangular pixel block;
in the embodiment of the present invention, the fitted plane is shown in fig. 5 (b), wherein 8 represents the fitted plane;
the plane equation is as follows:
wherein,the coordinates of each point on the first fitting plane of each triangular pixel block in the z-direction are represented,representing the coordinates of each point on the second fitting plane of each triangular pixel block in the z-direction, x representing the coordinates in the x-direction, y representing the coordinates in the y-direction, A1、B1And C1First fitting plane representing each triangle pixel blockCoefficient of area, A2、B2And C2Coefficients representing the second fitted plane for each triangular pixel block;
step 7.2, selecting the root mean square error, and obtaining the root mean square error of the two fitting planes of each triangular pixel block according to the two groups of fitting data points of each triangular pixel block, wherein the root mean square error is the minimum sum of squares of vertical distances from the fitting data points to the fitting planes (namely, the distances from the fitting data points to the fitting planes along the direction parallel to the z axis), and the formula is as follows:
wherein E is1The root mean square error of the first fitting plane of each triangular pixel block is represented; e2The root mean square error of the second fitting plane representing each triangular pixel block; x is the number ofkThe coordinates of the fitted data points of each triangular pixel block in the x direction are represented; y iskThe coordinates of the fitted data points of each triangular pixel block in the y direction are represented;the coordinates in the z-direction of the first set of fitted data points representing each triangular pixel block;the coordinates in the z-direction of the second set of fitted data points representing each triangular pixel block; k represents the kth fitting data point in each group of fitting data points and has the value range of [1, 2, 3, 4 ]]；
And 7.3, obtaining a normal equation of two groups of least square fitting planes of each triangular pixel block by ensuring the minimum root mean square error, specifically:
the minimum root mean square error is the partial derivativeAndandto zero, the formula is as follows:
step 7.4, solving the formula (5) and the formula (6) to obtain the coefficient A of the least square fitting plane1、B1、C1、A2、B2And C2；
Step 8, obtaining the strain rate of each triangular pixel block according to the relation between the obtained coefficient and the velocity partial derivative, namely obtaining a strain rate field in the plane of the measured object; the method specifically comprises the following steps:
step 8.1, respectively solving partial derivatives of equations of two least square fitting planes in the formula (1) to obtain a relation between coefficients of the least square fitting planes and speed partial derivatives;
the formula is as follows:
wherein,the coordinates of each point on the first fitting plane of each triangular pixel block in the z-direction are represented,representing the coordinates of each point on the second fitting plane of each triangular pixel block in the z-direction, x representing the coordinates in the x-direction, y representing the coordinates in the y-direction, A1And B1Coefficient representing the first plane of fit of each triangular pixel block, A2And B2Coefficients representing the second fitted plane for each triangular pixel block;
step 8.2, obtaining a velocity partial derivative and a strain rate by using a geometric equationThe relationship between;
the formula is as follows:
wherein,a strain rate tensor representing each triangular pixel block;represents a velocity component in the i direction; xjRepresents a coordinate in the j direction;represents a velocity component in the j direction; xiRepresents coordinates in the i direction; i represents a coordinate axis i which is an x axis or a y axis; j represents a coordinate axis j which is an x axis or a y axis;
step 8.3, converting the strain rate formula (7) into a common form in engineering;
the method specifically comprises the following steps:
strain rate per triangular pixel blockIs a tensor, for a two-dimensional problem，Expressed as:
wherein, XxRepresenting the coordinates in the x direction, i.e. x; xyThe coordinates in the y direction are represented as y;
order toThenCan be expressed as:
wherein,represents the linear strain rate in the x direction;represents the in-plane shear strain rate;represents the linear strain rate in the y direction;
and 8.4, combining the formula (2) with the formula (7) to obtain the strain rate of each triangular pixel block, namely obtaining a strain rate field in the plane of the measured object, wherein the formula is as follows:
in the embodiment of the present invention, fig. 6 is a strain rate field filling diagram (including diagram (a), diagram (b) and diagram (c)) obtained from the second to third images by using the method of the present invention; for comparison, fig. 7 shows strain rate field filling maps (including map (a), map (b) and map (c)) obtained from the second to third images using a digital image correlation method based on the N-R method; fig. 8 shows strain rate field filling maps (including map (a), map (b), and map (c)) obtained from the second to third images using a digital image correlation method based on a center difference method; as can be seen from FIGS. 6 to 8, the various strain rate fields are unevenly distributed, and in particularAndhigh-value or low-value strain rate zones are observed in the form of bands, and the strain at the positions is changed rapidly and is a future macrocracks;
in the embodiment of the invention, the digital image correlation method based on the center difference method and the digital image correlation method obtained by the method Andthe measurement ranges of the two-dimensional image correlation method are different and are better than the measurement results obtained by the digital image correlation method based on the N-R method; in particular, obtained by means of a digital image correlation method based on a central difference methodThe measurement range of (1) is (-7 to 19). times.10-3s-1，The measurement range of (1) is (-16-6) x 10-3s-1，The measurement range of (1) is (-17-8) x 10-3s-1Obtained by the process of the inventionThe measurement range of (1) is (-15 to 33) x 10-3s-1，The measurement range of (1) is (-21 to 9) x 10-3s-1，The measurement range of (1) is (-29 to 17) x 10-3s-1(ii) a In contrast, the measurement range obtained by the method of the present invention is larger than the measurement range obtained by the digital image correlation method based on the center difference method, which makes the main strain rate high value region more prominent, and meanwhile, the width of the high value region is narrower, which means that the method of the present invention can be used for describing the strain rate field more finely; from the measurement results obtained by the method, clear banded strain rate high-value areas and band-shaped strain rate low-value areas can be observed, while the measurement results obtained by the digital image correlation method based on the central difference method are fuzzy, and the strain rate high-value areas are mottled; in conclusion, the measurement results obtained by the method of the invention are superior to the other two methods.
Claims (4)
1. An optical measurement method of an in-plane strain rate field based on velocity linear fitting is characterized by comprising the following steps:
step 1, adopting shooting equipment to collect a plurality of images of a certain plane of a measured object in a loading process;
step 2, selecting a measurement image from the collected multiple images, determining the shooting time of each measurement image, and further obtaining the interval time of the measurement images at two adjacent times;
step 3, taking the plane of the first measurement image as an xoy plane, establishing a three-dimensional rectangular coordinate system oxyz, and discretizing the area of the measured object in the first measurement image into a non-overlapping and gapless triangular pixel block;
step 4, obtaining coordinates of three vertexes of the triangular pixel block, arranging 1 measuring point at each vertex position of the triangular pixel block, arranging N measuring points at non-vertex positions of each triangular pixel block in the xoy plane, wherein N is more than or equal to 0, and obtaining coordinates of the N measuring points on the x axis and the y axis;
step 5, obtaining a displacement field of a measuring point in a plane of a measured object in a loading process by adopting a digital image correlation method, and obtaining a velocity field of the measuring point in the plane according to the interval time of the measured images at two adjacent moments;
step 6, obtaining two groups of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system according to the x coordinate, the y coordinate and the speed of each measuring point in each triangular pixel block;
step 7, selecting error types, and obtaining the coefficient of the fitting plane of each triangular pixel block according to each group of fitting data points of each triangular pixel block;
and 8, obtaining the strain rate of each triangular pixel block according to the relation between the obtained coefficient and the velocity partial derivative, namely obtaining a strain rate field in the plane of the measured object.
2. The optical measurement method for in-plane strain rate field based on velocity linear fitting according to claim 1, wherein two sets of fitting data points of each triangular pixel block in the three-dimensional rectangular coordinate system are obtained according to the x coordinate, the y coordinate and the velocity of each measuring point in each triangular pixel block in step 6; the method specifically comprises the following steps:
step 6.1, in each triangular pixel block on the xoy surface, taking the x coordinate of each measuring point as the x coordinate of a fitting data point, taking the y coordinate of each measuring point as the y coordinate of the fitting data point, taking the component of the speed of each measuring point in the x-axis direction as the z coordinate of the fitting data point, and constructing a first group of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system oxyz;
and 6.2, in each triangular pixel block on the xoy surface, taking the x coordinate of each measuring point as the x coordinate of a fitting data point, taking the y coordinate of each measuring point as the y coordinate of the fitting data point, taking the component of the speed of each measuring point in the y-axis direction as the z coordinate of the fitting data point, and constructing a second group of fitting data points of each triangular pixel block in a three-dimensional rectangular coordinate system oxyz.
3. The method for optical measurement of in-plane strain rate field based on velocity linear fitting according to claim 1, wherein the selecting of error type in step 7 obtains the coefficients of the fitting plane of each triangular pixel block from each set of fitting data points of each triangular pixel block;
the planes are as follows:
wherein,the coordinates of each point on the first fitting plane of each triangular pixel block in the z-direction are represented,representing the coordinates of each point on the second fitting plane of each triangular pixel block in the z-direction, x representing the coordinates in the x-direction, y representing the coordinates in the y-direction, A1、B1And C1Coefficient representing the first plane of fit of each triangular pixel block, A2、B2And C2The coefficients representing the second plane of fit for each triangular pixel block.
4. The method for optical measurement of in-plane strain rate field based on velocity linear fitting according to claim 1, wherein the relationship between the obtained coefficient and the velocity partial derivative in step 8 is as follows:
wherein,the coordinates of each point on the first fitting plane of each triangular pixel block in the z-direction are represented,representing the coordinates of each point on the second fitting plane of each triangular pixel block in the z-direction, x representing the coordinates in the x-direction, y representing the coordinates in the y-direction, A1And B1Coefficient representing the first plane of fit of each triangular pixel block, A2And B2Coefficients representing the second fitted plane for each triangular pixel block;
the strain rate of each triangular pixel block is as follows:
wherein,a strain rate tensor representing each triangular pixel block; i represents a coordinate axis i which is an x axis or a y axis; j represents a coordinate axis j, either x-axis or y-axis.
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