CN113808029A - Strain smoothing method in digital image correlation - Google Patents
Strain smoothing method in digital image correlation Download PDFInfo
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Abstract
The invention discloses a strain smoothing method in digital image correlation. Then, grid cells and nodes are divided for the image, feature points in the cells are selected, and the displacement of the feature points is obtained through a digital image correlation method. And selecting the type of the displacement function in the unit, and fitting the displacement function in the unit according to the position coordinates and the displacement of the characteristic points. And calculating the average strain in the unit according to the fitted displacement function. And calculating the smooth strain of the node according to the average strain of all adjacent units of the node aiming at all the nodes. And performing difference on the smooth strains of all the nodes to obtain the full-field strain. The invention can improve the strain measurement precision of the digital image correlation method to a certain extent.
Description
Technical Field
The invention relates to an experimental mechanics, non-contact full-field strain measurement and digital image correlation method, in particular to a strain smoothing method in digital image correlation.
Background
In the fields of aerospace, building bridges and the like, the first requirement is to ensure the reliability of the structure. With the development of science and technology, the ability to apply controlled reparations to structures before irreversible damage occurs has become an important goal for many scientists. And the measurement result of the material response load representation provided by experimental mechanics has rich guiding significance for perfecting design, improving structure and monitoring damage. The displacement and the strain are used as important parameters of experimental mechanics, and have the important functions of analyzing the mechanical characteristics of the model, verifying the basic hypothesis, identifying the characteristics and the like. In the face of increasingly complex measurement requirements, the traditional displacement strain measurement method is very easy to find. Meanwhile, the finite displacement strain measurement result is far from being sufficient for the analysis work of a complex model. And aiming at the constraint of various measurement conditions, a new measurement technology capable of realizing full-field strain and non-contact measurement is developed.
Different methods that enable full-field measurements, each with their advantages of accuracy and applicability. And a Digital Image Correlation (DIC) method capable of simultaneously satisfying non-contact measurement conditions has been widely used in experimental mechanics due to its advantages of low experimental cost, relatively simple data acquisition process, etc., and has low requirements on measurement environment and vibration isolation, strong universality, and wide application in various engineering and subject fields, such as aerospace, biomedical, etc.
In Digital Image Correlation (DIC), how to accurately measure strain has been a concern for related researchers. Theoretically, strain is the derivative of displacement. However, in the actual DIC measurement process, due to various reasons such as noise and errors in pixel interpolation, the displacement measurement result has certain errors. When the strain is calculated differentially from the displacement measurement, errors in the displacement field are further amplified, resulting in inaccurate strain measurements. Related researchers have proposed various displacement field smoothing methods to improve the strain calculation accuracy, but most of the methods are complicated in mathematical form or greatly increase the calculation amount, so that the practical application is limited.
Disclosure of Invention
Aiming at the problems in the prior art, the invention discloses a strain smoothing method in digital image correlation. And then calculating the smooth strain of the node according to the average strain of all the units adjacent to the node. Through addition of the two methods, the strain calculation precision is obviously improved.
The invention is realized by the following steps:
a method of smoothing strain in digital image correlation, the method comprising:
step one, building a digital image related measurement system, and acquiring a reference image before deformation and a deformed image after deformation of a test piece;
step two, meshing the image according to the finite element mesh units and the unit nodes;
thirdly, calculating the displacement of a plurality of characteristic points in each grid cell according to a digital image correlation method;
step four, selecting the type of the displacement function in each unit, and fitting the displacement function of the unit according to the displacement of the unit characteristic points by using a fitting method;
calculating the average strain in the unit according to the fitted unit displacement function;
step six, calculating the smooth strain of the node according to the average strain of the grid unit adjacent to the node;
and seventhly, interpolating to obtain the full-field strain according to the smooth strain of each node obtained through calculation.
Further, in the second step, the mesh division method is a uniform mesh division method or a non-uniform mesh division method; and dividing the grid cells into triangular grids, rectangular grids or polygonal grids.
Further, the plurality of feature points in the unit are all specifically selected points, and specifically include: a cell node, a point on a cell edge, or a point inside a cell.
Furthermore, in the fourth step, the displacement function in the unit is fitted according to the type of the unit displacement function and the number of the characteristic points, and all fitting methods are applicable to the method.
Further, in the sixth step, the smooth strain calculation method includes:
in the formula (I), the compound is shown in the specification,
represents the smooth strain of the node point,
in order to be a strain in the conventional finite element,
for smoothing subdomains, consisting of all grid cells adjacent to a node, Φ (x) is a smoothing function, which can be defined as follows
In the formula (I), the compound is shown in the specification,
is the smooth subdomain area;
since the average strain in the adjacent cells of the node has been calculated, equation (1) is rewritten as follows
In the formula (I), the compound is shown in the specification,
for smooth subdomain areas, n is the total number of grid cells adjacent to the node, εiRepresents the average strain, Ω, of the i-th celliRepresenting the area of the ith cell.
The beneficial effects of the invention and the prior art are as follows:
the method is not limited to any grid division mode, and characteristic points are selected in each grid unit to perform displacement field fitting. The more the selected characteristic points are, the better the displacement field fitting effect is, and the higher the strain calculation precision is.
The invention can balance and accept the trade-off between the calculation efficiency and the calculation precision. And after the displacement field function is fitted, calculating to obtain the average strain in the unit. And the smooth strain of the node can be calculated according to the average strain of all the units adjacent to the node, and the strain calculation precision is further improved.
Drawings
FIG. 1 is a reference image and a deformed image in an embodiment of a method of strain smoothing in digital image correlation according to the present invention;
FIG. 2 is a meshing result of an embodiment of a strain smoothing method in digital image correlation according to the present invention;
FIG. 3 is a graph of fitted strain measurements in an embodiment of a method of strain smoothing in digital image correlation of the present invention;
FIG. 4 is a graph of smooth strain measurements in an embodiment of a method of smoothing strain in digital image correlation of the present invention.
Detailed Description
In order to make the objects, technical solutions and effects of the present invention more clear, the present invention is further described in detail by the following examples. It should be noted that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In order to realize the purpose of the invention, the method comprises the following specific steps:
the method comprises the following steps: constructing a digital image correlation measurement system, and acquiring a reference image before deformation and a deformed image after deformation of the test piece;
step two: carrying out grid unit division on the reference image, and recording the serial number of each unit and node;
step three: using the unit nodes, the unit edge midpoints and the unit centers as unit characteristic points, using pixel interpolation to obtain position coordinates of the characteristic points, and using a digital image correlation method to calculate the displacement of all the unit characteristic points;
step four: the displacement fit function within the selected cell, e.g. a first order polynomial, is of the form
Wherein u and v are displacements, x and y are position coordinates, and a0,a1,a2,b0,b1,b2Is the undetermined coefficient.
According to the position coordinates and the displacement of the unit characteristic points, a formula (4) can be obtained by fitting by using a least square method;
step five: calculating the average strain in each unit according to the displacement function obtained by fitting;
step six: calculating the smooth strain of the node according to the average strain of the grid units adjacent to the node, wherein the calculation method of the smooth strain comprises the following steps:
in the formula (I), the compound is shown in the specification,
represents the smooth strain of the node point,
in order to be a strain in the conventional finite element,
for smoothing subdomains, consisting of all grid cells adjacent to a node, Φ (x) is a smoothing function, which can be defined as follows
In the formula (I), the compound is shown in the specification,
is a smooth subfield area.
Since the average strain in the neighboring cells of the node has been calculated, equation (1) can be rewritten as follows
Wherein n is the total number of grid cells adjacent to the node, εiRepresents the average strain, Ω, of the i-th celliRepresenting the area of the ith cell.
And seventhly, interpolating to obtain the full-field strain according to the smooth strain of each node obtained through calculation.
The process according to the invention is described below by way of specific examples:
the simulated speckle image is generated by a computer gaussian speckle algorithm, the pixels are 300 × 300, the number of speckles is 1000, a reference image is generated, then the x-direction positive strain is set to be 0.002, the y-direction positive strain is set to be 0.003, and a deformation image is generated, as shown in fig. 1. The displacement field is calculated by the algorithm, and then the calculation result is compared with the real solution.
The specific implementation steps are as follows:
the method comprises the following steps: performing triangular meshing on the simulated speckle reference image generated by the computer, wherein the meshing result and the direction of a coordinate system are shown in FIG. 2;
step two: selecting triangular mesh nodes, trilateral midpoints and triangular centers as unit feature points, recording position coordinates of the 7 feature points, and calculating displacement of the 7 feature points by using a digital image correlation method;
step three: selecting a quadratic polynomial as a displacement function in a unit, as represented by formula (4), fitting a unit displacement field by using the position coordinates and displacement of 7 characteristic points and adopting a least square method;
step four: since the displacement field of the cell is a linear function, the strain in the cell becomes constant strain, and the average strain in the cell can be obtained by differentiating the displacement field function as shown in the following formula
From the measured constant strain of all cells, the full field strain is interpolated and the result is shown in fig. 3.
The results show that the mean of the x-direction positive strain measurements is 1998.6 × 10-6Standard deviation of 5.05X 10-5Maximum value of 2296.5 × 10-6Minimum value of 1678.3 × 10-6The maximum error is 14.8 percent, and the minimum error is-16.1 percent;
the mean value of the y-direction positive strain measurement is 2998.9X 10-6Standard deviation of 5.39 × 10-5Maximum value of 3450.4 × 10-6Minimum value of 2832.2 × 10-6The maximum error is 15 percent, and the minimum error is-5.6 percent;
step five: for each node, calculating the smooth strain of the point according to the formula (3) according to the average strain of the cells adjacent to the node;
step six: from the smooth strains of all nodes, the full field smooth strain is interpolated, and the result is shown in fig. 4.
The results show that the mean of the x-direction positive strain measurements is 1998.0 × 10-6Standard deviation of 1.28 × 10-5Maximum value of 2044.6 × 10-6Minimum value of 1910.2 × 10-6The maximum error is 2.2 percent, and the minimum error is-4.5 percent;
the mean value of the y-direction positive strain measurement is 2996.0X 10-6Standard deviation of 1.70 × 10-5Maximum value of 3054.3 × 10-6Minimum value of 2932.2 × 10-6The maximum error is 1.8 percent, and the minimum error is-2.3 percent;
the smooth strain and the fitting strain result are compared to find that the smooth strain method can effectively reduce data measurement errors and improve measurement accuracy.
Finally, it should be noted that the above embodiments are only intended to illustrate the implementation of the present invention and not to limit it; it should be understood that the implementation of the invention can be modified or part of the algorithm can be replaced equally without departing from the spirit of the invention, and all that is covered by the technical scheme of the invention.
Claims (5)
1. A method of smoothing strain in digital image correlation, the method comprising:
step one, building a digital image related measurement system, and acquiring a reference image before deformation and a deformed image after deformation of a test piece;
step two, meshing the image according to the finite element mesh units and the unit nodes;
thirdly, calculating the displacement of a plurality of characteristic points in each grid cell according to a digital image correlation method;
step four, selecting the type of the displacement function in each unit, and fitting the displacement function of the unit according to the displacement of the unit characteristic points by using a fitting method;
calculating the average strain in the unit according to the fitted unit displacement function;
step six, calculating the smooth strain of the node according to the average strain of the grid unit adjacent to the node;
and seventhly, interpolating to obtain the full-field strain according to the smooth strain of each node obtained through calculation.
2. The method for smoothing strain in digital image correlation according to claim 1, wherein in the second step, the gridding method is a uniform gridding method or a non-uniform gridding method; and dividing the grid cells into triangular grids, rectangular grids or polygonal grids.
3. The method according to claim 1, wherein the plurality of feature points in the cell are all specifically selected points, and specifically comprises: a cell node, a point on a cell edge, or a point inside a cell.
4. The method according to claim 1, wherein in the fourth step, the intra-cell displacement function is fitted according to the type of the cell displacement function and the number of the feature points, and all fitting methods are applicable.
5. The method for smoothing strain in digital image correlation according to claim 1, wherein in the sixth step, the method for calculating the smoothing strain comprises:
in the formula (I), the compound is shown in the specification,
represents the smooth strain of the node point,
in order to be a strain in the conventional finite element,
for smoothing subdomains, consisting of all grid cells adjacent to a node, Φ (x) is a smoothing function, which can be defined as follows
In the formula (I), the compound is shown in the specification,
is the smooth subdomain area;
since the average strain in the adjacent cells of the node has been calculated, equation (1) is rewritten as follows
In the formula (I), the compound is shown in the specification,
to smooth the sub-domain areaN is the total number of grid cells adjacent to the node, epsiloniRepresents the average strain, Ω, of the i-th celliRepresenting the area of the ith cell.
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Citations (4)
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|---|---|---|---|---|
| CN104616271A (en) * | 2015-03-06 | 2015-05-13 | 南京航空航天大学 | Adaptive displacement field smoothing method applicable to digital image correlation |
| CN104613888A (en) * | 2015-02-03 | 2015-05-13 | 清华大学 | Method for measuring deformation of object in smoke under flame smoke environment |
| CN104657955A (en) * | 2015-03-06 | 2015-05-27 | 南京大树智能科技股份有限公司 | Displacement field iteration smoothing method of kernel function based digital image correlation method |
| CN112819962A (en) * | 2021-02-10 | 2021-05-18 | 南京航空航天大学 | Non-uniform grid division and local grid density method in digital image correlation |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104613888A (en) * | 2015-02-03 | 2015-05-13 | 清华大学 | Method for measuring deformation of object in smoke under flame smoke environment |
| CN104616271A (en) * | 2015-03-06 | 2015-05-13 | 南京航空航天大学 | Adaptive displacement field smoothing method applicable to digital image correlation |
| CN104657955A (en) * | 2015-03-06 | 2015-05-27 | 南京大树智能科技股份有限公司 | Displacement field iteration smoothing method of kernel function based digital image correlation method |
| CN112819962A (en) * | 2021-02-10 | 2021-05-18 | 南京航空航天大学 | Non-uniform grid division and local grid density method in digital image correlation |
Non-Patent Citations (1)
| Title |
|---|
| X.XU: ""A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh"", FINITE ELEMENTS IN ANALYSIS AND DESIGN, 31 October 2010 (2010-10-31), pages 862 - 874, XP027173750 * |
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