CN115187578A - High-speed global deformation measurement method and system - Google Patents

Abstract

The invention provides a high-speed global deformation measuring method and a system, comprising the following steps: step S1: the optical axes of a camera and a lens are vertical to the surface of a sample, the camera is used for recording digital images of the sample in different states, an auxiliary global continuous displacement field and constraint conditions are introduced during image processing, and the displacement gradient of the field in each subset area are kept consistent with the calculation result of the local DIC; step S2: modifying the correlation function based on the augmented Lagrangian function and the constraint condition; and step S3: coordinating local subproblems by using an Alternating Direction Multiplier Method (ADMM) to find a solution of a global problem, and iteratively solving the problem; and step S4: a field of interest including strain, velocity is derived from the global displacement field. The invention uses the augmented Lagrange function, the calculation efficiency is far higher than that of the FEM-based global DIC algorithm, and the obtained global displacement field has continuity by introducing constraint conditions through the augmented Lagrange function.

Description

High-speed global deformation measurement method and system

Technical Field

The invention relates to the technical field of image processing and measurement, in particular to a high-speed global deformation measurement method and system.

Background

Digital Image Correlation (DIC) is an image-based non-contact optical measurement method for measuring the constantly changing coordinates of an object surface, the measured coordinate field being used to further derive fields of interest for displacement, strain and velocity. As long as the object surface has a suitable speckle pattern, the shape, motion and deformation of almost any object can be measured, even under extreme experimental conditions. DIC technology is essentially an image processing technology that, in addition to its non-contact, full-field measurement capabilities, has several unique features, such as simple, inexpensive experimental setup, easy implementation, and robustness. Theoretically, whatever imaging modality is used, measurements can be made using DIC techniques, provided that the images have significant intensity variations and unique correspondences to points on the object surface. Indeed, DIC technology has been applied to general metals, high molecular materials, composite materials, biological tissues and surface deformations, and can be used from several micrometers (e.g., fibers) to several tens of kilometers (e.g., ground deformations).

In the past decades, researchers have proposed various DIC algorithms based on their own thoughts. Most algorithms can be divided into two categories: subset-based local DIC algorithms and FEM (fine Element Method) -based global DIC algorithms. In the local subset DIC, a region of interest (region of interest) of a reference image is first decomposed into a plurality of subsets, and then a distortion of each subset is determined. Each subset in the local DIC is finite in size so that the distortion of each subset can be solved quickly. Because the solving processes of the subsets are independent, the running efficiency can be improved by using a parallel computing mode. However, just as the deformation of each subset is obtained independently, the overall deformation may be discontinuous and the strain field is more noisy. In FEM (Finite Element Method) based global DIC, a basis set (usually based on Finite Element discretization) is generally used to represent global deformation, and then the global image is analyzed to obtain parameters of the basis set, by which the overall deformation field of the object can be obtained. The global DIC calculates the object deformation based on FEM, so the obtained deformation field is coordinated throughout. However, global DIC is very computationally intensive and often takes up ten times as long as local DIC under the same conditions.

Patent document CN108956310B (application number: CN 201810347552.8) discloses a three-dimensional DIC-based geomembrane liquid swelling deformation testing device and a testing method, comprising a pressure testing system, a pressure control system and a three-dimensional DIC measuring system; the pressure test system comprises an upper membrane pressure chamber, a geomembrane diameter adjusting device, a lower membrane pressure chamber and a base which are coaxially arranged from top to bottom in sequence; speckles are uniformly sprayed on the upper surface of the geomembrane, and digital images recorded by the speckles in the three-dimensional DIC measuring system are not less than 3 pixels; the pressure control system comprises an on-membrane pressure control system and a under-membrane pressure control system; the three-dimensional DIC measuring system comprises a halogen lamp, a computer and two CCD cameras which are connected with the computer. When a series of digital images of the geomembrane surface speckle deformation shot by a single camera in a certain step are subjected to time sequence matching, the displacement of each calculated area is discontinuous and contains more noise by utilizing a subset-based local DIC principle, so that the precision of a subsequent calculation result is reduced. If the algorithm of the patent is adopted, a globally continuous displacement field can be obtained through solving, and a more accurate result can be obtained in subsequent calculation.

Disclosure of Invention

In view of the defects in the prior art, the invention aims to provide a high-speed global deformation measuring method and system.

The high-speed global deformation measuring method provided by the invention comprises the following steps:

step S1: the optical axes of a camera and a lens are vertical to the surface of a sample, the camera is used for recording digital images of the sample in different states, an auxiliary global continuous displacement field and constraint conditions are introduced during image processing, and the displacement gradient of the field in each subset area are kept consistent with the calculation result of the local DIC;

step S2: modifying the correlation function based on the augmented Lagrangian function and the constraint condition;

and step S3: coordinating local subproblems by using an Alternating Direction Multiplier Method (ADMM) to find a solution of a global problem, and iteratively solving the problem;

and step S4: a field of interest including strain, velocity is derived from the global displacement field.

Preferably, the step S1 includes:

when the displacement field is globally continuous, the displacement u and the displacement gradient F are not independent, and global constraint is met:

{F}＝D{u}

using discrete gradient operators in the formulaD, calculating the displacement gradient, using a first-order finite difference method of a uniform square grid, and introducing an auxiliary global continuous displacement field

This condition is processed to obtain two constraints:

in order to be a gradient operator, the method comprises the following steps,

is the gradient of the auxiliary global continuous displacement field.

Preferably, the step S2 includes:

the objective function of the subset DIC is:

the subsets DIC only have to satisfy the respective subset omega _i The target function is minimum, a global continuous displacement field is introduced, the target function is modified through an augmented Lagrange function and a constraint condition, a global optimal solution needs to be obtained, and the target function is as follows:

in the formula _i Representing the entire subset area, requiring a global displacement field

Therefore, the global objective function minimum is to be satisfied;

u _i represents X _i0 Displacement of (2); f _i Represented as subset Ω _i Uniform displacement gradient of(ii) a Dividing a reference image into a plurality of subsets in the subset DIC, wherein i is an index of each subset; f (X) represents the gray value at point X on the reference image; x represents the coordinates of a point in the digital image; g (X) represents the gray value at point X on the deformed image; x _i0 Represents the subset Ω _i The center of (a); beta is a corresponding constraint

The coefficient of the secondary penalty term; w is a group of _i Is a corresponding constraint

Lagrange multiplier of (a); mu is the corresponding constraint

The coefficient of the secondary penalty term;

representing the introduced global continuous displacement field and the quantity to be solved; v _i Is a corresponding constraint

Lagrange multiplier.

Preferably, the step S3 includes:

step S3.1: let W _i 、V _i 、

First solve u without change _i 、F _i The kth iteration is expressed as follows:

step S3.2: only handle

As variables, the objective function is as follows:

and updating Lagrange multiplier W according to the result obtained by iteration _i 、V _i This step is repeated until the iteration stop criterion is met, i.e.

Is sufficiently small.

Preferably, the step S4 includes:

and (3) taking the lower left corner of the image as an origin, the lower edge as an x axis and the left edge as a y axis, establishing a plane rectangular coordinate system, and deriving the strain according to the following formula:

e _xy representing the variation of the included angle of the two tiny line segments in the mutually perpendicular directions after deformation; e.g. of the type _yy The ratio of the length increment of the tiny line segment along the y-axis direction, which is generated by deformation, to the original length is expressed, and the length is positive when the tiny line segment is elongated; u represents displacement in the x-axis direction; v represents displacement in the y-axis direction.

The high-speed global deformation measuring system provided by the invention comprises:

a module M1: the optical axes of a camera and a lens are vertical to the surface of a sample, the camera is used for recording digital images of the sample in different states, an auxiliary global continuous displacement field and constraint conditions are introduced during image processing, and the displacement gradient of the field in each subset area are kept consistent with the calculation result of the local DIC;

a module M2: modifying the correlation function based on the augmented Lagrangian function and the constraint condition;

a module M3: coordinating local subproblems by using an Alternating Direction Multiplier Method (ADMM) to find a solution of a global problem, and iteratively solving the problem;

a module M4: a field of interest including strain, velocity is derived from the global displacement field.

Preferably, the module M1 comprises:

when the displacement field is globally continuous, the subset local displacement u and the local displacement gradient F are not independent, and global constraint is met:

{F}＝D{u}

in the formula, a discrete gradient operator D is adopted to calculate the displacement gradient, a first-order finite difference method of a uniform square grid is used, and an auxiliary global continuous displacement field is introduced

This condition is processed to obtain two constraints:

in order to be a gradient operator, the method comprises the following steps of,

is the gradient of the auxiliary global continuous displacement field.

Preferably, the module M2 comprises:

the objective function of the subset DIC is:

the subsets DIC need only satisfy the respective subset omega _i The target function is minimum, a global continuous displacement field is introduced, the target function is modified through an augmented Lagrange function and a constraint condition, a global optimal solution needs to be obtained, and the target function is as follows:

in the formula _i Representing the whole subset area, requiring a global displacement field

Therefore, the global objective function minimum is to be satisfied;

u _i represents X _i0 Displacement of (2); f _i Represented as subset Ω _i A uniform displacement gradient of; dividing a reference image into a plurality of subsets in the subset DIC, wherein i is an index of each subset; f (X) represents the gray value at point X on the reference image; x represents the coordinates of a point in the digital image; g (X) represents the gray value at point X on the deformed image; x _i0 Represents the subset Ω _i The center of (a); beta is a corresponding constraint

Coefficient of the secondary penalty term of (2); w is a group of _i Is a corresponding constraint

Lagrange multipliers of (a); mu is the corresponding constraint

The coefficient of the secondary penalty term;

representing the introduced global continuous displacement field and the quantity to be solved; v _i Is a corresponding constraint

Lagrange multiplier.

Preferably, the module M3 comprises:

module M3.1: let W _i 、V _i 、

First solve u without change _i 、F _i The kth iteration expression is as follows:

module M3.2: only byHandle

As variables, the objective function is as follows:

and updating Lagrange multiplier W according to the result obtained by iteration _i 、V _i This step is repeated until the iteration stop criterion is met, i.e.

Is small enough.

Preferably, the module M4 comprises:

taking the lower left corner of the image as an origin, the lower edge as an x axis and the left edge as a y axis, establishing a plane rectangular coordinate system, and deriving the strain according to the following formula:

e _xy representing the variation of the included angle of the two tiny line segments in the mutually perpendicular directions after deformation; e.g. of the type _yy The ratio of the length increment of the tiny line segment along the y-axis direction, which is generated by deformation, to the original length is expressed, and the length is positive when the tiny line segment is elongated; u represents displacement in the x-axis direction; v denotes displacement in the y-axis direction.

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

(1) According to the invention, the basis set is not used for forcing continuity, but an augmented Lagrange function is used, the calculation efficiency is far higher than that of a global DIC algorithm based on FEM, and the obtained global displacement field has continuity by introducing a constraint condition through the augmented Lagrange function;

(2) The method combines the advantages of local DIC (fast) and global DIC (strain coordination) algorithms, and has higher operation efficiency without losing continuity compared with local subset DIC and global DIC;

(3) The invention uses the alternative direction multiplier method ADMM to decompose the problem into a plurality of simpler problems, firstly solves the local subproblems, namely the displacement fields of all subsets, and then searches the solution of the global problem, thereby reducing the running time of the whole algorithm by using a parallel computing mode when solving the subproblems.

Drawings

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

FIG. 1 is an image of a sample for a shear test;

FIG. 2 is a strain field calculated by the subset DIC;

FIG. 3 is a strain field of a finite element based global DIC calculation;

FIG. 4 is a strain field calculated by the algorithm of the present invention;

FIG. 5 is a time comparison graph of each algorithm;

FIG. 6 is a flow chart of the method of the present invention.

Detailed Description

The present invention will be described in detail with reference to specific examples. The following examples will aid those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any manner. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the concept of the invention. All falling within the scope of the present invention.

The embodiment is as follows:

the invention provides a novel DIC algorithm and a high-speed global deformation measurement technology. This algorithm combines the advantages of local subset DIC (speed and parallel computation) and global DIC (displacement continuity and strain coordination). The basic idea is to compute object deformation using subset-based local DIC, but using continuity as a constraint. The specific method is to introduce an auxiliary global continuous displacement field, introduce a constraint that the auxiliary global continuous displacement field and the gradient thereof are equal to a local correlation value, and use an augmented Lagrange function to realize the constraint. Finally, the problem is solved iteratively by using an alternating direction multiplier (ADMM) to coordinate the local sub-problems to find a solution to a large global problem.

Referring to fig. 6, the high-speed global deformation measurement technique provided by the present invention includes the following steps:

step S1: and introducing an auxiliary global continuous displacement field and a constraint condition. Since each subset in the subset DIC is matched independently, the subset local displacement u and the local displacement gradient F are independent of each other and independent for each subset. This also results in the situation that the matched subsets may overlap, and the consistency of deformation cannot be guaranteed. However, if the displacement field is globally continuous, then the displacement and the displacement gradient are not independent, but satisfy a global constraint:

{F}＝D{u}

in the formula, a discrete gradient operator D is adopted to calculate the displacement gradient, the discrete gradient operator depends on a discretization method, and the invention uses a first-order finite difference method of a uniform square grid. Here an auxiliary global continuous displacement field is introduced

To handle this condition, two constraints can be obtained:

global continuous displacement field

Under the condition of satisfying continuity, the displacement and the gradient of the displacement should be as same as the subset DIC result as possible. The core idea of the invention is to add global continuous constraint on the result of the subset DIC and calculate to obtain a global continuous displacement field.

Step S2: the correlation function is modified based on the augmented Lagrangian function and the constraint condition. The augmented Lagrangian function is characterized in that a secondary penalty term is added on the basis of the Lagrangian function, and the method is the combination of a Lagrangian function method and a penalty function method. More details on the specific form of the method are available on the web and will not be described in detail here. The objective function of the subset DIC is:

the subsets DIC only have to satisfy the respective subset omega _i The target function is minimum, the invention introduces a global continuous displacement field, modifies the target function through an augmented Lagrange function and a constraint condition, and needs to obtain a global optimal solution, wherein the target function is as follows:

in the formula _i Representing the total subset area, the present invention requires the solution of the global displacement field, as opposed to the subset DIC satisfying the minimum of the respective subset objective function

So that a global (full subset area) objective function minimum is satisfied.

And step S3: the problem is solved iteratively by using an Alternating Direction Multiplier Method (ADMM) to coordinate local subproblems to find a solution to a large global problem.

First step order W _i 、V _i 、

First solve u without change _i 、F _i The kth iteration expression is as follows:

this step is essentially similar to the subset DIC and can be solved by the subset DIC algorithm.

The second step is only to handle

As variables, the objective function is as follows:

and updating Lagrange multiplier W according to the result obtained by iteration _i 、V _i . This step is repeated until the iteration stop criterion is met, i.e.

Is small enough.

And step S4: the field of interest is derived from the global displacement field. The strain is derived by:

taking a shear test as an example, the sample surface has a suitable artificial speckle, as shown in fig. 1, and is verified by comparing the results of the subset DIC, the FEM-based global DIC, and the algorithm of the present invention.

The strain is calculated using the subset DIC, the finite element based global DIC, and the algorithm of this patent, respectively. The subset DIC results are shown in FIGS. 2a to 2c, the finite element-based global DIC results are shown in FIGS. 3a to 3c, and the patent results are shown in FIGS. 4a to 4 c. FIGS. 2-4 each contain 3 subgraphs, representing e from left to right _xx 、e _xy 、e _yy The result of (1). It can be seen that the strain results calculated by the subset DIC contain more noise, while the finite element based global DIC and the results of this patent are more continuous. Meanwhile, the running time of each algorithm is recorded as shown in fig. 5, and the running time of the method is far lower than that of a global DIC based on finite elements. This example demonstrates that this patent combines the operating speed of a local DIC with the morphometric coordination of a global DIC.

The high-speed global deformation measuring system provided by the invention comprises: a module M1: the optical axes of a camera and a lens are vertical to the surface of a sample, the camera is used for recording digital images of the sample in different states, an auxiliary global continuous displacement field and constraint conditions are introduced during image processing, and the displacement gradient of the field in each subset area are kept consistent with the calculation result of the local DIC; a module M2: modifying the correlation function based on the augmented Lagrangian function and the constraint condition; a module M3: coordinating local subproblems by using an Alternating Direction Multiplier Method (ADMM) to find a solution of a global problem, and iteratively solving the problem; a module M4: a field of interest including strain, velocity is derived from the global displacement field.

The module M1 comprises: when the displacement field is globally continuous, the subset local displacement u and the local displacement gradient F are not independent, and global constraint is satisfied: { F } = D { u }, wherein a discrete gradient operator D is adopted to calculate the displacement gradient, a first-order finite difference method of a uniform square grid is used, and an auxiliary global continuous displacement field is introduced

This condition is processed to obtain two constraints:

in order to be a gradient operator, the method comprises the following steps of,

is the gradient of the auxiliary global continuous displacement field.

The module M2 comprises: the objective function of the subset DIC is:

the subset DIC only needs to satisfy the minimum target function of each subset omega i, a global continuous displacement field is introduced, the target function is modified through an augmented Lagrange function and constraint conditions, a global optimal solution needs to be obtained, and the target function is as follows:

in the formula _i Representing the entire subset area, requiring a global displacement field

Therefore, the global objective function minimum is to be satisfied; u. u _i Represents X _i0 Displacement of (2); f _i Represented as subset Ω _i Uniform displacement gradient of (a); dividing a reference image into a plurality of subsets in the subset DIC, wherein i is an index of each subset; f (X) represents the gray value at point X on the reference image; x represents the coordinates of a point in the digital image; g (X) represents the gray value at point X on the deformed image; x _i0 Represents the subset Ω _i The center of (a); beta is a corresponding constraint

Coefficient of the secondary penalty term of (2); w is a group of _i Is a corresponding constraint

Lagrange multiplier of (a); mu is the corresponding constraint

Coefficient of the secondary penalty term of (2);

representing the introduced global continuous displacement field and the quantity to be solved; v _i Is a corresponding constraint

Lagrange multiplier.

The module M3 comprises:

module M3.1: let W _i 、V _i 、

First solve u without change _i 、F _i The kth iteration expression is as follows:

module M3.2: handle only

As variables, the objective function is as follows:

and updating Lagrange multiplier W according to the result obtained by iteration _i 、V _i This step is repeated until the iteration stop criterion is met, i.e.

Is sufficiently small.

The module M4 comprises: and (3) taking the lower left corner of the image as an origin, the lower edge as an x axis and the left edge as a y axis, establishing a plane rectangular coordinate system, and deriving the strain according to the following formula:

e _xy representing the variation of the included angle of the two tiny line segments in the mutually perpendicular directions after deformation; e.g. of a cylinder _yy The ratio of the length increment of the tiny line segment along the y-axis direction, which is generated by deformation, to the original length is expressed, and the length is positive when the tiny line segment is elongated; u represents displacement in the x-axis direction; v denotes displacement in the y-axis direction.

It is known to those skilled in the art that, in addition to implementing the system, apparatus and its various modules provided by the present invention in pure computer readable program code, the system, apparatus and its various modules provided by the present invention can be implemented in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like by completely programming the method steps. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.

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

Claims (10)

1. A high-speed global deformation measurement method, comprising:

step S1: the optical axes of a camera and a lens are vertical to the surface of a sample, the digital images of the sample in different states are recorded by using the camera, an auxiliary global continuous displacement field and constraint conditions are introduced during image processing, and the displacement gradient of the field in each subset area are kept consistent with the calculation result of the local DIC;

step S2: modifying the correlation function based on the augmented Lagrangian function and the constraint condition;

and step S3: using an Alternative Direction Multiplier Method (ADMM) to coordinate local subproblems to find a solution of a global problem, and thus iteratively solving the problem;

and step S4: a field of interest including strain, velocity is derived from the global displacement field.

2. The high-speed global deformation measurement method according to claim 1, wherein the step S1 comprises:

when the displacement field is globally continuous, the displacement u and the displacement gradient F are not independent, and global constraint is met:

{F}＝D{u}

in the formula, a discrete gradient operator D is adopted to calculate the displacement gradient, a first-order finite difference method of a uniform square grid is used, and an auxiliary global continuous displacement field is introduced

This condition is processed to obtain two constraints:

in order to be a gradient operator, the method comprises the following steps,

is the gradient of the auxiliary global continuous displacement field.

3. The high-speed global deformation measurement method according to claim 1, wherein said step S2 comprises:

the objective function of the subset DIC is:

the subsets DIC only have to satisfy the respective subset omega _i The target function is minimum, a global continuous displacement field is introduced, the target function is modified through an augmented Lagrange function and a constraint condition, a global optimal solution needs to be obtained, and the target function is as follows:

in the formula _i Representing the whole subset area, requiring a global displacement field

Therefore, the global objective function minimum is to be satisfied;

u _i represents X _i0 Displacement of (2); f _i Represented as subset Ω _i A uniform displacement gradient of; dividing a reference image into a plurality of subsets in the subset DIC, wherein i is an index of each subset; f (X) represents the gray value at point X on the reference image; x represents the coordinates of a point in the digital image; g (X) represents the gray value at point X on the deformed image; x _i0 Represents the subset Ω _i The center of (a); beta is a corresponding constraint

The coefficient of the secondary penalty term; w is a group of _i Is a corresponding constraint

Lagrange multipliers of (a); mu is the corresponding constraint

The coefficient of the secondary penalty term;

representing the introduced global continuous displacement field and the quantity to be solved; v _i Is a corresponding constraint

Lagrange multiplier.

4. The high-speed global deformation measurement method according to claim 1, wherein said step S3 comprises:

step S3.1: let W _i 、V _i 、

First solve u without change _i 、F _i The kth iteration is expressed as follows:

step S3.2: handle only

As variables, the objective function is as follows:

and updating Lagrange multiplier W according to the result obtained by iteration _i 、V _i This step is repeated until the iteration stop criterion is met, i.e.

Is small enough.

5. The high-speed global deformation measurement method according to claim 1, wherein said step S4 comprises:

taking the lower left corner of the image as an origin, the lower edge as an x axis and the left edge as a y axis, establishing a plane rectangular coordinate system, and deriving the strain according to the following formula:

e _xy representing the variation of the included angle of the two tiny line segments in the mutually perpendicular directions after deformation; e.g. of the type _yy The ratio of the length increment of the tiny line segment along the y-axis direction, which is generated by deformation, to the original length is represented, and the length is positive when the tiny line segment is elongated; u represents displacement in the x-axis direction; v represents displacement in the y-axis direction.

6. A high-speed global deformation measurement system, comprising:

a module M1: the optical axes of a camera and a lens are vertical to the surface of a sample, the digital images of the sample in different states are recorded by using the camera, an auxiliary global continuous displacement field and constraint conditions are introduced during image processing, and the displacement gradient of the field in each subset area are kept consistent with the calculation result of the local DIC;

a module M2: modifying the correlation function based on the augmented Lagrangian function and the constraint condition;

a module M3: coordinating local subproblems by using an Alternating Direction Multiplier Method (ADMM) to find a solution of a global problem, and iteratively solving the problem;

a module M4: a field of interest including strain, velocity is derived from the global displacement field.

7. The high-speed global deformation measurement system according to claim 6, wherein said module M1 comprises:

when the displacement field is globally continuous, the displacement u and the displacement gradient F are not independent, and global constraint is met:

{F}＝D{u}

in the formula, a discrete gradient operator D is adopted to calculate the displacement gradient, a first-order finite difference method of a uniform square grid is used, and an auxiliary global continuous displacement field is introduced

This condition is processed to obtain two constraints:

in order to be a gradient operator, the method comprises the following steps of,

is the gradient of the auxiliary global continuous displacement field.

8. The high-speed global deformation measurement system according to claim 6, wherein said module M2 comprises:

the objective function of the subset DIC is:

the subsets DIC only have to satisfy the respective subset omega _i The target function is minimum, a global continuous displacement field is introduced, the target function is modified through an augmented Lagrange function and a constraint condition, a global optimal solution needs to be obtained, and the target function is as follows:

in the formula _i Representing the whole subset area, requiring a global displacement field

Therefore, the global objective function minimum is to be satisfied;

u _i represents X _i0 Displacement of (2); f _i Expressed as subset Ω _i A uniform displacement gradient of; dividing a reference image into a plurality of subsets in the subset DIC, wherein i is an index of each subset; f (X) represents the gray value at point X on the reference image; x represents the coordinates of a point in the digital image; g (X) represents the gray value at point X on the deformed image; x _i0 Represents the subset Ω _i The center of (a); beta is a corresponding constraint

Coefficient of the secondary penalty term of (2); w _i Is a corresponding constraint

Lagrange multiplier of (a); mu is a corresponding constraint

Coefficient of the secondary penalty term of (2);

representing the introduced global continuous displacement field and the quantity to be solved; v _i Is a corresponding constraint

Lagrange multiplier.

9. The high-speed global deformation measurement system of claim 6, wherein said module M3 comprises:

module M3.1: let W _i 、V _i 、

First solve u without change _i 、F _i The kth iteration expression is as follows:

module M3.2: handle only

As variables, the objective function is as follows:

and updating Lagrange multiplier W according to the result obtained by iteration _i 、V _i This step is repeated until the iteration stop criterion is met, i.e.

Is small enough.

10. The high-speed global deformation measurement system according to claim 6, wherein said module M4 comprises:

taking the lower left corner of the image as an origin, the lower edge as an x axis and the left edge as a y axis, establishing a plane rectangular coordinate system, and deriving the strain according to the following formula:

e _xy representing the variation of the included angle of the two tiny line segments in the mutually perpendicular directions after deformation; e.g. of the type _yy The ratio of the length increment of the tiny line segment along the y-axis direction, which is generated by deformation, to the original length is expressed, and the length is positive when the tiny line segment is elongated; u represents displacement in the x-axis direction; v represents displacement in the y-axis direction.

Images