CN-115187578-B - High-speed global deformation measurement method and system

CN115187578BCN 115187578 BCN115187578 BCN 115187578BCN-115187578-B

Abstract

The invention provides a high-speed global deformation measurement method and system, which comprises the steps of S1, recording digital images of a sample in different states by using a camera and a camera, introducing auxiliary global continuous displacement fields and constraint conditions during image processing, keeping the displacement and displacement gradient of the fields in each subset area consistent with local DIC calculation results, S2, modifying a correlation function based on an augmentation Lagrangian function and the constraint conditions, S3, finding a solution of a global problem by using an alternative direction multiplication method ADMM to coordinate the local sub-problem, and accordingly iteratively solving the problem, and S4, deriving a field of an interesting quantity comprising strain and speed according to the global displacement fields. The invention uses the extended Lagrangian function, the calculation efficiency is far higher than that of the global DIC algorithm based on FEM, and constraint conditions are introduced through the extended Lagrangian function, so that the obtained global displacement field has continuity.

Inventors

HE JI
Ren Enzhen

Assignees

上海交通大学

Dates

Publication Date: 20260512
Application Date: 20220810

Claims (6)

1. A high-speed global deformation measurement method, comprising: S1, enabling optical axes of a camera and a lens to be perpendicular to the surface of a sample, recording digital images of the sample in different states by using the camera, introducing an auxiliary global continuous displacement field and constraint conditions during image processing, and keeping displacement and displacement gradient of the field in each subset area consistent with local DIC calculation results; s2, modifying a correlation function based on the augmented Lagrangian function and the constraint condition; Step S3, coordinating the local sub-problems by using an alternate direction multiplication method ADMM to find a solution of the global problem, so as to iteratively solve the problem; Step S4, deriving a field of interest quantity comprising strain and speed according to the global displacement field; the step S2 includes: the objective function of the subset DIC is: Subset DIC only needs to satisfy respective subsets The objective function is minimum, a global continuous displacement field is introduced, the objective function is modified through the augmented Lagrangian function and the constraint condition, the global optimal solution is required to be obtained, and the objective function is as follows: In the middle of Representing all subset areas, requiring global displacement fields Thus, the global objective function minimum is to be satisfied; Representation of Displacement of (2); Represented as subsets Dividing the reference image into a plurality of subsets in the subset DIC, wherein i is the index of each subset; representing the gray value at point X on the reference image; Representing coordinates of a point in the digital image; Representing the gray value at point X on the deformed image; representing subsets Is defined by a center of (a); Is a corresponding constraint Coefficients of the quadratic penalty term of (2); Is a corresponding constraint Lagrangian multipliers of (2); Is a corresponding constraint Coefficients of the quadratic penalty term of (2); Representing an introduced global continuous displacement field, and obtaining a quantity to be calculated; Is a corresponding constraint Lagrangian multipliers of (2); The step S3 includes: step S3.1 order 、、 Unchanged, solve in advance 、 The kth iteration expression is as follows: Step S3.2, handle only As variables, the objective function is as follows: And updating Lagrange multiplier according to the result obtained by iteration 、 This step is repeated until the iteration stop criterion is met, i.e Is small enough.
2. The method according to claim 1, wherein the step S1 includes: when the displacement field is globally continuous, the displacement And displacement gradient Not independent, satisfies global constraints: Discrete gradient operators are adopted in Calculating displacement gradient, using first-order finite difference method of uniform square grid, introducing auxiliary global continuous displacement field Processing this condition, two constraints are obtained: For the purpose of the gradient operator, Is the gradient of the auxiliary global continuous displacement field.
3. The method according to claim 1, wherein the step S4 includes: Let the lower left corner of the image be the origin, the lower edge be the x-axis, the left edge be the y-axis, establish the rectangular coordinate system of the plane, derive the strain through the following formula: Representing the change amount of the included angle of the two tiny line segments in mutually perpendicular directions after deformation; the ratio of the length increment generated by deformation of the micro line segments along the y-axis direction to the original length is shown, and the elongation is positive; Representing displacement along the x-axis; representing displacement along the y-axis.
4. A high-speed global deformation measurement system, comprising: the module M1 is used for recording digital images of the sample in different states by using a camera, introducing an auxiliary global continuous displacement field and constraint conditions during image processing, and keeping the displacement and displacement gradient of the field in each subset area consistent with the local DIC calculation result; A module M2, modifying the related function based on the augmented Lagrangian function and the constraint condition; A module M3, wherein the local sub-problem is coordinated by using an alternate direction multiplication method ADMM to find a solution of the global problem, so that the problem is solved iteratively; Module M4 deriving a field of interest quantity including strain, velocity from the global displacement field; The module M2 includes: the objective function of the subset DIC is: Subset DIC only needs to satisfy respective subsets The objective function is minimum, a global continuous displacement field is introduced, the objective function is modified through the augmented Lagrangian function and the constraint condition, the global optimal solution is required to be obtained, and the objective function is as follows: In the middle of Representing all subset areas, requiring global displacement fields Thus, the global objective function minimum is to be satisfied; Representation of Displacement of (2); Represented as subsets Dividing the reference image into a plurality of subsets in the subset DIC, wherein i is the index of each subset; representing the gray value at point X on the reference image; Representing coordinates of a point in the digital image; Representing the gray value at point X on the deformed image; representing subsets Is defined by a center of (a); Is a corresponding constraint Coefficients of the quadratic penalty term of (2); Is a corresponding constraint Lagrangian multipliers of (2); Is a corresponding constraint Coefficients of the quadratic penalty term of (2); Representing an introduced global continuous displacement field, and obtaining a quantity to be calculated; Is a corresponding constraint Lagrangian multipliers of (2); the module M3 includes: Module M3.1 order 、、 Unchanged, solve in advance 、 The kth iteration expression is as follows: Module M3.2 handle only As variables, the objective function is as follows: And updating Lagrange multiplier according to the result obtained by iteration 、 This step is repeated until the iteration stop criterion is met, i.e Is small enough.
5. The high-speed global deformation measurement system according to claim 4, wherein the module M1 comprises: when the displacement field is globally continuous, the displacement And displacement gradient Not independent, satisfies global constraints: Discrete gradient operators are adopted in Calculating displacement gradient, using first-order finite difference method of uniform square grid, introducing auxiliary global continuous displacement field Processing this condition, two constraints are obtained: For the purpose of the gradient operator, Is the gradient of the auxiliary global continuous displacement field.
6. The high-speed global deformation measurement system according to claim 4, wherein the module M4 comprises: Let the lower left corner of the image be the origin, the lower edge be the x-axis, the left edge be the y-axis, establish the rectangular coordinate system of the plane, derive the strain through the following formula: Representing the change amount of the included angle of the two tiny line segments in mutually perpendicular directions after deformation; the ratio of the length increment generated by deformation of the micro line segments along the y-axis direction to the original length is shown, and the elongation is positive; Representing displacement along the x-axis; representing displacement along the y-axis.

Description

High-speed global deformation measurement method and system Technical Field The invention relates to the technical field of image processing and metrology, 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 changing coordinates of an object surface, and the measured coordinate fields can be used to further derive fields of interest for displacement, strain, and velocity. As long as the object surface has a suitable speckle pattern, almost any object shape, motion and deformation can still 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 some unique features such as simple, inexpensive experimental setup, easy implementation, and robustness. Theoretically, whatever imaging modality is used, the DIC technique can be used to measure as long as the image has a significant intensity variation and a unique correspondence to points on the object surface. Indeed, DIC technology has been applied to common metals, polymeric materials, composites, biological tissues and surface deformations, ranging from a few microns (e.g., fiber) to tens of kilometers (e.g., surface deformations) where DIC technology can be used. During the last decades, researchers have proposed various DIC algorithms based on their own ideas. Most algorithms can be divided into two classes, a subset-based local DIC algorithm and a FEM (FINITE ELEMENT Method) -based global DIC algorithm. In the local subset DIC, a region of interest (region of interest) of the reference image is first decomposed into a plurality of subsets, and then the deformation of each subset is separately determined. Each subset in the local DIC is limited in size and therefore the deformation of each subset can be solved quickly. Since the respective subset solving processes are independent of each other, the running efficiency can be improved by using a parallel computing manner. However, also because the deformations of each subset are obtained independently, the overall deformation may be discontinuous, and the strain field is subject to more noise disturbance. In FEM (FINITE ELEMENT Method) based global DIC, a basis set (typically based on finite element discretization) is typically used to represent global deformation, and then the global image is analyzed to obtain parameters of this basis set, from which the global deformation field of the object can be obtained. The global DIC is based on FEM to calculate object deformation, so the obtained deformation fields are coordinated everywhere. However, the global DIC is very computationally intensive, and often takes ten times as much time as the local DIC under the same conditions. Patent document CN108956310B (application number: CN 201810347552.8) discloses a geomembrane liquid expansion deformation testing device and a testing method based on a three-dimensional DIC, wherein the geomembrane liquid expansion deformation testing device comprises a pressure testing system, a pressure control system and a three-dimensional DIC measuring system, the pressure testing system comprises an on-membrane pressure chamber, a geomembrane diameter adjusting device, an under-membrane pressure chamber and a base which are coaxially arranged from top to bottom in sequence, speckle is uniformly sprayed on the upper surface of a geomembrane, a digital image recorded by the speckle in the three-dimensional DIC measuring system is not less than 3 pixels, the pressure control system comprises an on-membrane pressure control system and an under-membrane pressure control system, and 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 geomembrane surface speckle deformed digital images shot by a single camera are subjected to time sequence matching in a certain step, the displacement of each calculated area is discontinuous by utilizing the local DIC principle based on a subset, and more noise is contained, so that the accuracy of a subsequent calculation result can be reduced. If the algorithm of the patent is adopted, a global continuous displacement field can be obtained by solving, and a more accurate result can be obtained in subsequent calculation. Disclosure of Invention Aiming at the defects in the prior art, the invention aims to provide a high-speed global deformation measurement method and system. The high-speed global deformation measurement method provided by the invention comprises the following steps: S1, enabling optical axes of a camera and a lens to be perpendicular to the surface of a sample, recording digital images of the sample in different states by using the camera, introducing an auxiliary global continuous displacement field and