CN114492117A - Large-scale structure displacement field reconstruction method based on photogrammetry - Google Patents
Large-scale structure displacement field reconstruction method based on photogrammetry Download PDFInfo
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Abstract
The invention discloses a large structure displacement field reconstruction method based on photogrammetry, which reconstructs the full-field displacement distribution condition of a structure by utilizing displacement information of finite discrete points. The method comprises the following steps: finite element modeling and measuring point selection are carried out, and the position information of each node and the selected measuring point of the structure in a finite element coordinate system is obtained; arranging identification points, and then acquiring position coordinates of the limited measuring points before and after loading under a photogrammetric coordinate system by a single-camera multi-camera station photogrammetric method; solving a transformation matrix between two coordinate systems by a singular value decomposition principle; acquiring displacement information of the finite measuring points under a finite element coordinate system by using the translation matrix; and finally, expanding the displacement information of the limited measuring points by utilizing the two-dimensional Chebyshev basis function, thereby realizing the reconstruction of the displacement field of the large-scale structure. The feasibility of the invention is verified by designing a displacement field reconstruction experiment of the large-scale aircraft panel. The invention provides a feasible technical means for acquiring the full-field displacement of the large-scale structure.
Description
Technical Field
The invention belongs to the technical field of optical measurement experimental mechanics, and particularly relates to a large-scale structure displacement field reconstruction method.
Background
The composite material is widely applied to the field of aerospace due to the characteristics of light weight, high strength, strong designability and the like. For example, in the design process of various airplanes, composite materials are often adopted as the design materials of large-sized reinforced wall panels so as to reduce the weight and improve the bearing capacity of the large-sized reinforced wall panels. For a large structure, it is difficult to obtain the full-field deformation information, but the composite material reinforced wall plate usually bears the load effects of bending, compression and the like in the service process, so that the method has important engineering significance for ensuring the reliability of the design and obtaining the full-field displacement information of the large structure under the loading condition.
For a large-scale structure, although the traditional displacement and strain sensor has high precision and good stability, the displacement information of the whole field cannot be effectively acquired. The current common full-field displacement measurement method mainly comprises a measurement method based on digital image correlation, a modal superposition method, a Ko displacement theory and an inverse finite element method. The digital image correlation method needs to make artificial speckle patterns on the surface of the structure, and the measurement accuracy is reduced along with the increase of the field of view, so that the field of view is limited to ensure the measurement accuracy. The modal superposition method needs to expand modal shape information of a finite element solution structure, and when boundary conditions are difficult to determine, satisfactory reconstruction results cannot be obtained. The Ko displacement theory is based on the classical material mechanics beam theory hypothesis, and the full-field displacement information of a complex structure is difficult to obtain. The inverse finite element method is a full-field reconstruction method established based on the least square principle and the finite element theory, but the programming modeling is complex and the workload is large. A large-scale structure displacement field reconstruction method based on photogrammetry is rarely proposed at present. Therefore, in order to meet the actual requirements of engineering, a simple, convenient and quick displacement field reconstruction method aiming at a large-scale structure is urgently needed to be provided, so that the full-field displacement distribution condition of the structure is effectively obtained.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a large structure displacement field reconstruction method based on photogrammetry, which reconstructs the full-field displacement distribution condition of a structure by using the displacement information of limited discrete points. The method comprises the following steps: finite element modeling and measuring point selection are carried out, and the position information of each node and the selected measuring point of the structure in a finite element coordinate system is obtained; arranging identification points, and then acquiring position coordinates of the limited measuring points before and after loading under a photogrammetric coordinate system by a single-camera multi-camera station photogrammetric method; solving a transformation matrix between two coordinate systems by a singular value decomposition principle; acquiring displacement information of the finite measuring points under a finite element coordinate system by using the translation matrix; and finally, expanding the displacement information of the limited measuring points by utilizing the two-dimensional Chebyshev basis function, thereby realizing the reconstruction of the displacement field of the large-scale structure. The feasibility of the invention is verified by designing a displacement field reconstruction experiment of the large-scale aircraft panel. The invention provides a feasible technical means for acquiring the full-field displacement of the large-scale structure.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: selecting a measuring point and modeling a finite element;
establishing a finite element model according to the geometric characteristics of the structure to be measured, and obtaining position coordinate information of the full-field N nodes of the structure to be measured under a finite element coordinate system, and recording the position coordinate information as sitaxy; selecting measuring points from the N nodes, recording the number of the measuring points as N, and recording position coordinate information of the measuring points under a finite element coordinate system as sit;
step 2: arranging non-coding mark points at the measuring point positions, and arranging coding mark points outside the measuring point of the structure to be measured;
and step 3: carrying out single-camera multi-camera shooting measurement on the structure to be measured before and after deformation to obtain position coordinate information of measuring points before and after deformation under a shooting measurement coordinate system;
and 4, step 4: solving a translation matrix between the photogrammetry coordinate system and the finite element coordinate system by using singular value decomposition;
and 5: converting the position information of the lower measuring point of the photogrammetry coordinate system before and after deformation into the finite element coordinate system by using the translation matrix obtained in the step 4, and obtaining the displacement U of the measuring point by calculating the difference value of the position information of the lower measuring point of the finite element coordinate system before and after deformationn×1；
Step 6: and (3) constructing a two-dimensional Chebyshev polynomial matrix by using the position coordinate information of the N measuring points and the full-field N nodes obtained in the step (1) under the finite element coordinate system and the measuring point displacement under the finite element coordinate system obtained in the step (5), thereby realizing the displacement field reconstruction of the structure to be measured.
Further, the specific process of step 2 is as follows:
arranging non-coding mark points at the measuring point positions, and arranging coding mark points outside the measuring point of the structure to be measured; the non-coding identification points are two concentric circles, the inner part of the small circle is white, the part between the concentric circles is black, the outer part of the large circle is white, and the shape and the size of each non-coding identification point are the same and are used for acquiring position coordinate information of the measuring point before and after deformation; the code identification points are three concentric circles, the inside of the minimum circle is white, and the part between the minimum circle and the middle circle is black; the part between the middle circle and the maximum circle is equally divided into 15 small blocks, and for each small block, the coding mode is as follows: a 1 in the binary system if the tile color is white, and a 0 in the binary system if the tile color is black; the coding identification point is 15-bit binary coding, and the corresponding decoding process comprises the following steps: taking any small block of the 15 small blocks as a starting point, calculating binary codes of the continuous 15 small blocks according to a specified sequence, thereby obtaining the 15-bit binary codes of the identification point, converting the binary codes into decimal code numbers, and traversing all the small blocks, wherein the minimum value of the decimal code numbers is the code value of the code marking point;
further, the specific process of step 3 is as follows:
carrying out single-camera multi-camera shooting measurement on the structure to be measured before and after deformation to obtain a series of images to be analyzed; obtaining position coordinate information of the measured point of the measured structure under a photogrammetric coordinate system before and after deformation through image feature extraction and identification point positioning solution; wherein the position coordinate matrix before deformation is recorded as Ph1And the deformed position coordinate matrix is recorded as Ph2。
Further, the specific process of step 4 is as follows:
setting the coordinates of the measuring points under the finite element coordinate system and the photogrammetric coordinate system as PFEMi＝(XFEMi,YFEMi,ZFEMi) And PPhoi＝(XPhoi,YPhoi,ZPhoi) (ii) a The centroid coordinates of the selected measuring points are respectively
And
the centroid coordinates are calculated by the following expression:
solving a covariance matrix between lower measuring points of a finite element coordinate system and a photogrammetry coordinate system:
and carrying out singular value analysis on the covariance matrix by using a singular value SVD decomposition method to obtain:
H＝UEVT
v and U are orthogonal matrixes, and E is a diagonal matrix of singular values; the optimal rotation matrix for coordinate system translation is then:
R＝VUT
and then calculating a translation matrix T between the photogrammetry coordinate system and the finite element coordinate system by using the following expression:
further, the specific process of step 5 is as follows:
converting the position information of the measuring points under the photogrammetry coordinate system before and after deformation into a finite element coordinate system by using the translation matrix obtained in the step 4, and converting the converted deformationThe position coordinate information of the corresponding measuring points before and after the shape is marked as PFEM_ch1And PFEM_ch2If the displacement matrix of the measuring point under the finite element coordinate system is Un×1＝PFEM_ch2-PFEM_ch1。
Further, the specific process of step 6 is as follows:
let Chebyshev polynomial expression be CjWherein j represents the order; selecting an 8-order two-dimensional Chebyshev polynomial as a reconstruction basis function, wherein j is 0,1,2,3,4,5,7,8, x and y represent coordinates, and the specific form is as follows:
respectively substituting the position coordinate information sit and sitxy of the N measuring points and the full field N nodes obtained in the step 1 into an 8-order two-dimensional Chebyshev polynomial to obtain a corresponding basis function matrix which is marked as Cn×8And CN×8；
Setting the displacement matrix of the full-field node of the structure to be measured as UN×1(ii) a The displacement matrix at each measuring point and each node of the structure to be measured is taken as the weighting of the Chebyshev basis function, so that the weighting method comprises the following steps:
Un×1＝Cn×8×k8×1
UN×1＝CN×8×k8×1
solving coefficient k by using least square principle8×1：
k8×1＝(Cn×8 T×Cn×8)-1×Cn×8 T×Un×1
Finally, the coefficient matrix k is used8×1And the Chebyshev basis function matrix C of the full field nodesN×8Namely, solving to obtain a displacement matrix corresponding to the full-field node of the structure to be measured, thereby realizing the reconstruction of the displacement field of the large-scale structure:
UN×1＝CN×8×k8×1
＝CN×8×(Cn×8 T×Cn×8)-1×Cn×8 T×Un×1
the invention has the following beneficial effects:
the invention provides a large structure displacement field reconstruction method based on photogrammetry. The finite element modeling in the step 1 obtains the coordinate position information of the whole structure, and the complex and fussy geometric modeling process is avoided. And 3, through the photogrammetry process of a single camera and multiple camera stations, the process is simple, the operability is strong, the displacement information of the limited measuring points of the structure before and after loading can be quickly obtained, the complexity and the low efficiency of the laser-based test method are avoided, and initial data are provided for full-field reconstruction. And 4, calculating by using a singular value decomposition principle to obtain an optimal rotation and translation matrix between the two coordinate systems, thereby realizing the mutual transformation between photogrammetry and finite elements. Step 6, a Chebyshev basis function matrix is constructed by skillfully utilizing coordinate information of the measuring points and the full nodes, effective expansion of displacement values of the limited measuring points is realized, the basis functions are selected only by acquiring geometric information of the structure, a complex finite element modeling analysis process of the traditional modal superposition method for the structure is avoided, the complexity of work is greatly reduced on the basis of ensuring reconstruction accuracy, the analysis efficiency is improved, and the reliable full-field displacement distribution condition of the large-scale structure shown in FIG. 5 is finally obtained. As can be seen from the comparison graph shown in fig. 6, the difference between the displacement reconstruction value and the measured value of the structure is low, the reliability of the invention is verified, and a convenient, fast and accurate technical scheme is provided for the field of optical measurement experimental mechanics.
Drawings
FIG. 1 is a flow chart of a method for reconstructing a displacement field of a large structure based on photogrammetry.
FIG. 2 is a structural model diagram of a large aircraft panel according to an embodiment of the invention.
FIG. 3 is a schematic view of the arrangement of large aircraft wall panel measuring points according to the embodiment of the invention.
FIG. 4 is a diagram of an encoded marker and a non-encoded marker used in an embodiment of the present invention, wherein (a) the non-encoded marker and (b) the encoded marker.
FIG. 5 is a cloud diagram of the large aircraft wall displacement field reconstruction result according to the embodiment of the invention.
FIG. 6 is a comparison graph of the large aircraft wall panel measurement point reconstruction results according to the embodiment of the invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
In order to solve the problems of the current measurement technology, the invention provides a large structure displacement field reconstruction method based on photogrammetry, which combines the photogrammetry technology and the Chebyshev basis function fitting theory, thereby effectively obtaining the full-field displacement information of the large structure. The method has the characteristics of simple implementation and high precision.
The finite element modeling in the first step of the invention establishes the geometric characteristics of the whole structure and provides position coordinate information for reconstruction. And step two, the photogrammetry process of a single camera and multiple camera stations is carried out, the operation is simple, the position information of the measuring points before and after loading of the structure can be quickly obtained, and reliable initial data is provided for full-field reconstruction. And step three and step four, calculating by using a singular value decomposition principle to obtain an optimal rotation matrix and an optimal translation matrix between the coordinate systems, thereby realizing the interconversion between the photogrammetric coordinate system and the finite element coordinate system. And fifthly, a two-dimensional Chebyshev basis function is constructed by utilizing coordinate position information of the measuring points and the full nodes, so that the effective expansion of the displacement value of the limited measuring points is realized, and finally the full-field displacement distribution condition of the large-scale structure is obtained.
As shown in fig. 1, a method for reconstructing a displacement field of a large structure based on photogrammetry includes the following steps:
step 1: selecting a measuring point and modeling a finite element;
establishing a finite element model according to the geometric characteristics of the structure to be measured, and obtaining position coordinate information of the full-field N nodes of the structure to be measured under a finite element coordinate system, and recording the position coordinate information as sitaxy; selecting measuring points from the N nodes, recording the number of the measuring points as N, and recording position coordinate information of the measuring points under a finite element coordinate system as sit;
step 2: arranging non-coding mark points at the measuring point positions, and arranging coding mark points outside the measuring point of the structure to be measured;
and step 3: carrying out single-camera multi-camera shooting measurement on the structure to be measured before and after deformation to obtain position coordinate information of measuring points before and after deformation under a shooting measurement coordinate system;
and 4, step 4: solving a translation matrix between the photogrammetric coordinate system and the finite element coordinate system by using singular value decomposition;
and 5: converting the position information of the lower measuring point of the photogrammetry coordinate system before and after deformation into the finite element coordinate system by using the translation matrix obtained in the step 4, and obtaining the displacement U of the measuring point by calculating the difference value of the position information of the lower measuring point of the finite element coordinate system before and after deformationn×1；
And 6: and (3) constructing a two-dimensional Chebyshev polynomial matrix by using the position coordinate information of the N measuring points and the full-field N nodes obtained in the step (1) under the finite element coordinate system and the measuring point displacement under the finite element coordinate system obtained in the step (5), thereby realizing the displacement field reconstruction of the structure to be measured.
Further, the specific process of step 2 is as follows:
arranging non-coding mark points at the measuring point positions, and arranging coding mark points outside the measuring point of the structure to be measured; the non-coding identification points are two concentric circles, the inner part of the small circle is white, the part between the concentric circles is black, the outer part of the large circle is white, and the shape and the size of each non-coding identification point are the same and are used for acquiring position coordinate information of the measuring point before and after deformation; the code identification points are three concentric circles, the inside of the minimum circle is white, and the part between the minimum circle and the middle circle is black; the part between the middle circle and the maximum circle is equally divided into 15 small blocks, and for each small block, the coding mode is as follows: a 1 in the binary system if the tile color is white, and a 0 in the binary system if the tile color is black; the coded identification point is a 15-bit binary code, and the corresponding decoding process is as follows: the corresponding decoding process is as follows: and taking any small block of the 15 small blocks as a starting point, calculating binary codes of the continuous 15 small blocks according to a specified sequence to obtain the 15-bit binary codes of the identification point, converting the binary codes into decimal code numbers, and traversing all the small blocks, wherein the minimum value of the decimal code numbers is the code value of the code marking point.
Further, the specific process of step 3 is as follows:
carrying out single-camera multi-camera shooting measurement on the structure to be measured before and after deformation to obtain a series of images to be analyzed; obtaining position coordinate information of the measured point of the measured structure under a photogrammetric coordinate system before and after deformation through image feature extraction and identification point positioning solution; wherein the position coordinate matrix before deformation is recorded as Ph1And the deformed position coordinate matrix is recorded as Ph2。
Further, the specific process of step 4 is as follows:
setting the coordinates of the measuring points under the finite element coordinate system and the photogrammetric coordinate system as PFEMi＝(XFEMi,YFEMi,ZFEMi) And PPhoi＝(XPhoi,YPhoi,ZPhoi) (ii) a The coordinates of the center of mass are respectively
And
the centroid coordinates are calculated by the following expression:
solving a covariance matrix between lower measuring points of a finite element coordinate system and a photogrammetry coordinate system:
because the optimal rotation matrix requires that the root mean square deviation between two corresponding points obtains the minimum value, singular value analysis is carried out on the covariance matrix by using a Singular Value (SVD) decomposition method to obtain:
H＝UEVT
v and U are orthogonal matrixes, and E is a diagonal matrix of singular values; the optimal rotation matrix for coordinate system translation is then:
R＝VUT
and then calculating a translation matrix T between the photogrammetry coordinate system and the finite element coordinate system by using the following expression:
further, the specific process of step 5 is as follows:
converting the position information of the measuring points under the photogrammetry coordinate system before and after deformation into a finite element coordinate system by using the translation matrix obtained in the step 4, and recording the position coordinate information of the corresponding measuring points before and after the deformation after the conversion as PFEM_ch1And PFEM_ch2And the displacement information of the measuring point under the finite element coordinate system is Un×1＝PFEM_ch2-PFEM_ch1。
Further, the specific process of step 6 is as follows:
let Chebyshev polynomial expression be CjWherein j represents the order; selecting 8-order two-dimensional Chebyshev polynomials as a reconstruction basis function, wherein j is 0,1,2,3,4,5,7 and 8, and the specific form is as follows:
substituting the position coordinate information of the N measuring points and the full-field N nodes obtained in the step 1 under the finite element coordinate system into an 8-order two-dimensional Chebyshev polynomial to obtain a corresponding basis function matrix which is marked as Cn×8And CN×8；
Setting the displacement matrix of the full-field node of the structure to be measured as UN×1(ii) a At each measuring point and each node of the structure to be measuredThe displacement matrix is considered as a weighting of the Chebyshev basis functions, and therefore:
Un×1＝Cn×8×k8×1
UN×1＝CN×8×k8×1
solving coefficient k by using least square principle8×1：
k8×1＝(Cn×8 T×Cn×8)-1×Cn×8 T×Un×1
Finally, the coefficient matrix k is used8×1And the Chebyshev basis function matrix C of the full field nodesN×8Namely solving to obtain a displacement matrix corresponding to the full-field node of the structure to be detected, thereby realizing the reconstruction of the displacement field of the large-scale structure:
UN×1＝CN×8×k8×1
＝CN×8×(Cn×8 T×Cn×8)-1×Cn×8 T×Un×1
the specific embodiment is as follows:
1. and selecting a measuring point and modeling a finite element. And (3) establishing a CAD model of the structure according to the geometric characteristics of the large-scale aircraft wall plate shown in the figure 2, further performing a finite element modeling process of the structure, and performing grid division to obtain position coordinate information of the full-field N nodes of the structure to be detected under a finite element coordinate system, and recording the position coordinate information as sitaxy. And meanwhile, the selected measuring point positions and the number of the measuring points are shown in fig. 3, the measuring point positions reflect the deformation trend of the structure, the number of the measuring points is 130, and the coordinate information matrix of the measuring point positions is marked as sit for the large airplane wall plate structure.
2. And carrying out single-camera multi-camera photogrammetry. Firstly, arranging non-coding identification points according to the 130 measuring point positions determined in the first step, wherein the non-coding identification points are shown as concentric circles with white centers, and the shape and the size of each point are the same and are used for acquiring position coordinate information of the measuring points before and after deformation. And arranging a certain number of coded identification points at the same time to prepare for subsequent photogrammetry. The center of the coding point is circular, the ring at the center is a coding bit, the coding identification point used here is a binary coding identification point with 15 bits, the white background corresponds to 1 in the binary, and the black background corresponds to 0 in the binary. The resolving process is as follows: and decoding one of the mark points as a starting point in sequence, wherein the decoded minimum code value is the code value of the code mark point. The coded mark points are used for decoding and positioning the camera at different positions so as to solve the position of the camera. The encoded dots and non-encoded dots are shown in fig. 4.
And acquiring images of the same area of the large-scale structure to be detected by using the single-lens reflex camera at different positions and directions, carrying out a single-camera multi-camera shooting measurement process, and acquiring a series of images to be analyzed. And then the position coordinate information of the limited measuring points of the measured structure under the photogrammetric coordinate system is obtained through solving by methods such as image feature extraction, identification point positioning calculation and the like. The position coordinate matrix of the measuring point before loading is marked as Ph1(ii) a The position coordinate matrix after the deformation is loaded is recorded as Ph2。
3. And solving the translation matrix by singular value decomposition. And (3) obtaining a coordinate system conversion matrix by using the position information of the measuring points obtained in the step 1 and the step 2 under the two coordinate systems through a singular value decomposition method.
First, the centroid calculation of the common mark points, namely the selected measuring points, is carried out. Setting the coordinate of each measuring point under the finite element coordinate system and the photogrammetric coordinate system as PFEMi＝(XFEMi,YFEMi,ZFEMi) And PPhoi＝(XPhoi,YPhoi,ZPhoi) (ii) a The coordinates of the center of mass are respectively
And
the centroid coordinates can be calculated by the following expression:
solving a covariance matrix between public mark points under two coordinate systems:
because the optimal rotation matrix requires that the root mean square deviation between two corresponding points obtains the minimum value, the singular value analysis is carried out on the covariance matrix by using a Singular Value (SVD) decomposition method to obtain:
H＝UEVT
where V and U are orthogonal matrices and E is a diagonal matrix of singular values. The optimal rotation matrix for the coordinate transformation is then
R＝VUT
And then, calculating to obtain a translation matrix by using the following expression:
in conclusion, the transformation matrix between the photogrammetric coordinate system and the finite element coordinate system is solved.
4. Obtaining displacement information of measuring point under finite element coordinate system
And (4) converting the position coordinate information of the measuring points before and after loading in the photogrammetric coordinate system into the finite element coordinate system by utilizing the matrixes R and T obtained by solving in the step 3. Recording the position coordinate information of the corresponding measuring points before and after the transformation as PFEM_ch1And PFEM_ch2. Therefore, the displacement information of the measuring point under the finite element coordinate system is Un×1＝PFEM_ch2-PFEM_ch1。
5. Performing displacement field reconstruction of a structure
And (3) constructing a two-dimensional Chebyshev basis function matrix by using the position coordinate information sit of the 130 measuring points in the finite element coordinate system obtained in the step 1 and the position coordinate information sit _ xy of the full-field node, thereby realizing the reconstruction of the displacement field of the whole structure.
Let Chebyshev polynomial expression be CjWherein j represents the order. Selecting 8-order two-dimensional Chebyshev polynomials as reconstruction basis functions, wherein the two-dimensional Chebyshev polynomials are 0 order, 1 order, 2 order, 3 order, 4 order, 5 order, 7 order and 8 order respectively, and the specific form is as follows:
respectively substituting the position coordinate information sit and sitxy into the Chebyshev basis function to obtain a corresponding basis function matrix marked as Cn×8And CN×8。
Set point displacement matrix and structural full-node displacement matrix are U respectivelyn×1And UN×1(ii) a The displacement information at each node of the structure can be regarded as a linear weighting of the chebyshev basis functions, so that:
Un×1＝Cn×8×k8×1
UN×1＝CN×8×k8×1
displacement information U of limited measuring pointn×1The Chebyshev polynomial matrix C corresponding to the measuring point is obtained by solving the photogrammetry and the coordinate system translation processn×8The position coordinate determined by the geometric information is substituted, so that the coefficient k can be solved by using the least square principle only by requiring that the number of the measuring points is more than the order of the basis function8×1：
k8×1＝(Cn×8 T×Cn×8)-1×Cn×8 T×Un×1
Finally, the coefficient matrix k is used8×1And the Chebyshev basis function matrix C of the full field nodesN×8And solving to obtain the displacement information corresponding to the full-field nodes of the structure, thereby realizing the reconstruction of the displacement field of the large-scale structure.
UN×1＝CN×8×k8×1
＝CN×8×(Cn×8 T×Cn×8)-1×Cn×8 T×Un×1
Fig. 5 is a full-field displacement cloud image obtained by reconstructing the displacement field of the large-scale aircraft wall plate by using the method.
In order to verify the effectiveness of the method, a displacement field reconstruction experiment of the large-scale aircraft wall panel is designed, the full-field displacement distribution condition of the aircraft wall panel is successfully reconstructed by using the displacement information of 130 limited measuring points acquired by photogrammetry, and a full-field displacement distribution cloud picture is obtained.
Fig. 6 is a comparison graph of measured values and reconstructed values of the measuring points in the reconstruction experiment of the aircraft panel.
The method provided by the invention has the advantages that the reconstruction result of the plane wallboard reconstruction experiment is basically consistent with the actual measurement result of the photogrammetry, and the reliability and the accuracy of the method can be proved.
In summary, the invention discloses a method for reconstructing a displacement field of a large structure based on photogrammetry, which is characterized in that displacement values of limited measuring points of the large structure obtained by photogrammetry are expanded by using a two-dimensional Chebyshev basis function, so that the full-field displacement distribution condition of the structure is successfully obtained, and the method can be widely applied to the full-field deformation test of the large structure.
Claims (6)
1. A large structure displacement field reconstruction method based on photogrammetry is characterized by comprising the following steps:
step 1: selecting a measuring point and modeling a finite element;
establishing a finite element model according to the geometric characteristics of the structure to be measured, and obtaining position coordinate information of the full-field N nodes of the structure to be measured under a finite element coordinate system, and recording the position coordinate information as sitaxy; selecting measuring points from the N nodes, recording the number of the measuring points as N, and recording position coordinate information of the measuring points under a finite element coordinate system as sit;
step 2: arranging non-coding mark points at the measuring point positions, and arranging coding mark points outside the measuring point of the structure to be measured;
and step 3: carrying out single-camera multi-camera shooting measurement on the structure to be measured before and after deformation to obtain position coordinate information of measuring points before and after deformation under a shooting measurement coordinate system;
and 4, step 4: solving a translation matrix between the photogrammetry coordinate system and the finite element coordinate system by using singular value decomposition;
and 5: converting the position information of the lower measuring point of the photogrammetry coordinate system before and after deformation into the finite element coordinate system by using the translation matrix obtained in the step 4, and obtaining the displacement U of the measuring point by calculating the difference value of the position information of the lower measuring point of the finite element coordinate system before and after deformationn×1；
Step 6: and (3) constructing a two-dimensional Chebyshev polynomial matrix by using the position coordinate information of the N measuring points and the full-field N nodes obtained in the step (1) under the finite element coordinate system and the measuring point displacement under the finite element coordinate system obtained in the step (5), thereby realizing the displacement field reconstruction of the structure to be measured.
2. The method for reconstructing the displacement field of the large structure based on the photogrammetry as claimed in claim 1, wherein the specific process of the step 2 is as follows:
arranging non-coding mark points at the measuring point positions, and arranging coding mark points outside the measuring point of the structure to be measured; the non-coding identification points are two concentric circles, the inner part of the small circle is white, the part between the concentric circles is black, the outer part of the large circle is white, and the shape and the size of each non-coding identification point are the same and are used for acquiring position coordinate information of the measuring point before and after deformation; the code identification points are three concentric circles, the inside of the minimum circle is white, and the part between the minimum circle and the middle circle is black; the part between the middle circle and the maximum circle is equally divided into 15 small blocks, and for each small block, the coding mode is as follows: a 1 in the binary system if the tile color is white, and a 0 in the binary system if the tile color is black; the coded identification point is a 15-bit binary code, and the corresponding decoding process is as follows: and taking any small block of the 15 small blocks as a starting point, calculating binary codes of the continuous 15 small blocks according to a specified sequence to obtain the 15-bit binary codes of the identification point, converting the binary codes into decimal code numbers, and traversing all the small blocks, wherein the minimum value of the decimal code numbers is the code value of the code marking point.
3. The method for reconstructing the displacement field of the large structure based on the photogrammetry as claimed in claim 2, wherein the specific process of the step 3 is as follows:
carrying out single-camera multi-camera shooting measurement on the structure to be measured before and after deformation to obtain a series of images to be analyzed; obtaining position coordinate information of the measured point of the measured structure under a photogrammetric coordinate system before and after deformation through image feature extraction and identification point positioning solution; wherein the position coordinate matrix before deformation is recorded as Ph1And the deformed position coordinate matrix is recorded as Ph2。
4. The method for reconstructing the displacement field of the large structure based on the photogrammetry as claimed in claim 3, wherein the specific process of the step 4 is as follows:
setting the coordinates of the measuring points under the finite element coordinate system and the photogrammetric coordinate system as PFEMi＝(XFEMi，YFEMi，ZFEMi) And PPhoi＝(XPhoi，YPhoi，ZPhoi) (ii) a The centroid coordinates of the selected measuring points are respectively
And
the centroid coordinates are calculated by the following expression:
solving a covariance matrix between lower measuring points of a finite element coordinate system and a photogrammetry coordinate system:
and carrying out singular value analysis on the covariance matrix by using a singular value SVD decomposition method to obtain:
H＝UEVT
v and U are orthogonal matrixes, and E is a diagonal matrix of singular values; the optimal rotation matrix for coordinate system translation is then:
R＝VUT
and then calculating a translation matrix T between the photogrammetry coordinate system and the finite element coordinate system by using the following expression:
5. the method for reconstructing the displacement field of the large structure based on the photogrammetry as claimed in claim 4, wherein the specific process of the step 5 is as follows:
converting the position information of the measuring points under the photogrammetry coordinate system before and after deformation into a finite element coordinate system by using the translation matrix obtained in the step 4, and recording the position coordinate information of the corresponding measuring points before and after the deformation after the conversion as PFEM_ch1And PFEM_ch2If the displacement matrix of the measuring point under the finite element coordinate system is Un×1＝PFEM_ch2-PFEM_ch1。
6. The method for reconstructing the displacement field of the large structure based on the photogrammetry as claimed in claim 5, wherein the specific process of the step 6 is as follows:
let Chebyshev polynomial expression be CjWherein j represents the order; select 8The order two-dimensional chebyshev polynomial is taken as a reconstruction basis function, j is 0,1,2,3,4,5,7,8, x and y represent coordinates, and the specific form is as follows:
respectively substituting the position coordinate information sit and sitxy of the N measuring points and the full field N nodes obtained in the step 1 into an 8-order two-dimensional Chebyshev polynomial to obtain a corresponding basis function matrix which is marked as Cn×8And CN×8；
Setting the whole field node displacement matrix of the structure to be measured as UN×1(ii) a The displacement matrix at each measuring point and each node of the structure to be measured is taken as the weighting of the Chebyshev basis function, so that the weighting method comprises the following steps:
Un×1＝Cn×8×k8×1
UN×1＝CN×8×k8×1
solving coefficient k by using least square principle8×1：
k8×1＝(Cn×8 T×Cn×8)-1×Cn×8 T×Un×1
Finally, the coefficient matrix k is used8×1And the Chebyshev basis function matrix C of the full field nodesN×8Namely, solving to obtain a displacement matrix corresponding to the full-field node of the structure to be measured, thereby realizing the reconstruction of the displacement field of the large-scale structure:
UN×1＝CN×8×k8×1
＝CN×8×(Cn×8 T×Cn×8)-1×Cn×8 T×Un×1。
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