A structural damage diagnosis method based on iterative calibration image measurement

Abstract

This invention relates to a structural damage diagnosis method based on iterative calibration image measurement, belonging to the field of structural damage diagnosis. The method specifically includes the following steps: dividing the engineering structure into multiple substructures, each substructure containing at least three measurement points, with at least 2 / 3 of the measurement points in two adjacent substructures overlapping. Based on the characteristic relationship between the upper and lower structures, the homography matrix H is used to correct the upper structure to the same plane as the lower structure. The overall modal parameters of the structure are extracted using the relative displacements obtained from the tests, and damage identification is performed by combining this with the mode shape curvature. For each layer of the iteratively corrected structure, the natural frequencies and mode shapes of the overall structure are calculated based on the derived relationship between the Fourier spectrum of the local structural relative displacements and the overall structural characteristic quantities. The location of the damage is then determined based on the change in mode shape curvature, with the curvature calculated using the central difference method. This invention provides a convenient and economical method for identifying damage in engineering structures.

Description

Technical Field

[0001] This invention belongs to the field of structural damage diagnosis technology, and relates to a structural damage diagnosis method based on iterative calibration image measurement. Background Technology

[0002] Engineering structures such as high-rise buildings, bridges, and transmission towers are becoming increasingly common. Over long periods of operation, structural damage is inevitable, reducing reliability and leading to failure under natural disasters or load variations. Therefore, damage diagnosis is crucial for the timely detection of structural damage, and because structural vibration modes have clear physical meanings, they are widely used in structural damage diagnosis.

[0003] Existing modal analysis methods mainly include frequency domain decomposition (FDD), stochastic subspace method (SSI), and least squares complex frequency domain method (PolyMAX). FDD extracts frequencies and modes based on the power spectral density (PSD) matrix and singular value decomposition (SVD), requiring simultaneous collection of dynamic responses at all measurement points on the structure. SSI uses state-space equations and the dynamic response of the entire structure to extract frequencies, damping ratios, and mode shapes. PolyMAX calculates the frequency response function matrix using the dynamic response of the entire structure to extract frequencies, damping ratios, and mode shapes. Since frequencies and mode shapes are not very sensitive to structural damage, many more sensitive mode shape-based or frequency-and-mode shape-based indices have been proposed and used for damage detection. Commonly used in these include mode shape curvature, modal compliance difference, and modal compliance change rate. All of these methods require simultaneous acquisition of the dynamic response at all measurement points, or continuous acquisition of the dynamic response at a specified reference measurement point while measuring other points. Using traditional accelerometers for structural dynamic response measurement typically involves more hardware and extensive wiring.

[0004] Currently, computer image vision technology has made significant progress and is being widely integrated into multiple fields. Its low cost and ease of operation have accelerated the application of dynamic photogrammetry in engineering structural measurement. Traditional dynamic photogrammetry can extract the overall response from local images of a structure. However, due to the vertical arrangement of the structure, the test plates are not entirely on the same plane vertically, which will adversely affect the measurement of structural vibration response. Therefore, it is necessary to propose corresponding solutions. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a structural damage diagnosis method based on iterative calibration image measurement, which solves the technical problem that the vertical arrangement of the measurement structure and the fact that the test plates are not completely on the same plane in the vertical direction have an adverse effect on the damage identification of the engineering structure.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A structural damage diagnosis method based on iterative calibration image measurement, the method comprising the following steps:

[0008] S1: Divide the engineering structure to be measured into several substructures with the same number of measurement points. Each substructure contains at least three measurement points, and at least 2 / 3 of the measurement points in two adjacent substructures overlap.

[0009] The test plates at the bottom of each substructure also serve as calibration plates;

[0010] Both the test board and the calibration board are standard-sized checkerboard patterns;

[0011] S2: Using the test plate at the bottom of the overall engineering structure as the reference calibration plate, iterative calibration of each substructure is performed. The iterative calibration starts from the bottommost substructure and proceeds upwards sequentially.

[0012] Based on the pixel coordinates of the inner corner points of the checkerboard in the bottommost test board of the first substructure and the pixel coordinates of all inner corner points of the checkerboard, the homography matrix H1 of the first substructure is calculated. H1 is then used to correct distortion in each frame of the first substructure. Based on the distortion-corrected image, the pixel coordinates of the inner corner points of the topmost test board of the first substructure are determined, and the relative pixel positions of all inner corner points on the topmost test board relative to the first inner corner point at the top left of the topmost test board are calculated. In the second substructure, a test board corresponding to the topmost test board of the first substructure is found. Based on the actual relative pixel positions of the inner corners of the corresponding test board and the relative pixel positions of the inner corner points of the topmost test board calculated in the first substructure, a homography matrix H2 suitable for the second substructure is calculated. H2 is then used to correct distortion in each frame of the second substructure. This process is repeated until all substructures have been calibrated.

[0013] After all substructures have been calibrated, all substructure test images are calibrated to the same plane as the bottom test board.

[0014] S3: For each substructure, obtain the pixel coordinates of the inner corner points on each test board, calculate the difference in pixel coordinates between the inner corner points of two test boards, and the difference is the pixel displacement between the two test boards; calculate the conversion coefficient using the pixel length of the checkerboard square edge and the actual length, and convert the pixel displacement between the two test boards into the actual position change. The converted position change is the relative displacement between the two test boards, which is the relative displacement between the two layers. Based on the relationship between each layer, obtain the relative displacement between each layer in each substructure, which is the relative displacement between each node in each substructure.

[0015] S4: The first substructure contains supports or constraints. The relative displacement of each layer within the first substructure is obtained by testing, which is the absolute displacement of the engineering structure. The relative displacement of each layer within the first substructure is used to identify the natural frequencies of each order of the engineering structure. At the same time, Fourier transform is performed on the relative displacement of each layer within the first substructure to obtain the absolute displacement Fourier spectrum at the r-th modal frequency ωr of the relative displacement of each layer within the first substructure, which is the absolute displacement Fourier spectrum of the nodes in the first substructure.

[0016] The relative displacements between nodes obtained in S3 are subjected to fast Fourier transform to obtain the Fourier spectrum of the relative displacements between nodes. Using the Fourier spectrum of the relative displacements between nodes and the absolute displacement Fourier spectrum of each node at the r-th modal frequency calculated by the first substructure, the absolute displacement Fourier spectrum of other nodes in the engineering structure at the r-th modal frequency is calculated sequentially from bottom to top using the iterative calculation formula.

[0017] S5: Based on the calculated absolute displacement Fourier spectrum, construct the power spectral density matrix, and use the singular value decomposition method to extract the natural frequencies and mode shapes in the power spectral density matrix.

[0018] S6: The mode shape curvature is calculated using the central difference method. The change in mode shape curvature is calculated based on the obtained mode shape curvature. The location of the damage is determined based on the change in mode shape curvature.

[0019] Furthermore, in S1, each substructure is measured individually using photography.

[0020] Furthermore, in S2, distortion correction is performed on each frame of the substructure using a homography matrix, specifically as follows:

[0021] If the image coordinates of the upper calibration plate are i' = {u', v', l'} T The coordinates of the measured image are i = (u, v, l). T The relationship between the two can be expressed as:

[0022] i = Hi' (1)

[0023]

[0024] Where H∈[H1, H2……Hn], H1 is the homography matrix of the first substructure, H2 is the homography matrix of the second substructure, and Hn is the homography matrix of the nth substructure.

[0025] Furthermore, in S4, the iterative calculation formula is expressed as:

[0026]

[0027] Where q = (2, 3, ..., n-1) is solved iteratively, ω r X1(ω) represents the r-th modal frequency of the 3rd to nth nodes of the engineering structure; q is the node number; n is the total node number excluding supports; r ) and X2(ω r X3(ω) represents the absolute displacement Fourier spectra of nodes 1 and 2 of the first substructure, respectively; r ), X4(ω r ), ...,X n (ω r ) are the estimated Fourier spectra of the absolute displacements of the engineering structure, where The relative displacement δ between node q+1 and node q-1 of the substructure during the q-th measurement. q+1,q-1 Fourier spectrum.

[0028] Furthermore, in step S6, the mode shape curvature is calculated using the central difference method, and the calculation formula is as follows:

[0029]

[0030] in, and Let φ represent the curvature at position i of mode j before and after the damage, respectively. j (i) represents the element at position i in the j-th mode, where the superscripts u and d indicate before and after the damage, l i Let i be the length of the unit.

[0031] Furthermore, in step S6, the change in mode curvature is calculated based on the obtained mode curvature, using the following formula:

[0032]

[0033] The beneficial effects of this invention are as follows:

[0034] First, this invention uses homography matrix to establish the relationship between layers, correcting the layers of the structure on different planes to the same plane; based on the relative displacement of the substructures and the r-th order modal frequencies of the 3rd to nth nodes of the engineering structure, the estimated absolute displacement Fourier spectra of the 3rd to nth substructures are obtained; based on the absolute displacement Fourier spectra, the overall modal natural frequencies and mode shapes of the engineering structure are extracted; and then the mode shape curvature is used for damage diagnosis, thus realizing damage identification of the engineering structure more conveniently and economically.

[0035] Second, this invention is applicable to various structures such as frame structures, transmission towers, and bridges.

[0036] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0037] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0038] Figure 1 These are segmented photogrammetric images of the engineering structure of this invention;

[0039] Figure 2 The standard for the test board of this invention is a 7*11 chessboard pattern;

[0040] Figure 3 This is the first-order vibration mode diagram extracted in this invention;

[0041] Figure 4 This is a diagram showing the structural damage identification results based on the mode curvature of the present invention.

[0042] Figure 5 This is a flowchart of the present invention. Detailed Implementation

[0043] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0044] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0045] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0046] Please see Figures 1-5 This is a structural damage diagnosis method based on iterative calibration image measurement.

[0047] Step 1: The proposed method was validated in the laboratory using a planar frame structure. The frame consisted of small steel sheets, each 10mm wide and 1mm thick, with a length of 200mm. The five-layer planar frame structure had a width of 200mm and a total height of 1000mm. White noise excitation was applied using a non-contact vibrator.

[0048] Step 2: Divide the engineering structure into as follows Figure 1 The substructures shown are... Figure 1 Part 1, Part 2, Part 3, etc., as shown, were measured separately for each substructure during each photogrammetry session. For example... Figure 2 As shown, the test board is a standard 7*11 checkerboard grid. The bottom board of each substructure serves as both the test board and the calibration board. Both the test board and the calibration board are standard-sized checkerboard grids.

[0049] Step 3: Using the bottom test board A11 of the overall structure as the reference calibration board, perform iterative calibration of each substructure (Aij represents the j-th board of the i-th substructure, where j is 1, 2, 3 from bottom to top). Iterative calibration means that the calibration process starts from the bottom substructure and proceeds upwards sequentially. Specifically, firstly, based on the pixel coordinates of the inner corner points of the checkerboard grid in the bottom board A11 of Part 1 and the pixel coordinates of all inner corner points of the standard-sized checkerboard grid, calculate the homography matrix H1 of substructure Part 1. Then, use H1 to perform distortion correction on each frame of substructure Part 1, and based on the distortion-corrected image, determine the pixel coordinates of the inner corner points of the top board A13 of substructure Part 1, and calculate the relative pixel positions of all inner corner points on test board A13 with respect to the first inner corner point of the upper left corner of test board A13; then, since Part 1 and There are two identical test boards in Part 2, namely A12 and A21, and A13 and A22. Find the test board A22 in substructure Part 2 that corresponds to the topmost board A13 in substructure Part 1. Based on the actual relative pixel positions of the inner corner points of board A22 in Part 2 and the relative pixel positions of the inner corner points of the topmost board A13 calculated in Part 1, calculate the homography matrix H2 applicable to Part 2, and calibrate each frame of substructure Part 2. Repeat the above process until all substructures have been calibrated. After completing the above process, all substructure test images will be calibrated to be on the same test plane as the bottommost test board.

[0050] The homography matrix H is used to calibrate the upper structure onto the same plane as the lower structure. For the calibration plate correction, assume the image coordinates of the upper calibration plate are i = {u', v', l}. T The coordinates of the measured image are i = {u, v, l} T The relationship between them can be expressed as:

[0051] i = Hi' (1)

[0052]

[0053] Where H∈[H1, H2……Hn], H1 is the homography matrix of the first substructure, H2 is the homography matrix of the second substructure, and Hn is the homography matrix of the nth substructure.

[0054] Step 4: For each substructure, obtain the pixel coordinates of the inner corner points on each test board, and calculate the difference in pixel coordinates between the inner corner points of the two test boards. This difference represents the pixel displacement between the two test boards. Since the test board is a standard checkerboard, the conversion factor can be calculated using the pixel length of the checkerboard square edge and the actual length. Then, the pixel displacement between the two test boards can be converted into the actual position change. This actual position change is the relative displacement between the two test boards, that is, the relative displacement between the two layers.

[0055] Step 5: Since the first local structure contains supports or constraints, the relative displacement δ obtained from the test of local structure 1 is used. 1,0 ,δ 2,0 This refers to the absolute displacement of the engineering structure, which can be directly obtained from the relative displacement δ obtained by testing local structure 1. 1,0 ,δ 2,0 Identification of the natural frequencies of various orders of engineering structures; simultaneously, direct analysis of δ... 1,0 ,δ 2,0 Performing a Fourier transform, the Fourier transforms at the r-th modal frequency ωr are X1(ω r ) and X2(ω r Then, the absolute displacement Fourier spectrum at the r-th modal frequency of the 3rd to nth nodes of the engineering structure is calculated using equation (3).

[0056]

[0057] Where ωr is the r-th modal frequency of the engineering structure; q is the node number; n is the total node number excluding supports; X1(ω r ) and X2(ω r ) are the Fourier spectra of nodes 1 and 2 of the local structure Part1, respectively; X3(ω r ), X4(ω r ), ...,X n (ω) r The fourfold spectra of the estimated absolute displacements of the engineering structure are given by equation (3), which is iteratively solved by taking q = 2, 3, ..., n-1 in sequence. The relative displacement δ between node q+1 and node q-1 measured for local structure Part k. q+1,q-1 Fourier spectrum.

[0058] Step 6: Use the estimated absolute displacement Fourier spectrum {X1,X2,X3,X4,...,X... n The power spectral density (PSD) matrix is ​​constructed, and then singular value decomposition (SVD) is used to extract the natural frequencies and mode shapes. The extracted first-order mode shapes are as follows: Figure 3 As shown.

[0059] Step 7: Propose using the mode shape curvature method to diagnose damage. This method determines the location of damage based on changes in mode shape curvature, and the curvature is calculated using the central difference method. and Let represent the curvature at position i of mode j before and after the damage, respectively, calculated as follows:

[0060]

[0061] In the formula φ j (i) represents the element at position i in the j-th mode, where the superscripts u and d indicate before and after the damage, l i Let i be the length of element i. The rate of change of modal curvature can be expressed as:

[0062]

[0063] Damage identification results using modal curvature, such as Figure 4 As shown.

[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for structural damage diagnosis based on iterative calibration of image measurements, characterized by: The method comprises the following steps: S1: dividing the engineering structure to be measured into a plurality of substructures with the same number of measuring points, at least three measuring points being contained in each substructure, and at least 2 / 3 of the measuring points in two adjacent substructures being overlapped; The bottom test plate of each substructure also serves as a calibration plate; Both the test plate and the calibration plate are standard-size chessboard grids; S2: taking the test plate at the bottom of the whole engineering structure as a reference calibration plate to perform iterative calibration of each substructure, the iterative calibration starting from the substructure at the bottom and then proceeding upwards; According to the pixel coordinates of the inner corner points in the chessboard grid of the test plate at the bottom of the first substructure and the pixel coordinates of all the inner corner points of the chessboard grid, a homography matrix H1 of the first substructure is calculated, the homography matrix H1 being used to correct the distortion of each frame of image of the first substructure, the pixel coordinates of the inner corner points of the test plate at the top of the first substructure being determined according to the image after the distortion correction, and the relative pixel positions of all the inner corner points of the test plate at the top relative to the first inner corner point at the top-left corner of the test plate at the top being calculated; a test plate corresponding to the test plate at the top of the first substructure is found in the second substructure, a homography matrix H2 suitable for the second substructure is calculated according to the relative pixel positions of the inner corner points of the corresponding test plate and the relative pixel positions of the inner corner points of the test plate at the top of the first substructure, and the homography matrix H2 is used to correct the distortion of each frame of image of the second substructure; the above process is repeated in sequence until all the substructures are calibrated; After the calibration of all the substructures is completed, all the test images of the substructures are calibrated to the same plane as the test plate at the bottom; S3: for each substructure, the pixel coordinates of the inner corner points on each test plate are obtained, the pixel coordinate difference of the inner corner points between two test plates is calculated, the difference being the pixel displacement between the two test plates; a conversion coefficient is calculated by using the pixel length and the actual length of the square edge of the chessboard grid, the pixel displacement between the two test plates is converted into the actual position change, the converted position change being the relative displacement between the two test plates, i.e. the relative displacement between the two layers, and the relative displacement between the layers in each substructure is obtained according to the relationship between the layers, i.e. the relative displacement between the nodes in each substructure is obtained; S4: the first substructure contains a support or a constraint, the relative displacement of each layer obtained by testing in the first substructure being the absolute displacement of the engineering structure, the relative displacement of each layer obtained by testing in the first substructure being used to identify the natural frequencies of each order of the engineering structure, and the Fourier transform of the relative displacement of each layer in the first substructure is performed, i.e. the absolute displacement Fourier spectrum of each layer at the rth modal frequency ωr of the first substructure is obtained, i.e. the absolute displacement Fourier spectrum of the nodes in the first substructure is obtained. S3: The Fourier spectrum of the relative displacement between the nodes is obtained by performing a fast Fourier transform on the relative displacement between the nodes obtained in S2; the Fourier spectrum of the absolute displacement of each node at the rth modal frequency is calculated using the Fourier spectrum of the relative displacement between the nodes and the absolute displacement Fourier spectrum of each node at the rth modal frequency calculated in S1; the absolute displacement Fourier spectrum of each node at the rth modal frequency in the engineering structure is calculated in turn from bottom to top using an iterative calculation formula; S5: The power spectral density matrix is constructed according to the calculated absolute displacement Fourier spectrum, and the inherent frequency and mode shape in the power spectral density matrix are extracted using the singular value decomposition method; S6: The mode shape curvature is calculated using the central difference method, the change in the mode shape curvature is calculated according to the obtained mode shape curvature, and the damage occurrence position is determined according to the change in the mode shape curvature.

2. The method of claim 1, wherein: In S1, each substructure is measured separately in a photographic manner.

3. The method of claim 1, wherein: In S2, the homography matrix is used to correct the distortion of each frame of image of the substructure, specifically: If the image coordinates of the upper calibration plate are i' = {u', v', l'} T , and the coordinates of the measured image are i = (u, v, l) T , the relationship between them is represented as: i = Hi' (1) wherein H [H1, H2, …, Hn], H1 is the homography matrix of the first substructure, H2 is the homography matrix of the second substructure, and Hn is the homography matrix of the nth substructure.

4. The method of claim 1, wherein: In S4, the iterative calculation formula is represented as: where q = (2, 3, …, n-1) is iterated to solve, ω r is the rth modal frequency of the 3rd to nth node of the engineering structure; q is the node number; n is the total node number excluding the support; X1(ω r ) and X2(ω r ) are the absolute displacement Fourier spectra of node 1 and node 2 of the first substructure, respectively; X3(ω r ), X4(ω r ), …, X n (ω r ) are the Fourier spectra of the estimated absolute displacement of the engineering structure, wherein is the Fourier spectrum of the relative displacement δ q+1,q-1 between node q+1 and node q-1 measured by the qth substructure.

5. The method of claim 1, wherein: In S6, the mode shape curvature is calculated using the central difference method, and the calculation formula is as follows: wherein, and respectively represent the curvatures of the i-th position of the j-th mode before and after damage, φ j (i) is an element of the i-th position of the j-th mode, the superscripts u and d indicate before and after damage, l i is the length of the i-th element.

6. The method of claim 5, wherein: In S6, the change in the mode shape curvature is calculated according to the obtained mode shape curvature, and the calculation formula is as follows:

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