CN114997009A - Bridge bearing capacity rapid assessment method based on machine vision and model correction - Google Patents

Bridge bearing capacity rapid assessment method based on machine vision and model correction Download PDF

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CN114997009A
CN114997009A CN202210597897.5A CN202210597897A CN114997009A CN 114997009 A CN114997009 A CN 114997009A CN 202210597897 A CN202210597897 A CN 202210597897A CN 114997009 A CN114997009 A CN 114997009A
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亓兴军
丁晓岩
王珊珊
佀贞贞
孙绪法
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Shandong Jianzhu University
Shandong High Speed Group Co Ltd
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Abstract

The invention discloses a bridge bearing capacity rapid evaluation method based on machine vision and model correction. The method comprises two parts, wherein the first part is used for acquiring vibration data of a measuring point of a midspan section of the bridge and correcting a finite element model of the bridge, and the second part is used for evaluating the bearing capacity of the bridge; collecting vibration images of a bridge mid-span section measuring point in the moving process of a vehicle and after the vehicle drives away from the bridge by using a high-resolution high-frame-rate camera, identifying and extracting deflection time-course data of the bridge mid-span section measuring point in the moving process of the vehicle and free vibration deflection time-course data of the bridge mid-span section measuring point after the vehicle drives away from the bridge by using an image identification algorithm, calculating and identifying to obtain an actually-measured deflection influence line of the bridge mid-span section and an actually-measured bridge frequency, correcting and optimizing an initial finite element model by using the actually-measured deflection value and the bridge frequency as state variables and using parameters obtained by sensitivity analysis as design variables to obtain a bridge reference finite element model; and carrying out bridge bearing capacity evaluation based on the corrected reference finite element model.

Description

Bridge bearing capacity rapid assessment method based on machine vision and model correction
Technical Field
The invention relates to a bridge bearing capacity rapid evaluation method based on machine vision and model correction, and belongs to the technical field of bridge detection evaluation.
Background
The bridge evaluation is a process of evaluating the safety and reliability of the existing bridge and making engineering decisions by using static parameters such as strain and deflection or dynamic parameters such as frequency, damping and vibration mode. The currently commonly used bridge bearing capacity evaluation methods mainly comprise an appearance detection evaluation method, a load test evaluation method, a design specification evaluation method, an expert system evaluation method and the like, and the evaluation methods have self limitations: the appearance evaluation method and the expert system evaluation method are simple and depend on the experience of engineers and the professional level of experts, and a plurality of uncertain factors are contained in the evaluation process; the load test needs to interrupt traffic, and is time-consuming and labor-consuming; the actual deterioration condition of the bridge cannot be truly and reliably reflected on the basis of the design specification evaluation method, and the problems of design specification updating, load mode change and the like need to be faced, so that the accuracy of evaluation is influenced to a certain extent.
The bridge detection work is developed from manual detection and bridge detection vehicle detection to various nondestructive detections, in recent years, along with the rapid development and wide application of computer science and optics, a non-contact intelligent detection technology appears, and a better choice is provided for bridge detection, wherein a machine vision method is a bridge detection method which is currently concerned. The method is based on a machine vision theory and aims to enable a computer to replace manpower to automatically detect and identify the bridge in a long distance, high precision and low cost mode. The machine vision method avoids the defects of low speed, low efficiency, poor real-time performance and traffic influence of manual detection and bridge inspection detection.
The bridge field test comprises a dynamic test and a static test, and in the dynamic test, the frequency test precision of the structure is high and the overall effect of the structure can be reflected; in static test, the deflection test precision of the structure is high and reflects the whole effect of the structure, and the strain test data mainly reflects the local effect. Therefore, the invention selects two indexes of deflection and frequency to measure, and can reflect the overall static and dynamic performance of the bridge.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for rapidly evaluating the bearing capacity of a bridge.
The invention is realized by the following technical scheme: a bridge bearing capacity rapid assessment method based on machine vision and model correction is characterized in that: the device comprises two parts:
the first part is the vibration data acquisition and finite element model correction of a bridge midspan section measuring point, and the method comprises the following steps:
the method comprises the following steps: establishing an initial finite element model of the bridge according to a design drawing and relevant specifications, simulating a loading vehicle to move across the bridge floor by adopting a static method, and calculating a theoretical deflection influence line of a midspan section of the bridge and the theoretical frequency of 2-3 orders in front of the bridge;
step two: carrying out sensitivity analysis on bridge design parameters by using finite element software, and selecting bridge structure parameters with large influence on deflection and frequency as parameters to be corrected;
step three: a loading vehicle is adopted to slowly run through an actual bridge at a certain speed, a deflection measuring point with the same position as a finite element model is selected on a midspan section to serve as a machine vision measuring point, a high-resolution high-frame-rate camera is used for measuring a vibration image of the bridge midspan section measuring point in the moving process of the vehicle and a vibration image of the bridge midspan section measuring point after the vehicle drives away from the bridge, a dynamic image recognition program is compiled, a bilateral filtering algorithm is adopted for carrying out noise reduction on the images, an ACE image enhancement algorithm is utilized for improving the image contrast, RGB three-channel images are converted into single-channel images, and image gray processing is realized; adopting an image recognition tracking algorithm to recognize and extract a deflection time-course curve of a bridge mid-span section measuring point in the moving process of a vehicle and a free vibration deflection time-course curve of the bridge mid-span section measuring point after the vehicle drives away from the bridge, and respectively calculating and recognizing to obtain a bridge actual measurement deflection influence line and frequency;
step four: taking the parameters to be corrected of the bridge obtained in the step two as design variables, taking the actually measured deflection influence line and the actually measured frequency obtained in the step three as state variables, and constructing a target function by using the difference value of an actually measured value and a theoretical value as shown in the formula (1):
Figure BDA0003668822500000021
in the formula, ω i
Figure BDA0003668822500000022
Respectively a calculated value and an actual measured value u of the ith order natural frequency of the bridge i
Figure BDA0003668822500000023
Respectively calculating the static force deflection value and the measured value of the ith measuring point of the bridge; w is a i 、w′ i Is a weight coefficient; f is an objective function of the difference value between the actual measurement value and the theoretical value;
step five: and (3) carrying out finite element calculation result post-processing: analyzing and sorting the theoretical natural vibration frequency and mid-span deflection data of the bridge obtained in the first step, comparing the theoretical natural vibration frequency and mid-span deflection data with the measured values of the static and dynamic load tests, and substituting the measured values into a target function for calculation;
step six: judging whether the response of the objective function and the bridge structure meets the optimization precision requirement: if the requirements are met, the adopted calculation parameters are the optimal parameter values, the model correction process is ended, the bridge initial finite element model is corrected by the optimized design variables, and a reference finite element model capable of representing the actual working state of the bridge is obtained; if the requirement is not met, changing the design parameter value of the bridge and continuing to carry out the circular iterative analysis until the precision requirement is met;
the second part is bridge bearing capacity evaluation, which comprises the following steps:
the method comprises the following steps: a bridge static load test scheme is formulated according to highway bridge load test regulations, so that the loading efficiency is 0.95-1.05, a three-axle truck can be adopted as a loading vehicle, and the theoretical design deflection of the bridge under the test load is calculated based on an initial finite element model;
step two: according to the test load of the static load test scheme, the actually measured deflection of the midspan section of the bridge under the test load is obtained on the basis of the reference finite element model prediction, and the deflection reflects the structural deformation of the actual bridge;
step three: calculating the bridge deflection check coefficient by adopting the following formula
Figure BDA0003668822500000031
The method comprises the following steps of (1) evaluating the bearing capacity of a bridge by using a deflection check coefficient:
Figure BDA0003668822500000032
in the formula: s e Actually measured elastic deflection or strain value of main measuring points of the reference finite element model under the action of test load; s s And calculating the displacement or strain value for the theory of the main measuring point of the initial finite element model under the action of the test load.
Static load test structure check coefficient
Figure BDA0003668822500000033
Is the ratio of the actually measured elastic deflection of the measuring point under the action of the test load to the corresponding theoretical value. According to the regulation of the highway bridge bearing capacity detection and evaluation regulation,
Figure BDA0003668822500000034
when the value is less than 1, the actual condition of the bridge is superior to the design theoretical condition, and the bearing capacity of the bridge meets the design requirement.
The invention utilizes a finite element model correction optimization algorithm, adopts two indexes of measured data of bridge deflection influence line and frequency measured by a machine vision technology and theoretical data calculated by a finite element model to correct the model, and carries out bridge bearing capacity evaluation based on a corrected reference finite element model, thereby being a finite element model correction combined with static dynamic measured data and being capable of increasing the reliability of the corrected finite element model.
Further, the image recognition algorithm described in step three is a template matching method, an optical flow method, a feature point matching method, a shape-based matching method, or a deep learning-based target tracking method. The principle of identifying and extracting bridge displacement by the template matching algorithm is as follows:
firstly, in the first frame image, all the objects to be measured containing the preset are extracted in the form of a "template", which is a subset of the objects to be measured contained in the image. The template matching process is to use a preset template to search the position of the target in the subsequent image shot by the digital camera. The search process typically scans the template line by line from the top left corner of the image to the right until the best match is found. In the scanning process, the position where the template is overlapped with the image can be subjected to two-dimensional image correlation operation to obtain a correlation coefficient. When the correlation coefficient reaches a maximum value, it is considered that the best matching position of the target is found in the image.
As shown in FIG. 1, an initial (first frame) image g is obtained from a size of M N 0 The subset f of rectangular images extracted in (x, y) k (x, y) as a template for the kth target. The center coordinate of the kth template is noted as (x) k 0 ,y k 0 ) Then template f k (x, y) and g 0 The correlation coefficient of (x, y) is:
Figure BDA0003668822500000041
in the formula, i is 0,1,., M-1, j is 0,1,., N-1, t is an image capturing time;
assuming that the coordinate origin of the image is at the upper left corner, the correlation calculation process is to calculate the overlapped part of the template and the image from the upper left corner of the image by the template to obtain a correlation coefficient c k (i, j), after the calculation is finished, the calculation is carried out after the line of the template is moved to the right by one pixel. Moving down one pixel into a second row after reaching the rightmost edge, continuing to move from left to rightmost until one correlation pass is performed for each positionAnd (4) calculating. When the kth template completes all correlation calculations on the image at the time t, a set C of correlation coefficients is obtained k Set C of k The maximum in (b) represents the result that the template of the kth object has reached the best match with a certain subset on the image, and the object position is determined. The center coordinate of the target image subset located at this time is noted as (x) t k ,y t k )。
Due to the above-mentioned correlation coefficient c k (i, j) is sensitive to the geometric size of the template and the image and the variation of the gray value of the pixel, which has no influence on the matching of the same template in the same image. However, when the template and the image are changed, the geometric size and the gray value of the template and the image are changed, so a unified standard evaluation system needs to be established, all the matches are defined in the range of-1 to 1, and the matching effect can be compared by the size value of the correlation coefficient after being unified. Therefore, no matter how the size and the pixel range of the image and the template are changed, all matching can be evaluated by using the same standard, the matching precision of the same target at different moments (namely on different frames) in a time sequence and the matching precision of different targets at the same moment (namely on the same frame) can be measured, and the measurement index is the normalized correlation coefficient.
Since the monitored target points of the engineered structure do not "wander" out of a certain area (a certain subset of the image) within a certain working range, w t (x, y), and this area is the region of interest (ROI), through setting up the ROI, make search and match the task to only carry on in ROI small range instead of in the whole picture, reduce the unnecessary irrelevant matching process, can save the memory that the computer takes up, can reduce and match time. Here the normalized correlation coefficient is modified to be:
Figure BDA0003668822500000051
in the formula (I), the compound is shown in the specification,
Figure BDA0003668822500000052
as a template f k The mean value of the gray values of all the pixel points in (x, y),
Figure BDA0003668822500000053
the mean value of the gray values of all the pixel points in the image subset, i.e. the region of interest ROI.
After the template matching is completed, the position coordinates of the target on the image at the time t are determined, but the change of the target position in the image coordinates needs to be converted into the change in the actual space scale coordinates to obtain the displacement of the target. Assuming that the shooting direction of the camera is perpendicular to the two-dimensional motion plane of the target, and the distance between two points on the image, which are H pixels apart, in the actual space is H, the image-space scale conversion scaling factor is defined as:
Figure BDA0003668822500000054
image subset center coordinates (x) when best match of template center initial coordinates of kth target with target on image at time t is obtained t k ,y t k ) Thereafter, the horizontal displacement x of the kth target at time t k (t) and a vertical displacement of y k (t) are respectively:
Figure BDA0003668822500000061
according to the principle, the actually measured deflection influence line of the bridge is extracted according to the deflection time course of the midspan section of the bridge in the moving process of the vehicle.
Further, based on free vibration deflection time-course data of a bridge mid-span section measuring point after a vehicle drives away from the bridge, the front 2-3 order natural vibration frequency of the bridge is calculated and identified by adopting a structural modal parameter identification method, wherein the structural modal parameter identification method comprises a random subspace identification method or a least square complex frequency domain method or a frequency domain decomposition method or a peak value extraction method.
The invention has the beneficial effects that: for checking and calculating the bridge bearing capacity, the invention utilizes the correction result of the finite element model to check and calculate the bridge bearing capacity, which is the combination of the checking algorithm and the correction method based on the finite element model, the calculation parameters of the method are corrected according to the actual measurement data of the bridge site, the accuracy is higher, and the method has better feasibility and higher reliability. For a bridge load test, the method can quickly and efficiently evaluate the bridge bearing capacity by utilizing the check coefficient, and reduces the economic loss caused by the traditional load test. The method can obtain two-dimensional and three-dimensional displacement values of a bridge structure, makes up the defects of small static load data quantity and inaccurate dynamic load test result, requires less time in the acquisition process, can avoid the defects that the traditional dynamic and static load test needs a large amount of manpower and material resources and affects traffic, does not need to install a sensor on the bridge, removes the measurement error of the sensor and the error generated by the contact collision of the sensor and the bridge floor, is not easily influenced by the surrounding environment such as noise, wind and the like, and ensures that the detection result can accurately reflect the actual working state of the bridge. The method for rapidly evaluating the bearing capacity of the bridge does not need to interrupt traffic for carrying out a static load test, only needs a short few minutes of running clearance of social vehicles, avoids a large number of time-consuming and labor-consuming sensor installation procedures of the static load test and the bridge lower support erection procedure in the traditional deflection measurement, only needs a few minutes of temporary absence of vehicles on the bridge floor when actually measuring deflection influence lines and frequencies, and saves the time cost of the bridge load test. The method disclosed by the invention is simple and rapid in test process, can obviously improve the bridge detection efficiency, and has great engineering application value in highway and urban bridge detection.
Drawings
FIG. 1 is a diagram of image correlation operations and template matching;
FIG. 2 is a schematic diagram of a bridge finite element model according to an embodiment of the present invention;
FIG. 3 is a comparison graph of deflection influence lines across the midpoint after optimization in an embodiment of the invention;
FIG. 4 is a graph of theoretical deflection values in a static load test of a bridge in an embodiment of the present invention;
fig. 5 is a diagram of the measured deflection value of the static load test of the bridge in the embodiment of the invention.
Detailed Description
The invention will now be further illustrated by way of non-limiting examples in conjunction with the accompanying drawings:
the invention will be described in detail below with a 3-span continuous box girder bridge. The bridge is a prestressed concrete continuous box girder bridge, the total length of the bridge is 90 meters, the upper structure is a C50 prestressed concrete single-box single-chamber box girder with the length of 3 multiplied by 30m, the girder is high at 1.8m, the total width of the bridge deck is 8.0m, 0.5m (protective collision fence) +7.0m (roadway) +0.5m (protective collision fence), the support adopts a basin-shaped rubber support, the pavement layer adopts 80mmC40 concrete + bridge deck waterproof layer +50mm medium-grain asphalt concrete +40mm asphalt horseshoe resin macadam mixture, the guardrail adopts C25 concrete, the expansion joint adopts a 120-type toothed plate expansion joint, and the designed automobile load grade of the bridge is city-A grade.
The bridge bearing capacity evaluation steps are as follows:
(1) and (3) establishing a bridge finite element initial model, and calculating to obtain a theoretical deflection influence line of a midspan section and a bridge theoretical frequency under the action of a 36-ton loading vehicle as shown in figure 2.
(2) Adopting a 36-ton loading vehicle to drive through a bridge, selecting a deflection measuring point on the cross section of each span, and measuring and identifying the deflection time-course curve of the cross section of the bridge span in the driving process of the bridge deck by using a high-resolution camera; and simultaneously, measuring and identifying a free vibration deflection time-course curve of a bridge span middle section after the vehicle drives away from the bridge by using a high frame rate camera. In the test, the frame rate of the video recording camera is 60 frames/second, the sampling frequency of the visual system is 60Hz, the video is led into a computer, a plurality of pictures are cut according to the number of frames, the color pictures are converted into gray images, the sub-pixel edges of the images are fitted by using a polynomial, and the positions of all points on the edge of the main beam at all times are obtained. Selecting a gray template matching algorithm method to calculate the structural deflection, extracting actually measured deflection influence line data of different measuring points of the bridge after time course data of a vehicle driving time period on the bridge are dispersed, calculating the self-vibration frequency of the bridge by adopting a random subspace method, and identifying the time course data of the time period when the vehicle drives away from the bridge to obtain the first 2-3 orders of actually measured self-vibration frequency of the bridge. A single-lens reflex digital camera is adopted to obtain the motion trail of the cross-section measuring point, the model of the camera is Nikon D3400, and the camera is produced by Nikon manufacturers of the Kabushiki Kaisha.
(3) And (3) carrying out sensitivity analysis on main design parameters by using finite element software, and determining the sensitive design parameters which have large influence on deflection and frequency, such as: and taking the elastic modulus of the concrete and the section inertia moment of the bridge as design variables during model correction, carrying out model optimization design by combining the actually measured deflection influence line and the self-vibration frequency of the bridge, and obtaining a reference finite element model capable of representing the actual working state of the bridge after optimization analysis, wherein the values after optimization of the design variables are shown in a table 1. And then calculating and drawing a deflection influence line of the bridge reference finite element model under the action of a 36-ton loading vehicle, wherein the optimized bridge influence line is very close to an actually measured influence line. The theoretical deflection influence line, the actually measured deflection influence line and the optimized deflection influence line of the second span middle section measuring point of the bridge are shown in figure 3.
TABLE 1 before and after optimization of design variables
Figure BDA0003668822500000081
According to the steps (1), (2) and (3), calculating to obtain the maximum deflection value of the midspan section and the front 2-order frequency of the bridge, as shown in the table 2:
TABLE 2 comparison of deflection values and frequency values before and after model correction
Figure BDA0003668822500000082
(4) And (3) designing a bridge static load test scheme, selecting a midspan section of a second midspan as a control section, controlling the control section by the worst bending moment, calculating the loading efficiency to be 1.009, meeting the requirement that the loading efficiency in the specification is between 0.95 and 1.05, and calculating the maximum deflection value of a midspan measuring point in the initial finite element model under the working condition of the static load test, as shown in FIG. 4.
(5) And (4) correcting the initial finite element model of the bridge by using the optimized parameters obtained in the step (3), modifying design parameters such as the section moment of inertia, the elastic modulus of concrete and the like of the bridge, and calculating the maximum deflection value of the mid-span measuring point in the reference finite element model under the static load test working condition, namely the actually measured deflection, as shown in fig. 5.
(6) S calculated according to the steps (4) and (5) e Is 6.99mm, S s 6.25mm, calculating the deflection check coefficient according to a calculation method of the structure check coefficient in the Highway bridge bearing capacity detection and evaluation regulation, and calculating the deflection check coefficient according to a calculation formula
Figure BDA0003668822500000091
And (3) calculating to obtain the deflection checking coefficient of the actual bridge to be 1.1, indicating that the actual working condition of the bridge is worse than the original design theoretical condition, and judging that the bearing capacity of the bridge does not meet the design requirement according to the road bridge bearing capacity detection and evaluation regulation.
Other parts in this embodiment are the prior art, and are not described herein again.

Claims (3)

1. A bridge bearing capacity rapid assessment method based on machine vision and model correction is characterized in that: the method comprises two parts:
the first part is the acquisition of vibration data of a measuring point of a bridge midspan section and the correction of a bridge finite element model, and comprises the following steps:
the method comprises the following steps: establishing an initial finite element model of the bridge according to a design drawing and relevant specifications, and simulating that a loading vehicle drives across the bridge floor by adopting a static method to obtain a theoretical deflection influence line of a midspan section of the bridge and a front second-order theoretical frequency of the bridge;
step two: carrying out sensitivity analysis on bridge design parameters by using finite element software, and selecting structural parameters which have large influence on deflection and frequency as parameters to be corrected;
step three: a loading vehicle is adopted to slowly run through an actual bridge at a certain speed, a deflection measuring point with the same position as a finite element model is selected on a midspan section to serve as a machine vision measuring point, and a high-resolution high-frame-rate camera is used for acquiring a vibration image of the bridge midspan section measuring point in the moving process of the vehicle and a vibration image of the bridge midspan section measuring point after the vehicle drives away from the bridge; a dynamic image recognition program is programmed, a bilateral filtering algorithm is adopted to perform noise reduction processing on the image, an ACE image enhancement algorithm is utilized to improve the image contrast, the RGB three-channel image is converted into a single-channel image, and the image gray scale processing is realized; adopting an image recognition algorithm to recognize and extract a deflection time-course curve of a bridge mid-span section measuring point in the moving process of a vehicle and a free vibration deflection time-course curve of the bridge mid-span section measuring point after the vehicle drives away from the bridge, and respectively calculating and recognizing to obtain a bridge actual measurement deflection influence line and frequency;
step four: taking the parameters to be corrected of the bridge obtained in the step two as design variables, taking the actually measured deflection influence line and the actually measured frequency obtained in the step three as state variables, and constructing a target function by using the difference value of an actually measured value and a theoretical value as shown in the formula (1):
Figure FDA0003668822490000011
in the formula, ω i
Figure FDA0003668822490000012
Respectively a calculated value and an actual measured value u of the ith order natural frequency of the bridge i
Figure FDA0003668822490000013
Respectively calculating the static force deflection value and the measured value of the ith measuring point of the bridge; w is a i 、w i ' is a weight coefficient; f is an actual measurement and theoretical value difference value target function;
step five: carrying out finite element calculation result post-processing: analyzing and sorting the theoretical natural vibration frequency and mid-span deflection data of the bridge obtained in the first step, comparing the theoretical natural vibration frequency and mid-span deflection data with the measured values of the static and dynamic load tests, and substituting the measured values into a target function for calculation;
step six: judging whether the reaction of the objective function and the bridge structure meets the optimization precision requirement or not: if the requirements are met, the adopted calculation parameters are the optimal parameter values, the model correction process is ended, the bridge initial finite element model is corrected by the optimized design variables, and a reference finite element model capable of representing the actual working state of the bridge is obtained; if the requirement is not met, changing the design parameter value of the bridge and continuing to carry out the circular iterative analysis until the precision requirement is met;
the second part is bridge bearing capacity evaluation, which comprises the following steps:
the method comprises the following steps: a bridge static load test scheme is formulated according to highway bridge load test regulations, so that the loading efficiency is 0.95-1.05, a three-axle truck can be adopted as a loading vehicle, and the theoretical design deflection of the bridge under the test load is calculated based on an initial finite element model;
step two: according to the test load of the static load test scheme, the actually measured deflection of the midspan section of the bridge under the test load is obtained on the basis of the reference finite element model prediction, and the deflection reflects the structural deformation of the actual bridge;
step three: calculating the bridge deflection check coefficient by adopting the following formula
Figure FDA0003668822490000021
The method comprises the following steps of (1) evaluating the bearing capacity of a bridge by using a deflection check coefficient:
Figure FDA0003668822490000022
in the formula: s e The measured elastic deflection or strain value of the main measuring point of the reference finite element model under the action of test load is measured; s s And calculating the displacement or strain value for the theory of the main measuring point of the initial finite element model under the action of the test load.
2. The method for rapidly evaluating the bearing capacity of the bridge based on the machine vision and the model correction as claimed in claim 1, wherein: the image recognition algorithm in the third step is a template matching method, an optical flow method, a feature point matching method, a shape-based matching method or a deep learning-based target tracking method.
3. The method for rapidly evaluating the bearing capacity of the bridge based on the machine vision and the model correction as claimed in claim 1, wherein: based on free vibration deflection time-course data of bridge mid-span section measuring points after a vehicle drives off a bridge, the front 2-3 order natural vibration frequency of the bridge is calculated and identified by adopting a structural modal parameter identification method, wherein the structural modal parameter identification method comprises a random subspace identification method or a least square complex frequency domain method or a frequency domain decomposition method or a peak value extraction method.
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CN117421554A (en) * 2023-10-23 2024-01-19 江苏科技大学 Long-term vibration monitoring data-based long-span suspension bridge structure damage identification method
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CN117421554A (en) * 2023-10-23 2024-01-19 江苏科技大学 Long-term vibration monitoring data-based long-span suspension bridge structure damage identification method
CN117968992A (en) * 2024-04-01 2024-05-03 泰富特钢悬架(济南)有限公司 Steel plate elasticity detection device for steel plate spring
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