Bridge distributed stiffness identification method based on curvature envelope area and microwave radar

Abstract

The application discloses a bridge distributed stiffness identification method based on curvature envelope area and microwave radar, and has the advantages of multi-point deformation synchronous monitoring based on the microwave interference radar, application of the radar realizes synchronous measurement of the deformation displacement influence line of the multiple measuring points in the observation area when the calibration mobile load passes through the bridge, then the curvature envelope area influence line of the test area is calculated based on the essential relationship among the curvature, the rotation angle and the displacement through the measured displacement influence line, the bending moment envelope area influence line caused by the calibration mobile load is calculated through structural mechanics, and finally the unit stiffness of the bridge test area can be obtained by taking the average of the quotient of the bending moment envelope area and the curvature envelope area in the time scale. The application has the advantages of convenient equipment installation, quick and convenient measurement, good robustness and non-contact, overcomes the problems of difficult sensor layout and poor stability of the existing method, and has a good prospect of wide application in actual bridge stiffness identification.

Description

Technical Field

[0001] This invention belongs to the field of building structure health monitoring technology, specifically relating to a bridge distributed stiffness identification method based on curvature envelope area and microwave radar, which can realize the stiffness identification of bridges. Background Technology

[0002] Bridges are a vital component of modern transportation networks. However, during long-term service, they suffer from structural material aging, environmental corrosion, widespread overloading, and various man-made or natural disasters (such as ship collisions, earthquakes, and hurricanes). Therefore, the load-bearing capacity of bridges gradually decreases with their service life. Their structural integrity is closely related to their structural stiffness, which can be considered their resistance to structural deformation. Structural stiffness is typically associated with material parameters (such as the elastic modulus E) and geometric parameters (such as the moment of inertia I). ​​Therefore, it is necessary to periodically assess the true stiffness of bridge structures to ensure their safe operation.

[0003] Previous vibration-based stiffness identification methods have made some progress, mainly including time-domain and frequency-domain methods. However, vibration-based methods require densely packed sensors along the bridge, such as accelerometers, strain gauges, and linear variable differential transformers (LVDTs), which are costly, time-consuming, and require traffic interruption. In comparison, static load testing is also an effective means of assessing the actual condition of bridges, and stiffness can be indirectly estimated from displacement measurements under load. However, repeating load tests on every span of the entire bridge is costly. Therefore, it is necessary to adopt some rapid non-destructive testing method to assess the condition of bridges. Due to its relatively simple and fast measurement, influence line-based damage identification methods have recently been widely used. Furthermore, a robust and novel damage identification method based on rotational influence lines has recently been proposed, which uses only two measuring points at both ends of the bridge. The results show that the rotational influence line-based damage identification method can identify damage even at a distance from the sensor location, and the rotational influence line is highly sensitive to local damage changes. Although these damage identification methods can characterize stiffness changes at the damage location, they cannot identify the true stiffness of the bridge, let alone estimate the distributed stiffness. Traditional influence line measurement requires the deployment of contact sensors, which is time-consuming, labor-intensive, and carries certain risks. While vision-based displacement measurement technology overcomes this drawback as a non-contact method, it faces challenges in remote measurement under low-light conditions. Sensor systems based on microwave jamming radar technology primarily interfere with microwave electromagnetic signals at different times, offering a promising non-contact displacement measurement method. Unlike widely used point sensors, microwave jamming radar equipment can be considered a non-contact distributed sensing technology. Given this background, it is necessary to invent a fast, convenient, safe, and efficient method for identifying bridge stiffness to achieve non-destructive assessment of bridge performance. Summary of the Invention

[0004] Technical problem solved: This invention discloses a bridge distributed stiffness identification method based on curvature envelope area and microwave radar. It has the advantages of convenient equipment installation, fast and convenient measurement, good robustness and non-contact operation. It overcomes the problems of difficult sensor deployment and poor stability of existing methods and has a good prospect of being widely used in actual bridge stiffness identification.

[0005] Technical solution:

[0006] A method for identifying the distributed stiffness of bridge elements based on curvature envelope area and microwave radar, the method comprising the following steps:

[0007] S1, when the calibrated moving load p passes through the test bridge, the displacement influence line y(x) of each test unit node within the test bridge area is obtained using radar. i Synchronous monitoring is performed on x, t), where x i This represents the position of the front-end node of the i-th test unit, where i = 1, 2, ..., N, and N is the total number of nodes on the test bridge. N =l, where l is the span of the bridge being tested;

[0008] S2, for the front node position x of test unit i at a distance of Ax. i and backend node position x i+1 The displacement influence line is calculated using first-order difference to obtain the position x of the front node of test unit i. i and backend node position x i+1 The influence line of the rotation angle θ(x) i ,t),θ(x i+1 ,t), influence line of the rotation angle θ(x) i ,t),θ(x i+1 The curvature envelope area A of test unit i is obtained by subtracting the two (t) values. κ (x i ,t);

[0009] S3, Calculate the influence line A of the bending moment envelope area of ​​test unit i within the observation area caused by the calibration moving load p. M (x i ,t);

[0010] S4, for A M (x i ,t) and A κ (x i The uniform stiffness EI(x) of test unit i is obtained by quotienting x and t and averaging over the time scale. i ).

[0011] Furthermore, in step S1, the process of synchronously monitoring the displacement influence line y(xi,t) of each test unit node within the test bridge area using radar includes the following sub-steps:

[0012] S11, Adjust the radar parameters and set the observation area within the radar's main lobe range; drive the radar to continuously transmit signals to the test bridge and capture the echo signal from the bottom of the bridge within the main lobe range.

[0013] S12, the displacement influence line of all distance unit measuring points under the action of moving load in the observation area is measured by phase interferometry in the direction of the line connecting the radar and the measuring point. The distance H between the radar and the bottom of the bridge is calculated by the auxiliary positioning device of the radar.

[0014] S13, the true vertical displacement influence line y(x) of the node position to which the measuring point unit i belongs is obtained through geometric relationship transformation. i ,t):

[0015]

[0016] In the formula, y r (x i ,t) represents the position x of the front node of measuring point unit i. i Radial displacement influence line, R i Let be the radial distance of measuring point unit i.

[0017] Further, in step S2, the influence line θ(x) of the rotation angle is calculated using the following formula. i ,t):

[0018]

[0019] In the formula, y(x i+1 ,t) and y(x i ,t) represent the rear node positions x of measuring point unit i, respectively. i+1 and the position x of the front-end node i The actual vertical displacement influence line, where Δx is the position x of the rear node. i+1 and the position x of the front-end node i The distance between them.

[0020] Furthermore, in step S3, the load position x is moved according to time t. t The position x of the front-end node of test unit i i Backend node location x i+1 The relationship is used to calculate the influence line A of the bending moment envelope area of ​​test unit i. M (x i ,t):

[0021]

[0022] Where, x t P represents the location of the moving load, l represents the value of the moving load, and l represents the span of the test bridge.

[0023] Further, in step S4, the uniform stiffness EI(x) of test unit i is calculated using the following formula. i ):

[0024]

[0025] In the formula, T is the total time it takes for the calibrated moving load p to pass through the test unit i.

[0026] Furthermore, the influence line of the total bending moment envelope area is calculated using the following formula:

[0027]

[0028] In the formula A M_sum (x i ,t) represents the total area response of the bending moment envelope caused by each axis, d g v is the distance between the 1st axis and the gth axis, v is the speed of the moving load, and G is the total number of axes.

[0029] This invention provides a method for identifying the distributed stiffness of bridge elements based on microwave interferometric radar technology and curvature envelope area: First, utilizing the characteristics of non-contact synchronous measurement, the proposed microwave inference radar achieves the acquisition of multi-point displacement influence lines; then, based on the precise one-to-one correspondence between curvature envelope area and element stiffness, and using the essential relationship between curvature, rotation, and displacement, the bending moment envelope area is calculated using a calibrated moving load, and the observed displacement influence lines are used to calculate the bridge element stiffness; finally, taking advantage of the radar's ability to simultaneously measure multi-point displacement influence lines, and referring to the proposed element stiffness identification method, the stiffness of the monitored bridge elements is further identified.

[0030] Beneficial effects:

[0031] First, the bridge distributed stiffness identification method based on curvature envelope area and microwave radar of the present invention solves the shortcomings of traditional bridge multi-point displacement influence line measurement, which requires a large number of contact sensors, which is time-consuming, labor-intensive and costly to install.

[0032] Secondly, the bridge distributed stiffness identification method based on curvature envelope area and microwave radar of the present invention has the advantages of being fast, convenient, robust and accurate, and is suitable for identifying the distributed stiffness of bridges for bridge performance evaluation. Attached Figure Description

[0033] Figure 1This is a schematic diagram illustrating the principle of the bridge distributed stiffness identification method based on curvature envelope area and microwave radar according to an embodiment of the present invention.

[0034] Figure 2 This is a schematic diagram illustrating the principle of multi-point displacement influence line observation.

[0035] Figure 3 A schematic diagram illustrating the calculation principle of the influence line of the bending moment envelope area;

[0036] Figure 4 This is a schematic diagram illustrating the calculation principle of the influence line of the bending moment envelope area under multi-axis moving load.

[0037] Figure 5 This is a schematic diagram of the calculation results applied to the test bridge;

[0038] Figure 6 A schematic diagram of the influence lines of the curvature envelope area of ​​M5-6, M6-7, and M7-8 within the observation area;

[0039] Figure 7 A schematic diagram showing the influence lines of the bending moment envelope area caused by each axis and the total bending moment envelope area. Detailed Implementation

[0040] The following embodiments are provided to enable those skilled in the art to more fully understand the present invention, but do not limit the invention in any way.

[0041] See Figure 1 This embodiment discloses a method for identifying the distributed stiffness of bridge elements based on curvature envelope area and microwave radar. The method for identifying the distributed stiffness of bridge elements includes the following steps:

[0042] S1, when the calibrated moving load p passes through the test bridge, the displacement influence line y(x) of each test unit node within the test bridge area is obtained using radar. i Synchronous monitoring is performed on x, t), where x i This represents the position of the front-end node of the i-th test unit, where i = 1, 2, ..., N, and N is the total number of nodes on the test bridge. N =l, where l is the span of the bridge being tested.

[0043] S2, for the front node position xi and back node position x of test unit i with a distance of Δx. i+1 The displacement influence line is calculated using first-order difference to obtain the position x of the front node of test unit i. i and backend node position x i+1 The influence line of the rotation angle θ(x) i ,t),θ(x i+1 ,t), influence line of the rotation angle θ(x) i ,t),θ(xi+1 The curvature envelope area A of test unit i is obtained by subtracting the two (t) values. κ (x i ,t).

[0044] S3, Calculate the influence line A of the bending moment envelope area of ​​test unit i within the observation area caused by the calibration moving load p. M (x i ,t).

[0045] S4, for A M {x i ,t) and A κ (x i The uniform stiffness EI(x) of test unit i is obtained by quotienting x and t and averaging over the time scale. i ).

[0046] Specifically, the steps include the following:

[0047] Step 1: Displacement influence lines of multiple measuring points in the observation area.

[0048] The radar equipment continuously transmits signals to the test bridge. The radar antenna can only capture the echo signal from the bridge's underside within the main lobe area. Therefore, the bridge within the main lobe is considered the observation area. Using phase interferometry, the components of the displacement influence lines of all distance unit measuring points under moving load within the observation area can be measured in the direction of the line connecting the radar and the measuring points. Then, the distance between the radar and the bridge's bottom is calculated using the radar's built-in auxiliary positioning device. Finally, the true vertical displacement influence lines y(x) of all measuring point unit measuring points can be obtained through geometric transformation. i ,t).

[0049] Step 2: Calculation of the curvature envelope area.

[0050] By performing a first-order difference on the displacement influence lines of adjacent i-th and i+1-th measuring points within the observation area, the rotation influence line of the i-th measuring point can be obtained. By subtracting the rotation influence lines of adjacent i-th and i+1-th measuring points, the curvature envelope area influence line of the test unit i can be calculated.

[0051]

[0052]

[0053] Where θ(x, t) is the influence line of the rotation angle, A κ (x i ,t) is the influence line of the curvature envelope area.

[0054] Step 3: Calculation of the influence line of the bending moment envelope area.

[0055] As shown in the figure, the position of the moving load is within the interval [x] ix i+ There are three relative positional relationships among them. Before the moving load arrives at the interval, the relative positional relationship is 0 < x. t <x i (0 < t < x) i / v). When the moving load arrives at the interval, the relative positional relationship is x. i <x t <x i+1 (x i / v<t<x i+1 / v). When the moving load operates beyond this range, the relative positional relationship is x. i+1 <x t <1(x i+1 / v<t<l / v). The area of ​​the bending moment envelope can be calculated using the following formula:

[0056]

[0057] In the formula, v is the speed of the moving load, l is the span of the bridge, and P is the weight of the vehicle.

[0058] like Figure 4 As shown, in practice, when a vehicle moves on a bridge, the load input is the sum of the loads on each axle. Therefore, the influence line of the total bending moment envelope area is equal to the sum of the influence lines of the bending moment envelope area induced by each axle.

[0059]

[0060] In the formula A M_sum (x i ,t) represents the total area response of the bending moment envelope caused by each axis, d g This represents the distance between the first axis and the g-th axis.

[0061] Step 4: Identification of stiffness distribution in the bridge observation area.

[0062] like Figure 5 As shown, by combining the element stiffness identification method based on displacement influence lines, the interval [x1, x2] can be obtained. N The bridge region stiffness matrix is ​​as follows:

[0063]

[0064] in, For the test interval [x i x i+1 At time t j Uniform stiffness.

[0065] Substituting the calculated influence lines of the bending moment envelope area and the curvature envelope area into the above formula, we can obtain...

[0066]

[0067] Where R = v*Δx / l.

[0068] The present invention will be further illustrated below through specific embodiments. The test example is the identification of the regional distribution stiffness of a steel beam under the action of a two-axle trolley moving load.

[0069] The experimental testing system consists of three parts: a vehicle system, a model bridge system, and a monitoring system. The model vehicle is a steel vehicle with a 20cm axle spacing, weighing approximately 20kg. Its speed is controlled manually, so it can be considered to be moving at a constant speed. The model bridge has a cross-section of 10cm x 15cm, with a wall thickness of 3.5mm and an open rectangular steel tube. The test pier height is 1.2m, and the bottom of the test beam is 1.3m above the ground. Material property tests were conducted on the rectangular steel tube beam beforehand, and the Young's modulus of the tested steel was determined to be 2.1GPa using stress-strain curves. For comparison, the deformation and rotation of the nodes were simultaneously measured using an optical camera and a contact inclinometer to verify the measurement results.

[0070] The specific steps of the bridge element distributed stiffness identification method in this embodiment are as follows:

[0071] Step 1: To more accurately locate the measurement point and reduce echo signals from surrounding debris, five corner reflectors (M5-M8) were placed under the bridge. The elevation angle measured by the radar's built-in compass was 20.5°, and the beam centerline distance measured by the laser designator was 2.5m. The displacement influence lines of M5-M9 within the observation area were measured as the vehicle moved. The radar used was a self-developed radar device with a range resolution of 0.5m. The rotation influence lines of M5-M8 within the observation area were calculated using the first-order difference method. Further subtraction yielded the curvature envelope area influence lines of M5-6, M6-7, and M7-8 within the observation area. The results are as follows: Figure 6 As shown in the figure, the displacement influence line measured by the radar equipment is in good agreement with the result measured by the optical camera. Furthermore, the rotation angle calculated by the first-order difference method is also in good agreement with the result measured by the contact inclinometer.

[0072] Step 2: The trolley weighs 20kg. Assuming each axle weighs 10kg, the influence lines of the bending moment envelope area caused by each axle and the total bending moment envelope area, calculated using the bridge element distributed stiffness identification method of this embodiment, are as follows: Figure 7 As shown, the bridge unit distributed stiffness identification method in this embodiment can calculate the stiffness of the test unit within the observation area, and the error with the actual result is less than 5%, which meets the requirements.

[0073] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for identifying the distributed stiffness of bridges based on curvature envelope area and microwave radar, characterized in that, The method for identifying the distributed stiffness of bridges includes the following steps: S1, when the calibrated moving load p passes through the test bridge, the displacement influence line y(x) of each test unit node within the test bridge area is obtained using radar. i Synchronous monitoring is performed on x,t), where x i This represents the position of the front-end node of the i-th test unit, where i = 1, 2, ..., N, and N is the total number of nodes on the test bridge. N =l, To test the bridge span; S2, for the front node position x of test unit i at a distance of Δx. i and backend node position x i+1 The displacement influence line is calculated using first-order difference to obtain the position x of the front node of test unit i. i and backend node position x i+1 The influence line of the rotation angle θ(x) i ,t),θ(x i+1 ,t), influence line of the rotation angle θ(x) i ,t),θ(x i+1 The curvature envelope area A of test unit i is obtained by subtracting the two values ​​(t) from each other. κ (x i ,t); S3, Move the load position according to time t. Position of the front-end node of test unit i Backend node location The relationship is used to calculate the influence line of the bending moment envelope area of ​​test unit i within the observation area caused by the calibrated moving load p. : ； in, To move the load position, For moving load values, To test the bridge span; S4, for A M (x i ,t) and A κ (x i The uniform stiffness EI(x) of test unit i is obtained by quotienting x and t and averaging over the time scale. i ).

2. The bridge distributed stiffness identification method based on curvature envelope area and microwave radar according to claim 1, characterized in that, Step S1, which involves synchronously monitoring the displacement influence line y(xi,t) of each test unit node within the test bridge area using radar, includes the following sub-steps: S11, Adjust the radar parameters and set the observation area within the radar's main lobe range; drive the radar to continuously transmit signals to the test bridge and capture the echo signal from the bottom of the bridge within the main lobe range. S12, the displacement influence line of all distance unit measuring points under the action of moving load in the observation area is measured by phase interferometry in the direction of the line connecting the radar and the measuring point. The distance H between the radar and the bottom of the bridge is calculated by the auxiliary positioning device of the radar. S13, the true vertical displacement influence line of the node position of measuring point unit i is obtained through geometric relationship transformation. : ； In the formula, Let x be the position of the front node of measuring point unit i. i Radial displacement influence line, Let be the radial distance of measuring point unit i.

3. The bridge distributed stiffness identification method based on curvature envelope area and microwave radar according to claim 1, characterized in that, In step S2, the influence line θ(x) of the rotation angle is calculated using the following formula. i ,t): ； In the formula, and The positions of the rear nodes of measuring point unit i are respectively and front-end node position The actual vertical displacement influence line, Location of backend nodes and front-end node position The distance between them.

4. The bridge distributed stiffness identification method based on curvature envelope area and microwave radar according to claim 1, characterized in that, In step S4, the uniform stiffness of test unit i is calculated using the following formula. : ； In the formula, T is the total time it takes for the calibrated moving load p to pass through the test unit i.

5. The bridge distributed stiffness identification method based on curvature envelope area and microwave radar according to claim 1, characterized in that, The influence line of the total bending moment envelope area is calculated using the following formula: ； In the formula This represents the total response of the bending moment envelope area caused by each axis. The distance between the first axis and the g-th axis is given by v, where v is the speed of the moving load. It is the total number of axes.

Images