Method for identifying vertical and radial modal parameters of curved bridge based on mobile vehicle response

Abstract

The application provides a curve bridge vertical and radial modal parameter identification method based on mobile vehicle response, and the process comprises a data acquisition stage and a data processing stage. In the data acquisition stage, acceleration sensors Sv and Sl are installed at the axle center of a measurement vehicle; based on the vehicle-bridge coupling principle, the vertical and radial vibration responses of the bridge are transmitted to the vehicle M, so that the vehicle body generates vertical and lateral vibration; the measurement vehicle drives over the curve bridge, and the sensors Sv and Sl collect the vertical and lateral vibration response data of the vehicle body; in the data processing stage, the interference of the vertical and lateral frequencies ω vD and ω rD of the vehicle body is eliminated, so as to increase the visibility of the bridge frequency identification. The method effectively identifies the vertical and radial modal parameters of the curve bridge, and reduces the influence of the vertical and lateral (horizontal) responses of the vehicle body on the bridge modal parameter identification, which is of great significance for bridge health detection.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge health monitoring and detection, and particularly relates to a curved bridge vertical and radial modal parameter identification method based on mobile vehicle response. BACKGROUND

[0002] As an important part of traffic infrastructure, bridges play an important role in maintaining normal social production and life. However, bridges during service will be affected by vehicle load, environmental erosion and other factors, resulting in a decline in bridge structural performance. If the bridge health condition deteriorates seriously, it will directly endanger personal safety and cause significant losses to the society and economy. By the end of 2021, there were 961,100 highway bridges in China, with a total length of 738,021,000 meters. For nearly one million bridges in China, developing rapid and efficient bridge health detection technology is an important means to ensure the safe operation of bridges.

[0003] In order to detect the health condition of bridges, the method based on bridge vibration has attracted widespread attention. Generally speaking, the traditional health monitoring and detection method directly installs a large number of vibration sensing collection devices on the bridge, which can continuously collect the vibration response of the bridge. However, due to the high installation and maintenance cost, this method is usually used for health monitoring and detection of large-span, super-large-span bridges and special bridge structures. For the medium and small span bridges which account for more than 90% in China, the traditional method will result in high detection cost. Therefore, it is necessary to study economic and efficient bridge health monitoring and detection technology.

[0004] The closest prior art:

[0005] When a mobile vehicle passes through a bridge, the mobile vehicle and the bridge interact, that is, the mobile vehicle causes the bridge to vibrate, and the vibration is further transmitted to the mobile vehicle. Based on this characteristic, the bridge health detection method based on mobile vehicle response to obtain bridge vibration data has attracted widespread attention. This method arranges sensors on the mobile vehicle, which has the characteristics of mobility, economy and universality.

[0006] In the current research, only the vertical dynamic parameter characteristics of the mobile vehicle are considered, and the sensors are arranged in the vehicle body to collect the vertical vibration data of the vehicle body, which is mainly applied to the study of bridge vertical related modal parameters. In addition, the current technical research focuses on straight bridges, and the identification technology method for curved bridges based on mobile vehicle response is in a blank state. For curved bridges, in addition to the vertical bending response of the bridge, the radial (horizontal) modal parameters of the bridge can also reflect the health condition of the bridge. How to effectively identify the vertical and radial modal parameters of the curved bridge and reduce the influence of the vertical and lateral (horizontal) response of the vehicle body on the identification of the bridge modal parameters is of great significance to the bridge health detection. SUMMARY

[0007] The technical problem to be solved by the present application is to provide a curve bridge vertical and radial modal parameter identification method based on mobile vehicle response, which is a method that embodies wisdom and strategy.

[0008] (1) While considering the vertical dynamic parameters of the vehicle body, the lateral dynamic parameters of the vehicle body are fully considered, and sensors that can collect vertical and lateral responses are installed on the vehicle, based on the coupling effect of the vertical and horizontal directions of the vehicle bridge, the vertical and radial modal parameters of the curve bridge are indirectly identified from the vehicle body response;

[0009] (2) Based on the collected vertical and lateral responses of the vehicle body, the vehicle-curve bridge contact response algorithm for eliminating the influence of the vertical and lateral self-vibration of the vehicle body is used to realize efficient identification of the vertical and radial modal parameters of the bridge.

[0010] Technical scheme:

[0011] A curve bridge vertical and radial modal parameter identification method based on mobile vehicle response is a method that embodies wisdom and strategy, and the process is as follows:

[0012] Data acquisition stage:

[0013] Step 1: Install acceleration sensors S v , S l on the center of the vehicle axle; based on the coupling principle of the vehicle bridge, the vertical and radial vibration responses of the bridge will be transmitted to the vehicle M, so that the vehicle body produces vertical and lateral vibration;

[0014] Step 2: The measurement vehicle drives over the curve bridge, and the sensors S v , S l can collect the vertical vibration response and lateral vibration response of the vehicle body;

[0015] Data processing stage: use formula (8) to eliminate the interference of the vertical frequency and lateral frequency of the vehicle body, to increase the visibility of bridge frequency identification.

[0016] Specifically, the data processing stage includes three steps:

[0017] Step 3: Use formulas (10) and (11) to derive the vertical vibration response and lateral vibration response of the vehicle body collected by sensors S v , S l with respect to time t ;

[0018] Step 4: Substitute formula (10) and (11) into formula (9) to solve K i ;

[0019] Step 5: Calculate the vertical and radial response of the vehicle-curve bridge contact acceleration using formula (8), and identify the vertical and radial frequency of the curve bridge.

[0020] The formulas (8), (9), (10), (11) are respectively:

[0021]

[0022]

[0023] The method of the present application fills the gap of the identification technology method suitable for curve bridge based on the response of moving vehicle. It effectively identifies the vertical and radial modal parameters of the curve bridge and reduces the influence of the vertical and lateral (horizontal) response of the vehicle body itself on the identification of the bridge modal parameters, which is of great significance for bridge health detection. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 Flowchart of the method of the present application

[0025] Figure 2 Sensor arrangement scheme of the measurement vehicle system

[0026] Figure 3 Mechanical model of the theory of the present application: measurement vehicle-curve bridge system

[0027] Figure 4 Vertical response of the measurement vehicle based on the sensor arrangement of the method of the present application

[0028] Figure 5 Radial response of the measurement vehicle obtained based on the sensor arrangement of the method of the present application

[0029] Figure 6 Vertical contact acceleration response of the vehicle-curve bridge obtained based on the vehicle-curve bridge contact response calculation method of the present application

[0030] Figure 7 Radial contact acceleration response of the vehicle-curve bridge obtained based on the vehicle-curve bridge contact response calculation method of the present application DETAILED DESCRIPTION

[0031] A curve bridge vertical and radial modal parameter identification method based on the response of a moving vehicle is an application method, and the process is as follows (as shown in the figure): Figure 1

[0032] Data acquisition stage

[0033] Step 1: Place the acceleration sensor S​v S l Installed at the center of the measuring vehicle's axle, such as Figure 2 As shown. Based on the vehicle-bridge coupling principle, the vertical and radial vibration responses of the bridge will be transmitted to the vehicle, causing the vehicle body to vibrate vertically and laterally;

[0034] Step 2: The sensor S measures the distance as the vehicle travels across the curved bridge. v S l The vertical vibration response of the vehicle body can be collected. and lateral vibration response ;

[0035] Data processing stage: Eliminate the vertical frequency of the vehicle body using formula (8). and lateral frequency To reduce interference and increase the visibility of bridge frequency identification.

[0036] The above data processing stage specifically includes:

[0037] Step 3: Use formulas (10) and (11) to analyze sensor S v S l Collect the vertical vibration response of the vehicle body and lateral vibration response Conducting discussions about time t Differentiate;

[0038] Step 4: Substitute formulas (10) and (11) into formula (9) to solve. K i

[0039] Step 5: Calculate the vertical and radial response of the vehicle-curved bridge contact acceleration using formula (8), and identify the vertical and radial frequencies of the curved bridge.

[0040] like Figure 2 As shown, the vertical acceleration response of the vehicle was measured. And the lateral acceleration response of the measuring vehicle The vertical and lateral modal parameters of the curved bridge are identified by utilizing the vertical and lateral responses of the mobile measuring vehicle system crossing the curved bridge, respectively. This is the core innovation and technological contribution of the application method of this invention.

[0041] The first part presents the apparent theory formula to intuitively verify the effectiveness of the application method of this invention:

[0042] like Figure 3 The model shown in the figure has the following meanings for the letters:

[0043] x , y and z For the mechanical model, a three-dimensional coordinate axis system, , 、 for measuring the vertical and lateral displacements of the vehicle, 、 for measuring the vertical and lateral stiffness of the vehicle model, 、 for measuring the vertical and lateral damping of the vehicle model, 、 for measuring the vertical and lateral displacements of the vehicle at the contact points of the vehicle-curve bridge, u r 、 u a 、 u v and θ are the radial, axial, vertical and torsional displacement responses of the curved beam, O is the center of the curve bridge, R is the radius of curvature of the curve bridge, is the central angle of the curve bridge, m is the unit length mass of the curved beam, A is the cross-sectional area of the curved beam, E and G are the elastic and shear moduli, I z is the moment of inertia about the z axis, I y is the moment of inertia about the y axis, J is the torsional constant.

[0044] The measurement vehicle and the curved bridge beam are a coupled system, including the coupling of vertical responses and the coupling of radial (horizontal) responses. When the measurement vehicle travels over the curved bridge beam, the vertical and radial vibration responses of the curved bridge beam are transmitted to the measurement vehicle through the wheels, so that the measurement vehicle generates vertical and lateral vibrations. Therefore, vertical and lateral response acquisition sensors can be installed in the measurement vehicle to identify the vertical and radial vibration responses of the curved bridge beam.

[0045] When the measurement vehicle passes through the curved bridge beam, the apparent vertical and lateral vibration responses of the vehicle body object are Figure 3

[0046]

[0047] where the coefficients are

[0048]

[0049] In equations (1) and (2), is the driving frequency of the vehicle; and ​Vertical frequency of curve bridge due to driving effect and Radial frequency of curve bridge due to driving effect. As shown in above equations (1) (2), the vertical and radial frequencies of curve bridge can be identified from the vertical and lateral vibration responses of the measurement vehicle.

[0050] However, the vertical frequency and lateral frequency of the vehicle body will appear in the vertical and lateral vibration responses of the measurement vehicle, which will interfere with the identification of the radial frequency of curve bridge.

[0051] To eliminate the interference of the vertical frequency and lateral frequency of the vehicle body, the present application uses the vibration transfer relationship between the vehicle body response and the curve bridge response to inverse the vertical and lateral vehicle-curve bridge contact responses of the measurement vehicle and the curve bridge. Finally, the theoretical expressions of the vertical and lateral responses are as follows (the small black dots in the vehicle body and wheels are shown in this way Figure 3 ):

[0052]

[0053] In the above equations (3) (4), the coefficients are

[0054]

[0055] As can be seen from the above equations (3) (4), the vertical frequency and lateral frequency of the vehicle body are eliminated in the vehicle-curve bridge contact responses, so the application method of the present application necessarily improves the bridge frequency identification effect and identification accuracy relative to the traditional method.

[0056] Second part of theoretical verification

[0057] The feasibility of the present application will be verified by theoretical derivation through the following equivalent mechanical model, as shown in Figure 3 . The curve bridge is simplified as an Euler-Bernoulli simply supported beam model, m is the unit length mass of the curved beam, A is the cross-sectional area of the curved beam, E and G are the elastic and shear moduli, I z is the moment of inertia about the z axis, I y is the moment of inertia about the y axis, J is the torsional constant; u v andθ For curved beam vertical and torsional displacement response, u r And u a For curved beam radial and axial displacement response. The measured car system mass is , the vertical stiffness is , the lateral stiffness is , the vertical damping is , the lateral damping is , and the vehicle speed is .

[0058] When the measured car passes through the bridge, the vertical, rotational, axial, and radial vibration control equations of the curved bridge are respectively

[0059]

[0060] In the formula, is the Dirac function, the vertical contact force f c , the radial contact force f cr , and the torque T ( t ) are respectively

[0061]

[0062] In the formula, is the acceleration of gravity, is the eccentricity of the contact force relative to the z-axis.

[0063] Based on the theory of modal superposition method, the analytical expressions of the vertical, rotational, axial, and radial displacement responses of the curved bridge can be derived as

[0064]

[0065] By inputting the bridge response into the car body response, the vertical and lateral responses of the measured car system can be obtained, as shown in formulas (1) and (2). From the formulas, it can be found that the car body response can identify the left and right frequencies of the vertical vibration of the curved bridge and and the left and right frequencies of the radial vibration of the curved bridge and .

[0066] Further, to filter out the vehicle frequency interference, the vehicle-curved bridge contact response can be calculated by the proposed vehicle-curved bridge contact response calculation formula (8), and the theoretical expression of its acceleration response is shown in formula

[0067]

[0068] As can be seen from the above expression, the left and right frequencies of vertical vibration of the curved bridge can be identified in the vehicle-curved bridge acceleration contact response. and Left and right frequencies of radial vibration of curved bridges and Furthermore, the vertical and lateral frequencies of the vehicle body are filtered out. This verifies that the vertical and radial frequencies of the bridge can be extracted from the vehicle-curved bridge acceleration contact response, with even better results.

[0069] Part Three further provides the theoretical derivation of the algorithm.

[0070] The following steps are required:

[0071] (1) Install the acceleration sensor of the measuring vehicle system: install the acceleration sensor S v S l Installed at the center of the axle of the measuring vehicle to obtain the vertical acceleration response of the measuring vehicle. And the lateral acceleration response of the measuring vehicle ,See Figure 2 ;

[0072] (2) The measuring vehicle moves at a constant speed When the vehicle travels across the curved bridge to be measured, the signal acquisition system collects the vertical acceleration response of the measuring vehicle system. and lateral acceleration response .

[0073] (3) Calculate the vibration response at the vehicle-curved bridge contact point using vibration data collected by the acceleration sensor in the measuring vehicle. Measure the vertical and lateral vibrations of the vehicle crossing the curved bridge. Figure 1 The differential equation of motion for the trolley body is:

[0074]

[0075] To convert the displacement and velocity responses in the equations into quantities related to acceleration, time can be applied to equations (5) and (6). t Taking the second derivative and rearranging, we get

[0076]

[0077] In the formula Formula (7) is a second-order differential equation, which can be solved to obtain...

[0078]

[0079] In the formula:

[0080]

[0081] In the formula, j The index is the discrete sample point number.

[0082] The above formula (5) -> formula (8), and the process of substituting formula (9), (10), (11) into formula (8), is essentially a mathematical algorithm processing to achieve the conversion from the vehicle body expression response to the black dot (tire) expression response.

[0083] From the above mathematical processing process, it can be seen that the vertical and lateral vehicle-curve bridge contact responses can be calculated by measuring the vertical and lateral acceleration responses of the system itself and its dynamic physical parameters, and are independent of the physical properties of the curve bridge itself.

[0084] The following further numerically verifies the technical solutions of the present application by examples

[0085] Example 1

[0086] Example parameters:

[0087] Curve bridge span L = 30 m, the unit length mass of the curve bridge m = 2400 kg / m, the curvature radius of the curve = 100 m, the elastic modulus E = 33.2 GPa, the Poisson's ratio = 0.2, the cross-sectional area = 9 m 2 , the moment of inertia = 18.75m 4 , = 2.43 m 4 . The mass of the measuring vehicle 1000 kg, the vertical stiffness of the vehicle body = 1,500 kN / m, the lateral stiffness of the vehicle body = 1,000 kN / m, the vertical and lateral damping ratios of the vehicle body = = 5%, the running speed of the vehicle body is v = 10 m / s.

[0088] To verify that the method of the present application can identify the vertical and lateral frequencies of the curve bridge from the measuring vehicle response, numerical simulation is performed. Figure 4 The vertical response of the measuring vehicle based on the sensor arrangement of the method of the present application is Figure 5 The lateral response of the measuring vehicle based on the sensor arrangement of the method of the present application is

[0089] From Figure 4 , Figure 5 It can be seen that by using the sensor arrangement method of the method of the present application, the vertical and lateral frequencies of the curve bridge can be successfully identified from the vehicle body response of the measuring vehicle.

[0090] In order to verify the calculation effect of the method on the vertical and radial contact acceleration response of the vehicle-curve bridge, numerical simulation is carried out. Figure 6 The vertical contact acceleration response of the vehicle-curve bridge obtained based on the vehicle-curve bridge contact response calculation method, Figure 7 The radial contact acceleration response of the vehicle-curve bridge obtained based on the vehicle-curve bridge contact response calculation method.

[0091] From Figure 6 , Figure 7 It can be seen that the vehicle-curve bridge contact response calculation method proposed is almost consistent with the response directly extracted from the curve bridge in calculating the radial contact acceleration response of the vehicle-curve bridge. And the Figure 6 and Figure 7 are compared with Figure 4 and Figure 5 It can be found that the vehicle body frequency is filtered out in the vehicle-curve bridge contact response, and the visibility of the vertical and radial high-order frequencies of the curve bridge is improved. The whole vehicle-curve bridge contact response identification process only uses the measured response of the vehicle itself. Therefore, the vehicle-curve bridge contact response calculation method proposed is not limited to the structure form of the curve bridge.

Claims

1. A method for curve bridge vertical and radial modal parameter identification based on mobile vehicle response, characterized in that, A method of use, the process of which is: Data acquisition phase: Step 1: Acceleration sensor S v , S l is installed at the center of the measuring vehicle axle; based on the principle of bridge coupling, the vertical and radial vibration responses of the bridge will be transmitted to the vehicle M, so that the vehicle body produces vertical and lateral vibration; Step 2: Measure the vehicle driving over the curved bridge, sensor S v , S l Collect the vertical vibration response of the vehicle body and lateral vibration response ; Data processing stage: The interference of the vertical frequency and lateral frequency of the vehicle body is eliminated by formula (8) to increase the visibility of bridge frequency identification; The data processing phase includes three steps: Step 3: Derive the sensor S v , S l vertical vibration response of the car body and lateral vibration response with respect to time t ; Step 4: Substitute equations (10) and (11) into equation (9) and solve for K i ; Step 5: Calculate the vertical and radial response of the vehicle-curve bridge contact acceleration using formula (8), and identify the vertical and radial frequency of the curve bridge; The formula (8) is: The formula (9) is: The formula (10) is: The formula (11) is:

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