Bridge damping ratio identification method based on spatial position relationship of biaxial vehicle contact response

Abstract

The present invention proposes a bridge damping ratio identification method based on the spatial position relationship of the contact response of a dual-axle vehicle, comprising the following steps: step 1, arranging a dual-axle measurement vehicle; step 2, establishing a corresponding motion differential equation; step 3, deriving the dual-axle vehicle-bridge contact point displacement response using the dual-axle vehicle and bridge motion equations; step 4, performing Hilbert transform on the contact point acceleration response to obtain the contact point acceleration response instantaneous amplitude; step 5, processing the dual-axle vehicle-bridge contact point acceleration response data using Hilbert transform; step 6, identifying the bridge damping ratio based on the spatial position relationship of the dual-axle vehicle-bridge contact response. The present invention utilizes the front and rear contact responses of the dual-axle vehicle, combined with Hilbert transform, and based on the spatial position relationship of the instantaneous amplitude of the front and rear contact responses of the dual-axle vehicle, realizes the efficient construction of the bridge damping ratio, which is of great significance for bridge health monitoring.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge health monitoring and detection, and in particular relates to a bridge damping ratio identification method based on the spatial position relationship of a dual-axle vehicle contact response. Background Art

[0002] Bridges play a vital role in the safety and normal operation of lifeline systems. However, due to internal factors such as aging and fatigue, as well as external factors such as earthquakes, typhoons and floods, the durability, safety and maintenance management of bridges have become increasingly prominent. In order to facilitate engineers to evaluate the health of bridges, health monitoring based on bridge vibration has become an important means of detecting and maintaining bridges.

[0003] Promoting the development of bridge health monitoring technology is of great practical significance for ensuring the safety of bridge operation. The traditional bridge parameter identification and health monitoring methods mainly place sensors on the bridge to be tested to monitor the vibration data of the bridge under environmental or artificial excitation. Although the above monitoring system can monitor the status of the bridge at any time, it faces problems such as high construction and replacement costs, difficulty in effectively utilizing massive data, high labor consumption, and many dangerous operations. Therefore, it is imperative to reduce the cost of bridge health monitoring and achieve rapid monitoring. In recent years, the vehicle scanning method (VSM) has been proposed to identify the modal parameters of the bridge using a mobile measuring vehicle equipped with sensors. When the measuring vehicle passes through the bridge to be tested, the mobile vehicle and the bridge form a coupled system. The vibration generated by the bridge under the excitation of the mobile vehicle will be transmitted to the sensor installed on the test vehicle, and the sensor will record the bridge response. This method has the advantages of good mobility, strong economy, and high detection efficiency, and has been widely studied by scholars from various countries.

[0004] Damping, as one of the important characteristic parameters of bridges, has not been widely and deeply studied in the field of vehicle scanning method. Structural damage will cause changes in damping, and structural damping can be used as a sensitive coefficient to determine whether a bridge is damaged. Accurately identifying damping using the vehicle scanning method is of great significance for bridge health monitoring. Summary of the invention

[0005] The present invention aims to provide an accurate and efficient bridge damping ratio identification method. The method strategy of the present invention is: using the front and rear contact responses of a biaxial vehicle, combined with Hilbert transform, based on the spatial position relationship of the instantaneous amplitudes of the front and rear contact responses of the biaxial vehicle, to achieve efficient construction of the bridge damping ratio.

[0006] In this field, bridge damping ratio is an important modal parameter and one of the important indicators for evaluating the health status of a bridge. Therefore, the bridge damping ratio identification technology, that is, the bridge damping ratio identification visibility, can be applied to evaluate the health of a bridge.

[0007] The principle of this method is to establish the instantaneous amplitude of the acceleration response of the front and rear contact points of the dual-axis mobile measurement vehicle (see formula (1) A c1 (t) and formula (2)A c2 (t+t2)), and mathematically divide the instantaneous amplitudes of the acceleration responses of the front and rear contact points of the vehicle, and use the spatial position relationship between the two, that is, calculate through formula (5) to obtain the expression of the bridge damping ratio.

[0008] Specifically:

[0009] First, the acceleration response motion equation of the biaxial vehicle contact point is used in combination with the Hilbert transform to determine the instantaneous amplitude of the acceleration response of the front and rear contact points of the biaxial vehicle-bridge and solve the equations (see formulas (1) and (2)):

[0010]

[0011]

[0012] Among them A c1 (t), A c2 (t+t2) are the instantaneous amplitudes of the acceleration response of the front and rear contact points, are the acceleration responses of the front and rear contact points, are the Hilbert transform functions of the front and rear contact point acceleration responses, ξ b,n is the bridge damping ratio, ω b,n ,ω bD,n are the bridge frequencies without and with damping effects (see formula (12)), t is the travel time of the biaxial vehicle (when the biaxial vehicle enters the bridge, t = 0), t1 and t2 are the time when the front and rear axles of the biaxial vehicle enter the bridge (see formula (10), Δ stn,1 , Δ stn,2 are the deformation of the bridge caused by the front and rear axles when the vehicle body is stationary on the bridge (see formula (14)), L is the effective span of the bridge, v is the speed of the dual-axle vehicle, C b,n , D b,n is the amplitude coefficient, and its expressions are:

[0013]

[0014]

[0015] Where: A bD,n , B bD,n is the amplitude coefficient (see formulas (17) and (18)).

[0016] Furthermore, by using the spatial position relationship between the instantaneous amplitudes of the acceleration response of the front and rear contact points of the biaxial vehicle, the instantaneous amplitude of the acceleration response of the rear contact point is divided by the instantaneous amplitude of the acceleration response of the front contact point (1) (i.e., the algorithm of formula (5)). By transforming the form of the formula, a simplified expression of the bridge damping ratio can be obtained (see formula (6)):

[0017]

[0018]

[0019] The above scheme can realize the visibility of bridge damping ratio identification.

[0020] To achieve the above object, the technical solution adopted by the present invention comprises the following steps:

[0021] Step (1) Arrange a dual-axis measurement vehicle: Arrange a dual-axis measurement vehicle equipped with an acceleration sensor on the bridge, and use the front and rear axles of the measurement vehicle to collect the acceleration response of the dual-axis vehicle-bridge contact point.

[0022] Step (2) Establish the corresponding motion differential equation. According to the characteristics of the dual-axis measurement vehicle, the vehicle body vibration response equation (see formula (7) and (8)) and the bridge vibration response equation (see formula (9)) are established and expressed as:

[0023]

[0024]

[0025]

[0026] Where:

[0027]

[0028] Where m v To measure the vehicle mass, the damping coefficients of the front and rear axles are c v1 、c v2 , the stiffness coefficients are k v1 , k v2 , the distances from the center of the vehicle are d1 and d2 respectively. v ,θ v are the vertical displacement and rotation angle of the measuring vehicle, u and u c1 、u c2 They are the displacement of the bridge and the displacement of the contact points between the front and rear axles of the measuring vehicle and the bridge, where In the formula, the dot (·) represents the partial derivative with respect to time, and the apostrophe (′) represents the partial derivative with respect to displacement; δ() and H() are the Dirac function and the unit step function, respectively. The bridge under consideration is a homogeneous Bernoulli-Euler beam with an effective span of L, bending stiffness of EI, damping coefficient of c, and mass per unit length of m.

[0029] Step (3) uses the equations of motion of the biaxial vehicle and the bridge to derive the displacement response of the biaxial vehicle-bridge contact point (see formula (11)). According to the modal superposition method, combined with the zero boundary condition, the displacement response of the biaxial vehicle-bridge contact point can be solved using formula (9), which can be summarized as:

[0030]

[0031] Where: A d,n , B d,n is the amplitude coefficient (see formulas (15) and (16)), ω d,n is the driving frequency (see formula (13)). The expression of the parameters in formula (11) is:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] A bD,n =-A d,n , (17)

[0038]

[0039]

[0040] Where: S n is the speed parameter. The second derivative of formula (11) with respect to time t can give the acceleration response of the dual-axle vehicle-bridge contact point:

[0041]

[0042] Where:

[0043]

[0044] Step (4) Hilbert transforms the acceleration response of the contact point (see formula (20)) to obtain the instantaneous amplitude of the acceleration response of the contact point (see formulas (1) and (2)). To identify the bridge damping ratio, the acceleration response of the contact point (see formula (20)) is Hilbert transformed to obtain:

[0045]

[0046] Thus, the instantaneous amplitude of the acceleration response of the front and rear contact points is obtained:

[0047]

[0048]

[0049] Step (5) utilizes the spatial position relationship of the instantaneous amplitude of the acceleration response of the front and rear contact points in formulas (1) and (2), and divides formula (2) by formula (1) to obtain:

[0050]

[0051] By transforming formula (5), we can get the expression of bridge damping ratio:

[0052]

[0053] The present invention combines Hilbert transform and utilizes the spatial position relationship of the acceleration response of the front and rear contact points of the dual-axle vehicle-bridge to construct a concise expression of the bridge damping ratio, which is the core of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a schematic diagram of the process of the present invention;

[0055] Figure 2 The bridge damping ratio identification process proposed by the method of the present invention;

[0056] Figure 3 A dual-axle vehicle arrangement scheme for the method of the present invention;

[0057] Figure 4 It is the mechanical model used for numerical verification in Example 1 of the method of the present invention;

[0058] Figure 5 The contact response obtained by back-calculation of the measuring vehicle in Example 1 of the method of the present invention;

[0059] Figure 6 This is the bridge damping ratio identification result obtained in Example 1 of the method of the present invention. DETAILED DESCRIPTION

[0060] The technical solution provided by the present application will be further described below in conjunction with specific embodiments and accompanying drawings. The advantages and features of the present application will become more apparent with the following description.

[0061] It should be noted that the embodiments of the present application have better practicability and are not any form of limitation to the present application. The technical features or combinations of technical features described in the embodiments of the present application should not be considered to be isolated, and they can be combined with each other to achieve better technical effects. The scope of the preferred implementation of the present application may also include other implementations, and this should be understood by those skilled in the art of the present application embodiment.

[0062] Techniques, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0063] The drawings of this application are in very simplified form and in non-precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of this application, and are not intended to limit the restrictive conditions under which this application can be implemented. Any structural modification, change in proportional relationship, or adjustment of size should fall within the scope of the technical content disclosed in this application without affecting the effects and purposes that can be achieved by this application. The same reference numerals appearing in the drawings of this application represent the same features or components, which can be applied in different embodiments.

[0064] Example 1 Numerical Verification

[0065] Example parameters:

[0066] The span of the bridge is L = 30m, the mass per unit length of the bridge is m = 2400kg / m, the elastic modulus is E = 27.5GPa, and the moment of inertia of the section is I = 0.2m 4 , damping ratio ξ b = 2%. The mass of the measuring vehicle is m v =1000kg, the elastic stiffness of the front and rear axles are k v1 =550kN / m=k v2 =550kN / m, the damping coefficients are c v1 =c v2 =2.0kN·s / m, the distances to the center of gravity of the vehicle body are d1=0.5m and d2=1.5m respectively, and the running speed of the test vehicle is v=5m / s.

[0067] Figure 2This is the bridge damping ratio identification process proposed by the method of the present invention. When identifying the bridge damping, the two-axle vehicle passes the bridge at a speed v. When the front wheel of the two-axle vehicle passes the first contact point (Point 1), the instantaneous amplitude (A) of the acceleration response of the front contact point can be calculated by the data collected by the sensor. c1 (t)). After time t2, the rear wheel of the dual-axle vehicle passes the same contact point (Point 1), and the instantaneous amplitude A of the acceleration response of the rear contact point is calculated using the collected data. c2 (t+t2), use formula (6) to calculate the bridge damping ratio of the contact point (Point 1). Repeat the above steps until the two-axle vehicle passes through the bridge, and calculate the damping ratio of the entire bridge.

[0068] In order to verify the accuracy of the calculation result of the acceleration response of the dual-axle vehicle-bridge contact point finally obtained in step (3) of the method of the present invention, a finite element numerical simulation was performed on this embodiment. Figure 5 The contact point acceleration response theoretical results (see formula (20), namely Figure 5 Analytical), finite element numerical simulation results of bridge response (i.e. Figure 5 FEM:bridge), and the finite element numerical simulation results of the contact point acceleration response calculated from the vehicle response (i.e. Figure 5 Medium FEM:vehicle+back-calculation). Figure 5 For details on the back-calculation derivation process, please refer to the literature: YBYang, H.Xu, ZLWang, K.Shi, Using vehicle–bridge contact spectra and residue to scanbridge's modal properties with vehicle frequencies and road roughnesseliminated, Struct.Control.Health Monit.29(8)(2022)e2968.

[0069] from Figure 5 It can be seen that the contact point acceleration responses calculated using different methods are almost consistent with the theoretical values, and the contact point acceleration response results calculated using the method of the present invention are reliable.

[0070] In order to verify the effect of the method of the present invention on identifying the damping ratio of a bridge, a numerical simulation was carried out. Figure 6 This is the bridge damping ratio identification result obtained based on the method of the present invention.

[0071] from Figure 6It can be seen that the proposed method can accurately identify the bridge damping ratio. The error value is used to determine the accuracy of the bridge damping ratio obtained based on the method of the present invention, and the calculation formula is: The error value of the bridge damping ratio obtained based on the method of the present invention is only 4.00%, which verifies the accuracy of the proposed method.

[0072] The above description is only a description of the preferred embodiments of the present application, and is not intended to limit the scope of the present application. Any changes or modifications made by any person skilled in the art based on the above disclosed technical contents shall be deemed as equivalent effective embodiments and shall fall within the scope of protection of the technical solution of the present application.

Claims

1. A bridge damping ratio identification method based on the spatial position relationship of the contact response of a dual-axle vehicle, characterized in that: The following steps are involved: Step 1: Arrange the dual-axis measuring vehicle; Step 2: Establish the corresponding motion differential equation; Step 3, deriving the displacement response of the biaxial vehicle-bridge contact point using the biaxial vehicle and bridge motion equations; Step 4, performing Hilbert transform on the acceleration response of the contact point to obtain the instantaneous amplitude of the acceleration response of the contact point; Step 5: Process the acceleration response data of the dual-axle vehicle-bridge contact point using Hilbert transform; Step 6: Identify the bridge damping ratio based on the spatial position relationship of the dual-axle vehicle-bridge contact response; Step 1: a dual-axis measuring vehicle equipped with an acceleration sensor is placed on the bridge, and the front and rear axles of the measuring vehicle are used to collect the acceleration response of the dual-axis vehicle-bridge contact point. Step 2: According to the characteristics of the dual-axis measurement vehicle, the vehicle body vibration response equation and the bridge vibration response equation are established, which are expressed as: Where: Where m v To measure the vehicle mass, the damping coefficients of the front and rear axles are c v1 、c v2 , the stiffness coefficients are k v1 , k v2 , the distances from the center of the vehicle are d1 and d2 respectively; y v ,θ v are the vertical displacement and rotation angle of the measuring vehicle, u and u c1 、u c2 They are the displacement of the bridge and the displacement of the contact points between the front and rear axles of the measuring vehicle and the bridge, where The midpoint ( . ) represents the partial derivative with respect to time, and the apostrophe (′) represents the partial derivative with respect to displacement; δ() and H() are the Dirac function and the unit step function respectively; the bridge under consideration is a homogeneous Bernoulli-Euler beam with an effective span of L, bending stiffness of EI, damping coefficient of c, and mass per unit length of m; Step 3: According to the modal superposition method, combined with the zero boundary condition, the displacement response of the dual-axle vehicle-bridge contact point is obtained by using formula (9), which is summarized as: Where: A d,n , B d,n is the amplitude coefficient, ω d,n is the driving frequency, and the expression of the parameters in formula (11) is: A bD,n =-A d,n , (17) Where: S n is the speed parameter; the second derivative of formula (11) with respect to time t gives the acceleration response of the dual-axle vehicle-bridge contact point: Where: Step 4: Perform Hilbert transformation on the acceleration response of the contact point to obtain the instantaneous amplitude of the acceleration response of the contact point. The acceleration response of the contact point is as shown in formula (20). To identify the damping ratio of the bridge, perform Hilbert transformation on the acceleration response of the contact point to obtain: Thus, the instantaneous amplitude of the acceleration response of the front and rear contact points is obtained: In the formula, ω b,n ,ω bD,n are the bridge frequencies without and with damping effects, t is the travel time of the biaxial vehicle, t1 and t2 are the time when the front and rear axles of the biaxial vehicle enter the bridge, Δ stn,1 , Δ stn,2 are the deformation of the bridge caused by the front and rear axles when the vehicle body is stationary on the bridge, L is the effective span of the bridge, v is the speed of the dual-axle vehicle, C b,n , D b,n is the amplitude coefficient, and its expressions are: By using the spatial position relationship between the instantaneous amplitudes of the acceleration response of the front and rear contact points in formulas (1) and (2), and dividing formula (2) by formula (1), we can obtain: By transforming formula (5), we can get the expression of bridge damping ratio:

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