Cable force identification method and device for stay cable provided with external damper

Abstract

The invention belongs to the technical field of bridge structure health monitoring and detection data analysis, and discloses a cable force identification method and device for a stay cable provided with an external damper. For the current situation that the cable force recognition precision of a stay cable provided with an external damper cannot meet the engineering requirement, the analytical relationship between the frequency and the cable force of a stay cable-damper system is deduced by utilizing the coordination condition of the supporting position of the damper; the defined stay cable-damper transmissibility function effectively eliminates the interference of the main beam vibration information contained in the stay cable response spectrum analysis, and solves the influence of the external damper on the effective length of the stay cable. According to the cable force identification method, accurate identification of the cable force can be achieved only by installing two acceleration sensors at the supporting position of the external damper and the upper-section inhaul cable, a powerful basis is provided for the service state of the cable-stayed bridge inhaul cable, and the cable force identification method has wider applicability in actual testing.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge structure health monitoring and detection data analysis, and relates to a method and device for identifying the cable force of a stay cable equipped with an external damper. Background Art

[0002] As a key component of a cable-stayed bridge, the cable provides essential support for the safety and stability of the structure. Accurately identifying the cable force of the cable is of great significance for its condition monitoring and performance evaluation. Vibration-based cable force identification has become one of the most widely used cable force identification methods in the field of structural health monitoring and testing due to its advantages such as low cost, fast speed and non-destructiveness.

[0003] In order to control the large vibration of the cable caused by wind and rain excitation, an external damper is usually installed near the end of the beam. For example, a Chinese patent document with publication number CN112227180A discloses a combined vibration reduction device and method for a cable. The damper provides support stiffness and damping energy consumption, which increases the vibration frequency of the cable and shortens the effective vibration length, resulting in a large error in the cable force identified by the traditional method of selecting the length between the two anchor ends of the cable. At present, in order to solve the problem of cable force identification by the damper, the difficulty lies in that, on the one hand, the damper provides a time-varying damping force, and the damping force-deformation curve often has nonlinearity; on the other hand, Tang Shenghua et al. (the calculation method of the equivalent cable length of the cable considering the intermediate support) proposed a calculation method of the equivalent length of the cable in the cable force identification correction formula considering the external vibration reduction device. This is an empirical method for taking the equivalent coefficient based on a large amount of actual test data, which is undoubtedly difficult to apply to complex and changeable situations in practice.

[0004] In order to solve the above problems, the present invention provides a method and device for identifying the cable force of a cable installed with an external damper. The method derives the analytical relationship between the frequency and cable force of the cable-damper system through the coordination conditions of the external damper support position, defines the transfer function between the vibration response of the upper section of the cable at the damper support position and the vibration response at the support position, and establishes a cable force optimization algorithm based on the various order frequencies of the transfer function as the objective function, solving the problem of inaccurate value of the effective length of the cable by the external damper. At the same time, the cable-damper transfer function of the present invention effectively eliminates the interference of the main beam vibration information contained in the cable response spectrum analysis, avoids the difficulty in identifying the time-varying damping force of the damper and the problem of force-deformation nonlinearity, and realizes the accurate identification of the cable force under the operation state of the bridge, which is of great significance to the monitoring, early warning and evaluation of the cable force of the cable-stayed bridge. Summary of the invention

[0005] In view of the problems existing in the background technology, the present invention proposes a method and device for identifying the cable force of a cable installed with an external damper. The present invention realizes the cable force identification of the cable by measuring the vibration response of the upper cable and the vibration response at the support position of the external damper.

[0006] The technical solution of the present invention:

[0007] A method for identifying the cable force of a stay cable equipped with an external damper comprises the following steps:

[0008] Step 1: Establish a theoretical model of the cable-damper transmissibility function

[0009] (1) The theoretical model of the cable-damper system is established. The cable is divided into two sections by the damper. The coordinate systems of the two sections are as follows: Figure 2 As shown, the lower cable is 0≤x≤x1, and the upper cable is The vibration differential equation of the two cables is:

[0010]

[0011] Where l is the cable length, x1 is the distance from the damper support position to the anchor end of the beam end, x2 is the distance from the damper support position to the acceleration sensor position on the cable, x3 is the distance from the acceleration sensor position on the cable to the anchor end of the tower end, T is the tension of the cable, is the mass per unit length, E is the elastic modulus, I is the section inertia moment, v1(x, t) is the lateral displacement of the lower cable vibration, and v2(x, t) is the lateral displacement of the upper cable vibration; the tower end and the beam end of the inclined cable are approximately consolidated, the boundary conditions are v1(0, t) = 0, v1′(0, t) = 0, v2(0, t) = 0, v2′(0, t) = 0, and the coordination condition of the external damper support position is The acceleration at the damper support position is

[0012] (2) The vibration differential equations, boundary conditions and coordination conditions of the cable in step (1) are converted into the frequency domain, and the system of equations is obtained by combining them and expressed in the vector form of the following symbols:

[0013] V=H·C

[0014] Where, V = {0 0 0 0 -a d / ω 2 0 0 0} T , C={C1 C2 C3 C4 C5 C6 C7 C8} T and

[0015]

[0016] Where ω is the natural circular frequency of the cable, λ 2 =T / 2EI, Therefore, the upper cable x * =The frequency domain representation of the response at x3:

[0017]

[0018] (3) Define the cable-damper transfer function, that is, the upper cable x * = Vibration response at x3 and damper support position The ratio of the Fourier transform of the vibration response at:

[0019]

[0020] Step 2: Measure the cable-damper transfer function

[0021] (4) Damper support position The acceleration sensor is installed at the position and the vibration response is measured as a d (t), the position of the upper cable x * = The acceleration sensor is installed at x3 and the vibration response of the cable is measured to be a c (t); the measured cable-damper transmissibility function is calculated as:

[0022]

[0023] Among them, S DC (ω) is a d (t) and a c (t), S DD (ω) is a d (t) autocorrelation function;

[0024] (5) Using the peak picking method to identify the kth to nth order frequencies of the cable from the measured cable-damper transmissibility function;

[0025] Step 3: Optimal identification of cable forces in the cable-damper system

[0026] (6) The initial values ​​of the cable force and the section inertia moment are set according to the cable parameters. The cable force optimization process based on the frequency as the objective function satisfies the minimum of the following objective function:

[0027]

[0028] In the formula, f k,t represents the kth theoretical frequency of the transmissibility function, f k,mrepresents the kth measured frequency of the transmissibility function, f n,t represents the nth theoretical frequency of the transmissibility function, f n,m is the nth measured frequency of the transferability function, where m is the number of frequency orders chosen.

[0029] A device for identifying a cable force of a stay cable equipped with an external damper, comprising:

[0030] Measuring point arrangement module: used to obtain the target cable vibration monitoring data, including acceleration sensor, fixed bracket, and data line;

[0031] Data collector: synchronously collects the response data of each measuring point on the target cable, collects, stores and remotely transmits the data to the receiving end for data backup and subsequent analysis and processing;

[0032] Data analysis module: Through the proposed cable force identification program of the cable-damper system, the data analysis module is used to read the acceleration time-history response of the two measuring points of the target cable, run the identification program to automatically calculate the transfer function between the responses of the two measuring points, identify each order frequency from the cable-damper transfer function as the optimization target, use it to calculate the target function, optimize the cable force identification result, and automatically store the result data;

[0033] Output display module: used for outputting the two measuring point data of the target inclined cable, the frequencies of each order of the transfer rate function and the cable force identification results.

[0034] The beneficial effects of the present invention are as follows: the present invention solves the problem of low cable force identification accuracy of an inclined cable equipped with an external damper, avoids the reliance on empirical values ​​for the effective length of the cable in the traditional cable force identification correction formula, and achieves high-precision cable force identification by installing two acceleration sensors on the cable and the damper support position close to the beam surface of the inclined cable, effectively eliminating the interference of the main beam vibration information contained in the cable response spectrum analysis, and achieving accurate cable force identification under the operation state of the bridge, providing a strong basis for the service status of the cable of the cable-stayed bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the arrangement of sensors on the inclined cable of the present invention.

[0036] Figure 2 It is the theoretical model of the cable-damper system of the present invention.

[0037] Figure 3 This is the implementation process of the present invention.

[0038] Figure 4 This is a model of a three-tower cable-stayed bridge in an embodiment of the present invention.

[0039] Figure 5The acceleration response and spectrum diagram of the cable WN25 in the embodiment of the present invention are as follows: (a) cable acceleration response; (b) cable response spectrum; (c) damper support position acceleration response; (d) inclined cable-damper transfer rate function. DETAILED DESCRIPTION

[0040] The present invention is further described in detail below in conjunction with the accompanying drawings and a case analysis.

[0041] The implementation process of the system of the present invention is divided into three steps: "establishing a theoretical model of the cable-damper transmissibility function", "measuring the cable-damper transmissibility function" and "optimal identification of the cable force of the cable-damper system". The specific implementation method has been given above. Next, the feasibility of the method of the present invention is verified and the implementation is explained in combination with the on-site cable force test data of an actual three-tower cable-stayed bridge as a case.

[0042] like Figure 4 As shown in the figure, the span of the three-tower cable-stayed bridge is 42m+42m+300m+300m+42m+42m. Cable stays WNJ2, WNJ11, and WN25 are selected for analysis. Figure 1 As shown, acceleration sensors are arranged at the damper support position and on the cable. The acceleration vibration response of the two measuring points is synchronously collected at a sampling frequency of 100 Hz. Taking the WN25 cable as an example, the method of the present invention includes the following steps:

[0043] Step 1: Establish a theoretical model of the cable-damper transmissibility function

[0044] (1) The theoretical model of the cable-damper system is established. The cable is divided into two sections by the damper. The coordinate systems of the two sections are as follows: Figure 2 As shown, the lower cable is 0≤x≤x1, and the upper cable is According to the vibration differential equation of the two cables, the consolidation boundary conditions at the tower end and the beam end of the inclined cable and the coordination conditions of the support position of the external damper, the upper cable x * =The representation of the response at x3:

[0045]

[0046] (2) Define the cable-damper transfer function, that is, the upper cable x * = Vibration response at x3 and damper support position The ratio of the Fourier transform of the vibration response at:

[0047]

[0048] Step 2: Measure the cable-damper transfer function

[0049] (3) At the damper support position Position x of the upper cable * = x3, and install a fixed bracket and an acceleration sensor. Connect the data collector via a data cable, and measure the vibration responses of the two measuring points as a respectively. d (t), a c (t). The measured cable-damper transmissibility function is calculated as:

[0050]

[0051] Where S DC (ω) is a d (t) and a c (t), S DD (ω) is a d (t) is the autocorrelation function of

[0052] (4) Measured cable-damper transmissibility function, such as Figure 5 As shown in (d), the peak picking method is used to identify the 2nd to 9th order frequencies of the cable: 1.14, 1.82, 2.43, 3.05, 3.67, 4.27, 4.88, 5.48 (unit: Hz).

[0053] Step 3: Optimal identification of cable forces in the cable-damper system

[0054] (5) The initial values ​​of the cable force and section inertia moment are set according to the cable parameters. The cable force optimization process based on the frequency as the objective function satisfies the minimum of the following objective function:

[0055]

[0056] In the formula, f 2,t represents the second-order theoretical frequency of the transmissibility function, 1.14 represents the second-order measured frequency of the transmissibility function, f 9,t represents the 9th order theoretical frequency of the transmissibility function, 5.48 represents the 9th order measured frequency of the transmissibility function, and 8 represents the number of frequency orders selected.

[0057] During the field test, the cable force value of the cable tested by the jack tensioning method was taken as the true value for comparison. The proposed method was compared with the string vibration theory and the PFF formula (Piecewise-fitted formula for cable force identification considering bending stiffness, sag, and inclination) proposed by Luo Lanying et al. The results are shown in Table 1, which all indicate the reliability of the identification accuracy of the proposed method.

[0058] Table 1 Comparison of cable force identification results

[0059]

[0060] Note: IF is the identified cable force; RE is the relative error between the identified value and the theoretical value.

Claims

1. A method for identifying the cable force of a stay cable equipped with an external damper, characterized in that: The following steps are involved: Step 1: Establish a theoretical model of the cable-damper transmissibility function (1) The theoretical model of the cable-damper transfer rate function is established. The cable is divided into two sections by the damper. The lower section of the cable is 0≤x≤x1, and the upper section of the cable is The vibration differential equation of the two cables is: Where l is the cable length, x1 is the distance from the damper support position to the anchor end of the beam end, x2 is the distance from the damper support position to the acceleration sensor position on the cable, x3 is the distance from the acceleration sensor position on the cable to the anchor end of the tower end, T is the tension of the cable, is the mass per unit length, E is the elastic modulus, I is the section inertia moment, v1(x, t) is the lateral displacement of the lower cable vibration, and v2(x, t) is the lateral displacement of the upper cable vibration; the tower end and the beam end of the inclined cable are approximately consolidated, the boundary conditions are v1(0, t) = 0, v′1(0, t) = 0, v2(0, t) = 0, v2′(0, t) = 0, and the coordination condition of the external damper support position is The acceleration at the damper support position is (2) The vibration differential equations, boundary conditions and coordination conditions of the cable in step (1) are converted into the frequency domain, and the system of equations is obtained by combining them and expressed in the vector form of the following symbols: V=H·C Where, V = {0 0 0 0 -a d / ω 2 0 0 0} T , C={C1 C2 C3 C4 C5 C6 C7 C8} T and Where ω is the natural circular frequency of the cable, λ 2 =T / 2EI, Therefore, the upper cable x * =The frequency domain representation of the response at x3: (3) Define the cable-damper transfer function, that is, the upper cable x * = Vibration response at x3 and damper support position The ratio of the Fourier transform of the vibration response at: Step 2: Measure the cable-damper transfer function (4) Damper support position The acceleration sensor is installed at the position and the vibration response is measured as a d (t), the position of the upper cable x * = The acceleration sensor is installed at x3 and the vibration response of the cable is measured to be a c (t); the measured cable-damper transmissibility function is calculated as: Among them, S DC (ω) is a d (t) and a c (t), S DD (ω) is a d (t) autocorrelation function; (5) Using the peak picking method to identify the kth to nth order frequencies of the cable from the measured cable-damper transmissibility function; Step 3: Optimal identification of cable forces in the cable-damper system (6) The initial values ​​of the cable force and the section inertia moment are set according to the cable parameters. The cable force optimization process based on the frequency as the objective function satisfies the minimum of the following objective function: In the formula, f k,t represents the kth theoretical frequency of the transmissibility function, f k,m represents the kth measured frequency of the transmissibility function, f n,t represents the nth theoretical frequency of the transmissibility function, f n,m is the nth measured frequency of the transferability function, where m is the number of frequency orders chosen.

2. A device for identifying the force of a stay cable equipped with an external damper, characterized in that: include: Measuring point arrangement module: used to obtain the target cable vibration monitoring data, including acceleration sensor, fixed bracket, and data line; Data collector: synchronously collects the response data of each measuring point on the target cable, collects, stores and remotely transmits the data to the receiving end for data backup and subsequent analysis and processing; Data analysis module: Through the proposed cable force identification program of the cable-damper system, the data analysis module is used to read the acceleration time-history response of the two measuring points of the target cable, run the identification program to automatically calculate the transfer function between the responses of the two measuring points, identify each order frequency from the cable-damper transfer function as the optimization target, use it to calculate the objective function, optimize the cable force identification result, and automatically store the result data; Output display module: used for outputting the two measuring point data of the target inclined cable, the frequencies of each order of the transfer rate function and the cable force identification results.

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