Stay cable tension monitoring system and device under boundary disturbance

Abstract

The invention belongs to the technical field of bridge structure health monitoring data analysis, and discloses a stay cable tension monitoring system and device under boundary disturbance. The method aims at the cable-stayed bridge cable force on-line monitoring problem of an existing monitoring system, and cable force accurate identification during stay cable boundary disturbance in an operation state is achieved through tower end-cable-beam end vibration response data of the stay cable. The provided transmissibility function can effectively eliminate interference of tower-beam vibration information on frequency identification in a stay cable frequency spectrum, and real inherent characteristics under stay cable boundary disturbance are obtained; in the cable force optimization process, the bending rigidity serves as a parameter to be optimized, the problem that the cable force estimation precision is low due to the fact that the equivalent bending rigidity is inaccurate in a traditional cable force recognition formula is greatly solved, accurate recognition and real-time monitoring of the cable force by an existing monitoring system are achieved, and the method has wider applicability in practice.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge structure health monitoring data analysis, and relates to a stay cable tension monitoring system and device under boundary disturbance. Background Art

[0002] The cable is the key and vulnerable component of the cable-stayed bridge, providing essential support for the safe operation of the bridge. Due to the influence of multiple factors such as the external environment and external loads, the cable is easily damaged by factors such as vibration and corrosion. Over time, the tension changes or damage occurs, which in turn affects the safety of the bridge structure. Therefore, accurate identification of cable tension is of great significance for the health monitoring of bridge structures. The existing cable force identification methods mainly include pressure sensor method, jack method, strain measurement method, vibration frequency method, magnetic flux method, etc. Cable force identification based on vibration method has become one of the most widely used cable force identification methods in the field of structural health monitoring due to its simplicity, low cost, and non-destructiveness.

[0003] The vibration frequency method is to identify the natural frequency of the cable by obtaining the vibration response of the cable under environmental excitation or artificial excitation, and then estimate the cable force based on the physical relationship between the cable tension and frequency. The difficulty lies in the fact that the accurate identification of the true natural frequency of the cable and the determination of the nonlinear relationship between the cable force and the frequency under actual conditions are affected by the coupling of multiple factors such as bending stiffness, sag, inclination and complex and changeable boundary conditions (Minimal requirements for the vibration-based identification of the axial force, the bending stiffness and the flexural boundary conditions in cables). Since the two ends of the inclined cable are anchored on elastic structures such as the main tower and the main beam, the boundary conditions of the inclined cable are complex. In particular, when the bridge is in operation, the tower-beam end is disturbed under the action of vehicle load, causing the tower-cable-beam coupled vibration, making it difficult to determine the corresponding relationship between the cable force and the frequency. Scholars have successively proposed substructure cable force identification methods based on multi-point testing, which can effectively avoid the problem of difficult to determine complex boundaries (Tension force identification for cable of various end-restraints using equivalent effective vibration lengths of mode pairs; A two-step methodology for cable force identification). However, adding measuring points not only increases the sensor cost of field testing, but also cannot be applied to the existing bridge health monitoring system, because the monitoring of the cable-stayed cable is usually arranged with only one measuring point.

[0004] In order to solve the above problems, the present invention proposes a cable tension monitoring system under boundary disturbance. The system realizes the identification of time-varying cable force considering the boundary disturbance of the tower-beam end of the cable-stayed bridge by monitoring the vibration of the tower-cable-beam of the cable-stayed bridge. In the solution process, both the cable force and the bending stiffness are simultaneously identified as parameters to be optimized, which greatly avoids the problem of low accuracy of the identified cable force caused by inaccurate equivalent bending stiffness in the traditional cable force identification formula. At the same time, in the process of identifying the true natural frequency of the cable, the present invention compares the Fourier transform of the cable response and the tower-beam end response, effectively eliminating the interference of the tower-beam vibration information contained in the traditional cable response spectrum analysis, and realizes the accurate identification of the cable force changes caused by random loads under the operation state of the bridge, which is of great significance to the real-time monitoring, prediction alarm and status 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 system and device for monitoring the tension of a cable under boundary disturbance. The purpose of the present invention is to realize the tension monitoring of the cable under boundary disturbance by monitoring the vibration of the tower-cable-beam of the cable-stayed bridge. The monitoring system still only needs one measuring point on the cable, and at the same time uses the monitoring information on the upper main tower and the main beam, and uses the boundary disturbance information of the anchoring position at both ends of the cable as the excitation source of the cable vibration, which effectively analyzes the vibration mechanism of the cable under the operation state of the bridge. At the same time, the present invention uses the transfer function and the partial coherence function as an effective basis for analyzing the corresponding relationship between the cable force and the frequency under the boundary disturbance of the cable, and solves the problem of the time-varying bending stiffness and the boundary disturbance of the cable anchoring end in the cable force identification.

[0006] The technical solution of the present invention:

[0007] A stay cable tension monitoring system under boundary disturbance comprises the following steps:

[0008] Step 1: Transmissibility function between tower-cable-beam responses

[0009] (1) Establish a theoretical model of the cable under tower-beam boundary disturbance, such as Figure 2 As shown in (a), the vibration differential equation of the inclined cable is:

[0010]

[0011] Where T is the tension of the cable, is the mass per unit length, E is the elastic modulus, I is the section inertia moment, τ(x, t) is the dynamic increment of the cable force, y(x, t) is the geometric linearity of the cable under the action of its own weight, w(x, t) is the lateral displacement of the cable plane vibration, and the acceleration time history responses at the tower end and beam end anchorage are w t (t), w b (t), cable x = l c The acceleration time history response at is w c (t). The boundary conditions of the cable are:

[0012] w(0,t)=w t (t)

[0013] w′(0,t)=0

[0014] w(l,t)=w b (t)

[0015] w′(l,t)=0

[0016] Where l is the cable length, w(0,t) is the boundary condition of the cable at the tower end anchorage, i.e. x = 0, and w(l,t) is the boundary vibration response of the cable at the beam end anchorage, i.e. x = l.

[0017] (2) Combining the vibration differential equation of the inclined cable in step (1) and the boundary conditions, we can obtain x=l at any point of the cable caused by the tower end excitation. c The frequency domain representation of the response at is:

[0018]

[0019] In the formula, the vector e={exp(k 1 x)exp[k 2 (xl)]exp(k 3 x)exp(k 4 x)}, C={C 1 C 2 C 3 C 4} T , boundary conditions w t The Fourier transform of (t), λ 2 =T / 2EI,

[0020] Feature Matrix

[0021] Where A is the cross-sectional area, θ is the inclination angle of the cable, and L e is the effective length, ω is the natural circular frequency, and g is the gravitational acceleration.

[0022] Similarly, according to the beam end boundary condition Any point of the cable caused by excitation x = l c The frequency domain representation of the response at is:

[0023]

[0024] In the formula w b (t) is the Fourier transform of

[0025] (3) Calculate the theoretical cable-tower transfer function, i.e. x = l for the cable c The ratio of the response to the response at the anchor point of the cable tower, that is, x = 0:

[0026]

[0027] Similarly, the theoretical cable-beam transmissibility function is calculated, and the cable is x = l c The ratio of the response to the cable beam end anchorage, that is, x = l:

[0028]

[0029] Step 2: Partial coherence analysis between tower-cable-beam responses

[0030] (4) The tower-cable-beam responses of the cable-stayed cable are measured as w t (t), w c (t), w b (t), for a linear tower-cable-beam system, such as Figure 2 As shown in (b), the cable-tower partial coherence function and the cable-beam partial coherence function are calculated:

[0031]

[0032] In the formula, S tc (f) S bc (f) S tb (f) The cross-spectra between the cable-tower, cable-beam and tower-beam responses; S tt (f) S cc (f) and S bb (f) The auto-spectra of the tower, cable and beam responses, respectively; and are the coherence functions between the cable-tower, cable-beam and tower-beam responses, respectively;

[0033] (5) Calculate the measured transmissibility function using the measured tower-cable-beam response:

[0034]

[0035]

[0036] Step 3: Time-varying frequency identification based on partial coherence coefficient

[0037] (6) Compare the cable-tower partial coherence coefficient and the cable-beam partial coherence coefficient corresponding to each order frequency of the cable, and select the two-order frequencies with high correlation as the target frequencies for cable force optimization;

[0038] (7) The tower-cable-beam response is processed using a Hanning window that slides over time. The discrete-time Fourier transform is performed on the time segment signals to refine the spectral density and thus improve the frequency resolution. The time-varying frequency of the corresponding order of the cable is identified by calculating the transmissibility function under each time window.

[0039] Step 4: Cable force optimization process based on frequency as objective function

[0040] (8) The variation of the bending stiffness of the cable is subject to two theoretical limits. The minimum possible bending stiffness occurs in the initial state or at the curvature where the friction resistance between the steel wires has been exhausted. The section moment of inertia of the cable is the sum of the section moments of inertia of each steel wire. The maximum possible bending stiffness occurs under low curvature or high tension. The cross section composed of steel wires is approximately a solid cross section:

[0041]

[0042] Among them, d i is the diameter of the i-th strand of the cable, y i is the distance from the center of gravity of the i-th wire to the center of gravity of the cable, d c is the diameter of the circumscribed circle of the wire cross section, N S is the total number of wire strands;

[0043] (9) Set the initial values ​​of cable force and section inertia moment according to the cable parameters so that the section inertia moment satisfies the theoretical limit range [I min ,I max ] satisfies the following objective function minimum:

[0044]

[0045] In the formula, f j,TF,t represents the j-th theoretical frequency of a certain transfer rate function; f j,TF,m represents the jth measured frequency of a transferability function; n is the number of frequency orders selected.

[0046] The implementation process of the method for the cable tension monitoring system considering the tower-beam end boundary disturbance is as follows: Figure 3 shown.

[0047] A device for monitoring a stay cable tension under boundary disturbance, comprising:

[0048] Measuring point arrangement module: used to obtain vibration monitoring data of the target structure, including acceleration sensor, fixed bracket, and data cable;

[0049] Data collector: synchronously collects the response data of each measuring point on the target structure, collects, stores, and remotely transmits the data to the receiving end for subsequent data backup and analysis and processing;

[0050] Data analysis module: Through the proposed cable force optimization program under boundary disturbance, the data analysis module is used to read the acceleration time-history response of each measuring point of the target structure, run the optimization program to automatically calculate the partial coherence function and transmissibility function between the responses of each measuring point, select the frequency with higher coherence as the identification target, use it to calculate the objective function, optimize the time-varying cable force and bending stiffness, and automatically store the result data;

[0051] Output display module: used for the output of data of each measuring point of the target structure, coherence and time-varying frequency of each order frequency, and optimized time-varying cable force and bending stiffness.

[0052] Beneficial effects of the present invention:

[0053] 1. In view of the current situation that the boundaries of the cable-stayed cables in the operation state of the cable-stayed bridge are not ideally fixed but follow the disturbance of the tower-beam end, the present invention establishes the transfer rate function and partial coherence function between the tower end-cable-beam end responses of the cable-stayed bridge, which are used to identify the natural frequency of the cable-stayed cables under boundary disturbances, and realizes the online optimization of the tension and bending stiffness of the cable-stayed cables. The method of the present invention does not require additional arrangement of measuring points on the cables, and effectively utilizes the response information of the measuring points on the tower-beam structure, which can better realize the accurate identification and real-time monitoring of the cable force by the existing monitoring system.

[0054] 2. In order to avoid the problem of inaccurate cable force estimation results caused by inaccurate equivalent calculation of section inertia moment in traditional cable force identification formula, the present invention takes the theoretical limit of section inertia moment as one of the bases for the minimum convergence of the objective function in the cable force and bending stiffness optimization algorithm, thereby ensuring the rationality of the bending stiffness value and satisfactory accuracy of time-varying cable force identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Schematic diagram of the system and device of the present invention.

[0056] Figure 2 A cable-stayed model considering boundary disturbances established for the present invention includes: (a) a cable coordinate system; and (b) a linear tower-cable-beam system.

[0057] Figure 3 This is the implementation process of the present invention.

[0058] Figure 4 It is a diagram of a cable-stayed bridge model and a sensor arrangement diagram of a monitoring system in an embodiment of the present invention.

[0059] Figure 5 1 is the acceleration response and frequency spectrum of the cable WD25 in the embodiment of the present invention, wherein (ab) are the tower end; (cd) are on the cable; and (ef) are the beam end.

[0060] Figure 6 : is the time-varying cable force identification result of cable WD25 in the embodiment of the present invention. DETAILED DESCRIPTION

[0061] The present invention is further described in detail below in conjunction with the accompanying drawings and a case analysis.

[0062] The implementation process of the system of the present invention is divided into four steps: "transfer rate function between tower-cable-beam responses", "partial coherence analysis between tower-cable-beam responses", "time-varying frequency identification based on partial coherence coefficient" and "cable force optimization process based on frequency as objective function". The specific implementation method has been given above. Next, the feasibility of the method of the present invention is verified and its implementation is explained in combination with the monitoring data of an actual single-tower cable-stayed bridge as a case.

[0063] like Figure 4 As shown, the main span of the single-tower cable-stayed bridge is 258m, and the spacing between adjacent cables on the main beam is 8m. Cable-stayed cable WD25 is selected for analysis, and the parameters of the cable are shown in Table 1. Among them, accelerometers are arranged at the tower end, the cable, and the beam end of the cable WD25, and a displacement meter is arranged on the main beam. The collected data include: the vibration acceleration of the cable monitored at a sampling frequency of 50Hz, the vibration acceleration of the main beam monitored at a sampling frequency of 100Hz, the vibration acceleration of the main beam monitored at a sampling frequency of 100Hz, and the deflection (vertical displacement) of the main beam monitored by the displacement meter at a sampling frequency of 1Hz. The method of the present invention comprises the following steps:

[0064] Step 1: Transmissibility function between tower-cable-beam responses

[0065] (1) A theoretical model of the cable under tower-beam boundary disturbance is established. The relationship between the acceleration time-history response at the anchorages at the tower end and the beam end and the acceleration time-history response on the cable is established to obtain the theoretical CTTF and CBTF.

[0066] Step 2: Partial coherence analysis between tower-cable-beam responses

[0067] (2) According to the sensors arranged in the existing cable-stayed bridge health monitoring system, the tower end-cable-beam end response data of the cable-stayed cable WD25 in a certain period of time are collected as w t (t), w c (t), w b (t), such as Figure 5 The measured cable-tower partial coherence function, cable-beam partial coherence function, cable-tower transmissibility function, and cable-beam transmissibility function are calculated.

[0068] Step 3: Time-varying frequency identification based on partial coherence coefficient

[0069] (3) Compare the cable-tower partial coherence coefficient and cable-beam partial coherence coefficient corresponding to each order frequency of the cable. As shown in Table 2, the 8th and 9th order frequencies with higher coherence are selected as the target frequencies for cable force optimization. The corresponding frequencies are taken from the cable-beam transmissibility function.

[0070] (4) A Hanning window sliding over time is used to process the cable-beam response. The discrete-time Fourier transform is performed on the time segment signals to refine the spectral density and thus improve the frequency resolution. The 8th and 9th order time-varying frequencies of the cable are identified by calculating the cable-beam transfer function in each time window.

[0071] Step 4: Cable force optimization process based on frequency as objective function

[0072] (5) The theoretical range of the bending stiffness of the cable is shown in Table 1. The initial values ​​of the cable force T and the section inertia moment I are set according to the cable parameters shown in Table 1. The cable force and bending stiffness are optimized with the objective of minimizing the objective function. The identification results are shown in Figure 6 shown.

[0073] The change of cable force is negatively correlated with the change of beam end deflection of the inclined cable WD25, and the correlation coefficient is c WD25 =-0.80. The identification results of the cable section inertia moment are all within the theoretical range of bending stiffness shown in Table 1 [I min ,I max ] All of the above indicate the reliability of the recognition accuracy of the method of the present invention.

[0074] Table 1 Parameters of cable WD25

[0075]

[0076] Table 2 Partial coherence coefficient of cable WD25

[0077]

[0078]

Claims

1. A stay cable tension monitoring system under boundary disturbance, characterized in that: The following steps are involved: Step 1: Transmissibility function between tower-cable-beam responses (1) The theoretical model of the cable under tower-beam boundary disturbance is established. The vibration differential equation of the cable is: Where T is the tension of the cable, is the mass per unit length, E is the elastic modulus, I is the section inertia moment, τ(x, t) is the dynamic increment of the cable force, y(x, t) is the geometric linearity of the cable under the action of its own weight, w(x, t) is the lateral displacement of the cable in-plane vibration, and the acceleration time history responses at the tower end and beam end anchorage are w t (t), w b (t), cable x = l c The acceleration time history response at is w c (t); The boundary conditions of the cable are: w(0,t)=w t (t) w′(0,t)=0 w(l,t)=w b (t) w′(l,t)=0 Where l is the cable length, w(0,t) is the boundary condition of the cable at the tower end anchorage, i.e. x = 0, and w(l,t) is the boundary vibration response of the cable at the beam end anchorage, i.e. x = l. (2) Combining the vibration differential equation of the inclined cable in step (1) and the boundary conditions, we can obtain x=l at any point of the cable caused by the tower end excitation. c The frequency domain representation of the response at is: Where, vector e = {exp(k1x)exp[k2(xl)]exp(k3x)exp(k4x)}, C = {C1 C2 C3 C4} T , boundary conditions w t The Fourier transform of (t), λ 2 =T / 2EI, Feature Matrix Where A is the cross-sectional area, θ is the inclination angle of the cable, and L is e is the effective length, ω is the natural circular frequency, and g is the gravitational acceleration; Similarly, according to the beam end boundary condition Any point of the cable caused by excitation x = l c The frequency domain representation of the response at is: In the formula, w b Fourier transform of (t); (3) Calculate the theoretical cable-tower transfer function, i.e. x = l for the cable c The ratio of the response to the response at the anchor point of the cable tower, that is, x = 0: Similarly, the theoretical cable-beam transmissibility function is calculated, and the cable is x = l c The ratio of the response to the cable beam end anchorage, that is, x = l: Step 2: Partial coherence analysis between tower-cable-beam responses (4) The tower-cable-beam responses of the cable-stayed cable are measured as w t (t), w c (t), w b (t), for a linear tower-cable-beam system, calculate the cable-tower partial coherence function and the cable-beam partial coherence function: In the formula, S tc (f) S bc (f) S tb (f) The cross-spectra between the cable-tower, cable-beam and tower-beam responses; S tt (f) S cc (f) and S bb (f) The auto-spectra of the tower, cable and beam responses, respectively; and are the coherence functions between the cable-tower, cable-beam and tower-beam responses, respectively; (5) Calculate the measured transmissibility function using the measured tower-cable-beam response: Step 3: Time-varying frequency identification based on partial coherence coefficient (6) Compare the cable-tower partial coherence coefficient and the cable-beam partial coherence coefficient corresponding to each order frequency of the cable, and select the two-order frequencies with high correlation as the target frequencies for cable force optimization; (7) The tower-cable-beam response is processed using a Hanning window that slides over time. The discrete-time Fourier transform is performed on the time segment signals to refine the spectral density and thus improve the frequency resolution. The time-varying frequency of the corresponding order of the cable is identified by calculating the transmissibility function under each time window. Step 4: Cable force optimization process based on frequency as objective function (8) The variation of the bending stiffness of the cable is subject to two theoretical limits. The minimum possible bending stiffness occurs in the initial state or at the curvature where the friction resistance between the steel wires has been exhausted. The section moment of inertia of the cable is the sum of the section moments of inertia of each steel wire. The maximum possible bending stiffness occurs under low curvature or high tension. The cross section composed of steel wires is approximately a solid cross section: Among them, d i is the diameter of the i-th strand of the cable, y i is the distance from the center of gravity of the i-th wire to the center of gravity of the cable, d c is the diameter of the circumscribed circle of the wire cross section, N S is the total number of wire strands; (9) Set the initial values ​​of cable force and section inertia moment according to the cable parameters so that the section inertia moment satisfies the theoretical limit range [I min ,I max ] satisfies the following objective function minimum: In the formula, f j,TF,t represents the j-th theoretical frequency of a certain transfer rate function; f j,TF,m represents the jth measured frequency of a transferability function; n is the number of frequency orders selected.

2. A device for monitoring the tension of a stay cable under boundary disturbance, characterized in that: include: Measuring point arrangement module: used to obtain vibration monitoring data of the target structure, including acceleration sensor, fixed bracket, and data cable; Data collector: synchronously collects the response data of each measuring point on the target structure, collects, stores, and remotely transmits the data to the receiving end for subsequent data backup and analysis and processing; Data analysis module: Through the proposed cable force optimization program under boundary disturbance, the data analysis module is used to read the acceleration time-history response of each measuring point of the target structure, run the optimization program to automatically calculate the partial coherence function and transmissibility function between the responses of each measuring point, select the frequency with higher coherence as the identification target, use it to calculate the objective function, optimize the time-varying cable force and bending stiffness, and automatically store the result data; Output display module: used for the data of each measuring point of the target structure, the coherence and time-varying frequency of each order frequency, and the optimized time-varying cable force and bending stiffness output.

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