A cable-strut structure axial force identification method fusing translational and rotational vibration responses

Abstract

The application provides a cable-strut structure axial force identification method fusing translation and rotation vibration responses in the technical field of structural health monitoring and mechanical parameter identification, and comprises the following steps: arranging composite measuring points on a cable-strut structure, synchronously collecting translation and rotation vibration response time histories, and recording relative positions; extracting multi-order modal frequencies, displacements and angular vibration mode coefficients by using a modal identification algorithm; reconstructing a spatial continuous displacement vibration mode function according to a mapping relationship of the angular vibration mode being the slope of the displacement vibration mode along the cable-strut axial direction; finally, substituting the spatial continuous displacement vibration mode function into a tension beam vibration theory model, solving a characteristic equation inverse problem, and thus inversely obtaining the actual axial force of the cable-strut structure. The application has the following advantages: the cable-strut axial force can be identified with high precision under complex boundary conditions only by using a small number of measuring points, the dependence on a multi-point sensor array is reduced, the on-site installation difficulty and system measurement error are reduced; meanwhile, recording the inclination angle of the translation response sensor can avoid the vibration mode error introduced by the inconsistent measuring axes of multiple sensors.

Description

Technical Field

[0001] This invention relates to the field of structural health monitoring and mechanical parameter identification technology, and in particular to a method for identifying axial force in cable-stayed structures that integrates translational and rotational vibration responses. Background Technology

[0002] Cable-stayed structures (such as bridge cables, hangers, tie rods, and axially loaded components in building construction) are widely used in long-span bridges and spatial structures due to their excellent axial load-bearing capacity. Accurately identifying the actual axial force of a cable-stayed structure is a core indicator for assessing its safety and durability, and is of significant engineering importance for construction monitoring, operation and maintenance, and component replacement.

[0003] In current engineering operation and maintenance testing and health monitoring, indirect measurement methods, represented by vibration methods, are the most widely used. Vibration methods acquire the lateral vibration response of the cable and, combined with a mathematical model describing the mapping relationship between cable force and vibration characteristics, invert the axial force, offering advantages such as economy, convenience, and non-destructive testing. Existing vibration-based cable force measurement techniques can be further subdivided into the following two categories: The first type is the frequency method. This method only utilizes the first few natural frequencies of the cable and has no strict requirements on the measurement direction and amplitude of the vibration response. Its corresponding mechanical model is relatively idealized, typically assuming that the linear density and calculated length of the cable are known, and that the boundary conditions are ideal (e.g., hinged at both ends). This method is well-suited for long cables or scenarios with simple boundary conditions. However, for cable-stayed structures with short cables and complex boundary conditions (e.g., dampers installed at the ends), the uncertainty in the equivalent length and stiffness of the boundary conditions significantly affects the accuracy of the frequency method, often resulting in axial force identification errors exceeding 20%, which is difficult to meet engineering requirements.

[0004] The second category is improved methods combined with modal measurement. To overcome the limitations of the frequency method under complex boundary conditions, existing research has proposed identification strategies based on modal fitting. This method requires deploying multiple sensors on the target cable segment to obtain the vibration response at discrete points. Modal analysis is used to extract the modal values ​​at the measurement points, and theoretical modal functions are used for fitting, thereby deducing key parameters such as the effective vibration length. Finally, the axial force is calculated by combining the frequency. Although this method significantly improves the identification accuracy under complex boundary conditions, it has obvious limitations in practical applications: it heavily relies on a multi-point sensor array to capture the spatial distribution characteristics of the modal shapes. To achieve sufficiently accurate modal fitting, 3-4 or even more measurement points are often required. This typically means installing a large number of sensors in bridge towers or cable surfaces that are high off the ground and difficult to operate. This is not only inefficient and costly, but also makes it difficult to maintain consistent installation angles between the measurement axes of multiple sensors, introducing systematic modal measurement errors and severely restricting the widespread application of this technology in practical engineering.

[0005] Therefore, how to provide a method for identifying the axial force of cable-stayed structures that integrates translational and rotational vibration responses, so as to achieve high-precision identification of cable-stayed axial force with only a few measurement points under complex boundary conditions, reduce dependence on multi-point sensor arrays, reduce on-site installation difficulty and system measurement errors, and avoid mode shape errors introduced by inconsistent measurement axes of multiple sensors, has become an urgent technical problem to be solved. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a method for identifying the axial force of cable-stayed structures that integrates translational and rotational vibration responses. This method enables high-precision identification of cable-stayed axial force with only a few measurement points under complex boundary conditions, reducing reliance on multi-point sensor arrays, lowering on-site installation difficulty and system measurement errors, and avoiding mode shape errors introduced by inconsistent measurement axes of multiple sensors.

[0007] This invention is implemented as follows: a method for identifying axial force in cable-stayed structures that integrates translational and rotational vibration responses, comprising the following steps: Step 1: Select at least two locations along the axis of the cable-stayed structure to be tested and set up composite measuring points. Simultaneously collect the translational vibration response time history signal and rotational vibration response time history signal of each composite measuring point, and record the relative position of each composite measuring point. Step 2: The translational vibration response time history signal and the rotational vibration response time history signal are processed by the modal recognition algorithm to extract at least two modal frequencies of the cable-stayed structure under test, as well as the displacement mode shape coefficient and rotation mode shape coefficient of each mode at each of the composite measurement points; Step 3: Based on the mathematical mapping relationship between the displacement mode function represented by the displacement mode coefficient and the rotation mode represented by the rotation mode coefficient, that is, the rotation mode is the first derivative of the displacement mode function along the axial coordinate of the cable rod, the displacement mode coefficient and rotation mode coefficient obtained at each of the composite measuring points are used to mathematically reconstruct the spatial continuous displacement mode function of the cable rod structure under test or its local segments by combining the theoretical mode expression of the cable rod structure. Step 4: Substitute the modal frequencies and spatial continuous displacement mode shape functions into the tension beam vibration theory model, and calculate the actual axial force of the cable-stayed structure under test by solving the inverse problem of the vibration characteristic equation.

[0008] Furthermore, in step 1, the cable-stayed structure to be tested includes parallel wire cables, stranded cables, hangers, and tie rods in bridge engineering, as well as axially loaded components in building engineering.

[0009] Furthermore, in step 1, the translational vibration response time history signal includes displacement response, velocity response, or acceleration response; the rotational vibration response time history signal includes angular displacement response, angular velocity response, or angular acceleration response.

[0010] Furthermore, in step 1, when measuring the translational vibration response time history signal and the rotational vibration response time history signal, the measurement directions of the translational vibration response time history signal and the rotational vibration response time history signal at the same composite measuring point are consistent, which is used to measure the in-plane or out-of-plane vibration of the cable rod. Furthermore, the translational vibration response time history signal and the rotational vibration response time history signal are measured at the same location, or the distance between the two along the cable axis does not exceed 1m; The translational vibration response time history signal and the rotational vibration response time history signal are measured synchronously using an integrated vibration and rotation angle sensor.

[0011] Furthermore, in step 1, the sensors used to measure the translational vibration response time history signal and the rotational vibration response time history signal include contact sensors or non-contact sensors. The contact sensor includes a separate accelerometer and tilt sensor, or an integrated vibration and rotation sensor.

[0012] Furthermore, in step 1, the composite measuring points are positioned to avoid the ends of the cable rod and the middle support points of the cable rod, specifically at a distance of at least 10% of the free length of the cable rod from the support points.

[0013] Furthermore, step 1 also includes: While acquiring the translational vibration response time history signal and the rotational vibration response time history signal, the installation angle of the vibration sensor's measuring axis relative to the same reference direction at the composite measuring point and its dynamic change data are recorded.

[0014] Furthermore, in step 2, before using the modal recognition algorithm for identification, the translational vibration response time history signal and rotational vibration response time history signal of each composite measuring point are corrected by coordinate transformation using the installation angle and dynamic change data, so as to eliminate the system measurement error caused by the inconsistency of the sensor measurement axes of different composite measuring points.

[0015] Furthermore, in step 3, the mathematical reconstruction process specifically involves: Based on the general solution of the mode shape of the tension beam and its derivative relationship, a parameterized expression including the displacement mode shape function and the rotation mode shape function is established. The displacement mode shape function and its derivative are simultaneously fitted using the displacement mode shape coefficient and the rotation mode shape coefficient, and the unknown parameters in the parameterized expression are solved, thereby reconstructing the spatial continuous displacement mode shape function.

[0016] Furthermore, in step 4, the theoretical model of the tension beam vibration is an Euler-Bernoulli beam model that includes the coupling effect of the axial tensile force term and the section bending stiffness term.

[0017] The advantages of this invention are: 1. By setting up at least two composite measuring points on the cable-stayed structure under test, the translational vibration response time history signal and rotational vibration response time history signal of each composite measuring point are simultaneously collected. Utilizing the first-order derivative mathematical mapping relationship between the rotational mode shape coefficient and the displacement mode shape coefficient, a joint mathematical reconstruction is performed based on the displacement mode shape and rotational mode shape coefficient of the discrete measuring points to obtain the spatial continuous displacement mode shape function. Then, the extracted modal frequencies and spatial continuous displacement mode shape function are substituted into the tension beam vibration theory model (such as the Euler-Bernoulli beam model). By solving the inverse problem of the vibration characteristic equation, parameters such as axial force and effective vibration length are simultaneously identified, thereby achieving high-precision axial force identification with fewer measuring points under complex boundary conditions. At the same time, it is required that the translational and rotational response measurement directions of the same composite measuring point are consistent and the positions are close, or an integrated sensor is used. The installation angle of each sensor's measurement axis is recorded for coordinate transformation correction, thereby fundamentally avoiding the system mode shape error introduced by the inconsistent installation angles of traditional multi-point sensor arrays, significantly reducing the difficulty of on-site installation and operating costs.

[0018] 2. By integrating translational and rotational responses, the accuracy and robustness of axial force identification are significantly improved: Traditional cable-stayed axial force identification methods typically only utilize translational vibration responses (such as acceleration), resulting in a single dimension of modal information that is susceptible to interference from sensor installation location, uncertainties in cable-stayed boundary conditions, and test noise. This invention simultaneously acquires translational and rotational vibration responses at the same measuring point. The rotational response (i.e., the rotational mode shape) is theoretically the spatial derivative of the translational displacement mode shape along the axis. This inherent mathematical constraint provides redundant and complementary physical information for mode shape reconstruction, which is equivalent to adding a strong and effective regularization condition in the inversion calculation. This effectively suppresses measurement errors and spurious modes in modal identification, resulting in higher accuracy and stronger anti-interference capabilities for the final inversion calculation of axial force.

[0019] 3. Achieving accurate reconstruction of spatially continuous displacement mode shape functions, avoiding fitting errors caused by discrete measurement points: Existing technologies often rely only on displacement mode shape coefficients at finite discrete measurement points, approximating the first derivative of the mode shape (i.e., rotation angle) through numerical difference or interpolation. This approximation introduces significant discretization errors, especially when measurement points are sparse. This invention is based on the differential mapping relationship between displacement mode shape coefficients and rotation mode shape coefficients, and performs joint mathematical reconstruction of the two to obtain spatially continuous displacement mode shape functions. It directly uses the measured rotation angle information as the derivative value, which is equivalent to using precise "slope" constraints to guide curve fitting. It can derive a continuous mode shape function that better matches the actual deformation of the cable, providing high-quality input for subsequent vibration characteristic equation solving.

[0020] 4. Reduced implementation difficulty and cost of the testing system, with strong adaptability: Translational and rotational responses can be measured simultaneously using integrated vibration and rotation sensors, or by combining separate accelerometers and tilt sensors, allowing for minute spacing of no more than 1 meter between measurement positions. That is, it can be built using existing general-purpose sensors or by employing integrated translational and rotational sensors. Furthermore, the introduction of sensor installation angle recording and coordinate transformation correction eliminates system errors caused by inconsistent sensor measurement axes at different measuring points. Therefore, it significantly reduces the accuracy requirements and operational barriers for on-site testing, making it easier to promote and apply in complex environments such as actual bridges and buildings.

[0021] 5. Expanded applicability and ability to handle boundary condition uncertainties: The scope of measurement can be extended to parallel wire cables, strand cables, hangers, tie rods in bridge engineering, and various axially stressed components in building construction. Furthermore, when reconstructing the spatial continuous displacement mode function of the cable-stayed structure, the range of composite measurement points can be selected according to the actual situation, without needing to cover the entire length of the cable-stayed structure. This effectively avoids the model errors introduced by traditional methods due to the inability to accurately know the calculated length of the cable-stayed structure or boundary constraints (such as fixed connections, hinged connections, or elastic constraints). Attached Figure Description

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] Figure 1 This is a flowchart of a method for identifying axial force in cable-stayed structures that integrates translational and rotational vibration responses, according to the present invention.

[0024] Figure 2 This is a schematic diagram of the fusion scheme for measuring the vibration and rotation response of the cable-stayed structure according to the present invention.

[0025] Figure 3 This is the acceleration time history and its spectrum measured by the present invention.

[0026] Figure 4 This is the displacement angle time history and its spectrum measured by the present invention.

[0027] Figure 5 This is a schematic diagram of the mode shape function identified by acceleration in this invention.

[0028] Figure 6 This is a schematic diagram of the rotation mode identified by the rotation displacement in this invention.

[0029] Figure 7 This invention integrates the vibration mode identification and fitting results of acceleration and rotation position at two measurement points.

[0030] Figure 8 This refers to the time history before and after acceleration correction in this invention.

[0031] Figure 9 This invention uses the vibration mode and effective vibration length identified by acceleration before and after correction.

[0032] Figure 10 This is the test layout diagram of Embodiment 4 of the present invention.

[0033] Figure 11 It is the acceleration angle time history measured in the experiment of Embodiment 4 of the present invention.

[0034] Figure 12 This is the vibration mode identified and fitted by integrating the acceleration and rotation response of two measuring points in Embodiment 4 of the present invention.

[0035] Marker explanation: 1-The structure of the cable rod to be tested; 2-The end of the cable rod; 3-The middle support point of the cable rod; 4-The sensor. Detailed Implementation

[0036] The technical solution in this application embodiment has the following general idea: Utilizing the inherent derivative mapping relationship between displacement mode shape and rotation mode shape in the vibration of cable-stayed structures (rotation mode shape is the first derivative of displacement mode shape along the axial direction), translational and rotational vibration responses are simultaneously collected by setting only a small number of composite measuring points (at least two) on the cable-stayed structure under test. Based on this derivative constraint, the discrete displacement mode shape coefficients and rotation mode shape coefficients are jointly mathematically reconstructed to obtain a spatially continuous displacement mode shape function. Finally, the multi-order modal frequencies and the reconstructed continuous mode shape function are substituted into the characteristic equation of tension beam vibration considering bending stiffness (Euler-Bernoulli beam model) to solve the inverse problem. This achieves high-precision identification of cable-stayed axial force with fewer measuring points under complex boundary conditions, while avoiding the mode shape error introduced by the inconsistent installation angle of traditional multi-point sensor arrays.

[0037] Please refer to Figures 1 to 12 As shown:

[0038] Example 1: A preferred embodiment of the present invention, a method for identifying axial force in cable-stayed structures by integrating translational and rotational vibration responses, includes the following steps: Step 1: Select at least two locations along the axis of the cable-stayed structure to be tested and set up composite measuring points. Simultaneously collect the translational vibration response time history signal and rotational vibration response time history signal of each composite measuring point, and record the relative position of each composite measuring point. Specifically, the cable structure to be tested can be a parallel wire cable, strand cable, hanger, or tie rod in bridge engineering, or an axially loaded component in building engineering. Taking a cable-stayed bridge as an example, two locations approximately 1 / 4 and 1 / 2 spans away from the cable end anchor point are selected as composite measuring points along the cable axis. An integrated vibration and rotation sensor (such as a sensor integrating a MEMS accelerometer and gyroscope or tilt chip) is installed at each composite measuring point to simultaneously acquire in-plane vertical vibration acceleration time history signals and rotational displacement time history signals around the horizontal axis (perpendicular to the cable axis). During acquisition, the sampling frequency is recommended to be set to 5-10 times the estimated highest frequency of interest, and the sampling duration should ensure sufficient periods of free decay or environmental vibration signals are obtained. Simultaneously, a total station or laser rangefinder is used to record the relative distances of each composite measuring point along the cable axis, and the initial installation angle of each sensor's measurement axis relative to the global horizontal reference plane is measured.

[0039] Step 2: The translational vibration response time history signal and the rotational vibration response time history signal are processed by the modal recognition algorithm to extract at least two modal frequencies of the cable-stayed structure under test, as well as the displacement mode shape coefficient and rotation mode shape coefficient of each mode at each of the composite measurement points; Optionally, the modal identification algorithm can employ Feature System Implementation (ERA), Random Subspace Identification (SSI), or Frequency Domain Decomposition (FDD). Taking ERA as an example: the acceleration time history and rotational displacement time history of each measurement point are used to construct impulse response matrices. After constructing the Hankel matrix, singular value decomposition is performed to extract the observable and controllable matrices of the system. This allows for the identification of the first few modal frequencies (e.g., 3-6 orders) and damping ratios, and the displacement mode shape coefficients (obtained by normalizing the acceleration mode shape) and rotational mode shape coefficients of each measurement point under each mode order are obtained. Note that for translational responses, the extracted mode shape (or acceleration mode shape, which differs by a constant multiple) is the displacement mode shape (or rotational displacement mode shape). For rotational responses, the extracted mode shape (or rotational displacement mode shape) is the rotational mode shape. To improve the signal-to-noise ratio, bandpass filtering can be applied to the time history signal to filter out low-frequency drift below 0.1Hz and high-frequency noise.

[0040] Step 3: Based on the mathematical mapping relationship between the displacement mode function represented by the displacement mode coefficient and the rotation mode represented by the rotation mode coefficient, that is, the rotation mode is the first derivative (slope) of the displacement mode function along the axial coordinate of the cable rod, the displacement mode coefficient and rotation mode coefficient obtained at each of the composite measuring points are used to mathematically reconstruct the spatial continuous displacement mode function of the cable rod structure under test or its local segments by combining the theoretical mode expression of the cable rod structure. Step 4: Substitute the modal frequencies and spatial continuous displacement mode shape functions into the tension beam vibration theory model, and calculate the actual axial force of the cable-stayed structure under test by solving the inverse problem of the vibration characteristic equation.

[0041] In step 1, the cable-stayed structure to be tested includes parallel wire cables, stranded cables, hangers, and tie rods in bridge engineering, as well as axial load-bearing components in building engineering.

[0042] In step 1, the translational vibration response time history signal includes displacement response, velocity response, or acceleration response; the rotational vibration response time history signal includes angular displacement response, angular velocity response, or angular acceleration response.

[0043] In step 1, when measuring the translational vibration response time history signal and the rotational vibration response time history signal, the measurement directions of the translational vibration response time history signal and the rotational vibration response time history signal at the same composite measuring point are consistent, which is used to measure the in-plane or out-of-plane vibration of the cable rod. Furthermore, the translational vibration response time history signal and the rotational vibration response time history signal are measured at the same location, or the distance between the two along the cable axis does not exceed 1m; The translational vibration response time history signal and the rotational vibration response time history signal are measured synchronously using an integrated vibration and rotation angle sensor.

[0044] In step 1, the sensors used to measure the translational vibration response time history signal and the rotational vibration response time history signal include contact sensors or non-contact sensors. The contact sensor includes a separate accelerometer and tilt sensor, or an integrated vibration and rotation sensor.

[0045] In step 1, the composite measuring points are placed in a location that avoids the ends of the cable rod and the middle support points of the cable rod. Specifically, they are placed at a distance of at least 10% of the free length of the cable rod from the support points.

[0046] Step 1 further includes: While acquiring the translational vibration response time history signal and the rotational vibration response time history signal, the installation angle of the vibration sensor's measuring axis relative to the same reference direction at the composite measuring point and its dynamic change data are recorded.

[0047] In step 2, before using the modal recognition algorithm for identification, the translational vibration response time history signal and rotational vibration response time history signal of each composite measuring point are corrected by coordinate transformation using the installation angle and dynamic change data, so as to eliminate the system measurement error caused by the inconsistency of the sensor measurement axes of different composite measuring points.

[0048] In step 3, the mathematical reconstruction process specifically involves: Based on the general solution of the mode shape of the tension beam and its derivative relationship, a parameterized expression including the displacement mode shape function and the rotation mode shape function is established. The displacement mode shape function and its derivative are simultaneously fitted using the displacement mode shape coefficient and the rotation mode shape coefficient, and the unknown parameters in the parameterized expression are solved, thereby reconstructing the spatial continuous displacement mode shape function.

[0049] That is, based on the general solution of the displacement mode of the cable-stayed structure under test. and its corresponding rotation mode general solution By fitting the displacement mode coefficients with the rotation mode coefficients, the parameters in the general solution of the displacement mode and the general solution of the rotation mode are obtained, thereby reconstructing the displacement mode and the rotation mode. in, The displacement mode shape function represents the displacement along the axial coordinate x of the cable, and the mode shape represents the transverse vibration of the cable. The mode shape function representing the rotation angle along the axial coordinate x of the cable is, according to beam bending theory, equal to the first derivative of the displacement mode shape function with respect to x. ; x represents the position coordinates along the cable axis from the reference origin (such as one end of the cable); δ represents the undetermined constants (constant coefficients) determined by the boundary conditions; δ and γ represent the wavenumber parameters related to the axial force T, bending stiffness EI, mass per unit length m, and circular frequency ω of the cable-stayed structure. Specifically, they satisfy the characteristic equation: ; ; Or equivalently: ; .

[0050] In step 4, the theoretical model of the tension beam vibration is an Euler-Bernoulli beam model that includes the coupling effect of the axial tensile force term and the section bending stiffness term.

[0051] Example 2: This embodiment provides a numerical example demonstrating a high-precision method for identifying the axial force of a cable-stayed rod by integrating vibration and rotational responses. Consider a cable 8.49m long subjected to an axial force of 350kN. It is fixed laterally and longitudinally at both ends and equipped with rotational constraint springs with a rotational stiffness coefficient of 100N∙m; the bending stiffness of the cable-stayed rod is taken as... The mass per unit length is 5.93 kg / m. Accelerometers and rotation sensors were installed on the cable at distances of 0.2, 0.3, 0.4, and 0.7 times the length from the left end to measure its vertical acceleration and angular displacement about a horizontal axis perpendicular to the cable. Numerical methods were used to calculate the acceleration and angular displacement at the four measuring points under random excitation, as shown below. Figure 3 , Figure 4As shown. The Feature System Implementation Algorithm (ERA) is used for modal identification, and the mode shapes are obtained using acceleration or rotational displacement signals from four locations, as shown below. Figure 5 , Figure 6 As shown.

[0052] After identifying the mode shape coefficients at four locations, the mode shape function of the mid-segment of the reconstructed cable is fitted using the equivalent two-hinged tension beam method. The mode shape expression for the two-hinged tension beam is: ; in, Indicates the nth mode shape; express The value at measuring point j; This indicates the total number of measuring points used to measure the translational response; Indicates coefficient; This indicates the coordinates of the measuring point along the cable axis; This represents the effective vibrating cable length of the nth order vibration of the original cable rod, which is the equivalent length of the beam with hinged ends at both ends. This represents the coordinate system offset value of an equivalent beam with hinged ends. The expression for the corresponding rotation mode is: ; in, This represents the rotation mode vector of the nth mode; Indicates the nth rotation mode in the first order. The specific values ​​at each measuring point; This represents the amplitude coefficient of the nth rotation mode. This indicates the coordinates of the measuring point along the cable axis; This represents the equivalent coordinate system offset value corresponding to the nth mode.

[0053] Since mode shapes and rotational mode shapes need to be scaled and normalized separately during measurement, a single variable is used here. This indicates the amplitude of the rotation mode, rather than based on the mode shape. The first derivative with respect to x is obtained .

[0054] In the above formula, n can be estimated by combining the design parameters of the cable and the measured frequency values. Therefore, vibration acceleration fitting alone is insufficient. Sometimes, , and Since there are three unknowns, at least three mode shapes need to be measured at three measuring points. To ensure the accuracy and stability of the identification results, four measurement points are generally required; similarly, when fitting the rotational mode shape using the rotational time history alone, at least three measurement points are needed, and generally four are required for stable and accurate identification. However, the mode shape fitting identified through acceleration and rotational angle... and At that time, there were a total of , , and Since there are four unknowns, we can obtain the four values ​​of mode shape and rotation mode shape at the two measuring points respectively.

[0055] The sixth-order mode shape function curve obtained by fitting the mode shape values ​​obtained from four measurement points is shown in Figure 5 Represented by curves, the effective vibrating cable lengths obtained were 8.309, 8.312, 8.315, 8.321, 8.328, and 8.336 m, with corresponding modal frequencies of 14.65, 29.41, 44.46, 60.14, 76.39, and 93.40 Hz. The rotation mode shape function curves obtained using four measuring points are shown in... Figure 6 The effective vibrating cable lengths obtained by using curves are 8.304, 8.311, 8.316, 8.321, 8.328 and 8.336 m, respectively, and the corresponding modal frequencies are 14.58, 29.61, 44.48, 60.12, 76.39 and 93.42 Hz.

[0056] The mode shape and rotation mode shape curves are obtained by using only the mode shape and rotation mode shape values ​​at two measuring points, namely points 2 and 3. Figure 7 As shown, the effective vibrating cable lengths obtained are 8.306, 8.309, 8.314, 8.322, 8.328 and 8.336 m, respectively. The corresponding modal frequencies are the average values ​​of the frequencies identified by acceleration and rotational displacement, namely 14.62, 29.51, 44.47, 60.13, 76.39 and 93.41 Hz.

[0057] Then, based on the frequency of the tension beam at both ends and the relationship between the cable forces, that is: ; Where T represents the cable force, which is usually measured in Newtons (N) or kilonewtons (kN) and is the target value that needs to be solved; m represents the mass per unit length of the cable, which is usually measured in kg / m, that is, the weight of one meter of cable. This represents the effective computation length of the nth mode; The measured natural frequency (n-th order) is represented by E; n represents the modal order; E represents the elastic modulus of the material, usually expressed in Pascals (Pa); and I represents the moment of inertia of the cross section, usually expressed in Pascals (Pa). .

[0058] The cable force obtained by using the mode shape values ​​from four measuring points and identifying the effective cable length is 349.0 kN; the cable force obtained by using the rotational time history analysis from four measuring points and identifying the effective vibrating cable length is 349.2 kN; the axial force obtained by using the mode shape values ​​and rotational mode shape values ​​from two measuring points (1 and 3) and the effective vibration length and frequency is 348.9 kN. The cable forces obtained by all three methods are very close to the actual cable force of 350 kN, with a maximum error of 0.31%. It is evident that this invention effectively reduces the number of measuring points while maintaining accuracy, greatly improving the practical engineering applicability of the method.

[0059] Example 3: This embodiment provides a numerical example demonstrating the impact of sensor installation orientation error on mode shape and cable force identification when measuring translational vibration, and a method for correcting this error by increasing the measurement of the rotation angle around the cable axis. The rotation angle is θ around the X-axis, and then θ around the Y-axis. The coordinate system obtained later is therefore relevant to the triaxial acceleration measurements acquired by the accelerometer. The acceleration of the cable-stayed structure in the horizontal and vertical coordinate axes needs to be obtained by converting it using the following formula. The transformation matrix R is obtained by considering the instantaneous torsional signal from the sensor, resulting in a transformation matrix that varies with time. ; in, This represents the vibration component along the axis of the component (longitudinal direction); This represents the horizontal (lateral) vibration component perpendicular to the component's axis. This represents the vertical vibration component perpendicular to the axis of the component. , This represents the acceleration measurement value at the j-th measuring point; This represents the inclination angle of the j-th measuring point around the axis of the cable at time t; This represents the angle of inclination around the horizontal axis perpendicular to the cable rod axis at time t, measured by the j-th measuring point.

[0060] The transformation matrix defined here ignores the sensor's rotation angle around the vertical axis. The same method can be used when considering this rotation angle. Furthermore, if a further approximation is considered... In the vertical plane of the cable, there are .

[0061] Considering the same cable-stayed structure and parameters as in Example 2, here we consider the angles between the installation directions of the four sensors and the vertical direction as follows: , , and The simulation yielded the acceleration of the cable-stayed structure at four measuring points, as shown below. Figure 8As shown, the acceleration time history, corrected to include the measured rotation angle information, is also given in the figure. Figure 9 The first six mode shapes obtained from modal identification using data before and after correction, along with the fitted functions, are plotted as curves in the figure. Further, the effective vibrating cable length is obtained as follows: Figure 9 As shown, at this relatively small rotation angle, the effective vibrating cable length changes by approximately 0.6%. Combined with the frequency, the axial forces identified using acceleration before and after correction are 352.6 kN and 349.2 kN, respectively. It can be seen that the identification error after correction decreased from 0.74% to 0.23%, and the 95% confidence interval decreased from (349.5, 355.7) kN to (347.4, 350.6) kN.

[0062] Example 4: This embodiment provides an experimental example to verify the present invention. The experiment is as follows: Figure 10 As shown, the mass per unit length of the tensioned cable is 5.93 kg / m, and the length of the cable between the two anchorages is 8.17 m. A jack was installed at one end of the cable for tensioning, and a pressure gauge was installed at the other end to directly measure the cable force for comparison and verification. A 3-axis accelerometer and 2-axis tilt sensor was used. Simultaneously, the complex constraint changes of the cable were simulated by installing and removing the intermediate support. A total of 6 integrated sensors were used in the experiment; the sensor installation locations are shown below. Figure 10 The measurement is performed by hammering. Figure 11 The measured vertical acceleration and vertical bending angle of the cable are shown. In the data analysis, only the acceleration and angular displacement at measuring points 2 and 5 were used for mode shape and angular mode identification, yielding the results for the 2nd to 4th modes as follows: Figure 12 As shown, the frequencies obtained were 30.47, 46.57, and 62.26 Hz, and the effective vibration lengths were 7.420, 7.196, and 7.371 m, respectively. The identified cable force was 312.3 kN, which is very close to the 303.8 kN measured by the pressure gauge, with an error of 2.8%, achieving high-precision cable force identification at two measuring points.

[0063] While specific embodiments of the present invention have been described above, those skilled in the art should understand that the specific embodiments described are merely illustrative and not intended to limit the scope of the present invention. Equivalent modifications and variations made by those skilled in the art in accordance with the spirit of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for identifying axial force in cable-stayed structures by integrating translational and rotational vibration responses, characterized in that: Includes the following steps: Step 1: Select at least two locations along the axis of the cable-stayed structure to be tested and set up composite measuring points. Simultaneously collect the translational vibration response time history signal and rotational vibration response time history signal of each composite measuring point, and record the relative position of each composite measuring point. Step 2: The translational vibration response time history signal and the rotational vibration response time history signal are processed by the modal recognition algorithm to extract at least two modal frequencies of the cable-stayed structure under test, as well as the displacement mode shape coefficient and rotation mode shape coefficient of each mode at each of the composite measurement points; Step 3: Based on the mathematical mapping relationship between the displacement mode function represented by the displacement mode coefficient and the rotation mode represented by the rotation mode coefficient, that is, the rotation mode is the first derivative of the displacement mode function along the axial coordinate of the cable rod, the displacement mode coefficient and rotation mode coefficient obtained at each of the composite measuring points are used to mathematically reconstruct the spatial continuous displacement mode function of the cable rod structure under test or its local segments by combining the theoretical mode expression of the cable rod structure. Step 4: Substitute the modal frequencies and spatial continuous displacement mode shape functions into the tension beam vibration theory model, and calculate the actual axial force of the cable-stayed structure under test by solving the inverse problem of the vibration characteristic equation.

2. The method for identifying axial force in a cable-stayed structure by integrating translational and rotational vibration responses as described in claim 1, characterized in that: In step 1, the cable-stayed structure to be tested includes parallel wire cables, stranded cables, hangers, and tie rods in bridge engineering, as well as axial load-bearing components in building engineering.

3. The method for identifying axial force in a cable-stayed structure by integrating translational and rotational vibration responses as described in claim 1, characterized in that: In step 1, the translational vibration response time history signal includes displacement response, velocity response, or acceleration response; the rotational vibration response time history signal includes angular displacement response, angular velocity response, or angular acceleration response.

4. The method for identifying axial force in a cable-stayed structure by integrating translational and rotational vibration responses as described in claim 1, characterized in that: In step 1, when measuring the translational vibration response time history signal and the rotational vibration response time history signal, the measurement directions of the translational vibration response time history signal and the rotational vibration response time history signal at the same composite measuring point are consistent, which is used to measure the in-plane or out-of-plane vibration of the cable rod. Furthermore, the translational vibration response time history signal and the rotational vibration response time history signal are measured at the same location, or the distance between the two along the cable axis does not exceed 1m; The translational vibration response time history signal and the rotational vibration response time history signal are measured synchronously using an integrated vibration and rotation angle sensor.

5. The method for identifying axial force in a cable-stayed structure by integrating translational and rotational vibration responses as described in claim 1, characterized in that: In step 1, the sensors used to measure the translational vibration response time history signal and the rotational vibration response time history signal include contact sensors or non-contact sensors. The contact sensor includes a separate accelerometer and tilt sensor, or an integrated vibration and rotation sensor.

6. The method for identifying axial force in a cable-stayed structure by integrating translational and rotational vibration responses as described in claim 1, characterized in that: In step 1, the composite measuring points are placed in a location that avoids the ends of the cable rod and the middle support points of the cable rod. Specifically, they are placed at a distance of at least 10% of the free length of the cable rod from the support points.

7. The method for identifying axial force in a cable-stayed structure by integrating translational and rotational vibration responses as described in claim 1, characterized in that: Step 1 further includes: While acquiring the translational vibration response time history signal and the rotational vibration response time history signal, the installation angle of the vibration sensor's measuring axis relative to the same reference direction at the composite measuring point and its dynamic change data are recorded.

8. The method for identifying axial force in a cable-stayed structure by integrating translational and rotational vibration responses as described in claim 7, characterized in that: In step 2, before using the modal recognition algorithm for identification, the translational vibration response time history signal and rotational vibration response time history signal of each composite measuring point are corrected by coordinate transformation using the installation angle and dynamic change data, so as to eliminate the system measurement error caused by the inconsistency of the sensor measurement axes of different composite measuring points.

9. The method for identifying axial force in a cable-stayed structure by integrating translational and rotational vibration responses as described in claim 1, characterized in that: In step 3, the mathematical reconstruction process specifically involves: Based on the general solution of the mode shape of the tension beam and its derivative relationship, a parameterized expression including the displacement mode shape function and the rotation mode shape function is established. The displacement mode shape function and its derivative are simultaneously fitted using the displacement mode shape coefficient and the rotation mode shape coefficient, and the unknown parameters in the parameterized expression are solved, thereby reconstructing the spatial continuous displacement mode shape function.

10. The method for identifying axial force in a cable-stayed structure by integrating translational and rotational vibration responses as described in claim 1, characterized in that: In step 4, the theoretical model of the tension beam vibration is an Euler-Bernoulli beam model that includes the coupling effect of the axial tensile force term and the section bending stiffness term.

Images