A cable-stayed bridge vehicle-induced cable force real-time online extraction method based on cable force monitoring data

Abstract

The present application belongs to the field of bridge structure health monitoring, and discloses a cable-stayed bridge vehicle-induced cable force real-time online extraction method based on cable force monitoring data, and the steps are as follows: establishing a kernel density estimation model of operating cable force distribution; extracting static load cable force based on operating cable force distribution characteristics; real-time online updating of static load cable force based on moving window analysis; and establishing a time domain smoothing model of static load cable force response to further extract vehicle-induced cable force. In the present application, the kernel density estimation model of operating cable force distribution can be established to accurately fit when the prior information of cable force distribution is unknown, and the static load cable force is extracted based on the distribution characteristics; the moving window analysis model can effectively ensure sufficient sample capacity of the cable force distribution kernel density estimation model and real-time online updating of the static load cable force; the time domain smoothing model of cable force response can effectively eliminate noise and interference of external environmental factors, obtain the time-varying trend item of the static load cable force, and further realize real-time online extraction of the vehicle-induced cable force.

Description

Technical Field

[0001] This invention belongs to the field of bridge structural health monitoring, specifically relating to a method for real-time online extraction of cable-stayed bridge cable force based on cable force monitoring data. Background Technology

[0002] Stay cables are crucial components in cable-stayed bridges, transmitting loads. However, due to their small mass, high flexibility, and low damping, they are highly susceptible to abnormal vibration, corrosion, and fatigue damage under long-term exposure to adverse environmental factors (such as wind and rain vibration and corrosion) and alternating vehicle loads. This leads to cable deterioration and abnormal changes in cable force, which can severely impact the overall stress state and safe operation of the bridge. To ensure the safe operation of long-span cable-stayed bridges within their design service life, many bridges have been equipped with bridge health monitoring systems. Monitoring cable force is a vital component of these systems, serving as the most direct indicator of cable stress state. The cable force obtained by the health monitoring system is primarily caused by the structure's self-weight, random vehicle loads, and environmental factors, and is also affected by random noise. This makes it impossible to effectively assess the cable condition solely based on changes in cable force values. Therefore, it is necessary to separate the vehicle-induced response component of the cable force from the constant load, temperature response component, and random disturbance component to obtain the accurate static load trend term and vehicle-induced cable force of the stay cable, thereby providing a basis for the extraction of monitoring and early warning indicators based on vehicle-induced cable force.

[0003] Currently, existing methods for decoupling operational cable force monitoring data mainly employ signal processing and data correlation analysis. Signal processing methods primarily involve low-pass filtering, moving averages, and empirical mode decomposition (EMD). For example, Sun Zongguang et al., in their analysis and evaluation of cable force variability under probabilistic statistical conditions, proposed using EMD to separate the vehicle response component from the constant load and temperature response in cable force monitoring data. Li Hui et al., in their work on structural health monitoring data science and engineering, proposed using moving averages to decouple cable force caused by vehicle loads from the cable force trend term. Tao Xingwang et al., in their work on identifying vehicle weight and speed in cable-stayed bridges based on monitoring response, used wavelet analysis with bandpass filtering to effectively separate the vehicle excitation response and random interference components. However, these methods of decoupling cable force monitoring data based on signal decomposition and reconstruction suffer from problems such as unclear physical meaning and strong subjectivity in determining relevant parameters, leading to poor results in separating the static and dynamic components of cable force. Patent CN111062080A proposes a method for extracting vehicle-induced cable forces based on cable force monitoring data. However, this method requires hourly cable force data collection to calculate the mean and standard deviation, meaning the extraction cycle is one hour, thus preventing real-time extraction. Liu Xiaoling et al., in extracting the dead load cable forces of cable-stayed bridges under random traffic flow, used correlation analysis between temperature and cable force to eliminate the influence of temperature effects in cable force monitoring data and employed a distribution fitting method for extracting the dead load cable forces. However, this method requires additional known temperature data to separate the cable force temperature effect, and the distribution fitting process requires prior information about the cable force distribution. Therefore, it cannot be directly applied to extracting vehicle-induced cable forces from cable force monitoring data of different cable-stayed bridges. In summary, most of the methods mentioned above employ offline processing to separate the vehicle-induced cable force component from the constant load and temperature response, making it difficult to guarantee the real-time nature of data analysis. The determination of relevant parameters based on signal processing methods is highly subjective, and some methods require prior information from cable force monitoring data, making it difficult to guarantee their applicability to different cable force monitoring data of cable-stayed bridges. All of these factors have brought certain difficulties to the real-time online extraction method of vehicle-induced cable force of cable-stayed bridges based on cable force monitoring data.

[0004] Based on the shortcomings of the above methods in terms of real-time performance and applicability, this invention discloses a real-time online extraction method for vehicle-induced cable forces in cable-stayed bridges based on cable force monitoring data. Its main features include: 1) enabling rapid and accurate fitting of cable force distribution even when prior information on the monitored operational cable force distribution is unknown, thus ensuring the accuracy of the extracted static load cable forces; 2) effectively solving the problem of difficulty in guaranteeing real-time performance caused by offline extraction of vehicle-induced cable forces in existing methods. Therefore, this invention provides a prerequisite for ensuring real-time online early warning of cable anomalies in cable-stayed bridges based on vehicle-induced cable forces. Summary of the Invention

[0005] The purpose of this invention is to provide a method for real-time online extraction of cable-stayed bridge cable forces based on cable force monitoring data.

[0006] The technical solution of the present invention:

[0007] A method for real-time online extraction of cable-stayed bridge cable forces based on cable force monitoring data, comprising the following steps:

[0008] Step 1. Establish a kernel density estimation model for the operating cable force distribution.

[0009] Step 1. Establish a kernel density estimation model for the operating cable force distribution.

[0010] (1.1) Select a sample set of bridge operating cable forces consisting of L sample points as the initial sample set for the kernel density estimation model, where the value of L is not less than 1800; then perform kernel density estimation on the initial sample of measured operating cable forces and extract its distribution characteristic information, including the maximum probability density and its corresponding operating cable force, and establish the calculation formula of the cable force distribution kernel density estimation model as shown in equation (1):

[0011]

[0012] in, This is an estimate of the probability density of the operating cable force distribution at a given cable force value F; F i ,i∈[1,N] represents the i-th operational cable force sample; N represents the sample size of operational cable forces; K0(·) is the kernel function, chosen as the Gaussian kernel function; h represents the bandwidth of the kernel density estimation model, its value is calculated as h=c·N -1 / 5 Calculations show that c is 1.05 times the standard deviation of the operating cable force sample;

[0013] Step 2. Static cable force extraction based on probability distribution model

[0014] (2.1) Extract the operating cable force corresponding to the point with the maximum probability density in the kernel density estimation model of the operating cable force distribution, and use this as the representative value F of the static load cable force during this period. D The calculation formula is as follows.

[0015]

[0016] Among them, P max Estimate the point of maximum probability density for the kernel density distribution; F D This represents the extracted static load cable force. This represents the inverse probability density function for estimating the kernel density distribution of the operating cable force;

[0017] Step 3. Real-time online update of static cable force based on moving window analysis

[0018] (3.1) Select an appropriate moving window length based on the sampling frequency of the operational cable force monitoring data. The selection of the window length should ensure that there is sufficient sample capacity in the analysis of the operational cable force distribution kernel density estimation model. It should be the same as the sample capacity L corresponding to the initial sample set of operational cable force in step 1.

[0019] (3.2) The window movement step size is set to 1, i.e., one cable force sample point. Steps 1 and 2 are repeated to update the representative static load cable force values ​​at different times in real time. Within the time interval corresponding to the initial sample set of operating cable forces, the static load cable force at all times is taken as the representative static load cable force value obtained from the cable force distribution kernel density estimation within that time interval, i.e.:

[0020] F D,begin =F D,begin ×ones(L,1) (3)

[0021] Among them, F D,begin The initial sample set is calculated according to equation (2) and the static load cable force is the representative value of the time interval corresponding to the time interval; ones(L,1) is a row vector with L elements all equal to 1;

[0022] Step 4. Establish a time-domain smoothing model of the static load cable force response and then extract the vehicle-induced cable force.

[0023] (4.1) Based on the representative value of static load cable force obtained in step 3, the moving average method is used to smooth the static load cable force sequence and extract the trend term; the window width m should be the same as the moving window length in step (3.1), thereby extracting the time-varying trend term of static load cable force. The expression for cable force smoothing using the moving average method is shown in formulas (4) and (5):

[0024]

[0025]

[0026] Where m is the window width of the moving average method. The sliding average value of the static load cable force at time k;

[0027] (4.2) The vehicle-induced cable force is obtained by subtracting the static load cable force time-varying trend term extracted in step (4.1) from the measured operational cable force data;

[0028]

[0029] Among them, F k F represents the measured operational cable force at time k; v,k Let be the force exerted by the vehicle at time k.

[0030] The beneficial effects of this invention are:

[0031] 1. By establishing a kernel density estimation model for the distribution of operating cable forces, this invention can achieve rapid and accurate fitting of the cable force distribution when the prior information of the monitored operating cable force distribution is unknown. This ensures the real-time performance and accuracy of the extracted static load cable forces. Therefore, compared with existing methods, this invention can be directly applied to the extraction of cable forces in cable-stayed bridges of different structural types without prior information on the cable force distribution.

[0032] 2. The present invention, based on the moving window analysis method, can effectively ensure sufficient sample capacity for the cable force distribution kernel density estimation model and real-time online updates of static load cable force. Combined with the time-domain smoothing model, it can effectively eliminate noise and interference from external factors, thereby obtaining the time-varying trend term of static load cable force. On this basis, it can realize real-time online extraction of vehicle-induced cable force. Therefore, the present invention can effectively solve the problem that the real-time performance of existing methods is difficult to guarantee due to offline extraction of vehicle-induced cable force, and provides an effective method to ensure the real-time performance of cable force-based cable anomaly early warning method. Attached Figure Description

[0033] Figure 1 This is a flowchart of the method of the present invention.

[0034] Figure 2 The method of this invention provides a kernel density estimation model for the operating cable force distribution.

[0035] Figure 3 This is a representative value of the static cable force obtained by implementing the method of the present invention;

[0036] Figure 4 This is a schematic diagram illustrating the extraction of the time-varying trend term of static cable force using the method of the present invention;

[0037] Figure 5 The cable-stayed vehicle cable force obtained by implementing the method of the present invention. Detailed Implementation

[0038] The present invention will now be described in further detail with reference to the accompanying drawings and a calculation example.

[0039] The present invention provides a real-time online extraction method for vehicle-induced cable forces in cable-stayed bridges based on cable force monitoring data, comprising four steps: "establishing a kernel density estimation model for the distribution of operational cable forces," "static load cable force extraction based on a probability distribution model," "real-time online updating of static load cable forces based on moving window analysis," and "establishing a time-domain smoothing model of static load cable force response to extract vehicle-induced cable forces." The implementation process is as follows: Figure 1 As shown above, the specific implementation method has been given. The following will illustrate the usage and features of the invention with specific examples.

[0040] In this specific numerical example, actual cable force monitoring data from a double-tower, double-cable-stayed bridge in China is used for testing. Taking the operational cable force monitoring data from a single cable force sensor over two hours as an example, an initial time interval of 15 minutes (or 1800 sample points) is selected as the pre-stored sample for the kernel density estimation model. Then, kernel density estimation is performed on the pre-stored sample of operational cable forces, and the operational cable force corresponding to the point with the maximum extracted probability density is used as the representative static load cable force value for all operational cable force samples within the initial 15 minutes. Figure 2 A kernel density estimation model for the operating cable force distribution;

[0041] Secondly, a moving window analysis is performed, with a window length set to 1800 operational cable force sample points and a moving step size of 1 sample point. As the window moves according to the set step size, the operational cable force samples within the moving window length are substituted into the established operational cable force distribution kernel density estimation model, thereby achieving real-time online updates of static cable forces. The real-time update results of static cable forces based on the moving window analysis are as follows: Figure 3 As shown;

[0042] While the representative value of static cable force is updated in real time, the moving average method is used to smooth the static cable force sequence and extract the trend term. A window width of 1800 sample points is used, which allows for the real-time extraction of the time-varying trend term of the static cable force. The extraction results are as follows: Figure 4 As shown. Finally, the real-time vehicle-induced cable force is obtained by subtracting the extracted static load cable force time-varying trend term from the original operational cable force monitoring data, as shown in the figure. Figure 5 As shown.

Claims

1. A method for real-time online extraction of vehicle-induced cable force of a cable-stayed bridge based on cable force monitoring data, comprising the following steps: Step 1. Establishing a kernel density estimation model of operational cable force distribution (1.1) Selecting a bridge operational cable force sample set composed of L sample points as the initial sample set of the kernel density estimation model, and L is not less than 1800; then performing kernel density estimation on the initial sample of the measured operational cable force, and extracting its distribution characteristic information, including the maximum probability density and the corresponding operational cable force, and establishing the calculation formula of the cable force distribution kernel density estimation model as formula (1): wherein The probability density estimation value of the operating cable force distribution at a certain cable force value F; F i , i ∈ [1, N] is the i th operating cable force sample; N represents the sample capacity of the operating cable force; K0(·) is the kernel function, which is selected as the Gaussian kernel function; h represents the bandwidth of the kernel density estimation model, which is valued as h = c·N -1 / 5 , c is the standard deviation of the operating cable force sample, which is 1.05 times. Step 2. Static load cable force extraction based on probability distribution model (2.1) Extract the operating cable force corresponding to the maximum value point of the probability density in the kernel density estimation model of the operating cable force distribution, and take it as the representative value F of the static load cable force in this period of time D The calculation formula is as follows: where P max is the estimated probability density maximum point of the core density distribution; F D is the representative value of the extracted dead cable force; denotes the inverse probability density function of the estimated core density distribution of the operating cable force; Step 3. Real-time online updating of static load cable force based on moving window analysis (3.1) Selecting an appropriate moving window length according to the sampling frequency of the operational cable force monitoring data, and the selection of the window length should ensure sufficient sample capacity in the analysis of the operational cable force distribution kernel density estimation model, and it is appropriate to be the same as the sample capacity L corresponding to the initial sample set of the operational cable force in step 1; (3.2) The window moving step is set to 1, i.e. one cable force sample point, and steps 1 and 2 are repeated to update the static load cable force representative value in real time, wherein the static load cable force at all times within the time interval corresponding to the initial sample set of the operational cable force is taken as the static load cable force representative value obtained by the cable force distribution kernel density estimation in this time period, i.e. F D,begin = F D,begin ones(L, 1) (3) where F D,begin is the static cable force representative value for the time interval corresponding to the initial sample set calculated according to equation (2); ones(L, 1) is a row vector of L elements all equal to 1. Step 4. Establishing a time-domain smoothing model of static load cable force response and then extracting vehicle-induced cable force (4.1) On the basis of the static load cable force representative value obtained in step 3, the sliding average method is used to smooth the static load cable force sequence and extract the trend item; the window width m should be the same as the moving window length in step (3.1), and thus the time-varying trend item of the static load cable force is extracted, wherein the expression for cable force smoothing by the sliding average method is shown in formulas (4) and (5): wherein m is the window width of the moving average method, is the moving average value of the static cable force at the kth moment. (4.2) The vehicle-induced cable force is obtained by subtracting the static load cable force time-varying trend item extracted in step (4.1) from the measured operational cable force data. wherein F k is the measured operating cable force at the kth time; F v,k is the vehicle-induced cable force at the kth time.

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